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Making the Most of Midwinter 2018
Meeting must-dos for Denver | February 9–13, 2018
By Donna Hunter | November 1, 2017
Library professionals have a lot of roles to fill in our changing world. Data is becoming vaster, service needs more varied, and information more important than ever. At the American Library Association's (ALA) 2018 Midwinter Meeting & Exhibits in Denver, attendees can envision these roles by learning from industry experts and leaders, discussing innovative and diverse strategies with peers, and bringing home invigorating ideas to transform their libraries and communities.
ALA's Center for the Future of Libraries presents the second annual Symposium on the Future of Libraries, included with full registration for Midwinter. On Saturday, Sunday, and Monday (February 10–12), attendees can explore near-term trends inspiring innovation in academic, public, school, and special libraries and longer-term trends that will help professionals adapt to their communities' needs. Advance registration is not required.
The symposium integrates and builds on Midwinter's popular ALA Master Series and News You Can Use updates, which highlight library advances. It will include:
plenary sessions with the civic, education, and social innovators who are creating what's next for cities, campuses, and communities
insights from library professionals introducing new services, spaces, collections, and partnerships
discussion with experts and thinkers from allied professions and disciplines sharing their visions for the future and helping us think beyond our current work
emerging products and services for libraries in the exhibit hall
Compelling speakers
Midwinter showcases high-profile speakers, including bestselling authors, thought leaders, industry icons, and technology innovators.
Hear from acclaimed author and 826 National cofounder Dave Eggers at the Auditorium Speaker Series (Saturday, February 10). Eggers will be on hand to discuss his recently released nonfiction picture book, Her Right Foot (Chronicle Books, September).
Performer and slam poet Elizabeth Acevedo will present the Arthur Curley Memorial Lecture (Saturday, February 10), commemorating Curley's dedication to intellectual freedom and the library as a center of transformation. Acevedo's debut novel The Poet X (HarperCollins Children's Books) will be available in early 2018.
Elizabeth Acevedo
Science educator, mechanical engineer, and TV host Bill Nye and science journalist Gregory Mone will headline the Closing Session (Monday, February 12). Nye and Mone are coauthors of Jack and the Geniuses, a middle-grade series designed for STEM education (Amulet Books).
Attend the ALA President's Program (Sunday, February 11), where Jim Neal will introduce a community conversation on the "neutrality of libraries," including a formal debate, a panel of commentators, and audience discussion.
Be a part of the annual Martin Luther King Jr. Holiday Observance and Sunrise Celebration (Monday, February 12), honoring King's legacy and recognizing the connection between his life's work and the library world.
The exhibit hall
With more than 450 exhibitors, the exhibit hall offers attendees a breadth and depth of new and favorite library products, services, books, online services, tools, and technologies. Attend signings, take home ARCs, and enjoy specialty pavilions and live stages including the Book Buzz Theater, PopTop Stage, and What's Cooking @ ALA Cooking Demonstration Stage (Friday–Monday, February 9–12). Visit the website for more information.
Peer-driven sessions
Check out a wide range of institutes and ticketed events offered by ALA divisions, offices, and round tables for conveniently timed and in-depth professional development. Find details and register at the website.
Andrew Carnegie Medals for Excellence in Fiction and Nonfiction winners will be announced at the RUSA Book and Media Awards Ceremony and Reception (Sunday, February 11) alongside the Notable Books, Reading List, and Listen List selections and the Dartmouth Medal and Sophie Brody Medal for Jewish Literature recipients.
Honoring books, videos, and other outstanding materials for children and teens, the Youth Media Awards (Monday, February 12) will reveal the winners of the Newbery, Caldecott, Printz, and Coretta Scott King book awards and medals, among others.
Want to discover Denver?
Visit the informational website created for ALA by the city of Denver—which includes a list of attractions and special offers.
Need to convince your boss?
ALA has resources to help you make the case to your supervisor for attending. View outlined benefits, a budget worksheet, and testimonials from previous attendees.
Have career questions?
ALA's JobLIST Placement and Career Development Center will again offer free career counseling and connect job seekers and employers (Saturday and Sunday, February 10–11).
Visit alamidwinter.org
Track #alamw18 and follow us at @alamw on Twitter
Follow the Pinterest boards
Keep up with #alamw18 on Instagram
Be sure to check out the Midwinter Schedule in November—with mobile app to be released in December—to receive updates, organize your events, get tailored recommendations, and create a shareable calendar.
DONNA HUNTER is the marketing coordinator for Conference Services at the American Library Association.
#alamw18
ALA Midwinter Meeting and Exhibits
50 Years of Intellectual Freedom
The ALA Office for Intellectual Freedom celebrates its history
The Badass Librarians of Jeopardy!
For librarian contestants of the popular game show, cash, kudos, and stories galore | {
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/**
* sliderbutton.js - The JavaScript (non-JQuery reliant) slider button widget. Built to
* duplicate the behavior and basic look-and-feel of iPhone slider button widgets. Originally
* conceived as a JavaScript-only JQuery component, this has become largely CSS, so instructions
* on usage reside here in place of code, for the time being.
* @author Bryan Henderson
* @date 11/20/2013
*/
/**
* USAGE:
*
* HTML (use link element or @import to bring in /js/widgets/sliderbutton/sliderbutton.css:
* <div class="slider-frame">
* <span class="slider-button">Off</span>
* </div>
*
* In JQuery code blocks (i.e., $(document).ready), use this to set behavior:
*
* $('.slider-button').toggle(function(){
* $(this).addClass('on').html('On');
* },function(){
* $(this).removeClass('on').html('Off');
* });
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// HAPPY WIDGET ABUSE!! | {
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CHIPSEC is a security research and validation tool implemented in Python that allows for low-level access to hardware. The powerful scripting capabilities can be used for some tasks, including verification of security mitigations as well future security research. This workshop will provide an overview of the existing tool architecture and how to write modules and tools. Modules will focus on using CHIPSEC for verification of firmware mitigations. Tools will focus on using CHIPSEC to stress the system and perform tasks such as fuzzing interfaces. | {
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{"url":"https:\/\/math.stackexchange.com\/questions\/2585767\/integral-change-of-variable-limits","text":"# Integral Change of Variable Limits\n\n$$\\int_{-\\infty}^{\\infty} \\frac{dx}{x^2}(1-e^{-ax^2}) = 2\\sqrt{\\pi a} = \\int_{-\\infty}^{\\infty} (1 - e^{-a\/x^2})\\,dx$$\n\nThose two integrals are the same (check on Wolfram Alpha). Now, how do we get the integration limits on the LHS, i.e. how do we go from the RHS integral to the LHS integral? I would have thought the limits would go from (+\/-)infinity to (+\/-)1\/infinity = 0_+\/0_-, but apparently they don't.\n\nFor reference this is finding the strong line limit equivalent width of a spectral line, if any of you have tackled this problem before, and the hint we are given is the integral on the LHS, which we are meant to get from the RHS integral.\n\nThanks\n\nFirstly, your integrand is symmetric about zero and so it is ok to write $$\\displaystyle\\int_{-\\infty}^{\\infty} \\left(1-e^{-ax^2} \\right)\\dfrac{\\mathrm{d}x}{x^2} = 2 \\displaystyle\\int_0^{\\infty} \\left(1-e^{-ax^2} \\right) \\dfrac{\\mathrm{d}x}{x^2}$$ and $$\\displaystyle\\int_{-\\infty}^{\\infty} \\left(1-e^{-\\frac{a}{u^2}}\\right) \\mathrm{d}u=2 \\displaystyle\\int_0^{\\infty} \\left(1-e^{-\\frac{a}{u^2}}\\right) \\mathrm{d}u.$$\nAt zero itself, the integrand has a removable singularity (L'Hopital's rule shows the limit as $x$ approaches $0$ is equal to $0$) so the integral is not improper there. Let $u=\\dfrac{1}{x}$ so $\\mathrm{d}u = -\\dfrac{\\mathrm{d}x}{x^2}$ and $x^2=\\dfrac{1}{u^2}$. We understand that if $x=0$, then $u=\\infty$ and if $x=\\infty$ then $u=0$. This allows us to write \\begin{eqnarray*} 2 \\displaystyle\\int_0^{\\infty} \\left(1-e^{-ax^2} \\right) \\dfrac{\\mathrm{d}x}{x^2}&=-2 \\displaystyle\\int_{\\infty}^0 \\left(1 - e^{-\\frac{a}{u^2}} \\right) \\mathrm{d}u \\\\ &=2 \\displaystyle\\int_{0}^{\\infty} \\left(1 - e^{-\\frac{a}{u^2}} \\right) \\mathrm{d}u \\\\ &=\\displaystyle\\int_{-\\infty}^{\\infty} \\left(1-e^{-\\frac{a}{u^2}}\\right) \\mathrm{d}u, \\end{eqnarray*} as was to be shown.\nAs for why this substitution doesn't work in the original integral -- that would require $u=\\dfrac{1}{x}$ to be differentiable over the domain (of $x$-values) $\\mathbb{R}=(-\\infty,\\infty)$, but it is not even continuous at $x=0$.","date":"2019-10-17 18:10:36","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\": 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\": 0.9996260404586792, \"perplexity\": 315.789611746135}, \"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-2019-43\/segments\/1570986675598.53\/warc\/CC-MAIN-20191017172920-20191017200420-00191.warc.gz\"}"} | null | null |
ItaliaES
Club ItaliaES (en)
Free Conversation And
Fabrizio Paterlini – Piano Stories Tour – London
2 September, 2019 Por ItaliaES Eventi
Piano Stories Tour
Information about FABRIZIO PATERLINI concert in London
When: Wednesday 11th December 2019 at 7:45 pm
Where: Purcell Room, Southbank Centre, Belvedere Road, Lambeth, London SE1 8XX (UK)
Advance Tickets: 20-25 £ + booking fee
Box Office: 25 £
Event on facebook
FABRIZIO PATERLINI , Modern Classical
Fabrizio Paterlini is probably one of the most known Italian pianist you've never heard about.
His soothing piano music has an impressive number of fans around the world, who are only waiting the right occasion to see him performing live.
His latest tour in Russia, to say one, in May 2018 saw 6 sold out concerts (2 in a row in Saint Petersburg) in five different cities (including Moscow where he played in the stunning 1,500
capacity Svetlanov Hall located in the International House of Music building), moving more or less 5 thousand fans around the Country.
Stats on the digital platforms are impressive as well: at the time of writing, his Spotify page counts more than 950K listeners per month, and hits like "Soffia la notte" and "Fragments Found" have a total of nearly 50 million overall plays already.
His career, however, turned out differently from most other musicians: instead of building a fan base hitting the road and collecting shows, in the first years of his music career Fabrizio chose to focus on composing music and releasing albums (almost one per year): he founded its own label (Memory Recordings, which now became the first and only Italian modern classical label) and only in the recent years he is starting to increase the number of concerts held in front of a "real"
audience.
In 2018 he played in Russia, Germany, Switzerland and Italy and in September 2019 he scheduled already a big concert in Moscow, where he will play his music together with the Moscow
Philharmonic Orchestra.
In 2019, he is also organizing is first proper European tour, focusing his attention (at first) on the cities of London, Amsterdam, Madrid, Barcelona and Istanbul.
9:00 pm Mahmood en Madrid @ Sala BUT
Mahmood en Madrid @ Sala BUT
May 4 @ 9:00 pm – 11:15 pm
MAHMOOD EN MADRID ****CONCIERTO APLAZADO AL 04/05/2022**** El plazo para solicitar la devolución de la entrada caduca el 24/09/2021 European Tour 2022 Información del concierto de MAHMOOD en Madrid Fecha y hora: miércoles 4 de mayo de[...]
9:00 pm Ligabue – Europe Tour 2022 – Bar... @ Sala 1 Razzmatazz
Ligabue – Europe Tour 2022 – Bar... @ Sala 1 Razzmatazz
May 20 @ 9:00 pm – 11:00 pm
LIGABUE EN BARCELONA Europe Tour 2022 Información del concierto de LIGABUE en Barcelona Fecha y hora: sábado 20 de mayo de 2022 a las 21:00h Lugar: Sala 1 Razzmatazz, Carrer dels Almogàvers, 122 – 08018 Barcelona[...]
9:30 pm Zucchero en Barcelona @ Palau de la Musica
Zucchero en Barcelona @ Palau de la Musica
Jul 12 @ 9:30 pm – 11:30 pm
ZUCCHERO EN BARCELONA Información del concierto de ZUCCHERO en Barcelona Fecha y hora: martes 12 de julio de 2022 a las 21:30h (recuperación concierto del 22/6/2020 y 13/7/2021) Lugar: Palau de la Música Catalana, Calle de[...]
About ItaliaES
ItaliaES Events
ItaliaES Club
We Suggest
© 2021 ItaliaES: Organization Events & Shows | Booking Agency | Artist Management | {
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# **WHAT DOCTORS ARE SAYING ABOUT _IS YOUR THYROID MAKING YOU FAT?_**
"Dr. Siegal deserves to be commended for prescribing thyroid hormone the way he does and for having the courage to write about it."
—Alan R Gaby, M.D., past president of the American Holistic Medical Association and author of _The Patient's Book of Natural Healing_
"Supplemental 'natural' thyroid is often the Rosetta Stone of good health and should not be overlooked or underestimated. IS YOUR THYROID MAKING YOU FAT? makes a valuable contribution to the thyroid literature."
— Stephen E. Langer, M.D., president of the American Nutritional Medical Association and author of _Solved: The Riddle of Illness &M_
"IS YOUR THYROID MAKING YOU FAT? brings to light many heretofore unappreciated aspects of the dynamic between thyroid activity and a number of maladies."
— Dennis Gage, M.D., F.A.C.P., former acting director of the Obesity Center at St. Lukes-Roosevelt Hospital
**. . .**
# **WHAT PATIENTS ARE SAYING ABOUT DR. SIEGAL'S PROGRAM**
"My doctors told me that there was nothing wrong with my thyroid, but I just couldn't lose weight. Dr. Siegal found that my thyroid was underactive. After I started taking the natural thyroid, the weight seemed to fall off. I followed his diet and went from 184 pounds to 122 in about six months. I've got a new body."
—Virginia Brunson
"I was losing my hair, I had chills, and I was so worn out, I couldn't get my work done. I wasn't losing any weight until Dr. Siegal started me on the thyroid medication. No one ever told me I had that problem. Not only did the weight start coming off, but all these other problems went away. I'm not at my goal yet. I can't wait to get there."
— Elaine Lyons
"No one ever found a thyroid problem. Thank goodness Dr. Siegal realized what the problem was. I've lost 65 pounds. I don't even recognize myself when I look in the mirror. I can't believe it!"
—Myra Garcia
"I went to Dr. Siegal last July because of his reputation for getting weight off his patients. I never dreamed that my other problems might be helped. I started taking thyroid hormones in August and I no longer have those horrendous mood swings. I sleep better, and best of all, I'm losing weight steadily."
— Cindy Kirsh
**. . .**
# **WHAT READERS ARE SAYING ABOUT _IS YOUR THYROID MAKING YOU FAT?_**
"If after you've read this book, taken all the tests, filled out the checklists, kept track of your temperature, and tried his 28-day eating test, you don't think you got your money's worth I'd besurprised.... Dr. Siegal also gives strong arguments for the use of natural thyroid supplementation as opposed to the use of synthetics."
— Amy Shellase
"This book is great —I am giving it to my daughters to read, as they have a similar problem as me and are getting fed up with doctors who only go by lab results. Thanks for giving me some hope and having the courage to speak out against the 'establishment.' Wish there were more like Dr. Siegal."
— Roslyn Hodgins, Hammondville, NSW, Australia
"As a doctor of pharmacy candidate and published reviewer of medical literature, I am in constant contact with patients who complain that their doctor dismisses a metabolic problem as the cause of their obesity. While hypothyroidism certainly is not the cause of all obesity, Dr. Siegal makes a very convincing argu ment that, for many, it may be This book offers hope to those who don't overeat but can't seem to lose weight on any diet."
— S. Hileman, Ft. Lauderdale, FL
# Copyright
The information herein is not intended to replace the medical advice of your physician. You are advised to consult your health-care professional with regard to matters relating to your health, and in particular regarding matters that may require diagnosis or medical attention.
Copyright © 2000 by Sanford Siegal
All rights reserved. Except as permitted under the U.S. Copyright Act of 1976, no part of this publication may be reproduced, distributed, or transmitted in any form or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.
Wellness Central
Hachette Book Group
237 Park Avenue
New York, NY 10017
Visit our website at www.HachetteBookGroup.com
Wellness Central is an imprint of Grand Central Publishing.
The Wellness Central name and logo are trademarks of Hachette Book Group, Inc.
First eBook Edition: November 2009
Originally published in hardcover by Hachette Book Group.
ISBN: 978-0-446-57115-9
# _Acknowledgments_
Many people helped write this book; in a sense, thousands. They are the patients I've known for the last forty years.
Of the more recent contributors, I sincerely thank: my wife, Lyndol, for keeping my enthusiasm manageable; my friend, Peter Nguyen, for allowing me access to his knowledge of the biological world; my friends, Carmen and Greg Anderson, for their sage advice; my editor, Rick Horgan, for keeping me focused; my agent, Barbara Lowenstein, for her encouragement; my copy editor, Karen Thompson, for possessing the eye of an eagle; my son Marc Siegal, for making incomprehensible databases comprehensible; another son, Matthew Siegal, for his treasure chest of suggestions; a third son, Jason Siegal, for his critical input; and two great people, Cindy Hernandez and Beth Geisler, for dedicated slavery.
Contents
Copyright
Acknowledgments
Foreword by Alan R. Gaby
Foreword by Stephen E. Langer
Author's Note
Preface
1: But Doctor, I'm Telling the Truth
2: Hypothyroidism, the Greater Imitator
3: Disenchantment with the Laboratory
4: It's Not Always Overeating
5: Depression: The Thyroid Connection
6: Hypothyroidism Woes
7: Natural or Synthetic Treatment?
8: The Usual Way and the Better Way
9: Why Protein for Weight Loss
10: Cholesterol and Hypothyroidism
11: The Metabolic Function Index Test
12: How to Test Yourself
13: Evaluating Your Metabolism
14: Weight Loss Without Guesswork
15: For Your Doctor's Eyes Only
16: Debating My Position
17: Maintaining Weight, Hypothyroid or Not
Appendix A: Prescribing Thyroid Hormone When the Gland Is Normal
Appendix B: Historical Perspectives on Eating Meat and Fat
Appendix C: How to Customize Your Diet Test
Appendix D: Determining Your Frame Size
Appendix E: Evaluating Your Activity Level
Appendix F: Bibliography
Appendix G: Recommended Calorie Books
Appendix H: Other Reading
Appendix I: Sample Daily Menus
Appendix J: A Patient Fights Back
# _Foreword_
_by Alan R. Gaby, M.D._
In this book, Dr. Sanford Siegal argues that hypothyroidism (underactive thyroid) is a common condition that is frequently overlooked by the average doctor. While conventional medicine relies primarily on blood tests to diagnose hypothyroidism, Dr. Siegal points out that these tests are unreliable and often fail to detect the problem. Siegal further differs from most doctors by recommending the use of desiccated thyroid, an extract from animal thyroid glands that modern medicine has repeatedly labeled "obsolete."
While most doctors are strongly opposed to—or even horrified by—the idea of giving a potent hormone to people whose blood tests are normal, my own clinical experience with more than a thousand "thyroid cases" unequivocally confirms Dr. Siegal's observations. Moreover, while only about 30 percent of patients can tell the difference between desiccated thyroid and the most frequently prescribed form of thyroid hormone (levothyroxine), those who _can_ tell the difference nearly always prefer the natural preparation.
The symptoms of hypothyroidism are well known and include fatigue, depression, constipation, cold hands and feet, dry skin, fluid retention, slow thinking, weight gain, menstrual irregularities, and an increase in serum cholesterol. Although these symptoms can have many different causes, I've found hypothyroidism to be one of the most common causes. And yet, approximately 85 percent of my patients whose symptoms improved (often dramatically) with thyroid treatment had normal thyroid blood tests, including TSH (thyroid-stimulating hormone).
The idea that blood tests often fail to detect hypothyroidism is not as far-fetched as it might seem. By analogy, many diabetics require injections of insulin, even though the level of this hormone in the bloodstream may be normal or above normal. This phenomenon is known as insulin resistance. While there is plenty of insulin circulating in the blood, the hormone receptors on cell membranes are inefficient in responding to insulin's message. As a result, some diabetics require higher-than-normal concentrations of insulin in their bloodstream in order to achieve a normal insulin effect. Thyroid-hormone resistance is also known to occur, although it is thought to be a rare condition. However, it is possible that a more subtle form of thyroid-hormone resistance is present in a relatively large proportion of the population. If that is the case, then some individuals would need to maintain their thyroid hormone level near the top of the normal range in order to feel well. While the existence of subtle thyroid-hormone resistance has not been proven, it could explain the dramatic results seen by Dr. Siegal, myself, and hundreds of other doctors who diagnose and treat hypothyroidism on clinical grounds.
Nor should it be surprising that desiccated thyroid works better for some individuals than does synthetic levothyroxine. The former contains two different molecules with known hormonal effects and two other compounds whose functions are unknown, whereas the latter contains only one of these four molecules.
Doctors who oppose the use of thyroid hormone on clinical grounds and rely instead on blood tests point out that inappropriate use of thyroid hormones can put stress on the heart and promote the development of osteoporosis (bone loss). While it's true that overtreatment can cause these problems, I would argue that empirical use of thyroid extract, when done carefully, is neither inappropriate nor overtreatment. I have not seen any cardiac problems with thyroid therapy, although a few patients developed chest pain, which was resolved when the dosage was reduced. Nor have my patients shown any evidence of accelerated osteoporosis, although, to be on the safe side, I always recommend a bone-building nutritional supplement along with thyroid hormone.
Dr. Siegal deserves to be commended for prescribing thyroid hormone the way he does and for having the courage to write about it.
Alan R. Gaby, M.D.
Past President of the American Holistic Medical Association
and author of _The Patient's Book of Natural Healing_ and
_Preventing and Reversing Osteoporosis_
Seattle, Washington
November 1999
# _Foreword_
_by Stephen E. Langer, M.D._
World-famous actor-director Woody Allen once said, "The brain is my second favorite organ." If, as I suspect, his _favorite_ organ is the thyroid gland, we agree.
The thyroid is a butterfly-shaped organ in the neck that releases approximately one ounce of hormone a year. This hormone controls the metabolism of every cell in the body, from your hair follicles to your toenails, and is as necessary for life as food and oxygen. I learned decades ago from my mentor, Dr. Broda Barnes (whom I consider the father of modern thyroid medicine), that as many as 40 percent of the American public are suffering from undetected hypothyroidism (underactive thyroid), and that relying on thyroid blood tests (T3, T4, FTI, TSH) for a diagnosis is misleading and often unsuccessful.
In the book you're about to read, Dr. Siegal discusses Dr. Barnes's Basal Temperature Test (which Dr. Barnes published in a _JAMA_ article and which was promptly forgotten) and shares his own metabolic function index (MFI), which can be performed by anyone—at home, and without cost. This test can frequently serve as a much more sensitive indication of an underactive thyroid than the most commonly used laboratory tests.
A good doctor, however, should look at _all_ the evidence: i.e., he or she should perform a thorough medical history and physical examination, and do all appropriate lab work—including the Barnes test and the MFI—and only then rely on his or her own best clinical judgment as to whether or not supplemental thyroid is appropriate (usually it is).
In all my years of practicing preventive medicine, clinical nutrition, and anti-aging, I have found that prescribing thyroid medication when appropriate to patients suffering from the chronic problems enumerated in this book is the most important thing I can do to help my patients get well.
Without thyroid treatment, eating the best food and taking handfuls of nutritional supplements are wasted. Because of a sluggish metabolism, digestion suffers and the immune system does not perform optimally. A typical hypothyroid patient is therefore exhausted, prone to infections, overweight, has poor concentration, and suffers with many of the dozens of other symptoms known to accompany an underactive thyroid gland. The chronic debilitating symptoms of hypothyroidism are often misdiagnosed as chronic depression and treated with powerful antidepressant medication rather than thyroid hormone. This is not only wrong, it trivializes and patronizes a sick patient.
When a patient is placed on a small dose of thyroid hormone and gets appropriate medication and nutritional counseling, chronic problems like recurrent infections, migraine headaches, fibromyalgia, joint pain, high cholesterol, menstrual irregularities, acne and eczema, depression, and many others disappear like ice in the hot sun.
If it seems like I'm rhapsodizing about the benefits of supplemental "natural" thyroid, I am—it's often the Rosetta Stone of good health and should not be overlooked or underestimated. _Is Your Thyroid Making You Fat?_ makes a valuable contribution to the thyroid literature.
Stephen E. Langer, M.D.
President of the American Nutritional Medical Association
and author of _Solved: The Riddle of Illness_
Berkeley, California
November 1999
# _Author's Note_
In this age of political correctness, to avoid the appearance of gender bias, I might very well have written something like this:
"I always instruct a new patient that when he or she consults his or her family doctor, he or she must inform him or her of exactly what medications I have prescribed for him or her."
That's probably more pronouns than you can tolerate at one sitting, hence I've decided to adopt the following approach: Since most of my patients are female, I've referred to the generic patient as _she._ However, since male physicians still outnumber females, doctors are referred to as _he._
All of the tales of my patients are true, though to protect their privacy, I have used only first names and they are all pseudonyms. Where both a first and a last name are used, the name is real.
Dr. I. M. Conformist in Chapter 16 exists only in my imagination.
# _Preface_
I'm a practical man.
That's not to say that I don't sometimes do silly things, that I don't indulge in fantasies, that I don't take chances. But more often than not, I'm practical. I try to do what reason tells me is the best choice, the thing that is most apt to succeed. That aspect of my personality probably operates even more rigidly in my medical practice than in my personal life. This makes sense to me. I'm dealing with the well-being of my patients, and that is an area where I shouldn't let my emotions get in the way of my good sense.
I try to do for them what works. This book is about what works. Specifically, it is about the method I've developed for evaluating and treating people who are overweight, with the goal of improving their health. I've long since accepted that I can best do this by helping them to achieve a normal weight and to do it safely. I believe that my methods are practical.
We're bombarded with weight-loss diets. They come from every source imaginable: books, magazine articles, the Internet, the government, commercial "clinics," and, yes, even doctors. Many are based on theories. Sometimes these theories are stated in terms designed to make us believe they are facts. Researchers publish scads of scientific papers that are intended to add to the total knowledge of the subject, and doctors pick and choose from the information available and apply what they've read to the care of their patients.
This book isn't about theory, although I certainly touch upon it frequently. It is about what works. I've had forty years of treating nothing but overweight patients, hundreds of thousands of them in the United States and in foreign countries, and I've certainly seen what works and what doesn't work. This book is about a method of uncovering one specific and frequent cause of overweight, a cause that is more often overlooked than discovered. It is also about how to treat that problem properly after it is discovered. As a bonus, this book is also about how to lose weight, no matter what caused the weight gain.
My methods are practical. They've worked for me and my patients. I know they will work for you.
#
# _But Doctor, I'm Telling the Truth_
**M** y patient looks troubled.
"I don't care what that doctor says, there has to be something wrong with my metabolism."
She's one of today's new patients. Her name is Marie. We've just met. She doesn't hesitate to tell me of her dissatisfaction with the last doctor she saw. I gather that her former doctor thinks she just eats too much.
"He said the tests showed that my thyroid was just fine. I followed his diet but it was just like all the others. It didn't work. I just want to be thin. What's wrong with me?"
Her words and her manner don't startle me. I've heard such words spoken too many times in the past. I truly sympathize, but at the same time I'm impatient. There's work to be done. I've a lot of questions to ask. I will do an examination. Then there will be much explaining.
Clearly Marie wants to vent her feelings, and it may be doing her good. From experience with many others, I know those feelings. At this point, I can see that she will repeat her complaint for emphasis, but I don't want to be impolite, so I let her go on. And she does.
There's no complaint I've heard more frequently during that most important first patient visit than what Marie has just expressed. Her monologue is so typical that after the first few words I could have completed her remarks. In the last thirty-eight years, I've had literally thousands of patients voice that same complaint. Of course, they aren't all as bold as this patient. They don't all blame their former doctors. They do express this same discontent, but they phrase it in many different ways:
"I don't understand why I'm so fat; I eat very little."
"I've had my thyroid tested. There's nothing wrong. Why can't I lose weight?"
"Will you give me something to burn up this fat? Nothing seems to work."
"Maybe I have a thyroid problem or something."
"No matter what I do, it won't come off."
Let's make it clear why they're telling this to me in the first place. It is because I specialize in treating overweight problems. In my medical practice, those are the only kinds of patients I see. I don't accept those whose complaint is a sore throat, a broken arm, a nasty rash, or a nose that needs to be reshaped. For forty years, I've limited myself to helping people whose ailment is an excess of fat. My experience has been acquired from hundreds of thousands of overweight patients. (I've truly lost count.)
True, a formidable number of my new patients do admit to major indiscretions. "I eat like a pig" isn't that infrequent. Marie is clearly not in that camp.
She has come to me because she has an acquaintance who seems to have undergone some sort of metamorphosis. Her friend, a once pudgy, dull, couch potato, has a new svelte figure and radiates an astounding personality change. She's given up her menial employment and is going to school to learn court reporting.
Marie knows that her friend has been my patient for a while and that I must have had something to do with that transformation. She believes that the effect of the diet I prescribed for the lady was to reduce her weight and that all the other benefits were derived from some newfound confidence. Her remade friend is now proud of her body and has acquired a self-image that causes her to regard the world as her personal oyster.
She's wrong about her friend in a lot of ways.
First of all, it isn't diet alone that is responsible for the drastic improvement in the friend's shape. And it isn't newfound confidence that makes that lady get up and go. It is the medication I prescribed for her previously undiscovered ailment that is responsible for all the changes. Taking that medication, she would have emerged from hibernation even if she hadn't been fat and lost weight. Her friend has hypothyroidism.
Marie clearly doesn't know the whole story. She's hoping I have some sort of magic diet that will finally get the weight off of her. Unlike her friend, she doesn't need her psyche altered. She has enough motivation to do things and she would do them if she weren't so tired all the time. Of course, she blames that on the extra weight she is carrying.
She isn't going to find a magic diet at my office. She has already been on too many diets. She's hostile toward her last doctor because his diet didn't work. She followed it faithfully for almost a month and lost barely four pounds. At that rate it would take her forever to get thin. He didn't seem to listen to her when she told him that she loses poorly even on the strictest of diets.
Now she's trying again. What she's telling me is that there's something wrong with the way she handles food. It's her "metabolism or something." I sense that she isn't sure of this. After all, the last doctor spent a fair amount of her money at the medical laboratory and proved to her that there's nothing wrong with her metabolism. He said that her thyroid was fine and then explained to her that "thyroid" and "metabolism" were sort of the same thing. In making his explanation, he used such mysterious terms as TSH and T3 and T4. Who can argue when such scientific proof is presented? Does any ordinary mortal dare question TSH, T3, and T4?
Like Marie, at least half of my new patients believe that something has gone wrong inside of them. They declare that, given their eating habits, they shouldn't be as fat as they are.
Many of these people have been to other doctors and have had various laboratory tests intended to show whether there was some sort of metabolic problem. More often than not, the tests come back with the results quite normal. The lab asserts that there's nothing wrong with this person's thyroid. This is one of the few instances in which a patient is truly disappointed to find out that the lab tests rule out some disease. Were the tests to have suggested a metabolic abnormality, the patient's own character would nicely be off the hook. That would prove that the obesity isn't from a lack of discipline or from some character flaw. It would show that the patient's metabolism was the culprit. No such luck for the lady sitting across from me.
On the basis of laboratory tests, doctors often form their opinions. The problem is that many of them have more confidence in laboratory results than in their own good sense. Too often, they ignore the basic principles they learned during their training and rely upon high-tech innovations to show them the way. If we doubt our own perceptions when they are inconsistent with the output of high-tech procedures, we increase the chance for a faulty diagnosis. Consequently, I believe that a large number of people suffer from an ailment that causes them to be overweight and that this condition isn't diagnosed, or perhaps it is even ignored, by a lot of physicians. The ailment is hypothyroidism.
It might not be possible to find another doctor in my area who has done more thyroid testing of patients than I have. After all, I have forty years under my belt and each patient during that time has had at least a potential thyroid problem. By the time I had perhaps seen my five thousandth or ten thousandth patient, I was already pretty disillusioned with the value of thyroid tests. Today, years later, I regard those tests as practically useless. This awareness was the major motivation for my writing this book.
Since my particular interest is the patient's weight and how to get her to part with the excess portion, the subject of metabolism and the thyroid gland has become my passion. The problems that are associated with an improperly functioning thyroid gland and the resulting abnormal metabolism extend way beyond weight. After all, the thyroid gland is a major controller of how we feel, how we act, how we look, and how we function.
People know I'm obsessed with my patients' weight. That's what brings the patients to me in the first place. As with any other complaint, an early step in the process of managing weight is establishing a diagnosis. When I make a correct diagnosis of hypothyroidism, the weight problem is on its way to being solved, and the fallout from this success extends far beyond the pounds that are lost.
In the course of attacking my patients' obesity, I've seen the most fortuitous "cures" you can imagine. I've been given undeserved credit for benefits I never even contemplated. I've seen a moderately obese woman who was resigned to the fact that she was sterile become pregnant in her later years. What joy! All I was trying to do was get twenty-five pounds off her. Of course, such surprises were more dramatic in those early days. Today, I've come to expect these little miracles, even though I'm really not looking for them. I focus on my patient's weight problem. Whatever else happens is medical serendipity.
I have seen years of excruciatingly painful periods disappear in a flash as if by magic.
I have seen phlegmatic, depressed individuals who could barely motivate themselves to get up in the morning suddenly become upbeat dynamos.
I have seen debilitating pain that flits from one location to another, pain that had confounded a bevy of specialists over the years, quietly depart without fanfare.
I have seen hair come back, anemia disappear, memory return, laxatives discontinued, and chronic fatigue become a bad dream.
I don't mean to suggest that I'm the only doctor who knows about all of this. Plenty has been written about the miseries of hypothyroidism. There are even quite a few doctors who specialize in the thyroid gland alone. They and I do part company when it comes to the method of determining who has the ailment and who doesn't, and to a certain extent, what to do about it when we find that it exists.
As I've said, I specialize in treating overweight problems. Because I've seen so many patients over the years, I've developed some very definite and perhaps unique opinions on the subject. In the course of treating thousands of patients, one may change his opinion about ideas that he had previously believed to be incontrovertible.
It is my belief that when it comes to diagnosing problems involving metabolism, the laboratory not only fails us, it even gives us deceptive information about the patient. As a result, many of the patients who consult me have been told that their metabolisms are normal even though they display many of the signs and symptoms of a low metabolism.
The signs and symptoms of hypothyroidism are well known to most doctors. The subject has hardly been ignored in the literature that doctors read. I too read the literature. I'm sure that many doctors intuitively consider hypothyroidism when the patient gives them a history of her complaint. When my own intuition suggests to me that a patient has this affliction, I would naturally like some corroborating evidence. This is the point where doctors turn to the laboratory for help. The laboratory could supply the information that would confirm the diagnosis, but the fact is that it doesn't. I've come to mistrust the laboratory when it comes to the thyroid. Where, then, can I turn for help?
Years ago we had machines that were supposed to help us medical men with metabolic testing. I did thousands of basal metabolism tests with one of these machines, but I always regarded the results as suspect. There was another curious gadget that tested the response time of the Achilles tendon reflex in the ankle. It was an attempt to measure the known connection between the speed of our reflexes and thyroid function. I can still see that look the patient got when my nurse tapped her foot with a rubber hammer. Both of these machines were eventually discredited and yet as I look back, as imprecise as they were, they were probably more reliable than today's lab when it comes to hypothyroidism.
I haven't given up on the laboratory approach, but the search for adequate laboratory tests of thyroid function must continue.
In the 1970s there was a doctor who wrote on the subject. He also mistrusted the laboratory. He had great confidence in a test that he himself had developed. It was simple and easy to perform. Observing that those with hypothyroidism seemed to have a low body temperature, his patients were required to use the thermometer to help establish the diagnosis. I agree that the method has some value, but body temperature can be quite variable for a variety of reasons. I didn't feel that his test by itself could be relied upon as definitive.
Over the years, my own test evolved. Like so many nice discoveries, it was right "under my nose" all the time. It isn't as though one day I decided to invent a test for hypothyroidism. For a long time I had been aware that the inconsistency between what some people weighed and what they actually ate pointed in the direction of hypothyroidism. This knowledge, combined with other factors I observed in the patient, would lead me to make the diagnosis. What gradually emerged was a step-by-step approach to organizing that information so it would serve as a test applicable to all patients. With the testing method I now use, I feel I have at least a 90 percent chance of diagnosing hypothyroidism correctly. What's more, now you can actually do this on yourself, and in a later chapter I'm going to show you exactly how to do it. Stay calm. I'm not going to ask you to puncture yourself or to cause yourself any discomfort. You're going to be asked to eat certain things and to jot down some numbers. When you've completed the task, I believe that you will have a better idea of the state of your metabolism than you might receive from any medical laboratory.
The tests you will be performing will be the same tests that I use every day on my own patients. Whether your thyroid is at fault or not is information that could be invaluable to you if you've had difficulty losing weight, but the benefits could also extend far beyond simply regulating your weight. After you've done the testing, I shall instruct you as to what to do with that information. A low metabolism is correctable and reversible, but that will require the assistance of an attentive physician. I'm going to help you get that information to your doctor or help you find a sympathetic doctor.
If you learn that your thyroid is normal, and you have a weight problem, the testing will still be of value. You need to know that it is normal so that you may settle down to a serious diet with the confidence that it will certainly work.
Hypothyroidism is the medical term that is applied to an underactive thyroid, a gland that doesn't secrete sufficient hormone to allow the body to function normally. In many cases but not quite all, hypothyroidism results in an excess of weight. However, there are a host of other conditions and symptoms that also result from low thyroid function. Many who suffer from excessive fatigue are mistakenly told that they have chronic fatigue syndrome. A sizable number of women going through complicated and expensive treatment to facilitate pregnancy might have immediate success if their underactive thyroid glands were properly treated. Likewise, many menstrual abnormalities are the result of low thyroid function. Psychological problems are another manifestation of hypothyroidism. In general, a hypothyroid patient who receives proper treatment can experience an across-the-board improvement in her general sense of well-being.
For whatever reason, and the reason is often the laboratory, many physicians seem to go off in other directions when patients present themselves with the characteristic signs and symptoms of hypothyroidism. An October 1996 article in _McCall's_ magazine, "The Disease Doctors Miss," did a good job of explaining this phenomenon. It listed many of the symptoms that accompany hypothyroidism, and it was an appeal to the reader to prod her doctor into delving into the problem. This book has essentially the same general purpose, but it also invites you, the reader, and perhaps the victim, to take a very active role in determining whether you have a metabolic or thyroid problem.
Doctors particularly seem to ignore the patient's weight as a significant sign of hypothyroidism. This is probably because of the general tendency of the literature to downplay metabolic problems as the cause of obesity.
Of the many systems I could use to categorize my overweight patients, the simplest would place each of them in one of two categories:
1. Those who eat too much.
2. Those who don't eat too much.
As simple as that sounds, it isn't. In a sense, they all eat too much. But too much for what? The answer is too much for one's body to maintain its weight. One patient might think she eats only one-third the calories her best friend eats, but it is still too much because she's overweight and her friend isn't. If the standard by which "too much" is to be judged is the amount necessary not to create obesity, then everyone who is obese eats too much.
But "too much" may not be that much at all. I'm sure you know that each of us requires a somewhat different amount of food to maintain our respective weights. In some instances the variations among us are impressive. That is the essence of the differences in metabolism among various individuals of similar size. We do seem to burn up our calories at different rates.
When the body fails to burn sufficient calories, I choose to define that condition as hypothyroidism. The trouble is that no one has yet invented a simple gauge that we can attach to ourselves that will read out how many calories we're burning at a particular moment. Until such a device comes along, we're forced to infer how many calories we burn from some rather unreliable tables.
The questions of how many calories we need, how many we eat and how many we should eat, how many calories we burn and how many we should burn, have occupied me for a long time. When I find someone who is out of kilter with what should be, I know I'm dealing with a thyroid problem.
The thyroid gland is located in the front of your neck below your Adam's apple, and normally it takes very trained fingers to feel it. If you do feel it easily, or, more important, if your doctor feels it, it could mean that there's a problem there. If it is readily felt, then it is probably enlarged, and that could mean one of various abnormalities. If what your doctor feels are lumps or nodules, it is mandatory that you undergo further studies. But that isn't the subject of this book. A generally enlarged thyroid gland could mean an underactive thyroid gland. Let's leave it at that.
This little gland is terribly important to your welfare. Let's examine what it does and what happens when it doesn't do what it is supposed to do.
Since the thyroid gland supplies a couple of hormones that regulate our metabolic processes, abnormalities of the gland's function are present with both overproduction of the hormones and underproduction. What is interesting and yet troublesome is that some of the symptoms of both conditions can be remarkably similar. Fortunately other symptoms aren't, and that tends to differentiate clearly between the two. We generally speak of overproduction of hormones as producing _hyperthyroidism,_ a serious condition where bodily processes are speeded up. The typical hyperthyroid individual is the nervous irritable individual who seems "keyed up." Everything from eye problems to severe heart problems may accompany hyperthyroidism. The hyperthyroid sufferer is generally not overweight, and we shall not delve further into that condition.
Of course, there are a number of other diseases of the thyroid gland. There are what are known as autoimmune diseases, where one's own body attacks itself, and in this case the attack is on one's own thyroid gland. One of these is Graves' disease, a condition that got a lot of press when it was revealed that both President Bush and Mrs. Bush suffered from it. There are cancers of the thyroid and there are various nodules that can form and cause trouble. Everyone knows someone or has seen people with "goiter," which is extreme enlargement of the thyroid, usually but not always caused by too much thyroid hormone.
As I've pointed out, it is the underproduction of thyroid hormone that will concern us within these pages. More symptoms can be attributed to this single ailment than to virtually any other in the entire medical repertoire. Soon we shall review what they are. Perhaps in an effort to confound us, the disease usually displays only a few for each individual. Yet different individuals with the ailment may have virtually no symptoms in common with one another. This makes diagnosis very confusing for the doctor, and it is easy to go off in the wrong direction, suspecting other ailments.
The hyperthyroid patient often appears to be a bundle of energy; the hypothyroid one is the opposite. Slow movement, depression, and apathy are some of the qualities that are readily noticeable. In females, infertility and various menstrual abnormalities are common. The person may often feel cold (and actually may be cold!). The skin is dry, the hair lifeless, the cholesterol elevated, and, of more interest, obesity is often present. When you put these things together, you can almost bet that this is someone who has repeatedly tried to lose weight and failed.
If you are one of those for whom the diagnosis of hypothyroidism has already been correctly established, there may be real benefit in concentrating on Chapter 7, "Natural or Synthetic Treatment?," which deals with the medications used for treating hypothyroidism. Here again I'm at odds with the status quo. I believe that the drugs in standard use today for this malady aren't the best choice. I will tell you why my experience has brought me to that conclusion. It may be an uphill battle trying to convince your doctor that another approach might be better, but it is worth the attempt.
You will come across Chapter 15, which is intended to be read by your doctor. It is not strictly just for him or her. I won't mind if you choose to read it. It is essentially a condensation of what is contained in the rest of the book. It is included in the hope that you can convince your doctor to consider seriously what I have learned from my experience with these thousands of patients. I expect that there will be resistance on the part of the doctors who tend to reject ideas that don't come from their customary sources. Old habits die hard. If you can get your doctor to contact me, I will endeavor to convince him. I will even keep a list of those physicians who are willing to embrace what we know to be true. I will make the list available to readers who would like the information.
Because those who treat thyroid problems are so influenced by the dictates of the ivory-tower authorities who have ordained a rather monolithic approach to hypothyroidism, you may expect to hear, perhaps in the media, that what I have dared to include in this book is akin to heresy. I've preempted my critics by becoming my own critic, in a sense. I know what the criticism will be, and so I've constructed an imaginary conversation between one such expert and me. The debate ensues in Chapter 16, "Debating My Position."
Let's get started.
#
# _Hypothyroidism, the Greater Imitator_
**T** his book is about hypothyroidism, how it interferes with weight loss, and how it can be remedied.
Does this patient have hypothyroidism? That's the first thing that comes to mind when I glance at my new patient. After forty years of viewing these overweight individuals, I have concluded that for perhaps one-fourth of them, the answer to that question will turn out to be yes. I've no reason to believe that a cross section of my patient population is much different from one of the general population, and therefore I must conclude that about one-fourth of those who are overweight suffer from some degree of hypothyroidism. This is a startling assertion, one that will probably cause your family doctor's eyebrows to elevate.
Medical textbooks and articles will disagree with my numbers. You may read various estimates as to the prevalence of hypothyroidism, and my guess is that the estimates will generally be below 5 percent of the population. I believe that the percentage of the population suffering from hypothyroidism is at least twice that. Why does Dr. Siegal believe this? I can only blame it upon my experience with thousands of patients over the years. The disparity is probably the result of my unique definition of hypothyroidism. If other authorities are rather united in the 5 percent figure and I maintain that it is at least twice that, both sides may be correct if we accept that there can be more than one definition of the ailment.
My definition is based on the kind of grass-roots logic that seems to come with age and experience. I adhere to the kind of thinking that believes that if it looks like a horse, it probably is a horse. Fortunately, the word _probably_ gives me leeway if it were to become necessary for me to wriggle out of such a statement.
As a doctor, it's not hard to come up with a definition for a disease, particularly a new disease. You simply listen to the patients' complaints, look them over, do some lab tests or X rays, and then declare, "These patients have Siegal's disease." And who can dispute that? The task becomes more difficult when some other doctor has already defined Siegal's disease differently. I can hear him now: "How dare this upstart attempt to redefine my disease!"
In the end, this should not turn out to be some sort of useless word game. What counts is whether the definition of the ailment contributes to helping the patient with that particular problem. I will make a strong case for the assertion that my definition of hypothyroidism does just that.
Before we get to my definition of hypothyroidism, we will have to get to the meaning of some other words that will help you to understand hypothyroidism.
# Endocrine Glands
These are rather miniature chemical manufacturing devices positioned at various locations in your body. They are sometimes called ductless glands because they discharge their chemicals (hormones) directly into the bloodstream. Other glands distribute what they produce through small tubes called ducts. An example of the latter are the several sets of salivary glands that are responsible for keeping the inside of your mouth wet.
The thyroid gland is one of the endocrine glands. It sends its products directly into the bloodstream. The pituitary gland and the adrenal glands are other familiar examples of endocrine glands. Each of these glands produces its own unique chemical or chemicals that are needed to affect various processes in the body.
# Hormones
The chemicals produced by the endocrine glands are called hormones. Some glands normally produce more than one hormone. These powerful chemicals function as regulators of important body processes. For example, in females, the menstrual cycle is under the control of various hormones secreted by the endocrine glands known as ovaries, as well as by other glands. Repeatedly in this book, I shall refer to the particular hormones that are secreted by the thyroid gland.
Pharmaceutical companies manufacture a variety of hormone look-alikes. Birth-control pills that simulate the functions of the hormones of the ovaries are an example. We shall pay particular attention to the attempts that have been made to simulate the thyroid hormones.
Occasionally, the actual hormones are removed from the endocrine glands of animals and are used in human medicine. Before synthetic thyroid hormones were introduced in the 1950s, many people were treated with thyroid hormone that came directly from cows and hogs. Many doctors who had prescribed these could argue that animal-derived thyroid hormone was a quite satisfactory replacement when one's own hormone production was inadequate.
# The Thyroid Gland
If we were to rate the various endocrine glands as to relative importance, most authorities would probably put the pituitary gland at the top of the list. Not only does it have a prestigious location, attached to the brain, but it functions largely to regulate other endocrine glands. When its hormones reach other endocrine glands, it often causes those glands to secrete their own hormones. For this reason, the pituitary is often referred to as the Master Gland. One of the glands that is controlled by the pituitary gland is the thyroid gland.
The runner-up in the gland importance competition would undoubtedly be the thyroid gland. The body processes affected by its hormones are very many and diverse. The thyroid gland in turn controls the functions of other glands. The entire endocrine system is a complex interaction of these glands and their hormones. The ultimate purpose is to keep the human machine running properly. When the thyroid gland malfunctions, the entire body is thrown into a chaotic disequilibrium.
Your thyroid gland is located in front of the lower part of your neck. If you press your index finger into the very bottom of your neck in the front, you will find a distinct notch in the bone below. This is the top of a bone called the sternum, and the notch should distinctly cradle your finger. The next two or three inches above the notch to the left and the right is occupied by your thyroid gland. It actually has two parts, one on either side. Don't be concerned if you can't feel it. If the gland is normal in size, it is difficult to find. If it is enlarged, you may feel it; it has the consistency of a ripe peach. If you have considerable fat in this area, you will probably not be able to differentiate the gland from the surrounding fat. It is really not very important that you find your thyroid gland or even feel it. Let's leave that to your doctor. I was obliged to locate it for you. After all, if you're going to read a book about your thyroid gland, you should at least know where it is.
# **_What It Does_**
The thyroid gland has many functions, but the one I shall give the most attention to is how it controls the rate at which your body uses energy. If that sentence seems somewhat mysterious, I could perhaps clarify it by making substitutions for some of the words. I could replace "the rate at which" with "how fast." "Energy" could be "calories" or even "food." I could use the timeworn analogy of the automobile. Your body is the car and it needs fuel to power the engine. The fuel could come from the outside—in other words, your food. But your food must first be converted into a more refined type of fuel before your engine can utilize it. Your fuel could also come from your storage tank, that layer of fat you would like to be rid of. But even that must be converted into a different form before it can be "burned."
I have said that the thyroid controls how fast the fuel is used. A better explanation is that it controls how much fuel is needed to perform a particular task. In an automobile, the task is to move some passengers from Point A to Point B. Of course, a heavier car or a heavier load will need more fuel. So will a heavier body or one that is performing a more strenuous task. There is a distinction between our objectives when we compare our bodies with our cars.
With automobiles, fuel efficiency is what we strive for. Let's get the most miles per gallon. The auto industry, if we're to believe its spokespeople, is on a constant campaign to improve fuel efficiency, to build cars that will get more miles to the gallon. Strangely enough, those who are overweight would like to achieve the opposite effect. What they would hope for and what they probably don't have is a real gas burner. They want a very inefficient engine that will guzzle fuel. Of course, the fuel you want to waste is your stored fuel, your fat. If there is a day when you're too busy to eat, you will have to dip into your stored fat to supply energy to your engine. You would probably hope that your body would somehow use twice that amount of fuel (energy, calories) that day. At the same time, you would probably wish for your actual car to get twice the mileage from its fuel.
Your thyroid gland in secreting its hormones regulates this use of fuel by your body. If it malfunctions by secreting too little hormone, your body processes slow down. That is another way of saying that you use less fuel. This is one explanation for why some people weigh more than they should. There are other possibilities. It is quite possible that the gland doesn't malfunction but some other mechanism does, but the result is the same. If the targets of the thyroid hormone, the cells that actually carry out the fuel consumption, somehow don't interpret the stimulating effect of the thyroid hormone, fuel consumption doesn't increase. As I've indicated, the effect is the same: less fuel consumption. The solution to the problem is also the same, but how this problem can be solved will come later.
Part of my definition of hypothyroidism is derived from this concept. If the secretion of thyroid hormone isn't sufficient to cause the body to burn calories at a normal rate, it is hypothyroidism. If a "normal" amount of thyroid hormone is secreted but it doesn't achieve the calorie-consuming effect it should, we essentially have the same problem, and I still define it as hypothyroidism. The _hypo-_ prefix to a medical term means "low" or "not enough." The _hyper-_ prefix means just the opposite. There is indeed a _hyperthyroidism,_ a condition in which too many calories are consumed for a given task.
The abnormal burning of calories is the component of hypothyroidism that may generate the most interest, but there are many more signs and symptoms. There are so many and they affect so many diverse bodily systems that it is easy to confuse hypothyroidism with a multitude of other diseases. Even though doctors have nicknamed another disease, syphilis, the "great imitator" because its many manifestations can suggest a variety of other ailments, hypothyroidism may well be an even greater imitator. Presently, I shall go into an exploration of many of the conditions that may accompany hypothyroidism. What often makes the diagnosis difficult for the physician is the fact that although a variety of signs and symptoms is possible, in reality, the usual sufferer displays a relatively small number of them. You can see how confusing the diagnostic task could be. One patient could have three of the signs of hypothyroidism while another has three entirely different signs, yet they both have hypothyroidism. This, coupled with what I believe is a basic flaw in current theory regarding thyroid hormones, often leads to a missed diagnosis.
There is one symptom that is always present, and that is the abnormal consumption of calories. But this is an invisible symptom. You can't see it or feel that it is there. It operates silently and quite undercover. There are some who may dispute my statement that it is always present, but I declare it with the assurance that comes from viewing thousands of patients over many years. This is the common denominator of hypothyroidism, and this fact forms the basis of the MFI test that will be described later. This quirk of hypothyroidism is what enables me to single out those afflicted, often those who have previously been told there is nothing wrong with their thyroid gland.
Those who would dispute what I've just said will probably be quick to ask, "If that is true, why aren't all of those with hypothyroidism overweight?" That is indeed a good question, but it's one that isn't too difficult to answer. In order for anyone to become overweight, he or she must consume more calories than his or her body requires to function normally. The excess food (calories) is stored as fat. The hypothyroid patient who eats a _normal_ quantity of food over a period of time will gain weight because his or her usage of calories is less than it should be. But a hypothyroid individual who eats _less_ than a normal quantity of food may not gain. Remember, there are those who eat excessively, those who eat rather normally, and others who eat fewer calories than are generally needed to maintain a fixed weight, and this is irrespective of their thyroid function. Those who eat minimally may maintain their weight on a diet that would cause "normal" individuals to lose weight. In other words, the hypothyroid individual may still eat so little that the amount consumed is simply not enough to cause weight gain in spite of the low rate of metabolism.
# Thyroid Hormone Production
Research scientists tell us that the production of thyroid hormones by the thyroid gland is stimulated by another hormone from the pituitary gland. This hormone, thyroid stimulating hormone, is usually referred to as TSH. Its production is in turn triggered by yet another hormone. An important constituent of the thyroid hormones is iodine. The thyroid gland uses iodine found in the diet to manufacture its two main substances, which I shall call by their abbreviated names, T3 and T4. The gland actually produces about four times as much T4 as T3, but since the latter is much more potent, the net effect is that they each contribute about the same amount to the metabolic effect.
There are areas of the world where iodine in the food supply is deficient, and in these areas thyroid disease is far more prevalent. In the United States, this is particularly true around the Great Lakes. In Europe, Switzerland is the most noteworthy for this. The use of salt containing iodine (iodized salt) is widespread around the world, and this is probably a major factor in preventing the problem.
A frequent result of insufficient intake of iodine is goiter, which is simply an enlarged thyroid gland. There are various types of goiter, and goiter can even be caused by an excessive intake of iodine. It isn't difficult to spot individuals who have this enlargement at the base of their necks.
It is believed that T3 is actually the hormone that works directly upon the body's cells, but the cells have the ability to convert T4 into T3. Of course, before any of these hormones, TSH, T3, or T4, can do their work, they must be transported to the work site, and they are carried to these sites by the blood. Scientists have developed tests to detect the amounts of these hormones in the patient's blood, and it is logical that doctors use these tests in order to determine the status of an individual's thyroid function. From the blood levels of these substances, the diagnosis of an underactive (or an overactive) thyroid is made. In fact, doctors rely heavily upon these test results. They are used everywhere. They are the current basis for the diagnosis of hypothyroidism.
# The Causes of Hypothyroidism
The causes of most cases of hypothyroidism are unknown, although hereditary factors are certainly involved. It may skip generations. Other causes are man-made. It may result from other types of therapy. For example, irradiating the thyroid gland is a common treatment for an overactive gland (hyperthyroidism), and it generally results in some degree of underactivity. The surgical removal of a major portion of the gland would have the same result. Exposure to accidental radiation such as what happened at Chernobyl is another. The lithium drugs used to treat depression may also initiate hypothyroidism.
The vast majority of patients I see have no clear-cut cause that can be detected. If heredity is important, it isn't easily traced. Previous cases in a family often went undetected. I have my suspicions as to what some of the causes might be. I think it is curious that I see more cases in women who have had recent pregnancies than in those who have never been pregnant. Patients with hypothyroidism will often describe a recent emotional shock, or their lives may be particularly stressful.
Steroid drugs (such as prednisone or hydrocortisone) are often used to treat inflammation, allergy, and other conditions and are widely prescribed by doctors. Although these medications seem to work miracles in relieving many symptoms, there has always been controversy over their use or their overuse. I think it is more than coincidence that many of my hypothyroid patients have at some time or another had a course of steroid treatment.
There are even those cases where one's own body is the villain. One of these is the autoimmune disease Hashimoto's thyroiditis (named for its Japanese discoverer), in which substances in one's own blood attack the thyroid gland and destroy much of its functionality. Fortunately, this disease responds to treatment much like other forms of hypothyroidism.
# Other Thyroid Disorders
The thyroid gland can also be the site of various other medical problems, but it is beyond the scope of this book to examine them in detail. Just as hypothyroidism is characterized by insufficient amounts or effects of thyroid hormone, there may also be an overabundance of the hormone. As I have mentioned, this condition is called hyperthyroidism. The symptoms are quite different from hypothyroidism. As you might expect, they are somewhat the opposite. Even though this individual burns calories at a rate higher than normal, that effect can be overcome by eating excessively, and the individual may end up overweight. Usually those afflicted are quite thin, but don't be too quick to envy those souls. Their problem has the potential of being even more serious.
Hyperthyroidism is relatively common and perhaps missed less often by doctors than hypothyroidism. While one form of hyperthyroidism, Graves' disease, attacked President and Mrs. Bush, it was reported by the press that even the White House dog suffered from a thyroid disorder. This sent people scurrying to test the water supply at their residence, but they apparently came up with a blank. Since Graves' disease is common, this was probably just an unusual coincidence.
Like other body parts, the thyroid may play host to a variety of tumors and cancers. I don't treat these conditions. When they are suspected, the patient is referred to the appropriate specialist. If your interest in the thyroid gland goes beyond hypothyroidism, I would recommend some of the books listed in Appendix H.
# Signs and Symptoms of Hypothyroidism
I have mentioned that the signs and symptoms of hypothyroidism are many, yet a particular individual may have but a few. What follows is a list, which may not be complete, since new items seem to be added to the list constantly. You might conclude that anyone perusing this list might come to the conclusion that he or she is afflicted, and that is exactly why the ailment is so often missed. Who doesn't have some of these? Yet every case of constipation isn't hypothyroidism. Let's look at the list. I've placed the symptoms in alphabetical order.
Anemia
Brittle nails
Cold intolerance
Constipation
Depression
Dry or coarse hair
Dry skin
Fatigue
Hair loss
Headaches
Hoarse voice
Impotence
Infertility
Irritability
Low body temperature
Memory loss
Menstrual pain and other abnormalities
Miscarriages
Muscle pain or cramps
Overweight
Palpitations
Puffy facial features
Sleeping excessively
Slow pulse
Weakness
I'm sure that everyone who reads this list can identify with something on it. That doesn't make the diagnosis of hypothyroidism. Were there not some common factor that all hypothyroid victims possessed, the list would not be that helpful in diagnosing the ailment. Current thinking in most of the medical community is that the common factor is none of the above, but rather certain abnormal results obtained from blood tests. Experience has caused me to disagree. I believe that a far more reliable test is based on the common factor of low metabolic rate, the subnormal utilization of stored calories. I shall expand on this in the chapters to come, and you will learn how you can do a self-test of your own metabolic rate.
# I Want to Lose Weight
A patient doesn't consult me because of the usual symptoms of hypothyroidism such as hair loss, or depression, or because she hasn't been able to become pregnant. She is there because she has heard that I can help her to lose weight. If she has any of the symptoms from the above list, she probably has not connected them with her weight problem. To learn more about them, I must pry the information out of her. In the course of a medical history you learn a lot if you ask a lot of questions. Although I'm always looking for hypothyroidism, the physical appearance of a particular patient may be quite contrary to the stereotype for this ailment, and I relax my vigil. The right answers to a few questions can definitely put me back on the right track.
A statement that never fails to attract my attention is "No matter what I do, I can't lose weight," or something similar. "I really don't overeat" will also start the wheels turning. "The last doctor said there is nothing wrong with my thyroid" is particularly significant. It tells me that someone at least suspected hypothyroidism, either the doctor or the patient. If neither had entertained the idea, there would have been no point in the doctor making that assertion.
Now armed with a real suspicion, I'm ready for some further corroborating evidence: "Yes, my hair is very dry." "I have these aches and pains and no one can find out what's wrong with me." "I've had this raspy voice ever since my pregnancy."
This is all it takes for me to launch the test. It is actually what I refer to as the determination of the patient's Metabolic Function Index. It is my invention, so I had to give it a name. MFI is a lot easier to say, so that is what I will call it in these pages.
It will take about four weeks until I know what the MFI is for this patient, and until then she will be treated much as any other patient who comes to lose weight: a diet, counseling, perhaps medication to help with hunger, and perhaps treatment for some unrelated condition. If and when I find that she has a subnormal MFI, her treatment routine will change.
I don't mean to suggest that only suspicious cases are tested. In a sense, every patient is tested. An inadequate weight loss in four weeks coupled with a patient who has seriously complied with her instructions is a real red flag for hypothyroidism. For the patient who is under suspicion, I probably work harder to impress upon her the necessity for complying during this first month. I tell her that if she doesn't deviate from the diet, I (and she) will have valuable information that could serve her well in the future.
The prospect that she will once and for all learn why she cannot lose weight combined with the expectation that the problem can be corrected can be a powerful motive for cooperation. In this case cooperation means adhering strictly to a particular diet for four solid weeks. It isn't very hard to convince a patient that this exercise is worth the effort.
If you have truly had difficulty in losing weight, or if you're overweight and believe that the calories you consume don't account for it, it would be to your advantage to take the test in Chapter 12. If you have several of the signs and symptoms listed above, this should underline your need to know. You should take the test particularly if you have already had blood tests that supposedly ruled out a thyroid problem. No effort in obtaining valuable information about yourself is ever wasted.
Let's not be too quick to jump to conclusions. Yes, it may be your impression that you don't lose weight as you should. You may also have a few of the listed symptoms. That is the starting point for putting your curiosity to good use. I will give you the means to really find out.
Hypothyroidism is treatable, and when it is treated, weight loss suddenly becomes easier and most of its other manifestations are reversed.
# Summing Up
* Hypothyroidism is more widespread than it is generally believed to be.
* The thyroid gland controls the rate at which we use energy.
* Hypothyroidism has many different signs and symptoms, but a particular sufferer may only have a very few.
* Hypothyroidism is characterized by the slow burning of calories.
* There is a home test that one can perform based on calorie consumption that can show the presence or the absence of hypothyroidism.
#
# _Disenchantment with the Laboratory_
**P** atients who come to me for help have generally sought help before from other doctors, so-called clinics, or organizations. It is uncommon for me to see a new patient who has never attempted to lose weight with some outside help. Occasionally the help was from a magazine article or a diet book, but much more frequently it was through some more structured system.
There are the "clinics" that have no medical connection that give dietary advice and usually accompany their instructions with mandatory prepared meals that are sold to the client. There are the organizations that emphasize group enthusiasm (or shame) along with their diets. Any of these can work reasonably well if the client is well motivated and doesn't want to waste her money. In the long term they usually fail, since the client doesn't maintain whatever weight is achieved, and that is true for most methods.
Many people go to doctors to lose weight. Some of the best results as well as some of the worst seem to come from physicians. Many doctors take a real personal interest in their dieting patients, and some patients do perform admirably under their scrutiny. Unfortunately, there are also doctors who write a prescription for three months' worth of appetite suppressants and then tear a sheet off of a pad of diets, seeing the patient off with instructions to behave for the next three months. The success rate there is infinitesimal.
From talking to colleagues over the years and from listening to lecturers at seminars, I have the distinct impression that for many physicians, from that first moment an overweight patient walks through the door, there is the presumption, a well-entrenched mind-set, that she is a glutton and that, consistent with human nature, she will deny the fact that she is such. Thus, when she declares the proverbial "I eat like a bird," the classic cartoon balloon appears above the doctor's head, illustrating what is in his mind: The bird, a vulture, is flying off to its feast, its talons locked onto a substantial hog.
The fact is that in this arena, and perhaps others (or perhaps in no other), doctors mistrust the patient's honesty. What's more, the patient senses that the doctor doesn't believe her. I often see this in the uncomfortable way a patient informs me that she doesn't overeat. She isn't relaxed in telling me this, not because she is lying, but because she expects me to think she is lying. It isn't unusual for a lady to bring her husband into the treatment room with her. It's clear that he is there as a character witness to vouch for her honesty. ("Honest, Doc. She really doesn't eat.")
Nonetheless, disregarding their own preconceived notions, many physicians address the possibility of hypothyroidism by ordering tests that purport to supply the answers. Once this is done, the test results seem to become the end in themselves rather than a step along the way.
"Your thyroid gland tests normal. You really should lose that weight. I'm going to give you a diet...."
This all concerns a mythical doctor and his mythical patient. Allow me to expand on the mythical discussion:
"But, Doctor, I've tried low-calorie diets and they don't work. I told you how tired I am. I read this article in a magazine that said my weight problem and my fatigue could be due to—"
"Yes, we can't ignore that fatigue. I'm going to order some additional tests to try to rule out certain ailments...."
And so it goes. This scenario has repeatedly been played out to me by my patients.
I believe our doctor has dropped the ball. Infectious mononucleosis should not be at the top of his agenda. Had he not been so certain that his patient was lying from the beginning, he might have entertained the idea that the lab made a mistake. Laboratories do make mistakes. If this patient's lab work came back with a blood glucose reading of 275, he would probably have asked her to repeat the test before he pronounced her a diabetic. But since the thyroid results rubber-stamped what he believed from the onset, he had no difficulty in dismissing her protestations.
I must point out that I use the laboratory constantly in acquiring information about the states of my patients' health. Most laboratory tests are really quite reliable. But not all.
_I have virtually no confidence in the results of laboratory thyroid testing._
I suspect that people have been burned at the stake for uttering less blasphemous sentences.
I have ordered literally thousands of thyroid tests for my patients over the years. In the beginning and according to my training, I would accept the results as valuable tools to separate those overweight patients whose problem was complicated by an underactive thyroid from those with normal thyroid function.
Almost from the beginning, I would notice that some patients who professed their innocence in terms of overeating had normal thyroid values. It took a while for me to become brave enough to go against proper procedure and actually prescribe a small amount of thyroid hormone to someone who wasn't supposed to need it. On the relatively few occasions when I would do this, the patient's response to treatment was often dramatic. I'm not sure how I actually rationalized my deviation from what was considered proper. Perhaps I explained it to myself by excusing the lab for some error in technique, or by telling myself I had a patient whose blood had some mysterious quality that rendered it impossible to analyze accurately.
This began to happen more and more until I realized that although I was doing a lot of thyroid testing, I was very frequently ignoring the results. Eventually this evolved into my not bothering to run tests for which I knew I would ignore the results. I didn't do this casually. Perhaps the most disappointing aspect of the testing was that sometimes I would order a repeat test and get entirely different results. A more flagrant scenario was played out when on a few occasions I would order the tests three days in a row on the same patient and get totally diverse results. How would any doctor know which result to rely upon?
_I have virtually no confidence in the results of laboratory thyroid testing._ It was much easier to say that the second time after I had given my justification. I now know that if I were to use only the results of the most common thyroid tests, mainly the TSH, the T4, and the T3, I would be in the dark as to who had hypothyroidism and who didn't.
Why, then, do other doctors not feel the same way? I don't know the answer, but I can tell you that I'm mystified as to why. I'm sure that many of them have observed what I have. On several occasions I have spoken to other physicians about this, and I have had the distinct impression that a number of them have agreed with me. Their observations were similar. They recognized that the laboratory thyroid results often didn't seem to coincide with the patient's history and observations made during the physical. But that is where the scientific curiosity seemed to end. The doctors simply wrote off the discrepancy as some unexplained phenomenon and then continued to follow the old rules.
I have even had many doctors and nurses as patients over the years with whom I have discussed this. Some of them turned out to have hypothyroidism that was previously undiscovered, and they responded to treatment nicely. But I've never had the feeling that anything I had to say disturbed the status quo. If they were impressed, it didn't seem to go beyond the belief that they were unique and that my deviant treatment was applicable only in their particular case.
I'm not the first to voice such heretical statements concerning thyroid testing. Dr. Broda Barnes, in his 1976 book _Hypothyroidism: The Unsuspected Illness_ (co-authored by Lawrence Galton), expressed my same displeasure with laboratory testing. He also had treated thousands of patients and was frustrated by the lack of proper testing methods. He bemoaned the fact that science can monitor a man's heart while he's walking on the moon, but scientists can't develop an adequate test of thyroid function. He said,
The efforts through the various tests to measure thyroid activity by determining the amount of the hormone stored in the gland or alternatively the amount present in the bloodstream fail to do what really counts: provide an indication of the amount of thyroid hormone available and being used within cells throughout the body.
Barnes was pointing out that although the tests may indeed be accurate in determining how much thyroid hormone is in the blood at that moment, this knowledge may be useless. It is in the individual cells that the thyroid hormone does its work. If the hormone doesn't get to the cell or if the cell cannot accept or use the hormone, then it matters little how much of the substance is in the bloodstream.
Dr. Barnes actually relied upon a test of his own and although it was primitive, it was in his opinion still better than anything else around. It is a well-known fact that patients with hypothyroidism run a lower body temperature than the rest of the population. He instructed his patients (and his readers) to take their body temperature. I would agree with him that the temperature test is worth more than the blood tests. Yet to rely upon that method suffers from the fact that many other immediate body states can alter one's body temperature. An undetected infection is an example. If I have any criticism of Dr. Barnes's method, it is that he seems to have relied on a single temperature reading to make his decision as to hypothyroidism in the patient. It would seem that multiple readings over a period of days might be more reliable. Still, anything that points us in the right direction is useful. Later you will learn how I add a variation of Barnes's temperature test to my own method.
At this point, the idea isn't so much to second-guess your doctor as it is to do a little individual homework and, based on your results, make a decision as to how to proceed. If what you've read so far has you a little suspicious that you may have some degree of hypothyroidism, a later chapter will give you the means to investigate it for yourself. There are a couple of questions you should now be asking yourself:
Do I believe that my weight is justified by the diet I eat?
Do I have some of the other signs and symptoms of hypothyroidism?
Having asked these questions and stored the information in your brain, you may now go on to learn what thyroid testing is really all about.
Before your doctor does any specific testing for thyroid problems, he will generally have done a more general series of tests designed to uncover trouble spots in a variety of the body's systems. Twenty to thirty of these tests are usually lumped together as a group by the individual laboratories and are given a name by the lab, for example, the General Profile. Not all labs choose the identical group of tests for inclusion in this general profile, but certain tests will undoubtedly be included in every lab's choice. A general profile of this type will always include tests for blood glucose (sugar), cholesterol, blood urea nitrogen, serum sodium, etc. It isn't routine for laboratories to include any specific thyroid tests in this profile. They must be ordered separately. Even though twenty or more tests are done in such a profile, the patient is generally overjoyed to learn that only one blood specimen is needed for the entire group of tests.
After your doctor has examined the results of this laboratory profile, he may then focus in on any tests that come back with abnormal results and order further, more specific tests that will target particular body systems or specific ailments. As an example, if the physician finds the blood glucose level to be elevated, he will probably choose to order a glucose tolerance test,which will give much more specific information as to the presence of diabetes.
Since thyroid tests aren't a part of this profile, before the doctor orders further thyroid testing, something in the results will probably trigger his interest. The particular test that should alert him to the possibility of hypothyroidism is an elevated level of blood cholesterol. This is a frequent finding in hypothyroidism. Sadly, I see one patient after another who has been tested by the primary-care physician, been found to have an elevated cholesterol level, and been given a prescription for one of the new and obscenely expensive cholesterol-lowering agents with the admonition to stop eating so much fat.
The prevailing standard of medical care, but in my opinion not the proper one, would dictate that our physician should have ordered the next round of tests with the objective of ruling out hypothyroidism as the cause of the elevated cholesterol. If he were to have followed current practice guidelines, he would have ordered three more tests: the T3, the T4, and the TSH.
# The Standard Thyroid Tests
The T4 test in its most current form, done by radioimmunoassay, detects the amount of the thyroid hormone thyroxine (T4) circulating in the bloodstream. T4 accounts for 80 percent of the thyroid gland's production of hormones. If the blood levels of T4 are low, the theory is that the body's cells aren't getting enough of this hormone and the patient is thus suffering from hypothyroidism.
The T3 test similarly measures the amount of this other thyroid hormone found in the bloodstream. Although it accounts for only about 20 percent of the thyroid gland's production, it has a much more powerful effect, so that T4 and T3 share rather equally the total hormonal effect of the thyroid. Additionally, T3 is produced in the cells when T4 is converted into T3.
The TSH (thyroid stimulating hormone) test is generally accepted (but not by this doctor) as the most reliable screening test for overproduction or underproduction of thyroid hormones. TSH is actually a hormone of another gland, the pituitary gland, and this TSH causes the thyroid gland to secrete its hormones. The theory is that the pituitary gland recognizes an insufficient level of circulating thyroid hormones and secretes its TSH into the bloodstream. This causes the thyroid gland to secrete more hormones, T4 and T3. The pituitary gland now senses the increased production and shuts down its secretion of TSH. Thus, the two glands work together to keep the correct amount of thyroid hormones circulating.
Doctors make their diagnosis based on the blood levels of these various substances. Various combinations of high and low values for each of these tests should enable us to narrow down the site and nature of the problem. Repeatedly the literature speaks of the TSH test as the single most important tool for the diagnosis of thyroid problems.
There are even additional tests that further purport to narrow down the causes of the problem. All of this boils down to a very "scientific" organized system of diagnosing a disease that causes major inconveniences to the sufferer. It's all very nice and neat and methodical. The problem is that in the eyes of this practitioner, the method just doesn't work.
If I were to follow the "cookbook" set of rules that has been suggested by these preceding paragraphs (as I once did), my life would be a lot simpler. I would look at a few numbers on the lab reports, immediately see the problem, and respond according to an equally organized set of rules in treating (or not treating) my patient. But I can't do that.
I can't do that because I know from experience that the diagnosis of thyroid problems isn't that simple. I know that if I were to follow this accepted procedure I would miss more hypothyroidism than I would diagnose correctly. Furthermore, I would label some patients as hypothyroid when they weren't at all. It took a lot of years, a lot of patients, and a lot of thyroid tests to bring me to that conclusion. That is the purpose of this book. I want to alert you, the potential patient, as well as your doctor, not to accept the gospel of laboratory infallibility.
Is there any value at all in doing these tests? I've asked myself that question more times than I care to count. Suppose I form the impression that a particular new patient indeed has many signs that make me suspicious of hypothyroidism. Suppose I then subjected the patient to Dr. Siegal's MFI test, which I shall describe later, and it corroborates my suspicions. If I then run the "proper" thyroid tests and the results confirm that my suspicions were correct, I would be able to congratulate myself for being such a discerning doctor and I could proceed to treat my patient's hypothyroidism. If the course of treatment produced a radical improvement, i.e., the patient lost a ton of weight and virtually all of her symptoms disappeared, it would further attest to my skill as a physician.
But suppose in the above scenario I had performed the laboratory tests and the results clearly disagreed with my suspicions. Would I then act differently? Would I then say, "Everything points to hypothyroidism, but the laboratory has proven me wrong, so I must reject that idea"? Of course not. I would proceed to do exactly as I had done in the first example, perhaps leaving off the extra pat on the back. I would treat the patient for her hypothyroidism exactly as in the first example.
However, what if in this second scenario the patient didn't respond positively to treatment? I would have to accept that my judgment had been wrong and that the laboratory had been right. In practice, that hasn't happened, or, to be more exact, it has happened so seldom that I must regard it as the rare exception to the rule.
I introduced this series of hypothetical possibilities with the question of whether the lab tests have any value at all. It is clear that in my opinion they have little value, because they don't influence in any way my approach to the patient.
It isn't easy to take such an adverse position. One must question one's own judgment when it has such a minority viewpoint within a universe of supposedly competent scientists. Yet is my own personal experience not to be trusted? The laboratory has failed me. My own intuition, coupled with techniques I've yet to tell you about, has served me and my patients well. No, I must stick to my guns. There is a better way to determine who has hypothyroidism and who doesn't. You will soon learn my method. You may even learn why weight loss has been so difficult for you to achieve.
# Summing Up
* Many physicians place complete confidence in the laboratory results for thyroid function, ignoring obvious symptoms in their patients.
* The laboratory cannot be relied upon when diagnosing hypothyroidism.
* An indicator of low thyroid function is lower-than-normal body temperature.
* Elevated cholesterol in the blood is a common symptom of hypothyroidism.
#
# _It's Not Always Overeating_
**E** arly in the medical history of each new patient I take on I ask, "What do you think is the cause of your weight problem?" As you might expect, I get a variety of responses. Sometimes the blank stare that follows suggests that my patient has never considered that there was such a thing as a cause. It is accepted that being overweight is a condition that simply exists. For those patients, speculating as to the cause isn't worth the effort. But that isn't the usual response. Without a doubt, what I hear most is "I just eat too much."
This is certainly an honest response, and it doesn't always pop out that spontaneously. I often have to dig it out. Typical of such an exchange was my initial history-taking session with Cindy, who supervised the staff of a law office:
"What do you think has caused you to be overweight?" "Well, I've a very stressful job. I manage an office full of people and they drive me mad."
"What does that have to do with being overweight?"
"I don't have a minute to myself. I work maybe twelve hours a day. It's very stressful."
"Do you think stress makes you overweight?"
"Absolutely. If I had a more relaxed job, I don't think I would have this problem."
"Does eating have anything to do with it?"
"Of course. I have to eat what I can get. I don't have time to eat right. To top it off, the attorneys are always bringing goodies into the office. When you're hungry, it's hard to resist."
There is certainly a reluctance on my patient's part to admit that she overeats. It took several sentences before the word _eat_ or _food_ was even mentioned. I have concluded that people don't like to admit that they overeat. There must be some shame connected with it. They hem and haw so that they don't have to use those damning words. Still, Cindy was basically honest; she just took an oblique road to admitting that she overeats. About half of my new patients either immediately or eventually get around to confessing that they eat too much. Even then, what I hear more often is that they eat "the wrong things" rather than "too much." Cindy turned out not to have a thyroid problem; her test month resulted in an acceptable weight loss. She went on to become a model patient. Once she got into gear, she was able to resist those temptations.
A small number will explain their weight problems by indicating that obesity is a family trait. If I push them to elaborate upon how their genes contribute to weight, they will usually explain that their parents, their brothers and sisters, and assorted aunts and uncles are all obese. I try to probe deeper to see if they are pointing to a type of behavior—overeating—they learned from their relatives, or whether they are suggesting that they have inherited a metabolic problem. The latter is certainly a recognized concept. Hypothyroidism does seem to pass from one generation to the next.
The other half of my patients profess not to overeat. They express this with varying degrees of certainty: "I don't think I eat more than I should. My husband eats more than I do and he's thin." "I eat half as much as many of my friends and I'm still fatter than any of them." This half of my patient population suggests that there is a metabolic problem. They may not be clear that they are speaking of a thyroid problem, but they feel that there is _something_ wrong with them.
About half of the group who believe something is wrong with them are actually wrong about that. Their problem is that they do overeat. Perhaps they just don't realize how much they do eat, or, more likely, they are nursing some sort of denial mechanism. When questioned, the facts come out and the patients often seem embarrassed. They do make a distinction between "eating" and "snacking." Eating is what you do sitting down at specific, set times. Snacking is done on the run. I've even had patients who declared they never eat a meal and therefore can't understand why they have a weight problem. They are slow to accept that all that food they've eaten apart from meals amounts to more calories than the three meals they've missed.
It is the other half of that _something-must-be-wrong_ group that holds the greatest interest for me. These are the patients who truly don't overeat. It isn't unusual for me to have to elicit this information from someone who accompanies them into my office, a wife, a friend, a sister perhaps. They are sure they eat less than anyone else around them. They are also the most vocal in telling me about it. I've referred to these people earlier. They are emphatic and quite often somewhat angry. I'm not sure if this has resulted from the belief that they've been dealt the wrong cards in life or whether the stigma of excess weight has evoked undeserved disapproval from others. It is this very agitated state that works against their making their points. I expect that if these patients do have thyroid problems it would be more characteristic for them to be quite docile, and I'm always surprised to see this obvious agitation. The subject must be troubling enough for them to muster some gumption.
I estimate that about one-fourth of my patients do have some degree of hypothyroidism. This is probably at least double what is reported in the medical literature. It is hard for me to make an actual assessment of how prevalent hypothyroidism is. Remember, I see only those hypothyroid individuals who are overweight. There may be many out there who aren't overweight or perhaps are only moderately so, and they would have no reason to consult me.
There are degrees of hypothyroidism, and in the first encounter the disorder may not be obvious. In some, I can spot it before they've uttered a word. It is their characteristic puffy appearance, their slow-moving ways, their lack of enthusiasm. Yet in others I'm surprised to find that it exists. Some simply don't match the stereotype.
What is the stereotype? The textbooks describe a male or a female with puffy, dry skin, coarse hair, and a hoarse voice, who is slow to respond to questions, someone who projects the image of the couch potato. Yet I've seen hypothyroidism in individuals who had none of these characteristics. I'm not sure that there is any other ailment with such a multitude and diversity of symptoms. What confounds us doctors is the knowledge that only a fraction of these symptoms are usually present in a particular patient, and those symptoms could just as easily be associated with an entirely different ailment.
I remember a patient by the name of Jean who had a slew of hypothyroid signs and symptoms and who had had blood tests with her family doctor. She had accepted that she had a normal thyroid. She was not angry with anyone; she took it philosophically. She had so much respect for her family doctor that she couldn't bring herself to doubt him. She also knew that her meager eating habits should not have accounted for her 192 pounds. I'm not sure how she was able to rationalize this paradox in her mind. When I spoke of doing my thyroid test, she replied, "Oh no, I've really been tested. There's absolutely nothing wrong with my thyroid." Since the diet and test are the same thing, she was tested anyway. When I told her I believed she had a thyroid problem, she resisted my suggestion that she be treated for it. After a month of virtually no weight loss, she acquiesced and began to lose weight satisfactorily. She reached the goal we set and even continued to maintain her 128 pounds with the help of the thyroid hormone I had prescribed. If you were to approach her and ask her about herself, I wouldn't be surprised if she were to tell you that she has no thyroid problem.
Later I shall elaborate on what I believe to be the common denominator of hypothyroidism, the slow burning of calories. You must take care not to assume that this automatically equates to being overweight. Remember, excess weight occurs when one takes in more calories than one requires. Hypothyroid people need fewer calories. But if they are poor eaters and they don't take in more than they need, then they aren't overweight.
Hypothyroidism may be present from birth, and it is a severe problem when it exists in the newborn. Fortunately, pediatricians seem very attuned to discovering these afflicted babies, and it is my impression that in this country very few go untreated. It is the hypothyroidism that is acquired later with which I most frequently deal.
Today, I'm very attuned to spotting the potential victim, and every patient is evaluated with that possibility considered. This wasn't always the case. I have already spoken of how my methods have changed as my experience has broadened. I must admit that I cringe when I consider the number of cases I must have missed in those early years. I can remember repeated scenarios where I was completely befuddled by the patient who didn't lose weight adequately.
Back then, I was more in awe of the laws of the universe. I knew that in order for a person to lose one pound of body fat, his intake of calories had to be 3,500 calories fewer than the body needed during that period of time. I still believe this. That was the basis of my bewilderment. Cathy brought in the food diary she had meticulously kept for the preceding four weeks. Using her little calorie book, she had diligently calculated the calories in each morsel she had eaten. She had lost less than one pound over the four-week period, and her diet averaged 1,200 calories a day. That didn't add up. The charts said that Cathy needed about 2,000 calories a day just to maintain her weight. That means there was an 800-calorie deficit each day. In twenty-eight days the deficit was 22,400. That should have meant a loss of about six pounds. She had been tested with the usual laboratory thyroid workup. The laboratory tests revealed that her thyroid hormone levels were perfect. What was wrong? Maybe her arithmetic was bad. Maybe she forgot to include that hot-fudge sundae each night at bedtime. Maybe she was just storing a lot of water and she really had lost six pounds of fat. Maybe I wrote down the wrong weight on that last visit. Maybe...
Of course any one of these possibilities could have explained the discrepancy. But over the years this kind of thing happened again and again with hundreds of patients (maybe thousands). It finally sank in. These "normal" patients weren't all that normal. Abnormal problems require abnormal solutions. I truly can't remember the very first time I deviated from accepted protocol. But there had to be a first time, and that is when I prescribed thyroid medication to a patient who shouldn't have needed it, according to the laboratory. The result must have been successful, otherwise there would not have been a second time. There was a second time and then a third and eventually hundreds and then thousands. What was this successful result? Weight loss. Weight loss that met or at least approached the expectations given the calorie count of the diet. I was comfortable with the consensus of the literature that stated that thyroid hormone would not facilitate weight loss in those with normal thyroid function. The conclusion: Since these supposedly normal patients did finally lose weight, they hadn't had normal thyroid function.
The benefits to the patients didn't end with weight loss. There were other changes in my patients, some of which were as gratifying as the weight loss. I shall presently discuss other benefits of thyroid replacement therapy in hypothyroidism.
I have learned over the years that weight gain often begins with certain events that punctuate our lives, and when that is the case it is more often the result of hypothyroidism than of the irresponsible intake of food. One of the more obvious events is pregnancy. "I never had a weight problem until after I had my first child." One after another, patients have reported this to me. It has become more the rule than the exception.
I have repeatedly probed this circumstance with patients. "Are you sure you didn't eat more after the pregnancy than before?" Generally I hear the same answer. "Is it possible that your physical activity diminished after you had the baby?" "No." I don't mean to imply that this was always the case. Certainly many women have multiple pregnancies and don't succumb to hypothyroidism. But if it is going to occur, it quite often follows the first pregnancy and may indeed grow worse with subsequent pregnancies.
Other events seem to precipitate hypothyroidism. Many patients have reported sudden weight gains after severe emotional shocks or other traumatic events in their lives. I'm convinced that age itself is a factor, though this is a gradual process that takes place over years. Some studies suggest that weight gain accompanying the aging process results from diminished physical activity, but I suspect that there is also a decrease in thyroid function to explain the phenomenon.
Certainly medications play a part. If pregnancy isn't the chief trigger for thyroid-based obesity, then steroids certainly are. By steroids, I'm not referring to the anabolic substances that some weight lifters and athletes are known to use. There are other steroids. They are the cortisone-like substances that are so widely used (probably too widely used) in medicine. These drugs are usually varieties of prednisone or prednisolone and are very useful in treating a host of conditions. Often they are life-saving. Many asthmatics are repeatedly prescribed steroids. Even orthopedic problems are treated with steroids, often by injection into the joints. Of course, this is but another method of introducing them into the body, and although their action is concentrated in the specific injection areas, they eventually enter the general blood circulation.
Because the effect of steroid use is so dramatic, there is a tendency to overuse them when a lesser medication might accomplish the intended purpose. Steroids are drugs that simulate the hormones secreted by the adrenal glands, and their use over time inhibits the normal function of the adrenals. This is a case where the cure can be worse than the disease. At any rate, it is a most common occurrence for me to discover in my hypothyroid patient a history of having taken steroid drugs, often over an extended period of time.
A patient by the name of Jesus provided an interesting variation on the usual case of steroid misuse. He was Hispanic and had been in this country only a few months. His English was probably better than my Spanish, and we did seem to communicate. He should have been losing more weight than he was. He claimed to be doing all the right things. He swore that he stuck to the diet. He was about fifty pounds away from where he should have been and he was losing only three to four pounds a month. There was no question in my mind that he had a very low metabolic rate, and he was already taking a potent dose of thyroid medication to correct it. The dosage seemed right, and he had no signs of overdosage or any other ill effects.
He just wasn't losing. That happens sometimes. There was always the possibility that he wasn't truthful about following the diet or that I didn't understand him fully, but for the most part I rejected those possibilities.
Jesus had a rash on both of his forearms when I first saw him and he told me that he used some sort of cosmetic cream on it to keep his arms from becoming too dry. He was seeing a dermatologist, but he wasn't getting much relief. It looked like psoriasis to me, but I'm not a dermatologist. On his first visit, I had questioned him about any medication he was taking and he said he was taking nothing. As I do with all patients, I had cautioned him that if he were to be prescribed any kind of medication by another doctor, it was imperative that I know about it. I often prescribe appetite suppressants for my patients, and I have to be sure that combinations of medications are compatible.
On one visit, I asked, "How are the arms doing?"
He shook his head. With a grim expression he replied, _"Nada me ayuda,"_ which I interpreted to mean "Nothing helps."
(I'm translating.)
"Nothing? What are you doing for it now?" I asked.
"I'm taking these pills he gave me. At first I thought they helped, but I don't think they are working."
"What pills?"
"Those little ones. I have the bottle here."
The medication was methylprednisolone. This is a very widely prescribed steroid prescription with a cortisone-like action. It, like the steroids mentioned earlier, is used for a variety of ailments, everything from joint problems to asthma to allergies. It is frequently prescribed for a six-day period, during which the patient takes six tablets the first day and tapers down daily to one tablet on the sixth day. That's how it had been prescribed for Jesus months ago. The only problem was that Jesus, in order to play it safe, had decided to have the prescription refilled a number of times. He just took one tablet a day after that. I knew that the methylprednisolone was the problem. This wasn't the first time I had seen it interfere with weight loss.
I called for help from one of my bilingual assistants. I admonished Jesus for not keeping me informed of his actions, and he promised to be a good boy in the future. He stopped the methylprednisolone immediately. I explained to him that he should never have continued to take that medication beyond the original prescription period, that it could have other dire side effects beyond the weight problem.
Here is an example of the delicate balance that is maintained by the endocrine glands. The medicine that the other doctor had prescribed and which Jesus unwisely continued to take obviously had an effect on the thyroid. I've seen that same effect with other patients. I've also seen these steroids precipitate weight gain.
Further proof of the negative effect of steroids on weight loss came when Jesus stopped that medication. He began losing at a reasonable rate. The rash would come and go, but he refused to take any more steroids. Eventually he reached his goal.
Another hormone may play a part. Though not as dramatic, it may be that the female hormones that are so commonly prescribed for menopause have a similar effect in lowering metabolism. I'm certain that there is a general relationship between the use of these hormones and weight gain, but I'm undecided as to whether the weight gain is due to hypothyroidism. Perhaps after a few thousand more patients I will have a better idea. Incidentally, birth-control pills are related medications, and the same may hold true for them.
Obesity may not be the most dramatic symptom of hypothyroidism, but it is the one that _this doctor_ sees most frequently. I have indicated that I believe about one-fourth of my patients have some degree of hypothyroidism. How does hypothyroidism result in obesity? By lowering your need for calories. If a normal individual needs a certain number of calories per day to maintain weight, then a hypothyroid one of the same stature, age, activity level, etc., needs fewer calories. When one's need for calories is diminished but one's intake of calories isn't proportionately decreased, the result is too many calories and, thus, added stored fat. My patients have all come to me with weight to lose, and quite possibly you're reading this book because of your weight problem. I believe that if you're overweight, there is a one-out-of-four chance that you have some degree of hypothyroidism. As you read on you will learn how to test yourself.
In the process of testing yourself, you may learn that there is no reason for suspicion of hypothyroidism. The test relies upon your body's response to a certain fixed amount of calories. If you respond as a normal person would, we can erase that suspicion and you can get on with the process of losing weight, knowing that it will be no more difficult for you than for any other normal individual.
If the testing indicates that you're somewhat of a borderline case, decisions will have to be made, and those decisions will at least have to be shared with your doctor. Of course he will have to be a cooperative doctor, one who will listen to what you have to say. If the testing leaves little doubt that you have hypothyroidism, then the decision you will have to make is of a different type. You will be faced with getting the right kind of medical help to aid you in losing weight and in reversing some of those annoying symptoms.
Let's not place the cart before the horse. Let's first see how you compare with those who have some of the more common symptoms of hypothyroidism.
# Summing Up
* Many overweight people do not overeat.
* Hypothyroidism may be triggered by a variety of factors such as age, pregnancy, or medications.
#
# _Depression: The Thyroid Connection_
**I** rarely see a patient who has more than a few symptoms of hypothyroidism. I necessarily ignore the patient's weight as an indicator of hypothyroidism, since every one of my patients when first seen is overweight to some degree. Aside from a general "hypothyroid" look, which I've learned to recognize over the years, it is the first few sentences exchanged with a patient that can alert me to the possibility of hypothyroidism.
I will try to describe what I see and feel with this particular type of patient, but the task is difficult and my description may fall short of its mark. For one thing, I expect each of my new patients to be highly motivated at the time of the first visit. After all, my new patient has gone to the trouble of making that appointment and remembering to keep it a week or two later. That morning she groomed herself so as to make the best impression, and she's arrived on time with great expectations that she will once and for all conquer her weight problem. Reconsidering, perhaps she didn't arrive on time. I suspect, but I really haven't kept count, that the hypothyroid patient is more apt to be late than the ordinary patient. That's a sign you won't find in any textbook. Frankly, I hadn't given much thought to that until I began writing this paragraph.
Perhaps I should comment on why I think punctuality could be significant. Most patients are very excited about starting a weight-loss program. They are enthusiastic. They ask a lot of questions. They want to _get_ it right. They optimistically expect that their lives are about to change. This is the kind of patient you expect to arrive early. Perhaps the best explanation of what I see in the hypothyroid patient is a lack of caring or at least an inability to focus on a task. Being late could be a symptom of that, but I shouldn't read too much into it. After all, the whole thing could also be explained by a traffic jam that morning.
From the onset of our meeting, the patient's lack of focus influences our relationship. Other patients may launch into a diatribe, describing how obesity has interfered with their goals, their discourse often accompanied by expressive body and hand movements. They want to get their message across. They try hard to get me to feel their pain.
Not so with the hypothyroid patient. She is simply there. She states the obvious: that she wants to lose weight. But her declarations lack emotion. It is as though she is lackadaisically reading from a script.
In the course of my patient sessions, I have a number of little "canned speeches" I make. It isn't that I have rehearsed them or that I say the identical words each time, but when you repeat a concept several times each day for years, it does tend to become rather automatic. I generally explain to the patient that weight loss isn't easy. It takes motivation and a systematic adherence to instructions. While I'm reciting this wisdom, the patient will usually make good eye contact and continually nod to show that she is digesting each word. But not the hypothyroid patient. I'm not sure that she is even listening. When I finish a thought, to assure that my message was received I may ask, "Do you understand?" and I will generally get an apathetic nod. In fact apathy might be the best word to describe the aura that surrounds this patient.
The hypothyroid patient's lack of caring sometimes makes me wonder why she is there in the first place. I've concluded that in a very broad sense she does care, but she has trouble sustaining that feeling and expressing the appropriate emotions that should accompany it. She may even have cared more the day she made the appointment and has now forgotten how much she really cared. Forgetfulness seems to be the rule. She generally asks few questions, and when she does, they aren't important questions or useful ones. For example, rather than ask for more specific details on the dietary advice I have given her, my hypothyroid patient may ask, "When do you want me to come back?" or "Can I eat squash?" or other non sequiturs.
A variation on the above is the patient who appears angry or at least annoyed, not with anything specific, but perhaps with life in general. There is a certain degree of good fellowship that usually goes along with a visit to my office. With this patient, it may be absent. My patients aren't acutely "sick." As medical offices go, the atmosphere is rather positive. No one is there to find out if they are afflicted with a life-threatening illness. It is probably as happy an environment as can be expected in a doctor's office, save for perhaps that of an obstetrician. In spite of this, the hypothyroid patient doesn't seem pleased to be there. I wonder if the patient is there reluctantly. Did someone force her to come?
If you think I have chosen extreme examples to make my point, I haven't. Though this emotional affect isn't pronounced in all hypothyroid patients, in some it is even more extreme. It may even have the earmarks of hostility. This is perhaps the depressed patient, who is so well documented in the literature. The mood is also quite changeable; it may sometimes change within the course of one visit. On other visits, there may have been such a difference in personality that I felt like checking the name on the chart to make sure I was seeing the same patient. This could very well be the type of bipolar ailment that is known to be associated with hypothyroidism.
On this latter point, it should be noted that the medication lithium, which is frequently prescribed to treat depressive states and bipolar disease, has been implicated in precipitating hypothyroidism. I've seen a number of patients who had previously been on lithium and who have hypothyroidism. The possibility that there could be a connection is real.
I'm reminded of Mary. My first visit with Mary was pretty much along the lines of the one with the apathetic patient I've just described. She wasn't that much overweight, only about thirty pounds. That's not much in my practice. From the first I didn't have the feeling that we were really communicating. She seemed to be in a fog. A direct question would get a response, but at times it seemed as though she was responding to some other question, one I hadn't asked.
From Mary's routine history form, one that asks a multitude of questions about hereditary factors, past illnesses, habits, medications, etc., I noted that she was taking a mixture of drugs, the ones that are popularly used to treat depression and other psychological problems. In fact, Mary was taking more different mood-altering drugs than I had ever encountered in one patient. She had been seeing a variety of mental-health therapists for years. She described repeated "spells" of depression, during which she "believed" that she ate excessively. She was so vague in her answers I couldn't even be sure of exactly what medications she was taking or who had prescribed each of them. Her current therapist was apparently a nurse practitioner, whom I decided to contact, but I was frustrated in the attempt by Mary's refusal to give me her consent to do so.
I decided to proceed cautiously in treating her. That seemed to be the best course of action, given the whole scenario. For one thing, she was functioning. She did call and make an appointment. She did make it to the office. She did express her purpose in being there, and I thought there was a pretty fair chance that she could follow instructions.
From the first, I suspected hypothyroidism. Not that it was the total cause of Mary's long-standing problem, but perhaps it was a component. During my questioning, she certainly reported many of the signs and symptoms: dry skin, menstrual problems, very thin and dry hair, and she mentioned that she was always cold. When asked if anyone had ever suspected thyroid problems, she answered yes, but everything had turned out to be okay. She couldn't really tell me who tested her or how they did it.
After the examinations, I prescribed an 800-calorie diet for Mary and gave her detailed instructions on implementing it. She wasn't the most attentive listener, but I must say I've seen worse. The first four weeks of treatment of our patients isn't just treatment, it is actually a test of metabolism, and the weight loss achieved during this four-week period is used in calculating the metabolic state. When I saw Mary four weeks later, she had lost only two pounds. I knew from experience that a loss of two pounds meant that she hadn't exactly been faithful to the diet. On an 800-calorie diet, even those with the lowest possible thyroid function lose more than two pounds.
I went through a torturous questioning session that centered around other signs and symptoms of hypothyroidism. Mary had the earmarks, and in fact she was the textbook picture of hypothyroidism. I decided to go out on a limb. I prescribed the smallest dose of thyroid hormone, not so much in expectation of miraculous results, but more as a test of whether it might have any effect at all.
In the first few subsequent visits, I didn't see any improvement. Nor was there any adverse effect. The pulse and blood pressure are pretty fair indicators of negative effects, and both of these were still below what is considered normal. I had gradually been increasing the thyroid dosage during that time. Eventually there was a breakthrough, some weight loss—not much, but it was a hopeful sign. Then on a subsequent visit there was a substantial breakthrough, real weight loss. Accompanying it was an equally impressive change in mood. Over a period of weeks Mary evolved into an entirely different person. She came out of her stupor and gave every appearance of being a normal human being. During that time, on her own, she had stopped taking much of the medication others had prescribed for her.
Eventually, Mary reached her goal weight and was put on our maintenance plan, which is essentially exercise. The last time I saw her, she said that she didn't have those "spells" anymore, although she did get depressed on occasion. She was continuing with her therapist. I finally spoke to the nurse therapist (with Mary's permission). She was well aware of the changes in her patient. She hadn't realized that the thyroid treatment was in progress. I told her it was imperative that Mary continue taking thyroid hormone. The nurse said she would communicate this to the physician who had prescribed Mary's other medication.
What was accomplished? For one thing, Mary lost her thirty pounds and now feels good about herself, and I'm sure that affects her mood. You don't have to be a psychiatrist to see her psychological improvement. Clearly she has hypothyroidism, and it was exacerbating her psychological problems. She isn't cured, but she is more content, she is responsive, she is definitely functioning better. At least her hypothyroidism is under control.
Mary may be unique, but it is in the sense that every patient is in some way unique. She is representative of the psychological problems that arise from or are intensified by hypothyroidism. I can't tell you how many patients whom I've seen over the years have successfully dealt with their depression through thyroid replacement. I have no way of quantifying my results. I have a gut feeling that many cases of depression that are being treated with the ubiquitous mood-altering drugs are really the result of insufficient thyroid hormone. Even though other drugs may actually combat depression and without a doubt reverse some of the symptoms, their effectiveness may actually be a negative when you consider that they may inhibit patients from attempting to discover the real cause of their problems.
If depression is rampant in our society, so is fatigue. _Fatigue, tiredness, weariness_ are words my patients bandy about. They use them to describe the pressures of daily life. That kind of fatigue may show in their faces but not in their step. What they are really complaining of is being overwhelmed, but not actually of fatigue.
Real fatigue is far more dramatic. I can almost differentiate it by watching a patient's gait as she walks into my office. This kind of fatigue is generally present from the moment the patient awakens. Though it may sometimes be delayed a bit, it will generally show up before she is too far into her day. In the last few years, we've been told that there is a new disease that causes fatigue, chronic fatigue syndrome. If it isn't new (it may have been around since prehistoric times), it is now recognized. It has recently been given a name, which makes it easier to talk about.
If you read the medical textbooks on the subject, you will learn that the ailment defies all attempts to find some objective evidence for its existence. The laboratory tests are always normal, or are at least not helpful. If, for example, the hemoglobin concentration is low, then it isn't chronic fatigue syndrome (CFS); it is anemia. If the blood glucose is low, it isn't CFS; it is hypoglycemia. If you run out of tests to perform, it is CFS. What defines CFS is that if the doctor can find no other reason for the fatigue, then it is CFS.
I'm reminded of an exchange that takes place from time to time in my offices. Typically, a patient may tell me that for years she has suffered from a particular complaint and no one knew what was wrong until some very wise doctor recognized it immediately and told her exactly what it was. As an example, let's say the patient has been suffering for years from dizziness. A steady stream of doctors could not find the cause, until finally one guru announced that she had vertigo. Of course, vertigo is simply the medical term for dizziness. Our expert did nothing to help eradicate the symptom, but as long as he named it she thought he was a genius. I have had other patients in whom ringing in the ears was finally diagnosed as tinnitus, whose headaches turned out to be cephalgia, and whose stomach rumbling was eventually discovered to be borborygmus. (Look that one up.) Apparently it isn't very important that you cure an ailment, just as long as you give it an impressive name.
I suspect that many cases of chronic fatigue syndrome are really unrecognized hypothyroidism, unrecognized because the laboratory didn't find it. I have had patients who had been diagnosed with CFS, but the ailment abated after proper thyroid treatment. Is all CFS really hypothyroidism? Undoubtedly not. There may be dozens of other causes. I think we should rename CFS. A more honest name would be "undiagnosed fatigue."
It is estimated that as many as one in ten patients who walk into a doctor's office suffer from depression. Many attempts have been made to define depression and for the most part they are inadequate—the definitions don't encompass each individual case. In essence, depression is vague; it defies definition. Most doctors will admit that there is no hard-and-fast rule for identifying it. Many will admit that diagnosing depression boils down to this: "I don't really know what it is, but I know it when I see it."
It seems that a lot of doctors have seen it and profess to know it. That would account for the enormous number of prescriptions written for such drugs as Prozac,TM Zoloft,TM and Paxil.TM During the taking of the patient's history, a routine question asks what medications the patient is currently taking. It is almost a surprise when the patient replies that she is taking nothing. In female patients (the ones I see most) beyond their teens, possibly half have at some time or another been prescribed mood-altering medications. When asked if the medications had benefited them, a fair number reply in the affirmative, and probably as many others say no.
Though the doctor has prescribed the medication to treat what he sees as depression, the patient sees it as the antidote for stress. Stress is the buzzword generally used to justify why the medication was prescribed. The words _stress, anxiety,_ and _depression_ are bandied about with little thought as to what they really mean. My patient may be under stress because she couldn't find the right dress for the party this Saturday night, because she didn't get the raise she expected, or because her marriage of twenty-eight years just came to an end. They are all lumped together as the causes of stress. They all result in anxiety. The qualitative and quantitative differences among the causes of stress are ignored. The patient sees the solution to all of these problems as finding the right pill. With the right pill, the dress she wasn't crazy about now becomes acceptable and the husband who had become such a habit no longer seems that indispensable. I have the impression that the physicians' prescribing of these medications is close to a knee-jerk response. The patient utters the word _stress_ and the doctor reaches for the prescription pad.
I believe that in many cases there is a relationship between the apathy of persons such as Mary and full-blown depression, in which the individual virtually cannot function. They may both reflect an underlying problem with an underactive thyroid gland. If you will remember that thyroid insufficiency is consistently inconsistent, you will appreciate that a wide variety of moods and psychological problems may properly belong under the same banner. They are either caused by hypothyroidism or they are enhanced by it. I wonder what would happen to the sales of antidepressants if more cases of hypothyroidism were diagnosed and properly treated.
When I prescribe thyroid hormone to my patient because I have determined that her weight loss isn't consistent with her caloric intake, I now have my expectations alerted to more than a weight change. On follow-up visits, I'm more interested in what she has to tell me about how she feels than whether or not she has lost weight. I already know she will lose weight. It is her description of her mood, as well as what I observe of her manner, that tells me that we're on the right track. The weight loss is assumed and is generally there. The bonus is the conversion from apathy to alertness, from a depressed invalid to a functioning human being.
There are those who would argue that the prescribing of mood-altering drugs corrects chemical imbalances in the brain. Likewise, I would argue that when indicated, thyroid hormone corrects the imbalance created by an inadequate amount of thyroid hormone production. Thyroid hormone has a much broader range of activity. Whether its mechanism of action changes the chemistry of the brain is yet to be discovered. It is well known that thyroid hormone treatment is a useful adjunct to other forms of treatment of depression. In my own practice, I've seen it successfully replace other drugs with even more positive results.
In the recent book _The Thyroid Solution_ by a well-known endocrinologist, Dr. Ridha Arem, the doctor focuses on how frequently hypothyroidism is ignored as a cause of depression. He takes his colleagues to task for missing the diagnosis. He recognizes many of the reasons for this, some of which I've already alluded to. The laboratory results are given more importance than what the patient has to say. Medical schools have devoted little training to such subjects, and in general doctors are more attuned to recognizing mood problems as psychological rather than hormonal. Dr. Arem makes a strong case for a more vigilant examination for thyroid problems. He and I aren't in agreement when it comes to the value of laboratory testing, and I must stand my ground when it comes to the choice of medications to be used for treatment of hypothyroidism. But Dr. Arem has seen the same shameful disregard of hypothyroidism, and his book could open a lot of eyes.
If doctors would immediately consider the possibility of hypothyroidism when faced with the "depressed" patient, I believe we would see much less reliance on mood-changing drugs and a greater improvement in a broader range of patients' symptoms.
I believe that if more cases of hypothyroidism were recognized and then treated, the incidence of patients under treatment for depression would be greatly reduced. The use of mood-altering medications would consequently decrease, and the only ones who would be unhappy over the change would be the drug companies. As long as we continue to mask one of the frequent symptoms of hypothyroidism with their happy pills, we reduce our chances of diagnosing it.
# Summing Up
* Those with hypothyroidism are often listless and apathetic.
* The prescribing of thyroid hormone can often drastically change the personality of those with hypothyroidism.
* Some patients may be assumed to have depression or chronic fatigue syndrome when the problem is actually hypothyroidism.
* Better recognition of hypothyroidism could greatly reduce the reliance on antidepressants in treating depression.
#
# _Hypothyroidism Woes_
**T** hough the thrust of my medical practice is weight loss with perhaps emphasis on those for whom weight loss is problematic because of a thyroid disorder, I cannot ignore the various other aspects of my patients' well-being. I've previously pointed out that those whom I later conclude have hypothyroidism present a wide variety of other symptoms and complaints. I shall discuss briefly some of the more common and troublesome of them.
# Infertility
Pregnancy is one of those things that generally brings a weight-loss program to a screeching halt. My practice certainly has its share of pregnancies. Each month my offices can count on a few phone calls from patients who are in the process of losing weight but are now reporting that they are pregnant. They are either congratulated or consoled, as the case may be, but they are always advised to cease our program and to immediately see an obstetrician, who should, for the next few months, be in total charge of what weight-loss regime, if any, is advised.
The subject of pregnancy generally comes up with new patients. I bring it up. I want to be sure our new patient isn't pregnant at that moment. The history I take reviews a patient's past history in terms of how many pregnancies and how many live births she's had, and whether there was anything out of the ordinary with any of them. As you might expect, a certain percentage of these ladies, even though married for a few years, have had no pregnancies. I always inquire as to the reason. Was it voluntary? In a number of cases, I'm told that it was not; in essence, the patient informs me that she is sterile. This leads to a discussion of how she's pursued the problem, and it isn't unusual for the patient to relate the myriad of doctors and tests and even oddball methods that she's been involved in. Generally all this was to no avail.
I usually ask if the investigating doctors considered a thyroid problem. I can generally anticipate the answer. Frequently the reply is that it was suspected (and sometimes, shamefully, not suspected), but that she was tested thoroughly for thyroid problems and when none was found, the doctor went off in other directions. At this point, I don't pursue that train of questioning, mainly because I don't as yet have much of a feel for my new patient's thyroid status. If there are some obvious visible signs of hypothyroidism, I may expound a bit on my opinions of thyroid testing.
Four weeks later, when it is time to evaluate a patient's weight loss as an indicator of the state of her metabolism, I may conclude that this is indeed someone who could benefit from thyroid hormone replacement treatment. It becomes very important that I remember to tell her that although our chief interest is weight loss, she should recognize the possibility that she may become vulnerable to pregnancy once her thyroid problem is under treatment. Patients such as this generally don't use any birth-control methods, either because they would consider a surprise pregnancy a gift from above or because they are so certain pregnancy is impossible that there is no reason to try to prevent it.
Why am I so careful to issue my warning? I haven't always followed that course. In fact, in the early days it didn't really occur to me that there was any reason to warn my patients about pregnancy following thyroid treatment. One surprise after another has made me more cautious. I have had a number of "sterile" patients call me, usually within a month or two of starting on thyroid hormone, to inform me that they were pregnant. Many were delighted. Some were not. Even though some had gone through extensive efforts and expense to get pregnant in the past, they had resigned themselves to the fact it would never occur and had readjusted their goals in life. Pregnancy was no longer part of the plan. Getting pregnant now was a nuisance; in some cases it was viewed as a tragedy. I think some of these people were a little peeved at me. Fortunately, I've never been asked for child support as a consequence of some sort of twisted logic.
Of course now I always warn. And the pregnancies still occur and are generally wanted, but still sometimes they are not. I guess there are those who don't heed warnings. A few years back, Ali was one of the patients I warned.
Ali was a sophisticated European lady of forty-two with a charming accent and matching mannerisms. She was from eastern Europe, where I believe they don't suppress their inner feelings as the British or even Americans are wont to do. A visit with Ali was always a delight.
She had been a patient several years before. She had gotten to a perfect weight and was delighted. There was no effort to restrain herself after that or to follow my advice on how to maintain her figure, and so she returned to my office to start all over again. Ali had no children, had never been pregnant, and had spent a fortune on fertility treatments. For some reason, adoption didn't appeal to her (or perhaps to her husband). This time it appeared that she had developed hypothyroidism. It may actually have been present before, but I was now more accomplished at detecting it. She was put on thyroid replacement with the standard warning: "You might get pregnant." I believe she muttered something like "From your mouth to God's ears."
About six weeks later, Ali announced with considerable fanfare and emotion that her home-pregnancy test pronounced that she was pregnant. I had never seen such elation on my premises. She thanked me up and down and in every other direction. She said she was going to name the child after me. (I felt sorry for any little girl going through life as Sanford.) I advised her that she must see an obstetrician immediately and that she must inform him that she was taking thyroid medication and tell him the dose. I told her that I felt it was necessary for her to continue the medication through her entire pregnancy and undoubtedly afterward. I told her that miscarriages were very common in hypothyroid individuals. I asked her to have her OB call me.
Since Ali was no longer under my care, I lost track of her. She returned about a year later. I realized that she had never informed me of a birth, and I was quite sure she would have let me know. I cautiously asked. She said that two months into the pregnancy, she had had a miscarriage. After that she had been quite depressed. She had gained a lot of weight. Now she was ready to take it off. Her radiant spirit seemed somewhat dulled.
In taking my new history, I asked Ali what her current dosage of thyroid was. She calmly told me that she wasn't taking thyroid. The obstetrician had tested her and taken her off what I had prescribed. She gave no hint that she suspected that stopping the thyroid was a cause of the miscarriage. I certainly suspected it, but I wasn't about to kindle any unpleasant thoughts in her mind. I really think she knew, and I think she knew what I was thinking, but nothing more was said of it. I debated whether to put this incident into this book. I don't think she will mind.
I have other patients who became pregnant while taking thyroid medication under my care. Several have had successfully completed pregnancies, and I believe they had continued taking their thyroid medication.
To sum up, from my experience I believe that hypothyroidism is a frequent cause of infertility. It is often ignored because of reliance on the laboratory to find it. Miscarriage is also the result of insufficient thyroid hormone, and many pregnancies would result in live births if the mother were treated properly.
Not too many obstetricians would disagree with my assessment of the importance of proper thyroid function as a requirement for fertilization and sustaining the pregnancy. Where we obviously differ is in how to diagnose "proper thyroid function" and somewhat in how to treat it.
Of course, infertility in general isn't simply a female problem. A significant number of failed attempts at pregnancy can be blamed on the male, often insufficient production of sperm or other abnormalities of the sperm produced. It would not have been surprising to me if hypothyroidism in the male had been found to result in less or defective sperm production. Yet here again, the thyroid surprises. Studies have shown that hypothyroidism doesn't seem to affect sperm production. Therefore, infertility related to the thyroid gland seems to be strictly a female problem.
# Menstrual Problems
Even more frequent than infertility in hypothyroid patients are menstrual problems. If you recall, I have told you that the inconsistency of the symptoms of hypothyroidism is the only consistent characteristic of the ailment. You would expect menstrual abnormalities to accompany any affliction that resulted in infertility, and you would be correct. The menstrual abnormalities that accompany hypothyroidism run the whole gamut of such problems.
While one hypothyroid patient will complain of the complete absence of periods for long stretches, perhaps years, another will report two or three periods per month, and not with any regularity. The complaint may be of a very heavy flow, or it could just as frequently be of a scant flow. In many cases that time of month becomes a major traumatic event because of the discomfort. Far beyond what is described for premenstrual syndrome, the patient could become completely nonfunctional. She misses work, cannot concentrate, and is impossible to live with.
Some women seem more willing to accept what they regard as a curse than are others. Some relentlessly pursue one effort after another to get to the bottom of their trouble. I think this is more apt to occur when pain is the major component. That isn't surprising. Some of my patients have had every test imaginable. X rays and MRIs are commonplace. Virtually everyone in this intense category has had all the thyroid tests. A number have had D & Cs, a sort of last-ditch effort on the part of the gynecologist. I even recall that some patients have gone through exploratory abdominal surgery to find the cause of their painful periods, but with no positive finding or result.
Do you encounter the phrase "I know it when I see it" as frequently as I do? It seems as though it's being used more and more. It expresses one's frustration with not being able to define clearly something that should not be very difficult to define. For example, the head of Personnel might say, "I don't know how to describe the characteristics of a good employee, but I know it when I see it." That's the way I feel about many patients with hypothyroidism. My description of them feels inadequate, yet I know it when I see it.
I should explain that I don't _always_ know it when I see it. Often I'm fooled. That's one of the characteristics of hypothyroidism, and that's consistent with its inconsistency. Still, if I had to guess, I would say that in five minutes with a patient I could guess right about 60 to 70 percent of the time. If I were to make a guess in those five minutes and my answer were to be yes, it would be much more reliable than a "no" answer. That's another way of saying that in a number of cases the manifestations of the problem are very atypical. I'm fooled a lot when the patient doesn't display any outward signs. The one defining characteristic, the slow burning of calories, is the one that isn't obvious in those five minutes.
I guessed no for Monise. I would have expected her chart to say, under Occupation, movie star or model, or perhaps former model. Instead it said medical assistant. Yet, she was overweight, though only by thirty-five pounds for her five-foot-five-inch height. Don't be troubled by my use of _only._ I do that a lot. That's how I see 5'5" and 162.
Monise was full of life, as bouncy as they come. No hypothyroidism here, I thought. I was wrong. She seemed to have it all except for two things. One was her weight; the other I was to learn later. The first month her weight loss was a dismal three pounds. Monise swore she had deviated only once from that 800-calorie diet during the whole month, and that deviation was a single slice of pizza. Her three-pound weight loss told the story. It was inadequate. Later, I will show you how I knew she had a thyroid problem from that little bit of information. That is an important element in the _test_ you will be doing on yourself.
I had generally somewhat ignored the part of her history where Monise noted that she had painful periods. After all, I'm not a gynecologist and she didn't come to me for that. I didn't completely ignore it, but I must have reasoned that it had other causes. This lady's manner and appearance were very uncharacteristic of the more typical hypothyroid patient. When I saw her at that first four-week visit and encountered the three-pound loss, I became more interested in her periods. She told me that the whole experience was frightful. She had such pain that she was obliged to miss work at least two days a month. The doctor she worked for, a gynecologist, said that this happens in some women, and he had put her on birth-control pills. It helped only a little, but that was when the weight gain started. She blamed the pills for the weight problem and that is why she stopped them on her own. She obviously chose the pain over gaining weight. She elaborated on one additional point of interest: She was always cold.
It was clear enough that for this lady, three pounds in four weeks spelled hypothyroidism. Her menstrual problems and feeling cold were confirming evidence. I prescribed thyroid hormone. Four weeks later, there was an eight-pound weight loss; that was adequate. She was ecstatic, as I expected, but not about that. She reported that she had had her first pain-free period in years. No pain. To her it was a miracle. I had previously told her that there was the possibility that the prescription might help her periods, but I don't think she took it seriously. The rest of the story was uneventful. She got down to her goal weight, 127. Her periods were no longer a problem, and my guess is that she has maintained her weight. I know that her gynecologist continued to prescribe the thyroid hormone I had started her on.
There was a lesson in this for me. It reinforced what I had known for a long time. There is a delicate balance when it comes to trusting your own intuition in these matters. More specifically, go along with that gut feeling when you think the patient is hypothyroid, and don't trust it when you don't think so. You might very well be surprised. Yet, looking at the broader picture, I don't really need to rely completely on my intuition; the test I developed does a lot of the work for me. Still, it's a nice feeling when you guess right and really help someone.
When it comes to reversing the symptoms with proper treatment, there is a high degree of success when the cause is hypothyroidism. It is almost routine for a patient to tell me how improved that last period was. She will volunteer this information even though she didn't feel inclined to complain about the problem previously. I've seen every one of the manifestations of these previous paragraphs reversed by the prescribing of thyroid hormone. Particularly gratifying is that the patient doesn't have to wait very long to see the result. In some cases, the reports of improvement are actually seen during the first month.
Interestingly enough, I've seen patients who have come to me already on thyroid therapy but who still had menstrual complaints. In the course of my treatment, if I found it necessary to increase the dose of thyroid in order to facilitate a more normal rate of weight loss, the patient would often report a concurrent improvement in her menstrual difficulties. Improvement seems to be dose-related. When the patient gets the right amount of thyroid, the problems improve.
# Coldness
Are you always cold? Of course no one is _always_ cold, but do you complain frequently of being cold? Do you get into arguments with family members or fellow workers about turning up the heat or turning off the air conditioning?
If you or someone else meets the above description, it would be a bit premature to declare hypothyroidism immediately, but I'll bet you will be right more often than wrong. The fact is that hypothyroid people are apt to complain of being cold. I've never seen a reasonable explanation in the scientific literature for that symptom, although it is certainly well recognized. If I had to come up with an explanation, I would say that it isn't surprising, since it is like many other body parameters in hypothyroidism. Low rather than high seems to be the rule in hypothyroidism.
Remember, my belief is that the common denominator of hypothyroidism is the inability to burn calories at the "normal" rate. Since the thyroid gland controls the rate at which metabolic processes proceed, it would seem logical that if less fuel were consumed, less heat would be generated. The hypothyroid individual doesn't just feel cold, _he or she is cold._ We've already learned that. The body temperature is often reduced a degree or more in hypothyroidism. That was even the basis of Dr. Broda Barnes's test for hypothyroidism.
This reduction in metabolic processes can be seen in other areas. I expect my hypothyroid patient to have low blood pressure, and more of them do than don't. This is in spite of the fact that an overweight individual generally is more inclined to have an elevated blood pressure. Thus, when an obese patient has a low blood pressure, it is a double surprise. Normal blood pressure would have been unexpected, but low points the finger at the thyroid.
The rate at which the heart beats in the hypothyroid patient is just one more clue, if not a confirming finding. As you may know, a slow pulse often heralds someone in fine physical condition, quite often an athlete. Activities that make our pulses race barely change theirs. My overweight patient is out of shape and has to strain just to do ordinary tasks. A fast pulse would be usual during every activity, with the possible exception of sleep. Yet I'm apt to see just the opposite. Here is someone who outweighs me by a hundred pounds, doesn't do a lick of exercise, and her pulse rate is slower than mine. On the surface, that seems like an injustice, but it isn't. She is still paying the price for her weight, it is just not obvious from the usual vital signs.
The only vital sign that doesn't seem to be reduced in a hypothyroid patient is the respiratory rate. At rest, we're supposed to breathe in the neighborhood of sixteen times a minute. Inevitably, my patient has a rate of twenty or more, and when physically stressed, she will puff at an impressive rate.
I have spoken of the generally relaxed appearance (I restrain myself from calling it a stupor) of the hypothyroid patient. Every motion is slow, not so much deliberate but rather like watching a motion-picture film that is slowed just a little. Muscle movement generates heat. Since our hypothyroid individual moves minimally, less heat is produced. The counterpart is the athlete. A runner must dissipate the heat his effort produces by transferring it to the air that surrounds his body. We have a very efficient cooling system that depends upon the evaporation of our perspiration into the air to keep us at a cozy temperature. Depending upon weather conditions, the runner's body may not be able to rid itself of that heat, and during his run he may have quite an elevated body temperature.
Feeling cold and being cold are just part of the generalized underfunctioning of the hypothyroid individual. When the problem is reversed, generally by addition of thyroid hormone, the body temperature rises, the complaints of coldness become fewer, and all the other processes increase or speed up. Coldness is thus not so much a symptom as a manifestation of the combined effect of a group of other symptoms.
# Fibromyalgia, or "I hurt everywhere"
Fibromyalgia is believed to be almost as prevalent as I believe hypothyroidism to be, and I suspect that it isn't a coincidence. That's a lot of people to suffer from a disease that wasn't even recognized as a disease fifteen years ago. If you search medical textbooks written before that time, you will find nary a word about fibromyalgia.
Pain, stiffness, and muscle fatigue are the earmarks of this widespread problem. Specialists who deal with muscles and bones and joints and nerves have been deluged with such complaints for years, but since, as in the case of chronic fatigue syndrome, with which it is often associated, there was little that the laboratory could do to pin down an ailment, it was very slow to be recognized as a disease. Of course the ailment has probably been around for centuries, but, as with hypothyroidism itself, the signs and symptoms were so many and varied that it overlapped a host of other conditions. In short, we didn't have a name for it. The literature certainly describes similar conditions and calls them such things as fibrositis or myofascial pain syndrome. Years ago, one doctor developed a unique method of treatment that involved injecting anesthetic agents into very small painful areas, which she called trigger points. This technique has gained a reasonable amount of popularity and does seem to provide relief.
The pain is in the fibrous tissues of the body—muscles, tendons, ligaments, fascia—which is another way of saying it can be anywhere. In some it seems to locate in several "favorite" spots, while in others it acts capriciously. One minute pain is here and the next minute it has moved elsewhere.
Eventually the American College of Rheumatology recognized fibromyalgia as a specific disease entity and set forth criteria for diagnosing it. A major element in this diagnosis was the physician's ability to elicit pain by applying pressure to the numerous particular trigger points, specific sites known commonly to be associated with the reported pain of fibromyalgia.
It has been noted that fibromyalgia is found very frequently in those with hypothyroidism. Of course, every time I read a paper or book that makes reference to that fact, I must bear in mind that the author is probably defining hypothyroidism by the most widespread method, and that is the interpretation of laboratory reports. At least one author differentiates between fibromyalgia in those _with_ hypothyroidism and in those _without._ I make the presumption that he, like many others, is referring to hypothyroidism as confirmed by the usual laboratory tests. Since I've rejected that method as the single positive means of labeling a patient as hypothyroid, I'm not sure I'm ready to accept the distinction between those who have or don't have hypothyroidism. I believe that if all fibromyalgia isn't the result of low thyroid function, then at least a much greater percentage of it than is generally accepted does result from an absence of thyroid hormone.
I shall not go into the woes of fibromyalgia beyond saying that it is a hodgepodge of pain that can be anywhere or everywhere, pain that changes location at the drop of a hat and defies all efforts to eradicate it. The literature describes a collection of symptoms that turns out to look a lot like the corresponding list for hypothyroidism: headache, constipation, painful menstrual periods, depression, etc. Fibromyalgia is said to be frequently associated with chronic fatigue syndrome, and this isn't surprising since constant pain would certainly result in fatigue, whether physical or mental. Everyday painkillers can help and antidepressant medication is often used to treat it, but that is hardly a cure. If anything, by lessening the symptoms, physicians thwart any effort to investigate the cause earnestly.
I don't diagnose fibromyalgia in my patients. My prime purpose is to take weight off of them. Many come to me and report that fibromyalgia has been diagnosed by another doctor. Almost without exception, they haven't been treated with thyroid hormone because it was ascertained that they weren't candidates for it. Some of them are eventually put on thyroid by me in response to their demonstrating an inadequate response to the diet they've been following. I've never prescribed thyroid hormone to treat fibromyalgia per se. Yet I've seen many favorable results in terms of these complaints of pain in those in whom it has been diagnosed. Strangely, these particular patients aren't overly demonstrative over the flight of their pain; they simply take it in stride. I think many of them attribute the improvement to the weight loss and not to correcting the thyroid problem. That's all right. I'm certainly not sure what caused the change, but this improvement in aches and pains definitely seems to occur in my hypothyroid patients.
One chiropractor seems to have made a strong case for hypothyroidism as the cause of fibromyalgia. He advocates prescribing T3, one of the thyroid hormones. Another M.D. thyroid specialist reports that he has had very good results with a combination of two hormones, T3 and T4. Later, I will be discussing these medications, as well as one other.
I would like to see someone study the effects of thyroid hormone in patients who show _symptoms_ of fibromyalgia and _symptoms_ of hypothyroidism but who have gotten a thumbs-down from the laboratory on the latter diagnosis. I think there is an opportunity there for some researcher to really make a name for himself.
The connection between hypothyroidism and fibromyalgia and the fact that there is such an overlap of signs and symptoms seems to me beyond coincidence. That effective treatment of the former seems to also have a positive effect on the latter is something we cannot ignore.
# And More
I believe we don't suspect that many other patient complaints are really manifestations of hypothyroidism. We know that anemia, headaches, constipation, impotence, and even brittle fingernails can also be a part of it. Skin and hair problems are also frequent.
The skin of those with hypothyroidism has a certain puffiness to it. It looks like it is loaded with water, and it probably is. Dryness is a regular complaint, yet I've seen cases where the skin was oily. When I see hair that seems lifeless and possibly unmanageable, I take note. That reminds me of Helen.
The first time I saw Helen I was impressed by several things. Her weight alone didn't impress me. I've already seen too many five-foot-four ladies who weigh in the neighborhood of 243 pounds. What first caught my attention was how well groomed she was. It is often difficult for people that heavy to do a satisfactory job of looking nice. For one thing, the right clothes are hard to find. It strikes me as unusual that in a society with so much obesity, a lot of marketers don't take advantage of this. In general, clothes seem to be designed for thin people. Helen was one of the most handsomely groomed new patients I had ever met.
Another thing that was different about her was that she carried an attaché case. At the risk of sounding like a male chauvinist, which I'm not, the plain fact is that most women that come into my office carry a handbag. She didn't, only an attaché case. Soon, that was easily explained. She was an attorney. She presented a very professional image; her grooming, her attaché, her posture, the assurance in her walk, all contributed to the image of someone who is important. By the time I had seen Helen several times, I couldn't help noticing that her hair was particularly well coiffed. It was always perfect and the hairstyles seemed to vary a lot. She also changed hair coloring during those first few months. I guessed that she invested a lot of her earnings in the hairstylist.
She told a less than remarkable life story. She had been on every diet imaginable and had made the rounds of the weight-loss establishments and the diet doctors. A few years back, a doctor had said he thought she needed thyroid hormone, and he prescribed it. She didn't think it helped much with the weight loss and so eventually she didn't renew the prescription. Later, more than one doctor said that there was no thyroid problem.
There was. I prescribed thyroid medication again, but this time natural thyroid rather than the synthetic hormone she had taken years before. She didn't have many other symptoms of hypothyroidism. The fatigue she complained about could just as well have been caused by carting all that weight around. She did complain of falling asleep at the drop of a hat, a circumstance that had more than once proved inconvenient in the courtroom.
Helen needed the thyroid treatment and she was reasonably well motivated. In the months that followed, she lost weight nicely and seemed to be happy with her progress. I complimented her on that progress regularly. Sometimes I would also compliment her on her hairdo, and she accepted that graciously but without any desire to dwell on the subject.
Her thyroid dose had to be adjusted upward in a couple of steps, and we settled on a satisfactory dosage. It was the better part of a year before she told me her deep dark secret: _That wasn't her hair._
I really don't know if the women on my staff knew this; women have a way of discerning such things. I certainly didn't. I was shocked when she told me, but I've learned to maintain my composure when a patient shocks me. That isn't an infrequent event.
"Why didn't you tell me earlier?"
"I don't know. I was embarrassed."
"Is there a problem with your own hair?"
"There sure is. I don't have any. Correction, I didn't have any."
"What do you mean?"
"For years I had a hair problem. It was so thin that there were big bald patches. I couldn't go out in public that way. I have the biggest collection of wigs you've ever seen."
Then it came out. Helen's hair had been growing back. She said it was almost presentable. She would not let me see it. I had to take her word for it. She knew immediately that the thyroid hormone was responsible for the new hair. She was knowledgeable. When I first told her she had hypothyroidism, she read up on it. She had been optimistic that her weight would benefit from the treatment, but it was too much to hope that her hair would as well. To say the least, she was delighted, but in a dignified way. She had a very professional manner about her and she wasn't about to jump up and down.
A few months later, I got to see Helen's real hair. Shortly after I walked into the treatment room, I made one of my usual comments about her nice hairdo. It came out with one of those knowing glances we display when we know we're sharing a secret.
"You're wearing your hair shorter these days."
"You noticed."
"Of course. It looks very nice."
"It is my hair."
"What?"
_"It is my hair._ My real hair."
We shared warm smiles.
I've tried to give you an overview of hypothyroidism and its manifestations. As if we don't have enough already, I've no doubt that between the time I write the last word of this book and the time it reaches the bookshelves a few more signs and symptoms will be added. Hypothyroidism is indeed the Greater Imitator.
I haven't dwelled on any of these other signs and symptoms because my chief interest is how it affects your weight. From here on I will concentrate on that aspect of hypothyroidism.
# Summing Up
* Infertility is often caused by hypothyroidism.
* In the course of treating hypothyroidism, "infertile" women may become pregnant.
* Menstrual problems may be completely reversed in the hypothyroid patient who is treated properly.
* Feeling cold could be a sign of hypothyroidism.
* Multiple aches and pains often diagnosed as fibromyalgia may be eliminated by the use of thyroid hormone.
* A variety of other conditions, such as skin and hair problems, often respond well to thyroid treatment.
#
# _Natural or Synthetic Treatment?_
**I** n an earlier chapter I told you that the cause of hypothyroidism is that the body receives an insufficient supply of thyroid hormones for it to function properly. For our purposes,it isn't fruitful to argue whether the thyroid gland isn't doing its job or whether the problem is on the receiving end, that is to say, whether the various sites where the hormones act respond to the quantity of hormones available. The effect is the same: The body needs more thyroid hormone. It has been shown repeatedly that when the supply of thyroid hormone increases, the signs and symptoms of hypothyroidism are eradicated or at least improved.
The process by which we supply the body with hormones from external sources is popularly referred to as _hormone replacement therapy._ Every female who has entered menopause or who is close to that time has undoubtedly been exposed to the debate regarding whether estrogen replacement therapy is advisable. And it _is_ a debate. Some doctors lean one way, and others in the opposite direction. There isn't too much argument as to whether supplying estrogen and sometimes other female hormones improves the annoying baggage that goes with menopause. It is more a question of whether supplementing the patient's hormone production from the outside is risky. The patient's history as well as her family history often play an important part in the doctor's decision.
When a diabetic injects the hormone _insulin,_ it supplements the patient's own inadequate production of the hormone and allows the patient to function. Indeed, it may be life-saving. That is another type of hormone replacement therapy. The supplementation of a patient's own supply of thyroid hormone from a source outside one's own body is perhaps not quite so dramatic, but tell that to the sufferer of hypothyroidism. The changes that ensue can indeed be remarkable.
Nothing is more exciting to me than medical breakthroughs—medical firsts. I suppose there is a first time for anything. We recognize that the ability to create fire was one of the great milestones in the history of the human race. There must have been a first time when a human being intentionally did what was necessary to produce the spark he captured in some twigs that resulted eventually in a fire of his own making. It's a shame we don't know who he was so his name could have been enshrined in the books. I wonder if he had a name!
There was a first time a human being was supplied with thyroid hormone from an outside source. Before I tell you how and when it came about, I should first tell you why it was done. The recognition signs of hypothyroidism have been noted for perhaps a thousand years. We may not have had a clue as to what caused that excess weight or those abnormal menstrual periods or that overwhelming fatigue, but we knew that these symptoms, along with others, were sometimes present in combination in certain people, and that they did constitute some discrete unknown ailment. For most of the nineteenth century, the condition was referred to as myxoedema (sometimes the "o" is omitted). We still speak of myxedema today, but generally differentiate it from hypothyroidism as a more severe form of the latter. Much of the scientific literature that I've researched from the late 1800s and early 1900s lumps all hypothyroidism together as myxoedema.
In 1891 a doctor by the name of George R. Murray was the first to inject a thyroid substance from an animal (a sheep) into a human patient. The lady suffered from myxoedema with more of the classic signs of the ailment than are generally present, among them lethargy, slow speech, menstrual problems, and sensitivity to cold—in short, the works.
The improvement could not have been more dramatic, and so was born the modern treatment of hypothyroidism. True, we no longer strain the stuff through our handkerchiefs, but the treatment today is essentially what Dr. Murray started. What had been born was thyroid replacement therapy. Murray's success fostered a flurry of activity among doctors, and the following year no less than three doctors, working independently, showed that you could achieve the same effect by giving the thyroid juice by mouth. Since then we've certainly refined the product and its method of manufacture, and there has been some variation in the composition of the hormones used, but surprisingly little.
Preparations containing thyroid hormone slowly became available to the practicing physician. They underwent some name changes. At the turn of the century _iodothyrin_ from sheep was what doctors were using to treat hypothyroidism. Pharmacology books of the era readily admitted that its actual constituents were essentially unknown. By 1915, _Glandulae Thyroideae Siccae, U.S.P._ was an established product. The "U.S.P." stands for United States Pharmacopeia, a prestigious designation that establishes standards for the quality of medications. What eventually emerged in this country was Thyroid U.S.P., a standardized material that was extracted from the thyroid glands of animals we use for food: sheep, cows, and hogs.
Thyroid U.S.P. has been available for many years in tablet form, and it comes in a variety of strengths. This allows the physician a lot of versatility when prescribing thyroid. I began prescribing Thyroid U.S.P. to appropriate patients back in 1957 when I first began my practice. It was always gratifying to see a patient respond to proper treatment, and nothing made more of an impression on me than the response to thyroid treatment in a patient who really needed it.
There are other names for natural thyroid. It is often called desiccated thyroid. (Desiccated means dried.) Very often it is referred to as Armour Thyroid or simply Armour. This comes from its history. For years it was supplied by the Armour meatpacking people. Today it is manufactured by Forest Pharmaceuticals. Unquestionably, Armour is the most well-known name for natural thyroid.
There weren't many choices when it came to treating an underactive thyroid. The thyroid hormone I was prescribing for my patients wasn't much different from what Dr. Murray injected into Mrs. S. I'm sure mine was cleaner and I had a better idea of how much thyroid hormone was in each pill. Of course, he didn't know there was such a thing as thyroid hormone, but his thyroid juice accomplished the same purpose. I liked using natural thyroid on my patients, but I did have another choice.
During my first year in practice, synthetic thyroid hormone became available. There is an ongoing disagreement among our population as to the merits of "natural" as opposed to "synthetic" substances. Everyone from food producers to cosmetics hucksters proudly flaunts the word _natural. Synthetic_ has virtually acquired the synonym _unnatural._ Should we take natural or synthetic vitamins? Do we really like synthetic fabrics? Some do. Ask any sky diver what kind of parachute he prefers. Natural doesn't always win out. There is certainly a common bias when it comes to natural versus synthetic, for example, with fur coats. Yet, overall, natural seems to win the popularity contest.
Synthetic thyroid received more attention than would have been expected. There was a good reason—or at least a reason that explained this, good or bad. As effective as treatment with natural thyroid had been over the years, there was periodic grumbling about it. There were many reports, perhaps justified, that the physician could not rely upon the strength of the tablets. The actual potency didn't always seem to correspond to the strength printed on the label. In most cases, it was believed that the therapeutic effect was less rather than more than what was expected. There were reports that patients might be doing well with a prescription, but with refills they would find that the medication didn't seem to work as well. The doctor might then increase the dosage, perhaps by telling the patient to take an extra pill, and the situation would improve. Perhaps with the next refilling, the new dosage would appear too strong, the patient would have symptoms of being overmedicated, and the dosage would then have to be reduced. I'm reporting what was the prevalent thinking of many medical men. My own experience with natural thyroid was quite different.
An explanation for this mistrust of natural thyroid seemed to make the rounds. The problem was staleness. It was said that thyroid medication would deteriorate in potency as it sat on the pharmacy shelves. If you had your prescription refilled, you wouldn't know whether the product you were getting was fresh and potent or whether some of its potency had been lost. A major selling point of the synthetic preparation was that it was very stable and maintained its potency throughout its shelf life. Each year, its use increased, at the expense of natural thyroid. This confidence in the standardized nature of synthetic thyroid has lasted even to the present day, even though many physicians are unaware that the confidence they have in it should have been seriously shaken by what occurred just a few short years ago.
The "synthetic" thyroid hormone I have been speaking of is actually levothyroxine, or, more properly, levothyroxine sodium, which is commonly designated as T4. One manufacturer of this product dominates the market and receives most of the cash spent on thyroid medication. This is the product that boasted stability, reliable potency, and safety. In 1997, the government exploded the myth with this statement published in the _Federal Register:_
... [N]o currently marketed orally administered levothyroxine sodium product has been shown to demonstrate consistent potency and stability and, thus, no currently marketed orally administered levothyroxine sodium product is generally recognized as safe and effective.
What followed was a flurry of legal activity in which manufacturers of levothyroxine sodium were required to clean up their acts. Since overpayment for the products was an issue, class-action lawsuits were filed against manufacturers, and eventually there was a $41.8 million settlement.
I must say that I had never experienced any variability of thyroid medication with my patients. I was aware that there had been such a complaint against natural thyroid, and since I was seeing a sizable number of hypothyroid patients even after one year in practice, I decided to guard against "drugstore staleness" by obtaining my thyroid medication directly from the manufacturers and dispensing to my patients myself. In that way I knew that what I was dispensing was fresh. I didn't know whether the anecdotes about thyroid pills were true, but I decided to play it safe.
My natural curiosity finally got the best of me. I decided to begin prescribing synthetic thyroid to some of my patients. Everyone else was doing it. It seemed that I was out of step with progress. Those to whom I gave synthetic thyroid actually belonged to two groups. There were patients who clearly had hypothyroidism whom I had been treating for some time. Some of these had been diagnosed by a previous doctor and I was continuing their treatment with the synthetic thyroid he had prescribed. If I had to adjust the dosage up or down, I would do so.
Then there were some patients whom I arbitrarily switched from natural thyroid to synthetic. In making such a change, there is an entirely different dosage to be reckoned with. The manufacturers of the synthetic product publish what they believe to be the comparable dosage, so the job is somewhat easier.
Almost from the first, I suspected that I wasn't giving my patients the comparable dosage. The error was virtually always in one direction: The patient didn't seem to be getting enough of the hormone. That seemed easy to correct. I increased the dosage of the synthetic product. Yet even in doing so, I didn't get the same effect. The patient would voice her dissatisfaction, saying that she was becoming more fatigued, much as she had been before thyroid treatment. Perhaps her periods had become irregular, as before, or they were prolonged, or particularly painful. Some patients were very insistent that I switch them back to natural thyroid. Some were even angry that I had chosen to rock the boat.
There were occasions when I increased the dosage and the patient would then report symptoms that suggested I was giving too high a dose. A well-known sign of overdosage of thyroid hormone is a tremor of the hands. About the only time I have ever seen this was in some of the patients whose dose of synthetic thyroid hormone I was trying to adjust.
Another group to whom I prescribed synthetic thyroid were patients who had previously undiscovered hypothyroidism. Prescribing synthetic thyroid from scratch was much the same experience as it was in the other group. I had become accustomed to what to expect in the way of improvement with thyroid therapy, but it wasn't the same with these patients. Synthetic thyroid didn't seem to work as well as I had come to expect. It wasn't particularly as a result of my own observations that I came to this conclusion, but rather as a result of reports from the patients themselves.
I have never since gone back to prescribing synthetic thyroid from scratch, but I've continued to prescribe it to patients who had received it from other doctors. Over the years, many new patients of mine had been taking synthetic thyroid at the time of their first visit. I'm always reluctant to fix something that isn't broken, so if they have no complaint and seem to be doing well, I leave things as they are. If, however, it appears that they aren't getting sufficient thyroid, I will generally supplement the synthetic thyroid they are taking with my prescription for additional natural thyroid. They are thus taking a mixture of the synthetic and the natural. Often this works out quite well. If I'm still not satisfied, I may discontinue the synthetic and replace it entirely with what I believe to be the equivalent dose of natural thyroid.
I don't mean to suggest that synthetic thyroid doesn't work. It could hardly have achieved such widespread acceptance if it were of no value. But my own experience is that it doesn't work as well overall. If this is a personal bias, it is an honest one. Many of the improvements we see in a patient's condition are quite subjective, on the part of both the doctor and the patient. My hypothyroid patients feel that natural thyroid consistently works better, and I must trust their observations.
The names given to the various thyroid medications can be confusing. The following box may help.
**Thyroid Medications**
Different generic and brand names for the same thyroid medication can be confusing. Here and elsewhere you will find thyroid medication referred to with different names.
**Synthetic Thyroid**
These may all be considered the same:
T4
Levothyroxine
Levothyroxine Sodium
L-thyroxine
Thyroxine
Synthroid
Levothroid
Levoxyl
Eltroxin (Canada)
Tetraiodothyronine
**Synthetic Thyroid**
These may all be considered the same:
T3
Triiodothyronine
Cytomel
Liothyronine
**Naturai Thyroid**
Thesemay all be considered the same:
Thyroid U.S.P
Desiccated Thyroid
Armour Thyroid
Armour
Westhroid
Nature-Throid
I'm reminded of one experience involving natural thyroid. The patient's name was Gladys. It isn't that her case was much different from hundreds I had seen before and since, but I remember her very well. It is strange how you can forget a patient you saw last month, but others stay with you permanently.
Here was someone sincerely wanting to lose weight. She was sixty-five pounds over her acceptable weight. She was a systems analyst, a very responsible job dealing with computers. Her first visit wasn't the typical apathetic request for help in losing weight. She was agitated. She recounted how it just didn't come off. She had been to every diet facility imaginable. Nothing worked.
I'm wary of a patient who presents this type of history. This is the kind of person I'm ready to label as having psychological problems. She sees things very negatively: every treatment is either inadequate, or improper, or too expensive, in short—a rip-off. It may be administered by incompetents, or the facility is too inaccessible. She will always find some deficiency on which to focus. Having such excuses essentially gets the individual off the hook. After all, it isn't her fault she didn't lose weight. It was the fault of those programs she tried.
At first glance, I could have written her off as belonging to that not uncommon group. Not so. There was a difference with Gladys. She had given each of her treatment providers an adequate chance. She didn't stop because of the usual reasons. She stopped because she wasn't losing weight. She stopped treatment in each case when it became apparent that nothing would be accomplished by continuing the program. In fact, it was sometimes the program that gave up on her.
Gladys was quite pretty. She was neat in appearance and she must have given much thought to her wardrobe. You would not suspect that she had sixty-five pounds to lose. I knew from her history that she was single. She didn't talk about her social life or her sex life, as many patients do. I don't bring up the subject. I wait for the patient to do that. She was quite likable. I imagined that she had a social life.
I recall that Gladys had been to several doctors. She had been tested repeatedly. She was told her thyroid was normal. This is akin to saying she just ate too much. She knew she didn't. I don't recall that any of the physicians came right out and accused her of lying, but she felt the inference was there. She came to me on the recommendation of a friend who had been successful at losing weight with me. She was probably not hopeful that anything different would happen under my care. It is just that she wasn't yet ready to throw in the towel.
I sound sympathetic and I truly was. My relating to her that I had little respect for thyroid testing was sort of a shot in the arm. That got her interested. She believed she had a thyroid problem, and she came right out and asked me if I would give her thyroid hormone. She was very knowledgeable when it came to thyroid. She had done some reading. Of course, she also knew that the TSH test was considered the benchmark of thyroid diagnosis, and she had had a lot of normal TSH results in her life. As I recall, one of the previous tests indicated an overactive thyroid, one that is more likely to render the victim thin.
She appeared hopeful that I might treat her for hypothyroidism, and she was visibly disappointed when I told her it wasn't that simple. I had to have better evidence that her thyroid function was low. The first month of treatment was to be the test. She agreed, but her spirits were somewhat dampened by the delay in attacking the problem head-on.
I had the feeling from the beginning that I could rely on what this lady had to tell me. I was impressed with her sincerity coupled with her intelligence. She wasn't the typical apathetic hypothyroid patient. In my own mind, this lessened the odds that we would find hypothyroidism, but I kept an open mind, knowing the inconsistent nature of the illness.
Gladys's weight loss at the four-week visit was a meager two pounds. She recited the same earnest oaths of conforming 100 percent that I've heard so frequently. I believed her. She had eaten 800 calories for twenty-eight straight days and had lost only two pounds. That translated into a maintenance level of calories of 1,050 a day—remarkably low.
She knew the significance of all this and didn't waste any time in asking me, "Will you give me thyroid now?" This time the answer was yes. But I didn't acquiesce before questioning her several more times as to how she might have deviated from the diet. She stuck to her story. She had eaten 800 calories a day for twenty-eight days.
Gladys was started on one-half grain of natural thyroid per day. When she saw the medication that had been prescribed, she called me. She politely was questioning what I had given her. She knew what thyroid hormone looked like. She had seen pictures of the pills in books and had even known others who were taking it. She knew that the various doses of thyroid were of different pastel colors. The tablets I had prescribed were a dull, off-white shade. She wanted an explanation. I gave it to her.
What she was familiar with was synthetic thyroid, the commonly prescribed tablet, also known as levothyroxine or just T4. I told her that I had prescribed for her natural thyroid. She hadn't heard of that. I had to go into an explanation of how I felt that it was a better medication than the synthetic. I'm not sure she bought it. I think she was losing confidence. She agreed to follow through.
I had one more phone call during that next week. She had been doing some homework. She had read in some article that natural thyroid was an old drug that wasn't used much anymore because the synthetic variety was better. This didn't sit well with her. Why was I giving her inferior medicine? I had to explain that in my opinion, what I had prescribed was superior to the other. She of course was relying on the printed word. It is impressive how powerful is the printed word. It didn't matter that I had umpteen years of experience. When someone writes something and it gets published, it becomes truth. I was a little disappointed in Gladys. I thought she was smarter than that.
But the situation changed dramatically on her next four-week visit with me. She had lost five pounds. I wasn't delighted, although I thought we were making progress. She, on the other hand, was overjoyed. She seemed to think that was the most she had ever lost in a like period of time. The task of dealing with her intensity now became much easier. I upped her dosage to one grain a day. There was no evidence of any ill effects from the medication. The only other sign that we were getting somewhere was her report that she no longer seemed to need a sweater at work. Everyone else had been comfortable, but she had always been cold. She hadn't told me about this at the first visit. It certainly could be a significant finding.
It is terribly trite to say that the rest is history, but I will say it anyway. In the months that followed, Gladys's weight loss was consistently over ten pounds per four-week period. She reached her goal weight rather painlessly. She was the talk of her office. Incidentally, I hadn't realized what her potential was. I think she could have qualified as a supermodel. To my knowledge that wasn't her desire. I remember speaking to her family doctor at the time I discharged her. It was an uphill battle getting him to continue the thyroid I had prescribed. I must have been pleading. When he learned I had prescribed natural thyroid, it didn't make the job any easier. I doubt he had ever written a prescription for natural thyroid, but I prudently didn't ask him. He could not deny that the story I had told him was persuasive. He finally agreed, but said he would proceed very cautiously. That was a bigger triumph than getting her straightened out. I wouldn't be surprised if he eventually switched her to synthetic thyroid, but that's all right. Gladys will probably do fine with that.
Gladys wasn't that unusual a case. If anything was different about her case, it was that the problem was solved quite easily. I had determined that she had very low metabolic activity and I was expecting that the dose of thyroid would have to be increased considerably before any real results could be obtained. The first increase in dosage was all that was needed. It strengthened my suspicion that there is somewhat of a threshold dosage that works for each hypothyroid individual. Until you reach that dosage, results are inconclusive. Once you cross the threshold, magic happens. This is my hypothesis; it's unproven, but this seems to be the case.
Another nice thing about treating Gladys was that she was so compliant that it established the validity of the treatment so decisively. Had she been a troublesome patient or lacked motivation, there would have had to be a lot more heart-to-heart discussions. Here was a lady who knew what she wanted and went right to the task of accomplishing it. I wish all my patients were like Gladys.
Why has the pendulum swung so strongly in favor of synthetic thyroid? I truly don't know the answer. I can only guess. I know that marketing must have played a part. I know that in speaking to various doctors over the years, I've been surprised at how many shared my opinion of the superiority of the natural product. What is more puzzling is the fact that in spite of this, they were still more apt to prescribe the synthetic. I suppose there is a tendency to find safety in numbers. I suppose most doctors aren't comfortable with prescribing what the majority of their colleagues are not. Remember, in terms of official recognition, Thyroid U.S.P. is still, as ever, a reputable product. It is simply not prescribed that much.
There is another possible explanation for this apparent paradox. Perhaps it is best explained by quoting from Goodman and Gillman's textbook on pharmacology from 1965. I might point out that this textbook was the standard for pharmacological information at the time. Keep in mind that synthetic thyroid hormone had been available and in wide use for about seven years. Here is the book's assessment of a reason for the prejudice directed at natural thyroid:
Thyroid U.S.P. is a highly satisfactory preparation for clinical use. Its continued popularity doesn't derive merely from a reactionary attitude, although at first sight the preparation might seem to be crude, old-fashioned, and poorly standardized. It is evidently uniformly well absorbed unless it has an enteric coating, and the potency is sufficiently standard that variation cannot be detected clinically if the official preparation is prescribed. A few years ago a large batch of material came into the hands of a number of distributors in the United States and Europe and, although of proper iodine content, it later proved not to be thyroid at all. The episode gave thyroid a bad name because several publications about the unreliability of thyroid were made before the hoax was uncovered. Recent analyses indicate that the triiodothyronine in thyroid contributes significantly to the thyromimetic effect, and this may in part explain the greater effectiveness of the product than anticipated from its content of thyroxine.
Several things are notable about this passage. Notice that it talks about the "greater effectiveness" of this product over synthetic thyroid (thyroxine or T4), which by then was in wide use. That is totally consistent with my own observations. Has something changed since 1965? If natural thyroid worked better during that era, could it be less effective today? Both products are still the same as they were then.
The above quote does point out how rumor and innuendo play such a role in forming our opinions and our biases. Natural thyroid may never have recovered from the adverse publicity. I wonder how many physicians who have graduated from medical school since, let us say, 1965 have ever prescribed natural thyroid or have had any personal experience with it. In fact, I wonder how many are even sure it still exists and is available to them.
In my own practice, natural thyroid, or Thyroid U.S.P. as it is properly called, is the medication I use to treat hypothyroidism. I believe doctors should take a new look at thyroid replacement therapy, consider whether they are getting the optimum results from their patients with their current course of treatment, and, above all, try this long-standing and still approved medication on some of their patients.
I'm going to go into a perhaps more persuasive reason why natural thyroid deserves serious consideration. In the quotation above, Goodman and Gillman suggest that the triiodothyronine in Thyroid U.S.P. significantly contributes to its effectiveness. I've spoken to you of triiodothyronine earlier. For simplicity we call it T3. The other major thyroid hormone found in your own thyroid gland as well as in natural thyroid is T4. Synthetic thyroid contains only T4. Let's be sure you understand the lineup. Natural thyroid contains both T3 and T4, while synthetic contains only T4. The Goodman and Gillman textbook suggests that natural thyroid is superior because of the additional T3. Dr. Siegal concurs, but he isn't the only one.
In the first piece of scientific literature in a long time to substantiate my position, a paper published in the February 1999 _New England Journal of Medicine_ indicated that T4 alone didn't work as well in the treatment of depression caused by hypothyroidism as the mixture of T4 and T3. Although the researchers didn't specifically advocate the use of natural thyroid to supply the two hormones, they did report the benefits of the mixture. They apparently used the two hormones as individual substances in combination. This is but a short step away from using natural thyroid, which normally combines the two.
This paper has great significance. First because it was published in our most prestigious medical journal, a publication known to accept only the highest-quality work. Second, it seems to confirm what many of us have had faith in. You may expect much follow-up and fallout from that article.
Actually the follow-up began within the same issue of the journal. The study was commented on in an editorial, which took the position that the study was promising but conservatively concluded that we should not switch our patients to the combination of two hormones yet. The editorial author seems to have ignored the fact that the "switch" was made years ago. Using one hormone, T4, was a switch away from using the two hormones. Remember that both hormones are present in natural thyroid, which was the acceptable standard for years. More correctly, the editorial writer could have advised, "Let's not go _back_ to two hormones yet." He seems to believe that the ratio of T4 to T3 should be about 10 to 1, but he doesn't explain how he came to this conclusion. In the study he is commenting on, the ratios of T4 to T3 given to subjects varied considerably. Strangely enough, the ratio of T4 to T3 from thyroid hormone derived from cows has been shown to be a little over 9 to 1, very close to what he feels is ideal.
Perhaps an even more important substantiation of the value of natural thyroid comes from what I believe to be the most important of the sources: the patients. I've told you that when my own patients have had the opportunity to compare the effects of natural and synthetic thyroid they overwhelmingly choose the natural. This preference doesn't come from my patients alone. There are a number of Web sites where extensive information about thyroid problems is available. Here, organizations dealing with thyroid problems disseminate information, but there are also a number of sites that are essentially conducted by laypersons. One of the best is apparently the labor of love run totally by Mary Shomon. Among her many offerings is the exchange of information and comments from viewers who suffer from thyroid problems. It is my observation that the majority of her viewers seem to have hypothyroidism. You only have to monitor this site for a few sessions to realize the general discontent of many of them toward their physicians. It is surprising how many of these people are quite knowledgeable when it comes to natural thyroid.
One of the offerings on Ms. Shomon's Web site is a letter written by a patient, Shirley Grose, to her doctor. She had no compliments for him. He apparently made disparaging statements about the Armour Thyroid she had been taking. He refused to prescribe it for her. The lady had done her homework. In her letter to him, she may have made a better case for natural thyroid than I have. She demanded answers as to how he substantiated his opinion of her natural thyroid preparation. I wonder if she ever received those answers.
I have had a number of patients who would have liked to have sent similar letters to their former doctors, but they may not have had the research or writing skills of Ms. Grose. As a result, they vented their feelings on me. I think they would have applauded her saying to her doctor, "I would like to know why you thought I was unqualified to say how my own body felt."
A fuller version of Shirley Grose's story is found in Appendix J.
On that same Web site, viewers actually seek help from others in searching for doctors who will prescribe natural thyroid. Sometimes they make reference to a "Barnes" type of doctor.
I have mentioned Dr. Broda Barnes previously. He's probably been the most critical of some of the dogma surrounding the recognition and treating of hypothyroidism. In his 1976 book, _Hypothyroidism,_ he chastises the doctors who rely on the laboratory tests in preference to responding to the obvious symptoms of the patient. Clearly, Barnes used natural thyroid to treat his patients. He gives dosages only for natural thyroid. Yet nowhere in his book does he actually compare natural with synthetic thyroid. He virtually ignores the existence of synthetic thyroid. I cannot help but speculate as to this omission. It isn't logical that a doctor writing about hypothyroidism would not even mention the then most common drug used to treat the ailment. It smacks of an intentional omission. Was some sort of pressure exerted upon him to ignore the medication he didn't endorse? Was this a politically correct position forced upon him? A few years back, I made an effort to locate him and ask him the question. I was too late. He had passed on.
Though Dr. Barnes is gone, the Broda O. Barnes, M.D., Research Foundation, Inc., is dedicated to carrying on his work. In their literature they seem to affirm that he was critical not only of blood testing for thyroid problems. According to them, his position on medication was:
Patients taking thyroid replacement therapy have much better improvement to symptoms with natural desiccated thyroid hormone rather than synthetic thyroid hormones.
Here's a story that seems apropos. I've treated a lot of husband-and-wife teams over the years. This generally works out very well. They tend to keep each other motivated. Sometimes I suspect that competition spurs each of them on. They generally, but not always, support the efforts of their mate. If the husband is about to throw in the towel, the wife will often give him a pep talk and get him on the right track.
A man might come to me after his spouse has already been a patient. The wife might come home and say, "Honey, it's about time you lost weight too. It's terribly bad for your health. I want you to make an appointment with Dr. Siegal." That rarely works. He'll make the appointment all right to satisfy his wife, but the motivation isn't there. This is the type of case that generally doesn't end in success.
Some pairs are wonderful. I'm thinking of Sherwin, Fran, and Armando. That's not a pair, that's a threesome. Armando is the fifteen-year-old son. Fran came first. This fifty-three-year-old lady had only twenty-five pounds to lose. At the end of two weeks, the scale showed she was down nine pounds, a clear signal that there was no thyroid problem. Her husband and son made appointments. When teenagers make appointments I always speak to the parents first. Below age fifteen, I tend to discourage the parents from pursuing the medical route. From experience I have learned that at that age there is very little motivation do what is unpleasant. It takes a certain level of maturity to have the discipline necessary to diet. Kids just don't have it. And I don't want them to fail. I don't think that failure at that age is healthy. (Is it at any age?)
Nonetheless, I accepted Armando as a patient. He seemed more mature, more adult, than many of my adult patients. It turned out that he was just that. He took the no-nonsense approach to dieting and in three months lost forty-two pounds and was put on a maintenance program that was essentially a lot of exercise. Patients like Armando make it all worthwhile.
I didn't learn that Sherwin was himself a physician until I saw him for the first time. I have to confess that I find physician patients generally trying. I'm always sure they are suspiciously evaluating my every move, just as I do when I go to a physician. As much as I hate the idea, I suspect I'm not myself at these times, and this embarrasses me. Sherwin gave me no reason to feel self-conscious. He acted like any other patient. If I hadn't been told he was a doctor, I wouldn't have known.
Worse than that, Sherwin was a specialist in internal medicine. I must tell you how unusual that is. He was the first—not the first physician I'd treated, but the first internist. I've had scads of doctors as patients and they've come from a variety of specialties. I don't know why internists don't darken my door, but I imagine they have no reason to think I know more about losing weight than they do. (All this is just speculation.)
Dr. Sherwin weighed 248 pounds and he was five feet nine inches tall, with a medium build. A proper weight for him would have been about 160. He was by far the most serious case of the three. His first month's weight loss was only six pounds. He said he'd been totally compliant, and that meant he was a candidate for treatment with thyroid hormone. I expected opposition to the idea. He had had our usual battery of lab tests, but they didn't include thyroid tests. I awaited, "What, no thyroid tests?" But he didn't say that and there was no opposition. I kept thinking, Why is he not asking me the obvious? I prescribed his medication. He didn't act differently than any other patient in these circumstances. To boot, I had prescribed natural thyroid. I was willing to bet he had never written a prescription in his life for natural thyroid. But I'm sure he had written a million of them for synthetic thyroid.
Sherwin had to have his thyroid dose adjusted a couple of times, and eventually the weight came off quite well. After the first forty pounds he mentioned that he hadn't known that it was possible to feel so well. He has referred many patients to me. The whole family was a success story, and yet as I look back, I can't help but wonder. All the internists I know diagnose hypothyroidism by the book. They don't prescribe natural thyroid. I would like to have known why he was so accepting of treatment that I knew he didn't give to his own patients. I wanted so to know, but I never had the courage to ask. (If he reads this, maybe I'll get my answer.) I wanted to know why Sherwin never questioned my methods. I've treated many other doctors and we always get into "doctor talk." I remember asking my receptionist after his first visit, "Are you sure he's a doctor?"
When Sherwin was discharged, I mentioned that he would have to continue taking the thyroid medication. He asked me for the exact information as to dosage and said he would obtain it himself. And that was that.
Sherwin will always be a mystery to me, but a pleasant one.
I believe that natural thyroid will again regain its popularity. I don't see how the good results I have been getting from it for so many years can be ignored. A combination of new research, patients' feedback, doctors willing to listen as well as others willing to speak out, can make the change.
In a later chapter as well as in the chapter for doctors, I will explain how I use natural thyroid to treat hypothyroidism.
# Summing Up
* Natural thyroid hormone has been in use for over 100 years for treating hypothyroidism.
* The synthetic hormone, though effective, is not as effective as the natural hormone.
* There has been an unwarranted bias against natural thyroid.
* Many hypothyroid patients are aware of the difference between the two and request natural thyroid from their doctors.
* Most doctors are unfamiliar with natural thyroid and choose to prescribe the synthetic variety.
#
# _The Usual Way and the Better Way_
**I** f you've ever made a visit to a doctor, and who hasn't, you've probably at one time or another had some laboratory tests performed. To learn more about you, it is certainly standard procedure for your doctor to go beyond what he can see, feel, or hear. That's where laboratory tests come in.
When we think of laboratory tests, we tend to think of blood tests, where someone inserts a needle into a vein and withdraws some blood, which then is subjected to strange and mysterious analysis. There are other procedures that still fall under the realm of lab tests, and these have nothing to do with blood. Still other lab tests involve the examination of other body fluids. There are also tests that have nothing to do with removing any body fluids or other pieces of you. Your eye doctor might do various tests that could probably be classified as lab tests in which he may not even make physical contact with you. A stress test is one where your heart's response to physical exertion is monitored. Since we're presently interested in your thyroid gland, you should know that all tests relating to the thyroid aren't simply blood tests.
We, of course, are concentrating on a particular aspect of your thyroid gland. We would like to know whether it is supplying you with enough of its thyroid hormones. The words in the last sentence were chosen precisely. Your thyroid gland may indeed be supplying a "normal" amount of the thyroid hormones, but we're interested in knowing whether that amount is "enough" for you.
Remember, two thyroid hormones are known to regulate our metabolism. We've called them T3 and T4 for short. T3 is much more potent than T4, but it is present in the thyroid gland in a much lesser amount. It acts very quickly upon the cells that receive it, and then it dissipates rapidly. Because of this fast action, the patient gets somewhat of a jolt after taking it and in a sense becomes _hyperthyroid_ for the moment. This can produce undesirable side effects. T4, on the other hand, is slower to act and is converted inside the cells to T3 before it performs its regulatory functions. Because of this more gradual action, most doctors prescribe T4 alone to treat hypothyroidism, the disease characterized by an inadequate supply of the hormones.
It is only logical that we would like to know just how much T3 and T4 are in a patient's bloodstream. Logic tells us that if the amounts are lower than normal, that should certainly account for hypothyroidism. The situation becomes more complicated when you realize that there is another endocrine gland involved in all of this. The pituitary gland, often referred to as the master gland because it exerts much regulatory effect upon the whole endocrine system, produces a hormone called thyroid stimulating hormone, a name generally shortened to TSH. It is believed that the pituitary gland monitors the amount of T3 and T4 in the circulation constantly, and when it finds that the amount is "subnormal," it releases its hormone, TSH, into the bloodstream. The name given to TSH suggests what happens next. The thyroid gland, in turn, monitors the amount of TSH in the bloodstream, and when that amount increases, it is stimulated to release more of its hormones into the bloodstream.
A perpetual cycle is thus created. When the pituitary senses that there is an abundance of T3 and T4 in the bloodstream, it stops releasing TSH, and when the thyroid senses this drop in TSH, it stops releasing T3 and T4. This reciprocal process is what is believed to regulate our metabolism.
Since two glands are involved in this process, it should be clear that a problem with either of them could upset the balance of this delicate regulatory mechanism. By assessing the amounts of the three substances involved, T3, T4, and TSH, doctors hope to figure out what the problem is and where the problem is. That all seems quite straightforward, and it would seem that it isn't that difficult to analyze one's thyroid status.
Let's look at some theoretical laboratory results and then think through the meaning. For simplicity we will look only at a couple of combinations of T4 values and TSH values. Suppose the amount of TSH in the blood is determined to be higher than normal, and at the same time the amount of T4 is lower than normal. We could conclude that the low T4 meant the thyroid gland wasn't putting out enough T4. The high TSH value tells us that the pituitary gland is aware of this and is trying to get the thyroid gland to increase its production, but obviously that isn't happening. That should tell us that the problem is with the thyroid gland and not with the pituitary. The pituitary is doing its job, but the thyroid gland is not. That's clear enough, isn't it?
Suppose both values are low, the TSH as well as the T4. It looks like the thyroid gland isn't putting out enough T4, but since the pituitary isn't putting out TSH in order to stimulate T4 production, suspicion falls on a defective pituitary. Of course, both glands could be malfunctioning, but that is less likely.
Most doctors have great confidence in the conclusions that they draw from such lab results relating to the thyroid, and this seems very clear-cut. If it looks like the patient isn't getting enough thyroid hormone, supply it to her. I've lost track of how many tests of thyroid function I have done over the years. Even though I've done tons of them, you've already been told I have little confidence in them. Why? As I've just explained, the theory seems sound. But things don't always work as they are supposed to work.
For one thing, some of the tests of thyroid function are known to be unreliable if the patient is already taking thyroid medication, and the fact is that many of them are. They may be told that they must discontinue taking the medication for varying periods of time in order to get accurate results, and the literature certainly differs in what those time periods are. The thyroid hormones are carried in the blood combined with a protein called thyroid binding globulin. If there is too much of this substance or perhaps not enough of it in the blood, it definitely can affect the lab findings for T3 and T4. Doctors often have to test for thyroid binding globulin in order to reinterpret the T3 and T4 results.
Of course, another possibility for error is the same possibility that exists for all lab work, namely human error. I have, for example, sent blood specimens from the same patient drawn on successive days and gotten such varied results that no conclusions could be drawn. There is an even more curious phenomenon that occurred on several occasions. On these occasions, determined to get to the bottom of my displeasure with the lab results I was getting, I decided to take the blood specimen from a particular patient and divide it into two different portions, sending them both to the lab, but under different fictitious names. The reports always gave somewhat different results, sometimes with very large discrepancies.
The real problem may be quite remote from any of this. Is the amount of thyroid hormone circulating in the blood really all that important? It is recognized that the hormone does its work only when it reaches the cells that will be affected by it. Is it possible that cells in one person react differently from those in another? Could there be a defect not in the thyroid or its hormones, but in other parts of the body so that they don't take proper advantage of the hormone? I don't know the answer. Certainly that explanation has been suggested.
It became apparent to me that given the doubts I had about the reliability of the lab, I needed to look in other directions if I were to be able to help these overweight patients who also had many of the signs and symptoms of hypothyroidism.
I have said that blood tests aren't the only kinds of laboratory tests. When I was first in practice, a very well accepted test of metabolism and presumably thyroid function was the BMR test, which stood for basal metabolic rate. The word _basal_ referred to a baseline, the patient's condition when she was at her most serene and relaxed. It was generally assumed that this was when the patient awoke in the morning, before eating anything, and before encountering the stresses of the day.
We would see the patient as early as possible, before breakfast, ask her to lie on a treatment table in a darkened room for a half hour or so, and we would then quietly and calmly hook her up to an apparatus. It had an oxygen mask. There were varieties of these machines that doctors used to run this test. I remember that one of my machines had a sort of clothespin gadget we used to squeeze the nostrils shut so that all breathing, in and out, was through a tube placed in the mouth. The machine measured the amount of oxygen the patient consumed over a period of time and also measured the amount of carbon dioxide she expelled through the mouth. From these figures a calculation was made, and we could tell the patient something like this:
"Your BMR result is minus-twenty-three. This means that your metabolism is low. You're what is called underactive. We need to start thyroid treatment."
That's all there was to it. The test was very popular. It was being done left and right. Eventually it began to lose favor. The theory itself was sound enough, but the problem was the technique of administering it. It was supposed to measure the patient under basal conditions. This hardly meant after she had gotten up, made the bed, showered, brushed her teeth, done her hair, made breakfast, gotten the kids off to school, and then had driven ten miles in traffic to the doctor's office. The half hour or so of rest in the office was supposed to nullify those stimulating effects. It was argued that the only way to do the test properly was for the doctor to be at the patient's home when she awoke, and then immediately attach the mask and begin. Obviously, this wasn't too practical. I'm not sure that if one of my patients awakened to find me glaring down at her it wouldn't influence the result, or, worse, precipitate a heart attack.
No one argued that the best place to do the test was in the hospital, where the patient had stayed overnight. This was frequently done. Of course, that ran up the cost. Certainly much of the criticism of the test was valid; I never did have a lot of confidence in the results. Still, I acted on the results if my own observation of the patient was consistent with the BMR result. Again, the theory was sound enough but the implementation was difficult.
I'm not sure that the theory behind blood tests is quite as sound. On balance, as flawed as the BMR was, I think I had more confidence in it than I have in blood testing. In spite of the fact that the most authoritative textbook on the thyroid of the 1970s devoted twenty-three pages to that test alone, by the end of that decade the BMR test was fading into oblivion.
It was replaced by something rather bizarre. Did a doctor ever hit you with a little chrome hammer that had a triangular red rubber head? Aside from allowing him an outlet for aggression, this test does have some useful purpose. Certain reflexes are diminished and sometimes accentuated with various ailments. The doctor might tap your leg just below the knee and you would both watch that involuntary kick. There is a similar reflex that we all have that involves the tendon that runs up the back of your leg from your heel. It is known that in hypothyroidism there is a delay in the relaxation phase in this type of reflex after the hammer taps that tendon. Opportunistic people invented machines to measure this time delay. The patient was asked to kneel on a stool while the tester used one of those hammers to tap the Achilles tendon. The foot would jerk and the machine would take its measurement of one phase of that movement of the ankle. I have to say that I found this very useful. I think the results were quite valid. They seemed to coincide with my own observations of the patient. For some reason or other, the whole method fell out of favor; my machines eventually needed repairs and there were no longer parts for them, nor was there anyone who knew anything about them. So much for Achilles reflex testing.
There is another kind of testing that is quite different from any I've described so far. I particularly like this kind of test because it deals with what the doctor sees, feels, and hears while he is with the patient. In 1969 a group of researchers from Scotland wrote a paper in which they reported on how they had used their own senses (really only three) to diagnose hypothyroidism. The test is usually referred to as the Billewicz index, although six others co-authored the paper. The test was based solely on observation of the patient. It included the patient's history as well as what was observable. They listed thirteen signs of symptoms of hypothyroidism (mental lethargy, dry skin, constipation—you should know them by now). They then listed eight physical signs (dry skin, slowing of ankle jerk, etc.). They then evaluated each patient for each of these signs and symptoms. They very cleverly gave more weight (importance) to some than to others. The result they called their diagnostic index.
No blood tests, no expensive machines, just observations and common sense. Of course nothing is without its problems. The researchers used a control group, which is another way of saying that they wanted to compare the scores of those whom they were testing and whom they knew to be hypothyroid with the scores of the control group, whom they knew didn't have hypothyroidism. The problem, as I see it, is that they determined who had it and who didn't have it in advance by using the results of the then accepted blood tests. Ironically, years later there are papers published that use the Billewicz index as a check of the validity of blood-test analysis. Think about it. Isn't there some sort of endless-loop nonsense afoot?
Yet I like the Billewicz approach. In fact, I like it so much that I've included a concept derived from theirs in Chapter 13, "Evaluating Your Metabolism." The difference is that there is no preconceived impression of whether you have the problem or not. We start from scratch. You take the test, then we decide whether you have the problem.
I have spoken of Dr. Broda Barnes, the doctor who wrote a book all about hypothyroidism and who some might believe wrote it entirely with a poison pen. He was terribly critical of his profession when it came to thyroid. At any rate, Dr. Barnes had his favorite test. He knew that those with hypothyroidism have a low body temperature. So he took his patients' temperatures. That doesn't seem all that inventive, does it? Actually, he didn't do it himself. He had them take their own temperatures. He placed great value in this. Dr. Barnes's patients' body temperatures were a major consideration when it came to diagnosing them. I've said that I thought this method had merit. Perhaps I'm not quite as enthusiastic as Dr. Barnes about it, but it does make sense. You will hear more about this later.
Is blood testing useless? I guess I'm not ready to say that yet. Certainly many patients are tested by conventional means, put on therapy, and many of them do quite well. My complaint is that many cases are missed or ignored because of the blood-test results. If I won't admit that blood testing is useless, do I feel it is useful? In my experience, not very. I think there are better ways. I think the Billewicz test has value. I think Dr. Barnes's temperature test is useful. In combination, the individual value of each test is probably multiplied. I also think that the test I use on my patients, the one that gets right to the heart of the matter, is the most valuable. You will be able to decide for yourself.
I will describe briefly the Metabolic Function Index test, but there is much more about it later in the book. If you decide to take the test, you will be asked to eat a diet of 1,000 calories per day for a four-week period. You will lose weight on that diet, guaranteed. The question is, how much. Based on how much you lose, with some simple arithmetic, I will show you how to calculate how many calories it takes for you to maintain your weight, that is, not to lose or gain. You will then compare that amount with how many calories it _should have_ taken you to maintain your weight. There is little math involved in all this. It's not very difficult. Your sixth-grader should be able to do it.
Your Metabolic Function Index, your MFI, will be expressed as a percentage of normal. If you turn out to have an MFI of 100 percent, you don't have a metabolic problem. If it turns out to be 75 percent, you do have a problem.
The reason I have so much confidence in my test is that it goes right to the crux of the problem. There is nothing hidden. It is really quite simple. Here is how it works: If it is known that hypothyroid individuals don't burn sufficient calories, let's eat a certain number of calories and then let's see how fast we burn them up. That's all there is to it.
In Chapter 11 you will get the exact details of how to run this test on yourself.
# Summing Up
* Over the years, there have been a variety of tests to determine the state of one's thyroid function.
* Not all thyroid tests have been blood tests.
* The metabolic function test in this book investigates the problem directly by comparing one's own burning of calories with that of a "normal" person.
#
# _Why Protein for Weight Loss_
**Y** ou cannot help but have noticed that there is a lot more being said about protein diets than there has been for many years. In fact, if you're a sufficiently young adult, you may not be aware that high-protein diets were once very popular. Is it not evident that there are varied opinions on what role protein should play in our diets?
During my growing-up years, I think there was every bit as much interest in diets and getting thin as there is today. But there was a difference: People weren't as intense when it came to searching for the "magic" cure for obesity. Sure, there was plenty of nonsense around, even then. One of my hobbies is to collect memorabilia of weight-loss schemes that were popular through the years—you know, articles, advertisements from newspapers or magazines, that kind of thing. Even a hundred years ago you could buy soap that would wash out your excess fat. There were batteries, magnets, and even the makings of tapeworms could be purchased in capsule form. But the purveyors of all this stuff weren't nearly as sophisticated as our current crop of vendors.
One of the reasons most of the newspaper and magazine ads for weight-loss potions and devices didn't seem to attract a sizable audience was that everyone knew how to lose weight without this outside help. There was no mystery. Maybe folks were no more apt to follow what they believed to be the proper weight-loss diet than they are today, but there was little doubt among the masses as to how to lose weight. As a result, even though there were a few diet books around, their approach was the usual conservative advice on sensible eating, and they really didn't sell very well.
Of course, diet books have been around for a long time. Even though there is dietary advice widely dispersed through the Bible and it is present in other ancient writings, the first real diet book came from England. In 1727, Dr. Thomas Short wrote a treatise titled _Discourse Concerning the Causes and Effects of Corpulency._ It's fun to read. Among other things, he believed that bad air was partially responsible for "corpulency" and advised his readers not to live near marshes. The first diet book that had any kind of readership also came from England, but 136 years later. William Banting had battled obesity for years. He was disappointed in the medical attempts to cure him until one doctor apparently gave him the right diet. He was so impressed with his results that he rejoiced by printing a pamphlet, his _Letter on Corpulence,_ in 1863. It told the world about the diet that finally worked for him. For a frame of reference of the times, our Civil War was going on then. Americans were too occupied, but the English took his advice to heart. At least at first, he distributed it free. Perhaps because the price was right, the pamphlet was a "best-seller."
Banting's _Letter_ had such an impact that it was the standard of diet in England as well as the United States for perhaps fifty years. The medical men didn't particularly like it, but eminent physicians debated its value in the most prestigious journals for half a century on both sides of the Atlantic.
The Banting diet wouldn't excite anyone today. For one thing, it is quite vague. Dr. Banting virtually didn't specify quantities for many of the foods he recommended. There was no doubt that it was a high-protein diet. Banting had his readers eating lots of meat, fish, and fowl. About the only things he excluded from those categories were pork and salmon. He recognized that they were quite fatty. Banting's diet was rather low in carbohydrate. He forbade things in that category: bread, sugar, potatoes, and beer. He did allow two or three glasses of wine, a concession that may have contributed to his popularity.
I have said that during my formative years everyone knew how to lose weight. What I mean is that they knew the general principles, and I believe that those principles owed much to Banting. What they knew was that the best diet food was protein: meat, fish, and fowl. We also knew what made us fat. Strangely enough, it wasn't fat. I think everyone knew that fat carried a lot of calories, but the real enemy was an abundance of carbohydrate. We knew that if you wanted to get thin, you had to curtail the bread and potatoes.
A milestone in promoting this concept was the Holiday Diet of 1950. It wasn't a diet to follow while on vacation. It got its name from _Holiday Magazine,_ then the top travel magazine. A Dr. Pennington who worked for the Du Pont company apparently had great success with reducing overweight employees there. He was written up in _Holiday,_ and there were even follow-up articles. The magazine was deluged with information about the diet. What was the diet? You can sum it up in one word: meat. The dieter was to eat a half pound of fat meat three times a day with minimal accompanying vegetables. If the meat wasn't fat enough for his liking, Pennington advised how to add more fat to it.
Pennington wasn't unique. Before and after, others were advocating similar diets. Dr. Blake Donaldson, in a charming book called _Strong Medicine,_ informed us that
there are only two absolutely necessary foods for humans—fresh fat meat and water.
Restaurants at the time didn't ignore the needs of the overweight client. Diet plates were very common. What would you expect to find on them? A meat patty and perhaps a green vegetable or a salad.
I started practicing general medicine in 1957, and I couldn't ignore the prevalence of obesity in my practice. By 1960, I had all I could do just to handle those who were overweight, so I decided to limit myself to just that type of patient. In 1968, the first very big diet book in ages came out. It was written by a really cute old doctor by the name of Irwin Stillman. Cute? Sure. He was a frequent visitor on the late-night talk shows. Everyone loved him because he said funny things. His diet? You guessed it: lots of protein and virtually no carbohydrate. That, at least, was Dr. Stillman's basic diet. The problem is that he had so many alternate diets in his book that I don't see how anyone could have made a decision as to which one to follow.
What I've been trying to get across is that for an important segment of our history, high protein and low carbohydrates were the standard methods of weight loss. This wasn't limited to the public's perception of what to eat to lose weight. The majority of doctors subscribed to the same concept. If there was any controversy, it had to do with fat. Some said eat it; others said don't.
In the 1970s things began to change. Meat fell into disfavor. We started hearing more and more about complex carbohydrates. Self-styled gurus (in a sense we're all self-styled) started singing the praises of low-protein, high-carbohydrate, and low-fat diets. Protein was tolerated in limited quantities, but fat was the real enemy. Exercise was promoted and the gyms proliferated and prosper to this day, although membership certainly dwarfs participants. Little books that told you how much fat was in each morsel of foods you might eat were for sale at all the checkout counters. In previous decades, similar books told you how much carbohydrate was in your foods so you could reject those that had more than a smidgen. Now we were being told to load up on carbohydrates.
What resulted? It is obvious from the patients I see. My impression: _We as a society have never been fatter than we are today._ If the carbohydrate craze wasn't the cause, it certainly wasn't the cure. One after another, my patients were telling me they had tried this diet and that diet and the only thing that happened is that they got fatter and fatter. Strangely enough, they didn't seem to blame the diet. Instead, they believed there was something wrong with their bodies. After all, they had followed the advice that had been given them. They were too young to know that this kind of advice changes from decade to decade, and even if they did know it, they believed that the most recent advice was always better than all that old stuff.
Among the experts, there is a lot of support for the proposition that a calorie is a calorie and it doesn't matter if it comes from an animal or a plant or lettuce or butter. There has been a mountain of research done during the first half of the twentieth century concerning whether carbohydrates, proteins, and fats were indeed interchangeable in the diet when it came to supplying energy (calories). No one disputes how much energy (how many calories) the individual food groups contain. We know that carbohydrate and protein each store 4 calories per gram and that fat stores 9 calories per gram. (There are about 454 grams in a pound.) The question arises that when we eat each of these, do we end up with those amounts? The most dedicated and thorough research was done years ago to answer this question, and there were indeed some very definite answers.
What we're speaking of is named the specific dynamic action of foods. When you eat your protein, carbohydrate, and fat, each of them goes through a very different process of digestion, and before any of them are assimilated into your body to be used for growth or repair, or fuel, or to be stored as fat, your system must burn up a certain amount of energy (calories) to do the work of converting them into a more usable form. Just as you burn up a certain number of calories when you run for the bus, your body burns up a certain amount in making your food available to you. Scientists through experimentation discovered very early that protein burns up so much energy (as compared to carbohydrate and fat) in the process of digestion and assimilation that you get only a fraction of the protein calories that went into your mouth. The rest of the protein calories are used up in making it suitable for you to use. One of these researchers declared in 1969 that protein used up five times as many calories as did carbohydrate in providing its calories to the body, and seven times as much as fat. Here was a rationale for those diets that seemed to advocate virtually unlimited intake of meat.
The interesting thing about the specific dynamic action concept is that it died. Most theories become extinct when new concepts prove them wrong. We realize we've made errors in the past and once we investigate things with new and improved methods, we find that we've drawn the wrong conclusions. Not so in the case of the specific dynamic action of protein. As a concept, it simply died. Somewhere early in the last half of the twentieth century, scientists seem to have lost interest. They went off in other directions. I find this most interesting. Here we had a viable concept to explain a problem that had been needling us for years, and researchers just turned their backs on it in wholesale numbers. Today, you still see it referred to in the literature from time to time, but only by esoteric scientists studying other organisms. I rarely find even a mention of specific dynamic action when considering human nutrition.
In the early 1900s a Norwegian explorer by the name of Stefansson seemed to have become obsessed with convincing the world that the only diet for the human race was meat and fat. He had been shipwrecked and lived among Canadian Eskimos for one winter. He observed that they as well as he thrived on that kind of diet. When he got back to civilization he spent the better part of a year participating in a famous experiment where he and another man ate only meat and fat. The result certainly supported his position. He promoted his ideas in his many books, and in one, _The Fat of the Land,_ the preface was authored by the most renowned cardiologist of our time, Dr. Paul Dudley White. Dr. White's name was a household word at that time. He was the doctor who tended to President Eisenhower when he had his heart attack.
My preference for high-protein diets for weight loss comes from my own experience. Over the years I have used a variety of diets on my patients. I've seen the results of each firsthand. I've learned a lot. It's the kind of learning that can't come from reading books or scientific papers. I've seen what doesn't work, what works a little, and what works very well. I, of course, go for the best result. The bottom line: _Consistently, my patients do better on high-protein diets._
In Chapter 11 you will learn the details of the kind of diet I believe has the best chance of helping you lose your weight quickly, comfortably, and safely. I assume that you won't be surprised to learn that it is a high-protein diet.
For more on protein, see Appendix B.
# Summing Up
* High-protein diets have been the standard for losing weight since the middle of the nineteenth century.
* The trend continued for at least 100 years.
* It was followed by a move toward much more carbohydrate, much less protein, and low fat, and during that period obesity has probably become more prevalent.
* The pendulum now seems to be swinging back to the high-protein type of diet for weight loss.
* The author has seen the high-protein approach as the most viable type of diet for controlling hunger and achieving the objective.
#
# _Cholesterol and Hypothyroidism_
**I** n the last chapter I explained my partiality to high-protein diets for my patients who are in the process of losing weight. We all equate protein with meat, and to many of us meat conjures up the evil specter of cholesterol and its partner in crime, saturated fat.
If you're fifty years old or younger, you probably can't remember a time when cholesterol wasn't a hot topic.
I probably took first notice of cholesterol in 1953, when a doctor by the name of Ancel Keys reported on the relationship between the level of cholesterol in the bloodstream and the incidence of coronary heart disease. I was still in medical school then, but when I first began my practice, I took up the banner like most practicing physicians and became an advocate of prudent eating. This meant that my patients had to cut way down on foods that contained saturated fats and cholesterol.
The information seemed to be clear enough. A busy doctor doesn't have time to research every new report. He must have some faith in what he is told. And, in this case, he was told plenty. It seems that the media has always had a love affair with the subject of cholesterol. Cholesterol isn't just the buzzword of recent decades; it's been a really hot topic since the fifties.
Like all practitioners, I read my share of papers in medical journals, but they were just a fragment of what was available to read. The popular press influences medical judgment perhaps as much as does the serious literature. When your doctor receives a daily barrage from the media of well-meaning advice on how to lower one's cholesterol, it has to influence what he tells his patients.
I tend to go overboard when I'm involved in a cause, and so I suspect that my efforts to convince my patients of the proper course of diet were probably more extreme than the average doctor's. I told them to cut down on animal fats, reduce dairy products drastically—in short, to be prudent. "The prudent diet" was around for years. I still hear references to it.
The cholesterol subject got a shot in the arm in the form of a nicely packaged set of materials, led by an impressive book labeled _Report of the Expert Panel on Detection, Evaluation, and Treatment of High Blood Cholesterol in Adults,_ sent to me and to every other doctor in the country in 1988 by the National Heart, Lung, and Blood Institute, which was a division of the U.S. Department of Health and Human Services. You've got to show some respect for anything you receive adorned with such an impressive bunch of words, especially when it is put together so colorfully and professionally. Furthermore, it was full of names of every important medical school and hospital you could think of. This package wasn't the usual junk mail that doctors receive and which they promptly chuck into the wastebasket. This gift was from our government.
Here was an organized dissertation of the whole cholesterol story. It included a bit of history, instruction on how to evaluate your patients as to who in the population was at risk, a section on dietary treatment, and a segment on drug treatment of high cholesterol.
This was clearly a set of instructions designed for me to follow in my practice. The implication was unmistakable: Thou shalt do this. These were orders from above. It was my solemn duty as a physician to carry out this program.
With so much hype for the government's cause, it was about time for me to learn what this cholesterol business was all about. Of course I read the government materials, and they certainly made a good case for my pursuing their goals. Cholesterol did seem to be the killer and saturated fats its accomplice. Still, in the back of my brain was this disturbing feeling that there had been some alternative views of the whole thing. I couldn't even remember from what quarters these diverse thoughts came, but I decided to bone up on the subject. That was a few years back, but I've never lost interest in the project.
I have learned that the dissent over the importance of controlling one's cholesterol isn't trivial, even though it comes from a relatively small number of individuals and they don't seem to have the clout to get their message across.
Possibly, the first piece of dissent I ever read was a book by a Dr. Edward R. Pinckney, titled _Cholesterol Controversy,_ written in 1973, fourteen years before the government really got that interested. He pointed out that the link between heart disease and cholesterol was simply not proved. He accused government agencies of having "allowed health associations and food industries to play havoc with the anxieties of millions and millions of people by permitting this unproved doctrine to be promoted."
A number of others have expressed similar doubts since that time, and a few books have been written on the subject. A 1989 article in the _Atlantic Monthly_ titled "The Cholesterol Myth" fueled the controversy. The author, Thomas J. Moore, certainly suggested that a conspiracy involving the food industry, the drug industry, and government cooperation was out to deceive the public into believing stories about the villain cholesterol.
He was joined by others. A man by the name of Russell Smith did a tremendous amount of research in collecting everything known on the subject, came to the same conclusions, and presented his findings in a 1991 book. The controversy has since cooled somewhat, and even those who believe that the whole subject has been taken too seriously seem to be willing to play it safe by at least following dietary guidelines that purport to keep cholesterol under control.
Of course, we now know that there is "good" cholesterol and "bad" cholesterol and that we really don't mind when the former is elevated. In fact, a high level of good cholesterol, HDL, is said to be protective against cardiovascular disease. The scope of this book doesn't include an in-depth look at the whole cholesterol question. As a result, please assume that when I speak of high cholesterol, I'm referring to the alleged negative effects from elevated cholesterol that necessarily includes the bad part.
I have seen my share of high cholesterol readings. That isn't surprising when you consider that all of my patients come to me weighing more than they should. It is also expected that as the patient loses weight, the cholesterol will fall. The low-saturated-fat diet I prescribe for my patients is one factor promoting this. The weight loss itself contributes to lowering the cholesterol, as does the exercise prescription the patient is given.
Of my patients who are shown to be hypothyroid, cholesterol levels are higher than in those who don't have thyroid problems. That is one of the many indications that cause me to suspect hypothyroidism. Every new patient is required to have some routine laboratory testing, and cholesterol tests are included. I'm not sure if it is safe to say that every single "untreated" hypothyroid patient I have ever seen had an elevated cholesterol, but I really don't think I can remember an exception. When I see high cholesterol, I immediately think of hypothyroidism.
It is a rather general rule that as my patients lose weight, the cholesterol levels fall. This is even true of those whose cholesterol levels are normal at the onset. There is quite a range of what is considered normal cholesterol levels, so a drop doesn't take them out of the normal range.
In those patients I've diagnosed with hypothyroidism, the drop in cholesterol values once they've been placed on thyroid hormone treatment is more dramatic. The cholesterol lowering seems to take place in advance of what would have been attributed to weight loss. Many of these were previously aware of high cholesterol readings and have been admonished by their doctors to stop eating fat and to lose weight. Others have been put on cholesterol-lowering drugs, which did seem to have some beneficial effect. In spite of this, it is rare for me to see an obese patient who has achieved a normal cholesterol through the use of cholesterol-lowering medications. The cholesterol may have dropped, but it was still somewhat elevated.
On the other hand, treatment with thyroid hormone has resulted in many patients getting their cholesterol levels into the normal range, sometimes in conjunction with the other medications, but frequently without any other medication. It is commonplace for my hypothyroid patients to control their cholesterol readings totally through the use of thyroid hormone. They are always delighted when I take them off the cholesterol-lowering drugs. For one thing, these prescriptions are very expensive. These patients also know that there is some concern over liver damage from use of these drugs, and they welcome not having to have blood tests to monitor this possibility.
Unlike my disdain for thyroid testing of the blood, I have no cause to believe that cholesterol testing is inaccurate. Needless to say, I've done thousands of those tests also, and I'm quite satisfied that they are consistent and useful.
My purpose in including this chapter is to alert you to the possibility that if your cholesterol is found to be high, this could be useful information and it might very well point your doctor in the direction of suspecting hypothyroidism. Unfortunately, I believe that this particular finding is frequently overlooked. The drug companies have done a good job of convincing the practicing physician that they have the answer to the cholesterol problem and that writing the correct prescription for their products will do it.
If you choose to take the MFI test described in the next chapter and the result indicates that you could have a problem with hypothyroidism and you know your cholesterol is also elevated, it is time for action.
I believe you should diplomatically introduce the subject of your high cholesterol and its possible relationship to the thyroid when you visit your doctor. You could say, "Doctor, I read somewhere that high cholesterol is sometimes related to thyroid problems. Do you think that applies to me?" How is that for being subtle? You don't want to offend your doctor, but it's your body and your life. Act accordingly.
I believe that proper treatment of your low thyroid function can be a major step in lowering your cholesterol. Whether you're from the camp that accepts the current attitude toward cholesterol or are more attuned to those who question it, there is probably no harm in playing it safe. Proper treatment of your thyroid problem would be expected to lower your cholesterol levels, and your doctor will certainly be pleased with that result.
So far we've explored the thyroid and how its underactivity can affect your well-being. You've learned that the problem is often missed or ignored and why. We've delved into how hypothyroidism is treated. We have an inkling of the kind of diet that will reduce your weight, whether you have a thyroid problem or not. And you know there is a test you can give to yourself that could change your life. Now, let's get to it.
# Summing Up
* The blood cholesterol level is usually elevated in those with hypothyroidism.
* The role of elevated blood cholesterol as a cause of heart disease is questioned by some authorities.
* Thyroid-related elevated cholesterol often responds to treatment with thyroid hormone without resorting to other cholesterol-lowering drugs.
#
# _The Metabolic Function Index Test_
**I** t's time to get down to business.
You're about to test your metabolism. That's essentially another way of saying that you will be testing your thyroid. But that may not be exactly correct either. What we're really testing is whether your body is supplying itself with enough thyroid hormone. From a practical standpoint, it is all the same thing. The nuances of how we play with the words have little to do with the actual goal of this exercise. We're about to find out whether you burn up enough calories, and if you don't, you will find out what you can do about it.
You indeed may be someone who is already taking a prescription for thyroid hormone. If that is the case, it will probably be for levothyroxine, T4, but there is always the possibility that your doctor, like me, prefers to prescribe natural thyroid. The test you will perform has value whether you are known to have hypothyroidism or you have undiscovered hypothyroidism. It is even valuable if you don't have hypothyroidism. In that event, it will tell you that you don't need hormone replacement therapy and that a reduced-calorie diet will have you losing weight like all those "normal" people do.
If you're currently taking some form of thyroid, natural or synthetic, the test will serve as a check on whether you're receiving the right amount. It will inform you whether the amount of thyroid hormone you're taking is sufficient to cause you to burn calories at a normal rate. Remember, I've indicated that the most revealing sign of hypothyroidism is the inadequate burning of calories. This test will reveal whether the added thyroid you're taking brings your metabolism into the normal range. It may serve to inform you that you need more thyroid hormone.
The theory behind the test you will be performing on yourself is based upon how you handle food energy in comparison to a theoretically normal person with your same characteristics. When it is completed you will know how you stack up against that "normal" individual.
The normalcy we're investigating is limited to how you process energy. You will recall that we use the word _energy_ rather loosely in this book as synonymous with _calories_ or perhaps even _food._ That's where we get our energy, from food. This is the scientists' use of the word _energy._ It isn't the popular usage, where energy may mean pep or enthusiasm or stamina. The word _calorie_ is actually a unit of energy, just as the pound is a unit of weight or the inch is a unit of length.
Picture an imaginary person whom we shall call our _model._ Of course, if you're to compare yourself to some normal model, we must know something about that model. We want the model to have your physical characteristics. A major part of the calculation you will make later on is aimed at defining this model or normal person.
Here, briefly, is what the task entails: We will be looking at someone with your same height, weight, age, and activity level, and we're going to determine how many calories that model requires each day to maintain his or her weight. Suppose with our calculations we were to come up with 2,150 calories. That would mean that a "normal" model individual with your same characteristics would neither lose weight nor gain weight on a diet of 2,150 calories per day. We shall call this our standard caloric maintenance level and for convenience will abbreviate it as the SCML.
The test takes twenty-eight days to complete, but your task during those twenty-eight days is little more than to follow a particular diet for that period of time. The diet is a 1,000-calorie diet that will certainly result in weight loss even in the reader with the most severe hypothyroidism. The tables you will consult and the few calculations you will make at the conclusion of the diet period are based on staying on the diet for twenty-eight days. They will have no validity if you stop the diet earlier. Let's approach this test seriously, with all the fervor of a mad scientist. The information you will gain will be very valuable to you. You will discover how your metabolism compares with the norm. You will know what it takes for you to lose weight. You may answer the perplexing question of why it has been difficult for you to lose weight or maintain weight. Don't treat this casually. You have a task ahead of you. Not a difficult one, but a serious one.
The 1,000-calorie diet may not be that different from other low-calorie diets you've tried in the past. It isn't particularly difficult to follow. It is designed for convenience. After all these years of treating overweight patients, I'm well aware of the time constraints that plague many of my patients. It offers the convenience of prepared packaged meals from the supermarket as an alternative to cooking up a storm.
Will the test cut into your busy schedule? Absolutely not. Aside from the requirement to eat according to the instructions, your other tasks should take less than three minutes a day. You need only to record your weight on the first day and then again on the twenty-ninth day. There is a two-minute task you will perform before your day actually begins, indeed, before you even get out of bed. The largest task will be to use the tables and to make the necessary calculations. That all happens at the end of the twenty-eight-day diet.
As valuable as my MFI test should be to my patients, there are always a few who simply will not comply sufficiently for four straight weeks so that I can get a valid reading of their metabolism. Immediately, Lucy comes to mind.
Lucy was five feet four inches tall and weighed 263 pounds. Those figures spell danger. Everyone who laid eyes on her had to be aware that she was in big trouble. Lucy told me right from the first that she had a thyroid problem. She had been tested several times, but had rejected what the doctors told her. She knew she had a thyroid problem and she wasn't ashamed to tell me about it. She wasn't angry with her former doctors. She wasn't the type to be angry with anyone.
"I don't eat that much, but I do have a yen for candy. I play cards with my friends three times a week and there is always candy. I just can't resist." In spite of this, Lucy was adamant that her diet didn't account for her bulk.
She had various other symptoms that tended to confirm her own diagnosis. If I had been forced to make a yes or no guess at that moment, it would have been an emphatic yes. I told her that I felt she was probably hypothyroid and would most likely benefit from taking thyroid hormone, but first we needed to confirm it. I told her about the MFI test. Her attitude: "Let's go."
Four weeks later, I learned that the test was marred by several social events that occurred during the month. She had tried, but she had lost nothing. Absolutely nothing. That told me a lot. Hypothyroidism or not, "nothing" isn't an option. She apologized and said that next month she would adhere and I would get the information I needed.
I recall that the next month wasn't much better; Lucy lost only a pound or two. In an extreme case that could have been valid, but she freely admitted her indiscretions. She asked me to prescribe thyroid hormone anyway, appealing to my sympathy. She said she could hardly make it through her day and she needed that act of mercy. She knew all about thyroid treatment, and my usual lecture wasn't needed. I did lecture her on the necessity of giving me one good month so that I could confirm her problem. Lucy promised she'd try again.
She broke her promise. The months that followed were each like an instant replay. I would emphasize the necessity for one good month of 800 calories a day, she would entreat me to give her the thyroid, I would refuse, and she would promise again. Would you believe that this went on for over a year? She lost only thirteen pounds for the whole year, not enough to matter at all.
Finally, I got tough. I told her that this game we were playing was ridiculous. I suggested that there was no point in her going on. This was nothing new to me. I've had to do that with patients many times. I was being honest, but at the same time I knew she would end up going to another doctor or "clinic" and wouldn't do any better. I wanted her to stay with me, but I also wanted results. The only way to really help Lucy was to force her into action. My veiled threat of giving up on her worked. The next month, I got what I wanted. She had lost five pounds and I felt certain she was being honest.
You, like Lucy, must be honest, but with yourself. If you momentarily stray from the diet, you won't have to worry about my reprimanding you. If you stray, you must honestly record your indiscretions on the Excess Calorie Sheet.
When the four weeks are over, the final task shouldn't take more than fifteen minutes. A pocket calculator could help if you don't feel like multiplying.
Let's begin.
On page 161 you will find the MFI Calculation Form. On the morning you're to start your diet, you must weigh yourself. This should be done before eating or drinking anything and after you've completed your morning bathroom functions. You will be weighing yourself again at the end of the twenty-eight days. What is important is that both weighings be done under identical conditions. You may want to use your own bathroom scale if you know that it is reasonably accurate. Otherwise, look for a good scale. Perhaps a friend has a doctor's scale, one of those where you slide the weights around. I've seen high-quality scales in supermarkets. Ideally you would want your nude weight both at the beginning and at the end. This can be accomplished even if you use the scale in your supermarket. Bear with me. It can be done. I promise you will not be arrested in the act.
# Your Nude Weight
The easiest way to do this is to get on the scale while you're naked as a jaybird. That could prove inconvenient if you're weighing yourself in a public place. But there is a way. You must know the weight of the clothing you're wearing and then subtract it from what you weigh clothed. I'm speaking of the weight of all of the clothing, every last item. Even if your home scale isn't accurate enough to weigh you, it should be good enough to weigh your clothing. Don't weigh your clothes by placing them on the scale. That won't work. Here is how you do it.
At home, weigh yourself while wearing specific clothes. Mark down the weight. Now remove all the clothes, step on the scale, and weigh yourself nude. Mark down your nude weight. Subtract the second weight from the first. The difference is the weight of your clothes. Armed with that information, you may now go to some accurate scale and weigh yourself while wearing those exact same clothes. Subtract the weight of your clothes. That is your nude weight. Now wasn't that easy?
If it isn't possible to obtain your nude weight, you will have to estimate the weight of your clothes and subtract it from your dressed weight. If you choose to do this, take the time to indicate exactly what you were wearing at the time of the weighing. Note everything: outer clothes, underwear, the particular pair of shoes, etc. You will want to wear the exact same outfit when you do your final weighing. The more precise you are, the more reliable the result.
There is another little task you must do before you begin the test. I want you to take your temperature. This should be the first thing you do on the day you start the diet, in fact it should be done while you're still in bed, before you've walked around, before you've brushed your teeth, before you've had your coffee. You must therefore prepare for it the night before. There should be a thermometer on the night table next to your bed, already shaken down and ready for use. Pop it into your mouth, under your tongue, as soon as you awaken. Leave it in for about two minutes. Write down the result next to the first date on the Daily Temperature Chart on page 174.
Please buy yourself a glass thermometer for a couple of bucks if you don't already have one. These are the ones with the thin shiny column of mercury inside. Don't worry. The mercury won't harm you as long as it remains on the inside. Some of the results from the newer gadgets are questionable. I believe that your temperature is best taken in your mouth and not in your ear. So take your temperature, write it down, shake down the thermometer, and get it ready for the next day. You will need to take your temperature most mornings for those twenty-eight days and record these readings on the chart. Don't forget to do it before you get out of bed. If you forget and remember later, don't take your temperature that day. Leave that day blank on the Daily Temperature Chart. Try not to miss too many days. I would like to see at least fifteen readings for the twenty-eight days. For females, don't record temperatures on the days during menstruation. In fact, to play it safe, exclude the day before and the day after also.
Of course, such daily temperature readings won't be valid if you're ill during the test. If you have a cold or other infection, there is no point in recording those temperature readings on the chart. Then again, if you're really sick, you will probably not be performing the test during that time. So pick a time when you're healthy, and start again.
Your intention is (I hope) to follow the 1,000-calorie diet to the letter, but it is possible that you may slip up a bit. I hope these distractions will be infrequent. Nonetheless, we don't want the whole test to be abandoned just because you weakened on a few occasions. You will still have a valid test if you have prepared for that possibility in advance. Put aside a sheet of paper that you've labeled "Excess Calories for the 28 Days." Make two columns, one for the date, and one for the excess calories for that particular date. As the test proceeds, write in the dates when you exceeded the 1,000-calorie allowance, and next to each jot down your estimate of how many extra calories (above 1,000) you ate that day. To repeat, don't count all the calories that day, only the amount over 1,000. At the end of the twenty-eight days, add up all the excess calories. You will need this number when it comes to calculating your MFI.
A variation on this test is described in Appendix C. It explains how to adjust the 1,000 calories per day to a higher amount and still have a valid test.
Of course, in order to do this, you must have a means of estimating how many calories were in that hamburger you just had. This can be hard to do, or not so hard, depending on how prepared you are. If it happens in one of the fast-food franchises, you can often get the information right there. They may have posted their nutritional information or the clerk may be able to help you. If the excess occurs as the result of eating some packaged food, the answer will probably be on the nutritional chart on the package. If it occurs at home or at a friend's house or at a street-vendor's hot dog cart, you will need to consult one of the excellent "calorie books" that are around. See Appendix G.
If you never deviate (an inspiring thought), you don't have to buy one of those books, but it is always wise to be prepared for the unexpected.
Here is what your Excess Calorie List might look like:
_Excess Calories for the 28 Days_
---
_June,_ | _23_ | _240_
| _28_ | _220_
_July_ | _4_ | _750_
| _9_ | _125_
| _10_ | _340_
| _11_ | _50_
| _16_ | _210_
| | _1,935_
Now it's time to begin the diet. Go to Chapter 12 for the details.
# Summing Up
* The Metabolic Function Index test provides the convenient and accurate means for assessing the adequacy of the rate at which the individual burns calories.
* The twenty-eight-day test can be performed on oneself at home.
* The accuracy of the test depends upon the care that is exerted in following the instructions.
* Two other corroborating tests will also be furnished.
* A high-protein diet is encouraged as a means of controlling hunger during the test.
#
# _How to Test Yourself_
**T** his diet is the test diet that you will follow for the twenty-eight days of the test. If it then seems advisable (to be discussed later), you will continue with the very same diet as your weight-loss diet. This is the diet to follow until you've achieved your proper weight.
There has been a lot of controversy over the years around how to determine what an ideal weight should be. Various authorities will give more or less importance to such factors as height, age, and bone structure. Information derived from publications of the Metropolitan Life Insurance Company has been among the most accepted during this century, though even these sources weren't free of criticism. The BBW (baseline body weight) table on page 166 should serve as a guide, although it was intended as a baseline for the later calculation of your Metabolic Function Index. You may use it as a general guide of what you should weigh, but realize that there is no such thing as an exact proper weight. This particular table doesn't take into consideration such things as frame size and age, but those will be factored into our calculations later. You may consider 5 percent above or below the given weight acceptable.
The essential requirements of any diet that is to be followed over a period of time are threefold: effectiveness, safety, and convenience. We might focus on safety as the most important of these, but in a sense they share rather equal importance since each is essential if the program is to be a success. I've endeavored, here and in my practice, to present a set of instructions that embraces those three elements.
# Effectiveness
The statement that follows may seem a bit smug. _You will lose weight on this diet._ How can I be so sure of myself? It's simple: _Everyone loses weight on a 1,000-calorie diet._ That's even more smug, but I have equal confidence in that one. In some cases the loss might seem to be painfully slow and meager. If that is the case, the explanation for this will seem clearer when you examine the results of the MFI test. If you have any degree of hypothyroidism, the weight loss will be less than expected. Indeed, that is why you will suspect hypothyroidism; it is because the weight loss is inadequate. No matter how meager, you will lose something on a diet of 1,000 calories per day. No one has a metabolism that low.
# Safety
I'm often asked whether the weight-loss diet I prescribe for my patients is a proper diet. The answer is always no. This answer usually results in eyebrows being raised, and they don't really come down again until I have completed my explanation: "No, it isn't proper. A proper diet doesn't result in weight loss, nor does it result in weight gain. By its very definition, a proper diet results in what will maintain you at a proper weight and in good health, and permanently to boot. If you are to lose weight, the diet must necessarily be improper."
If I still have the patient's attention, I go on. "To lose weight you must eat fewer calories than your body burns. For the most part, the greater the deficiency you create, the faster the weight loss. Once you've achieved your normal weight, we can then shift our attention to a proper diet."
Of course this is just a bit of verbal gymnastics, but it does help to get my point across. If we want to elaborate on the use of the word _proper,_ I may then add that the diet they've been given is indeed a _proper_ diet for losing weight.
The diet that is specified in these pages isn't the exact diet I use with my patients. The difference is in the number of calories per day. The diet you will be following for the MFI test supplies 1,000 calories per day. Later, with the help of your doctor, you may be placed on a few more calories per day, although in some instances, perhaps it will be a few less. By contrast, in my own practice I use an 800-calorie diet and I'm quite comfortable in doing so. I have a wealth of information that shows me that patients do quite well on that number of calories and that surprisingly few problems arise. Of course, my patients are seen very frequently and are monitored very closely. Since you aren't my patient and I will not be personally checking you, I'm more comfortable with your getting a few more calories per day, if your doctor approves, and I do feel strongly that you should make a few visits to your doctor during those four weeks just to be sure everything is going well. My own patients are seen weekly during that period. The MFI test you will be taking is based upon your following a 1,000-calorie diet for four weeks, and all the calculations are based upon those numbers.
A variation of this test is described in Appendix C. It explains how to adjust the 1,000 calories per day to a higher amount and still have a valid test.
# Convenience
Let's face it, if a diet you are given puts too much of a burden on you, if it is too much in conflict with your lifestyle, you will probably abandon it. In fact, you may already have done just that enough times in the past. Remember, virtually any diet that comes from a magazine or from a book will result in weight loss if—here is where the big IF comes in— _if you follow the diet._ Have you ever declared, "I wasn't able to follow that diet"?
The likelihood of remaining on a diet decreases as the time spent on it increases. In my own experience, those who successfully achieve their weight goal do it quickly. Those who frequently falter along the way and thus prolong the time required are more apt to abandon the effort. This also seems to apply to "maintenance diets." How many people gain back the weight in spite of the seemingly proper maintenance diet advocated by one of these diet clinics or organizations! Was it because the longterm diet they had been given was improper? No, I don't think so. The diet would have worked to maintain weight if the dieters had followed it. There's the rub! They didn't follow it.
This also seems to be the rule in my medical practice. If I give a patient a lifetime diet (which I have in the past), I know it will be followed for a while—a week, a month, or even a year. But eventually the patient will get away from it, particularly if the office visits have come to a halt, and I will generally see that person again when the decision to lose weight kicks in once more. That is why I've developed a rather unconventional approach to weight maintenance.
Convenience in a diet necessarily means that the diet is practical; it is one that can be followed in the course of the usual day's activities. I tend to personalize such things and present a diet in terms of what would suit my own needs. I'm a busy guy, much like most of my patients. I suspect that with the help of a few professional chefs I could write a cookbook that would meet the specifications of the type of diet I would really prefer for my readers. They could then spend the day acquiring a whole host of ingredients, dumping them in the kitchen, and then putting in their time at the stove cooking up a storm. If the quantities served fell within the guidelines, they could even lose weight while dining on succulent meals. But is that a practical option for the majority of people? Have I not heard of a celebrity who acquired a personal chef to ensure that her weight-losing experience wasn't too painful? With a rare exception, my patients must seek more practical means.
Practicality means convenience, and the diet that follows is geared to convenience. I've minimized the time spent in the kitchen. Anything that speeds up the process of providing the food is considered a plus. A microwave could help immensely. At least during the twenty-eight-day period of the test, I think you might also want to dispense with the trappings that make dining such a pleasure. The fine china, the lace tablecloth, the dimmed lights, the candelabra, and the dinner music all seem to favor an eating orgy rather than a weight-loss meal. In short, eat what you're supposed to and get it over with. Let's save the fine dining for some future time.
Your goal will be to eat 1,000 calories a day of a diet very high in protein, with a moderate amount of carbohydrate, and a relatively small amount of fat. A common dietary recommendation is that 30 percent of our calories come from fat and 55 to 60 percent from carbohydrates. That leaves but 10 to 15 percent from protein. As you've read here, I can't go along with that distribution for a weight-loss diet. I like protein for weight loss. We're going to reduce your fat intake to no more than 25 percent and increase the protein all the way up to at least 28 percent. That will leave the carbohydrates supplying about 47 percent of your calories. Remember, these values are for the percentage of calories that come from each of the three groups. This doesn't translate directly into the weight of food in each group. That last statement may sound confusing, but you don't have to dwell on it. Remember not to use those figures in searching for food. I will give you very good guidelines for that task. The diet itself will specify quantities of foods that will result in the above distribution so that you will not have to worry about what percentage of this or that is in what you're eating.
Could you eat more protein and less of the other two? Yes. I would even prefer it. The problem with that is practicality. I have already spoken of convenience. The availability of a higher-protein diet than I've settled for could be the stumbling block. Were I to insist upon higher protein and less fat and carbohydrate, virtually no frozen dinners would be acceptable.
The closer you come to supplying the 1,000 calories a day, the more accurate will be the result you obtain in calculating your MFI. In spite of this, I don't consider exact adherence to the specified foods and quantities a cast-in-stone requirement. That may seem inconsistent, but I'll explain why it isn't. What really counts is that you eat 1,000 calories per day. How you get to that number is somewhat less important. The main reason for following my instructions exactly is that the job will be easier. Specifically, you will be less hungry than if the distribution of nutrients is altered. If you're a total maverick and choose your own 1,000-calorie mix, as long as you're accurate, I expect the bottom line to be acceptable. You can do it your way, but I'll bet you will be less hungry and more comfortable if you do it my way.
# Emphasis on Protein
This is a high-protein diet, perhaps not as high in protein as some of the bizarre diets currently circulating, but high enough to accomplish its purpose. If we ignore the specific dynamic action of protein that I spoke of in an earlier chapter, we can get down to this subject of eating protein for hunger control. After years of addressing my patients' struggles with hunger, I'm convinced that an abundance of protein keeps hunger manageable, but a little carbohydrate—surprisingly little—can make you ravenous. Like other advice in this book, this observation is based upon experience. The counterpart of this canon is that when patients confess to deviating from my recommendations, when they overdo carbohydrates at the expense of protein, they report an uncomfortable degree of hunger that causes them to eat more calories than are allowed. When patients really complain that the diet doesn't satisfy hunger, it is often difficult for me to pry out of them honest information about what they've been eating. I must often probe relentlessly until I secure the admission that this person complaining of hunger has been eating bread or drinking orange juice or using enough breath mints to deodorize a regiment.
What I've reported aren't theoretical concepts that come from an institutionally sponsored study or from work on laboratory animals. This information is admittedly "anecdotal." But it does come from real people, thousands of them, earnestly seeking the help of their doctor.
# Breakfast
One of the more common problems with low-calorie diets is constipation. Without getting into the semantics involved, the complaint that I hear so often may not be constipation at all, but rather infrequent bowel movements. Let's get right to the issue. You will not have the same bowel movements when you're eating 1,000 calories a day as when you were eating 3,000 calories a day. There is simply not enough bulk and generally much less fiber for that to happen. The fact that your bowel movements often skip a day or two may not literally be constipation, but whatever name it is called, it is distressing to most dieters. I generally draw the line at what makes my patient physically uncomfortable. If this infrequency causes real physical discomfort, it is time for action. Of course, the best course of action is prevention.
What does breakfast have to do with it? For the most part, we're going to solve this troublesome problem at breakfast. Breakfast is going to be a cereal, and preferably one with a good amount of dietary fiber. That should essentially solve the problem of constipation. Choose the ½ cup (1 oz.) serving size of the one below or experiment with others. There is a simple way to boost the fiber content of any cereal and nullify the constipating effect of low-calorie eating: Add bran. A good choice comes in a jar. Add a heaping tablespoonful of Kretschmer Toasted Wheat Germ to your cereal. It will boost the calories by only about 15, but will add 3 grams of fiber.
If you choose cereals other than the one below, look for those that have 180 calories or less (without the milk) per 2-ounce serving. Use milk with it (2 percent fat is desirable), but there is no point in using more than you need, since it does have about 16 calories per ounce. Use just enough milk to wet the cereal. There is no need to slosh it on. Be aware of how many ounces of milk you have used. As a breakfast beverage, you may have a cup of coffee or tea, or if you're one of those addicts, a diet soda is acceptable. If you must lighten your coffee, use milk with 2 percent fat. Don't forget to count its calories into your day's total. I like the following best because of the low calories:
| **Calories per Ounce**
---|---
Kellogg's All-Bran with Extra Fiber| 54
# Lunch
The extent to which your lunch contributes to the day's 1,000 calories is a matter of personal preference. You will have a lot of leeway. It doesn't matter particularly whether lunch or dinner is the "main" meal. I even see a fair amount of patients who insist that they never have lunch. If you're comfortable with that, it's okay. It will necessarily allow you to have a bigger dinner, a requirement that should not be too distressing to you. My medical practice is now principally in South Florida, where there is a predominantly Latin influence. In most of the Latin countries, the midday meal is the main meal, and this diet could easily be varied to accommodate that as well as other cultural preferences. Again, the bottom line is 1,000 calories; when you eat them is less important.
# Dinner
The majority of readers will probably choose to have their main meal in the evening. As you would expect, the food choices that follow are designed to slant the diet in the direction of protein. Carbohydrates will generally be from those that are the more complex, and fat will be minimal. A little arithmetic will be required to add up the day's calories. You must come as close to 1,000 as possible. You could probably do quite well simply by using the calorie values specified in this chapter, but if you want to expand into foods that I haven't included, you will need the help of one of the better "calorie books." I have recommended some of these in Appendix G.
Frozen dinners are particularly convenient, and you may want to use them frequently. They may be eaten for lunch as well. Just keep track of the calories. The frozen dinners I've selected and which are listed later in this chapter are particularly desirable because of their distribution of nutrients. You may use others that aren't on the list, but try not to deviate too often. As a bonus for following my recommendations and availing yourself of the listed foods, I believe you will have the least problem with hunger.
# Snacks
I'm certainly not encouraging you to have snacks during the test. The typical snack that comes in those gloriously colorful bags is certainly not advised. Yet one positive purpose for a snack is to make up for not eating enough calories that day. If by evening your total for the day is 900 calories, you should supplement that day's intake with 100 calories of something. I'm not suggesting that you order a pizza. Choose something from the lists provided.
# Packaged Foods and Frozen Foods
I like frozen foods because they work for my patients. Busy people particularly like the convenience of the whole meal in a box. Once they understand what is available and which of them suits their tastes, they do well with these single meals in a box. They share the advantages of other packaged products in that you know exactly what you're getting in terms of calories. You don't need a calorie book. It's all there on the nutritional panel. I have listed some of the frozen foods I've evaluated. I didn't choose them from those mouthwatering pictures on the box or even from the taste; I haven't tasted many of them. The selection process had only to do with the nutritional information supplied to me by the manufacturer or that I copied directly from the nutritional panel on the package. Like my other food choices, you will note that the products listed have more protein and less fat for the amount of calories they supply than many other products that didn't make it onto my lists. Remember that all calorie counts in my frozen-meal lists are for one serving, an amount that is specified on the package. With most of these frozen dinners, a whole package constitutes a single serving.
There is considerable variation in the number of calories of the various frozen dinners I've chosen, but none is above 400 calories. You must take into account how each will fit in with your 1,000-calorie day. If you haven't had many calories by dinnertime, you should probably choose one that has a larger number of calories. You may even have to supplement your evening meal with something additional to reach the 1,000-calorie mark. This all takes planning, but it is worth the effort. You will acquire valuable information about yourself.
# The Food Tables and Recommendations
The information I'm providing for you comes from the best sources available. With packaged foods, I've contacted the manufacturers, and if they were cooperative, I've used their information. Some of the data comes directly from the actual packages on supermarket shelves in various parts of the country. Some has been provided by restaurant chains. Much of it comes from the government. The United States Department of Agriculture maintains an enormous database of the nutritional makeup of foods in this country. I've used the latest version of this database to make my calculations.
With fresh food, things like fruits, vegetables, meats, and poultry, items that are loose or packaged by the supermarket and which don't have nutritional information, I've provided the calories per ounce, ignoring what is a normal serving. You will decide on the serving size and therefore how many calories that number of ounces contains. With that information, you can be very precise in supplying as many calories as you need to contribute to the 1,000 for the day. You will need a food scale for the test, but you can dispense with it for your remaining time on the diet.
Remember that my recommendations are based upon my experience, particularly as it relates to hunger, but don't consider them that rigid. Rather than abandon the diet and the test, you could go outside my recommendations. In the end the test will still be valid if you've kept track of the calories. As an example, were you to use the higher-calorie non-dairy creamers in your coffee, keep track of the calories and you will still be okay. But remember, if you squander your calories on such things, you will have less to allocate to "real" food.
In keeping with my preferences, I've only included information on those foods I recommend. If you go outside my choices, and you may, you will have to obtain the information from the food package.
With packaged foods, you will find that I've included only the more recognizable brand names, those that are generally available throughout the country. There are many lesser-known brands, regional brands, and house brands of supermarkets that are just as good. If the nutritional panel on the package becomes a habit, you won't go wrong.
I have listed my choices by rather loosely chosen alphabetized categories.
# _Sample Daily Menus_
See Appendix I (pages 260-64).
# _Beef_
Your selection of beef is limited, but you may indeed have beef. Choose cuts that have 5 percent or less of fat. The government grades beef by the amount of fat it contains. Whether you agree or not, the fattest is considered the best; the highest grade is U.S. Prime. For that reason, Prime isn't advisable for this diet. The next two lesser grades are Choice and Select, which have respectively less fat. There are grades below Select with even less fat, but they are quite tough unless cooked to death. Remember that the calories per ounce given below are for raw beef and you should make your calculations from that value. After cooking you will have fewer ounces, mainly because of water loss, but the calories will be changed very little.
**Beef cut** | **Grade**
---|---
Beef, round, full cut | Choice
Beef, round, eye round | Choice
Beef, round, tip round | Choice
Beef, round, top round | Choice
Beef, shank, cross-cuts | Choice
Beef, chuck, arm pot roast | Select
Beef, round, full cut | Select
Beef, round, bottom round | Select
Beef, round, eye of round | Select
Beef, round, top round | Select
Beef, short loin, top loin | Select
Beef, top sirloin | Select
Beef, short loin, T-bone steak | Select
What is supplied here is the latest information from our government. The names of the cuts are taken from the government's database. The calories are counted with beef trimmed to _VA_ inch fat. You should eat the "separable lean only" part of the meat. The calories per ounce for each of the cuts above varies from 34 to 39, so you may make your calculations based upon a middle number of 37.
Ground beef deserves special mention. All of the prepackaged ground beef I've found in supermarkets contains too much fat. The lowest was marked extra-lean, but it still had 10 percent fat. If you must have ground beef, choose one of the acceptable cuts above and have the meat department grind it for you. That way it will satisfy the requirement.
_Example:_ If you need a 225-calorie meat portion for dinner, use 6 ounces. Six times 37 is 222. That's close enough.
# _Beverages_
I would like you to drink plenty of fluid, which really means water. Yet, in the end, whatever you drink is basically flavored water. Sometimes the "water" is combined with sugar and results in a lot of calories (juices, for example). For this test, let's forgo fruit juices and juice drinks even though they may be loaded with vitamins. Bubbly water such as seltzer and club soda are fine, but make sure the "seltzer" has no calories. I've seen flavored seltzers on the shelves that were high in calories. They were nothing more than the usual soda pop without the coloring agent. Bottled or canned soda pop should always be of the "diet" variety, and unless you have more than three a day, you don't need to count the calories.
There are some non-carbonated beverages you may wish to use. Crystal Light and sugar-free Kool-Aid each have 5 calories per 8-ounce glass.
Coffee and tea are also allowed. I've never observed caffeine to be a factor as far as weight loss is concerned. The problem arises with what you add to coffee or tea. Sugar should be out. Artificial sweeteners are allowed; they have virtually no calories. You should discipline yourself to add only low-fat milk with 2 percent fat to lighten coffee. Figure 15 calories per ounce, which is 2 tablespoonfuls. As to other "lighteners," they simply have too many calories, which you get at the expense of other good solid food. Given that you will have only 1,000 calories, you don't want to squander them. If you must, there are some fat-free non-dairy creamers with about 7 calories per ounce (2 tablespoonfuls). Their availability varies and is often regional. Check your supermarket, read the labels, and count the calories.
Regular unsweetened tea is fine, cold or hot, as are a number of "diet" teas. Lipton, for example, has several of them with 5 calories per 8-ounce glass. Don't forget to count those calories if you have three glasses or more per day.
# _Bread_
Save it till you're thin. It's all carbohydrate. Have faith—you will be able to eat bread again.
# _Butter and Margarine_
Of course not. All fat and way too many calories to waste. There are some pretty fair attempts at least to reproduce the flavor. I actually think the sprays are useful. Don't overdo them and you won't have to count their calories. Try these:
I Can't Believe It's Not Butter! Spray
Parkay Buttery Spray
There is also a spread, Fleischmann's fat-free 5-calorie spread, with that amount per tablespoonful.
# _Candies_
I really can't find any I could recommend. Watch out for the so-called sugar-free variety. They are free of sugar only through a technicality. They may be sweetened with concentrated fruit juice, which is really just another name for sugar. (Baked goods also.) The calories on the label tell the story. The candies with sorbitol could keep you closer to the bathroom than you care to be.
# _Cheese_
Most cheese is just too high in fat and therefore in calories for you even to consider it. There are some attempts to imitate the flavor of real cheeses, and you may experiment with them if you must. The label names can be very confusing, particularly because of the variety. Try to look for the names I've spelled out here and pay close attention to the nutritional panel on the package.
| **Calories per Ounce**
---|---
Kraft Free Singles American, Swiss, or Sharp Cheddar (1 slice) | 30
Polly-O Free Natural Non-Fat Ricotta (1/8 cup) | 25
Kraft Philadelphia Free Fat-Free Cream Cheese (several varieties) | 30
Breakstone's Free Fat-Free Cottage Cheese | 20
Light n' Lively Fat-Free Cottage Cheese | 20
# **Chicken, Canned**
There are a number of satisfactory varieties of lesser-known brands. On the label, the chicken should be listed at 60 calories per 2-ounce serving. Some have a few more calories than 30 per ounce. Try to stick to those with 30 per ounce. Here are some name brands:
| **Calories per Ounce**
---|---
Hormel Premium Chunk Breast of Chicken in Water | 30
Swanson Premium Chunk White Chicken in Water | 30
# **Crabmeat, Imitation**
This is also called surimi. It is fish made to resemble crabmeat and flavored to simulate it. There are other varieties that imitate lobster. There are a number of brands, and they all seem to have between 26 and 30 calories per ounce. Surimi has more carbohydrate than I like, but you might want to give it a try.
# **Deli Meats**
I recommend these because they are easy to come by and high in protein, just the thing for someone who is always on the run. I've eaten my share of them. In this instance, since the products are sliced, I specify the calories per slice as well as the calories per ounce. These types of products come in a variety of presentations and different-sized slices. Many more are acceptable than I've listed here. The following should give you a variety of choices.
**Fat-Free Cold Cuts** | **Calories per Slice** | **Calories per Ounce**
---|---|---
Louis Rich | |
Turkey Breast, Oven Roasted | 25 | 25
Turkey Breast, Hickory Smoked | 25 | 25
Oven Roasted Breast of Turkey | 25 | 25
Rotisserie Flavor Breast of Turkey | 25 | 25
Chicken Breast, Oven Roasted Deluxe | 30 | 30
Turkey Ham | 30 | 30
Turkey Pastrami | 30 | 30
Oscar Meyer | |
Ham, Baked Cooked | 23 | 31
Ham, Boiled | 20 | 27
Turkey, White, Oven Roasted | 30 | 30
Canadian-Style Bacon | 25 | 30
Hillshire Farm | |
Pastrami | 10 | 30
Honey Ham | 10 | 30
Hormel | |
Light & Lean 97 Sliced Ham | 25 | 25
Sliced Mesquite Smoked Turkey Breast | 30 | 30
# _Dressings_
Be careful here. The fine reputation that salads enjoy as diet food is unwarranted when the dressing has a zillion calories. Look for 30 calories or less per ounce, which is usually specified as 2 tablespoonfuls. Be careful. The calories can mount up with these. Here are a few salad dressings:
| **Calories per Ounce**
---|---
Weight Watchers |
Creamy Italian | 30
Caesar | 10
Italian | 10
Pritikin |
Dijon Balsamic Vinaigrette | 30
# _Mayonnaise_
The real stuff is out, but there are some pretty fair imitations. Remember that an ounce is about 2 tablespoonfuls. Try these:
| **Calories per Ounce**
---|---
Kraft Mayo Fat-Free |
Mayonnaise Dressing | 10
Weight Watchers Whipped Dressing | 15
Kraft Miracle Whip Free Dressing | 15
# _Eggs_
Unfortunately, whole eggs aren't acceptable because of the fat content of the yolk. By contrast, the white of the egg is about the highest-quality protein you can obtain, and it is virtually pure protein. A single egg white (from a large egg) adds about 18 calories. The difference in the calories in the egg white alone of eggs of different sizes is so minimal that you may ignore it and count 18 calories for any _egg._ You can do some creative things with _egg_ white; you can blend it into a number of foods, such as vegetables, and it enhances them, particularly if you use some spices.
The "imitation" egg products are also quite good. They are essentially egg whites flavored to simulate whole eggs, and they have no fat and very little carbohydrate. I've listed some of the more popular brands. Don't forget to pay attention to the calories and include them in your daily total. Usually 2 ounces approximates one large egg.
| **Calories per Ounce**
---|---
Second Nature Fat-Free | 13
Table Ready Real Egg | 15
All Whites | 13
Better 'n Eggs | 14
Egg Beaters | 15
# _Fish and Seafood_
This category is perhaps the best "diet" food. It is high in protein and generally very low in carbohydrate. However, some varieties of fish (though not shellfish) are quite high in fat. Salmon is an example of an unacceptable fish for our purposes.
There are many choices of fish, and their availability may depend upon where you live. I've never even heard of some of the fish in the acceptable list I've compiled, but I've done my homework and I've given you the data. There may be some confusion inherent in the names of various fish. Striped bass is acceptable, but freshwater bass is not. Bluefin tuna has too much fat, but all the other varieties of tuna are just fine, including the canned variety (packed in water).
Virtually all shellfish may be eaten: crab, lobster, shrimp, clams, mussels, conch, etc. The trick is to know what quantity you will be eating. If you buy raw oysters or clams in the shell, you will need to weigh the edible portion while it is raw. This task could be more than you bargained for. Since there are so many other fish and seafood choices, you may choose to postpone the pleasure of eating some of these until after the test diet.
The list of fish I've provided is quite long. There are simply so many choices when it comes to fish. I've actually shortened the list to include only those with the least amount of fat per ounce. There should be enough choices here to satisfy your needs, yet if you have a yen for a particular fish, look it up in a calorie book. It will probably have more calories per ounce than those listed here, but that simply means you will eat a slightly smaller amount of it. An example is shrimp with 30 calories per ounce. If you would like to have 6 ounces of shrimp (180 calories) for dinner, I'm sure you can make it fit in.
If the fish is purchased fresh, you will need to know the weight of the portion you will be eating in order to calculate the calories. In the case of fish and seafood, I've given you the calorie count per ounce, raw, to make it easy to calculate. If you buy frozen fish, which has nutritional labeling, you can read the number of ounces and the calories directly from the label.
See also "Tuna, Canned" as a separate category in this chapter.
**Fish and Seafood (22 calories per ounce)**
Cod, Atlantic and Pacific
Crayfish
Monkfish
Pollock, walleye
Pout, ocean
Roughy, orange
**Fish and Seafood (26 calories per ounce)**
Bass, striped
Catfish, channel, wild
Cisco
Crab, Alaska king
Crab, blue
Crab, Dungeness
Crab, queen
Cusk
Dolphinfish
Flatfish (flounder and sole species)
Grouper, mixed species
Haddock
Ling
Lingcod
Lobster, northern
Ocean perch, Atlantic
Perch, mixed species
Pike, northern
Pike, walleye
Pollock, Atlantic
Rockfish, Pacific, mixed species
Sea bass, mixed species
Sucker, white
Sunfish, pumpkin seed
Tilefish
Turbot, European
Whiting, mixed species
Wolffish, Atlantic
# _Frozen Meals_
This could very well be the best category for a busy person. You simply pop the meal in the microwave and in a few minutes it is ready. I've selected a relatively small number from those available in the supermarket. The selection was based on a careful evaluation of such values as the protein content, the fat content, and the total calories. Remember, these aren't the only frozen foods you may eat, but these are the ones I recommend. As long as you count the total calories and keep track of them, the test will be valid. For maximum hunger control while doing the test, follow my preferences. I've investigated the nutritional content of the most well-known brands. In most cases I had the cooperation of the manufacturers. Bear in mind that the calories provided below are for the entire meal.
**HEALTHY CHOICE**
**Category** | **Product Label** | **Calories**
---|---|---
Entrée | Swedish Meatballs | 280
Entrée | Breaded Chicken Breast Strips | 270
Entrée | Chicken & Vegetables Marsala | 240
Entrée | Chicken Fettucini Alfredo | 280
Entrée | Fiesta Chicken Fajitas | 260
Entrée | Grilled Chicken Sonoma | 230
Entrée | Grilled Chicken w/Mashed Potatoes | 170
Entrée | Homestyle Chicken and Pasta | 270
Entrée | Country Roast Turkey w/Mushrooms | 230
Meal | Beef & Peppers Cantonese | 280
Meal | Traditional Beef Tips | 260
Meal | Chicken Broccoli Alfredo | 300
Meal | Chicken Cantonese | 280
Meal | Chicken Dijon | 270
Meal | Roasted Chicken | 230
Meal | Southwestern Grilled Chicken | 260
Meal | Country Inn Roast Turkey | 250
Meal | Traditional Breast of Turkey | 290
Bowl Creations | Roasted Potatoes with Ham | 200
**STOUFFER'S LEAN CUISINE ENTRéES**
**Category** | **Product Label** | **Calories**
---|---|---
American Favorites | Baked Chicken | 230
American Favorites | Salisbury Steak | 280
Café Classics | Chicken a l'Orange | 260
Café Classics | Chicken and Vegetables | 270
Café Classics | Chicken in Peanut Sauce | 290
Café Classics | Glazed Chicken | 240
Café Classics | Herb Roasted Chicken | 250
Entrée | Cheese Cannelloni | 230
Entrée | Chicken Fettucini | 300
Entrée | Homestyle Turkey | 230
Hearty Portions | Salisbury Steak | 380
Hearty Portions | Grilled Chicken and Penne Pasta | 380
Hearty Portions | Oriental Glazed Chicken | 350
Hearty Portions | Roasted Chicken with Mushrooms | 340
**WEIGHT WATCHERS**
**Product Label** | **Calories**
---|---
Chicken Fettucini | 300
Slow-Roasted Turkey Breast | 220
Chicken Carbonara | 300
Penne Pollo | 290
Pepper Steak | 240
Traditional Lasagna with Meat Sauce | 300
Grilled Salisbury Steak and Gravy | 290
# _Fruit, Canned_
This is a little easier than fresh since the weights are specified and there is no debris.
| **Calories per Ounce**
---|---
Apple sauce, unsweetened | 13
Apricots, water pack | 8
Cherries, sweet, water pack | 14
Grapefruit, sections, canned | 11
Peaches, water pack | 7
Pears, water pack | 9
Pineapple, water pack | 10
Tangerines (mandarin oranges) | 11
# _Fruit, Fresh_
If you must have fresh fruit, stick to fruits with lower calories, which means those with the least carbohydrate. It is difficult to calculate the exact calories with fruit, because in many cases you don't eat the entire fruit (the apple core, pits, seeds, etc.). There is also a lot of variation in the calorie count of fruits from different regions. California grapefruit can have a lot more calories than the Florida variety. How would you calculate the amount of grapefruit you ate? It's difficult. Try to postpone the fresh fruit till after the test.
# _Fruit, Frozen_
Frozen fruit may be regarded similarly to fresh. There is the advantage that because it is packaged, the weight of the contents and the calorie count are specified on the label, and there is generally no debris to subtract. Stay with the lower-calorie varieties, the unsweetened ones. Here are a few:
| **Calories per Ounce**
---|---
Apples | 15
Blueberries | 16
Boysenberries | 15
Cherries | 14
Melon balls | 11
Strawberries | 11
# _Gelatin Desserts_
If you must have dessert, these are probably the best choices. Both Jell-O and Royal have sugar-free varieties. If you make them according to the directions, a ½ cup serving has 10 calories. Jell-O also has ready-to-eat refrigerated portions with 10 calories per little cup.
# _Grains_
You should forgo grains during the test because they are too high in carbohydrate. If you must have them, try to count the calories accurately.
# _Ketchup_
Use a small amount but count it—15 calories per tablespoonful.
# _Mustard_
Mustard is so low in calories that you do not have to count it if you only use a teaspoonful or two.
# _Nuts and Seeds_
Can't you do without these high-fat, high-calorie foods for four weeks?
# _Pickles_
Pickles have always been viewed as the ideal diet snack and they probably deserve the reputation. They are quite low in calories and some of the brands on the shelves indicate "0" calories per serving. Of course that is not quite true; a technicality allows them that license. The FDA permits food producers to round down anything that contains less than 5 calories per serving to zero. You may regard them as a zero-calorie food and not count them in your daily total.
# _Pork_
It may be a surprise that some selected cuts of pork are acceptable. Weigh the separable lean portions only. You can assume an average of 37 calories per ounce:
Pork, fresh, loin, tenderloin, raw
Pork, fresh, loin, sirloin (chops or roasts), boneless, raw
Pork, cured, ham, steak, boneless, extra-lean, unheated
Pork, cured, ham, extra-lean (approximately 4 percent fat),
canned, unheated
Pork, cured, ham, extra-lean (approximately 4 percent fat),
canned, roasted
# _Poultry_
Chicken and turkey are good choices for this diet. There is surprisingly little difference between the calories per ounce of chicken and turkey and the various cuts, dark or light, of each. Calculate the calories of the raw meat at 32 calories per ounce. Of course no skin or fat should be included.
# _Soups_
Obviously we're speaking of canned or other packaged soups. It would be almost impossible to calculate the calories in homemade soup. Soup is far from my first choice for the test diet. It's essentially a carbohydrate food and sometimes has considerable fat. Soup is in the category of things you may choose to have on infrequent occasions. Just remember to note the calories on the package. Soup made from bouillon cubes or powder is acceptable because it is so low in calories.
# _Spices, Seasonings, Sauces_
In general you may use dry spices to flavor your foods. Some of them have considerable calories per ounce, but what makes them acceptable is the fact that you use so little of them that the amount doesn't even have to be counted. For example, black pepper has 93 calories per ounce, but I doubt that you would ever use enough to give you even 5 calories. In general the seeds that are used as spices, such as celery seed, poppy seed, and caraway seeds, are very high in calories because of their fat content, but if you use them sparingly, you won't have to count them.
Sauces for which only drops are necessary, such as hot sauces, needn't be counted. Some Worcestershire sauces proclaim zero calories, but actually have closer to 5 per teaspoonful. Two teaspoonfuls don't have to be counted.
# _Tuna, Canned_
I have included this as a separate category from "Fish and Seafood" because it is such a popular diet food and it deserves special attention. By now you know that tuna comes packed in water as well as oil, and here I will address only the water-packed variety.
You probably aren't aware of how many different names are used on the labels to describe tuna. "Chunk," "light," "white," "solid," "fillets," "premium," and even others create confusion. Three major brands, Bumble Bee, Starkist, and Chicken of the Sea, all offer satisfactory tunas that contain 60 calories for a 2-ounce serving (¼ cup). That's 30 calories per ounce. Others have more calories. Look for the "60" on the label.
It's not tuna, but a nice variation could be canned Bumble Bee Fancy White Crabmeat with 30 calories per 2-ounce serving.
# _Vegetables_
Vegetables are chosen for their low calorie and low carbohydrate content. Although the selection is somewhat limited, you should be able to manage. If you will be using fresh vegetables, raw or cooked, a food scale is essential so that you can keep an accurate count. It is easier with canned or frozen vegetables, since the package tells you the quantity. Vegetables such as peas may be eaten, but they have a bit more carbohydrate. Regardless of which you choose, if you keep track of the calories, your calculations will come out well.
**Vegetables, Raw** | **Calories per Ounce**
---|---
Asparagus | 8
Beans, kidney | 11
Carrots | 13
Celery | 5
Cucumber, peeled | 4
Lettuce, iceberg | 4
Lettuce, romaine | 5
Mushrooms | 9
Onions | 11
Peas | 24
Radishes | 6
Spinach | 8
Squash, summer | 6
Squash, zucchini | 5
Tomatoes | 7
**Vegetables, Cooked (Drained)** | **Calories per Ounce**
---|---
Asparagus | 9
Beans, kidney | 13
Carrots | 13
Cauliflower, cooked | 8
Celery | 6
Peas | 24
Spinach | 8
Squash, summer | 5
Squash, zucchini | 6
**Vegetables, Canned (Drained)** | **Calories per Ounce**
---|---
Asparagus | 7
Beans, snap | 5
Carrots | 7
Mushrooms | 9
Hearts of palm | 10
Peas | 20
**Vegetables, Frozen (Drained)** | **Calories per Ounce**
---|---
Asparagus, raw | 9
Asparagus, cooked | 10
Broccoli, raw | 9
Carrots, raw | 12
Carrots, cooked | 11
Cauliflower, raw | 8
Cauliflower, cooked | 7
Peas, raw or cooked | 23
Squash, zucchini | 6
# _Vinegar_
The ordinary varieties have virtually no calories and may be used. The fancier flavored types such as balsamic, which is currently "in," may have from 10 to 40 calories per ounce. Check the label.
# Eating Out
The hardest time for keeping track of your calories will be when eating in restaurants. Most restaurants don't supply nutritional information on their foods. By contrast, the most popular fast-food chains do, but they don't generally break down such things as a hamburger sandwich. I've listed the items that are acceptable from some of the fast-food franchises. Remember, if the restaurant posts the calorie count of their super-duper hamburger sandwich, their numbers include the bun, the tomato, the mustard, and everything else. If you eat only the meat and the lettuce, you will have to estimate the calories. Here is where some of the calorie books can really come in handy. Some of them contain data for popular restaurants. Don't neglect keeping track of your calories when you're away from home.
# Fast Food
There aren't too many choices in this category. Most fast food is too high in fat or too low in protein. To give you an idea, of the popular hamburgers, Burger King and McDonald's regular hamburgers are listed at 320 calories. Wendy's lists their ¼ pound single burger at 360 with nothing on it, 420 with everything, but the meat patty alone is 200. Its fat content is about 7 percent, a bit high for my kind of diet. Here are some acceptable items:
**KFC**
**Category** | **Item** | **Calories per Serving**
---|---|---
Original Recipe | Breast with skin removed | 129
Tender Roast | Breast with skin removed | 169
Note: The information supplied by KFC indicates that the Tender Roast breast meat is a larger portion.
**BOSTON MARKET**
**Item** | **Calories per Serving**
---|---
¼ White Meat Chicken without skin or wing | 170
Skinless Rotisserie Turkey Breast | 170
Chicken Noodle Soup | 130
Steamed Vegetables | 35
Fruit Salad | 70
# Vitamins and Minerals
Because of the broad leeway in the choice of foods, it is impossible to be sure that nutritional needs are being met in terms of vitamins and minerals. It is therefore prudent to play it safe by taking daily vitamin-mineral supplements.
There are many satisfactory products on the market. The few suggested below simply represent the type of formula you should be selecting.
Unless you have some specific vitamin deficiency, use the following as a checklist of the minimum amounts the vitamin and mineral supplement should contain:
Vitamin A | 5000 I.U.
---|---
Vitamin B1(Thiamine) | 1.2 mg.
Vitamin B6(Pyridoxine) | 1.5 mg.
Vitamin B12 | 2.4 meg.
Vitamin C | 90 mg.
Vitamin E | 30 LU.
Vitamin K | 80 mg.
Vitamin D | 15 meg.
Vitamin B2(Riboflavin) | 1.3 mg.
Niacin | 15 mg.
Folic acid | 400 meg.
Pantothenic acid | 5 mg.
Biotin | 30 mg.
Choline | 550 mg.
Iron | 15 mg.
Zinc | 15 mg.
Iodine | 150 mg.
Selenium | 70 mg.
Calcium | 1300 mg.
Phosphorus | 1250 mg.
Magnesium | 410 mg.
If you are already taking a satisfactory combination of vitamins and minerals, there may be no reason to change.
The following are among those that are satisfactory:
Walgreen's
Lederle
Bayer Consumer
Bristol Myers
Therapeutic M
Centrum
One-A-Day Maximum
Theragran-M
It would be a good idea to supplement formulas such as those above with two extra tablets of a calcium/magnesium (500 mg. calcium each) mixture and an extra vitamin C tablet.
# Keeping Seore
Of course, you're going to try to come as close as possible to 1,000 calories a day. I'm certain that on many days you will deviate by a few calories. There may be other times when you really overdo it. All isn't lost if that happens. What is necessary is for you to know the extent of the variation and to make a note of it. When the twenty-eight days are over, you will have the opportunity to correct the calculations to encompass these variations, but you will need to know exactly what they are. Keep an Excess Calorie Sheet for that purpose.
As an example, if on a particular day your total calories added up to 920, you should make a note on your Excess Calorie Sheet that you were 80 calories under your requirement. You will need to keep a running total of these variations so that at the end of the twenty-eight days you know how many fewer or extra calories you ate during that entire period. I suspect that at the end you will be over rather than under the amount. Remember, don't keep track of the total calories you consumed, only the amounts that were over or under the 1,000.
Here is one more plea for accuracy. There is no point in going through a twenty-eight-day exercise if you won't be able to rely on the outcome. You will lose weight even if you stray somewhat, but we're hoping to get more than weight loss out of these four weeks. During that period you must try to be as precise as possible. After the test is over, if you still have more weight to lose, you may remain on the same diet, but accuracy will not be all that important. A few calories more or less per day may affect the speed of that future weight loss to an extent, but you will have already obtained the information you need.
To repeat, if you stick to packaged foods, it is easier to keep score. Just add up the calories given to you on the package. If you buy "fresh" food, it will require more effort and you will need a food scale, an item that is easily obtainable. Remember to weigh only the portion of the food you will eat. Of course, this means you don't include the bones from meat, what you peel from fruits and vegetables, or what you've left on your plate. If you've weighed a quantity of food and have calculated the calories from the number of ounces but you don't eat it all, you can still calculate the right amount. Weigh the portion you haven't eaten and subtract it. Remember, you're a researcher now performing a very important scientific experiment, and research must be meticulous.
For a sample of daily menus, see Appendix I.
# Summing Up
* Appreciate the importance of this exercise. You're collecting valuable information.
* Eat as close to 1,000 calories a day as possible.
* If you deviate from that amount, keep track on an Excess Calorie Sheet of how many more or less calories you've eaten each day.
* For maximum hunger control, try to stick to my food-choice recommendations.
* Follow the diet for exactly twenty-eight days.
#
# _Evaluating Your Metabolism_
**Y** our strict diet is over. Well, maybe not quite. It depends on whether you have reached your proper weight, and in most cases you will not have. Now we're going to find out if your metabolism is as it should be. If it is not, I will tell you how to proceed to lose the rest of your excess weight. If it turns out that your thyroid is working just fine but you still need to lose more weight, I will address that in short order. Let's forget about your diet for a moment and get to the task of calculating your metabolic function index (MFI). I presume it is early in the morning of the day after Day Twenty-eight.
Don't read the rest of this chapter until you've completed the twenty-eight-day diet. If you're impatient and insist on reading on, make sure you reread this when you've completed the diet.
You will be working with the MFI Calculation Form shown on page 161. I won't mind if you slap that page down on a copy machine and copy it and then work from the copy.
**MFI Calculation Form**
---
Metabolic Function Index
**(1) Day 1 Date_______Weight (nude)** (Early morning) |
**(2) Day 29 Date_______Weight (nude)** (Early morning) |
**(3) 28-day weight loss**
Subtract line (2) from line (1). |
**(4) UCML (Uncorrected Caloric Maintenance Level)**
From the UCML Table on page 164. |
**(5) EC (Total Excess Calories for the 28 Days)**
From your own list of excess calories for the entire 28 days. |
**(6) CCML (Corrected Caloric Maintenance Level)**
See the Excess Calories Table on page 165. |
**(7) BBW (Baseline Body Weight)**
See BBW Table on page 166. |
**(8) SCML (Standard Caloric Maintenance Level)**
See the proper SCML Table for your sex, age group, and activity level on pages 168–. Use the BBW in (7) above to determine your SCML. |
**(9) Metabolic Function Index (MFI)**
Divide line (6) by line (8). Move the decimal point 2 digits to the right. |
# Necessary Information
There are a few things you will need to know to make the calculations. One of them is your height in inches. For example: If you're 5 feet 10 inches, you're 70 inches tall.
You will need to decide on your activity level. It will be inactive, moderate, or active. Some examples follow. If you sit at a desk most of the day or you do light housework with no exercise program, you should probably classify yourself as inactive. If you exercise 3 or 4 times a week for about 45 minutes or if your job has you constantly moving and on your feet, you could be in the moderate class. Anything beyond that, such as tennis several times a week, a regular gym workout or jogging, sports activities, etc., probably classifies you as active. I'll elaborate on this just ahead.
When considering such subjects as ideal or normal weight, it is customary to classify individuals by the size of their body "frames." Generally, the classification refers to small, medium, and large frames.
I have found that most people can identify their frame size from their own observations. Anyone who knows you can make an equally authoritative guess. Although it isn't difficult for any of us to judge someone's frame size by our own experience, it is desirable to have some objective standard upon which to rely. One such standard involves taking a measurement across the elbow. The distance between the bony protrusions on the two sides of the elbow are measured. To learn how to do this, go to Appendix D.
# The MFI Calculation Form
**(1) Day 1:** You have already filled in the date when you started the diet and your weight on Day 1.
**(2) Day 29:** Now you must fill in your weight on the morning following the twenty-eight-day diet. Next to "Day 29," write in your current weight. If you used your "nude" weight on Day 1, this should also be the nude weight. The same conditions should prevail in terms of eating, drinking, using the bathroom, etc. If the weight on Day 1 was taken as soon as you emerged from sleep, after going to the bathroom, and before eating or drinking anything, do exactly the same thing now.
**(3) 28-Day Weight Loss:** Subtract the second weight from the first weight. Write in the result in the box marked "28-Day Weight Loss."
# _Calculating the Caloric Maintenance Levels_
**(4) UCML (Uncorrected Caloric Maintenance Level):** You're now going to find out your actual caloric maintenance level, which was determined over the twenty-eight-day period. Look on the UCML Table that follows on page 164. UCML stands for uncorrected caloric maintenance level. Find your twenty-eight-day weight loss in the left-hand column. The numbers in the column to the right are the corresponding UCMLs for each weight loss. Write in the UCML on the MFI Calculation Form. This figure represents the number of calories per day it takes to maintain your weight, the number that would have resulted in no weight loss or weight gain over the twenty-eight-day period if you had eaten an average of exactly 1,000 calories per day. Of course, you have kept an Excess Calorie Sheet, and we're going to correct for that next.
**(5) EC (Total Excess Calories for the 28 Days):** If you deviated from the diet on a few occasions and you've kept an Excess Calorie Sheet, total the number of excess calories you consumed for the entire twenty-eight days. If the number is less than 1,400 you may ignore it, but if it is over, mark it in the "EC" box.
**(6) CCML (Corrected Caloric Maintenance Level):** Consult the Excess Calories Table. Locate your total weight loss in the left column. Choose the nearest excess-calorie total across the top of
**UCML TABLE**
Uncorrected Caloric Maintenance Level
**28-DAY WEIGHT LOSS
IN POUNDS** | **UCML**
---|---
1 | 1125
2 | 1250
3 | 1375
4 | 1500
5 | 1625
6 | 1750
7 | 1875
8 | 2000
9 | 2125
10 | 2250
11 | 2375
12 | 2500
13 | 2625
14 | 2750
15 | 2875
16 | 3000
17 | 3125
18 | 3250
19 | 3375
20 | 3500
21 | 3625
22 | 3750
23 | 3875
24 | 4000
25 | 4125
_**Example:** If you've lost 5 pounds during the twenty-eight-day diet, your UCML is 1,625 calories._
the table. Where the two intersect is your CCML (your corrected caloric maintenance level). Write the CCML in the box on the MFI Calculation Form. If your EC was 1,400 or less, it can be ignored, and your CCML will then be the same as your UCML.
**EXCESS CALORIES TABLE**
Corrected Caloric Maintenance Level
**EC (Excess Calories)**
---
**28-day weight loss** | **0** | **1500** | **2000** | **2500** | **3000** | **3500** | **4000** | **4500** | **5000** | **5500**
1 | 1125 | 1179 | 1196 | 1214 | 1232 | 1250 | 1268 | 1286 | 1304 | 1321
2 | 1250 | 1304 | 1321 | 1339 | 1357 | 1375 | 1393 | 1411 | 1429 | 1446
3 | 1375 | 1429 | 1446 | 1464 | 1482 | 1500 | 1518 | 1536 | 1554 | 1571
4 | 1500 | 1554 | 1571 | 1589 | 1607 | 1625 | 1643 | 1661 | 1679 | 1696
5 | 1625 | 1679 | 1696 | 1714 | 1732 | 1750 | 1768 | 1786 | 1804 | 1821
6 | 1750 | 1804 | 1821 | 1839 | 1857 | 1875 | 1893 | 1911 | 1929 | 1946
7 | 1875 | 1929 | 1946 | 1964 | 1982 | 2000 | 2018 | 2036 | 2054 | 2071
8 | 2000 | 2054 | 2071 | 2089 | 2107 | 2125 | 2143 | 2161 | 2179 | 2196
9 | 2125 | 2179 | 2196 | 2214 | 2232 | 2250 | 2268 | 2286 | 2304 | 2321
10 | 2250 | 2304 | 2321 | 2339 | 2357 | 2375 | 2393 | 2411 | 2429 | 2446
11 | 2375 | 2429 | 2446 | 2464 | 2482 | 2500 | 2518 | 2536 | 2554 | 2571
12 | 2500 | 2554 | 2571 | 2589 | 2607 | 2625 | 2643 | 2661 | 2679 | 2696
13 | 2625 | 2679 | 2696 | 2714 | 2732 | 2750 | 2768 | 2786 | 2804 | 2821
14 | 2750 | 2804 | 2821 | 2839 | 2857 | 2875 | 2893 | 2911 | 2929 | 2946
15 | 2875 | 2929 | 2946 | 2964 | 2982 | 3000 | 3018 | 3036 | 3054 | 3071
16 | 3000 | 3054 | 3071 | 3089 | 3107 | 3125 | 3143 | 3161 | 3179 | 3196
17 | 3125 | 3179 | 3196 | 3214 | 3232 | 3250 | 3268 | 3286 | 3304 | 3321
18 | 3250 | 3304 | 3321 | 3339 | 3357 | 3375 | 3393 | 3411 | 3429 | 3446
19 | 3375 | 3429 | 3446 | 3464 | 3482 | 3500 | 3518 | 3536 | 3554 | 3571
20 | 3500 | 3554 | 3571 | 3589 | 3607 | 3625 | 3643 | 3661 | 3679 | 3696
21 | 3625 | 3679 | 3696 | 3714 | 3732 | 3750 | 3768 | 3786 | 3804 | 3821
22 | 3750 | 3804 | 3821 | 3839 | 3857 | 3875 | 3893 | 3911 | 3929 | 3946
23 | 3875 | 3929 | 3946 | 3964 | 3982 | 4000 | 4018 | 4036 | 4054 | 4071
24 | 4000 | 4054 | 4071 | 4089 | 4107 | 4125 | 4143 | 4161 | 4179 | 4196
25 | 4125 | 4179 | 4196 | 4214 | 4232 | 4250 | 4268 | 4286 | 4304 | 4321
_**Example:** If your total weight loss was 5 pounds and you ate an excess of 3,400 calories over the 28-day period, your CCML is 1,750._
**(7)BBW (Baseline Body Weight):** You're now going to find out how many calories a day are needed to maintain weight by a "model" person with your same characteristics. You will need to know the baseline body weight (BBW) for a person of your gender, your height, and your frame size. You will find that weight in the BBW Table that follows. Remember that height is expressed in inches. Find your height in the left column and note the weight that corresponds to your frame size in the columns to the right. Write this in the " **BBW** " box on the **MFI** Calculation Form.
**BBW TABLE**
Baseline Body Weight
**MEN** | **WOMEN**
---|---
**Height** | **SMALL FRAME** | **MEDIUM FRAME** | **LARGE FRAME** | **Height** | **SMALL FRAME** | **MEDIUM FRAME** | **LARGE FRAME**
62 | 117 | 127 | 136 | 58 | 97 | 106 | 115
63 | 120 | 130 | 140 | 59 | 99 | 108 | 117
64 | 123 | 133 | 143 | 60 | 101 | 111 | 120
65 | 126 | 137 | 147 | 61 | 104 | 114 | 123
66 | 129 | 140 | 151 | 62 | 107 | 117 | 126
67 | 134 | 145 | 156 | 63 | 110 | 120 | 130
68 | 138 | 149 | 160 | 64 | 113 | 123 | 133
69 | 142 | 153 | 164 | 65 | 116 | 127 | 137
70 | 146 | 157 | 168 | 66 | 119 | 130 | 141
71 | 150 | 162 | 173 | 67 | 123 | 134 | 145
72 | 154 | 166 | 178 | 68 | 127 | 138 | 149
73 | 158 | 171 | 183 | 69 | 131 | 142 | 153
74 | 162 | 175 | 188 | 70 | 136 | 147 | 158
75 | 167 | 180 | 193 | 71 | 140 | 151 | 162
76 | 171 | 184 | 197 | 72 | 144 | 156 | 167
_**Example:** Convert your height to inches. If you're a 5-foot-4-inch female, use 64 inches. If you have a medium frame, the BBW is 123._
**(8) SCML (Standard Caloric Maintenance Level)** : There is a group of tables on pages 168– labeled standard caloric maintenance level (SCML). These will tell you how many calories would be required to maintain your proper weight if your metabolism were within normal limits. The multiple SCML tables are geared to your sex, your age, and your activity level. There are three activity levels: sedentary (inactive), moderately active, and active. To help you decide which table applies to you, the following examples may be helpful.
**Sedentary:** You spend most of the day sitting, occasionally walking for a few minutes at a time. You have no exercise program or at best you exercise an hour or so a week. Examples: secretary, taxi driver, typical desk job.
**Moderately Active:** You're on your feet most of the day and you do considerable walking. You have an exercise program two to three times a week. Examples: store clerk, nurse, physician, appliance repairman, mail carrier. "Moderately active" can also include someone with a sedentary occupation who exercises three to four times a week or participates in something like swimming or tennis three to four times a week.
**Active:** Laborer, tile-setter, auto mechanic, furniture mover, in other words a job with no sitting and constant movement all day. Also someone with a more sedentary job who puts in at least an hour of heavy exercise like jogging almost every day might just make it into this category.
Go to the SCML table that is specific for your sex, age group, and activity level. There are twelve different tables for women and the same for men. _Be sure you're using the right table for your age, sex, and activity level._ In the left column find the BBW that is closest to the BBW you've just determined. To the right is the SCML value to be recorded in the box on the MFI Calculation Form. This represents the number of calories that would be needed to maintain your weight if you had a normal metabolism.
**SCML TABLE FOR WOMEN**
Standard Caloric Maintenance Level
**SEDENTARY
AGE 16-18** | **MODERATELY
ACTIVE AGE 16-18** | **ACTIVE
AGE 16-18**
---|---|---
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1821 | 100 | 2081 | 100 | 2601
110 | 1898 | 110 | 2170 | 110 | 2712
120 | 1976 | 120 | 2258 | 120 | 2823
130 | 2054 | 130 | 2347 | 130 | 2934
140 | 2131 | 140 | 2436 | 140 | 3045
150 | 2209 | 150 | 2525 | 150 | 3156
160 | 2287 | 160 | 2613 | 160 | 3267
170 | 2364 | 170 | 2702 | 170 | 3377
180 | 2442 | 180 | 2791 | 180 | 3488
**SEDENTARY
AGE 19-30** | **MODERATELY
ACTIVE AGE 19-30** | **ACTIVE
AGE 19-30**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1630 | 100 | 1863 | 100 | 2328
110 | 1723 | 110 | 1970 | 110 | 2462
120 | 1817 | 120 | 2077 | 120 | 2596
130 | 1910 | 130 | 2183 | 130 | 2729
140 | 2004 | 140 | 2290 | 140 | 2863
150 | 2098 | 150 | 2397 | 150 | 2997
160 | 2191 | 160 | 2504 | 160 | 3130
170 | 2285 | 170 | 2611 | 170 | 3264
180 | 2378 | 180 | 2718 | 180 | 3397
**SEDENTARY
AGE 31-60** | **MODERATELY ACTIVE
AGE 31-60** | **ACTIVE
AGE 31-60**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1714 | 100 | 1959 | 100 | 2449
110 | 1770 | 110 | 2022 | 110 | 2528
120 | 1825 | 120 | 2086 | 120 | 2607
130 | 1880 | 130 | 2149 | 130 | 2686
140 | 1936 | 140 | 2212 | 140 | 2765
150 | 1991 | 150 | 2275 | 150 | 2844
160 | 2046 | 160 | 2339 | 160 | 2923
170 | 2102 | 170 | 2402 | 170 | 3003
180 | 2157 | 180 | 2465 | 180 | 3082
**SEDENTARY
AGE over 60** | **MODERATELY ACTIVE
AGE over 60** | **ACTIVE
AGE over 60**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1503 | 100 | 1717 | 100 | 2147
110 | 1569 | 110 | 1794 | 110 | 2242
120 | 1636 | 120 | 1870 | 120 | 2337
130 | 1703 | 130 | 1946 | 130 | 2433
140 | 1770 | 140 | 2023 | 140 | 2528
150 | 1837 | 150 | 2099 | 150 | 2624
160 | 1903 | 160 | 2175 | 160 | 2719
170 | 1970 | 170 | 2252 | 170 | 2815
180 | 2037 | 180 | 2328 | 180 | 2910
**SCML TABLE FOR MEN**
Standard Caloric Maintenance Level
**SEDENTARY
AGE 16-18** | **MODERATELY ACTIVE
AGE 16-18** | **ACTIVE
AGE 16-18**
---|---|---
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 2025 | 100 | 2459 | 100 | 3182
110 | 2136 | 110 | 2594 | 110 | 3357
120 | 2248 | 120 | 2729 | 120 | 3532
130 | 2359 | 130 | 2865 | 130 | 3707
140 | 2470 | 140 | 3000 | 140 | 3882
150 | 2582 | 150 | 3135 | 150 | 4057
160 | 2693 | 160 | 3270 | 160 | 4232
170 | 2805 | 170 | 3406 | 170 | 4407
180 | 2916 | 180 | 3541 | 180 | 4582
190 | 3027 | 190 | 3676 | 190 | 4757
200 | 3139 | 200 | 3811 | 200 | 4932
210 | 3250 | 210 | 3946 | 210 | 5107
220 | 3361 | 220 | 4082 | 220 | 5282
**SEDENTARY
AGE 19-30** | **MODERATELY ACTIVE
AGE 19-30** | **ACTIVE
AGE 19-30**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1924 | 100 | 2337 | 100 | 3024
110 | 2022 | 110 | 2455 | 110 | 3177
120 | 2119 | 120 | 2573 | 120 | 3330
130 | 2216 | 130 | 2691 | 130 | 3483
140 | 2314 | 140 | 2809 | 140 | 3636
150 | 2411 | 150 | 2928 | 150 | 3789
160 | 2508 | 160 | 3046 | 160 | 3942
170 | 2606 | 170 | 3164 | 170 | 4095
180 | 2703 | 180 | 3282 | 180 | 4248
190 | 2801 | 190 | 3401 | 190 | 4401
200 | 2898 | 200 | 3519 | 200 | 4554
210 | 2995 | 210 | 3637 | 210 | 4707
220 | 3093 | 220 | 3755 | 220 | 4860
**SEDENTARY
AGE 31-60** | **MODERATELY ACTIVE
AGE 31-60** | **ACTIVE
AGE 31-60**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1969 | 100 | 2391 | 100 | 3094
110 | 2043 | 110 | 2480 | 110 | 3210
120 | 2116 | 120 | 2570 | 120 | 3326
130 | 2190 | 130 | 2660 | 130 | 3442
140 | 2264 | 140 | 2749 | 140 | 3558
150 | 2338 | 150 | 2839 | 150 | 3674
160 | 2412 | 160 | 2928 | 160 | 3790
170 | 2486 | 170 | 3018 | 170 | 3906
180 | 2559 | 180 | 3108 | 180 | 4022
190 | 2633 | 190 | 3197 | 190 | 4138
200 | 2707 | 200 | 3287 | 200 | 4254
210 | 2781 | 210 | 3377 | 210 | 4370
220 | 2855 | 220 | 3466 | 220 | 4486
**SEDENTARY
AGE over 60** | **MODERATELY ACTIVE
AGE over 60** | **ACTIVE
AGE over 60**
**BBW** | **SCML** | **BBW** | **SCML** | **BBW** | **SCML**
100 | 1541 | 100 | 1871 | 100 | 2421
110 | 1627 | 110 | 1975 | 110 | 2556
120 | 1713 | 120 | 2080 | 120 | 2691
130 | 1799 | 130 | 2184 | 130 | 2826
140 | 1885 | 140 | 2288 | 140 | 2961
150 | 1970 | 150 | 2393 | 150 | 3096
160 | 2056 | 160 | 2497 | 160 | 3231
170 | 2142 | 170 | 2601 | 170 | 3366
180 | 2228 | 180 | 2706 | 180 | 3501
190 | 2314 | 190 | 2810 | 190 | 3636
200 | 2400 | 200 | 2914 | 200 | 3771
210 | 2486 | 210 | 3019 | 210 | 3906
220 | 2572 | 220 | 3123 | 220 | 4041
_**Example:** If you're a 5-foot-4-inch female with a medium frame, you've determined that your BBW is 123 pounds. If you're age 35 and moderately active, the table lists your SCML as 2,086 calories._
For more help with determining your activity level, see Appendix E.
**(9) Metabolic Function Index (MFI):** Now divide the CCML by the SCML. Move the decimal point two digits to the right and round it off to a whole number. This represents your metabolic function index stated as a percentage. Write this in the "MFI" box.
_**Example:** Divide your CCML, 1,750, by your SCML, 2,086. The result is 0.839. Now move the decimal point two digits to the right (83.9) and round it off to 84. Your MFI is 84 percent._
# Interpretation of the MFI Results
The lower the percentage, the lower is your metabolic rate. There is room for error throughout the test and the calculations, so that a minimal deviation from 100 percent should not be considered as necessarily abnormal. I regard 90 percent as the borderline, and I would consider 90 percent as an indication of very mild hypothyroidism. As the MFI percentage falls lower, the likelihood of hypothyroidism becomes more certain. At 80 percent, I believe we have full-blown hypothyroidism, and some people will have an MFI much lower than that. We will still want to confirm our results with the corroborating tests that follow.
An MFI of 80 percent would represent a female who in order to maintain her weight must eat 400 calories a day less than another female who doesn't have hypothyroidism. I would also expect that the hypothyroid female would have several annoying symptoms not possessed by the normal individual.
In my practice, I've seen patients who have had an MFI as low as 60 percent, and I have had others whose medical histories would have suggested an even lower MFI, but they didn't have the discipline to allow us to perform an accurate test. I don't know what the lower limit of MFI is, but I'm sure it would impress even me.
Let's go over the examples given above. The hypothetical five-foot-four-inch lady who lost five pounds during her twenty-eight-day test diet didn't lose as much as a "normal" person would have lost. Had she eaten during that period the number of calories that would have maintained her weight, she would have had to have eaten 1,750 calories a day. The normal person of her same type would have maintained her weight on 2,086 calories. Our lady needs only 84 percent of the calories of that normal person. Her 84 percent classifies her as hypothyroid. Recognize that there is room for error in the entire process. A value of 90 percent is a questionable indicator of hypothyroidism. It is a borderline case in which I have to make an intelligent decision, and I can't do that without considering all of her information. In my opinion, the 84 percent is reason enough to treat her.
The MFI should give you a clear-cut look at how you handle calories in the real world. It isn't based on mysterious laboratory tests done behind closed doors by machines that are as subject to error as the individuals who operate them. I feel that the results of the MFI are almost irrefutable. Yes, it is true that you could have weighed yourself incorrectly or you may have used an inaccurate scale. You could have been mistaken as to your height. You might have suppressed remembering your true age, and your arithmetic could be shameful. But if you do your work carefully, the result is valid. It represents a study done by a real human being, on a real human being, in the real world, with real food. The resulting weight loss is real. If it turns out that you need 25 percent less food in order to maintain your weight than someone else does who is much like you, who would argue that there isn't something different about your metabolism?
Let's now see if another test corroborates what we've learned about you. Look at the Daily Temperature Chart below. In Chapter 11 you were asked to write in your temperature on Day 1.
**DAILY TEMPERATURE CHART**
| **Date** | **Temperature** |
---|---|---|---
1 | ______ | _______ |
2 | ______ | _______
3 | ______ | _______
4 | ______ | _______
5 | ______ | _______
6 | ______ | _______
7 | ______ | _______
8 | ______ | _______
9 | ______ | _______
10 | ______ | _______
11 | ______ | _______
12 | ______ | _______
13 | ______ | _______
14 | ______ | _______
15 | ______ | _______
16 | ______ | _______
17 | ______ | _______
18 | ______ | _______
19 | ______ | _______
20 | ______ | _______
21 | ______ | _______
22 | ______ | _______
23 | ______ | _______
24 | ______ | _______
25 | ______ | _______
26 | ______ | _______
27 | ______ | _______
28 | ______ | _______
| Total | _______
If you've followed instructions, there should be from 15 to 28 temperature readings recorded on the chart. I'm going to ask you to add up all the temperature readings and put the total on the line labeled "Total of Temperature Column." You may want to use a calculator for that and the next step. Now count the number of readings. It should be 15 or more. Place that number on the line labeled "Total Number of Readings." Now divide the total of the temperature readings by the number of readings. This will give you the average daily temperature, which you should place on that line. If the average daily temperature (ADT) is greater than 98.6 degrees, subtract 98.6 from the ADT and place it in the box labeled "Temperature Difference," putting a plus sign (+) in front of it. If the average daily temperature (ADT) is less than 98.6, subtract the ADT from 98.6 and place it in the box labeled "Temperature Difference" and put a minus sign (-) in front of it.
_**Example:** You've added up 18 temperature readings and they total 1742.4. Divide by 18. The ADT is 96.8. Subtract 96.8 from 98.6. The result is a temperature difference of -1.8._
For an interpretation of this, I will go back to Dr. Broda Barnes, who had great confidence in this test. In his experience he found that a temperature from one to three degrees below normal was indicative of hypothyroidism. Obviously, the lower the temperature the more certain and perhaps the more severe is the hypothyroidism. Therefore, a temperature difference of —1 is suspicious. A difference of —2 or even —3 definitely points in the direction of hypothyroidism. This is information that you will want to present to your doctor when the time comes.
Incidentally, if you have positive numbers for the temperature difference, this should also be investigated. Such a constant fever isn't normal either, but it indicates an entirely different problem, possibly infection. It might also suggest an overabundance of thyroid hormone, which could mean hyperthyroidism. In any case, this constant fever should be reported to your doctor.
Now we will go on to an entirely different kind of test to corroborate our findings in the MFI test. The signs and symptoms of hypothyroidism described earlier are quite helpful in making the diagnosis. In fact the more of these that are present, the more certain the diagnosis. Even though I've seen cases where only two or three signs or symptoms were present, I don't think I've ever seen a case where more than four or five were present and the patient didn't have hypothyroidism. I've adapted tests done by other researchers to fit the needs of the layman who wants to investigate whether his own symptoms suggest hypothyroidism.
The test we will do is essentially taken from the Billewicz index, a well-regarded method of evaluating hypothyroidism without laboratory tests. This should serve the reader well in providing additional corroborating evidence to be presented to the physician.
The Signs and Symptoms Index Form follows on page 179. You're asked to decide yes or no as to how each of them applies to you. Your answers must be definite. There is no "maybe" answer. So choose what is more probable, yes or no. Instead of putting down a check mark, you're asked to circle the number under either "Yes" or "No." You must circle one or the other for each of the items. Don't skip any. The numbers assigned to each symptom are a method of assigning a relative importance to each of them. Note that a yes or no answer for the same symptom may not have the same value. This was a well-conceived bit of research by those who developed the questionnaire.
Some of these will be hard or impossible for you to evaluate on your own. You will need help. With some you may wish to ask the opinion of someone else who knows you. Let's try to get accurate answers. The following section will give you some help with determining whether to put down a yes or no for the individual items.
**Diminished Sweating:** You can decide this for yourself. I've had many patients who have told me, "I never perspire." Whether that is exactly true or not, it is sufficient that they think that they perspire less than they should, less than the average person. For yes, circle the 6, for no, circle the 2.
**Dry Skin:** This one is easy. You don't have to ask anyone else. You should have an impression. Circle 3 for yes, circle 6 for no.
**Cold Intolerance:** Not everyone with hypothyroidism feels cold, but some people do. Are you frequently cold? Are you the one who needs a sweater when everyone else seems comfortable? Circle 4 for yes, circle 5 for no.
**Weight Increase:** Here I've taken license with the original intent of the authors of the study. If you've had an unexpected, unexplained weight gain that didn't seem to be related to an increase in your intake of food, answer yes. If you feel that you're overweight and it isn't justified by the amount you eat, answer yes. Circle the 1 in the proper column.
**Constipation:** Another easy one. You feel either that you are or that you are not. Circle 2 for yes, 1 for no.
**Hoarseness:*** This is one where you may ask the opinions of those around you. Often we don't know what our own voice sounds like. Have you heard a tape recording of your voice? If there has been a change in the character of your voice, you may not be aware of it. Circle 5 for yes, 6 for no.
**Numbness:** I have translated this from the medical word, paresthesia, which also might include tingling or a prickly feeling. It could be anywhere on the body, as long as it is bothersome and has no other explanation. Circle 5 for yes, 4 for no.
**Deafness:*** I don't mean total deafness. This is anything that leads you to believe you don't hear as well as you should. You may want to ask the opinions of others. Circle 2 for yes, 0 for no.
**Slow Movements:*** Here is where friends and family can be of help. The question is, Do you seem to move more slowly than most people? It isn't simply whether you're a couch potato or not, or someone who would rather read or watch TV than do physical things. It goes beyond that. Are your movements actually slower than those of others? Think about it. We all know people who do everything quickly and have jerky movements. This is the opposite. There are those who move at the proverbial snail's pace. This is an important one. Try to get an accurate answer. Circle 11 for yes, 3 for no.
**Coarse Skin:*** You should be able to answer this very quickly. Circle 7 under either yes or no.
**Cold Skin:*** You can't determine the temperature of your own skin. Ask others if you usually have cold skin. Circle 3 for yes, or 2 for no.
**Puffiness Around Eyes:** Again, your opinion along with assistance from others should help you come up with the answer. Circle 4 for yes, 6 for no.
**Pulse Rate:** Do you know how to take your own pulse? You should. It is very useful. Learn how. For the present, find someone who seems to know what they are doing and let him do it, and while you're at it, get him to teach you how. Sit for a few minutes and then count the number of heartbeats for a full minute (sixty seconds). If it is 66 or less, circle the 4 for yes, otherwise circle the 4 for no.
# **Calculating Your Signs and Symptoms Index**
Use the Signs and Symptoms Index Form that follows.
**The Signs and Symptoms Index Form**
Circle the number under **"Yes"** or **"No"** that best describes you. You may want to ask the opinion of others for the four items with asterisks (*). See explanation of signs and symptoms that precedes this form (pages 176–).
| **YES** | **NO**
---|---|---
Diminished Sweating | 6 | 2
Dry Skin | 3 | 6
Cold Intolerance | 4 | 5
Weight Increase | 1 | 1
Constipation | 2 | 1
Hoarseness* | 5 | 6
Numbness | 5 | 4
Deafness* | 2 | 0
Slow Movements* | 11 | 3
Coarse Skin | 7 | 7
Cold Skin* | 3 | 2
Puffiness Around Eyes | 4 | 6
Pulse Rate | 4 | 4
Total of Each Column | ____ | ____
Index Score | |
_(Subtract Column 2 from Column 1)_ | __________
Add up all the circled numbers in the "Yes" column and put the total below. Add up all the circled numbers in the "No" column and put the total below.
Subtract the total of the "No" column from the total of the "Yes" column. That is your index score.
A score of 25 or greater strongly suggests hypothyroidism. A score of 20 to 24 is suspicious. A score below that doesn't rule out hypothyroidism. It is still quite possible. The higher scores do tend to confirm a low MFI index.
A comment on the test seems to be in order. The test was designed by researchers and was intended to be used by doctors for evaluating patients. It wasn't intended for the layman to test himself. Certainly, testing oneself does introduce a new possibility of subjective error. Still, I'm not sure that a doctor is better than your best friend at evaluating your hoarseness or your slow movements.
I have purposely omitted one very important sign that the researchers included: the sluggishness of the ankle jerk. If you will recall, I spoke earlier about the Achilles reflex test, a test I particularly liked. The researchers who developed the symptoms test were drawing on this same phenomenon. They wanted the doctor to evaluate the movement of the ankle after the tendon had been tapped with a medical hammer. This takes some experience, both to give the tap as well as to evaluate the result. We don't want any broken bones when someone enthusiastically applies a sledgehammer to the ankle. But, as a result of the omission, the test isn't exactly as it was intended. A yes to the ankle-jerk test would have added a significant 15 points, whereas a normal reflex would have subtracted only 6. This could tend to throw the interpretation values I've given you off a bit. The error would be in the direction of underestimating who has hypothyroidism. I'm going to stick to my guns. I think as the test has been given to you, it should prove quite useful.
# Putting the Tests into Perspective
We have performed the principal test and two corroborating tests. Remember that I've applied these very principles in my own practice over many years on thousands and thousands of patients. They've served me and my patients well. I really want to share this information. I don't believe that such a systematic approach to self-help in discovering hypothyroidism has ever been presented to the public.
Could some find fault with the theory, the methods, and the interpretation? Of course. You can find fault with anything. Is it perfect? Obviously not. What in medicine or in any other discipline is perfect? This is, however, a serious attempt to fill a gap I believe exists. More importantly, I believe it can help a sizable number of our population.
Let's go on to how you may use the information you've obtained.
# Summing Up
* Calculating the results of the MFI test gives the reader a clear-cut view of whether his or her thyroid function is normal.
* An additional corroborating test measures body temperature for evaluation as a sign of hypothyroidism.
* A test based on a questionnaire of symptoms provides further corroboration.
#
# _Weight Loss Without Guesswork_
**T** his chapter is full of assumptions.
I will assume that you've done a fine job of conducting the MFI test and that you're now ready to put the results to good use. You've followed the instructions meticulously and have arrived at a good estimate of how your thyroid functions. There are various possible outcomes of your testing. You may have learned that you burn up calories every bit as efficiently as the next person, and as a consequence there is no reason why any sensible low-calorie diet would not work for you.
Or you may have learned that you don't burn calories properly. You haven't lost the pounds that were expected on a 1,000-calorie diet. Worse, you may have lost so little that considerable hypothyroidism is indicated. In any case, you're being rewarded for your effort with valuable information. The solution to the problem isn't yet obvious, but you have the information that can help you find that solution. Let's look at the possibilities.
# Your Metabolism Is Normal and You Have Weight to Lose
Here is one of those assumptions. Your MFI test gave you a value of 96 percent. Though that is a few points below 100 percent, the theoretical normal, this isn't low enough to suggest a thyroid problem. There is too much room for variation in the different aspects of the test to call 96 percent hypothyroidism. Bear in mind that it is still possible. You may have deviated from procedure enough that 96 percent should really have been, say, 89 percent, in which case we would suspect mild hypothyroidism or what the literature commonly calls subclinical hypothyroidism.
At anything above 90 percent, I would make the assumption that I didn't have hypothyroidism and get to work losing weight with a sensible diet. The diet you followed during the 28-day test is a sensible diet and, what's more, I know it works. So why not get busy and just do it?
Should you handle the diet differently as your weight-loss diet than you did as your test diet? Somewhat. You don't have to be as scrupulously exact as I asked you to be during the test. We're no longer gathering information. The 1,000-calorie diet should continue to result in weight loss and at about the same rate it did during the test. If you lost ten pounds during the test, you will probably lose another ten in the next four weeks. You certainly don't have to keep an Excess Calorie Sheet. A few more calories a day or a few less will probably not be noticed.
Can you increase the number of calories per day? The answer is yes, but you will have to pay the price, a slower rate of weight loss. I find that motivated patients generally tolerate a 1,000-calorie diet quite well. In my own practice, I actually use an 800-calorie diet, but I watch my patients very carefully. This will have to be a decision for your own doctor to make. I would recommend that you don't pressure your doctor to approve a lesser number of calories than he seems comfortable with, and I certainly don't recommend that you go against your doctor's orders.
Bear in mind that each 125-calorie-per-day addition to your diet is expected to result in 1 pound less of weight loss for the four-week period. Thus, if you change to a 1,250-calorie diet, you will be expected to lose 2 pounds less than with a 1,000-calorie diet.
You may ask, "Why not eat a few hundred more calories per day and be more comfortable even though you lose a little slower?" The answer is that I'm not sure you will be more comfortable. It has never seemed to me that patients enjoyed a 1,200-calorie diet any more than they did an 800-calorie diet. Let's face it. Dieting isn't fun. Its justification is the reward at the end. That vision of a slim body is a powerful motivator. But fun it is not. The impression that we're asked to get from watching television commercials for weight-loss products suggests that the process of losing weight is one of the great joys of life. Let's get rid of those unrealistic expectations. The joy is in the result, not in the process.
There is another reason for fewer calories and faster weight loss. It is my impression, gleaned from those thousands of patients, that the longer losing weight takes, the less likely it is to be successful. Success is a two-pronged affair. It should be noted here that I define the first stage of success as reaching the particular goal weight that was set in the beginning. The final step in success is maintaining that weight for a lifetime.
I have noted that patients who frequently falter along the way are less likely to reach their goal weights. The opposite is certainly true. The patient who exhibits fanaticism and who never deviates virtually always achieves the goal, and of course it is done in record time. That kind of patient completes that important first step and is eager to do what is necessary to maintain that new figure for a lifetime.
If you choose to go much above 1,000 calories per day, I believe you will lower your odds of success. I must tell you that I'm not a gambler by nature. I like the odds to be on my side, not on the side of the "house." I think you slant the odds in your favor when you follow my 1,000-calorie diet.
In spite of what I've just said about my preference for 1,000 calories per day, I can at least show you what to expect in the way of weight loss if you go above 1,000 per day. The chart that follows is based upon a twenty-eight-day period. You may wonder why I consistently gravitate to exactly four weeks. It is because of the extreme variability of weight loss when viewed over a shorter period. My own medical practice is geared to reevaluation every four weeks, even though I'm seeing the patient more frequently than that. I find that weight comparisons over four weeks are reliable. The table that follows on page 186 shows you how much weight loss to expect in a four-week period based upon your corrected caloric maintenance level, which you learned from the MFI test. I told you that the information would prove valuable to you, and this is but one example of that. In the table, find your CCML (corrected caloric maintenance level) in the left column that matches your CCML on Line (6) on your MFI Calculation Form (page 161). Across the top of the table are the various daily calorie counts for the diet you are or will be following. Where the two intersect is the expected twenty-eight-day weight loss. If you've done the MFI test diligently, you will be surprised how accurate a predictor of weight loss this is.
Here is another way you can keep the odds in your favor. Every diet book tells you to see your doctor before you start a diet. I generally have the impression that this advice is given without much conviction that it's really necessary or that the reader will follow it. I really believe you should see your doctor, not just at the beginning, but also during the course of the diet. I will give you my reasons.
We're looking for success, and I've defined success as permanently achieving a proper weight. Again, I will refer to the odds. It is my impression that my patients have a greater chance for success in achieving the weight objective with the help of my overseeing the process than do those who try to do it on their own. They are certainly more successful than those who try those kooky schemes that are advertised so widely. I would like to think this success stems entirely from my superior knowledge of dieting methods, but unfortunately I cannot give myself that much
**TABLE OF EXPECTED WEIGHT LOSS**
Pounds Lost in 28 Days on Various Calorie Diets
---
**Daily Calorie Count of Diet**
**CCML** | **1000** | **1200** | **1400** | **1600** | **1800**
**1000** | 0 | -1.6 | -3.2 | -4.8 | -6.4
**1100** | 0.8 | -0.8 | -2.4 | -4 | -5.6
**1200** | 1.6 | 0 | -1.6 | -3.2 | -4.8
**1300** | 2.4 | 0.8 | -0.8 | -2.4 | -4
**1400** | 3.2 | 1.6 | 0 | -1.6 | -3.2
**1500** | 4 | 2.4 | 0.8 | -0.8 | -2.4
**1600** | 4.8 | 3.2 | 1.6 | 0 | -1.6
**1700** | 5.6 | 4 | 2.4 | 0.8 | -0.8
**1800** | 6.4 | 4.8 | 3.2 | 1.6 | 0
**1900** | 7.2 | 5.6 | 4 | 2.4 | 0.8
**2000** | 8 | 6.4 | 4.8 | 3.2 | 1.6
**2100** | 8.8 | 7.2 | 5.6 | 4 | 2.4
**2200** | 9.6 | 8 | 6.4 | 4.8 | 3.2
**2300** | 10.4 | 8.8 | 7.2 | 5.6 | 4
**2400** | 11.2 | 9.6 | 8 | 6.4 | 4.8
**2500** | 12 | 10.4 | 8.8 | 7.2 | 5.6
**2600** | 12.8 | 11.2 | 9.6 | 8 | 6.4
**2700** | 13.6 | 12 | 10.4 | 8.8 | 7.2
**2800** | 14.4 | 12.8 | 11.2 | 9.6 | 8
**2900** | 15.2 | 13.6 | 12 | 10.4 | 8.8
**3000** | 16 | 14.4 | 12.8 | 11.2 | 9.6
**3100** | 16.8 | 15.2 | 13.6 | 12 | 10.4
**3200** | 17.6 | 16 | 14.4 | 12.8 | 11.2
**3300** | 18.4 | 16.8 | 15.2 | 13.6 | 12
**3400** | 19.2 | 17.6 | 16 | 14.4 | 12.8
**3500** | 20 | 18.4 | 16.8 | 15.2 | 13.6
**Note: Minus values indicate a weight gain.**
credit. The phenomenon of the patient having to make regular visits to my office, to confront my staff, to face me directly on a regular basis, is probably as responsible for their success as is the actual method used. That is one reason, a very good reason, why you should diet under the auspices of your doctor. In case I didn't make the reason clear enough, I will state it succinctly: _Conducting your diet with your doctor's help will increase your chances for success._
Another reason for working with your doctor is safety. You should be examined before you embark on a diet. For one thing, it is a good excuse to have a physical. Who knows what demons are lurking inside you, unrelated to diet! He will undoubtedly do lab work first, and an electrocardiogram is always advisable. Play it safe. Let's do this the right way.
It's probably a good idea to reread Chapter 11 before you go on with the diet. The advice given for my preferences in the various lists and text are still applicable. Get started. Let's get that weight off.
Bear in mind that I'm speaking of you, the reader, and this section deals with the reader who doesn't have a thyroid problem impeding weight loss. For those who do have an abnormal MFI test result, the road to success with the doctor could be a rockier one.
# Your MFI Test Is Abnormal
Suppose your test result is 90 percent or lower. Depending on how low it is, losing weight could turn out to be a real burden. You may be in a category of patients I see all too often. These are people who suspect something is wrong, and often have been told there is nothing wrong. If your result is 80 percent or lower, it would be difficult, taking all the factors into consideration, to conclude that there is nothing wrong. A value of 80 percent could represent someone who cannot maintain her weight on a diet of about 1,600 calories a day when she should be maintaining at the 2,000-calorie level. I would also be willing to bet that someone with that score would also have several of the symptoms of hypothyroidism I've previously covered. You will probably have body temperature at least one degree below "normal," and there is a good chance that you complain of always feeling tired. The work is cut out for you. A doctor must be found, one who will listen, and an effort must be made to correct the problem.
Your first choice should be your family doctor or your "primary care physician," as they are now called. Make the appointment and be prepared for resistance. Your job is to let him know about your symptoms of hypothyroidism. You should previously have copied and filled out the "letter to your doctor" that follows. You must get across the information that you've just completed a test where you ate 1,000 calories per day for four weeks and you lost only a certain number of pounds. Tell him that you followed exact instructions to determine how many pounds would have been lost by a "normal" person like you and that your percentage of that amount was low enough to indicate you weren't normal.
The form letter that follows on page 189 is a summary of the tests you've performed. It is presented in a simplified manner and is intended to supply information about you to your doctor. Fill in the blanks. Make a photocopy of it if you like. The information that is asked for is on your MFI Calculation Form.
Your 28-day weight loss goes in blank (3).
Your daily caloric maintenance level (CCML) goes in blank (4).
The theoretical caloric maintenance level (SCML) goes in blank (5).
Your percentage of normal (MFI) goes in blank (6). Your average daily temperature, which goes in blank (7), is on your Daily Temperature Chart in Chapter 13.
Your signs and symptoms score is on the Signs and Symptoms Index Form (also in Chapter 13).
My guess is that your doctor will say this is interesting and that the next step is to test your thyroid. You already know my feelings on that subject, but it would be prudent not to object, although you might point out that you've just read a book in which
**Date__________**
**Dear Dr.__________**
**I have just completed a home test specified in a book by Dr. Sanford Siegal titled _Is Your Thyroid Making You Fat?_ The test compares how I burn calories as compared to a normal individual with my same characteristics. I have followed a 1,000-calorie-per-day diet for twenty-eight days and have carefully recorded my weight change during that time.**
**Here are the results:**
**I lost** **pounds over the 28-day period.**
**My daily caloric maintenance level was calculated to be calories.**
**Theoretically, a person like me should maintain weight at calories.**
**My caloric maintenance level is percent of that of a normal person.**
**Additionally, my daily body temperature averages ° F.**
**I answered questions regarding my symptoms of hypothyroidism and received a score of_____. Dr. Siegal has suggested that a score of 25 or greater is suspicious of hypothyroidism.**
**I hope this information will prove helpful.**
**Sincerely,**
______________________________________
the author casts doubt on the value of such testing. Except that you may have to pay for the testing, there is no reason not to have it done. For one thing, your TSH test may come back elevated and your doctor will then accept the fact that you're hypothyroid. This is the path of least resistance. You will still have one more hurdle, but we will get to that soon enough.
This is neither the best-case scenario nor the worst. The best would be if your physician told you that he was aware that thyroid tests are questionable, that he was aware of my book and was pretty much in agreement, and that since you had all the earmarks of hypothyroidism, including a high cholesterol, he was going to give you a cautious try on thyroid hormone treatment. Don't expect that to happen. Instead, hope he will just listen.
There is more ammunition you can use. Chapter 15 in this book is written just for him. It takes into account that your doctor is a busy man, so I've tried to summarize the whole issue into as few words as possible. You might just get lucky. He might just read it.
There is even more. Virtually everyone is into the Internet these days. Tell him that I have a Web site (drsiegal.com) that will give him even more information. If he will contact the site, I will send him more information that may sway his thinking. Of course the information will not be about you personally, but it will summarize the concepts contained in my book. There is even another alternative. My Web site will allow you to request that I send him the information, and he will know you made the request.
Suppose all fails. Your doctor is unmoved. He says there is nothing wrong with your thyroid and tells you to follow this or that diet and quit worrying. You will then have a decision to make. If his arguments seem stronger than mine, the decision should not be difficult. If you feel you haven't had a fair hearing, you have other choices. You may even ask for his cooperation in this. Second opinions among doctors are a standard procedure. He should not even mind recommending a colleague for that opinion. A few doctors are insecure enough that they regard someone's seeking a second opinion as a threat of some sort or at least a questioning of their competence. Let's hope your doctor isn't one of those.
You may run into the same problem with other doctors. My own Web site may be of help. I've started collecting the names of physicians around the country who have taken an interest in my findings and who, to varying degrees, have observed what I have and are willing to keep an open mind when it comes to thyroid problems. I expect the list to grow, and I would gladly share names of doctors in your area with you. Again, my Web site will be your source for this information. Look for it at:
www.drsiegal.com.
The second hurdle I spoke of has to do with the choice of thyroid hormone to treat your problem. You've been told repeatedly that the vast majority of doctors treat hypothyroidism with synthetic thyroid, also known as levothyroxine or thyroxine or T4. You also know that synthetic isn't my choice. I consistently get better results by prescribing natural thyroid, otherwise known as Thyroid U.S.P. or desiccated thyroid, or sometimes Armour. Again, I will make the point that synthetic thyroid works for many patients. I just find that natural thyroid works better. Ideally, I would like to see your hypothyroidism treated with natural thyroid. Since it is a recognized and accepted medication available in all pharmacies, you may have less of a problem getting that point across than the previous one. My Web site (and others) may be able to help you find a doctor who will prescribe natural thyroid.
Let's now adopt a positive outlook. Your doctor accepts that you're hypothyroid and has prescribed one of the varieties of thyroid hormone. He should schedule frequent visits to assess the value of the medication you're taking. I believe that for the first year you should be reevaluated each month for the proper dosage. Since I don't consider the laboratory a suitable indicator for proper dosage, the determination becomes somewhat of an art. (Medicine in general has sometimes been characterized as an art rather than a science.) Still, there are objective signs, and I'm sure that your physician will monitor them. Your blood-cholesterol reading could help. Of course it will also be influenced by your diet. Your temperature will tell him something. Your blood pressure and your pulse rate contribute. Mostly the information that you report will tell the story. Nothing tells me more than the patient reporting, "I no longer have that terrible tired feeling."
As for your weight-loss diet, there is no reason why it should be very different from what was spoken of in the previous section, the one dealing with the reader who doesn't have a thyroid problem. If you're treated correctly, you too will not have a thyroid problem, or at least it will be corrected by supplying the right hormones. Your weight loss in this corrected condition should be the same as for a "normal" person.
If the assumption is that you've suspected your metabolism wasn't normal and you have been frustrated in efforts to confirm that suspicion, the MFI test should go a long way toward ending that frustration. Do the test, present your findings, and get on with feeling better. It is worth the effort.
# Getting the Job Done
Staying with a diet is a task that requires as much thought and planning as any other major undertaking in your life. I happen to think that achieving a normal weight should be a high-priority item on your agenda. I'm often shocked at how casually some people regard this matter. They may pay lip service to how badly they want to lose weight, but often their subsequent behavior makes that concern somewhat suspect.
I have seen overachievers whose lives are organized to the hilt conduct their weight-losing effort in a shamefully slipshod manner. What is required, as with any other task worth doing, is planning. Plan each day in advance. What will you eat that day? Where will it come from? What forces could intervene to sidetrack your efforts? How will you counter those problems?
The support of others—a spouse, a friend, a parent—can be helpful, but don't count on it. I don't know how many times I have been told, "I don't get any support from my..." It would be nice if those who profess to love us would do what they could to make the job easier, but help is not always there, and an exploration of the psychological overtones of why it is not is beyond the scope of this book.
"My husband likes to go out and eat good meals on the weekends and I can't just sit there and eat lettuce."
"Here I am trying my best to get healthy and she makes these fantastic meals. I don't know if she tries to make them more enticing when I'm dieting or if they just seem that way."
Of course, such actions on the part of those who purport to love us provide a very convenient excuse for why we can't succeed. In the end, you have to stand on your own two feet and get the job done. If you count on support, it may not be there.
I'm reminded of an incident where the lack of support was not very subtle. Mariola came to me weighing 212, a bit much for her five-foot-four-inch small frame. She was doing fabulously well. She had mentioned that her husband did not want her to get down as low as I had suggested, but I sort of ignored that hint. She had reached 180 when I received a phone call from him. "I don't want her to lose any more weight." Without asking why, I tried to explain why she should. He cut me off, and this time his anger was apparent. "No more," he said emphatically. I knew it would be hard for him to understand this, but I had to tell him. "Mr._____, I'm really not permitted to discuss your wife's medical treatment with you without her permission. Even though you are her husband, the rules say that I may not talk to you about her. I'm really very sorry, but..." Again he wasn't interested in my explanation. His voice was now quite loud. "If she loses any more weight, I'll be out there to get you." He hung up.
Thank goodness he never did appear, principally I suppose because she never reappeared. Obviously, he used other means to solve his problem.
Your husband, your wife, your boyfriend, girlfriend, or whoever may not be as assertive as Mariola's husband, so don't be shocked if you are not receiving the support you believe you deserve. Like many other tasks in life, losing weight is a lonely one.
# Medication for Weight Loss
The subject of medications for suppressing hunger during a weight-loss diet has become rather controversial as a result of the unfortunate phen-fen interlude. You will recall that a combination of two medications, both approved but not sanctioned as a combination by the Food and Drug Administration, was being passed out rather indiscriminately by a variety of opportunistic health-care providers with resultant harm to a number of individuals. One of the two drugs has since been withdrawn from the market, but the other, phentermine, is still considered to be proper and acceptable for aiding the dieter.
Your doctor will make the final decision as to whether this type of medication will be useful to you after a careful evaluation. I will only add that I prescribe such medications for many of my patients and I believe they can be quite helpful. Bear in mind that this type of medication is quite apart from the thyroid hormone I have discussed in this book. Appetite-suppressing medication may indeed be prescribed for those with hypothyroidism or those without.
# Summing Up
* A reader with normal thyroid function should be able to lose weight effectively by following the diet presented in this book.
* A reader whose thyroid function is determined to be low by the MFI test results will need the assistance of a physician to correct the problem.
* The reader is instructed how best to approach the physician with the results of the testing.
* Anyone, whether hypothyroid or not, should diet under the supervision of his or her physician.
#
# _For Your Doctor's Eyes Only_
**D** octor,
You have probably been asked to read this chapter by one of your patients. It is quite possible that he or she has just completed the test in this book and there may be a question regarding the state of the patient's thyroid. This chapter is actually a summary of the entire book _Is Your Thyroid Making You Fat?_ and should suffice to give you a good idea of my position on testing for hypothyroidism as well as the treatment. I would, of course, be honored if you would read the entire book, but I know how demanding a medical practice can be, and it is my hope that you will at least read this chapter.
I have limited my practice to the treatment of obesity for many years; in fact the millennium year will mark my fortieth year of dealing solely with overweight problems. My multiple offices have seen hundreds of thousands of patients during that time, and I don't need to tell you what a learning experience comes out of that type of repetition in a rather narrow field of interest.
The subject of the thyroid comes up with at least half of my patients, and it isn't I who introduces the subject. Many patients suspect they have an underactive thyroid, and they may actually state it in those terms. Quite frequently they allude obliquely to the suspicion that all isn't right with them by telling me they have something wrong with their bodies, that they cannot lose weight on the same diets that work for everyone else. They may even use the term _metabolism,_ though frequently they use it incorrectly. A smaller number are much more knowledgeable. They know about hypothyroidism, and they know the various symptoms that may accompany it. The Internet has certainly become a tool of education in this area. What has frustrated them is that a doctor has tested them and told them there is nothing wrong with their thyroid gland.
This latter type of patient is often discontented with the diagnosis and even angry with the practitioner. They suspect that he distrusts the history of their eating habits they've given him. They don't like the implication that they are lying. This doesn't lend itself to a good doctor-patient relationship.
If we consider the two possibilities—one, that the patient is telling the truth and is eating a meager diet, and the other, that the patient is a liar and eats excessive amounts—it should be obvious that only one is consistent with a normal metabolism. My own experience, if not my own common sense, tells me that not all of these patients whose thyroid gland tests normal but who profess to eat reasonably can be lying. If some are telling the truth, it should be obvious that, at least in their case, there seems to be a deficiency of thyroid hormone. If there is any other reason for the phenomenon, I can't find it in the literature.
What then can we conclude from this? My conclusion is that lab testing doesn't demonstrate the deficiency of thyroid hormone in some patients. Does the lab ever help in the diagnosis of hypothyroidism? Obviously, yes. There are probably millions of people who take levothyroxine as a result of laboratory testing, and their symptoms are improved or even abated. If we conclude that laboratory testing sometimes demonstrates hypothyroidism and at other times misses it, how valuable is the lab in assisting with the diagnosis?
I'm reminded of a test that was popular a few years ago. It was a saliva test done on a pregnant woman to determine the sex of her unborn child. It was given in stores that sold maternity clothes or infants' clothes. The manufacturer of the test guaranteed accuracy by refunding the fee if it turned out that the results were in error. My guess is that they ended up keeping half of the fees.
I think there's an analogy there, but we're dealing with a more serious subject. If I can't rely on a test to have an accuracy of at least 90 percent, how can I rely on it at all? Even if I accept that hypothetical 90 percent figure and act accordingly, am I not potentially ignoring a serious medical problem in 1 out of 10 patients I've tested? The fact is that doctors rely so heavily on the lab results of the TSH and perhaps the T3 and T4, and occasionally a few other tests, that they don't seem to consider any other evidence. You might want to ask yourself this question: Under what circumstances would I start a patient on thyroid medication if the laboratory gave me no indication of a thyroid problem?
My own experience in performing these tests on patients was essentially a disaster. I believed the tests were accurate, and I was very reluctant to question what was so universally accepted. I shudder to think how many patients saw in my facial expression the belief that they were lying about their food consumption. What strengthened my cynicism were the occasions when I would test the same patient several days in a row and get such broadly varying results that I couldn't come to any conclusions. I won't even dwell on the few times I tested the lab by dividing the same blood specimen in half and sending it to the lab under two different names, only to receive the most disturbing results.
Obviously, my experience comes from a multitude of individual anecdotes about my patients. This isn't the usual way medical phenomena are reported. I don't have a university sponsor to add prestige to my findings. I am a practicing physician. I don't receive grants from pharmaceutical giants to fund my observations. Food companies don't subsidize my research, and the government agencies that fund research haven't paid me one cent. Yes, my findings are what the medical literature sometimes tolerates as "anecdotal evidence." I have a lot of that.
Is not all research anecdotal? Is it all not simply a collection of many, many anecdotes organized in a coherent fashion so that the researcher can draw conclusions from it? That's what I've done, not with the help of mainframe computers, shameful grants, or a staff of eager medical students. But my conclusions are every bit as valid, in my mind, mainly because of the volume of information I've acquired.
Haven't you within your own practice come to conclusions about the diagnosis and treatment of patients that are born of your own observations and experience and that are divergent from the mainstream of medical thought? That's exactly what I've done. I can't deny my observations or the conclusions I've drawn from them. I think I have a right to these conclusions. Forty years. Thousands of patients.
There is a monthly medical publication I receive called the _Cortlandt Forum._ Each issue devotes a substantial portion to short segments of anecdotal gems that come from practicing physicians around the country. I've found them to be a treasure of information. I'm not sure this kind of grass-roots research is worth much less than the ivory-tower variety.
# My Test
We all know the multitude of signs and symptoms associated with hypothyroidism. I'm sure you see your share of patients who have the typical puffy dry skin, who seem to do everything at a snail's pace, who are always cold, whose hair is thin, and who perhaps exhibit other telltale signs. I imagine that you proceed to order a TSH and maybe some other tests. Perhaps the cholesterol is elevated, and perhaps by reflex you envision the patient gobbling down globs of saturated fat. When the TSH comes back and it's normal, what do you do? That dilemma frustrated me for years.
Because of my lack of confidence in the help I was getting from the lab, I had to look for other means. I knew full well that each hypothyroid patient didn't have every last one of the twenty-five or so signs associated with the ailment. Yet there is one common denominator, a factor that is inherent in the function of thyroid hormone. That single element is the inability of the patient to burn calories at the same rate as the euthyroid individual.
Over the years there have been a number of methods designed to measure the rate at which we use calories. I suspect that all suffer from the fact that the method itself introduces error into the calculation by actually changing the metabolic rate while the patient is undergoing testing. Years ago, I routinely did a basal metabolic rate test using a machine that measured inspired oxygen and expired carbon dioxide. That method fell out of favor a number of years ago because it was said to make the patient apprehensive and thus influence the outcome of the test.
The BMR test was replaced in many physicians' offices with Achilles reflex testing, a machine we would hook up to our EKG to use it as a recording device. We would tap the Achilles tendon on the kneeling patient and make a tracing, which would demonstrate the time lag in the recovery from the ankle jerk after the tap. We had a set of standards to compare the patient's response to some normal response. I actually liked the test, and it was generally right on when it came to substantiating the patient's signs and symptoms. Achilles reflex testing was eventually abandoned as the blood tests became more sophisticated and supposedly more accurate.
I've said that I believe the only common denominator of all hypothyroid patients is the substandard burning of calories. In a sense they have a more efficient engine than the norm; they seem to get more miles per gallon out of their calories. I expect you to now interject the question, "Why, then, aren't all hypothyroid patients overweight?"
The answer is inherent in what it is that makes us overweight. We become overweight when we ingest more calories than our system needs. The normal or underweight hypothyroid individual must be taking in a smaller number of calories than is normal. This is understandable. All of us aren't gluttons who will eat until the tank will hold no more. There are people who aren't that much into food. They can either take it or leave it, and usually they leave it. Thus, on an intake of calories that would result in most people losing weight, they do not lose. They simply maintain their weight.
As soon as I accepted the fact that this slow metabolism was the universal factor, it didn't seem very difficult to measure it. We have a wealth of useful data. During the first half of the twentieth century, there was much research in developing methods for determining our caloric needs. Various formulas were devised, the most well-known of which is the Harris-Benedict formula. It has been massaged, critiqued, and supposedly improved over the years, and it is still used to calculate caloric needs, particularly of patients who must be fed involuntarily, such as comatose patients or the elderly. Various factors enter into the calculation: age, sex, frame size, etc. These calculations lead to a value for the baseline metabolism of the individual. By applying factors that correct for various activity levels, we can come up with an intelligent guess as to how many calories a "normal" individual needs in order to maintain his or her weight, in other words, the corrected caloric maintenance level, which for convenience I've dubbed the CCML.
The test I've devised and which I use in my practice involves monitoring the patient's calorie intake over a fixed period of time and also noting the weight change during that same period. We know that each pound of weight lost represents a caloric deficit of 3,500 calories. Since we know the total caloric deficit for the period, we divide this number by the number of days represented and we arrive at the average daily caloric deficit. We know (1) how many calories the reader (or the patient) consumed during the test period, and (2) what the weight loss was during that period. By adding the two, we have the number of calories that would have maintained the weight of the individual during the diet period. By dividing that number by the number of days the person dieted, we arrive at the daily corrected caloric maintenance level (CCML) for that individual.
By dividing the actual maintenance level by the standard (expected) maintenance level, then multiplying by 100, we come up with a percentage of normal. I've boldly named this percentage the Metabolic Function Index (MFI). (I couldn't bring myself to name it the Siegal index.)
As an example, if an individual should require 2,000 calories per day to maintain her weight and the testing she had done shows that she would maintain her weight eating 1,400 calories per day, her MFI is 70 percent. My experience tells me that she is hypothyroid. I arbitrarily regard 90 percent as the cutoff point, mainly because there is certainly room for error in the calculations. Below that number is some degree of hypothyroidism.
The method I use is unique, but not bizarre. It gets right to the heart of the matter and it doesn't rely upon a distant laboratory for its accuracy. True, my readers need to have done everything correctly and I've emphasized this in these pages, but since they have a direct interest in the outcome, I suspect the average reader will expend great effort to see that the results are valid. I actually think readers of this book will produce a more valid result than will my own patients who believe I'm sitting in judgment of their deeds. The reader has to answer only to herself or himself.
If you question the validity of such an exercise as I've described, ask yourself, What could cause this substandard loss of fat other than insufficient thyroid hormone? Assuming that there isn't a lot of fluid retention on the day the test ended or that there isn't extreme dehydration, I believe the conclusions are valid. Readers are cautioned to be alert for the possibility of fluid retention.
The true weakness of the test is that it relies on the honesty of the patient. I wouldn't be surprised if patients sometimes deceive me about their straying from the diet because of embarrassment. As I've said, I think they are less likely to lie to themselves when they are taking the test in this book. I've tried to impress upon my readers the virtues of honesty.
There are two other "tests" the reader is asked to take. One involves simply taking one's temperature on arising. It is based on the common knowledge that those with hypothyroidism generally run a lower body temperature than those with normal thyroid function. If you exclude times when the reader is ovulating or when she has an infection, you can form an impression of whether the body temperature points to a low metabolic rate. A doctor by the name of Broda Barnes wrote a book in 1976 in which he espoused the belief that this was _the_ test for hypothyroidism. The book is still in print after all these years. This must attest to the fact that there are people who still want to know what he had to say. He, like me, wasn't enamored with the usual laboratory testing. I've asked my readers to take serial temperature readings as sort of a corroboration of what the MFI test reveals.
A second corroborating test is based simply on the reader asking questions of himself or herself. The idea is to see if the reader has the signs and symptoms that are prevalent in hypothyroidism. The questions are adapted from a 1969 study in which a group of Scottish researchers attempted to develop a practical method of diagnosing hypothyroidism that wasn't invasive. What made their test unique was the clever weighting method they assigned to each symptom and that a positive or negative answer weren't necessarily weighted equally. * I can tell you that when I see a new patient with a hoarse, raspy voice who obviously moves very slowly and who tells me she never sweats, I suspect hypothyroidism, and I will be right much more often than wrong.
# Thyroid Medication
Today's standard treatment of hypothyroidism is almost universally the prescribing of levothyroxine. This, as you know, is one of the thyroid hormones and is the one that is secreted in the greatest quantity. It is often abbreviated as T4, and for brevity I shall use that designation. I would guess that at least 90 percent of the thyroid hormone prescribed in this country is T4, although T3 (triiodothyronine) is sometimes prescribed. Even less frequent is the prescription of desiccated thyroid.
Desiccated thyroid has various synonyms, among them Thyroid U.S.P., which is probably the most proper. Frequently it is called Armour Thyroid and sometimes simply Armour because of its long-term association with the Armour meat company that was the source of the animal thyroid glands used to make the product. Repeatedly in this book, I've referred to it as "natural thyroid," which distinguishes it from synthetic T4.
If you're a lot younger than I, you may only vaguely know of the existence of Thyroid U.S.P., since its use fell off dramatically with the introduction of synthetic T4 in the 1950s. It is still a United States Pharmacopeia drug, and virtually all pharmacies stock it.
You may have guessed that I've devoted these previous paragraphs to this explanation for more than a history lesson. The fact is that I prefer the use of Thyroid U.S.P. to synthetic T4. The reason for this is as simple as it gets: I find that it works better.
More history may help to explain my position: The first use of thyroid hormone in humans dates back to 1891, when a doctor by the name of Murray crudely extracted some soup from sheep thyroid glands and injected it into a myxedematous patient with a remarkable outcome. He reported his findings with the usual degree of British understatement in the _British Medical Journal._ Within a very short time others realized they could achieve the same effect by giving sheep thyroid orally. For the next fifty years or so, hypothyroidism was treated with essentially that method.
For the first fifty years of the 1900s, desiccated thyroid was virtually the only choice. It was prescribed widely and essentially controlled hypothyroidism admirably. Its use wasn't without criticism. From time to time there were complaints from physicians as well as patients that subsequent prescriptions of it didn't seem to have the same therapeutic effect as the previous one. It was suggested that the potency was quite variable and that the physician could not rely upon the strength printed on the label. One explanation is that the product lost potency on the pharmacy shelves and there was little regulation of matters dealing with shelf life. Its reputation wasn't helped by an incident involving unscrupulous suppliers importing a large quantity of a totally bogus substance.
When synthetic T4 became available in the fifties, it was believed to be much more stable on the shelf and therefore more reliable as to dosage. The reasoning was that even though our own thyroid glands produce both T4 and T3, the former is converted within us to T3 anyway, so why bother giving the mixture. I, like many other physicians, began switching my patients from Thyroid U.S.P. to synthetic T4. I must point out that I had never had the experience of the erratic potency that had been reported but, always willing to keep up with the times, I began changing my patients over to T4.
Almost immediately I began to hear complaints. Patients would report a lethargy that was something new. Weight loss in a number of patients was noticeably decreased. In short, many symptoms of hypothyroidism seemed to be increasing. Patients themselves expressed dissatisfaction by making comments like "Why did you change my medicine?" or, more directly, "This new stuff you gave me is no good."
I never did switch the whole practice over to T4, but I was also not that quick in going back to Thyroid U.S.P. in those who had been switched. I was skeptical as to my own observations and as to what was being reported to me by patients. Who was I to doubt the most recent medical dicta?
Another frequently repeated scenario starts with a patient who comes to me having previously been diagnosed as hypothyroid and who is already taking synthetic T4 prescribed by another doctor. At the point when I began to doubt the efficacy of T4, I would often switch the patient from T4 to Thyroid U.S.P. The change was often dramatic. Almost without exception I could see an improvement. There were those patients who reported that previously their doctors had reduced the amount of synthetic T4 they had been taking because of annoying side effects, such as increased blood pressure, fast pulse rate, or even tremors. I've rarely seen the same effect from comparable doses of Thyroid U.S.P.
Eventually I abandoned T4, and for years I've been prescribing Thyroid U.S.P. exclusively and I'm quite satisfied with the results. To repeat the simple answer to the question of why I prescribe Thyroid U.S.P.: _Because it works better._
The bloom began to disappear from the rose when the potency of the widely dispensed synthetic T4 was brought into question. In 1997 the government dictated that although levothyroxine had been marketed for years, because of inconsistent stability and potency manufacturers would be required to submit new drug applications (NDAs) for the product. The following is actual wording from the _Federal Register:_
No currently marketed orally administered levothyroxine sodium product has been shown to demonstrate consistent potency and stability and, thus, no currently marketed orally administered levothyroxine sodium product is generally recognized as safe and effective.
The very complaints that for years had plagued the prescribing of Thyroid U.S.P. now seemed at least as applicable to synthetic thyroid.
I have essentially told my readers the story I've just told you. They may be asking you to prescribe Thyroid U.S.P. I hope the previous explanation will be helpful to you as you make this decision.
A paper published in _The New England Journal of Medicine_ in February 1999 served to strengthen my belief. This book was well into preparation at that time, and I was pleased to be able to support my beliefs by alluding to that study. Researchers found that substituting T3 for some of the T4 hypothyroid patients were receiving produced a better result than did T4 alone. Thyroid U.S.P. contains both T3 and T4.
Whether you choose to try Thyroid U.S.P. on some patients is a choice you may decide to make. I would expect that if you do, your experience will be much like mine.
In my conversations with other doctors regarding patients under our joint care, I've frequently been asked why I use such an obscure drug. (They believe it to be obscure.) Can you imagine how many times I've had to go through the explanation I've just given you?
You're certainly aware of the paradox that exists between the degree of ignorance of some patients and the remarkable degree of knowledge of others. In this electronic age, we can't underestimate the astuteness of our patients. Thyroid patients' comments are very conspicuous on an excellent Web site devoted to the entire subject of thyroid disorders (thyroid.about.com). Of interest is a letter posted by a patient. It is to her doctor, and it is poignantly critical of his refusal to prescribe Thyroid U.S.P. for her.
I will get down to how I initiate treatment on a patient whose MFI tells me she doesn't burn calories at the normal rate. I give the patient a trial of Thyroid U.S.P. A frequent starting dose is ½ grain daily. In many instances that isn't sufficient, and I see the patient frequently and observe her as well as listen to her subjective reports. If I am 99 percent certain of hypothyroidism, I may start with 1 grain. My routine is to increase the dosage by ½ grain no more often than once a month when the signs and symptoms seem to warrant it. In every case, I monitor the amount by how the patient looks and feels and by what she reports to me. Remember, the patient is in my office primarily to lose weight, and it was the observation of the rate of weight loss that resulted in the assessment of hypothyroidism. Thus, weight loss is one of the more important determinants of my thyroid dosage. I would always prefer to err on the side of conservatism, and so a reasonable but not spectacular rate of weight loss is what I seek. The general overall state of well-being of the patient is even a greater influence in the judgment I make.
For the majority of the patients I see who have hypothyroidism, 1 to 1 ½ grains of Thyroid U.S.P. seems to be the proper dose. In some instances, I go higher. Except in the most rare of cases, perhaps 1 or 2 patients in my entire practice, I haven't had to exceed 3 grains, although in the literature much higher doses have been reported to have been needed.
# Thyroid for the Euthyroid Patient
It has been some years since thyroid medication has been advocated as a weight-loss tool. In the past it was used extensively without regard to the thyroid status of the individual receiving it. Searching the literature, I haven't found conclusive evidence that using thyroid for weight loss was ever harmful, although there is certainly enough opinion that it should not be done.
I have had no personal experience with prescribing thyroid to the euthyroid patient. I prescribe it after I determine that the patient needs it. However, if the standard for determining who is hypothyroid are the chemical laboratory tests, then indeed I could be accused of giving thyroid to a euthyroid patient. Of course, whether I'm guilty in the eyes of those doing the accusing might depend upon what day they did their tests. The point is that I've never seen anyone suffer harm from thyroid medication unless it was an obvious allergy, such as an urticaria. I explain this by reasoning that the thyroid was needed by those for whom I prescribed it.
As long as the standard remains the results of lab testing, I cannot evaluate the literature with any sense of accomplishing anything. The scientific literature in general assigns the diagnosis of hypothyroidism to those with an elevated TSH. If the baseline is what I consider to be an erroneous assumption, how can I draw valid conclusions? Totally disregarded are the signs and symptoms the patient presents as well as the obvious inappropriate response to what should be a deficiency of calories in the diet.
The question of whether thyroid medication, irrespective of thyroid disease, is an appropriate treatment for obesity is one that should be researched. I haven't prescribed thyroid in that instance, and I'm not about to embark on such a research project. Given the general apathy toward the whole subject, I also have my doubts as to whether anyone else will. [There is more about this concept in Appendix A.]
# Emphasis on Protein
In recent years there has been a dramatic shift in what is considered the best type of diet to follow. We now have the Food Pyramid, which displays a suggested diet of a considerable amount of carbohydrate, little fat, and a small amount of protein. This expresses the general dietary recommendations of what "experts" have been advocating for years. This has been applied not just to general diet, but also to reducing diets. Prior to that and extending back to the middle of the nineteenth century, a diet high in protein and relatively low in carbohydrate was considered to be the ideal reducing diet. There were plenty of published studies to substantiate that a high-protein diet produced the best weight-loss result.
It is my observation that the obesity problem has become more widespread and more severe with the current emphasis upon carbohydrate. Of course I'm not alone. Very recently there have been a host of books and magazine articles singing the praises of the high-protein diet. Some advocate very high fat at the same time, and this has been severely criticized. Fat in the diet adds much to the satisfying quality of food and it does slow the gastric emptying time. Whether those factors justify the added nine calories per gram or the possible dangers aren't matters that I will address here. But, at the moment, protein seems to be in.
I have always felt that the high-protein diet was the best for my patients. Like many other aspects of my practice, what I do with my patients is based upon what seems to serve them best. I've had a lot of years to observe the effects of various techniques, and I've had a lot of patients on whom to make these observations. The bottom line is that my patients get the best results when they eat a high-protein diet.
We could debate whether this is due to the specific dynamic action of protein. This concept is well established and has never been disproved, but it is for the most part ignored. Quite simply, protein digestion and assimilation requires a greater expenditure of calories by the body than does carbohydrate or fat. There is more about this in [Chapter 9.]
At any rate, my reason for advocating protein is much like the reason I like the metabolic test I use and the medication I prefer: _They simply work better._
# The Diet
The diet I've advocated in this book is designed to work. I've avoided the gimmicks and nonsense that accompany so many of the magic diets out there. What I advise is what I've found the majority of patients can follow. The diet has no magic. It is designed to meet the needs of the majority of my readers.
I like the 1,000-calorie level. In my own practice, more frequently I advocate 800. I'm comfortable with it and I try to get patients to make weekly visits in order to monitor it. Some cannot tolerate that few calories and so I must go up to 1,000 or more, and the weight loss is slightly slower. By the same token, I've found no advantage in going too much lower than 800 calories. Below that, the metabolic rate probably falls and weight loss slows, so there really is no advantage. Furthermore, it confuses the hypothyroidism situation and makes adjusting the thyroid dose more of a task. Of course, this is your patient and you must decide on the diet. If you aren't comfortable with 1,000 calories or the emphasis on protein, certainly other combinations will work as long as the calories are restricted. A few calories more will still result in weight loss, even if at a slower rate. The important thing is to encourage the patient to reach the goal that has been set. If the patients don't get to the target weight, rarely do they maintain the weight they've achieved. Invariably, they gain it back. I go to lengths to emphasize to my patients that they must get to the goal weight that has been set for them.
I make free use of packaged foods, frozen, canned, or otherwise. I tend to ask my patients to stick with foods for which they can easily determine the calorie count. There are enough of these to keep them interested. Packaged foods have the calorie counts clearly stated, and for many of the bulk foods I've provided the necessary caloric information. One of the calorie books I've recommended can come in handy.
I'm quite flexible about how the reader is permitted to exercise options. Three meals a day isn't an absolute requirement. The lifestyle of many allows only two, and the individual is often quite comfortable with that. Likewise, the distribution of calories between the meals doesn't seem all that important. I've seen no proof that it makes a bit of difference. So whether it is a bigger breakfast or a bigger dinner isn't material. The important item is the calorie count. If you stress the importance of that, neither you nor they can go wrong.
Without a doubt, the average patient will have fewer or less productive bowel movements when eating 1,000 calories a day, down from the customary 3,000. This is the basis for a frequent complaint. It is generally reported as constipation, but I reserve that term for times when the patient is truly physically uncomfortable. Some people are perhaps overly concerned about having a daily bowel movement, and my insistence on a high-fiber cereal for breakfast probably contributes to their peace of mind.
# The Patient May Need Your Cooperation
The patient's basic motivation is the major factor in whether the whole exercise turns out to be a success or a fiasco. A close second on the list of what helps is the encouragement given by the caregiver, in this case, you. I believe you must continually support, encourage, warn, and, in some cases, criticize, but in every case you need to convey the impression that you expect the patient to achieve a normal weight. You must nurse them through the times when they've followed the instructions scrupulously and have for a week or so shown no weight loss. As far as the scale is concerned, even in the most rigid adherents, weight does not come off a little each day. It comes off in spurts, sometimes intermingled with weight gain. You, as well as the patient, should have faith in the science. Quite simply, an adult human cannot continually eat 1,000 calories a day over the long haul and not lose weight.
**Contact me**. I would love to hear from you. Perhaps you have questions. I will answer them to the best of my ability. The best means to contact me is through my Web site. The address is: www.drsiegal.com.
#
# _Debating My Position_
I don't resent criticism, even when, for the sake of emphasis, it parts for the time with reality.
— _Winston Churchill_
**T** he methods of diagnosis and treatment I've described in these pages are assuredly different from what you've been exposed to in the past. Perhaps you've been told you have normal thyroid function based on laboratory work that was done, and perhaps I've raised some questions in your mind that maybe it's just not so. Perhaps you already know you have hypothyroidism and are being treated with synthetic thyroid hormone, but I've cast some doubt on whether you're getting the optimal treatment. Perhaps you're having difficulty losing weight and are wondering whether the methods I've described in this book will really work for you.
If these concepts seem contrary to what you've been told in the past, you must understand that they will seem even more divergent to the majority of doctors who read this book or hear about it. Doctors aren't shy when it comes to voicing opinions. I know that by the time you read this, you will have heard contrary opinions. I don't know how severe the criticism will be, but I do know it will be there. I also expect some degree of approval from a number of physicians who have had the same type of experiences with their patients that I've had with mine. I even hope to enlist some converts who will at least consider seriously what I've reported here and implement some of these ideas into their medical practices.
True debates over new ideas of this type often make their way into the media. Yet it would be rare for the public ever to have the benefit of a full-scale debate that covers both sides of an issue. What you will generally get is a one-sided declaration from some authority. If the authority happens to be me, it will obviously be one-sided because, as fair as I wish to be with my critics, I believe what I believe, and as I've said before, my experience is what has shaped my opinions. If the authority is another doctor, he also has a right to his opinions. That's what a debate is for. Both sides can be expressed freely and the audience can decide. But the likelihood of a full-scale debate is slim.
Since I anticipate some one-sided criticism, perhaps from your own doctor, and perhaps from articles in newspapers or magazines or perhaps on TV or radio, I've decided to reproduce such a debate here. I will fairly represent the criticism of what I have to say, and I will respond to it. I believe I know most of the arguments that will be used, and I believe I can express them fairly.
Here is a mythical confrontation between the noted thyroid authority, whom I shall name Dr. I. M. Conformist, and Dr. Siegal.
DR. CONFORMIST: Thank you for meeting with me, Dr. Siegal. I've been reading from your book. I found it interesting, but there is much I would like to discuss with you.
DR. SIEGAL: I welcome your interest.
DR. CONFORMIST: As you certainly are aware, some of the concepts you've expressed seem to be directly in conflict with what is generally accepted as standard when it comes to the treatment of hypothyroidism. Are you not troubled by that?
DR. SIEGAL: I'm not troubled by it, but I would prefer not to find it necessary to disagree with so much current thought in this area. However, that is the reason for this book. I can't ignore what my patients have taught me. The reason for this book is that I do disagree. I believe that what I've presented here can be very useful to my readers. My secret hope is that it will foster more research in this area.
DR. CONFORMIST: I have no problem with your recognition of the signs and symptoms of hypothyroidism, although you do seem to think it is more prevalent than what is generally believed. But you do seem to be quite critical of the standard methods of diagnosis, methods that are universally accepted.
DR. SIEGAL: Yes, they are widely accepted, but I don't accept them. I believe there are a number of other doctors who don't. It's been over twenty-five years since Dr. Barnes wrote his book on the subject, and I happen to agree with much of what he had to say. Do you know that his book is still in print? That's unusual for a popular medical book. It must have made an impression on readers who could relate to what he had to say. Most books of that type are usually gone from the bookstores in a few months.
DR. CONFORMIST: I've heard of Dr. Barnes's book, but I must confess I haven't read it.
DR. SIEGAL: Dr. Barnes criticized the practice of diagnosing thyroid problems through the use of the laboratory. He felt that the diagnosis of hypothyroidism was often missed by physicians who had too much confidence in the laboratory. That has also been my experience.
DR. CONFORMIST: Why are you so negative on thyroid tests such as the TSH?
DR. SIEGAL: It seems that most doctors accept lab results even when they seem to be in conflict with their own observations. We all know that labs can make mistakes, and no one berates them for it. What I'm speaking of is quite different. I believe that tests such as the TSH, even when done flawlessly, miss the diagnosis of hypothyroidism quite frequently. What is my evidence for this? Many patients I've seen and whom I believed to have hypothyroidism had normal laboratory values. As soon as they started taking thyroid hormone, their symptoms abated. They showed no ill effects on later follow-up. Is this not persuasive evidence of my position? Much of the research that's done starts with the premise that the lab tests are infallible. If, for example, you wished to test a medication only on hypothyroid patients but you excluded some from the study because it was determined from the lab that they weren't candidates, in my opinion, you would have a flawed experiment.
DR. CONFORMIST: The TSH test is the first step in investigating thyroid function, whether overactive or underactive. Yet you say you have no confidence in it.
DR. SIEGAL: I've done thousands of thyroid tests on my patients over the years, TSH and others. As I look back, I realize they were virtually of no help in aiding in the diagnosis of hypothyroidism.
DR. CONFORMIST: The medical community disagrees: I use the test regularly with my patients and I uncover many cases of hypothyroidism.
DR. SIEGAL: I'm certain you do. My concern isn't with those that are discovered, it is with those that go undiscovered. Do you think some slip by?
DR. CONFORMIST: I'm sure that has happened on a few occasions and those were probably borderline cases, so-called subclinical hypothyroidism.
DR. SIEGAL: How do you know you haven't missed many more cases?
DR. CONFORMIST: Because I have tested my patients and the tests have shown me who has the ailment and who doesn't.
DR. SIEGAL: But that is exactly my point. You rely on the test results exclusively. What if the tests are flawed?
DR. CONFORMIST: The medical community didn't accept these tests without a lot of research to back them up. We have to trust the scientists.
DR. SIEGAL: I do trust them, but I can't ignore what I've seen with my own eyes. Do you ever see patients who have multiple symptoms of hypothyroidism but the TSH comes back normal or even low?
DR. CONFORMIST: Yes, that happens sometimes.
DR. SIEGAL: How do you account for it?
DR. CONFORMIST: The patient has normal thyroid function and therefore I must look elsewhere for the cause of the patient's symptoms.
DR. SIEGAL: With this type of patient, are you usually successful in finding the cause of their symptoms?
DR. CONFORMIST: Sometimes yes and sometimes no. As you know, we doctors aren't always successful in arriving at a diagnosis. Some ailments simply defy discovery.
DR. SIEGAL: Would you consider treating a patient for hypothyroidism if she had all the symptoms but the laboratory said she didn't have the ailment?
DR. CONFORMIST: I won't say I would never do it, but it would be a rare occasion.
DR. SIEGAL: If, on one of those rare occasions, you prescribed thyroid hormone and there was a dramatic improvement in the patient's condition, would you continue the treatment?
DR. CONFORMIST: Yes, I suppose so.
DR. SIEGAL: This is essentially what I'm doing, except it seems to happen with greater frequency. It appears that the only difference you and I have so far is when it comes to confidence in certain specific lab results.
DR. CONFORMIST: So you are saying that you've had a number of patients who test normal but actually have hypothyroidism?
DR. SIEGAL: Yes, literally thousands over the last forty years. I haven't kept track of the numbers.
DR. CONFORMIST: But how do you know you haven't been prescribing thyroid hormone to patients who have normal thyroid function?
DR. SIEGAL: The patient tells me. If there is a clear-cut reversal of the symptoms, I can only conclude that I was correct. The patient knows. I think we have to listen to our patients. If my patient changes from an apathetic recluse to a socially competent individual and at the same time her periods straighten out, her depression vanishes, and she is able to lose weight for the first time in her life, then I have to assume that I was correct. And if her hopeless infertility for which she's spent thousands of dollars on diagnosis and treatment ends in a pregnancy two months after starting on thyroid hormone, then I'm even more certain that I was right.
DR. CONFORMIST: You ask the readers to take this test of yours. A doctor would have to have a lot of confidence in your method to ignore the laboratory in favor of your test.
DR. SIEGAL: I have confidence in the method because over the years it has served me better than the lab has in this area. You understand this isn't a blanket condemnation of laboratory tests. My complaint specifically targets thyroid tests. As to whether a doctor will try my test and accept the results, I hope I've made a good case for trying it. If after hearing the patient's history he is convinced she has a weight problem in spite of her moderate eating habits, I hope he will entertain the possibility of hypothyroidism. I expect the doctor to listen to everything the patient says and assume that he is hearing the truth unless there is some special reason to doubt what the patient has said.
The history tells me a lot. Are you aware of the questionnaire that is part of the testing? It is quite valuable. It was adapted from a well-known study aimed at finding an alternate and perhaps more cost-effective means of diagnosing hypothyroidism.
What about the patient's body temperature? Don't you agree that a low body temperature, though not definitive, is certainly consistent with hypothyroidism? And what about a high blood cholesterol? I've seen one case after another of patients whose cholesterol was brought under control where there was nothing to account for the improvement except for the thyroid hormone they had been prescribed.
There are other doctors who believe just as I do, but they are simply not vocal. More importantly, there are intelligent and perplexed patients who feel the same way. Do you know that there is a Web site where patients air their complaints against doctors who ignore their hypothyroidism? They regularly post messages asking others to find them a doctor who will look beyond lab results.
DR. CONFORMIST: Let's move on. I noticed that you prescribe desiccated thyroid for your hypothyroid patients. I run into desiccated thyroid every now and then, and when a new patient has been taking it, I usually switch her over to levothyroxine (synthetic thyroid). I don't know anyone who prescribes desiccated thyroid anymore.
DR. SIEGAL: I do. And I do it for one simple reason: It works better. That's not to say that synthetic thyroid doesn't work, but natural thyroid works better. By the way, I like to call it "natural thyroid" in order to avoid confusion with the synthesized varieties.
DR. CONFORMIST: Has it not been established that the strength of what you call natural thyroid is inconsistent and that the potency can vary considerably?
DR. SIEGAL: I've researched the subject completely. I find no documentation that natural thyroid is unreliable, even though I've heard that rumor. I do know that it was actually the potency of synthetic thyroid that was questioned by the FDA and serious sanctions were imposed on the manufacturers. Keep in mind that after all these years, natural thyroid is still a U.S.P. drug, as is levothyroxine sodium. In a recent book by DR. Arem, a recognized thyroid expert, he recounts how some of his patients, when he switches them from natural to synthetic, complain. They tell him it doesn't work as well. He, however, seems unconvinced. Unlike DR. Arem, I am convinced. Perhaps I've heard it more often than he has. I've dealt with the problem so frequently over the years that there is no question about it in my mind. Natural thyroid works better than the synthetic levothyroxine. Have you prescribed much desiccated thyroid?
DR. CONFORMIST: No. As long as I have been in practice, the literature has specified levothyroxine as the drug of choice.
DR. SIEGAL: That is certainly the case. You're speaking of synthetic thyroid. I wonder how many doctors would change their minds if they were to prescribe natural thyroid for some of their patients and see the results I've seen. On that same Web site I mentioned earlier, the one where thyroid patients commiserate with one another, one of the most frequent complaints is that some doctor took them off the natural thyroid that worked for them and they cannot find another doctor who will prescribe it. They plead for the name of a doctor who will help them.
I believe that the reason for the popularity of synthetic thyroid has more to do with marketing than any other factor. We doctors are bombarded with advertising, and it must certainly shape our prescribing tendencies, otherwise why would the drug companies spend so much money trying to get us to prescribe their products?
DR. CONFORMIST: I have the impression that you use thyroid hormone as a weight-loss medication.
DR. SIEGAL: Absolutely not. I don't prescribe thyroid hormone unless I'm convinced the patient has hypothyroidism. In those cases, it isn't for weight loss, but to correct the thyroid problem. But in the course of doing that, it may indeed help the weight loss because now the metabolism is brought up closer to normal. We may someday learn that it can be used for weight loss in the patient who isn't hypothyroid, but so far I haven't done it.
DR. CONFORMIST: As to your MFI test, I haven't heard of any testing that used a patient's caloric maintenance level as a basis for the diagnosis of hypothyroidism.
DR. SIEGAL: To my knowledge, it hasn't been done before. Isn't it logical that the number of calories that maintain a patient's weight is intimately connected with how the thyroid functions? Do you have some reason to believe it isn't accurate? Suppose a patient of yours is on a 1,000-calorie diet and in a month loses only 2 pounds. That translates into that patient maintaining her weight on 1,250 calories a day. What other explanation could there be for this other than hypothyroidism?
DR. CONFORMIST: I don't know. There could be some other hormonal imbalance. Maybe she is retaining a lot of fluid. Maybe she's stretched the truth a bit.
DR. SIEGAL: I look for other explanations, such as the water retention you mentioned. It's not difficult to detect. The point is, Doctor, that is how I make the diagnosis of hypothyroidism. If the patient doesn't burn calories at the same rate as someone with normal thyroid function, I call that hypothyroidism. It's really quite simple. Besides, the important thing isn't what you call their signs and symptoms, but rather what you can do to alleviate them. When a patient presents me with such an underactive metabolism, it is almost a certainty that she has several other hypothyroid symptoms. If administering thyroid hormone makes her feel better and she starts losing weight, I'm satisfied with the name I've given her condition. In the end, the name isn't what is important, it is the welfare of the patient. There is no question that some patients will fudge about their eating habits, and I've become rather skilled at sensing when my patient isn't all that truthful. We have to be careful that we don't categorize patients as liars as a catchall for our frustrations. If we can't explain the reason for what the patient reports, it isn't always because we're being deceived.
DR. CONFORMIST: The diet you recommend for weight loss is slanted very much in the protein direction. It doesn't conform to the USDA's Food Pyramid.
DR. SIEGAL: It is my impression that the pyramid was intended as a guide to "proper eating" habits. I'm not sure that it is even proper for maintaining weight, although that is an entirely different subject. There is nothing proper about a diet for losing weight. To lose weight you must follow a deficient diet, one that is deficient in calories. I've chosen the high-protein diet for the same reason I've done all these other things, because it works. I've watched twenty years or more of this emphasis on carbohydrate in the diet and I've seen the obesity problem seriously worsen during that time. High protein, moderate carbohydrates, and very little fat results in weight loss with minimal hunger in a motivated patient.
DR. CONFORMIST: Doctor, your ideas are different. Is it good to shake patients' confidence in their physicians? This cannot be to their benefit.
DR. SIEGAL: I've agonized on this point. What would you do? You seem to be in disagreement with my ideas. Should you restrain yourself from criticizing me? These aren't my "ideas." These are the conclusions from my observations. I didn't simply read some scientific papers and put all the information in them together into a book. Everything I've reported is based upon my experience with thousands of patients. Should I not share this information?
I didn't really know how to end this interview. My position is clear, and it is unlikely that Dr. Conformist will withdraw from his. In the real world, the interview will probably end when the moderator says that it is time to take a commercial break.
If it seems unusual that I have taken the time to criticize my own work, so be it. I've done so because I believe there is the possibility that you will hear bits and pieces of the type of criticism I've described above. It is likely that any criticism will be onesided, so in the interest of fairness or, more importantly, in your best interests, I've organized the criticism and have presented both sides.
My Web site is there for you, your doctor, and anyone else to use to communicate with me. You'll find me at www.drsiegal.com.
#
# _Maintaining Weight, Hypothyroid or Not_
**S** ometime during the course of treatment of a patient, the subject of weight maintenance will come up. When a patient first begins the program, it seems perhaps too optimistic even to entertain that thought, but when it appears that the goal is in sight, how she will maintain a normal weight in the future becomes a real concern.
_The vast majority of people who lose weight gain it back._ This occurs in spite of the best intentions of the weight loser, let alone the lofty motives of those who facilitated that weight loss. It applies to my patients as well as to those who got their direction from some magazine article. Whether you join an organization that uses group enthusiasm to motivate you or you buy questionable packaged meals from one of those widely advertised "clinics," or even if you succeeded through the devoted efforts of your doctor, the fact is that the odds favor your gaining back what you've lost.
Strangely enough, my patients seem convinced that they will not regain the weight. "I will never again allow this to happen" seems to be the frequent slogan. The patient who proclaims this really believes that. But it does happen, and, what's more, she allows it to happen.
There is a certain sameness to all weight-maintenance efforts. One clinic presents a particular set of eating rules that will keep you thin for a lifetime. A book says to make sure you eat this much of this and that every day, but keep this and that below a certain amount. Your doctor may speak in terms of units of food or exchange groups. It all amounts to the same thing. Everyone says that the way to maintain your weight is to follow some sensible eating regime for the rest of your life. Who could fault such sage advice? Of course it will work. You eat what you're supposed to and you will never gain back your weight. That's obvious.
But virtually everyone does gain back the weight. Why? Because they don't follow that very fine advice. That is the rule. Anyone who does spend the rest of his days eating exactly what he's been told to is the rare exception.
My question to all concerned is, What good is it to pass out advice you know no one will follow? One answer is that it gets the advice-giver off the hook. If I tell my patient that for the rest of her life she must eat this and that and she disobeys me, I'm home free. But what about my conscience? What if, in my heart, I knew she would not follow that advice, in spite of the fact that she thought she would? What then? Can I still claim innocence?
This is the crux of the problem. There is a lot of good advice out there that no one follows. What's more, anyone who has dealt with overweight patients over the years knows that what I'm reporting is right on. Any doctor who has seen a few thousand overweight patients knows that once the weight is lost, it is easily regained in spite of the good intentions of the patient.
This knowledge is enough to make one throw up one's hands and look for a more satisfying job, like selling refrigerators in Antarctica. But there is one ray of hope.
Not all of my patients gain back the weight they have lost. There is a relatively small number who do maintain the weight, and possibly way into the foreseeable future. Two observations characterize this group.
Everyone who maintains weight long term seems to have first reached the goal weight that was set for them. I will tell you quickly that I don't really know the reason for this. But it does seem to be a fact, at least in my own practice. A patient may have lost one hundred pounds or so, yet still have another twenty or thirty to go. She may be so overjoyed at the change that she no longer perceives any kind of problem. I may emphasize to her that she is now at the stage when many patients first come to me. She now has twenty-five pounds to lose, and it is very common for a new patient to come in who has twenty-five pounds to lose. This doesn't seem to make an impression on certain people. The crisis of that first hundred pounds is over and she simply can't motivate herself further.
This is the patient who is certain to gain back the weight.
Whether the prerequisite of reaching the goal weight in order to increase the likelihood of permanent success is a physical or a psychological phenomenon is beyond my ability to investigate. I've repeatedly told you that I'm a practical kind of doctor; if it works, do it. If you don't know why it works, and it causes no harm, do it anyway. While the dedicated scientists are delving into the answers, I can help a lot of people.
My first admonition to a new patient is that she must achieve the goal weight that is determined for her. I even go so far as to say that she should not even start the program if the intention isn't to reach the goal. It will be a total waste of time and perhaps even be counterproductive.
This poses a problem with some of my patients, and it is generally the female patient. There are many women who don't want to be as thin as I want them to be. This group is usually in the fourth decade of life or beyond. Some honestly tell me that the concern is that they will look older. They know that as the fat layer disappears, the skin will become looser. The skin is being stretched and wrinkles are consequently minimal. They know that after losing weight they may begin to show their true age, and this isn't acceptable to them. I have a hard time convincing them otherwise. This matter of vanity seems to be far more powerful than the desire for health.
I've pointed out that at least in the case of females, one rather large study shows a straight-line relationship between what you weigh and how long you live. For those overly concerned about that loose skin, there seems to be little concern about how long they live. They just want to look their best. Of course, there are vast differences in the elastic qualities of skin in different individuals. In some, I've seen no hint that an enormous amount of weight has been lost, yet in others, it is quite obvious.
At any rate, my advice has to be predicated on my patient's health and not on how she stacks up to the ladies on the magazine covers. I insist that my patients reach the goal I set for them.
Though I'm sure that a proper weight is a requirement of weight maintenance, it isn't the only requirement. Getting to your goal weight isn't absolute insurance that you will stay there. A second factor is always present in my patients who maintain weight, and that is exercise. I never see anyone maintain weight who isn't into a sufficient amount of exercise.
If the prescribing of a maintenance diet doesn't work, the prescribing of an exercise program does. There is no accurate way to measure exactly how much exercise the average person needs, but I believe that in the majority of my patients, burning up an extra 400 to 500 calories a day above and beyond their normal activities will go a long way toward keeping them thin. This applies to those who have no metabolic problem whatsoever as well as those I'm treating for hypothyroidism. Of course, the latter group must be taking the proper dose of thyroid hormone or even that 400 to 500 calories of hard work will not maintain them.
How is this accomplished? With cardiovascular (aerobic) exercise. I don't favor one type over another. Your personal preferences should dictate this, but you must burn up 500 calories a day and you shouldn't miss more than one or two days a week. Many of my patients are members of well-equipped exercise facilities, and they can accomplish burning 500 calories per day at those places. Whether they choose the treadmill, the stepping machines, the ski machines, or the bicycles or a combination of several of them isn't as important as whether they are consistent.
There is a tendency for these places to advocate weight training at the expense of cardiovascular exercise, and I think you should be alert to that. Many of these "personal trainers" with the beautiful bodies can make a strong case for weight lifting. I don't see the necessity for it and I think it can actually be counterproductive, particularly if the time spent on the weights (or the weight machines) is borrowed from the time on the aerobic activity. The only real argument for weight training, in my opinion, comes from studies that seem to suggest it reduces the development of osteoporosis in women. I don't know if anyone has compared weight training with straight cardiovascular exercise as to that benefit.
It is difficult to assign calorie values per minute or per hour to various activities. This is particularly true when it comes to machines, which can be quite variable in the amount of effort required to work on them correctly. Many of the machines come with caloric expenditure readouts, and although I don't have much confidence in these calculations, they can still serve as a guide. They are certainly better than working totally in the dark. If you belong to an exercise facility, ask for their help in determining what you must do to burn up 500 calories.
The simplest activity is walking. It requires the least amount of preparation and you don't have to purchase designer tights to do it, nor does it require a paid membership. The streets for the moment are still free for you to use. You must walk at the right pace or you're wasting your time and not accomplishing the goal. The pace is fifteen minutes (or faster) for each mile covered. That's fast walking, possibly as fast as you can walk. If you were to cover your mile in much less time, you wouldn't be walking, you would be jogging or running. That too would be acceptable. There are arguments in favor of walking over jogging, and vice versa, and you must decide what is right for you. Just remember the 500 calories.
You must have asked yourself by now, When is he going to mention the diet for maintenance? The answer is now, except that there is none. I've already told you that the biggest failure in the whole weight-loss scenario is failure of most people to maintain the weight they have achieved. This is in spite of all the well-meaning efforts of those who have provided such well-thoughtout maintenance diets. I no longer waste paper supplying these, and I don't waste my breath advocating them. I know that the odds of my patient staying on the diet, particularly if she doesn't have to stare me in the face periodically, are nil. The key is exercise, constantly, and enough of it, and in the majority of cases that will do it. Remember, you must first achieve your proper weight.
Since I don't supply a diet and in fact declare that there is no diet, does that mean you can eat everything your little heart desires? In my own practice I generally say yes, but sadly add before the end of the sentence, "within reason." That is, of course, the catch. What is within reason for one isn't within reason for another. So this is where you will have to feel your way. I've found that the vast majority of those with normal thyroid function, or with thyroid function that has been brought up to normal with medication, will maintain their weight eating very comfortably as long as they burn up the required calories. For most this can mean a dessert after dinner a few times a week, a daily glass of wine with the meal, and popcorn at the movies. There are areas where overdosing can catch up with you—things like regular sodas, sugar in coffee, etc. Why not continue to drink diet sodas and use artificial sweetener?
Of course you aren't limited to 500 calories' worth of exercise a day. If you've become a fanatic, as some do, you may do more. That will give you even more leeway when it comes to food. Bear in mind that each of you is different. What works for one doesn't necessarily work for another. Experiment to see how much exercise you need for your particular eating preferences. It may not be much fun maintaining weight, but it is certainly a nicer task to contemplate than losing weight.
As for your thyroid, if it was determined that there is simply not a problem there, what I've just given you is your method. If, however, you're one of those who has been shown to burn calories insufficiently and you've been put on thyroid hormone by your doctor, you must be vigilant to see that the amount you're getting is proper. The chances are that you feel much better after taking the thyroid hormone than you did before. You can use this general feeling as a benchmark of how you should feel in the future. Your requirement for thyroid hormone could change over time. You should be vigilant to look for this possibility. In some ways you're more qualified to suspect that a change is necessary than your doctor. You're the one who knows how you feel. Be assertive with him, but not obnoxious. You must preserve the relationship.
On a number of occasions I have had to raise the daily dose of thyroid hormone in a patient. I've also had to lower it, but much less frequently. Even in those cases, I don't think it was because of a true change in metabolism, but rather simply a matter of having prescribed a larger dose than was necessary.
As a parting word, I would like you to know that I've sincerely given you the information that has come from my years of dealing with overweight patients, with emphasis on those with hypothyroidism. I know other doctors may disagree. I suspect that most of that disagreement will come from those who strictly follow the literature rather than relying on their own hands-on experience. A lot of people in my own medical practice have been helped by taking my advice. I hope this advice will help you.
I would welcome hearing from you. My Web page awaits you. Contact me at www.drsiegal.com.
# Summing Up
* Methods advocated for maintaining weight that concentrate on lifetime eating habits are notable failures because the public refuses to adhere to them.
* For the achieved weight to be maintained, the subject must have reached a proper goal weight.
* Weight maintenance is best accomplished by using exercise as the means rather than diet.
# _Appendix A: Prescribing Thyroid Hormone When the Gland Is Normal_
A definition of euthyroid is a good place to start. This is a medical term that refers to a thyroid gland that functions normally—that is to say, one that supplies the right amount of thyroid hormone, neither too much nor too little.
By now, you're aware that I question the common way "too much" or "too little" is determined. The majority of doctors will look at the results of laboratory blood tests, often only one, the TSH test, and make the determination. The fact that I disagree with this method doesn't negate my acceptance of the definition in the previous paragraph. The hallmark of hypothyroidism is "too little," and I've already explored in detail how I determine "too little."
The question arises, Might the use of prescribed thyroid hormone have any place as a medication for those who are euthyroid, those with normal thyroid function? Earlier in the book I've emphatically stated that I have no experience with doing this. I've confined my prescribing of thyroid hormone to those whom I've diagnosed as having hypothyroidism. Perhaps I should have underlined that previous sentence, since I would not want to have my mention of thyroid hormone for the euthyroid misconstrued. _At this time, I don't advocate the use of thyroid hormone as a medication for those who are euthyroid._ I italicized the last statement to give it emphasis, and don't be surprised if you see it repeated more than once in the pages to follow.
Is there a case for prescribing it? No, but there may be in the future. I cannot make a case for prescribing thyroid to people with normal thyroid glands but I can certainly make a case for extensive study of its effect on euthyroid individuals in order to determine if it has value in those people. The effect of using thyroid hormone in some patients is so dramatic that it seems to fulfill its being designated a wonder drug. Of course, I'm speaking of the use of natural thyroid hormone, which, as you know, is my preference. To simplify this section, I will not differentiate among the specific hormonal products, but will lump them together as "thyroid hormone" or simply "thyroid." Yes, I can make a strong case for finding out if it can benefit those who don't have hypothyroidism.
Given that the differences in the varying degrees of hypothyroidism are so subtle, it is easy to see that it may be difficult to draw a fine line between those who have a minimal case, the so-called subclinical variety, and those who have nothing more than a suspicious symptom or two. Could someone in this category feel better by taking an even smaller dose of thyroid than I usually prescribe? The standard smallest tablet of natural thyroid available is about 15 milligrams. Might 7.5 milligrams or even a smaller amount have some value?
I will have no difficulty finding doctors who reject this idea. They will undoubtedly take the position that the hormone is specific for replacement in those who are shown to have a deficiency and could be harmful to anyone else. If they were pressed to explain how thyroid hormone could be harmful, I would expect to hear that it is known to raise blood pressure and pulse rate. One who doesn't need it might become jittery or shaky. It could cause palpitations. I will be the first to concur that those are all possibilities. I would then ask these dissenters if they've ever prescribed a medication that had that same potential for adverse effects upon a patient. Did they do it with the hope that it would help even though there was a chance of an adverse effect? Let's look at a concrete example.
I think it is common for doctors, when confronted with a patient who has a runny nose or is sneezing, to prescribe medications that contain drugs such as phenylephrine, phenylpropanolamine, or pseudoephedrine. I realize that those words are a mouthful, but they are all substances in the category of vasoconstrictors—they narrow blood vessels. In the process of doing so, they tend to shrink the membranes that line the nasal passages, and thus facilitate the passage of air into the nose. These types of medications are prescribed universally and can even be purchased without a prescription in the form of various "cold" preparations or allergy treatments. They are commonly referred to as decongestants.
One characteristic of these decongestants is that they have the common side effect of increasing the pulse rate and elevating the blood pressure. There are even dire warnings that the doctor or the purchaser must use caution when the user has certain medical conditions. I wonder if the doctor who prescribes these for the patient who has a moderately fast pulse or a blood pressure approaching borderline exerts as much caution as he might advocate for trying thyroid on a patient who could benefit from thyroid medication.
The fact is that such a prejudice toward the use of thyroid in all but the most blatant cases is so prevalent that doctors don't apply the same set of rules to it as they do to decongestants. I might speculate that using decongestants in the wrong patient is far more dangerous than using thyroid in the wrong patient.
I might get an argument as to the wisdom of my last statement. If so, I would challenge anyone to do a better search of the literature than I've done and demonstrate proof that the trial of thyroid in a supposed euthyroid individual carries more danger than, let us say, prescribing aspirin to someone who has never taken the drug before.
Aspirin has occasionally been referred to as the wonder drug of the century. I would guess that it has taken away more headaches than any other drug in history. Many arthritis sufferers rely on it to quell their agony. It is now the first medicine to be given with a suspected heart attack. In spite of these wondrous testimonials, aspirin can also be very dangerous. It has been implicated in precipitating Reye's syndrome in children. Many people owe their ulcers to using aspirin, and it could be life-threatening to someone allergic to it.
We don't generally hold back on prescribing medications that have great potential to heal and only minimal potential to cause harm to the subject. We must factor into the equation whether any harm done is reversible. Can it be stopped in its tracks? When a doctor observes an uncomfortably fast pulse in someone who has taken a decongestant, he simply stops the use of the decongestant. If our patient breaks out in a rash after his first aspirin tablet, we discontinue it and mark on his chart, "Allergic to aspirin." Could not thyroid medication be stopped at the first sign of a problem?
This might sound like I'm advocating the use of thyroid in the euthyroid. _I'm certainly not._ It's time for repetition. _At this time, I don't advocate the use of thyroid hormone as a medication for those who are euthyroid._ Is there a time when I will? Possibly. When its use in that area has been carefully studied and the potential for benefit far outweighs the potential for harm.
Do I see this happening in the future? Quite possibly. There is certainly a case for investigating that possibility. It may be that much smaller doses than are customary can benefit the euthyroid. There may be those who have some elements of hypothyroidism that my MFI test doesn't pick up. But for the present, don't even think of trying to talk your doctor into prescribing thyroid if you aren't hypothyroid.
And once again: _At this time, I don't advocate the use of thyroid hormone as a medication for those who are euthyroid._
# _Appendix B: Historical Perspectives on Eating Meat and Fat_
We should well ask ourselves why we love meat and fat so much. Like many other characteristics we possess, the answer probably lies in our genes. We, the human race, are meat and fat eaters because our ancestors were meat and fat eaters.
I see my share of vegetarians. They are apt to point out that we humans have more of the physical characteristics of other primates like chimps or gorillas, essentially vegetarian animals. They point to the teeth and the fingernails and the thumbs, etc. They say we don't have the same kind of teeth as lions and tigers or even the family dog. I can't argue with that. It really doesn't look like we were designed for meat-eating. But what we were designed for and what serves us best aren't necessarily the same.
The process of evolution changes us so that we can adapt from what we were designed for. Were we designed to travel in steel vehicles with rubber tires, to leave them in underground parking garages while we go to work in an office on the fiftieth floor of a skyscraper? We may not have been designed to eat other animals, but that's exactly what we've been doing ever since we got up off all fours.
Early man was clearly a hunter-gatherer. He hunted animals and gathered fruits, nuts, and berries. Every evidence is that the hunting was more productive than the gathering. It takes a lot of berries to satisfy the needs of an extended family, but a wild boar all by itself can do the job admirably. And the fatter it was, the more food energy (calories) it provided. Early man wasn't interested in how his cholesterol was doing. He wanted the most calories he could get for his "buck." For over a million years, man has been a hunter and a meat-eater. He wasn't able to go to the supermarket and pick out fresh fruits and vegetables.
The nice thing about we humans is that we do adapt. Adaptation isn't limited to humans. All species adapt. If you eat meat long enough because it is expedient to do so, even though you were originally designed for other things, your body undergoes changes. Over a million years this adaptation becomes more established, until eventually you fare better in the new environment than in the old.
Over virtually all of man's history, the quest for food was his chief occupation. His day was spent searching for food. Man had to go where the food was. He was for the most part nomadic. He followed the herd, so to speak. The plant foods he ate were gathered. You can't grow your own crops if you're constantly on the move. He was a hunter. A number of anthropological writers have said that the predatory predilection survives today. We're still essentially hunters; it is instinctual.
One of the better authors on this subject was Robert Ardrey. He was actually a writer of plays as well as Hollywood films. But his true love was anthropology and ethology, and he devoted years to research in this field. Between 1961 and 1976 Mr. Ardrey wrote four books on the subject of the origins of man's basic nature. He talked with the foremost researchers of his time. Ardrey gives the impression of, at the same time, both loving and hating the human race. His first book, _African Genesis,_ was sort of a homage to Raymond Dart, who made a most important discovery, the bones of a man who lived 4 to 5 million years ago in Africa, and whom Dart named _Australopithecus africanus._
Dart was convinced that his _Australopithecus_ was both a tool maker and big-game hunter. His find broke new ground, for it moved man's origins from Asia to Africa, and emphasized our hunting nature. His paper that followed, _The Predatory Nature of Man,_ wasn't well received. It rocked the boat. Only most recently have his findings become more widely accepted.
By the time Robert Ardrey had written his fourth book, _The Hunting Hypothesis,_ he seemed to have clearly developed his thesis:
Man is man, and not a chimpanzee, because for millions upon millions of evolving years we killed for a living.
Ardrey knew that for perhaps 500,000 years, our ancestors were continuously dependent upon killing to survive. Because of our "big brain" and our inventive nature, we were able to do it well, perhaps surpassing all other animals in that skill.
Not everyone agreed, but Ardrey had the evidence, and his proof was hard to refute. His critics were armed more with rhetoric than with solid evidence. His friend Louis Leakey, possibly the most famous researcher in anthropology of the time, wasn't as certain as Ardrey that man had been such a great hunter. There was no dispute that man was a carnivore, a meat-eater, but Leakey leaned toward the notion that man got his meat by settling for "roadkill," or by being a scavenger. In other words he felt that early man was more inclined to let other animals do his dirty work, the kill, and that he simply took the leftovers.
Ardrey disagreed. He didn't believe man could sustain life that way. He felt that if man had the guts to steal food from fierce beasts, he had the courage to go after his own prey. In a debate with Louis Leakey, reprinted in _Psychology Today_ in 1972, Ardrey makes his point:
If we go back 500,000 years to _Homo sapiens,_ the big-brained man, there isn't much question about what went on. They were definitely hunters. This heritage has had a tremendous effect upon us in terms of natural selection. Those men who had an efficient capacity for violence, who enjoyed violence, were the men who survived and passed on their genes. If you didn't like to go out and hunt, you wouldn't get the girl, and you wouldn't get any food—you'd just be an extra mouth to feed. And I would assert that we didn't live off of spinach. This is a fashionable point of view much promoted in American anthropology. Lettuce is great for diets, but not for men who have to work for a living. We had to live off meat.
Dr. Lyall Watson independently developed similar ideas, but with some differences. Watson, a South African zoologist and a director of the Johannesburg Zoo, shared Ardrey's opinion of the killing nature of early man. In his book _The Omnivorous Ape,_ he states:
Man is what he is and does what he does because he once was a killer. He was hungry and needed food, and the food he most wanted was meat. So he applied his growing brain to the problem of killing—and started a chain of circumstances that still affects our lives today. Because our ancestors needed greater speed, they became more upright and today we have vertical men. Because they needed artificial weapons, tools were developed and today we have elaborate instrumentation. Because cooperation was essential, their brains became even more complex, and a language and a culture came into being. Today we also have spinal disorders, ballistic missiles and racial disturbances, but we have had to take the bad with the good. Both were produced by our diet.
Notice that Watson at least seems to be saying that man "was" a killer. He uses the past tense. That should make a lot of people a lot more comfortable. He obviously differs from Ardrey in that he believes we have channeled that aggressive nature in more socially acceptable directions.
Man relinquished his role as a killer and hunter when he became a settled farmer about 10,000 years ago. He became domesticated and well fed, but he still needed to hunt.... In a million years of hunting, man formed close ties with other adult males in the tribe and grew used to a life involving constant risks and challenges. So he turned work into an activity that involved him, with other men, in a recurring gamble that has many characteristics of the hunt. To take an example from only one kind of work, he set aside hunting grounds (business centers) where the prey (his rivals) could be stalked (with the aid of industrial espionage) and captured (in a take-over bid). In the all-male gatherings that have always followed the hunt, the money hunter is able to boast his prowess and of the "killing" he has just made.
It wasn't until about 10,000 years ago that things began to change. Most authorities put man's entry into farming at between 8,000 and 13,000 years ago. Things moved very slowly back then. A hundred generations would go by and there was possibly no change in the farming techniques. Some experts feel that although man farmed, he really didn't get his act together until about 5,000 years ago.
Desmond Morris, another zoologist, took note of this in his entertaining and informative best-seller of the late sixties, _The Naked Ape:_
We were driven to become flesh-eaters only by environmental circumstances, and now that we have the environment under control, with elaborately cultivated crops at our disposal, we might be expected to return to our ancient primate feeding patterns. In essence, this is the vegetarian... creed, but it has had remarkably little success. The urge to eat meat appears to have become too deep-seated. Given the opportunity to devour flesh, we are loth to relinquish the pattern.
According to Watson, you're thus unique in the animal world. He recognizes four eating patterns: insectivores, herbivores (plant-eaters), carnivores (flesh-eaters), and omnivores (eaters of a mixed diet). Many animals have undergone evolutionary changes in their diets. Some have made only a single change during their history. Others have made two changes. Man is the only animal to make three such changes.
The only animal ever to move from insect eating to fruit picking to meat eating to eating absolutely anything. Man.
Of course, we men lack some of the characteristics necessary to really do a good job of digesting plant foods. It's not surprising. We've just started to eat them. We are, so to speak, trying them out. Cows, for example, are real herbivores. They digest the cellulose that makes up the main portion of fruits and vegetables. We, on the other hand, can't digest cellulose, so it passes right through us. That isn't necessarily bad. Many writers (including this one) have written books extolling the virtues of eating this fibrous material. It apparently acts as somewhat of a sweeping compound to cleanse the intestinal tract.
The dawn of agriculture required our hunters to stay put and watch the crops grow. This was a major change, and it was the major force in the growth of villages, cities, countries, and boundary lines. Agriculture changed the human experience and we now added plant foods to our diets.
In the scheme of things, 10,000 years is an instant. It is an insignificant period of time for an adaptation to take place in the human race. It is unlikely that we're physically much different from our 10,000-year-old ancestors.
Evolutionary changes take place slowly, very slowly. I cannot emphasize enough how slow the process is. We commonly describe things using the adjective _slow._ We may speak of our trip home from work as being slow, or say that Congress is slow to act, or that Third World countries are slowly becoming industrialized. Believe me, those are all fast. Evolution is slow.
Human beings haven't changed much in the last few thousand years. Borrow a dozen men from one of Caesar's legions, put shorts and Nikes on them and send them to your local fitness club, and they will get lost among all the other bodies. Or put the right suit on one of them, give him a good haircut, and let him walk down Madison Avenue with an attaché case and no one will notice anything unusual.
As for our nutritional needs, we're probably still cavemen. That's why we still love meat. That's why the fast-food restaurants. That's why the steak houses. That's why the cookouts.
That is one of the reasons I prefer a high-protein diet for my patients. They also prefer it and that is important, because if they aren't repelled by the food selections, they are more inclined to stay with the diet. A more important reason for my preference is because a high-protein diet works.
# _Appendix C: How to Customize Your Diet Test_
The MFI test I described earlier is the one I recommend. It results in a twofold benefit. Not only do you learn whether your thyroid is causing your weight problems, but you also lose a substantial amount of weight in the process.
There will be those of you who have had a lot of experience with past diets, and there will be others who have never dieted seriously. For some, 1,000 calories a day may be a fearful prospect. I know from experience that it isn't. You can do it. The expectation of spending the rest of your days wearing normal-sized clothing should spur you on. Nonetheless, I'll give you an alternative.
There is nothing magic about a 1,000-calorie diet. I could calculate valid results on my patients while they were eating any number of calories per day. I could even arrive at the result if they ate a widely different number of calories from day to day. In order for me to do so, there really are only two things I need to know. _I must know how many calories my subject consumed for the entire twenty-eight-day period, and I must know exactly how much weight was lost during that time._ Once I have that information, the rest is the kind of thing we do every day with our pocket calculators.
Why did I not present this information earlier? I've already told you. I believe that if 1,000 calories is chosen and the subject adheres to my food choices in accomplishing it, hunger will be minimal, there will be impressive weight loss, and there may be no need for the pocket calculator. By standardizing to 1,000 calories, I was able to make the whole thing very simple for you to accomplish. I did all the calculations in advance and gave you nice neat little tables to work with. Were I to have allowed variable amounts of calories, I would have had to supply you with a similar set of tables for each different calorie count. That would have been quite complex, and there would have been too much room for error.
For the adventurous willing to make their own calculations, I present the following method. Get your thinking cap on.
One of the two bits of information you need is easy. Weigh yourself at the beginning of the twenty-eight days and also at the end, just as specified earlier in the book. You need to know how many pounds you lost eating a certain number of calories. The "certain number of calories" is going to take dedication.
You're going to count every calorie you ate during the entire twenty-eight-day period meticulously and mark them down. It sounds more difficult than it is. You're obviously embarking on this alternate method because you're going to follow a diet other than the one I recommend. That's okay. In a sense, the original diet also required counting the calories, but the idea was to shoot for 1,000, and if you varied a bit, you kept a record of how many you went over 1,000 on an Excess Calorie Sheet. If you're going to follow Test B (Do you like that name?), then you will do exactly the same thing, except the excess calories are presumably going to be greater. What you will be marking down on your Excess Calorie Sheet will be bigger numbers such as "460" or "530" instead of perhaps "175" or "80." If you aren't going to be marking down numbers that large, there is little reason for you to be following Test B. You are back to Dr. Siegal's original test diet.
In Chapter 13 you were asked to calculate your uncorrected caloric maintenance level based on a 1,000-calorie diet. What is accomplished by this is that you learn your daily maintenance level after you've spent four weeks eating _exactly_ 1,000 calories per day. The UCML table is still appropriate because, in a sense, you're still basing your performance on 1,000 calories per day, but you're simply exceeding your quota by a much larger amount than I advised. However, you can't use the table titled CCML because the number of calories in excess is now "off the charts," as they say. One solution is to make your own chart. Don't panic. You don't really have to make a chart, but you do have to make some calculations.
Here are your complete instructions:
Use the MFI Calculation Form on page 161.
1. Write in your weight on Day 1.
2. Write in your weight on Day 29.
3. Subtract Line (2) from Line (1).
4. Obtain your UCML from the UCML Table on page 164.
5. Write in your excess calories for the entire twenty-eight days on Line (5).
6. Divide that number by 28 and jot it down somewhere as the value of your daily excess (DE). Add the UCML to the DE. This is your CCML.
7. Get your BBW in Line (7) from the BBW Table on page 166.
8. Choose the proper SCML Table on pages 168– and write in your SCML.
9. Divide the CCML in Line (6) by the SCML in Line (8). Move the decimal point two digits to the right and round it off to the nearest whole number. That is your MFI.
This example illustrates the process. Here is the MFI Calculation Form:
**MFI Calculation Form**
Metabolic Function Index
**(1) Day 1 Date _ 9/4/99_ Weight (nude)** (Early morning) |
---|---
**(2) Day 29 Date _ 10/3/99_ Weight (nude)** (Early morning) |
**(3) 28-day weight loss**
Subtract line (2) from line (1). |
**(4) UCML (Uncorrected Caloric Maintenance Level)**
From the UCML Table on page 164. |
**(5) EC (Total Excess Calories for the 28 Days)**
From your own list of excess calories for the entire 28 days. |
**(6) CCML (Corrected Caloric Maintenance Level)**
See the Excess Calories Table on page 165. |
**(7) BBW (Baseline Body Weight)**
See BBW Table on page 166. |
**(8) SCML (Standard Caloric Maintenance Level)**
See the proper SCML Table for your sex, age group, and activity level on pages 168–. Use the BBW in (7) above to determine your SCML. |
**(9) Metabolic Function Index (MFI)**
Divide line (6) by line (8). Move the decimal point 2 digits to the right. |
The subject is a thirty-eight-year-old female who is five feet eight inches tall and who has a large frame. She is rated as moderately active. The only difference from the usual way of calculating her MFI as explained in Chapter 13 is when it comes to the CCML.
The DE was calculated by dividing her total excess for the month in Line (5) by 28. Then in Line (6), add the UCML to the DE. This total becomes your CCML. The rest of the task is the same as explained in Chapter 13.
You may now go back to Chapter 13 for an interpretation of the results.
# _Appendix D: Determining Your Frame Size_
When considering such subjects as ideal or normal weight, it is customary to classify individuals by the size of their body "frames." Generally, the classifications are small, medium, and large frames.
Although it isn't difficult for any of us to judge someone's frame size by our own past experience, it is desirable to have some objective standard upon which to rely. One such standard involves taking a measurement across the elbow. The distance between the bony protrusions on the two sides of the elbow is measured.
The process is easier if you get someone to help in the procedure.
# How to Measure Your Frame Size
1. Locate the two prominent bones that extend outward on each side of your elbow at the ends of your elbow crease.
2. Place a letter-sized sheet of paper on a flat tabletop.
3. Center your elbow on the sheet of paper with your arm straight, elbow crease and palm up.
4. With a sharp pencil, accurately mark the position of each of these bones on the paper so that the distance between the two marks measures the distance across your elbow. Be sure to keep the pencil vertical.
5. With a ruler, measure the distance between the two pencil marks.
6. Use the table below to determine your frame size based on your sex and age.
**ELBOW MEASUREMENT**
**Age** | **Small** | **Medium** | **Large**
---|---|---|---
Males | | |
18–24 | ≤25/8′′ | >25/8′′ and <31/16′′ | ≥31/16′′
25–34 | ≤25/8′′ | >25/8′′ and <31/8′′ | ≥31/8′′
35–44 | ≤25/8′′ | >25/8′′ and <33/16′′ | ≥33/16′′
45–54 | ≤25/8′′ | >25/8′′ and <33/16′′ | ≥33/16′′
55–64 | ≤25/8′′ | >25/8′′ and <33/16′′ | ≥33/16′′
65–74 | ≤25/8′′ | >25/8′′ and <33/16′′ | ≥33/16′′
Females | | |
18–24 | ≤2¼′′ | >2¼′′ and <29/16′′ | ≥29/16′′
25–34 | ≤2¼′′ | >2¼′′ and <211/16′′ | ≥211/16′′
35–44 | ≤2¼′′ | >2¼′′ and <213/16′′ | ≥213/16′′
45–54 | ≤2¼′′ | >2¼′′ and <27/8′′ | ≥27/8′′
55–64 | ≤25/16′′ | >25/16′′ and <27/8′′ | ≥27/8′′
65–74 | ≤25/16′′ | >25/16′′ and <27/8′′ | ≥27/8′′
_**Example:** A forty-year-old female with a measurement of 2'A" has a medium frame._
# _Appendix E: Evaluating Your Activity Level_
In Chapter 13, in the process of calculating your Metabolic Function Index, you are asked to evaluate your activity level. You are given three choices: sedentary, moderate, and active. If you were simply to make the choice without serious study of your activities, I think you would probably guess right. Yet I have seen patients who were not even close in their estimation of their activity levels.
A worker in a busy office might tell me, "My job is so active that I don't have a minute's rest. Yes, I sit, but a million times a day I have to get up and run to another desk and then run back to answer a phone call. By the end of the day, I'm beat." I may risk bursting her bubble, but I need to pry for more information. I try to pin her down to a more realistic number than "a million times." I suggest numbers. Between this and that number? Eventually, I get an admission that seems reasonable. Let's settle on twenty-five, which is probably overestimating.
This lady sits for most of the day. Each excursion to another desk takes perhaps one minute. Does she really run, or is that a figure of speech? When she gets to her destination does she stand still and talk for a while? What is the bottom line? I will give her, at best, a total of thirty minutes of ordinary walking and the rest of the time sitting at a desk. I dare say, her day doesn't even compare with an ordinary shopping trip to the mall. It just seems to her that she is getting a lot of exercise. Clearly, she is sedentary.
Don't give such sports as golf or bowling more credit than they deserve. I've had to disparage the exercise value of bowling to too many patients. Let's look at the facts.
If you are a particularly bad bowler, you will roll 20 balls per game. If we analyze that activity and put a time line on it, we will have the following:
1. Getting up from the bench and picking up the ball—5 seconds.
2. Holding the ball and staring at the pins—5 seconds.
3. Pulling your arm back, taking three steps, bending your knees, and releasing the ball—4 seconds.
4. Staring at the result—3 seconds.
5. After every other ball, walking back to your seat—5 seconds.
It looks like the whole process took about 20 seconds, though only 4 of those involved anything more than walking or standing. That means that for each game the bad bowler has 3 minutes or so of total _activity_ (I can't bring myself to use the word _exercise),_ but really only 80 seconds of that even resembles exercise. Now multiply those figures by the number of games.
I hope you see the point. It is easy to delude ourselves into believing that we are more active than we really are. I rarely see anyone err on the opposite side—that is, underestimate their activity level.
As for golf, it's really not much better. If you walk the course, it's a nice walk, but you stand still more than you walk. If you use a cart, forget it. Try adding up the number of seconds spent swinging the clubs. Putting certainly shouldn't count. I know I'm going to be hearing from golfers on this one.
It's quite important that you select the proper activity level. At the extreme ends, a mistake could account for a thousand calories or more per day. An area for confusion arises when there is a mixture of varied activities. What about the guy who sits at a desk five days a week but runs six miles both on Saturday and Sunday? There are people who do just that.
Your principal daily activity is not hard to evaluate. If you sit at a desk or drive a car most of the day, that is considered sedentary. (Brain work burns up very few calories.) If you are on the move constantly and virtually never sit down (standing still excluded), you may be in the moderate class. If you never put down your shovel, you are active.
Let's use as a rule of thumb that a sedentary individual who burns an extra 2,000 calories per week in more energetic activity moves to the moderate class. One with moderate activity has to burn an extra 4,000 a week to get into the active class. "Active" is not achieved easily. Some pretty good guesses have been made when it comes to estimating how many calories various activities burn up per hour. Let's look at what some activities are worth in terms of calories.
Walking, brisk | 300-400
---|---
Bicycling, fast | 300-400
Gardening | 300-375
Weight training | 150-350
Housework | 150-200
Calisthenics | 300-400
Tennis | 400-550
These are only examples of various activities, and you can interpolate them into other activities. It is impossible to assign absolutely dependable calorie counts for each activity because there is such variation in how they are performed, as well as in the weight of the person involved in them. Estimate to the best of your ability.
_**Example:** You have a sedentary occupation but you play two hours of tennis (singles) twice a week. You are probably burning an extra 2,000 calories a week and therefore you would move up into the moderate category._
Exercise machines at many gyms frequently give a readout of calories consumed. I don't have much confidence in their absolute accuracy, but they are probably better than your own guessing. Use them.
# _Appendix F: Bibliography_
Barnes, B. O., "On the Genesis of Atherosclerosis," _Journal of the American Geriatrics Society,_ 21(8): 350-354.
Barnes, B., "Basal Temperature versus Basal Metabolism," _"Journal of the American Medical Association,_ 119(14): 1072-1074.
Billewicz, W. Z.; Chapman, R. S.; Crooks, J.; Day, M. E.; Gossage, J.; Wayne, S. E.; & Young, J. A., "Statistical Methods Applied to the Diagnosis of Hypothyroidism," _Quarterly Journal of Medicine,_ 38(150): 255-266.
Bishnoi, A., & Sachmechi, I., "Thyroid Disease During Pregnancy," _American Family Physician,_ 53(1): 215-220.
Boothby, W., & Sandiford, I., "Summary of the Basal Metabolism Data on 8,614 Subjects with Especial Reference to the Normal Standards for the Estimation of the Basal Metabolic Rate," _The Journal of Biological Chemistry,_ 54(4): 783-803.
Bradfield, R. B., & Jourdan, M. H., "Relative Importance of Specific Dynamic Action in Weight-Reduction Diets," _The Lancet,_ 2(7830): 640-643.
Briefel, R. R.; McDowell, M. A.; Alaimo, K.; Caughman, C. R.; Bischof, M. D.; & Johnson, C. L., "Total Energy Intake of the U.S. Population: The Third National Health and Nutrition Examination Survey, 1988-1991," _The American Journal of Clinical Nutrition_ , 62: 1072S-1080S.
Bunevicius, R.; Kazanavicius, G.; Zalinkevicius, R.; & Pragne, A. J., "Effects of Thyroxine as Compared with Thyroxine Plus Triiodothyronine in Patients with Hypothyroidism," _The New England Journal of Medicine,_ 340(6): 424-429.
Butte, N. F.; Moon, J. K.; Wong, W. W.; Hopkins, J. M.; & Smith, E. O'Brian, "Energy Requirements from Infancy to Adulthood," _The American Journal of Clinical Nutrition,_ 62: 1047S-1052S.
Calloway, D. H., & Zanni, E., "Energy Requirements and Energy Expenditure of Elderly Men," _The American Journal of Clinical Nutrition,_ 33: 2088-2092.
Campbell, R. C.; Welle, S. L.; & Seaton, T. B., "Specific Dynamic Action Revisited: Studies of Hormonal Regulation of Energy Expenditure in Man," _Transactions of the American Clinical and Climatological Association,_ 99: 136-143.
Cheraskin, E., "A Different Methodologic Approach to 'Ideal Weight': A Study of the Ponderal Index (PI)," _Medical Hypothesis,_ 29: 55-58.
Clark, H. D., & Hoffer, J. L., "Reappraisal of the Resting Metabolic Rate of Normal Young Men," _The American Journal of Clinical Nutrition,_ 53: 21-26.
Cushing, G. W., "Subclinical Hypothyroidism: Understanding Is the Key to Decision Making," _Postgraduate Medicine,_ 94(1): 95-107.
Denicoff, K. D.; Joffe, R. T.; Lakshmanan, M. C.; Robbins, J.; & Rubinow, D. R., "Neuropsychiatric Manifestations of Altered Thyroid State," _American Journal of Psychiatry,_ 147: 94-99.
Doucet, J.; Trivalle, C.; Chassagne, P.; Perol, M. B.; Vuillermet, P.; Manchon, N. D.; Menard, J. F.; & Bercoff, E., "Does Age Play a Role in Clinical Presentation of Hypothyroidism?" _Journal of the American Geriatrics Society,_ 42(9): 984-986.
Drinka, P. J., & Nolten, W. E., "Subclinical Hypothyroidism in the Elderly: To Treat or Not to Treat?" _The American Journal of the Medical Sciences,_ 295(2): 125-128.
Faulkner, R. A., & Bailey, D. A., "Critical Evaluation of Frame Size Determination in the 1983 Metropolitan Life Weight for Height Tables," _Canadian Journal of Public Health,_ 80: 369-372.
Feldmesser-Reiss, E. E., "The Application of Triiodothyronine in the Treatment of Mental Disorders," _Journal of Nervous and Mental Disease,_ 127: 540-546.
Feurer, I. D.; Crosby, L. O.; Buzby, G. P.; Rosato, E. F.; & Mullen, J. L., "Resting Energy Expenditure in Morbid Obesity," _Annals of Surgery,_ 197(1): 17-21.
Flat, J. P., "Body Composition, Respiratory Quotient, and Weight Maintenance," _The American Journal of Clinical Nutrition,_ 62: 1107S-1117S.
Frankenfield, D. C.; Muth, E. R.; & Rowe, W. A., "The Harris-Benedict Studies of Human Basal Metabolism: History and Limitations," _Journal of the American Dietetic Association,_ 98(4): 439-445.
Friedman, M. I., "Control of Energy Intake by Energy Metabolism," _The American Journal of Clinical Nutrition_ , 62: 1096S-1100S.
Frisancho, R., "New Standards of Weight and Body Composition by Frame Size and Height for Assessment of Nutritional Status of Adults and the Elderly," _The American Journal of Clinical Nutrition_ , 40: 808-819.
Garrow, J. S., & Hawes, S. F., "The Role of Amino Acid Oxidation in Causing 'Specific Dynamic Action' in Man," _British Journal of Nutrition,_ 27(1): 211-219.
Gold, M. S.; Pottash, A. L. C.; & Extein, I., "Hypothyroidism and Depression: Evidence from Complete Thyroid Function Evaluation," _JAMA,_ 245(19): 1919-1922.
Gross, M. A., "Achilles-Reflex Timing in Diagnosis of Thyroid Status," _New York State Journal of Medicine_ , 71(19): 2283-2291.
Gruhn, J. G.; Barsano, C. P.; & Kumar, Y., "The Development of Tests of Thyroid Function," _Archives of Pathology and Laboratory Medicine_ , 111: 84-100.
Gupta, S. P.; Kimar, V.; & Ahuja, M. S., "Evaluation of Achilles Reflex Time as a Test of Thyroid Function," _Southern Medical Journal,_ 66(7): 754-758.
Haggerty, J. J., Jr.; Stern, R. A.; Mason, G. A.; Beckwith, J.; Morey, C. E.; & Prange, A. J., Jr., "Subclinical Hypothyroidism: A Modifiable Risk Factor for Depression?" _American Journal of Psychiatry_ , 150: 508-510.
Henley, W. N., & Koehnle, T. J., "Thyroid Hormones and the Treatment of Depression: An Examination of Basic Hormonal Actions in the Mature Mammalian Brain," _Synapse_ , 27: 36-44.
Hernandez, J. J. C.; Garcia, J. M. M.; & Diez, L. C. G., "Primary Hypothyroidism and Human Spermatogenesis," _Archives of Andrology,_ 25: 21-27.
Heymsfield, S. B.; Darby, P. C.; Muhlheim, L. S.; Gallagher, D.; Wolper, C.; & Allison, D. B., "The Calorie: Myth, Measurement, and Reality," _The American Journal of Clinical Nutrition,_ 62: 1034S-1041S.
Hill, J. O.; Melby, C.; Johnson, S. L.; & Peters, J. C., "Physical Activity and Energy Requirements," _The American Journal of Clinical Nutrition,_ 62: 1059S-1066S.
Himes, J. H., & Bouchard, C., "Do the New Metropolitan Life Insurance Weight-Height Tables Correctly Assess Body Frame and Body Fat Relationships?" _American Journal of Public Health,_ 75(9): 1076-1079.
Howland, R. H., "Thyroid Dysfunction in Refractory Depression: Implications for Pathophysiology and Treatment," _Journal of Clinical Psychiatry,_ 54: 47-54.
Ireton-Jones, C. S., & Turner, W. W., Jr., "Actual or Ideal Body Weight: Which Should Be Used to Predict Energy Expenditure?" _Journal of the American Dietetic Association,_ 91(2): 193-195.
Jonckheer, M.; Block, P.; & Molter, F., "Use of the Achilles-Tendon Reflex in Thyroid Clinical Investigation," _Acta Endocrinologica,_ 63(1): 175-184.
Klatsky, S. A., & Mason, P. N., "Thyroid Disorders Masquerading as Aging Changes," _Annals of Plastic Surgery,_ 28(5): 420-426.
Klein, I., "Thyroid Hormone and the Cardiovascular System," _The American Journal of Medicine,_ 88: 631-637.
Knapp, T. R., "A Methodological Critique of the 'Ideal Weight' Concept," _JAMA_ , 250(4): 506-510.
Koutras, D. A., "Disturbances of Menstruation in Thyroid Disease," _Annals of the New York Academy of Sciences,_ 816: 280-284.
Krebs, H. A., "The Cause of the Specific Dynamic Action of Foodstuffs," _Arzeneimittelforschung,_ 10: 369-373.
Krupsky, M.; Flatau, E.; Yarom, R.; & Resnitzky, P., "Musculoskeletal Symptoms as a Presenting Sign of Long-standing Hypothyroidism," _Israel Journal of Medical Sciences,_ 23: 1110-1113.
Krzanowski, J. J., "Thyroid Hormone: Basis for Its Hypocholesterolemic Effects," _Journal of the Florida Medical Association,_ 78(6): 383-385.
Lindemann, C. G.; Zitrin, C. M.; & Klein, D. F., "Thyroid Dysfunction in Phobic Patients," _Journal of Clinical Psychiatry,_ 54(2): 47-54.
Lusk, G., "The Fundamental Requirements of Energy for Proper Nutrition," _Journal of the American Medical Association,_ 70(12): 821-824.
_____, "The Physiological Effect of Undernutrition," _Physiological Reviews,_ 1(4): 523-552.
Mariotti, S.; Barbesino, G.; Caturegli, P.; Bartalena, L.; Sansoni, P.; Fagnoni, F.; Monti, D.; Fagiolo, U.; Franceschi, C.; & Pinchera, A., "Complex Alteration of Thyroid Function in Healthy Centenarians," _Journal of Clinical Endocrinology and Metabolism,_ 77(5): 1130-1134.
Matsuzawa, Y.; Tokunaga, K.; Kotani, K.; Keno, Y.; Kobayashi, T.; & Tarui, S., "Simple Estimation of Ideal Body Weight from Body Mass Index with the Lowest Morbidity," _Diabetes Research and Clinical Practice,_ 10: S159-S164.
Mazzaferri, E. L., "Recognizing the Faces of Hypothyroidism," _Hospital Practice,_ 93-110.
Mifflin, M. D.; St. Jeor, S. T.; Hill, L. A.; Scott, B. J.; Daugherty, S. A.; & Koh, Y. O., "A New Predictive Equation for Resting Energy Expenditure in Healthy Individuals," _The American Journal of Clinical Nutrition,_ 51: 241—247.
Mitchell, H. H., "The Physiological Effects of Protein," _The Journal of Nutrition,_ 1(3): 271-292.
Mitchell, M. C., "Comparison of Determinants of Frame Size in Older Adults," _Journal of the American Dietetic Association,_ 93(1): 53-57.
Montoro, M.; Collea, J. V.; Frasier, S. D.; & Mestman, J. H., "Successful Outcome of Pregnancy in Women with Hypothyroidism," _Annals of Internal Medicine,_ 94(1): 31-34.
Monzani, F.; del Guerra, P.; Caraccio, N.; Pruneti, C. A.; Pucci, E.; Luisi, M.; & Baschieri, L., "Subclinical Hypothyroidism: Neurobehavioral Features and Beneficial Effect of L-thyroxine Treatment," _Clinical Investigation,_ 71: 367-371.
Mooney, C. J.; James, D. A.; & Kessenich, C. R., "Diagnosis and Management of Hypothyroidism in Pregnancy," _Journal of Obstetrical Gynecological Neonatal Nursing,_ 27(4): 374-380.
Nordyke, R. A., & Gilbert, F. I., Jr., "The Achilles Reflex Thyroid Function Test: Evaluation of a New Instrument," _The American Journal of the Medical Sciences,_ 259: 419-423.
Nuttall, F. Q., & Doe, R. P., "The Achilles Reflex in Thyroid Disorders," _Annals of Internal Medicine,_ 61(2): 269-288.
Pavlou, K. N.; Hoefer, M. A.; & Blackburn, G. L., "Resting Energy Expenditure in Moderate Obesity: Predicting Velocity of Weight Loss," _Annals of Surgery,_ 203(2): 136-141.
Powell, J. T.; Carter, G.; Woolcock, N.; Greenhalgh, R. M.; Fowler, P. B. S.; & Zadeh, J. A., "The Relationship Between Serum Cholesterol and Serum Thyrotropin in Women with Peripheral Arterial Disease," _Annals of Clinical Biochemistry,_ 28: 316-319.
Rees-Jones, R. W., & Larsen, P. R., "Triiodothyronine and Thyroxine Content of Desiccated Thyroid Tablets," _Metabolism,_ 26(11): 1213-1218.
Ridgway, E. C., "Modern Concepts of Primary Thyroid Gland Failure," _Clinical Chemistry,_ 42(1): 179-182.
Roberts, S. B.; Fuss, P.; Heyman, M. B.; & Young, V. R., "Influence of Age on Energy Requirements," _The American Journal of Clinical Nutrition,_ 62: 1053S—1058S.
Roza, M., & Shizgal, H. M., "The Harris-Benedict Equation Reevaluated: Resting Energy Requirements and the Body Cell Mass," _The American Journal of Clinical Nutrition,_ 40: 168-182.
Santiago, G., & Kennedy, J., "On Specific Dynamic Action, Turnover, and Protein Synthesis," _Perspectives in Biology and Medicine,_ 9(4): 578-585.
Sawin, C. T.; Hershman, J. M.; Fernandez-Garcia, R.; Ghazvinian, S.; Ganda, O. P.; & Azukizawa, M., "A Comparison of Thyroxine and Desiccated Thyroid in Patients with Primary Hypothyroidism," _Metabolism,_ 27(10): 1518-1525.
Schneeberg, N. G., "Pseudo-hypothyroidism," _Postgraduate Medicine,_ 79(7): 103-111.
Schultz, L. O., "Lose, Overweight, Desirable, Ideal: Where to Draw the Line in 1986?" _Journal of the American Dietetic Association,_ 86(12): 1402-1407.
Seale, J. L., "Energy Expenditure Measurements in Relation to Energy Requirements," _The American Journal of Clinical Nutrition,_ 62: 1042S-1046S.
Selenkow, H. A., "Hypothyroid Women with Rising Serum Cholesterol Values," _Consultant,_ 26.
Shafer, R. B., & Nuttall, F. Q., "Achilles Reflex in Thyroid Disorders: A 10-year Clinical Evaluation," _The American Journal of the Medical Sciences,_ 264(4): 313-317.
Souetre, E.; Salvati, E.; Wehr, T. A.; Sack, D. A.; Krebs, B.; & Darcourt, G., "Twenty-Four-Hour Profiles of Body Temperature and Plasma TSH in Bipolar Patients During Depression and During Remission and in Normal Control Subjects," _American Journal of Psychiatry,_ 145: 1133-1137.
Starr, P., "Atherosclerosis, Hypothyroidism, and Thyroid Hormone Therapy," _Advances in Lipid Research,_ 16: 345—371.
Stavig, G. R.; Leonard, A. R.; Igra, A.; & Felten, P., "Indices of Relative Body Weight and Ideal Weight Charts," _Journal of Chronic Disease,_ 37(4): 255-262.
Stoffer, S. S., "Menstrual Disorders and Mild Thyroid Insufficiency: Intriguing Cases Suggesting an Association," _Postgraduate Medicine,_ 72(2): 75-81.
Surks, M. I., & Ocampo, E., "Subclinical Thyroid Disease," _The American Journal of Medicine,_ 100: 217-223.
Taaffe, D. R.; Thompson, J.; Butterfield, G.; & Marcus, R., "Accuracy of Equations to Predict Basal Metabolic Rate in Older Women," _Journal of the American Dietetic Association,_ 95(12): 1387-1392.
Takeda, T.; Suzuki, S.; Liu, R.; & DeGroot, L. J., "Triiodothyroacetic Acid Has Unique Potential for Therapy of Resistance to Thyroid Hormone," _Journal of Clinical Endocrinology and Metabolism,_ 80: 2033-2040.
Tokunaga, K.; Matsuzawa, Y.; Kotani, K.; Keno, Y.; Kobatake, T.; Fujioka, S.; & Tarui, S., "Ideal Body Weight Estimated from the Body Mass Index with the Lowest Morbidity," _International Journal of Obesity,_ 15: 1-5.
Valenta, L. J., & Elias, A. N., "How to Detect Hypothyroidism When Screening Tests Are Normal," _Postgraduate Medicine,_ 74(2): 267-274.
Van Lanschot, J. J. B.; Feenstra, B. W. A.; Vermeij, C. G.; & Bruining, H. A., "Calculation versus Measurement of Total Energy Expenditure," _Critical Care Medicine,_ 14(11): 981-985.
Walsh, B. J., & Morley, T. F., "Comparison of Three Methods of Determining Oxygen Consumption and Resting Energy Expenditure," _Journal of the American Osteopathic Association,_ 89(1): 43-46.
Weigley, E. S., "Average? Ideal? Desirable? A Brief Overview of Height-Weight Tables in the United States," _Journal of the American Dietetic Association,_ 84(4): 417-423.
Westphal, S. A., "Unusual Presentations of Hypothyroidism," _The American Journal of Medical Sciences,_ 314(5): 333-337.
Whybrow, P. C.; Prange, A. J., Jr.; Treadway, C. R.; & Hill, C., "Mental Changes Accompanying Thyroid Gland Dysfunction," _Archives of General Psychiatry,_ 20: 48-63.
Wiberg, G. S.; Devlin, W. F.; Stephenson, N. R.; Carter, J. R.; & Bayne, A. J., "A Comparison of the Thyroxine: Tri-iodothyronine Content and Biological Activity of Thyroid from Various Species," _Journal of Pharmacy and Pharmacology,_ 14: 777-783.
Williams, A. D.; Meister, L.; & Florsheim, W. H., "Chemical Identification of Defective Thyroid Preparations," _Journal of Pharmaceutical Sciences,_ 52(9): 833-839.
Woeber, K. A., "Subclinical Thyroid Dysfunction," _Archives of Internal Medicine,_ 157: 1065-1068.
Wolfstein, R. S., "Dietary Cholesterol and Atherosclerosis," _The Western Journal of Medicine,_ 146(5): 621-622.
Wren, J. C., "Thyroid Function and Coronary Atherosclerosis," _Journal of the American Geriatrics Society,_ 16(6): 696-704.
Zulewski, H.; Muller, B.; Exer, P.; Miserez, A. R.; & Staub, J., "Estimation of Tissue Hypothyroidism by a New Clinical Score: Evaluation of Patients with Various Grades of Hypothyroidism and Controls, _"Journal of Clinical Endocrinology and Metabolism,_ 82(3): 771-776.
# _Appendix G: Recommended Calorie Books_
If your tastes run beyond the selection of foods in Chapter 12 there are several calorie books I recommend.
Duyff, Robert Larson, _Complete Food and Nutrition Guide._ Chronimed Publishing, 1998.
Natow, Annette B., and Heslin, Jo-Ann, _The Most Complete Food Counter._ Pocket Books, 1999.
Netzer, Corrine T., _The Dieter's Calorie Counter._ Dell Trade Paperback, 1998.
Thompson Pennington, Jean A., _The Essential Guide to Nutrition and the Foods We Eat._ HarperCollins, 1999.
# _Appendix H: Other Reading_
These are books that deal with the same general subject matter. They will give you further information, although I don't necessarily agree with their total content.
Arem, Ridha, _The Thyroid Solution._ Ballantine Books, 1999.
Barnes, Broda O., and Galton, Lawrence, _Hypothyroidism: The Unsuspected Illness._ Thomas Y. Crowell Co., 1976.
Rosenthal, M. Sara, _The Thyroid Sourcebook._ Lowell House, 1998.
Rubenfeld, Sheldon, _Could It Be My Thyroid?_ The Thyroid Society for Education and Research, 1996.
# _Appendix I: Sample Daily Menus_
These are not specific recommendations but rather examples of what a typical 1,000-calorie daily diet might look like. I obviously chose what would please me (and it has) when dieting.
**EXAMPLE ONE**
**Breakfast** |
---|---
One Serving (1 cup) Kellogg's Raisin Bran | 200 calories
4 oz. Milk 2% fat | 64 calories
1 cup Coffee with 1 oz. Milk 2% fat | 16 calories
**Lunch** |
Stouffer's Lean Cuisine Chicken in Peanut Sauce | 290 calories
Diet Soda | 0 calories
**Dinner** |
8 oz. Orange Roughy, broiled with spices | 176 calories
½ cup Le Sueur Early Peas (canned) | 60 calories
½ cup SW Small Whole Carrots (canned) | 30 calories
Salad |
4 Large Leaves of Romaine Lettuce | 12 calories
4 Tablespoons Weight Watchers Caesar Salad Dressing | 20 calories
1 cup Jell-O, Sugar Free | 20 calories
1 cup Coffee with 1 oz. Milk 2% fat | 16 calories
**Total for the Day** | **904 calories**
**Notes on Example One**
1. The breakfast is cereal I strongly recommend (see Chapter 12). A variety of cereals will fill the bill.
2. Lunch is a frozen meal, which should prove quite adequate.
3. Dinner is actually a large serving of fish with sufficient vegetables and a salad. The fish serving size is probably bigger than the portion served in many restaurants. You can broil the fish or make it in a skillet with one of the nonstick sprays. You can jazz it up with spices, garlic, or a little Worcestershire sauce, and you don't have to count their calories.
4. The canned veggies make it easy to count their calories.
5. The salad is a real find. The quantity is large, the calories are only 32, and it happens to be quite tasty. If you prefer another kind of lettuce, use it.
6. You even get a dessert. It's not strawberry cheesecake, but it's not bad either.
7. I have intentionally chosen some items that are not in the food lists in Chapter 12 to show that leeway is certainly permitted.
8. The total for the day is 96 calories less than 1,000, so you can make up those calories with a snack or add that many to another day. Don't forget to put 96 on your Excess Calorie Sheet with a minus sign in front. I purposely went under 1,000 to demonstrate that you can have a substantial menu and still be below 1,000 calories.
**EXAMPLE TWO**
**Breakfast** |
---|---
6 oz. Tomato Juice | 35 calories
½ cup Kellogg s All-Bran | 50 calories
4 oz. Milk 2% fat | 64 calories
½ cup Egg Beaters (Prepared any way) | 60 calories
1 cup Coffee with 1 oz. Milk 2% fat | 16 calories
**Lunch** |
Healthy Choice Southwestern Grilled Chicken | 260 calories
Diet Soda | 0 calories
**Dinner** |
6 oz. Tomato Juice | 35 calories
Stouffer s Lean Cuisine Hearty Portions Salisbury Steak | 380 calories
6 oz. Strawberries, frozen | 66 calories
1 cup Coffee with 1 oz. Milk 2% fat | 16 calories
**Total for the Day** | **982 calories**
**Notes on Example Two**
1. We still fell a bit short of 1,000, but there should be plenty to eat.
2. If you mind having tomato juice twice in the day, skip one or try a little Worcestershire sauce in the dinner one.
3. The ½ cup of Egg Beaters represents two eggs. One way to prepare them is to scramble them in a skillet using nonstick spray.
4. If you want to add the salad from Example One, you will be over 1,000 by only 14.
**EXAMPLE THREE**
**Breakfast** |
---|---
6 oz. Tomato Juice | 35 calories
½ cup Kellogg s All-Bran | 50 calories
4 oz. Milk 2% fat | 64 calories
½ cup Egg Beaters (Prepared any way) | 60 calories
1 cup Coffee with 1 02. Milk 2% fat | 16 calories
**Lunch** |
Salad |
4 Large Leaves of Romaine Lettuce | 12 calories
4 Tablespoons Weight Watchers Caesar Salad Dressing | 20 calories
1 can (6 02.) Chunk Light Tuna in water | 150 calories
Diet Soda | 0 calories
**Dinner** |
6 02. Tomato Juice | 35 calories
12 02. Top Sirloin Steak, Choice | 444 calories
1 can Del Monte Mixed Vegetables (l6l/2ounces) | 80 calories
6 02. Strawberries, fro2en | 66 calories
1 cup Coffee with 1 02. Milk 2% fat | 16 calories
**Total for the Day** | **1,048 calories**
**Notes on Example Three**
1. I've repeated a lot of items from the other examples to demonstrate an easy way to have a varied menu. The lunch and dinner main courses have been changed with a healthy serving of mixed vegetables at dinner added.
2. The substantial 12-ounce steak at dinner, hardly considered a diet course, should surprise as well as please those who crave that type of thing.
3. We've finally gone over 1,000 calories, but only by 48. Be sure to include those on your Excess Calorie Sheet.
# _Appendix J: A Patient Fights Back_
Although I have repeatedly observed patients whose course of treatment with natural thyroid reinforced my opinion of its superiority over the synthetic variety, perhaps none of their stories were as dramatic as that of another lady, who was _not_ a patient of mine. I discovered her "story" while surfing the Internet, and I am grateful that she has allowed me to reprint it here.
Shirley Grose is a freelance writer. Her work involves painstaking research, and her thought processes must be functioning well if she is to do her work properly. In a letter to me she described what had been happening to her.
Before I knew anything was wrong with me, I tried to leave our small rural town for a business trip. I could not remember how to operate the ATM machine. I was nearly in tears; I then attempted to leave town, to complete my appointment, which was a couple hours' drive. I did not know how to leave town. I could not remember. I thought, of course, I had Alzheimer's disease. Amazingly enough, I hid these things from my family and from my personal physician. Even when my daughter noticed that I introduced myself to someone whom I knew quite well, she still did not quite comprehend that I did not remember this person. I could not remember friends' and neighbors' names or the names of flowers and trees.
Her local doctor diagnosed hypothyroidism and prescribed synthetic thyroid, and the dose was adjusted upward when her symptoms did not improve. She visited an endocrinologist in a nearby city, who confirmed her need for large doses of synthetic thyroid. From day to day Shirley's condition wavered, and she was dissatisfied with her progress.
Shirley was an avid researcher and knew that natural thyroid was another drug used for her condition. She was grasping at straws and was able to convince her local doctor to prescribe it. There was discernible improvement. A "cyst" had been found in her neck, and she traveled again to consult another endocrinologist, one with fine credentials.
The second endocrinologist had definite opinions about the use of natural thyroid and would not prescribe it for her. The letter she wrote to him after her visit is the one I came across on the Internet by accident. The letter was lengthy, and I have edited out parts, yet it retains its basic purpose. I have also edited out the brand name of the synthetic thyroid preparation she took since it adds nothing to the understanding of the issue.
Dear Doctor ______ :
I would like for you to clarify several points which came up during our recent discussion. You said Armour Natural Thyroid, my thyroid replacement preference, was impure, not predictably the same strength and old-fashioned. I am concerned about this information because I have uncovered some research that indicates flaws in this reasoning.
Would you clarify your statements on Armour Natural Thyroid product? If you feel those statements were valid, can you provide documentation to confirm your opinion that Armour Thyroid is an inferior product to [synthetic thyroid]? Is [synthetic thyroid] really a "new" product or was it "grandfathered in" around 1930? I would like to know why, when I changed to Armour Natural Thyroid, you didn't consider the definite improvement in my health important. I would like to know why you felt I was unqualified to say how my own body felt. Why would you insist upon prescribing a drug that I have tried and does not work well with my body?...
Your first statement during my consultation as a new patient was that the Armour Natural Thyroid should be discarded; it was full of impurities, it was of inconsistent strength, and it "went out in the 70s." [Synthetic thyroid] was the drug of choice. Armour was clearly inferior. I explained that I felt better on the Armour Thyroid. You ordered me to throw the Armour Natural Thyroid away and take the [synthetic thyroid] dosage you prescribed. You said that a TSH test would not be valid if taken while on Armour Natural Thyroid. Can you document this last statement? I understand the TSH is considered one objective measurement for thyroid supplementation; however, I question the inference that a patient's subjective opinion is unimportant. You seem to disregard how your patients feel. Have there been any major published studies indicating which product the health consumer preferred? Customers have apparently had no choice in thyroid medication in most instances. Therefore, sales volume is not indicative of customer preference. Also, does the [synthetic thyroid] company fund or in any way contribute to organizations to which you belong or to the university itself? If so, does this influence your decision to singularly prescribe [synthetic thyroid]?
At the end of my appointment, when you began to write my prescription for [synthetic thyroid], I indicated that would not be necessary. You asked, "Why?" I said I was continuing with the Armour Thyroid at the dosage my family physician had prescribed. Your response was, "You don't need to return, do you?" I said, "No, I don't." You further explained you did not use the Armour Natural Thyroid, and you would not treat me if I continued taking it.
Do you refuse to treat thyroid cancer patients who refuse to take [synthetic thyroid]? Should I develop thyroid cancer at some point in the future, would you refuse treatment to me on the basis that I chose not to take [synthetic thyroid]? Can you legally refuse to treat a patient who has thyroid cancer because the patient takes Armour Natural Thyroid? Why should I or any patient be intimidated into taking what they feel is an inferior product? Why should I or any patient suffer a lesser quality of life because of physician bias for a particular brand name?...
I would sincerely appreciate an answer with documentation in writing about the statements you have made about [synthetic thyroid] and Armour Thyroid. I feel these are important questions, not only for me, but for the future physicians _____ University educates. These future doctors, including the student who took my thyroid history, have not been given complete information, which would allow them and their patients to make educated decisions about their health and their lives.
Sincerely,
Shirley E. Grose
In her letter to me, Shirley went on to describe the contrast in her life before and after taking the proper dosage of natural thyroid hormone:
When the medicine finally took effect, I felt like I was standing in the middle of a tornado's aftermath. I could see nothing standing around me. My life had been destroyed. My driving license had run out six months previously, my garbage was piled up for lack of payment, my fire insurance had been canceled for nonpayment.... I had to relearn basic math skills that revolved around my job. I aged overnight. I reached for my hair and it fell out in my hands. I had been athletic with a good body. Within three months my body swelled to the point where I wore only large, loose dresses. At one point, I could not walk the short distance to my car. I walked to the bathroom, sometimes ate something when I could force it down, and I slept deeply for all but about one hour a day in the first two months after diagnosis. I could not bear the sound of the phone, nor could I withstand the slightest stress. The depression was frighteningly deep....
[My current doctor] gradually increased the natural thyroid. The recovery was not instant, but occurred over a year-and-one-half span, but one day on Armour natural thyroid was more potent than the two months on [synthetic thyroid]. My heart "buzzed" with [synthetic thyroid], for lack of a better word; it calmed and worked smoothly with Armour natural thyroid. My weight fell off slowly....
The last time that I spoke to her, Shirley told me she was feeling just fine.
# **ALSO AVAILABLE FROM WARNER BOOKS**
****_DOCTOR, WHAT SHOULD I EAT?_****
****Nutrition Prescriptions for Ailments in Which Diet Can Really Make a Difference by Isadore Rosenfeld, M.D.****
Isadore Rosenfeld cuts through nutritional hype, myths, and trends to offer specific food recommendations to treat more than fifty common health conditions, including Parkinson's disease, infertility, heart disease, pms, jet lag, and multiple sclerosis. Based on the latest research and supplemented with sensible menus and nutrition charts, this _New York Times_ bestseller offers sound, accessible advice to help maintain good health.
_"Extraordinary..._. _I'm giving it five stars_."
**—Ann Landers**
****_30 LOW-FAT VEGETARIAN MEALS IN 30 MINUTES
by Faye Levy_****
You can cook it tasty... cook it fast... and cook it _100% vegetarian._ It's easy with Faye Levy's 100 low-fat, low-cost, fast-fixing, and boldly seasoned vegetarian dishes. Here are recipes that focus on pasta, beans, rice and other grains, one-pot menus, soups, salads, and fruit desserts—all bursting with flavor. Faye will guide you step by quick step through irresistibly delicious and healthy menus that will save you time and money!
**_KATHY SMITH'S WALKFIT TM FOR A BETTER BODY_**
**Convenient Flexible Inexpensive Effective Fun**
**by Kathy Smith with Susanna Levin**
The star of America's bestselling fitness videos, Kathy Smith presents WALKFITTM, a complete program based on the safest and most natural exercise of all. It is for people who don't have time to exercise, can't always get to the gym, or don't want to be bothered with expensive equipment. From warm-up stretches to sure-fire techniques for building speed, there is specific advice for seniors, teens, fitness buffs, the overweight, and everyone in between— including expectant and new moms.
_ARE YOU DIETING AND EXERCISING— AND STILL GAINING WEIGHT?_
_ARE YOU TAKING VITAMINS AND MINERALS— AND STILL HAVE DULL SKIN AND HAIR?_
_ARE YOU SLEEPING EIGHT HOURS A NIGHT— AND STILL FEEL TIRED ALL DAY?_
IF SO... you may be one of the hundreds of thousands of people who suffer from hypothyroidism, a thyroid gland malfunction that makes it virtually impossible to lose weight and that can cause a wide range of other conditions. In this book, weight-loss trail-blazer Dr. Sanford Siegal gives you a 28-day diet plan that helps most people lose pounds fast—and serves as an important indicator. That's because if you don't lose a lot of weight on the plan, you'll know that you may very well have a sluggish thyroid, a condition that most conventional tests fail to detect. A diet book witrr a difference, filled with groundbreaking medical insight and case studies, here is a guide to taking control of your weight and your health that _finally_ answers the question...
**IS YOUR THYROID MAKING YOU FAT?**
"AN ABSOLUTE MUST FOR THOSE WHO'VE ALMOST LOST FAITH IN WEIGHT LOSS."
—Robert Fried, Ph.D., coauthor of _The Arginine Solution_
"DR. SIEGAL HAS CREATED A UNIQUE METHOD TO IDENTIFY PEOPLE WITH A SLUGGISH METABOLISM. THE MEDICAL COMMUNITY SHOULD TAKE NOTICE."
—Steven R. Peikin, M.D., Professor of Medicine at Robert Wood Johnson Medical School and **author of** _The Complete Book of Diet Drugs_
* Billewicz, W. Z., et al., "Statistical Methods Applied to the Diagnosis of Hypothyroidism," _Quarterly Journal of Medicine,_ New Series XXXVIII, No. 150, April 1969,
| {
"redpajama_set_name": "RedPajamaBook"
} | 7,864 |
<?php
/**
* Order administration interface, based on ModelAdmin
* @package shop
* @subpackage cms
*/
class OrdersAdmin extends ModelAdmin{
private static $url_segment = 'orders';
private static $menu_title = 'Orders';
private static $menu_priority = 1;
private static $menu_icon = 'shop/images/icons/order-admin.png';
private static $managed_models = array(
'Order' => array(
'title' => 'Orders'
)
);
/**
* Restrict list to non-hidden statuses
*/
public function getList() {
$context = $this->getSearchContext();
$params = $this->request->requestVar('q');
//TODO update params DateTo, to include the day, ie 23:59:59
$list = $context->getResults($params)
->exclude("Status",Order::config()->hidden_status); //exclude hidden statuses
$this->extend('updateList', $list);
return $list;
}
/**
* Replace gridfield detail form to include print functionality
*/
function getEditForm($id = null, $fields = null) {
$form = parent::getEditForm($id, $fields);
if($this->modelClass == "Order"){
$form->Fields()->fieldByName("Order")->getConfig()
->getComponentByType('GridFieldDetailForm')
->setItemRequestClass('OrderGridFieldDetailForm_ItemRequest'); //see below
}
return $form;
}
/**
* Ensure that SearchForm selection remains populated.
*/
public function SearchForm() {
$form = parent::SearchForm();
$query = $this->request->getVar('q');
if($query && isset($query['Status'])){
$form->loadDataFrom(array(
'q' => array(
'Status' => implode(',', $query['Status'])
)
));
}
return $form;
}
}
class OrderGridFieldDetailForm_ItemRequest extends GridFieldDetailForm_ItemRequest{
private static $allowed_actions = array(
'edit',
'view',
'ItemEditForm',
'printorder'
);
/**
* Add print button to order detail form
*/
public function ItemEditForm() {
$form = parent::ItemEditForm();
$printlink = $this->Link('printorder')."?print=1";
$printwindowjs =<<<JS
window.open('$printlink', 'print_order', 'toolbar=0,scrollbars=1,location=1,statusbar=0,menubar=0,resizable=1,width=800,height=600,left = 50,top = 50');return false;
JS;
$form->Actions()->push(
LiteralField::create("PrintOrder",
"<button class=\"no-ajax grid-print-button\" data-icon=\"grid_print\" onclick=\"javascript:$printwindowjs\">"._t("Order.PRINT","Print")."</button>"
)
);
return $form;
}
/**
* Render order for printing
*/
public function printorder() {
Requirements::clear();
//include print javascript, if print argument is provided
if(isset($_REQUEST['print']) && $_REQUEST['print']) {
Requirements::customScript("if(document.location.href.indexOf('print=1') > 0) {window.print();}");
}
$title = i18n::_t("ORDER.INVOICE","Invoice");
if($id = $this->popupController->getRequest()->param('ID')) {
$title .= " #$id";
}
return $this->record->customise(array(
'SiteConfig' => SiteConfig::current_site_config(),
'Title' => $title
))->renderWith('OrderAdmin_Printable');
}
} | {
"redpajama_set_name": "RedPajamaGithub"
} | 4,906 |
Q: Create rule to make request only contain certain keys I am using the Lumen Framework, which utilizes the Laravel Validation
I wanted to create a Validator Rule to make the Request->input() json only contain specific keys at the root like "domain" and "nameservers". Not more and not less.
Example passing the rule:
{
"domain":"domain.tld",
"nameservers":
{...}
}
Example not passing the rule:
{
"domain":"domain.tld",
"nameservers":
{...},
"Hack":"executeSomething()"
}
I tried to use to use several default validation rules to achieve this but wasnt successful.
My approach was now to put the request in another array like this
$checkInput['input'] = $request->all();
to make the validator validate the "root" keys.
Now this is my Approach:
create the validator
$checkInput['input'] = $request->all();
$validator = Validator::make($checkInput, [
'input' => [
'onlyContains:domain,nameservers'
],
]);
creating the rule
Validator::extend('onlyContains', function($attribute, $value, $parameters, $validator){
$input = $validator->getData();
$ok = 0;
foreach ($parameters as $key => $value) {
if (Arr::has($input, $attribute . '.' . $value)) {
$ok++;
}
}
if (sizeof(Arr::get($input, $attribute)) - $ok > 0) {
return false;
}
return true;
});
It seems i got the desired result, but i am asking if there is maybe smarter solution to this with the default rules provided by Laravel/Lumen.
A: You are trying to do a blacklisting approach blocking out fields that are not intended. A simple approach, that is utilized a lot, is to only fetch out the validated. Also you are trying to do logic, that goes against normal validation logic, to do it a field at a time.
This is also a good time, to learn about FormRequest and how you can get that logic, into a place where it makes more sense.
public function route(MyRequest $request) {
$input = $request->validated();
}
With this approach, you will only ever have the validated fields in the $input variable. As an extra bonus, this approach will make your code way easier to pick up by other Laravel developers. Example form request below.
public class MyRequest extends FormRequest
{
public function rules()
{
return [
'domain' => ['required', 'string'],
'nameservers' => ['required', 'array'],
];
}
}
A: You should use prohibited rule.
For eg:
$allowedKeys = ['domain', 'nameservers'];
$inputData = $request->all();
$inputKeys = array_keys($inputData);
$diffKeys = array_diff($inputKeys, $allowedKeys);
$rules = [];
foreach($diffKeys as $value) {
$rules[$value] = ['prohibited'];
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 4,802 |
{"url":"https:\/\/www.jiskha.com\/archives\/2012\/08\/17","text":"# Questions Asked onAugust 17, 2012\n\n1. ## geometry\n\nCampsite F And G Are On Opposite Sides Of The Lake.A Survey Crew Made Measurements Shown On The Diagram .What Is The Distance Between The Two Campsites?\n\n2. ## chem\n\nAspirin, C9H8O4, is produced from salicylic acid, C7H6O3, and acetic anhydride, C4H6O3: C7H6O3 + C4H6O3 --> C9H8O4 + HC2H3O2 a. How much salicylic acid is required to produce 1.5 x 10^2 kg of aspirin, assuming that all of the salicylic acid is converted to\n\n3. ## physics\n\nIn one day, a 75-kg mountain climber ascends from the 1500-m level on a vertical cli to the top at 2400 m. The next day, she descends from the top to the base of the cli , which is at an elevation of 1350 m. What is her change in gravitational potential\n\n4. ## Science - Chemistry\n\nWhat happens when you mix Sodium Bicarbonate, Bromothymol blue, and Calcium Chloride? What is Bromthymol blue used for in this experiment?\n\n5. ## math\n\nal has twice as many baseball cards as frank and four times as many football cards as joe. the expression 2x+4y can be used to show the total number of baseball and football cards Al has. If the answer is y, then what is the question?\n\n6. ## physics\n\nsuppose the glider is initially at rest at x=0, with the spring unstretched. You then apply a constant force in the +x direction with magnitude 0.610 N to the glider. what is the glider's velocity when it has moved 0.100m?\n\n7. ## English\n\nWhich one of the following is a correct example of the plural possessive case? A. woman's plans B. it's place C. men's plans D. stone's throw is it a?\n\n8. ## physics\n\na slingshot will shoot a 10 pebble 22.0 m straight up. a) how much potential energy is stored in the slingshot rubber band? B) With the same potential energy is stored in the rubber band, how high can the slingshot shoot a 25g pebble?\n\n9. ## physics\n\ndriving in a car with constant speed of 12m\/s,then encounter to a bump that has a circular cross-section and a radius of 35m.find the apparent weight of a 70 kg person in the car over the top of bump\n\n10. ## physic\n\n3 charges sit on vertical equilateral triangle the side of each is 30.0 cm. if the triangle are A= +4.0 uC B=+5.0 uC and C=+6.0 uC (clockwise from top) what is the force on each charge?\n\n11. ## science\n\nfour bodies of mass 1kg, 2kg,3kg, and 4 kg are situated at four corners of a square of side 2m, take the origin at the center of square. find m.i. if the system passing through the centre and perpendicular to the plane of square\n\n12. ## physics\n\nAmass of 0.5 kg is whirled at 120 rpm in a horizontal circle at the end of a string 2 meters long. Neglecting the force due gravity, find: (a) the angular velocity (b) the centripetal acceleration.\n\n13. ## chem\n\nwhen hydrocarbons are burned in a limited amount of air CO as well as CO2 form. When 0.450 grams of a particular hydrocarbon was burned in air, 0.467 grams of CO, 0.733 grams of CO2, and 0.450 grams of H20 were formed. a. What is the empirical formula? I\n\n14. ## physics\n\nA 45 g superball traveling at 28.0 m\/s bounces off a brick wall and rebounds at 24.5 m\/s. A high-speed camera records this event. If the ball is in contact with the wall for 3.60 ms, what is the magnitude of the average acceleration of the ball during this\n\n15. ## geometry\n\nThe sides of a quadrilateral are 3, 4, 5, and 6. Find the length of the shortest side of a similar quadrilateral whose area is 9 times as great.\n\n16. ## statistics\n\nA random sample of 84 shoppers were interviewed and 51 said they prefer to shop alone rather than with someone such as friends or family. Let p represent the proportion of all shoppers at this mall who would prefer to shop alone. Find a point estimate for\n\n17. ## English\n\nIdentify the sentence that contains a noun clause in italics. A. What Betty wants is to harvest the corn. B. When should Betty harvest the corn? C. Betty wants to harvest the corn. D. Betty would like to harvest the corn. Is it D?\n\n18. ## The young child and the environment\n\nFrequent and intense stress in children Over long periods of time can A, cause children to become more sympathetatic others. B, help increase their memory skills. C,stop brains production of cortisol. D, give children problems With controlling negative\n\n19. ## physical\n\nA 0.8 kg block of wood has an initial velocity of 0.25 m\/s as it begins to slide across a table. The block comes to rest over a distance of 0.72m. a) what is the average frictional force on the block? b)How much work is done on the block by friction? c)How\n\n20. ## Math\n\nLineing up the decimals then subtracting. 9.61-0.268 . I need to know how?\n\n21. ## history\n\nA staple food transplanted from Southeast Asia to the Mediterranean world as a result of the Islamic Empire was a. rice b. wheat c. yams d. potatoes i think b\n\n22. ## Chem\n\nIndicate which of the following are exact numbers. the mass of a stapler? i think its inexact because all staplers are different sizes. Is that correct? Also,the mass of a postage stamp. is that inexact? because they can also be diff. sizes?\n\n23. ## math\n\nHow do I calculate the doasage of Amoxicillin suspension 125mg\/5ml if the dose ordered is 3\/4 tsp Po Bid?\n\n24. ## math\n\nThe temperatures in degree celcius at midnight on 10 consecutive days were 4,1,3,0,-2,-1,-5,-3,1,-2. How many of these temperatures are within 2.2 degree celcius of 1 degree celcius?\n\n25. ## English\n\nWhat is a cliche and what is a sentence that's an example?\n\n26. ## social studies\n\nhow long does it take from Taipei, Taiwan to Miami,FL?? This is not a homework! i just wanna know it by myself cus my friend is going to visit me dis summer. i can't get the info from google or yah\n\n27. ## MATH\n\n1;The lengths of two sides of atrisngle are 12cm and 15cm.between what two measures should the length of the third side fall.\n\n28. ## Social Studies\n\nFounded by Oliver H. Kelley, the organization that came to be known as the _______ provided educational, social, and cultural activities to its rural members.\n\n29. ## English\n\nMy new boss is being picky about a test I made for students. I wrote a question that reads \"how many people in your family?\" It seems perfectly acceptable to me in an MC quiz for beginners, however the boss is saying it should read \"how many people are\n\n30. ## English\n\nI also need help with my English synthesis and transformation, 1) I was absent from school yesterday, so I did not meet the new principal. If I had_________________________________. 2) You must not tell the secret. Many want to know the secret. No\n\n31. ## physics\n\nA velocity vector 33{\\rm ^{\\circ}} below the positive x-axis has a y-component of -14{\\rm m\/s} .\n\n32. ## English\n\nWhen making multiple choice quiz for students about speaking. Do I need to use question marks in the answer choices. Example- Hello how are you. a)fine thank you and you b)good wasup c)I'm ok Answer (a) is the answer to the question but in itself is a\n\n33. ## Science\n\nWhat is matter?\n\n34. ## Quantitave Methodology\n\nRashid can paint two square metres of fence in ten minutes. therefore, the time it will take him to paint a fence three metres high and 26 metres long will be?\n\n35. ## math\n\ncos^2x-sinxcosx-1\/2=o\n\n36. ## Algebra\n\nOn a map, 1 inch equals 17.5miles. If two cities are 1.5 inches apart on the map, how far are they actually apart?\n\n51. ## math\n\nhow many different positive four-digit integers can be formed if the first digit must be 2, the last digit cannot be zero, and digits may be repeated? I know the answer is 900 but I'm not sure how I would get the answer? thanks!\n\n52. ## chemistry\n\na sample of Na2SO3.H2O weighing 0.62g is addedto 100ml.1NH2SO4 .THE resulting solution will be?\n\n53. ## Economics\n\nSuppose; C = 500 + 0.80(Y \u2013 400) I = 400 G = 400 (X \u2013 M) = -100 Solve for income or GDP\n\n54. ## CRITICAL THINKING\n\nWhat is critical thinking?\n\n55. ## Math\n\nDoes |x^2-3x+3|=3 have a solution? My answer was that there isn't a solution. Am i right?\n\n56. ## physics\n\nwhich one best describes appr. uniform velocity? 1. a hockey puck sldng across the ice 2. a baseball pitched toward a batter 3. the tip of the minute hand on a clock 4. an olympic sprinter running the 100m\n\n57. ## writing\n\nI need help rewording a sentence: \"Robotics is a broad field\"\n\n58. ## calculus\n\nsuppose the set of points have the following coordinates:(-2,3),(4,-4),(2,-3). please calculate the moment of this set of points about the x-axis and also about the center.\n\n59. ## physics\n\nwhich is true consdering torque and angular momentum: 1. spinnng figure skaters tuck their arms in to stop. 2. a high diver can flip forward faster than he can spn around the axis runnng from his head to his feet? 3. it is easier to turn the rudder on an\n\n60. ## history\n\nThe animating principles of Benedict's rules for monks are the quest for salvation and A. knowledge obtained solely through communion with God. B. the subordination of willfulness. C. extremes of self-mortification. D. the application of personal\n\n61. ## Spanish\n\n11. Si ---------- el n\u00famero de mi jefe, le -------- para decirle que no puedo ir al trabajo hoy. A. sabr\u00eda, llamara B.llamar\u00eda, supiera C. supiera, llamar\u00eda D.llamara, sabr\u00eda My Ans: C 12. ------------ a la fiesta si ----------- encontrar un vestido\n\n62. ## college algebra\n\nfind the vertical, horizontal, oblique asymptotes, if any, for the given rational function. R(x)=10x^2+19x-15 -------------- 2x+5 please show how you arrived with the answer! thank you\n\n63. ## art\n\nwhat are the principles of art\n\n64. ## Social Studies\n\nIn the election of 1860 the _____ won the electoral votes of all the free states except a fraction of the new jersey votes.\n\n65. ## statstic\n\n\u2022 Suppose you were preparing two way tables of percent ages for the following pairs of variables .how would you run the percentages?\n\n66. ## Algebra2\n\nDoes |x^2-3x+3|=3 have a solution?\n\nSi ---------- el n\u00famero de mi jefe, le -------- para decirle que no puedo ir al trabajo hoy. sabr\u00eda, llamara llamar\u00eda, supiera supiera, llamar\u00eda llamara, sabr\u00eda 12. ------------ a la fiesta si ----------- encontrar un vestido apropiado para llevar. A.\n\n68. ## math\n\nThe isoceles triangle represents the roof of a birdfeeder. 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, ou plus simplement , est une franchise d'animation japonaise créée par Yoshiyuki Tomino et Hajime Yatate pour le studio Sunrise en 1979. Appartenant au genre mecha, elle présente divers éléments classiques de la science-fiction — guerres spatiales, univers scientifiquement avancé — mais innove par sa volonté de réalisme, aussi bien à travers la narration qu'à travers les éléments technologiques. Les robots géants, essence du genre mecha, y sont donc pour la première fois ramenés au rang de simples armes de masse au Japon. Cette idée novatrice, qui reflète alors l'ouverture du public traditionnel des séries animées aux adultes, donne naissance à un sous-genre de la science-fiction japonaise nommé « real robot ».
Après des débuts difficiles, Gundam connaît le succès au début des années 1980 et ne le quittera plus jusqu'à nos jours ; ainsi, une trentaine de séries, d'OVA et de films sont réalisés pour la franchise, ainsi que des dizaines de mangas, de romans, de jeux vidéo et même de parodies via SD Gundam. Si les productions audiovisuelles constituent le cœur de la saga, Gundam repose en fait sur le second pilier que représentent les produits dérivés, et notamment les maquettes de robots (nommées Gunpla). Économiquement parlant, la franchise est la licence la plus rentable de la multinationale Namco Bandai, générant de nos jours environ 50 milliards de yens annuels. La plupart des critiques se portent d'ailleurs sur cette perception d'exigence économique qui prendrait le pas sur la créativité.
Mais le succès est avant tout culturel : pratiquement inconnu en francophonie, Gundam est un profond phénomène de société au Japon. La plupart des spécialistes académiques du sujet définissent clairement son impact comme majeur sur l'animation et la culture populaire japonaise, comparant régulièrement la franchise avec Star Wars en Occident. Cela se manifeste par une présence tangible dans la vie quotidienne de l'Archipel, que ce soit à travers les publicités, les magasins, les expositions d'art ou encore la construction d'une statue de dix-huit mètres près de Tōkyō. On ne peut toutefois pas parler d'hégémonie dans la mesure où la saga s'est peu exportée et a souvent été concurrencée par des séries comme Macross ou Evangelion.
Concept et terminologie
Mobile Suit Gundam appartient à un sous-genre de la science-fiction très populaire au Japon : le mecha. Le concept principal du genre est de mettre en scène des robots (au sens le plus large) télécommandés ou pilotés par un humain, voire par une intelligence artificielle. Plus précisément dans Gundam, ces robots sont des machines de guerre dirigées de l'intérieur (dans un cockpit), que l'on appelle , et qui peuvent évoluer aussi bien sur Terre que dans l'espace. Quant au terme Gundam, il désigne dans pratiquement toutes les séries un prototype de mobile suit plus puissant et technologiquement plus avancé que les modèles standards.
À l'origine, le créateur de la franchise, Yoshiyuki Tomino, avait nommé son projet Freedom Fighter Gunboy, ou plus simplement ; le terme était un mot-valise associant « » (« arme à feu » en anglais), et « » en référence au public ciblé. C'est ensuite l'équipe Yatate qui propose de remplacer ce terme par « Gundom », en référence cette fois au mot anglais « » (« liberté »), concept qui revenait très souvent dans le projet initial. Cependant, pour des raisons esthétiques sur les katakanas, Tomino décide de modifier légèrement le mot en « Gundam », terme dès lors définitif. Par ailleurs, Gundam a parfois été employé en tant que rétro-acronyme, comme « » dans Gundam Seed.
Historique
L'avant Gundam
Parmi les principales influences du genre mecha au Japon figure le roman Étoiles, garde-à-vous ! de Robert A. Heinlein, dans lequel sont mis en scène des sortes d'exosquelettes puissamment armés qui ressemblent énormément aux robots de Gundam. Bien que le genre fasse ensuite une première apparition dans le monde de l'animation japonaise avec Astro le petit robot d'Osamu Tezuka, la première série consacrée aux robots géants au Japon fut certainement Tetsujin 28-gō, sortie dès 1956 et qui donna naissance à toute une vague de séries mechas telles que Mazinger Z (1972) ou Goldorak (1975). Toutes ces séries pionnières du genre partagent une caractéristique essentielle : les robots sont invariablement gigantesques et surpuissants, de véritables armes surréalistes. On décrit communément ces machines comme des « super robots » (ou « super mechas »), terme qui désigne aussi un sous-genre à part entière de la science-fiction japonaise ; à l'époque, ces séries de super robots présentent un certain code scénaristique suivi par tous les réalisateurs, que l'on appelle parfois l'école traditionnelle ou robotto anime.
Mobile Suit Gundam : la rénovation du genre mecha
Derrière l'idée originale de Gundam se cache un homme : Yoshiyuki Tomino. Ce dernier acquiert durant les années 1960 et 1970 une certaine expérience dans l'animation, ayant par exemple été assistant au studio Mushi Production sur Astro le petit robot. En 1976, il s'essaye au genre mecha avec Yūsha Raideen (produit aussi par Sunrise) ; cependant, cette série suit scrupuleusement les codes de l'école traditionnelle. Grâce à ses succès, il comprend qu'il a désormais une plus grande liberté dans la conduite de ses histoires. C'est donc en 1979 qu'il écrit et réalise Mobile Suit Gundam avec l'aide de Hajime Yatate (pseudonyme désignant en fait un collectif de créateurs du studio Sunrise), série de mechas qui propose alors une approche novatrice du genre : en effet, les robots sont bien moins puissants et fantaisistes, et se voient plutôt confinés dans le rôle de simples armes évoluées. Dans la mesure où ces mechas se voulaient le plus proche possible de notre science contemporaine, on les désigna par le terme de « robots réalistes », en opposition aux super robots. Bien qu'en apparence très simple, l'idée de Tomino rénove alors profondément le genre.
Pourtant lors de sa sortie, Mobile Suit Gundam ne remporte pas un franc succès, si bien que les producteurs décident même de l'écourter, la tronquant de sept épisodes en raison des faibles scores d'audience. Une compilation en trois films reprenant majoritairement des séquences de la série avec quelques scènes inédites sort cependant en cinéma en 1981 ; de manière surprenante, elle connaît un bon succès grâce au bouche-à-oreille. C'est aussi à ce moment, en 1980, que Bandai commercialise les premières maquettes et jouets Gundam, les Gunpla, qui se vendent extrêmement bien. La série gagne ainsi une certaine popularité au début des années 1980, suffisamment en tout cas pour qu'en 1984 Sunrise commande à Tomino une suite : Mobile Suit Zeta Gundam. Commande, ou plutôt impose, comme l'auteur le clame lui-même. Afin de ne pas subir l'échec relatif de la première série, Tomino apporte une note plus sombre et dramatique au scénario, ainsi que des personnages plus nuancés, loin de tout manichéisme. Indiscutablement, Zeta Gundam est un succès très important au Japon, à l'origine de la longévité exceptionnelle de la franchise.
Fort de cette réussite, le studio Sunrise engage Tomino à poursuivre l'histoire par Mobile Suit Gundam ZZ dès 1986, qui vise un public plus jeune (rencontrant d'ailleurs un succès plus mitigé), puis par le film Mobile Suit Gundam : Char contre-attaque. Les scénarios de ces premières œuvres, de Mobile Suit Gundam à Char contre-attaque, se suivent tous chronologiquement selon une ligne de temps inventée par Tomino : l'Universal Century. De nombreux personnages ou organisations y apparaissent ainsi de manière plus ou moins régulière, et le film Char contre-attaque se veut être la conclusion de cette saga originale en mettant en scène la fin du long affrontement entre la Fédération terrienne et Zeon d'une part, Amuro Ray et Char Aznable de l'autre.
En 1989 sort pour les dix ans de la franchise Mobile Suit Gundam 0080 : War in the Pocket de Fumihiko Takayama, qui présente plusieurs particularités : ce sont d'abord les premiers OVA tirés de Gundam, et c'est ensuite la première œuvre non réalisée par Tomino. Ces changements permettent un scénario assez différent, reposant encore plus sur les émotions et les relations entre les personnages que sur les mechas. En revanche, ils ne présentent qu'un point de vue alternatif à la saga originale, puisqu'ils se déroulent durant la même période de l'Universal Century avec des personnages différents.
Une mue difficile après la saga originale
Le début des années 1990 est une période financièrement délicate pour les studios d'animation japonais, Sunrise ne dérogeant pas à la règle. De plus, la saga de l'Universal Century s'étant achevée avec Mobile Suit Gundam : Char contre-attaque, le studio ne se montre guère prêt à investir lorsque Tomino propose de relancer Gundam en s'orientant vers une nouvelle histoire et de nouveaux personnages en 1991. L'auteur n'obtient finalement le feu vert que pour réaliser un seul film, Mobile Suit Gundam F91. Ce dernier, résumant en fait les treize premiers épisodes de la série voulue par Tomino, se déroule trente ans après la saga originale, mais l'accueil est décevant et le projet abandonné. Cette tentative de renouveau est donc un échec, d'autant plus que les OVA Mobile Suit Gundam 0083 : Stardust Memory, qui prennent place eux juste après l'histoire de Mobile Suit Gundam, c'est-à-dire toujours dans le cadre de la première saga, sont un véritable succès. Sunrise en conclut d'ailleurs que le format OVA peut être économiquement rentable, et l'utilisera souvent par la suite. Malgré cela, la décennie des années 1990 est compliquée pour la franchise.
C'est finalement SD Gundam qui prend le premier la succession de l'Universal Century. Sorti entre 1986 et 1990, il s'agit en fait d'une parodie de Gundam dans laquelle les mechas sont représentés selon les codes graphiques du SD ( en anglais). L'accueil fut si enthousiaste que SD Gundam sera décliné en de nombreuses saisons et séries et vivra en marge des productions de la franchise.
De même, la vente de maquettes connaît une croissance soutenue, si bien que Bandai diversifie grandement son offre en y incorporant de nombreuses innovations techniques. La société instaure aussi son système de « grades » censés différencier les gammes de Gunpla en fonction de leur qualité (et donc souvent, de leur prix) : la première gamme du genre, nommée « », réédite ainsi quatre Gundam très populaires de l'Universal Century dès .
La relève de Tomino
À partir de Mobile Suit Victory Gundam sorti en 1993 (fruit d'un Tomino oppressé par Sunrise, alors sur le point d'être racheté par Bandai), d'autres réalisateurs parfois renommés se voient confier la réalisation des séries Gundam, avec en premier lieu Mobile Fighter G Gundam (1994) pour les quinze ans de la série, puis Gundam Wing (1995) et After War Gundam X (1996), qui recevront d'ailleurs toutes un succès moins important que les premières séries — Neon Genesis Evangelion écrase à l'époque toute concurrence. Fait particulier de ces œuvres, elles se déroulent dans des univers parallèles permettant de se démarquer de l'Universal Century et d'attirer de nouveaux téléspectateurs, Sunrise ayant tiré les conclusions de l'échec de Gundam F91. Gundam Wing présente plus spécifiquement une certaine évolution dans l'histoire de la franchise : en effet, elle adopte un ton plus moderne qui commence à toucher le public jusqu'alors ignoré, le public féminin. De plus, cette série reste principalement connue pour être l'une des premières à avoir été exportée en Occident (même la toute première en France), ainsi que pour avoir remporté un succès important aux États-Unis.
Turn A Gundam, en 1999, est l'occasion de voir une nouvelle fois Tomino réaliser un anime Gundam. L'histoire se déroule deux mille ans après les autres séries et apporte une conclusion à tous les univers, qui doivent par conséquent converger dans le temps. Après cinq ans d'interruption, Tomino rompt en de nombreux points avec ses premières créations plus sombres dans cette série ; la conception des mechas, confiée à l'Américain Syd Mead, y est aussi très différente.
Ce n'est réellement qu'en 2002 avec Mobile Suit Gundam SEED que la franchise connaît de nouveau un immense succès, réalisant de fait ses meilleurs scores d'audience depuis Mobile Suit Zeta Gundam. Une gamme record de 120 maquettes en est tirée par la suite. Cette popularité entraîne la production d'une suite immédiate, Mobile Suit Gundam SEED Destiny (2004), et des ONA Gundam SEED C.E.73 Stargazer (2006). Finalement, la franchise pose avec Gundam SEED les prémices d'une renommée internationale jusqu'alors timide, si bien que les OVA Gundam Unicorn bénéficient en 2010 d'une sortie mondiale. Entre-temps est également sorti Mobile Suit Gundam 00, le seul anime à se dérouler dans notre ère en 2307, qui rencontre un accueil plutôt enthousiaste, si bien qu'un film en est tiré fin 2010. Depuis, Sunrise en partenariat avec le studio Level-5, concepteur des jeux Professeur Layton et Inazuma Eleven, lance fin 2011 Mobile Suit Gundam AGE, un nouveau concept qui suivra trois générations de pilotes de Gundam lors d'un conflit armé s'étendant sur une période d'environ cent ans. Après ce succès mitigé, sort en 2014 Gundam Reconguista in G, qui est à ce jour, la dernière série Gundam réalisé par son créateur originel, Yoshiyuki Tomino.
Caractéristiques
Le réalisme
L'idée de concevoir une série mecha de manière réaliste est l'innovation principale de Mobile Suit Gundam, posant les bases d'un nouveau sous-genre de la science-fiction appelé . Cet aspect se manifeste très concrètement dans deux composantes des anime : le rôle des robots dans l'histoire, et la narration proprement dite.
Les « real robots »
Les robots de Gundam sont les premiers à garder une dimension humaine dans l'animation japonaise. Bien que faisant figure d'armes technologiques de pointe, ils demeurent vulnérables et obéissent aux mêmes contraintes matérielles et physiques que nos armes contemporaines, comme la production de masse par les États et la nécessité d'une logistique poussée pour la maintenance et l'acheminement sur le théâtre des opérations ; ces robots sont quelque part rétrogradés du rang de deus ex machina à celui de « simple » arme. Il n'est d'ailleurs pas rare que la machine d'un des personnages principaux soit sévèrement endommagée (comme Bernie dans Mobile Suit Gundam 0080) ou remplacée (Char Aznable en est l'exemple type). Tomino décrit la façon dont il concevait son projet ainsi :
Ce besoin de réalisme sur les robots s'est traduit lors de la phase de production par de fortes contraintes dans leur mise en scène, qui se devait cohérente et plausible dans les moindres détails, notamment vis-à-vis de la science. Par conséquent, un poste particulier fut créé spécialement pour la conception des mechas (le en anglais) ; lors de toute la saga Universal Century, c'est Kunio Ōkawara qui s'en est chargé, gagnant ainsi une grande popularité.
Gundam repose sur un univers de science-fiction technologiquement avancé, mais plausible. En conséquence, un certain nombre d'éléments technologiques prennent racine dans des théories scientifiques bien réelles, tranchant avec les productions précédentes. Dès l'origine sont abordés les points de Lagrange où les colonies spatiales sont installées grâce à la gravité particulière qui y règne (sujet notamment étudié à travers les cylindres O'Neill). Plus tard avec Mobile Fighter G Gundam, ce sont les thèmes des nanotechnologies et des biomachines qui sont succinctement abordés. De plus, les interfaces homme-machine dans le cockpit explorent des pistes variées, mais cohérentes avec l'avancée de la recherche (superposition d'images 2D ou 3D, écrans panoramiques, apprentissage assisté par ordinateur, etc.).
La narration
Cette volonté de réalisme se trouve néanmoins poussée bien plus loin que le simple cas des robots : c'est tout le contexte des scénarios qui suit la même dynamique en se voulant le reflet de notre monde, ou du moins d'un monde technologiquement et humainement plausible. Par conséquent, géopolitique, stratégie militaire et trahisons forment la toile de fond de la plupart des séries, dans laquelle se fondent les relations et les personnages en une intrigue complexe. Ce traitement a pour but de mettre en exergue les conceptions, les aspirations et la psychologie des protagonistes, et finalement de montrer que rien n'est entièrement bon ou mauvais, à l'instar de notre monde. D'ailleurs, certains antagonistes comme Char Aznable acquièrent parfois une popularité plus importante que les personnages principaux. Le réalisme se traduit ainsi par le refus du manichéisme, même si certaines productions n'évitent pas les stéréotypes.
Bien souvent dans Gundam, c'est surtout la souffrance des personnages qui est soulignée (le contexte étant toujours la guerre) ; on retrouve donc avec récurrence une ambiance sombre et dramatique qui contraste largement avec une certaine idéalisation des combats que l'on remarque souvent dans l'animation japonaise de l'époque. L'exemple de Kamille Bidan qui sombre petit à petit dans le désespoir durant Mobile Suit Zeta Gundam illustre bien ce point, ou plus récemment les Gundam meister de Gundam 00. Enfin, cette richesse du scénario veut s'exprimer aussi par les nombreuses évolutions des convictions et de la façon de penser des personnages au fil des événements, idée tangible à travers par exemple les fluctuations de la rivalité entre Char Aznable et Amuro Ray en fonction des morts tragiques et des retournements d'alliance. D'une manière plus générale, maintenir l'ambiguïté sur l'identité des « méchants » reste un élément récurrent de la franchise. Néanmoins, certaines séries Gundam ont fait le pari – parfois peu heureux – d'adopter un univers moins pesant, comme la première partie de Mobile Suit Gundam ZZ qui tente de toucher un public plus jeune par ses gags.
Enfin, Gundam repose toujours sur des narrations « locales » (centrées sur une guerre ou un personnage, donc une période temporelle bien délimitée), mais s'inscrivant dans une trame globale, caractéristique classique des grandes sagas de science-fiction où l'univers fictif joue un rôle crucial – on parle souvent du genre space opera. Ainsi, la combinaison de toutes les séries permet de faire émerger une seule et même « grande narration » que le spectateur reconstruit lui-même. Pour Aruma Hiroki, , indépendante des qui s'y déroulent. Dans les années 1970 et 1980 au Japon, ce style narratif attire un large public et fait le succès de longues sagas comme Macross, Brave Story, et bien sûr Mobile Suit Gundam. Ce genre de narration se rapproche d'ailleurs du mythe, un peu en opposition avec le côté technologique de la franchise.
Bien qu'appartenant au genre mecha, cette narration caractéristique rapproche par conséquent la saga du space opera, autre sous-genre de la science-fiction.
La guerre
Comme évoqué ci-dessus, Gundam prend toujours pour contexte la guerre, à l'image de nombre de séries mechas. Là encore, la manière de mettre en scène les combats se veut empreinte de réalisme, c'est-à-dire de tragique. Nombre de personnages s'en retrouvent traumatisés (comme Amuro Ray ou Kamille Bidan), accentuant le côté sombre des scénarios. Finalement, le message véhiculé est de dépeindre la guerre comme vaine et inutile ; souvent, les principaux protagonistes qui se battent à échelle humaine réalisent qu'ils ne peuvent réellement influer sur les conflits et empêcher les morts injustes, ce qui est particulièrement le cas dans Victory Gundam. Mobile Suit Gundam 0080 est quant à lui souvent décrit comme un exemple poignant d'antimilitarisme, en adoptant le point de vue d'un enfant qui devient ami avec un soldat ennemi ; il apprend au fil des morts que la guerre n'est pas un jeu. Ce courant sombre de la science-fiction sera poussé encore plus loin par des séries comme Evangelion ou Bubblegum crisis, avec leur univers déshumanisé.
D'autres aspects de ce sujet sont ponctuellement explorés ; dans Gundam Wing, les auteurs se posent explicitement la question du pacifisme, qui y semble impraticable : en effet, malgré tous les efforts faits pour la paix, les batailles se succèdent jusqu'au point d'orgue de l'histoire. Les principaux protagonistes de Mobile Suit Gundam: Iron-Blooded Orphans sont des enfants soldats, exploités par des compagnies de mercenaire en collusion avec les autorités en place. Plus récemment, Mobile Suit Gundam 00 s'inspire du terrorisme, thématique centrale du début des années 2000.
Plus intimement, Gundam ravive la mémoire collective du traumatisme de la Guerre du Pacifique, s'opposant ainsi aux séries de « super robots » des années 1960 qui glorifiaient la technologie militaire. Pour Williams et Stahl, Tomino présente à l'origine une allégorie de la guerre allant à l'encontre des idées victimisantes de ses contemporains : il critique tout militarisme ou impérialisme de la part des élites et montre l'absurdité de l'idée de « défaite noble » ; quel que soit le point de vue, ce sont les civils qui restent avant tout les premières victimes. Montrer sa propre perception des conséquences de la Seconde Guerre mondiale constituerait ainsi un des points de départ de Mobile Suit Gundam.
Le style Tomino
Yoshiyuki Tomino, créateur de la franchise et auteur de toute la saga Universal Century, a insufflé un style scénaristique relativement caractéristique à ses œuvres. Bien que n'ayant réellement réalisé moins de la moitié des séries Gundam, il est intéressant de relever ces points plus en détail (c'est-à-dire, en passant outre les notions générales du réalisme et du drame), car on les retrouve souvent dans toutes les autres séries. Tout d'abord, la plupart de ses personnages principaux sont décrits et introduits de la même manière : des adolescents communs vivants bien loin des instances dirigeantes de leur monde ; ils sont pourtant toujours mêlés brutalement à la guerre et se retrouvent contre leur gré aux commandes d'un prototype de mobile suit puissant et unique nommé Gundam – Mark Simmons y reconnaît là l'influence des super robots –, proposant finalement une sorte de métaphore du passage à l'âge adulte. Peter Appelbaum, dans une analyse de la littérature contemporaine, y définit à ce sujet la notion de « héros Gundam », un enfant qui remédie aux lâchetés et aux errements des adultes dans un conflit qui n'est pas le sien. Sa tâche est donc de sauver le monde grâce à la technologie qu'il doit se réapproprier. Bien sûr, dans Gundam, ce héros reste tragique ; Tomino est d'ailleurs connu pour terminer ses séries par la mort de la plupart des personnages (y compris des principaux) dans des batailles épiques, y insufflant ses frustrations ; au Japon, ce détail deviendra populaire parmi les adeptes de la franchise à travers l'expression (littéralement, ).
Un peu plus profondément se trouve dès la première série un concept important de Gundam : les ou êtres évolués, c'est-à-dire des humains ayant développé des capacités psychiques supérieures (comme la télépathie), probablement dues à la vie dans l'espace. Ce principe de l'évolution a une influence sur le traitement des personnages, entre ceux qui s'en méfieront (comme la Fédération au début) et ceux qui militeront pour l'élévation de l'humanité (Char Aznable). À travers les newtypes, Tomino se permet donc d'adopter un point de vue plus philosophique sur l'évolution humaine, thématique que l'on retrouve souvent dans la saga par la suite.
Le système des calendriers
La chronologie des premières séries suit un calendrier inventé par Tomino : l'Universal Century. Donc, même si dix années séparent Mobile Suit Gundam et le film Char contre-attaque, le contexte reste fortement lié, et plusieurs personnages apparaissent dans plusieurs histoires différentes. Cependant, après l'échec de Gundam F91, Sunrise décide de déplacer les scénarios dans des mondes alternatifs dotés de leur propre calendrier. Bien que proche de l'idée classique en science-fiction des univers parallèles, il ne s'agit cependant que d'une transposition dans un contexte différent, sans lien réellement fort. Ces mondes sont listés ci-dessous par date de création :
Universal Century (U.C.) : le premier calendrier de référence donc, dont l'an un correspond à l'établissement de la première colonie spatiale habitée par l'humanité ;
After War (A.W.) : cet univers est en fait une suite alternative à la saga originale, dans laquelle les colonies spatiales auraient toutes été détruites. C'est donc un univers post-apocalyptique faisant suite à l'Universal Century ;
Future Century (F.C.) : le Future Century est un autre univers alternatif à l'Universal Century, dans lequel les colonies auraient pris le contrôle de la Terre ;
After Colony (A.C.) : cet univers se déroule après la création des premières colonies spatiales par les terriens, où ces derniers maintiennent un joug tyrannique ;
Correct Century (C.C.) : le Correct Century, imaginé par Tomino lui-même, se veut en fait être le futur lointain de tous les autres univers parallèles. Il se pose donc un peu en conclusion de Gundam et de l'affrontement récurrent entre habitants de l'espace et habitants de la Terre ;
Cosmic Era (C.E.) : ce calendrier se situe aussi juste après la création des premières colonies spatiales par la Terre ;
Anno Domini (A.D.) : l'Anno Domini réfère à notre calendrier réel, l'histoire se déroulant dans un futur relativement proche (2307) ;
Reguild Century (R.C.) : ce calendrier se situe à la suite de l'Universal Century. L'Humanité est entrée dans une nouvelle ère de prospérité époque qui espère voir la paix durer. Gundam : G no Reconguista se déroule en l'an 1014 de ce calendrier ;
Post Disaster (P.D.) : après un grand conflit entre la Terre et la colonie de Mars connu sous le nom de « la Guerre des Calamités », la relation entre les deux planètes n'est toujours pas au beau fixe. la première mention de ce calendrier vient de la série Mobile suit Gundam : Iron-blooded orphans en l'an 323 de ce dit calendrier.
L'Universal Century reste cependant l'univers le plus populaire, et la majorité des productions s'y déroulent. Les séries SD Gundam se placent elles dans des mondes parodiques (tels Neotopia ou Mirisha), sans réelles connexions. D'autres parts, les OVA Gundam Evolve (2001) se déroulent eux dans plusieurs des calendriers sus-cités.
Le dessin
Même si le concept général reste très similaire, on retrouve un trait relativement différent d'une série à l'autre, tant en matière de personnage qu'en matière de mecha, ce qui conduit même parfois à des anachronismes, comme le film Mobile Suit Zeta Gundam : A New Translation qui présente un mélange d'animation ancienne et récente. Turn A Gundam se distingue aussi avec son Gundam totalement différent des autres séries (des proximités avec les Zakus de l'Universal Century restent présentes), dessiné par Syd Mead. À partir de Gundam SEED, la 3D est régulièrement utilisée, avec pour point d'orgue les OVA MS IGLOO qui sont conçus entièrement en trois dimensions.
Phénomène économique et social
Une manne très rentable
Financièrement parlant, Gundam est un filon inestimable pour Namco Bandai qui génère environ de yens (près de d'euros) de revenus par an grâce aux produits de la franchise. Depuis le début, le modèle commercial de Gundam repose clairement sur deux piliers : les anime et les produits dérivés (maquettes, musiques, etc.) ; en 2000, les ventes cumulées de toutes les marchandises estampillées Gundam depuis l'origine étaient estimées à de dollars (environ 40 milliards d'euros).
D'un côté donc, les anime les plus populaires (Zeta Gundam ou Gundam SEED) ont réalisé des scores moyens d'audience par épisode supérieurs à 6 % avec des pointes au-delà de 10 % selon le magazine Weekly the Television, tandis que les sorties cinémas ont souvent été satisfaisantes, comme Mobile Suit Zeta Gundam, A New Translation dont les recettes sont proches du milliard de yens. Cela ne signifie cependant pas que toutes les séries Gundam ont connu de tels résultats ; en particulier dans les années 1990, Gundam Wing et After War Gundam X sont victimes de la concurrence d'autres anime comme Evangelion.
Quant aux produits dérivés, ils font de Gundam la licence la plus rentable possédée par Bandai. Il faut remonter au début des années 1980 pour comprendre la genèse du modèle économique de la franchise. En effet, à la suite des faibles audiences de la première série en 1979, Bandai fait le pari de produire des maquettes de robots plus élaborées que de simples jouets. Leur succès fulgurant participe à la relance la franchise au début des années 1980. Sur l'année 2004, selon une enquête gouvernementale japonaise, les maquettes en plastique Gundam (nommées « Gunpla ») dominent largement le marché en représentant environ 90 % des ventes de figurines en pièces détachées au Japon, et 40 % des ventes globales de maquettes ; finalement, cela représente environ 360 à 400 millions d'unités écoulées depuis l'origine. Des magasins entiers sont ainsi réservés à Gundam dans les grandes villes japonaises. Fort de ces ventes, Bandai réinvestit beaucoup dans la recherche de nouvelles méthodes de production : en 2006 par exemple, la société annonce pouvoir atteindre un niveau de détails de l'ordre de 40 micromètres.
Par la suite, la franchise a souvent été utilisée à des fins marketings à cause de ce succès. Dès le début, un grand nombre de produits dérivés aux couleurs du personnage Char Aznable a été créé (y compris une carte de crédit), provoquant la colère de Tomino qui y voit un pillage commercial peu sain et en désaccord avec ses principes.
La musique n'est pas communément citée comme l'élément central de l'œuvre, mais génère régulièrement des revenus importants comme les bandes originales de Mobile Suit Gundam Seed et Mobile Suit Gundam Seed Destiny qui ont été sacrées « album d'animation de l'année » par la Recording Industry Association of Japan en 2004 et 2006, avec plus d'un million d'albums écoulés chacune (disques d'or). En tout, le nombre de CD parus est estimé à plus de soixante-dix.
Depuis Gundam Wing, la franchise prend une dimension internationale. Cependant, malgré un certain succès aux États-Unis et en Asie de l'Est (notamment la Corée du Sud), les consommateurs de produits Gundam restent très majoritairement japonais.
Clés sociologiques du succès
Le mecha constitue depuis ses débuts un genre très apprécié au Japon, ce dès la fin des années 1960. La science y est en effet perçue comme un vecteur d'évolution : . Cependant, le choc des bombardements atomiques de Hiroshima et Nagasaki fait comprendre aux Japonais le réel intérêt d'une technologie avancée ; loin de la prendre en aversion, l'Archipel en fait le moteur de sa reconstruction d'après-guerre, au point de devenir selon l'expression de K. T. Greenfeld une . Cet amour de la technologie explique donc l'intérêt du pays pour les mechas, et forme en 1979 un terreau fertile pour une série comme Mobile Suit Gundam.
Toutefois, il est naturel de se demander comment Gundam a pu imposer auprès du public son style novateur, mais très éloigné d'une glorification jusqu'au-boutiste de la technologie. Un élément de réponse couramment avancé renvoie à la transformation de la société japonaise dans sa manière de percevoir l'animation à la fin des années 1970 : le public regardant les anime, traditionnellement des enfants, évolue pour toucher des spectateurs plus âgés. Yoshiyuki Tomino fait d'ailleurs lui-même cette analyse. Avec ses scénarios sombres, voire tragiques, la franchise a finalement suivi la même transformation de fond en traitant de sujets plus adultes. Cette idée se retrouve aussi dans la commercialisation de maquettes plastiques élaborées à la place des habituels jouets, qui touchent en majorité les hommes entre vingt et trente ans. En effet, les maquettes d'engins militaires étrangers étaient déjà fortement plébiscitées dans les années 1960 par les jeunes japonais et Bandai a pu viser ces modélistes confirmés, notamment en insistant sur le haut degré de personnalisation des Gunpla.
À la fin des années 1990, Gundam opère un second changement de fond en s'ouvrant au public féminin, jusque-là largement ignoré. Cette volonté est tangible dès Gundam Wing, où les dessins s'inspirent du yaoi dans la veine des Samouraïs de l'éternel et où l'histoire se focalise sur les relations entre cinq garçons séduisants. En 2002, Mobile Suit Gundam SEED continue sur cette lancée et présente une exception notable dans l'histoire de la franchise puisque selon son producteur, plus de la moitié de ventes de DVD concernent les filles en 2003.
Mais surtout, Gundam est aujourd'hui intrinsèquement lié à la « culture otaku », dont elle est une des sagas les plus emblématiques. De multiples raisons peuvent expliquer ce phénomène, mais c'est avant tout le rapport étroit avec la science et la technologie, ainsi que la complexité de la saga qui sont communément avancés, permettant à l'otaku d'explorer et expliciter l'univers en profondeur ; Patrick Macias et Tomohiro Machiyama font le parallèle entre les adeptes de Gundam et ceux de Star Wars ou Star Trek aux États-Unis sur ce point. Pour ces raisons, Gundam est un sujet populaire du fandom, à travers par exemple cosplays, jeux de rôles, dōjinshi, etc.
Influence sur l'animation japonaise
Héritage de la franchise
Il a fallu attendre longtemps avant de voir émerger des analyses et des critiques académiques sur les mechas — et donc Gundam. Aujourd'hui, les anime s'étant internationalisés, on dispose de publications importantes ; parmi la diversité des sources émerge toujours une appréciation dithyrambique sur la popularité et l'importance de la franchise. Ainsi, selon G. Poitras, , tandis que Gresh et Weingerg estiment qu'elle marque . Pour Helen McCarthy et Jonathan Clements, la saga est , comparable là encore à Star Trek ou Star Wars en Occident. Pour M. Gilson, . Parmi les auteurs francophones, Nicolas Finet écrit notamment : . Gresh et Weingerg vont plus loin en assénant que Gundam . De fait, différentes séries des années 1980 comme Gundam, Galaxy Express 999 et Macross contribuent à poser les fondements tant graphiques que scénaristiques de l'animation moderne.
Le réalisme laissé en héritage par Gundam – qui a donc initié le genre des real robots (« robots réels ») – a marqué durablement l'animation japonaise. Parmi les séries ultérieures et très connues de real robot figurent Macross, Patlabor ou Full Metal Panic. D'autres ne peuvent réellement s'y classer, mais en conservent une certaine inspiration, comme Evangelion à travers la confrontation entre l'interface du mecha et la psyché parfois instable du jeune pilote. Ainsi, ce genre devient rapidement prépondérant parmi les séries de mechas japonaises. Au-delà, ce sont bien sûr les animateurs qui ont été marqués par Gundam. Gorō Taniguchi, le scénariste de Code Geass, confie par exemple s'être inspiré de Char Aznable pour son personnage de Zero. Plus généralement, le concept et le mode narratif de la franchise ont souvent été repris ou copiés, comme le notent Brenner ou Helen McCarthy pour qui nombre de séries de robots plus récentes sont en partie des « clones » de Gundam.
Une question se pose désormais quant au futur de la franchise. En effet, certains spécialistes estiment qu'elle ne répondrait plus vraiment aux attentes du public d'aujourd'hui, qui préfère des séries courtes et un univers plus implicite à la manière d'Evangelion. Une thèse qui ne fait d'ailleurs pas l'unanimité, notamment chez Adam Barkman qui cite en contre-exemple le succès très récent (2007) de Mobile Suit Gundam 00 au Japon.
Critiques
Le manque d'innovation résultant de la prépondérance des impératifs économiques et commerciaux demeure le principal reproche adressé à la franchise, qui sacrifierait donc la créativité à des motifs purement comptables. En effet depuis 1990, de nombreuses reprises, suites ou histoires parallèles ont été créées, et les mêmes traits de scénario se retrouvent plus ou moins dans toutes les productions récentes, sans grande originalité. La multiplication des univers et des va-et-vient temporels rend par la même occasion les chronologies complexes à suivre, et propices aux anachronismes. La franchise se retrouve donc réduite au rang de selon Animeland. Helen McCarthy résume avec pessimisme ce sentiment : .Yoshiyuki Tomino lui-même confie d'ailleurs lors d'une interview qu'il a plus ou moins été contraint par le studio à produire des suites de sa série :
Dans un autre registre, l'influence de la franchise sur le jeune public a parfois été abordée sous l'angle plus surprenant de la secte Aum. Les idées de ce groupuscule radical, essentiellement basées sur la théorie du complot, ont souvent été comparées aux thèmes véhiculés par les séries d'animation sombres comme Gundam. Tomino ne nie pas que la mise en scène d'éléments illustrant les doctrines de la secte dans ses premières œuvres a pu influencer négativement des adolescents pour qui les limites entre réalité et monde virtuel sont moins tangibles qu'autrefois.
Importance dans la culture populaire
Une icône populaire au Japon
Véritable pierre angulaire du genre mecha, Gundam est une série extrêmement populaire sur l'archipel, et y est par voie de fait très présente dans la vie quotidienne. Au rang des exemples de notoriété figurent par exemple deux séries de timbres éditées au Japon, qui représentent des personnages et des mobile suits de la série. L'uniforme militaire de la Fédération terrienne (première série) a aussi été repris sur une affiche électorale, que la presse a qualifiée d'« affiche Amuro » (du nom du personnage Amuro Ray) ; suivant la même idée, l'État a réalisé une affiche pour les pompiers mettant en scène un Gundam. Quant à l'armée, elle se sert du terme Gundam comme nom de code pour désigner l'équipement avancé du soldat.
Les campagnes d'habillages publicitaires (concernant par exemple les trains, les avions, etc.) sont trop nombreuses pour être listées de manière exhaustive. Parmi celles-ci, un exemple frappant est la construction d'un Gundam grandeur réelle — soit dix-huit mètres — en plein Shizuoka en 2009, à quelque de Tōkyō, qui devrait drainer en moins d'un an selon les autorités locales.
Dans un contexte plus culturel, une grande partie du musée Bandai à Mibu (auparavant Matsudo) est réservé à Gundam. Le magazine Newtype, extrêmement populaire au Japon, en tire aussi évidemment son nom. Enfin, une exposition artistique consacrée à Gundam a été organisée par la fondation Cartier pour l'art contemporain ; Tatsumi et Bolton y entrevoient une orientation intéressante de l'art moderne dans deux publications intitulées Gundam and the Future of Japanoid Art (lit. « Gundam et le futur de l'art Japanoid »).
On retrouve aussi des références et clins d'œil dans un grand nombre de séries d'animation, allant de School Rumble à Great Teacher Onizuka en passant par Otaku no Video, Suzumiya Haruhi ou Nogizaka Haruka no himitsu.
Au pays des nouvelles technologies et des robots qu'est notoirement le Japon, l'idée de créer de véritables mobile suits y a été sérieusement étudiée. En 2008 notamment, une conférence internationale à Hiroshima (la Gundam Academy) a réuni des spécialistes de divers horizons, le but étant d'étudier la « faisabilité » réelle d'une telle machine. Il s'agit d'ailleurs de la première conférence académique inspirée par une fiction.
Dans le monde
Comparé aux mangas en général, Gundam s'est plutôt mal exporté dans le monde. En France, très peu d'œuvres ont été commercialisées par Beez (filiale française de Bandai) et aucun réel engouement ne s'y est créé. Le pays le plus sensible à la franchise hors Japon sont les États-Unis, où certaines séries comme Gundam Wing ont connu un certain succès lors de leur sortie. Bandai y est aussi mieux positionné sur des marchés comme les jouets et les jeux vidéo. Néanmoins, le concurrent récurrent de la franchise, Macross, s'y est incontestablement mieux implanté via son dérivé Robotech. Le « phénomène Gundam » est donc exclusivement japonais pour l'heure.
Les Gunplas, maquettes issues de la franchise, remportent un franc succès.
Le modèle de Gundam RX-78-2 apparait dans le film Ready Player One lors de la bataille finale.
Listes des œuvres
Séries, films et OVA
Pierres angulaires de la franchise, les séries, films et OAV en sont naturellement les produits principaux ; leur liste exhaustive est donnée ci-dessous. Pour la signification des dates et abréviations de la chronologie interne, se référer à la section « Le système des calendriers » ci-dessus.
SD Gundam
À l'origine, SD Gundam se veut simplement être une parodie de l'univers Gundam pour enfant publiée au format yonkoma. Mais à l'aune de son succès, de nombreuses suites et produits dérivés en sont rapidement tirés, si bien que SD Gundam constitue aujourd'hui une franchise à part, en marge de Gundam mais administrée de la même manière, c'est-à-dire en combinant séries et produits dérivés habituels (jeux vidéo, mangas, maquettes, etc.). Parfois, on note des interactions plus directes, comme la diffusion au cinéma de Gundam F91 qui était précédée d'un court-métrage de SD Gundam.
Nouvelles et mangas
La franchise compte un nombre extrêmement important de romans et de mangas, souvent dérivés des séries animées. Tomino lui-même avait pour habitude de publier sous forme de nouvelles les scénarios de ses séries, avec néanmoins des différences marquées, les récits étant plus adultes et réfléchis ; par exemple, Amuro Ray et Sayla Mass ont des relations sexuelles dans le roman Mobile Suit Gundam, alors qu'ils ne sont même pas explicitement amants dans la série. La question existentielle soulevée par le phénomène des newtype y est aussi plus développée.
Les critiques entourant ces productions sont très inégales, tout comme leur succès d'ailleurs ; même en France, Animeland les juge d'un côté sévèrement en raison de la pauvreté de l'écriture et des dessins, tandis que le manga Gundam : The Origin y est plébiscité de l'autre comme étant un . Il semble par conséquent qu'il faille résolument différencier les simples adaptations — qui peuvent être perçues comme des produits dérivés d'un intérêt encyclopédique peu marqué — des réelles histoires originales et parallèles pour couvrir l'ensemble de ces productions de manière pertinente.
Parmi les magazines de prépublications phares de la franchise, on trouve Gundam Ace, Comic BonBon et Newtype.
Jeux vidéo
C'est d'abord sur les bornes d'arcade que l'on trouve les premiers jeux vidéo Gundam, et ce jusqu'en 1993 avec la production sur Super Nintendo de Kidō Senshi Z Gundam: Hot Scramble. Il est parfois difficile de fixer une limite très claire à ces produits, étant donné que certains comme Dynasty Warriors: Gundam mélangent les robots et les personnages de plusieurs séries différentes. Le real robot se retrouve par la suite dans un grand nombre de jeux vidéo, parfois extrêmement populaires sur l'Archipel, comme Armored Core, Super Robot Wars, Zone of the Enders, Another Century's Episode ou encore Metal Gear.
Communément, les jeux naissent de la collaboration ponctuelle entre Sunrise et un studio de développement chargé de l'aspect plus technique (modélisation 2D et 3D en premier lieu), pour une durée de production d'un à deux ans en moyenne.
Cinéma
Gundam a été porté une seule fois au cinéma en prise de vue réelle, via le long métrage américain intitulé G-Saviour. Réalisé en 2000 pour les vingt ans de la franchise, il se déroule dans l'Universal Century, mais sans rapport avec les séries.
Récemment en 2018, une courte scène du film Ready Player One, du réalisateur Steven Spielberg, présente une bataille entre un Gundam (le RX-78) et MechaGodzilla. Ayant remporté un item au début du film, un personnage secondaire, Daito, devient capable de se transformer en Gundam pendant 30 secondes.
Le 12 avril 2021, Netflix annonce que le réalisateur Jordan Vogt-Roberts dirigera et produira une adaptation de Gundam pour la plateforme de streaming, avec les studios Legendary Pictures et Sunrise.
Annexes
Notes
Sources et références
Articles
(mémoire de master Aesthetics and Visual Arts)
Bibliographie
,
Articles connexes
Mecha
Science-fiction
Histoire des anime
Robot et robot militaire
Mécatronique
Colonisation de l'espace
Liens externes
Site officiel local et site officiel international
Site officiel nord-américain
Site officiel français
Site officiel asiatique
Encyclopédie amateur Gundam France | {
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<!DOCTYPE HTML>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta charset="utf-8" />
<title>JSON-RPC Demo for JQuery Terminal Emulator</title>
<meta name="author" content="Jakub Jankiewicz - jcubic@onet.pl"/>
<meta name="Description" content="Demonstration for JQuery Terminal Emulator using call automaticly JSON-RPC service (in php) with authentication."/>
<script src="../js/jquery-1.7.1.min.js"></script>
<script src="../js/jquery.mousewheel-min.js"></script>
<script src="../js/jquery.terminal-min.js"></script>
<link href="../css/jquery.terminal.css" rel="stylesheet"/>
<script>
jQuery(document).ready(function($) {
$('body').terminal("json-rpc-service-demo.php", {
login: true,
greetings: "You are authenticated",
onBlur: function() {
// the height of the body is only 2 lines initialy
return false;
}
});
});
</script>
</head>
<body>
</body>
| {
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var fs = require('fs');
var YUI = require("yui3").YUI;
YUI({
filter: 'debug',
debug: true
}).use('parallel', function(Y) {
Y.log('Reading this directory and reading the contents of each file..');
var stack = new Y.Parallel();
fs.readdir(__dirname, stack.add(function(err, files) {
files.forEach(function(f) {
fs.readFile(__dirname + f, stack.add(function(err, data) {
//Do something here..
}));
});
}));
stack.done(function() {
Y.log('All callbacks have fired..');
});
});
| {
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Q: C# DataGridview форматирует все строки вместо нужных после загрузки данных из datable Всем привет datagridview форматирует все строки вместо тех что указаны в условии. У меня есть бд DataTabe из неё загружаю данные dataGridView1.DataSource = dataTable; а заполняю datable так dataTable.Rows.Add("Здесь какие данные") при запуске в load формы инициализирую столбцы
dataTable1.Columns.Add("1");
dataTable1.Columns.Add("2");
dataTable1.Columns.Add("3");
dataTable1.Columns.Add("4");
dataTable1.Columns.Add("5");
dataTable1.Columns.Add("6");
dataTable1.Columns.Add("7");
dataTable1.Columns.Add("8");
dataTable1.Columns.Add("9");
dataTable1.Columns.Add("10");
dataTable2 = dataTable1.Clone();
dataGridView1.Columns["Column1"].DataPropertyName = "1";
dataGridView1.Columns["Column2"].DataPropertyName = "2";
dataGridView1.Columns["Column3"].DataPropertyName = "3";
dataGridView1.Columns["Column4"].DataPropertyName = "4";
dataGridView1.Columns["Column5"].DataPropertyName = "5";
dataGridView1.Columns["Column6"].DataPropertyName = "6";
dataGridView1.Columns["Column7"].DataPropertyName = "7";
dataGridView1.Columns["Column8"].DataPropertyName = "8";
dataGridView1.Columns["Column9"].DataPropertyName = "9";
dataGridView1.Columns["Column10"].DataPropertyName = "10";
В событии CellFormatung
private void dataGridView1_CellFormatting(object sender, DataGridViewCellFormattingEventArgs e)
{
DataGridViewRow row = this.dataGridView1.Rows[e.RowIndex];
if (e.Value.GetType() != typeof(System.DBNull))
{
if (Convert.ToString(e.Value) == "1")
{
for (int i = 0; i < dataGridView1.ColumnCount; i++)
{
//dataGridView1[i, e.RowIndex].Style.BackColor = Color.FromArgb(69, 84, 78);
//dataGridView1.Rows[e.RowIndex].DefaultCellStyle.BackColor = Color.FromArgb(69, 84, 78);
row.DefaultCellStyle.BackColor = Color.FromArgb(69, 84, 78);
}
}
}
При форматирование у меня весь datagridview форматируется
а должны форматироваться только те строки где ячейка равна 1, после того как добавил datable такое началось. До того как не использовал бд, форматировалось всё хорошо
И ещё не могу теперь взять индекс выделенной строки в datagridview
string Name = dataGridView1[1, dataGridView1.CurrentRow.Index].Value.ToString();
Вот такие проблемки начались когда начал загружать данные из datatable.
Эту бд привязывать как нужно или почему код перестал работать?
A: private void dataGridView1_RowPrePaint(object sender, DataGridViewRowPrePaintEventArgs e)
{
if (dataGridView1.Rows[e.RowIndex].Cells[1].Value.ToString() == "1")
{
this.dataGridView1.Rows[e.RowIndex].DefaultCellStyle.BackColor = Color.FromArgb(69, 84, 78);
}
}
Событие RowPrePaint при отрисовке строк помогло, теперь всё работает корректно
| {
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Q: Error: package or namespace load failed for 'tabulizer' I use this code to convert a web pdf to a csv file that worked perfectly so far:
library(tabulizer)
#Read
lst <- extract_tables(file = 'https://www.stoxx.com/document/Reports/SelectionList/2020/November/sl_sxebmp_202011.pdf')
#Format
#Split elements as first element has variable names
d1 <- lst[[1]]
lst2 <- lst[2:length(lst)]
#Process
#Format first element
d1 <- as.data.frame(d1,stringsAsFactors = F)
names(d1) <- d1[1,]
d1 <- d1[2:dim(d1)[1],]
#Format list
lst2 <- lapply(lst2,function(x) {x <- as.data.frame(x,stringsAsFactors=F)})
#Bind all element in lst2
d2 <- do.call(rbind,lst2)
#Assign same names
names(d2) <- names(d1)
#Bind all
d3 <- rbind(d1,d2)
write.csv(d3, file = "C:/Users/m3254/OneDrive/Bolsa/Stoxx/STOXX_All_Europe_800_202011.csv")
I got these error messages today:
> library(tabulizer)
Error: package or namespace load failed for 'tabulizer':
.onLoad failed in loadNamespace() for 'tabulizerjars', details:
call: NULL
error: .onLoad failed in loadNamespace() for 'rJava', details:
call: fun(libname, pkgname)
error: JAVA_HOME cannot be determined from the Registry
> #Read
> lst <- extract_tables(file = 'https://www.stoxx.com/document/Reports/SelectionList/2020/November/sl_sxebmp_202011.pdf')
Error in extract_tables(file = "https://www.stoxx.com/document/Reports/SelectionList/2020/November/sl_sxebmp_202011.pdf") :
no se pudo encontrar la función "extract_tables"
Could somebody help me about that?
| {
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Lindenbergia este un gen de plante din familia Scrophulariaceae.
Specii
Cuprinde circa 15 specii.
Note
Scrophulariaceae | {
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{"url":"https:\/\/softwarerecs.stackexchange.com\/questions\/30578\/library-to-solve-a-large-sparse-linear-equation-system-ax-b-almost-banded-mat","text":"# Library to Solve a large sparse linear equation system $Ax=b$ (almost banded matrix)\n\nI'm looking for a tool or library implementing a fast algorithm in C or JAVA for solving the equation $Ax=b$, where $A$ is a $N*N$ sparse matrix with $5$ non-zero diagonals $(-N,-1,0,1,N)$.\n\nmy problem is that $N$ is really big ($N$ can get up to\u00a0$1-5e7$).\n\nI now solve it in matlab but it is really slow so I'm looking for another methods in other languages to do it faster.\n\nupdate:\n\nSorry for the lack of information, I'll update my question and try to clarify my problem.\n\nI'm solving numerically the 2D laplace equation on a rectangular domain (the difficulty may arise from the rectangle dimensions - 1 mm*100 nm) with a mixed boundary conditions.\n\nneumann boundary at left and down sides, dirichlet boundary at the upper side, and at the right side the derivative equal to some function.\n\nby using the finite difference method I get the matrix A with 5 diagonals (each point is coupled with its 4 neighbors and itself).\n\nI tried all the built-in functions in matlab for solving linear equations including \"bicgstab\" with no success (the solution explode).\n\nthe backslash operator with a matrix of N*N (where N=5e7) takes about 13 minutes give or take.\n\nhere is an example of the matrix where N=36.\n\n## migrated from math.stackexchange.comMar 16 '16 at 11:02\n\nThis question came from our site for people studying math at any level and professionals in related fields.\n\n\u2022 How are you solving it in Matlab? How long does it take in Matlab? How many gigabytes of memory does $A$ take up? \u2013\u00a0littleO Mar 16 '16 at 8:04\n\u2022 Have a look at hindawi.com\/journals\/mpe\/2015\/232456 It could be of interest. arxiv.org\/pdf\/1409.4802.pdf gives details about performance. \u2013\u00a0Claude Leibovici Mar 16 '16 at 8:06\n\u2022 In Matlab, I created a sparse matrix $A$ with $5 \\times 10^7$ rows, $5 \\times 10^7$ columns, and five nonzero diagonals, and I solved $Ax = b$ using the backslash operator in 20 seconds. Is that similar to what you're observing? \u2013\u00a0littleO Mar 16 '16 at 8:21\n\u2022 Depends how sparse it is. If the bandwidth is $O(\\sqrt{N})$ then it would be tough indeed. \u2013\u00a0Svetoslav Mar 16 '16 at 8:52\n\u2022 Hi dor, and welcome on SR! Could you please edit your question and include some details on license\/cost requirements (e.g. must it be available for free, must the license allow for commercial use, etc.)? The better you describe your requirements, the closer answers can match. For a guideline, be warmly welcomed to check with What is required for a question to contain \"enough information\"? Good luck, and fingers crossed! \u2013\u00a0Izzy Mar 16 '16 at 11:07\n\nThe notation is not clear to me, but assuming that the diagonal is zero, the first superdiagonal consists of copies of 1, the second superdiagonal consist of copies of N and that matrix is anti-symmetric, then the matrix A is singular for odd N.\n\nIf my original interpretation of the notation is correct, then the matrix B is also singular for odd N.\n\nOn the positive side, this is one of the nicest test matrices I have played with in a while.\n\nA=@(N)toeplitz([0 1 N zeros(1,N-3)],[0 -1 -N zeros(1,N-3)]);\n\nB=@(N)toeplitz([0 1 zeros(1,N-3) N],[0 -1 zeros(1,N-3) -N]);\n\nIn particular, the reduced row echelon form of B is most entertaining.\n\n\u2022 And what exactly is the library you recommend? \u2013\u00a0Thomas Weller Mar 17 '16 at 17:15\n\u2022 @ThomasWeller: There is no recommendation to make. The matrices are singular for odd N. The OP wanted software that could handle any N. That software does not exist. What can be salvaged is a surprisingly nice class of test matrices A=A(N) for which A(2k) has a slowly growing condition number, while A(2k+1) is singular. \u2013\u00a0Carl Christian Mar 17 '16 at 20:14\n\u2022 I confess I have no clue what OP is talking about. Neither do I have a clue what you're talking about. This site is about software recommendations. If there's no software to recommend, because e.g. a mathematical answer is always 42, then I would say the question is not on-topic and should be closed because it does not show research effort. \u2013\u00a0Thomas Weller Mar 17 '16 at 20:24","date":"2019-10-22 22:02:46","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\": 0.5834619998931885, \"perplexity\": 742.6441319727259}, \"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-2019-43\/segments\/1570987824701.89\/warc\/CC-MAIN-20191022205851-20191022233351-00540.warc.gz\"}"} | null | null |
LEICESTER owner Vichai Srivaddhanaprabha died after his helicopter crashed outside of the King Power Stadium, the club have announced.
Srivaddhanaprabha was picked up from the pitch at around 8.30pm on Saturday evening following Leicester's 1-1 draw with West Ham.
His helicopter spiralled out of control shortly after and crashed into the car park outside of the ground before bursting in to flames.
And Leicester have released a statement confirming he died along with four more people.
The club did not confirm the names of the other passengers but Leicestershire Police have revealed they were Srivaddhanaprabha's staff members Nursara Suknamai and Kaveporn Punpare, pilot Eric Swaffer and passenger Izabela Roza Lechowicz.
Leicester's statement read: "It is with the deepest regret and a collective broken heart that we confirm our Chairman, Vichai Srivaddhanaprabha, was among those to have tragically lost their lives on Saturday evening when a helicopter carrying him and four other people crashed outside King Power Stadium.
"None of the five people on-board survived.
"A man of kindness, of generosity and a man whose life was defined by the love he devoted to his family and those he so successfully led.
"Leicester City was a family under his leadership.
"It is as a family that we will grieve his passing and maintain the pursuit of a vision for the Club that is now his legacy.
Srivaddhanaprabha took over the club in 2010 and helped guide them to promotion to the Premier League in 2014.
After avoiding relegation in their first season back in the top flight in 2014-15, they shocked the world by lifting the Premier League crown against the odds in the next.
In 2016-17, they embarked on an historic first-ever Champions League campaign, where the Foxes punched above their weight once again as they reached the quarter-final of Europe's top competition.
They have since gone on too become an established top-flight club.
And tributes have poured in from all around the football world in recognition of the work he had done at Leicester.
Foxes striker Jamie Vardy, who was top scorer in their Premier League title-winning campaign, posted a touching tribute on his Instagram account alongside a picture of himself with Srivaddhanaprabha.
The distraught star said: "Struggling to find the right words....but to me you are legend, an incredible man who had the biggest heart, the soul of Leicester City Football Club.
Left-Back Ben Chilwell has come through the youth ranks during Srivaddhanaprabha's tenure and is now a key part of the first team.
And he said: "I can't believe it, I am heartbroken to hear that no one survived the crash yesterday.
"Vichah was one of the best people you could wish to meet, making you happy made him happy, he was away smiling and laughing.
"What he did not just this football club but for Leicester as a city is incredible.
James Maddison was signed in the summer by Srivaddhanaprabha. | {
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\subsection{\label{sec:supplement}Supplemental Material}
\begin{figure*}
\includegraphics[width=\textwidth]{posterior6.pdf}
\caption{\label{fig:posterior}The convergence of the posterior distribution (marginalized 1D and 2D distributions) with respect to the construction of the flux power spectrum emulator. Each set of colored contours shows the estimate of the posterior at different stages of building the emulator. The green contours are our final estimate of the posterior (with an emulator with 89 training simulations in total); there is no statistically significant change in the posterior in the final stages of building the emulator (from after thirty optimization simulations are added). The darker and lighter shaded areas respectively indicate the 68\% and 95\% credible regions. In each projection, crosses indicate the projected positions of emulator training simulations (expect for \(\tau_0 (z = 4.6)\) projections which are densely sampled by simulation post-processing). The crosses are colored according to the stage of the emulator by which the training simulations are added. For the dark matter parameters \([\mathrm{log}(m [\mathrm{eV}]), \mathrm{log}(\sigma [\mathrm{cm}^2])]\), the initial training simulations fully span the \([\alpha, \beta, \gamma]\) sub-volume and do not project onto those axes; however, the initial simulations contribute to the final emulator as we always emulate in \([\alpha, \beta, \gamma]\). We show, for clarity, the IGM parameters only at our central redshift bin \(z = 4.6\); there is similar convergence at the other redshifts we consider.}
\end{figure*}
\begin{figure}
\includegraphics[width=\columnwidth]{convergence3.pdf}
\caption{\label{fig:convergence}The convergence of the posterior distribution (\textit{from top to bottom}, the 1D marginalized posterior means, \(1 \sigma\) and \(2 \sigma\) constraints) with respect to the construction of the flux power spectrum emulator. Each colored line shows the number of sigma shift (defined by the marginalized posteriors at a given optimization epoch) in the summary statistics from one iteration of the emulator from the previous. There is no statistically significant change in the posterior summaries in the final stages of building the emulator. The black dashed lines indicate shifts of \(0.2 \sigma\).}
\end{figure}
Figures \ref{fig:posterior} and \ref{fig:convergence} demonstrate the convergence of our bounds with respect to the construction of the flux power spectrum emulator by active learning. In both marginalized 1D and 2D posterior distributions (Fig.~\ref{fig:posterior}) and summary statistics of the posterior (Fig.~\ref{fig:convergence}), we see that the addition of further training simulations does not change the constraints. We also see convergence in the active learning as the exploration term of the acquisition function we use to select optimization simulations\footnote{For the selection of active learning simulations, we maximize an acquisition function which is a weighted sum of an exploration term \(\vec{\Sigma}_\mathrm{emu}^\mathrm{T} (\vec{\theta}) \Sigma_\mathrm{data}^{-1} \vec{\Sigma}_\mathrm{emu} (\vec{\theta})\) and an exploitation term \(\mathcal{P}(\vec{\theta}|\vec{d})\), where \(\vec{\Sigma}_\mathrm{emu}\) is the emulator error, \(\Sigma_\mathrm{data}\) is the data covariance and \(\mathcal{P}(\vec{\theta}|\vec{d})\) is the natural logarithm of the posterior probability given data \(\vec{d}\) \citep{2019JCAP...02..031R}. The exploration term tends to add simulations where the emulator model is least constrained, while the exploitation term tends to add simulations at the peak of the posterior.} tends towards zero. This indicates that the acquisition of training simulations is dominated by exploitation, \mbox{i.\,e.,}\xspace we tend to add further simulations only at the peak of the posterior and so the true posterior peak has been found \citep[see][]{2019JCAP...02..031R}. Since we anticipate no constraint on the dark matter mass \(m\) parameter, we restrict the addition of active learning simulations to a range of fixed values (as seen in Fig.~\ref{fig:posterior}) in order to guarantee that we span fully this axis. Our final results (the green contours in Fig.~\ref{fig:posterior}) use a flux power spectrum emulator with 89 training simulations in total: 50 from the initial set presented in Ref.~\cite{2020RogersPRD} and 39 optimization simulations added by active learning \citep{2019JCAP...02..031R}.
We compare our results to a previous bound on the mass of ultralight axion dark matter that we set \citep{2020RogersPRL} by comparing the linear matter power spectrum transfer function \(T(k)\) at the respective 95\% credible limits from the two analyses. These coincide at a wavenumber where the power spectrum in both models is suppressed by 25\% relative to the cold dark matter case. This indicates that the equivalent length-scale \(\lambda_{0.75}\) is, to first order, the scale driving our bounds both on the dark matter -- proton interaction and ultralight axion dark matter (see also Fig.~\ref{fig:scale}). This is consistent with previous results using both Lyman-alpha forest \citep{2017PhRvL.119c1302I} and Milky Way satellites \citep{2021PhRvL.126i1101N} data. However, in general, the exact scale driving dark matter limits will depend on the dataset and model under consideration. Therefore, approximate bounds derived using equivalent scales (\mbox{e.\,g.,}\xspace half-mode scale) to translate between different dark matter models are not as accurate as the forward modeling approach we use here. The IGM and cosmological model over which we marginalize is statistically consistent in our light dark matter and axion bounds. In Fig.~\ref{fig:posterior}, similar to the axion case and previous high-redshift (\(z \sim 5\)) Lyman-alpha forest analyses \citep[\mbox{e.\,g.,}\xspace][]{2017PhRvL.119c1302I}, we find no significant degeneracy between the dark matter and other parameters. As in our axion analysis, in order to map to the dark matter emulator we present in Ref.~\cite{2020RogersPRD}, we model the light dark matter transfer function using a parametric model fit to calculations from a modified Boltzmann code \citep{2014PhRvD..89b3519D}: \(T(k) \equiv \left[P_\mathrm{pDM}(k)/P_\mathrm{CDM}(k)\right]^\frac{1}{2} = [1 + (\alpha (m, \sigma) k)^{\beta (m)}]^{\gamma}\). Here, \(\log(\alpha [h^{-1}\,\mathrm{Mpc}]) = -7.5 \times 10^{-3} \mathcal{M}^3 - 2.3 \times 10^{-3} \mathcal{M}^2 + 0.013 \mathcal{M} - 0.018 \mathcal{S}^3 - 0.90 \mathcal{S}^2 - 4.2 \mathcal{S} - 24.1\); \(\beta = -2.3 \times 10^{-4} \mathcal{M}^2 - 0.082 \mathcal{M} + 2.4\); and \(\gamma = -4.46\), where \(\mathcal{M} = \log(m [\mathrm{eV}])\) and \(\mathcal{S} = \log(\sigma [\mathrm{cm}^2])\).
\begin{figure}
\includegraphics[width=\columnwidth]{validation5.pdf}
\caption{\label{fig:validation}Leave-one-out cross-validation of the flux power spectrum emulator. Each violin plot shows the distribution of the ratio of empirical (emulator mean - truth) to predicted (\(\Sigma\)) emulator error for the leave-one-out cross-validation simulations. \textit{From left to right}, the cross-validation in different wavenumber \(k\) bins and \textit{from top to bottom}, for different redshifts \(z\). The left sides of the violins consider only the initial training simulations, while the right sides consider all the simulations.}
\end{figure}
Figure \ref{fig:validation} shows our leave-one-out cross-validation test for the flux power spectrum emulator. This leaves out in turn the training samples for each of the 89 simulations in our training set. We find that the distribution of the ratio of empirical error (difference between true flux power spectra and emulator prediction) to modeled error (as predicted by the emulator) is close to a unit Gaussian. This indicates a good fit for the emulator model. The deviation from a unit Gaussian is strongest in the lowest redshift bin, with the smallest wavenumber bin slightly over-fit (the predicted error overestimating the empirical error) and the largest wavenumber bin slightly under-fit (the predicted error underestimating the empirical error). We show the cross-validation test for the full training set, as well as the initial set of simulations only, in order to highlight that even the initial base emulator is well fit.
We note that the emulator fit (with the initial and final training sets) is improved with respect to the version used in our axion analysis \citep{2020RogersPRD}. This arises from some modifications made to the emulator model. We use a more complex and flexible Gaussian process kernel to model the covariance between training points \(K(\vec{\theta}, \vec{\theta'})\) \citep{rasmussen2003gaussian}, which is better suited to the multi-dimensional parameter space we consider. This kernel is the product of a rational quadratic kernel \(\sigma_\mathrm{RQ}^2 \left(1 + \sum_i \frac{(\theta_i - \theta'_i)^2}{2 l_i^2}\right)^{-a}\) and a linear kernel \(\sum_i \sigma_{\mathrm{linear},i}^2 \theta_i \theta'_i\), then added to a constant noise kernel \(\sigma_\mathrm{noise}^2\). Here, \(i\) indexes the physical parameters at each redshift bin (since we emulate the three redshift bins independently) and the kernel hyperparameters \([\sigma_\mathrm{RQ}, \sigma_{\mathrm{linear},i}, \sigma_\mathrm{noise}, a, l_i]\) are optimized by maximizing the marginal likelihood of the training data. The rational quadratic kernel allows for a spectrum of length-scales in the modeled covariance. For this more complex kernel, we use a different hyperparameter optimization method that runs a truncated Newton algorithm 35 times with different initial conditions. This explores more thoroughly the highly non-convex hyperparameter likelihood surface. We anticipate that these emulator model improvements will assist in future uses of our dark matter emulator to test other dark matter models.
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{"url":"https:\/\/blog.jverkamp.com\/2013\/12\/21\/rock-paper-scissors\/","text":"# Rock-paper-scissors\n\nQuick and to the point: let\u2019s write a program to play rock-paper-scissors12.\n\n**\n\nHow do we do it? Well, first we need to decide on a scheme for user input. Since Racket is pretty much awesome and read will deal rather nicely with symbolic input, let\u2019s go ahead and use rock for rock, paper for paper, etc3. Then we can impose an ordering on the three possible values:\n\n; Ordering function for rock\/paper\/scissors\n(define (rps>? p1 p2)\n(or (and (eq? p1 'rock) (eq? p2 'scissors))\n(and (eq? p1 'scissors) (eq? p2 'paper))\n(and (eq? p1 'paper) (eq? p2 'rock))))\n\nNow we want a REPL\u2013a read, eval, print loop. Basically, we want to read in input from the user, evaluate it as either a play or a special quit command, print out the results, and then loop back (unless we\u2019re told to quit.) Sounds straight forward enough:\n\n; Play a game of rock\/paper\/scissors against a given opponent\n(define (play-rps brain)\n(printf \"Enter rock, paper, or scissors (quit to exit).\\n\")\n\n; Read player input, evaulate it, print response, loop (unless quit)\n(let repl ([wins 0] [rounds 0])\n(printf \"> \")\n(case player\n; Playing a round, run the computer brain\n[(rock paper scissors)\n(define computer (brain))\n(printf \" computer chooses ~a\" computer)\n(cond\n; Player beats computer\n[(rps>? player computer)\n(printf \", you win!\\n\")\n(brain 'lose)\n(repl (+ wins 1) (+ rounds 1))]\n; Computer beats player\n[(rps>? computer player)\n(printf \", computer wins :(\\n\")\n(brain 'win)\n(repl wins (+ rounds 1))]\n; Player and computer tie\n[else\n(printf \", it's a tie\\n\")\n(brain 'tie)\n(repl (+ wins 1\/2) (+ rounds 1))])]\n; Done player, print stats and exit\n[(quit)\n(printf \"You won ~a%. Good job.\\n\" (round (* 100 (\/ wins rounds))))]\n; Who knows. Maybe if we repeat ourselves it will be helpful\n[else\n(printf \"Unknown input.\\nEnter rock, paper, or scissors (quit to exit).\\n\")\n(repl wins rounds)])))\n\nOne particular oddity that might stand out in this code is the usage of the brain function which is passed in as our opponent. There are two different ways that it could be called. Either it\u2019s called with no arguments in order to chose a next play or it\u2019s given a single argument (either win, lose, or tie) to potentially update the brain\u2019s internal state. That\u2019s really all you need to do some really interesting things as we get to later.\n\nTo start with though, let\u2019s make a really simple, completely random brain:\n\n(define (random-symbol)\n(list-ref '(rock paper scissors) (random 3)))\n\n; Just choose at random\n(define random-brain\n(case-lambda\n[()\n(random-symbol)]\n[(result)\n(void)]))\n\nHere, we\u2019ll use case-lambda to control which way we\u2019re calling the function and a helper function to choose a random symbol (we\u2019ll need that again later). In this case, the update functionality never actually does anything. Let\u2019s see it in practice:\n\n> (play-rps random-brain)\nEnter rock, paper, or scissors (quit to exit).\n> rock\ncomputer chooses paper, computer wins :(\n> rock\ncomputer chooses rock, it's a tie\n> paper\ncomputer chooses scissors, computer wins :(\n> scissors\ncomputer chooses rock, computer wins :(\n> rock\ncomputer chooses paper, computer wins :(\n> rock\ncomputer chooses paper, computer wins :(\n> quit\nYou won 8%. Good job.\n\nSarcastic, isn\u2019t it? Anyways, let\u2019s try to right a few more brains. For example, what if we make a really stubborn brain that always chooses the same symbol, no matter what:\n\n; Always choose the same thing\n(define (make-stubborn-brain favorite)\n(case-lambda\n[()\nfavorite]\n[(result)\n(void)]))\n\nHere we\u2019re using a higher order function. If we wanted to play with a stubborn brain, we\u2019d do it something like this:\n\n> (play-rps (make-stubborn-brain 'rock))\n\nOr perhaps one that tends to play in streaks and only rarely (and randomly) changes what they\u2019re going to play:\n\n(define (random-symbol-except not-me)\n(let loop ([maybe-me (random-symbol)])\n(if (eq? maybe-me not-me)\n(loop (random-symbol))\nmaybe-me)))\n\n; Tend to be 'streaky', potentially change reponse a given % of the time\n(define (make-streaky-brain swap-chance)\n(define current-choice (random-symbol))\n(case-lambda\n[()\n(when (< (random) swap-chance)\n(when (currently-chatty)\n(printf \"It's okay, I didn't like ~a anyways...\\n\" current-choice))\n(set! current-choice (random-symbol-except current-choice)))\ncurrent-choice]\n[(result)\n(void)]))\n\nInteresting, you can also make the exact opposite (a brain that always changes) by upping that to 100%:\n\n> (play-rps (make-streaky-brain 1.0))\n\nNow we have a second function that choose a random\u00a0different symbol. Only sometimes do we change the state of the brain. Also mostly because it\u2019s amusing, we can now have chatty brains. To do that though, you\u2019ll have to turn on the currently-chatty parameter:\n\n> (parameterize ([currently-chatty #t])\n(play-rps (make-streaky-brain 0.25)))\nEnter rock, paper, or scissors (quit to exit).\n> rock\ncomputer chooses paper, computer wins :(\n> scissors\ncomputer chooses paper, you win!\n> scissors\nIt's okay, I didn't like paper anyways...\ncomputer chooses scissors, it's a tie\n> quit\nYou won 50%. Good job.\n\nBuilding on that idea, we could actually make use of the feedback and make a scaredy brain. For this one, it will play the same thing over and over until it loses and then switches.\n\n; Choose the same thing until you lose, then switch\n(define scaredy-brain\n(let ([current-choice (random-symbol)])\n(case-lambda\n[()\ncurrent-choice]\n[(result)\n(case result\n[(lose)\n(when (currently-chatty)\n(printf \"Maybe ~a isn't so great after all...\\n\" current-choice)\n(set! current-choice (random-symbol-except current-choice)))])])))\n\nIt does have a pretty big weakness though, can you figure out what it is?\n\nFinally, let\u2019s do something a little more complicated and make a copycat. Basically, whatever you play, it will play next round:\n\n; Copy the last thing the player chose\n(define copycat-brain\n(let ([next-choice (random-symbol)])\n(case-lambda\n[()\nnext-choice]\n[(result)\n(set! next-choice\n(case (list next-choice result)\n[((rock win) (scissors tie) (paper lose)) 'scissors]\n[((rock tie) (scissors lose) (paper win)) 'rock]\n[((rock lose) (scissors win) (paper tie)) 'paper]))])))\n\nThat same technique could easily be used to always choose the symbol that would beat your last play (based on the idea that you\u2019ll be streaky). Why don\u2019t you try it out yourself?\n\nNow we have a bunch of different brains, what if we wanted to play them against each other? Well, you can just write another function, a lot like play-rps above. Only this time, we\u2019ll pass in two brains and a number of rounds to play:\n\n; Play two computers versus each other for n rounds\n(define (play-cpu\/cpu brain1 brain2 rounds)\n(define wins\n(for\/sum ([i (in-range rounds)])\n(define play1 (brain1))\n(define play2 (brain2))\n(cond\n[(rps>? play1 play2)\n(brain1 'win) (brain2 'lose)\n1]\n[(rps>? play2 play1)\n(brain1 'lose) (brain2 'win)\n0]\n[else\n(brain1 'tie) (brain2 'tie)\n1\/2])))\n(printf \"Player 1 won ~a% of ~a rounds.\\n\" (round (* 100 (\/ wins rounds))) rounds)\nwins)\n\nLet\u2019s write up a quick script to try all of the different brains off against each other:\n\nrandom stubborn:rock stubborn:paper streaky:0.1 streaky:1.0 scaredy copycat\nrandom 50% 50% 50% 50% 50% 50% 50%\nstubborn:rock 50% 50% 0% 49% 50% 100% 50%\nstubborn:paper 50% 100% 50% 53% 50% 0% 50%\nstreaky:0.1 50% 51% 48% 50% 50% 49% 50%\nstreaky:1.0 50% 50% 50% 50% 51% 50% 50%\nscaredy 50% 0% 100% 50% 50% 50% 50%\ncopycat 50% 50% 50% 50% 50% 50% 50%\n\nYay for pretty much completely arbitrary comparisons!4\n\nAnd that\u2019s all there is to it. Like always, I\u2019ve got my code up on GitHub: jpverkamp:rps.rkt\n\nEnjoy!\n\n1. Or **roshambo\u00a0for those of you otherwise inclined [return]\n2. Inspired by a post on Programming Praxis [return]\n3. You get the idea [return]\n4. Can you figure out why almost all of them are 50%? [return]","date":"2019-06-25 07:33:51","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 0, \"mathjax_display_tex\": 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\": 0.45776963233947754, \"perplexity\": 11001.983477782027}, \"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-2019-26\/segments\/1560627999814.77\/warc\/CC-MAIN-20190625072148-20190625094148-00130.warc.gz\"}"} | null | null |
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\section{Introduction\label{sec:intro}}
When the anomalous magnetic moment of the muon, \gmtwo, was measured at BNL several years ago\cite{Bennett:2006fi},
it showed a discrepancy with the Standard Model (SM) expectation that has since been widely interpreted as
a hint for new physics not far from the
electroweak symmetry-breaking (EWSB) scale. After taking into account a recent update\cite{Davier:2016iru} of the lowest-order hadronic contributions to the SM calculation, the discrepancy, \deltagmtwomu,
is estimated to be at the level of $\sim3.5\,\sigma$:
$\deltagmtwomu = (27.4 \pm 7.6 ) \times 10^{-10}$.
(A second recent review of the hadronic vacuum polarization
contributions and uncertainties\cite{Jegerlehner:2017lbd} yields an even more convincing $\deltagmtwomu = (31.3 \pm 7.7 ) \times 10^{-10}$.)
While the interest in this anomaly never really went away, it is bound to receive a boost by the start of the new Muon g-2
experiment at Fermilab\cite{Grange:2015fou,Chapelain:2017syu},
which will improve the statistical precision of the measurement by a factor of four or so with respect to BNL.
Additionally, just a few years after the Fermilab experiment, \gmtwo\ will also be measured
at J-PARC\cite{Ishida:2009zz,Mibe:2010zz,Iinuma:2011zz,Saito:2012zz,Otani:2015jra}, which is expected to reach a comparable sensitivity even if the experimental setup is different.
From the theory standpoint, the anomaly can be accommodated in many scenarios beyond the Standard Model (BSM)
(see, e.g.,\cite{Jegerlehner:2009ry} for a comprehensive review). Early on, the impact of new physics 1-loop contributions to \deltagmtwomu\cite{Leveille:1977rc,Moore:1984eg} was investigated predominantly in the framework of supersymmetry\cite{Fayet,Grifols:1982vx,Ellis:1982by,Barbieri:1982aj,Romao:1984pn,
Kosower:1983yw,Yuan:1984ww,Vendramin:1988rd,Moroi:1995yh,Cho:2000sf,Martin:2001st}, but
the consequences of a positive measurement for more generic models were also explored\cite{Czarnecki:2001pv,Lynch:2001zs}.
Recently, among the large number of studies appearing every year on the topic,
Ref.\cite{Freitas:2014pua} and Refs.\cite{Queiroz:2014zfa,Lindner:2016bgg}
have adopted a systematic approach based on simplified models instead of focusing on specific constructions.
Simplified models are characterized by a limited number of free parameters and classified according to
the gauge quantum numbers of the particles introduced and
the Lorentz structure of their interactions, and can be confronted with
a variety of experimental information, like LEP/LHC constraints in\cite{Freitas:2014pua} or flavor observables in\cite{Lindner:2016bgg}.
In this paper, extending the approach of\cite{Freitas:2014pua,Queiroz:2014zfa,Lindner:2016bgg},
we try to answer the following question: in case a positive measurement of \deltagmtwomu\ is obtained with
large significance at Fermilab, what information can we infer on the couplings, masses, and quantum numbers of the
new particles involved in the process,
provided we require that the same physics also yields the
relic density of dark matter in the Universe.
As the nature of dark matter constitutes one of the greatest mysteries in contemporary particle physics,
we think it is enticing to entertain the idea that a positive measurement at Fermilab and J-PARC could open a
window into the nature of the dark sector, possibly in conjunction with other experimental signatures.
In fact, we will show that requiring the same physics to be responsible for the \gmtwo\ anomaly and dark matter
leads to strong bounds on the allowed parameter space and introduces a series of complementary signatures,
in particular at the high-luminosity LHC, in future electroweak precision experiments and, to a lesser extent,
in dark matter direct detection searches.
Obviously, this complementary approach is not original. It is invoked for instance in supersymmetry,
where neutralinos, sleptons, and charginos often provide at the same time a good fit to \deltagmtwomu\ and the correct relic abundance.
It has also been recently adopted for other BSM models\cite{Belanger:2015nma}, and there exists at least one
previous study of possible complementary signatures for \gmtwo\ and dark matter in
simplified models based on a minimal set of assumptions\cite{Agrawal:2014ufa}.
Like Ref.\cite{Agrawal:2014ufa}, we define in this paper a set of minimal extensions of the SM that
provide a viable weakly interactive massive particle (WIMP) dark matter candidate
and have the potential to give a positive signal in the upcoming \gmtwo\ experiments.
Unlike that work, however, we will not employ the effective field theory approach,
nor limit ourselves to SM singlets in the interactions with the muons.
Rather, inspired by Ref.\cite{Freitas:2014pua}, we consider a set of scenarios in which both the dark matter and the
BSM lepton mediator can transform non-trivially under the SU(2) gauge group. We will also
always adopt the relic abundance as an important constraint on the parameter space.
The models we construct are based on the following requirements:
\begin{itemize}
\item The dark matter interacts with the muons through renormalizable couplings
\item Interactions are CP conserving and invariant under the SM gauge group, SU(2)$\times$U(1)
\item Each model satisfies the constraints from perturbativity and unitarity
\item The measurement of the relic abundance is an active constraint on the parameter space.
\end{itemize}
We do not consider in this paper dark matter lighter than the mass of the muon so that, to make it stable,
we introduce an additional discrete symmetry, $\mathbb{Z}_2$, under which the dark matter is odd and the SM is even.
Also note that the dark matter must be \textit{leptophilic} to evade the stringent current bounds from direct detection experiments,
and for this reason we neglect dark-matter interactions with quarks.
The first of the requirements listed above limits the allowed interactions to fermion--(pseudo)scalar--fermion and fermion--(axial)vector--fermion types. As one of the participating fermions is necessarily the muon, the discrete symmetry forces us to additionally introduce
$\mathbb{Z}_2$-odd colorless fermions, which must be \textit{vector-like} (VL) to evade the bounds from electroweak precision observables (EWPOs) and to not introduce gauge anomalies.
Note that all our assumptions are trivially satisfied by Yukawa-type interactions fermion--(pseudo)scalar--fermion,
once the appropriate scalar potential is spelled out. Conversely, interactions involving (axial)vector particles
require additional assumptions, namely the definition of extra dark gauge groups and charges, as well as a careful treatment of lepton-flavor violating processes.
For this reason, in this paper we limit ourselves to discussing fermion--(pseudo)scalar--fermion interactions only.
For the sake of simplicity, and unlike Refs.\cite{Freitas:2014pua,Agrawal:2014ufa}, we also do not require
universal Yukawa interactions of the BSM sector with the SM leptons, which could give extra constraints from LEP measurements. We rather assume that the new scalars and fermions couple exclusively to the SM muons. Lepton-flavor violating processes are obviously absent in such a setup.
This assumption may seem somewhat \textit{ad hoc}, but it allows us to focus on effects arising in the muon sector only, without imposing additional model-dependent symmetries aimed at enforcing Minimal Flavor Violation.
It can also perhaps be seen as realistic in light of the recent flavor anomalies at LHCb\cite{Aaij:2017vbb},
which seem to point to the existence of lepton-flavor non-universality.
The paper is organized as follows. In \refsec{sec:gm2} we briefly review the expressions of the 1-loop new physics contributions
to \gmtwo\ in the case of scalar couplings. In \refsec{sec:models} we introduce the Lagrangians
of our simplified models and describe their couplings to the muons.
In \refsec{sec:constraints} we review the constraints we apply, and in \refsec{sec:results} we present and extensively discuss
the results of our numerical analyses. We finally summarize our findings and conclude in \refsec{sec:summary}.
\section{Muon $\boldsymbol{g-2}$ contributions from scalar interactions\label{sec:gm2}}
\begin{figure}[t]
\centering
\includegraphics[width=0.50\textwidth]{Plots/G2_Fig1.pdf}
\caption{The 1-loop contribution to \deltagmtwomu\ in the presence of a new scalar field $S$ and a new lepton $E$.
A photon line attached to whichever particle is electrically charged is implied.}
\label{fig:g2_gen}
\end{figure}
The generic 1-loop contribution to the muon anomalous magnetic moment involving the $\mathbb{Z}_2$-odd sector
is schematically shown in \reffig{fig:g2_gen},
where at least one of the particles in the loop must be electrically charged,
and there is an implied photon line attached to the charged propagator.
Interaction terms in the Lagrangian of the models we consider are given by
\be\label{scalarint}
\mathcal{L}\supset (g_s\,\bar{\psi}_{E}\psi_{\mu}\phi_S+ig_p\,\bar{\psi}_{E}\gamma^5\psi_{\mu}\phi_S+\textrm{h.c.})
-m_E\,\bar{\psi}_E\psi_E-V(\phi_S),
\ee
in terms of a Yukawa coupling $g_s$ ($g_p$) of the muon to a (pseudo)scalar field $S$ -- whose dynamics is described by an
appropriate scalar potential $V(\phi_S)$ -- and a generic heavy fermion $E$ of mass $m_E$.
The specific value of \gmtwo\ depends on the electric charge and spin quantum numbers of the particles running in the loop.
Considering, for example, a charged fermion and a neutral scalar, one gets
(see, e.g.,\cite{Jegerlehner:2009ry,Lindner:2016bgg} for a review of the calculation)
\begin{multline}
\deltagmtwomu=\frac{m_{\mu}^2}{8 \pi^2 m_S^2}\left[\left(|g_s|^2+|g_p|^2\right)\int_0^1dx\,\frac{x^2(1-x)}{(1-x)(1-\lambda^2 x)+\epsilon^2\lambda^2 x}\right.\\
+\left.\epsilon\left(|g_s|^2-|g_p|^2\right)\int_0^1dx\,\frac{x^2}{(1-x)(1-\lambda^2 x)+\epsilon^2\lambda^2 x}\right],\label{mastergm2}
\end{multline}
in terms of the mass ratios of the new particles to the muon,
$\epsilon=m_E/m_{\mu}$, $\lambda=m_{\mu}/m_S$\,.
Note that the chiral structure of the underlying model plays a crucial role in determining the size of \gmtwo.
If one sets $g_p=0$, the dominant contribution in \refeq{mastergm2} arises from the second term, which is enhanced by a large factor $\epsilon$.
On the other hand, the presence of a non-zero pseudoscalar coupling will reduce the size of this term, and in the case when
$|g_s|=|g_p|$ the only remaining contribution is the one in the first line of \refeq{mastergm2}.
This well-known fact is often used to obtain, by simple inspection of the Lagrangian, back-of-the-envelope estimates
of how well a specific model can perform with respect to \gmtwo.
The prescription is best recast in terms of $c_L$ and $c_R$, the couplings of the new physics to the left- and right-chiral
Weyl components of the muon.
One can explicitly write the scalar and pseudoscalar coupling of \refeq{scalarint} as $g_s=(c_R+c_L)/2$
and $i g_p=(c_R-c_L)/2$, and the integrals can be easily calculated for $\epsilon\lambda$ fixed in the approximation $\lambda\ll 1$.
By defining
$\epsilon^2\lambda^2=m_E^2/m_S^2\equiv r$, one gets
\be
\int_0^1dx\,\frac{x^2(1-x)}{1-x+r x}=\frac{2+3r-6r^2+r^3+6r\ln r}{6\,(r-1)^4}\equiv\mathcal{F}_1(r)
\ee
\be
\int_0^1dx\,\frac{x^2}{1-x+r x}=\frac{3-4r+r^2+2\ln r}{2\,(r-1)^3}\equiv\mathcal{F}_2(r)\,,
\ee
which lead to the well known formula
\be\label{chiralint}
\deltagmtwomu=\frac{1}{16\pi^2}\sum_{S^0,E^{\pm}}
\left[\frac{m_{\mu}^2}{m_S^2}\left(|c_L|^2+|c_R|^2\right)\mathcal{F}_1(r)
+2\,\frac{m_{\mu} m_E}{m_S^2}\,\Re(c_L c_R^{\ast})\,\mathcal{F}_2(r)\right]\,,
\ee
where we have generalized \refeq{mastergm2} to include all possible charged fermion and neutral scalar states coupling to the muon.
Equation~(\ref{chiralint}) expresses the fact that much larger values of \gmtwo\ can be expected if the new physics
cross-couples to \textit{both} chiral states of the muon, providing a chirality-flip term that is enhanced proportionally
to the mass of the new fermions.
Note, incidentally, that if $\Re(c_L c_R^{\ast})$ is positive, \deltagmtwomu\ is positive.
One can follow a similar procedure to derive the \gmtwo\ formula for the case of charged scalars and
neutral fermions in the loop, obtaining
\be\label{chargescal}
\deltagmtwomu=\frac{1}{16\pi^2}\sum_{S^{\pm},E^0}\left[-\frac{m_{\mu}^2}{m_S^2}\left(|c_L|^2+|c_R|^2\right)\mathcal{G}_1(r)
+2\,\frac{m_{\mu} m_E}{m_S^2}\,\Re(c_L c_R^{\ast})\,\mathcal{G}_2(r)\right]\,,
\ee
where
\be
\mathcal{G}_1(r)\equiv\frac{1-6 r+3 r^2+2 r^3-6 r^2\ln r}{6(r-1)^4}
\ee
\be
\mathcal{G}_2(r)\equiv\frac{-1+r^2-2 r\ln r}{(r-1)^3}\,.
\ee
This contribution is negative when either $c_L$ or $c_R$ are equal zero, but can become positive for
$\Re(c_L c_R^{\ast})\neq 0$.
Finally we will also need the contribution to \gmtwo\ from a doubly charged fermion and a charged scalar in the loop.
In this work we will just use the one for the $c_L$ coupling, which reads\cite{Freitas:2014pua}
\be\label{doubl_char}
\deltagmtwomu=\frac{1}{16\pi^2}\sum_{S^{\mp},E^{\pm\pm}}
\left(\frac{m_{\mu}^2}{m_S^2}\,|c_L|^2\,\mathcal{H}_1(r)\right),
\ee
where
$\mathcal{H}_1(r)=2\mathcal{F}_1(r)+\mathcal{G}_1(r)$.
\section{Muophilic portal models\label{sec:models}}
Before we introduce our simplified models for \gmtwo\ and dark matter, we start by defining the notation we adopt throughout the paper.
We indicate the SM Weyl spinor fields with lower-case letters, and the new $\mathbb{Z}_2$-odd fields with capital letters.
The quantum numbers of the leptons and Higgs boson of the SM are
\begin{equation}
l:(\mathbf{1},\mathbf{2},-1/2)\,\,\,\,\,\,\, e_R:(\mathbf{1},\mathbf{1},-1)\,\,\,\,\,\,\, \phi:(\mathbf{1},\mathbf{2},1/2),
\end{equation}
with respect to SU(3)$\times$SU(2)$\times$U(1).
When written explicitly, the lepton doublet reads $l=(\nu_L,e_L)^T$ and the Higgs field is $\phi=[0,(v+h)/\sqrt{2}]^T$ after EWSB.
The Dirac fermion of charge $-1$ is constructed as $\psi_e=(e_L,e_R)^T$, as usual.
For the SM muon Yukawa coupling we use the convention, in Weyl notation,
\be
\mathcal{L}\supset -y_{\mu}\,\phi^{\dag} l\,e_R^{\ast}+\textrm{h.c.}\label{LagrSM}
\ee
As was discussed in \refsec{sec:intro}, we limit ourselves to considering CP conserving, renormalizable Yukawa interactions.
We extend the SM particle content with new heavy scalar fields and VL leptons,
which provide generally safe extensions of the SM because they do not introduce gauge anomalies and they
avoid the stringent bounds on chiral fermions from LEP and SLC precision measurements.
In the context of non-supersymmetric models, VL leptons for the \gmtwo\ anomaly have also been considered
in\cite{Czarnecki:2001pv,Kannike:2011ng,Kanemitsu:2012dc,Dermisek:2013gta,Freitas:2014pua,Belanger:2015nma}.
We will next classify our models according to the transformation properties of the new scalar and fermion fields under the SM gauge group.
\subsection{Models with a real neutral scalar singlet\label{sec:realsca}}
We begin with the simplest case, extending the SM by a singlet real scalar field,
\begin{equation}\label{scalarqn}
s:(\mathbf{1},\mathbf{1},0).
\end{equation}
For simplicity, we assume in this work that any new introduced scalar is \textit{inert},
in the sense that it does not develop a vacuum expectation value (vev).
The most general $\mathbb{Z}_2$-symmetric renormalizable scalar potential that includes
mass terms and quartic interactions for both the Higgs and the BSM scalar, as well as a portal coupling between the two, takes the form
\begin{equation}
\label{scalpot_real}
V=-\mu^2 \phi^{\dag}\phi+\frac{\lambda}{2} (\phi^{\dag}\phi)^2+\frac{\mu_s^2}{2} s^2+\frac{\lambda_s}{2} s^4+\lambda_{12}s^2\phi^{\dag}\phi\,,
\end{equation}
in terms of 5 free parameters: $\mu$ and $\lambda$, the SM mass and quartic coupling,
$\mu_s$, $\lambda_s$, and the portal coupling $\lambda_{12}$.
The tree level mass of the BSM scalar is in this case given by
\begin{equation}
\label{real_mass}
m_s^2=\mu^2_s+\lambda_{12}v^2.
\end{equation}
The parameters of the scalar potential are constrained by theoretical requirements.
In order to guarantee that the electroweak vacuum is a global minimum,
it is required that $\mu_s^2+\lambda_{12}\,v^2>0$. One also needs $\mu_s^2>0$, so that the direction $v=0,v_s\neq 0$ is not a minimum and the scalar $s$ remains inert. The latter also guarantees that the $\mathbb{Z}_2$ symmetry is preserved in the electroweak broken phase. As a result, there is no mixing between the new scalar and the SM Higgs.
Vacuum stability, i.e. requiring that the potential is bounded from below, requires $\lambda>0$, $\lambda_s>0$, and
$\lambda_{12}>-\sqrt{\lambda\lambda_s}$. Moreover, perturbative unitarity bounds give $\lambda<4.2$,
$\lambda_s<4.2$, and $\lambda_{12}<25$\cite{Lewis:2017dme}.
\begin{figure}[t]
\centering
\includegraphics[width=1.0\textwidth]{Plots/G2_Fig2.pdf}
\caption{Starting from the left, the first 3 diagrams show the well-known scalar portal interactions that can potentially lead to the correct
dark matter relic abundance. The last diagram on the right depicts the $t$-channel ``bulk'' mechanism via a new heavy fermion $E$.}
\label{fig:hportal}
\end{figure}
The scalar potential given in \refeq{scalpot_real} features well known dark matter properties
(see\cite{McDonald:1993ex,Bento:2000ah,Burgess:2000yq,Davoudiasl:2004be,Patt:2006fw,Barger:2007im} for early
papers exploring the Higgs portal). The WIMP is here the scalar $s$, which efficiently annihilates in the early Universe
through the interaction vertices depicted in the first three diagrams of \reffig{fig:hportal}.
However, it is also well known that the portal coupling and dark matter mass are subject to strong bounds from direct detection searches,
which, after the most recent bound from XENON-1T\cite{Aprile:2017iyp} are considered,
exclude the mass range $m_{\textrm{DM}}=m_s\approx 10-800\gev$ if one imposes the
relic density constraint. This is precisely the mass range where the new scalar field and VL leptons can positively contribute
to the \gmtwo\ anomaly.
Interestingly, the presence of VL fermions opens up additional mechanisms for dark matter annihilation,
as shown in the last diagram on the right of \reffig{fig:hportal}.
The limits from direct detection searches can be then easily evaded, thanks to the leptophilic nature of the interaction between the
dark matter scalar and the SM. By borrowing a term often used in supersymmetry, we will hence refer to this mechanism as
the \textit{bulk}. (See, e.g, Refs.\cite{Drees:1992am,Baer:1995nc} for a definition of the bulk in supersymmetry,\cite{Bai:2014osa} in the context of simplified models, and\cite{Fukushima:2014yia,Belanger:2015nma} in relation to \gmtwo.)
We will see in what follows that, once the new fermions are introduced in the theory to explain the \gmtwo\ anomaly, the bulk
emerges in the vast majority of cases as the favored mechanism for the dark matter relic density.
However, we leave in our numerical scans the portal parameters of the scalar potential free to float,
as they are allowed by the symmetries and can be constrained to small values case by case by the phenomenology.
Besides, this also allows us to investigate regions of the parameter space characterized by a mixed bulk/portal mechanism for dark matter.
For the nature of the VL fermions, we consider all possibilities allowed by the SM gauge symmetry:\medskip
\textbf{Model 1: Fermion singlets.}
In the first class of models we add a pair of charged lepton SU(2) singlets,
\begin{equation}
E:(\mathbf{1},\mathbf{1},-1),\quad E':(\mathbf{1},\mathbf{1},1),\label{singqn}
\end{equation}
which are odd under $\mathbb{Z}_2$.
We can write new muophilic Weyl terms in the Lagrangian,
\begin{equation}\label{mod1lag}
\mathcal{L}\supset -Y_S\,E\,e_R^{\ast} s -M_E E' E+\textrm{h.c.},
\end{equation}
in terms of a new Yukawa coupling to the second generation, $Y_S$, and a new VL mass, $M_E$.
One can also construct a new Dirac spinor, $\psi_{\widetilde{E}}=(E,E'^{\ast})^T$,
which leads to the Dirac-type interaction
\begin{equation}
\mathcal{L}\supset -Y_S\, \bar{\psi}_{\widetilde{E}}P_R\psi_e\,s +\textrm{h.c.}\,,\label{Dirac1}
\end{equation}
with $P_R=(1+\gamma_5)/2$.
From \refeq{Dirac1} one can immediately read off the scalar and pseudoscalar couplings of \refeq{scalarint}:
$g_s=Y_S/2$ and $i g_p=Y_S/2$.
Alternatively, one can use the chiral formalism defined before \refeq{chiralint} and get
$c_L=0$, $c_R=Y_S$, which can be then plugged in
to calculate \deltagmtwomu.
Since in this scenario the amplitude is not enhanced by a chirality-flip term one expects to fit the \gmtwo\ anomaly
either in the presence of large $Y_S$ values, or with relatively small mass for the new scalar and fermion particles.
We subject Model~1, and all the models we define in the next paragraphs and sections,
to several constraints from different experiments, which we describe in detail in \refsec{sec:constraints}.
This will allow us to systematically discriminate which region of the parameter space is more likely to
give a signature in future \gmtwo\ experiments,
within the individual model themselves and in relation to the others.
The constraints we consider in Model~1 are
\begin{itemize}
\item LHC 13 TeV bounds from searches for leptons and missing $E_T$\cite{ATLAS:2016uwq,CMS:2017fij}
\item LHC 13 TeV mono-jet search bounds\cite{Aaboud:2016tnv}
\item EWPO constraints from the $Z$ lineshape and asymmetry data at LEP
and measurements of the muon lifetime and $W$ mass\cite{Olive:2016xmw}
\item Where applicable (portal couplings), direct detection constraints from LUX\cite{Akerib:2016vxi} and XENON1T\cite{Aprile:2017iyp}.
\end{itemize}
\medskip
\textbf{Model 2: Fermion doublets.}
One can instead add to the Lagrangian a VL pair of SU(2) doublets,
\begin{equation}\label{vl_doublets}
L:(\mathbf{1},\mathbf{2},-1/2),\quad L':(\mathbf{1},\mathbf{\bar{2}},1/2),
\end{equation}
where we explicitly write the doublets as $L=(N_1,E_1)^T$ and $L'=(N_2,E_2)$.
The heavy Dirac lepton of charge $-1$ is given, similarly to Model~1,
by $\psi_E=(E_1,E_2^\ast)^T$, and there is also a heavy Dirac neutrino, whose
mass is at the tree level degenerate with the charged lepton's.
As before we write new muophilic Weyl terms,
\begin{equation}
\mathcal{L}\supset -Y_D\,L'l s-M_L L'L+\textrm{h.c.}
\label{Lagr1}
\end{equation}
or, explicitly,
\begin{equation}
\mathcal{L}\supset -Y_D\,E_2\,e_L\,s - Y_D N_2\,\nu_L\,s +\textrm{h.c.}\,,
\label{Lagr1b}
\end{equation}
which lead to the same type of Dirac interaction with muons as in \refeq{Dirac1}:
\begin{equation}
\mathcal{L}\supset -Y_D\, \bar{\psi}_{E}P_L\psi_e\,s +\textrm{h.c.}\,,
\end{equation}
where $P_L=(1-\gamma_5)/2$.
As before, one can read off $g_s=Y_D/2$, $-ig_{p}=Y_D/2$, or $c_L=Y_D$, $c_R=0$.
The effect on the calculation of \gmtwo\ ends up being the same as in Model~1.
\newpage
\textbf{Model~3. Fermion singlets and fermion doublets.}
The most straightforward way of introducing a chirality-flip term in the \gmtwo\ calculation is letting
the singlet and doublet fermions of Model~1 and Model~2 mix with each other through the SM Higgs vev.
One can thus write down
\begin{equation}
\mathcal{L}\supset -Y_S\,E\,e_R^{\ast} s-Y_D\,L'l s-\widetilde{Y}_1\,\phi^{\dag}L\,E'-\widetilde{Y}_2\,L'\phi\,E-
M_E E'E-M_L L'L+\textrm{h.c.}\,,\label{doubsing}
\end{equation}
where, in agreement with the SM and $\mathbb{Z}_2$ symmetries, we have introduced two additional
Yukawa couplings to the Higgs boson, $\widetilde{Y}_1$ and $\widetilde{Y}_2$\,.
There are now two, charged, heavy Dirac leptons, and their mass matrix
in the basis $\{(E_2,E')\times(E_1,E)^T\}$ is given by
\begin{equation}\label{physmas}
M_C= \left( \begin{array}{cc}
M_{L} & \frac{\widetilde{Y}_2\,v}{\sqrt{2}} \\
\frac{\widetilde{Y}_1\,v}{\sqrt{2}} & M_{E} \\
\end{array} \right),
\end{equation}
and is diagonalized in the usual way by two unitary matrices $U$ and $V$,
with the convention that $\textrm{diag}(m_{E_1^p},m_{E_2^p})=U^{\ast}M_C V^{\dag}$.
For each heavy lepton, $E_{i=1,2}^p$,
the product $c_L^i c_R^{i\,\ast}$ depends on the mixing parameters:
\bea\label{mixing}
c_L^i c_R^{i\,\ast}&=& -Y_D V_{i1}\,Y_S U_{i2}\nonumber\\
&\approx& Y_D Y_S\,\frac{\max(M_L,M_E)\,M_{C\{ij\}}+\min(M_L,M_E)\,M_{C\{ji\}}}{m_{E^p_j}^2-m_{E^p_i}^2}\big|_{j\neq i}\,,
\eea
where the second line of \refeq{mixing} is given in terms of $M_{C\{12\}}=\widetilde{Y}_2v/\sqrt{2}$ and $M_{C\{21\}}=\widetilde{Y}_1v/\sqrt{2}$. Note that $c_L^i c_R^{i\,\ast}$ vanishes when \textit{both}
$\widetilde{Y}_1$ and $\widetilde{Y}_2$ are zero, thus reproducing the limit of Models~1 and 2.
We subject Model~3 to the constraints described above for Model~1. Since the explicit mixing terms of \refeq{doubsing}
break chiral symmetry, we expect the constraints from EWPOs to bite significantly into the parameter space that produces
an enhancement in \deltagmtwomu.
Note also that by introducing an additional source of chiral-symmetry breaking this terms
potentially induce large loop corrections to the muon mass.
However, as was pointed out in, e.g.,\cite{Fukushima:2014yia} for the equivalent supersymmetric case,
these first order corrections do not depend on the cut-off scale and can be simply treated as a mild source of fine tuning, which should
be minimal after the constraints from EWPOs are taken into account.
\subsection{Models with a complex neutral scalar singlet\label{sec:compscal}}
We extend the models of \refsec{sec:realsca} by replacing the real scalar field of \refeq{scalarqn} with a complex scalar.
We define $S=(s+ia)/\sqrt{2}$\,, expressed in terms of 2 real degrees of freedom.
The $\mathbb{Z}_2$ symmetric scalar potential now reads,
\begin{eqnarray}
V&=&-\mu^2 \phi^{\dag}\phi+\lambda/2\; (\phi^{\dag}\phi)^2+\mu_S^2/2\;|S|^2+\lambda_S/2\; |S|^4+ \lambda_{12}|S|^2\phi^{\dag}\phi\nonumber\\
& &+(\mu_S'^2/2\;S^2+\lambda_S'/2\;S^4+\lambda_{12}'S^2\phi^{\dag}\phi+\lambda_{22}'/2\;S^2|S|^2+\textrm{h.c.})\,,
\end{eqnarray}
where we have introduced new portal couplings, $\lam'_{12}$ and $\lam'_{22}$, which again we leave free to float but
will not play an important role in the dark matter discussion.
Tree-level vacuum stability requires in this case $\lambda>0$, $\tilde{\lambda}_s>0$, $\tilde{\lambda}_a>0$, $\lambda_S>-1/6\sqrt{\tilde{\lambda}_a\tilde{\lambda}_s}$, $\lambda_{12}-2\lambda_{12}'>-\sqrt{\lambda\tilde{\lambda}_a}$, and $\lambda_{12}+2\lambda_{12}'>-\sqrt{\lambda\tilde{\lambda}_s}$,
where $\tilde{\lambda}_s=\lambda_S+2\lambda_S'+2\lambda_{22}'$, $\tilde{\lambda}_a=\lambda_S+2\lambda_S'-2\lambda_{22}'$.
The $\mathbb{Z}_2$ symmetry is preserved if $\mu_S^2-2\mu_S'^2>0$ and $\mu_S^2+2\mu_S'^2>0$.
The masses of dark sector scalars are given at the tree level by
\begin{eqnarray}
m_s^2&=&\frac{1}{2}(\mu^2_S+\lambda_{12}v^2+2\mu_S'^2+2\lambda_{12}'v^2)\nonumber\\
m_a^2&=&\frac{1}{2}(\mu^2_S+\lambda_{12}v^2-2\mu_S'^2-2\lambda_{12}'v^2)\,.
\end{eqnarray}
Thus, this scenario is endowed with two possible dark matter candidates, a scalar and a pseudoscalar WIMP
(see, e.g.,\cite{Barger:2008jx,Gonderinger:2012rd} for early studies of the complex scalar/Higgs portal).
By mirroring the models of \refsec{sec:realsca}, we introduce \textbf{Model~1a},
\textbf{Model~2a}, and \textbf{Model~3a}, obtained by performing in the Lagrangians of
Eqs.~(\ref{mod1lag}), (\ref{Lagr1}), and (\ref{doubsing}) the substitutions $s\rightarrow S$ and $s\rightarrow S^{\ast}$.
For example, Model~1a is characterized by the Lagrangian
\begin{equation}
\mathcal{L}\supset -Y_S\,E\,e_R^{\ast} S -Y_{S^{\ast}}\,E\,e_R^{\ast} S^{\ast} -M_E E' E+\textrm{h.c.},
\end{equation}
from which one reads the chiral couplings of the muon to the scalar and pseudoscalar fields:
$c_R^{(s)}=(Y_S+Y_{S^{\ast}})/\sqrt{2}$\,, which can become significant even within the perturbativity bound for the individual Yukawa couplings, and $c_R^{(a)\ast}=i(Y_S-Y_{S^{\ast}})/\sqrt{2}$, which instead, being expressed as a difference, is in general a bit smaller. Besides, $c_L^{(s)}=c_L^{(a)}=0$ like in the model with a real scalar.
Similar arguments apply to the corresponding extensions of Models~2 and 3 of \refsec{sec:realsca}.
In particular, in Model 3a, we mirror the singlet/doublet fermion mixing of Model~3 by adding 2 additional Yukawa couplings,
which have the effect of broadly opening up the parameter space, and making it more difficult to constrain.
We conclude this subsection by pointing out that we do not treat in this work models with charged scalar singlet fields
and neutral fermions only, as in their simplest implementation they provide a negative contribution to \deltagmtwomu, see \refeq{chargescal}.
We shall see in subsequent sections, however, that in the presence of neutral fermion mixing the second term of \refeq{chargescal}
can provide a positive contribution to \gmtwo.
\subsection{Models with a scalar doublet\label{sec:scadoub}}
Finally, we consider models with an inert scalar doublet in place of the inert scalar singlet of
\refsec{sec:realsca} and \refsec{sec:compscal}.
We introduce
\begin{equation}\label{doubqn}
\Phi:(\mathbf{1},\mathbf{2},1/2),
\end{equation}
where $\Phi=(S^+,S^0/\sqrt{2})^T$ in terms of a charged scalar field $S^{\pm}$ and a neutral complex $S^0=s+ia$.
At the tree level the scalar potential reads,
\begin{eqnarray}
V&=&-\mu^2\,\phi^{\dag}\phi+\lambda/2\; (\phi^{\dag}\phi)^2+\mu_{\Phi}^2/2\, \Phi^{\dag}\Phi+\lambda_{\Phi}/2\; ( \Phi^{\dag}\Phi)^2\nonumber\\
& &+\lambda_3\,\Phi^{\dag}\Phi\,\phi^{\dag}\phi+\lambda_4\,(\Phi^{\dag}\phi)(\phi^{\dag}\Phi)+(\lambda_5\,(\Phi^{\dag}\phi)^2+\textrm{h.c.})\,.
\end{eqnarray}
Vacuum stability requires $\lambda>0$, $\lambda_{\Phi}>0$, $\lambda_{3}>-\sqrt{\lambda\lambda_{\Phi}}$, and $\lambda_{3}+\lambda_{4}\pm2\lambda_{5}>-\sqrt{\lambda\lambda_{\Phi}}$, as well as $\mu_{\Phi}^2>0$.
At the tree level the masses of dark sector scalars are given by
\begin{eqnarray}\label{doublet_mass}
m_s^2&=&\frac{1}{2}\mu^2_{\Phi}+\frac{1}{2}v^2(\lambda_3+\lambda_{4}+2\lambda_{5})\nonumber\\
m_a^2&=&\frac{1}{2}\mu^2_{\Phi}+\frac{1}{2}v^2(\lambda_3+\lambda_{4}-2\lambda_{5})\nonumber\\
m_{S^{\pm}}^2&=&\frac{1}{2}(\mu^2_{\Phi}+v^2\lambda_3)\,.
\end{eqnarray}
As a consequence, the dark matter can be either a scalar or pseudoscalar, but additional constraints on the parameter space arise
from the condition that the charged scalar is not the lightest one, and it evades the LEP limit, $m_{S^{\pm}}>100\gev$.
The portal interactions and dark matter of this class of models have been investigated extensively
(early studies include\cite{Barbieri:2006dq,Ma:2006km,Ma:2006fn,LopezHonorez:2006gr,Majumdar:2006nt})
but, once more, in most of the cases described here the relevant mechanism for the relic density will be provided by the bulk.
The fermion fields can in this case be grouped in 4 categories according to their SU(2) representation:
singlet, doublet, triplet, and adjoint triplet. As before, we also consider the possibility of doublet/singlet mixing and doublet/triplet mixing through the Higgs vev.
\medskip
\textbf{Model~4. Fermion singlets.}
In terms of the singlets defined in \refeq{singqn} the Lagrangian reads
\begin{equation}
\mathcal{L}\supset -Y_S\,\Phi^{\dag}l\,E' -M_E E E'+\textrm{h.c.},
\end{equation}
where we have introduced, with some redundancy in the notation, a new Yukawa coupling, $Y_S$, and VL mass, $M_E$.
Writing explicitly the components of the SM doublet, one gets
\be\label{scal_doub_fer_sing}
\mathcal{L}\supset -Y_S\left(\nu_L S^-E'+e_L \frac{S^{0\ast}E'}{\sqrt{2}}\right)+\textrm{h.c.}\,,
\ee
which gives $c_L^{(s)}=Y_S/\sqrt{2}$, $c_L^{(a)}=-iY_S/\sqrt{2}$, and
$c_R^{(s,a)}=0$.
Note that even though the chiral structure of \refeq{scal_doub_fer_sing} resembles the scalar singlet case of Model 1a,
the presence of a non-zero coupling of VL fermions to muon neutrinos will have an important impact on the LHC phenomenology.
\medskip
\textbf{Model~5. Fermion doublets.}
For the VL doublets introduced in \refeq{vl_doublets}, the Lagrangian reads
\begin{equation}\label{doubdoub}
\mathcal{L}\supset -Y_D\,\Phi^{\dag}L e^{\ast}_R -M_L L' L+\textrm{h.c.}\,,
\end{equation}
in terms of a new Yukawa coupling, $Y_D$, and VL mass, $M_L$.
Beside a positive contribution to \gmtwo, similar to \refeq{scal_doub_fer_sing} and \refeq{Lagr1b}, there is
a negative contribution due to the charged scalar field,
\begin{equation}\label{sca_doub_fer_doub}
\mathcal{L}\supset -Y_D \left(N_1 S^- e^{\ast}_R+\frac{E_1 S^{0\ast}}{\sqrt{2}} e^{\ast}_R\right)+\textrm{h.c.}
\end{equation}
This feature suggests that boosting \gmtwo\ to the experimentally measured value may be more challenging in this case, see \refeq{chargescal}.
\medskip
\textbf{Model~6. Fermion singlets and fermion doublets.}
The fermion doublets of Model~5 can mix with the singlets of Model~4 through the Higgs boson vev.
The Lagrangian includes the terms
\be
\mathcal{L}\supset -Y_S\,\Phi^{\dag}\,l\,E'-Y_D\,\Phi^{\dag}L e^{\ast}_R
-\widetilde{Y}_1\,\phi^{\dag}L\,E'-\widetilde{Y}_2\,L'\phi\,E+\textrm{h.c.}\,,
\ee
with two additional Yukawa couplings, in a fashion similar to Model~3 in \refsec{sec:realsca}.
Note, however, that even if the mixing provides a source of chiral symmetry breaking similar to the one giving a boost to
\gmtwo\ in Model~3, we do not expect an enhancement in this model.
The reason is that there are two neutral real scalar fields, $s$ and $a$,
whose couplings to the muon have opposite parity but the same size.
One can read off from Eqs.~(\ref{scal_doub_fer_sing}) and (\ref{sca_doub_fer_doub}) that $c_{L}^{(a)}=-i c_{L}^{(s)}$ and
$c_{R}^{(a)\ast}=-i c_{R}^{(s)\ast}$, so that $\Re(c_{L}^{(a)}c_{R}^{(a)\ast})=-\Re(c_{L}^{(s)}c_{R}^{(s)\ast})$ and
the last term in \refeq{chiralint} is identically zero.
As a consequence, Model~6 does not result much more interesting from a
phenomenological point of view than the individual models comprising it, and we do not consider it further.
\medskip
\textbf{Model~7. Fermion triplets.}
In this case one extends the SM by adding fermion SU(2) triplets with the following quantum numbers,
\begin{equation}
\Psi_T:(\mathbf{1},\mathbf{3},-1)\,,\quad \Psi'_T:(\mathbf{1},\mathbf{\bar{3}},1)\,,
\end{equation}
which can be parameterized in terms of a neutral, charged, and doubly charged component as
\[ \Psi_T'=
\left( {\begin{array}{cc}
\frac{\Psi^+}{\sqrt{2}} & \Psi^{++} \\
\Psi^{0} & -\frac{\Psi^+}{\sqrt{2}}
\end{array} } \right),
\]
and equivalent decomposition applies to $\Psi_T$.
The Lagrangian reads
\begin{equation}
\mathcal{L}\supset -Y_T\,\Phi^{\dag}\,\Psi'_T\,l -M_T\,\textrm{Tr}(\Psi_T'\,\Psi_T) +\textrm{h.c.}\,,
\end{equation}
which is expanded into
\begin{equation}\label{trip}
\mathcal{L}\supset -Y_T\,\left(-\frac{\Psi^+ S^{0\ast}}{2}+\Psi^{++} S^-\right)e_L
-Y_T\left(\frac{\Psi^{0} S^{0\ast}}{\sqrt{2}}+\frac{\Psi^+S^-}{\sqrt{2}}\right)\nu_L+\textrm{h.c.}
\end{equation}
Equation~(\ref{trip}) includes the well-known doubly-charged fermion/charged scalar coupling, which will generate the
large positive contribution to \gmtwo\ given in \refeq{doubl_char}.
Note that in this case too, the quantum numbers allow for doublet/triplet fermion mixing through the Higgs vev.
As in the case just discussed above, however, the couplings of $s$ and $a$ to the muon have opposite parity and equal size, providing, again, an identical cancellation of the chirality-flip term.
\newpage
\textbf{Model 8. Fermion adjoint triplet.}
If the hypercharge of the VL fermion is zero, one obtains an adjoint SU(2) triplet:
\begin{equation}
\Psi_A:(\mathbf{1},\mathbf{3},0)
\end{equation}
where the triplet's matrix form is
\[ \Psi_A=
\left( {\begin{array}{cc}
\frac{\Psi^0}{\sqrt{2}} & \Psi^+ \\
\Psi^- & -\frac{\Psi^0}{\sqrt{2}}
\end{array} } \right),
\]
in terms of a charged fermion and a neutral Majorana field.
The Lagrangian in this scenario reads
\begin{equation}
\mathcal{L}\supset -Y_A\,(i\sigma_2\Phi)^T \Psi_A l -M_A \textrm{Tr}(\Psi_A\Psi_A)+\textrm{h.c.}
\end{equation}
This gives
\begin{equation}
\mathcal{L}\supset -Y_A \left(\frac{\Psi^0 S^{+}}{\sqrt{2}}+\frac{\Psi^{+} S^0}{\sqrt{2}}\right)e_L
-Y_A \left(\frac{\Psi^0 S^0}{2}-\Psi^- S^+\right)\nu_L+\textrm{h.c.}
\end{equation}
Like in Model~5, there is here a negative contribution to \gmtwo\ arising from the coupling of the muon with the charged scalar.
\medskip
\textbf{Model 9. Fermion adjoint triplet and fermion doublets.}
Positive contributions to \gmtwo\ arise when the adjoint fermion triplet mixes with the doublet through the SM Higgs vev.
As before, we add to the Lagrangian
\be\label{adj_mix}
\mathcal{L}\supset -\widetilde{Y}_1\,(i\sigma_2\phi)^T\Psi_A L -\widetilde{Y}_2\,(i\sigma_2\phi^{\ast})^T\Psi_A L' +\textrm{h.c.}
\ee
Note that, besides the mixing between two heavy charged fermions, \refeq{adj_mix} leads to the additional
presence of two heavy neutral fermions mixing with each other.
The chirality-flip contribution to \gmtwo\ is not suppressed in this case as, on the one hand,
$c_{L}^{(a)}=i c_{L}^{(s)}$ and
$c_{R}^{(a)\ast}=-i c_{R}^{(s)\ast}$, and on the other there is an additional positive-value loop involving the heavy
mixing ``neutrinos'', see the last term in \refeq{chargescal}.
\bigskip
We conclude this section by pointing out that we do not treat cases with scalar SU(2) triplets in this work.
The reason is twofold. On the one hand, it was pointed out in Ref.\cite{Freitas:2014pua} that in some cases
(scalar triplet/fermion doublets, scalar adjoint triplet/fermion doublets, and scalar triplet/fermions adjoint-triplet and singlet)
the 1-loop contribution to \gmtwo\ is negative.
On the other hand, even for the cases where a positive contribution exists (scalar adjoint triplet/fermions triplet and singlet),
the correct dark matter
relic density can only be obtained with the scalar mass in the range of 5.5\tev\cite{Araki:2011hm}, which is obviously too
high to accommodate the \gmtwo\ anomaly.
\section{Experimental constraints\label{sec:constraints}}
We review in this section the experimental constraints that can affect the allowed parameter space of the
BSM models introduced in \refsec{sec:models}.
\subsection{Electroweak precision observables}
We subject all our models to electroweak precision constraints. Since VL fermions do not have tree-level
axial-vector couplings, their contribution to EWPOs is expected to be small. However, in the models with mixing between
fermions of different representations, and in models with scalar multiplets whose components are not mass-degenerate,
loop-induced effects can be significant.
In this work we compare to the experimental data two observables. We calculate the $Z\mu\bar{\mu}$ effective coupling
and confront the result with precision fits for $g_A$ and $g_V$ from the $Z$ lineshape and asymmetry data
at LEP and SLC\cite{ALEPH:2005ab}, as reported by the PDG\cite{Olive:2016xmw}. We also confront the corrections to the
$W$ mass with its measured value.
To calculate loop corrections to the $Z\mu\bar{\mu}$ couplings and $W$ mass we follow the formalism of\cite{Hagiwara:1994pw},
which was adopted in, e.g.,\cite{Cho:1999km} for a precision analysis of supersymmetry.
The conventions for Passarino-Veltman functions are also taken from\cite{Hagiwara:1994pw,Cho:1999km} and we
use \texttt{LoopTools}\cite{Hahn:1998yk} for their calculation.
The impact of precision observables in models with VL fermions for the \gmtwo\ anomaly
has been also recently investigated in\cite{Kanemitsu:2012dc}.
\medskip
\textbf{1. Oblique parameters.}
Oblique parameters $S$, $T$ and $U$\cite{Peskin:1991sw} capture the BSM contributions to the gauge bosons' vacuum polarization.
$S$ is related to the difference between the number of the left- and right-handed weak fermion doublets,
thus providing a measure of the breaking of the axial part of SU(2).
This means that in the models with degenerate VL fermions the contribution to $S$ vanishes.
The oblique parameter $T$ is related to the difference between the $Z$ and $W$ bosons' self-energies,
thus providing a measure of the breaking of the vector part of SU(2).
As a result, it is sensitive to the mass splitting between the components of an electroweak doublet\cite{Olive:2016xmw},
\be
\Delta T=\frac{1}{32\pi^2 v^2\alpha}\sum \Delta m^2,
\ee
where $\alpha$ is the fine-structure constant, the sum runs over all non-degenerate doublets, and
\be
\Delta m^2=m_1^2+m_2^2-\frac{2m_1^2m_2^2}{m_1^2-m_2^2}\ln\frac{m_1^2}{m_2^2}.
\ee
In cases where VL fermions mix, as in Model~3, 3a, and 9,
their contribution to the parameters $S$ and $T$ can be parameterized in terms of the mixing matrices and of the physical masses.
When calculating these effects, we use formulas derived in Ref.\cite{Joglekar:2012vc}.
A contribution to the oblique parameter $U$ is generally much smaller and can be neglected.
\medskip
\textbf{2. $\boldsymbol{Z\mu\bar{\mu}}$ vertex corrections.}
\begin{figure}[t]
\centering
\includegraphics[width=0.90\textwidth]{Plots/Zmmu.pdf}
\caption{One-loop BSM contributions to the $Z\mu\bar{\mu}$ vertex in extensions of the SM with a generic new fermion $F$ and a scalar $S$. }
\label{fig:zmumu}
\end{figure}
One-loop corrections to the coupling of the $Z$ boson with the left-handed and right-handed muon arise from diagrams
like the ones depicted in \reffig{fig:zmumu}.
They are given by
\be
\Delta g_{L,R}^{\mu}=\frac{1}{\sqrt{4\sqrt{2}G_FM_Z^2}}\left[g_{L,R}^{\textrm{SM}}\,\Sigma'_{L,R}(0)-\Gamma_{L,R}(M_Z^2)\right],
\ee
where the $\Sigma'$ terms are the derivatives of the self-energy functions of the external fermion legs at zero momentum,
$\Gamma_{L,R}(M_Z^2)$ arise from triangular vertex corrections, and
$g_{L,R}^{\textrm{SM}}=(-\hat{s}_{\textrm{W}}^2 Y+\hat{c}_{\textrm{W}}^2 T_3)\,g/c_{\textrm{W}}$.
In terms of Passarino-Veltman functions the $\Sigma'$ terms read
\be
\Sigma'_{L,R}(0)=\frac{1}{16\pi^2}\left[\sum_{F_i,S_j}|c_{L,R}^{ij}|^2\left(B_0+B_1)\right(0;m_{S_j},m_{F_i})\right],
\ee
where $c_{L,R}^{ij}$, the couplings of the generic new fermion $F_i$ and scalar $S_j$ to the muon, are given for our models
in \refsec{sec:models}.
The contributions from triangle diagrams are
\begin{multline}\label{Z_gam}
\Gamma_{L,R}(M_Z^2)=-\frac{1}{16\pi^2}\sum_{F_i,S_j,F_k,S_l}\left\{ c_{L,R}^{ij\ast}c_{L,R}^{kj}\left[g_{L,R}^{Zik}\, m_{F_i}m_{F_k} C_0(p_1,p_2:m_{F_i},m_{S_j},m_{F_k})\right.\right.\\
\left.+g_{R,L}^{Zik}\,\left(-M_Z^2 C_{12}-M_Z^2 C_{23}-2C_{24}+\frac{1}{2}\right)(p_1,p_2:m_{F_i},m_{S_j},m_{F_k})\right]\\
\left.-c_{L,R}^{ij\ast}c_{L,R}^{il}\,g^{Zjl}\,2\,C_{24}(p_1,p_2:m_{S_j},m_{F_i},m_{S_l})\right\}\,,
\end{multline}
where the $g^{Zik}_{R,L}$ and $g^{Zjl}$ give the SM-like couplings of the $Z$ to the new fermions and scalars.
\begin{figure}[t]
\centering
\includegraphics[width=0.50\textwidth]{Plots/Z_lineshape.pdf}
\caption{An estimate of the 95\%~C.L. region in $g_A^{\mu}$, $g_V^{\mu}$ from a fit of $Z$ lineshape and asymmetry data
at LEP and SLC\cite{ALEPH:2005ab}. The ellipse is obtained by rescaling the 39\%~C.L. region given in\cite{Olive:2016xmw}.}
\label{fig:Zline}
\end{figure}
After evaluating the observable couplings $g_V^{\mu}= g_L^{\mu}+g_R^{\mu}$ and $g_A^{\mu}=g_L^{\mu}-g_R^{\mu}$ from $g_L^{\mu}\equiv -0.2682+\Delta g_L^{\mu}$ and
$g_R^{\mu}\equiv 0.2313+\Delta g_L^{\mu}$, we compare them to the 95\%~C.L. contour presented in \reffig{fig:Zline},
which we have approximately determined by rescaling up the 39\%~C.L. contour given in\cite{Olive:2016xmw}.
We also confront all our models with rough estimates of the reach in the possible future high-precision experiments
GigaZ\cite{Erler:2000jg}, with an estimated improvement of a factor 20\cite{Baer:2013cma}
in the systematic uncertainty, and TLEP\cite{Gomez-Ceballos:2013zzn}, with an improvement of a factor 100.
The discovery potential of those experiments through precision measurements of $Z$-boson observables was
also analyzed, e.g., in the context of leptoquarks in~Ref.\cite{ColuccioLeskow:2016dox}.
In principle, our models introduce loop contributions to the $h\rightarrow \mu^+\mu^-$ decay rate as well.
However, these are supposed to be well within the present and foreseeable future uncertainties at the LHC, and for this reason we do not discuss them in this paper any longer.
\medskip
\textbf{3. Constraints from the $\boldsymbol{W}$ mass.}
Additionally, we calculate the corrections to the $W$ mass in our models.
We follow, again, Refs.\cite{Hagiwara:1994pw,Cho:1999km}, which parameterize
\bea
M_W&=&M_W^{\textrm{SM}}+\Delta M_W\\
\Delta M_W&=&-0.288\Delta S+0.418 \Delta T+0.337 \Delta U-0.126 \frac{\Delta\overline{\delta}_G}{\bar{\alpha}},
\eea
in terms of the usual oblique parameters $S,\,T,\,U$. We use $M_W^{\textrm{SM}}=80.361\gev$ and $\bar{\alpha}^{-1}=127.95$.
We neglect $\Delta U$, which is small, and we calculate the corrections to the $S$ and $T$ parameters using analytic formulas of
Ref.\cite{Joglekar:2012vc} for the fermions, and of Ref.\cite{Barbieri:2006dq} for the scalars.
We calculate $\Delta\overline{\delta}_G=2 \delta^{v}$, the correction to the muon lifetime, as
\be\label{muondec}
\delta^{v}=\frac{\sqrt{2}}{\hat{g}}\,\Gamma^{W\mu\nu_{\mu}}(0)-\frac{1}{2}\left[\Sigma'_{\mu_L}(0)+\Sigma'_{\nu_{\mu}}(0)\right]\,,
\ee
where $\hat{g}$ is the $\overline{MS}$ value of the weak coupling constant and, once more,
$\Sigma'$ and $\Gamma^{W\mu\nu_{\mu}}$ parameterize corrections to the external legs and triangle diagrams
modifying the $W\mu\nu_{\mu}$ vertex.
When expressed in terms of the Passarino-Veltman functions they are given by
\be
\Sigma'_{\mu_L,\nu_{\mu}}(0)=\frac{1}{16 \pi^2}\sum_{F_i,S_j} |c^{ij}_L|^2 (B_0+B_1) (0; m_{S_j}, m_{F_i})
\ee
and
\begin{multline}\label{mulife_vert}
\Gamma^{W\mu\nu_{\mu}}(0)=\frac{1}{16 \pi^2}\sum_{F_i,S_j,F_k,S_l}\left\{-c_L^{ij\ast}c_L^{kj}\left[g_L^{Wik} m_{F_i}m_{F_k}C_0\left(0;m_{F_i},m_{S_j},m_{F_k}\right)\right.\right.\\
\left.\left.+g_R^{Wik}\left(-2 C_{24}+\frac{1}{2}\right)\right]\left(0;m_{F_i},m_{S_j},m_{F_k}\right)
+c_L^{ij\ast}c_L^{il}g^{Wjl}\,2C_{24}\left(0;m_{S_j},m_{F_i},m_{S_l}\right)\right\}\,,
\end{multline}
where the symbols have equivalent meaning as in \refeq{Z_gam}.
\subsection{Collider constraints}
In all our models, we apply a default hard cut on the mass of new charged particles, $m_{E^{\pm},S^{\pm}}>100\gev$ to roughly
take into account LEP~II limits.
Moreover, since the VL fermions are charged under the SM electroweak gauge symmetry group, they can be pair-produced at the
LHC in Drell-Yan processes, $pp\to Z,\gamma,W^{\pm}\to F\,\bar{F}$, and subsequently undergo Yukawa-driven decays into a DM scalar and a muon, $F\to S\, \mu$, thus leading to a characteristic 2 leptons plus missing energy (MET) signature.
Such a topology has been investigated by both ATLAS and CMS in the context of supersymmetry in the searches dedicated to sleptons, charginos and neutralinos.
In this work, we employ two different 2-lepton searches based on 13\tev\ data: the ATLAS search\cite{ATLAS:2016uwq}, based on hard leptons in the finals state, with an integrated luminosity of 13.3\invfb; and the CMS search\cite{CMS:2017fij}, based on soft leptons,
with an integrated luminosity of 35.9\invfb. We numerically recast these two experimental analyses for
the models introduced in \refsec{sec:models}, following the procedure described in detail in\cite{Kowalska:2015zja,Kowalska:2016ent}
and references therein.
The main kinematical variable used in the ATLAS search to discriminate between the signal and the SM background is the
stransverse mass $m_{T2}$\cite{Barr:2003rg}, with the end point correlated to the mass splitting between fermion and dark matter scalar, $\delta m$.
As a result, the sensitivity of the search weakens when the mass splitting decreases, dropping to zero when $\delta m\approx 70\gev$.
Conversely, the CMS analysis targets low-momentum leptonic final states and therefore can test the compressed spectra region,
where the mass difference between fermion and dark matter is smaller than $\sim40\gev$.
Singlet scalar dark matter can be pair-produced at the LHC through the off-shell Higgs boson, $pp\to h^*\to S\,S$.
The cross-section is in this case directly proportional to the size of the portal couplings and is not expected to be significant, given the discussed stringent bounds from direct detection experiments. For doublet scalar dark matter, Drell-Yan production with electroweak-size cross section is also possible, $pp\to Z,\gamma,W^{\pm}\to \Phi^{\dagger}\,\Phi$.
Such a signature can be probed by monojet searches, which tag an energetic jet from initial-state radiation recoiling against the produced dark matter. To capture this possibility, we recast the ATLAS 13\tev\ analysis\cite{Aaboud:2016tnv} with 3.2\invfb\ of data.
Besides the present exclusion bounds, we also calculate the sensitivity of ATLAS searches\cite{ATLAS:2016uwq,Aaboud:2016tnv}
with the assumed luminosity of $300\invfb$ at the LHC 14\tev\ run.
If $m_{DM}<m_h/2$, the Higgs boson can invisibly decay into dark matter with branching ratio proportional to the portal coupling(s). For completeness, we apply the CMS upper bound on the corresponding branching ratio, $\textrm{BR}(h\to\textrm{invisible})<0.24$
at the 95\% confidence level\cite{Khachatryan:2016whc}.
In the models characterized by the mixing of fermions with different SU(2) quantum numbers through the Higgs boson vev
(Models~3, 3a, 9) we also apply $2\sigma$
constraints from the branching ratio $\textrm{BR}(h\rightarrow \gamma\gamma)$ at the LHC,
which has been measured, e.g, by ATLAS\cite{ATLAS-CONF-2017-045}:
$R_{\gamma\gamma}\equiv\textrm{BR}(h\rightarrow \gamma\gamma)/\textrm{BR}(h\rightarrow \gamma\gamma)_{\textrm{SM}}=0.99\pm0.14$.
We calculate the $R_{\gamma\gamma}$ ratio at one loop following, e.g.,\cite{Kearney:2012zi}:
\be
R_{\gamma\gamma}\approx \left|1-0.109\sum_{i=1,2}\frac{2\,C_{hii}\,v}{m_{E^p_i}}\,A_{1/2}\left(\frac{4 m_{E^p_i}^2}{m_h^2}\right)\right|^2,
\ee
in terms of the physical masses defined in \refeq{physmas}, and the tree-level couplings of the Higgs boson $h$ to the heavy fermions,
$C_{hii}=(\widetilde{Y}_1 V_{i1}U_{i2}+\widetilde{Y}_2 V_{i2} U_{i1})/\sqrt{2}$. The loop function $A_{1/2}(x)$ can be found in\cite{Kearney:2012zi}.
Finally, we recall that we apply to all our models the relic density constraint from Planck\cite{Ade:2015xua}, $\abund=0.1188\pm 0.0010$,
to which we add in quadrature a $\sim10\%$ theoretical uncertainty, and the XENON1T 90\%~C.L. upper bound on the spin-independent
cross section \sigsip\cite{Aprile:2017iyp} as a hard cut.
\section{Numerical analysis\label{sec:results}}
We present now the results of the numerical analysis of the models introduced in \refsec{sec:models}.
We will start with a brief description of the numerical tools utilized in the study.
Each of the considered models has been generated with {\tt SARAH}\ v.4.9.3\cite{Staub:2013tta} and the corresponding {\tt SPheno}\cite{Porod:2003um,Porod:2011nf} modules have been produced to calculate mass spectra and decay branching ratios.
Flavor observables, including \deltagmtwomu, have been calculated with the {\tt FlavorKit}\ package\cite{Porod:2014xia} of {\tt SARAH}-{\tt SPheno}.
Model files for {\tt CalcHEP}\cite{Belyaev:2012qa} were also generated and passed to {\tt MicrOMEGAs}\ v.4.3.1\cite{Belanger:2013oya} to calculate dark matter related observables.
In order to efficiently scan the multidimensional parameter space, all the packages were interfaced to
{\tt MultiNest}\ v.3.10\cite{Feroz:2008xx} for sampling. We emploied a Gaussian likelihood function to find the regions favored by
the dark matter relic density and \deltagmtwomu.
The parameters of the models were scanned in the following ranges:
\bea
0.001 \leq &\rm{Yukawa\;\; couplings} &\leq \sqrt{4\pi},\nonumber\\
-1 \leq &\rm{portal\;\; couplings}& \leq 1,\nonumber\\
100\; \rm{GeV} \leq & M_{L,E,T,A} & \leq 10000\; \rm{GeV},\nonumber\\
(10\gev)^2 \leq & \mu_s^2, \mu_S^2, \mu_{\Phi}^2 & \leq (5000\gev)^2, \nonumber\\
-0.5\,\mu_S^2 \leq & \mu_S'^2 & \leq 0.5\,\mu_S^2.
\eea
The LHC limits from the ATLAS 2-lepton and monojet searches have been implemented using the recast procedure described in detail in\cite{Kowalska:2015zja,Kowalska:2016ent} and adapted to handle non-SUSY scenarios. To this end, {\tt UFO} files have been generated with {\tt SARAH}\ and passed to {\tt MadGraph5$\_$aMC@NLO}\cite{Alwall:2014hca}, where a set of new BSM processes with a corresponding output for {\tt PYTHIA}\cite{Sjostrand:2007gs} were created. Finally, the hadronization products were passed to the fast detector simulator {\tt DELPHES 3}\cite{deFavereau:2013fsa}.
We perform our numerical analysis at the tree level.
In doing so, we are relying on some underlying assumptions that may not be always warranted,
especially in theories including several scalar fields like the ones investigated here.
Scalar masses are affected by significant loop corrections, in particular those that depend on the BSM Yukawa couplings which,
as we shall see, in general have to be sizable to accommodate the experimentally measured value of \deltagmtwomu.
{\tt SARAH}\ v.4.9.3 allows one to calculate 1-loop corrections to all scalar masses, and define the input parameter at a high
renormalization scale of choice.
However, it has been pointed out\cite{Braathen:2017izn} that the results so implemented maintain a significant residual
dependence on the renormalization scale. One should therefore make use of the full 2-loop calculation,
which has only become available very recently\cite{Braathen:2017izn}.
Thus, in this work we limit ourselves to the assumption generally adopted in the literature when dealing with non-supersymmetric
BSM scalar fields, i.e., that it is possible to absorb corrections to the scalar masses into the counterterms of the free parameters.
Note that effects of 1-loop corrections to the scalar mass in relation to the relic density in inert scalar models have been
analyzed, e.g., in\cite{Hambye:2007vf,Goudelis:2013uca}. In Ref.\cite{Goudelis:2013uca}, in particular, it was shown that as long as the
input parameters are defined not far above the EWSB scale, say up to 10\tev\ or so, the parameter space regions in agreement with the relic
density are not altered drastically with respect to the tree level.
\subsection{Real scalar with a singlet or doublet VL fermion\label{sec:result1}}
We begin our discussion with \textbf{Model~1}, characterized by the addition of a real scalar particle and VL fermion singlet fields to the spectrum of the SM.
The $\mathbb{Z}_2$-odd scalar plays the role of the dark matter particle in this case, and we will refer to it with
$m_{\textrm{DM}}\equiv m_s$ interchangeably.
\begin{figure}[t]
\centering
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_sigsip_G2SSDM.pdf}
}%
\\
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_mFC2_G2SSDM.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/Yuk_mFC_G2SSDM.pdf}
}%
\caption{(a) The ($m_{\textrm{DM}}$, $Y_S$) plane for Model~1 (real scalar field and VL fermion singlet).
In cyan, the parameter space favored at $2 \sigma$ by the relic density is shown, while the one favored
by the \gmtwo\ measurement is shown in dark blue. Green region corresponds to those values of model parameters where both constraints are satisfied simultaneously.
(b) The parameter space common to the relic density and \gmtwo\ in the ($m_{\widetilde{E}}$, $m_{\textrm{DM}}$) plane. Gray triangles show the parameter space excluded by the ATLAS 2 hard leptons search\cite{ATLAS:2016uwq}, whereas dim gray diamonds show
that excluded by the CMS 2 soft leptons search\cite{CMS:2017fij}.
(c) Same as (b) but in the ($m_{\widetilde{E}}$, $Y_S$) plane. The projected reach of precision measurements at GigaZ\cite{Erler:2000jg}
and TLEP\cite{Gomez-Ceballos:2013zzn} is also shown.}
\label{fig:real_sing}
\end{figure}
In \reffig{fig:real_sing}(a) we present a plot of the model's parameter space in the plane of the new coupling to the muon, $c_R=Y_S$,
versus the dark matter mass. The parameter space allowed at $2 \sigma$ (including a $\sim10\%$ theory error)
by the relic density is shown in cyan, and we highlight with a darker shade the region in which $\abund\approx 0.12$ is due with good approximation exclusively to the bulk. The \gmtwo\ constraint is shown in dark blue and
we do not impose at this stage any LHC or precision constraints.
Higgs-portal dark matter plays a small role, almost exclusively limited to the region above $0.8-1\tev$, in which the recent
bounds from XENON1T can be evaded. Note that the relic abundance imposes a lower bound on the mass of the scalar particle,
$m_s=m_{\textrm{DM}}\gsim 40-50\gev$, as the bulk mechanism loses its efficiency when the spread between
$m_s$ and $m_{\widetilde{E}}$ is significant (recall that $m_{\widetilde{E}}\gsim100\gev$ by LEP bounds).
As we shall see below, this lower bound on the dark matter mass is model-dependent and can be evaded in other scenarios.
The parameter space allowed at $2\sigma$ by the combination of relic density and \gmtwo\ is
shown in green. The $2\sigma$ region from the BNL measurement places an upper bound on the mass of the dark matter scalar, $m_s\lesssim 170-180\gev$, beyond which one is forced to resort to non-perturbative values for the new Yukawa coupling $Y_S$,
independently of the size of $m_{\widetilde{E}}>m_s$.
In \reffig{fig:real_sing}(b) we show the points of the allowed parameter space -- the green region of \reffig{fig:real_sing}(a) -- in the
($m_{\widetilde{E}}$, $m_{\textrm{DM}}$) plane, best suited for interpreting the LHC constraints. We also apply here
the constraints from precision observables, which have no visible effect in this case due to the VL nature of the new fermion.
Both 2-lepton + missing $E_T$ bounds are applied and the excluded points are shown with gray triangles and dim gray diamonds.
The ATLAS bound is quite aggressive, and excludes most of the parameter space in the picture,
with the exception of a limited region in which $m_{\widetilde{E}}$ and $m_s$ become increasingly close to each other,
as the $m_{T2}$ variable loses its discriminating power for compressed and semi-compressed spectra.
We have also calculated the reach of the ATLAS search with 300\invfb, but the latter shows little if any impact
on the surviving region, due to the intrinsic ineffectiveness of $m_{T2}$ for these spectra.
On the other hand, the remaining parameter space is extensively tested by the CMS low-momentum search,
which allows one to exclude BSM fermions with masses lower than $140\gev$ for a dark matter scalar heavier than
$\sim 60\gev$.
Note, incidentally, that neither the monojet search nor Higgs invisible decays
can provide a complementary way of testing the surviving region due to the smallness of the portal Higgs coupling.
The same points are shown in \reffig{fig:real_sing}(c), in the plane of the new Yukawa coupling, $Y_S$, versus the VL fermion mass.
The CMS soft-lepton search excludes in this case essentially the whole parameter space with $Y_S\lesssim 1.5$.
Because of the overall large Yukawa values, future precision experiments like GigaZ or TLEP, with a projected
improvement by a factor 20 or more over LEP, have the potential to probe the surviving region.
We show with dashed lines the projected reach of these experiments in precision measurements of $Z$-physics observables.
Note also that, quite possibly, $e^+ e^-$ colliders like the ILC or TLEP may be able to cover the surviving region directly by
pair production of the charged particles $\widetilde{E}^{\pm}$.
A precise estimate of the direct reach of electron/positron colliders in this case requires a numerical simulation of the event generation and detector response, which is beyond the scope of this paper.
One might wonder at this point if a large BSM Yukawa coupling, which is required to fit \deltagmtwomu\,, can
remain perturbative up to the Planck scale. We have checked that this is often not the case.
For example, in Model~1, $Y_S\approx 1.5$ induces a breakdown of perturbativity at about $10^5\gev$.
This, however, does not necessarily pose a problem here, as we are dealing with simplified models that, by constuction, are not
meant to be UV complete.
It is not hard to imagine that in a more general framework the asymptotic behavior of $Y_S$ could be modified in a way that makes the Landau Pole below the Planck scale disappear.
\begin{figure}[t]
\centering
\includegraphics[width=0.55\textwidth]{Plots/mFC_g2_G2SSDM.pdf}
\caption{The measurement of \deltagmtwomu\ as a function of the VL fermion mass and the new Yukawa coupling in Model~1.
The scalar dark matter mass is fixed here at $m_s=m_{\textrm{DM}}=80\gev$, but the plot is not very sensitive to its value.
The horizontal red solid lines show the $2\sigma$ region of the BNL experiment.}
\label{fig:g2_real_s}
\end{figure}
We summarize the case of Model~1 in \reffig{fig:g2_real_s}, where we present predictions for this model based
on an eventual measurement of \gmtwo\ at Fermilab. The different bounds discussed above are applied.
The surviving parameter space in Model~1 is thus confined to a very narrow strip.
\textbf{Model~2}, characterized by the coupling of the muon to a real scalar singlet and a fermion doublet,
does not show significant differences from Model~1 at the tree level. This could have been anticipated by a simple inspection of the
two Lagrangians, \refeq{mod1lag} and \refeq{Lagr1}. The dark matter particle is the same in both cases and
the contributions to the \gmtwo\ calculation are also the same,
as one can simply switch the role of $c_L$ and $c_R$ in \refeq{chiralint} (and one of them is always zero).
The bounds from EWPOs are easily satisfied in both models, as both lack an explicit source of chiral-symmetry violation beyond the VL mass.
The LHC multi-lepton bound is in principle stronger for the fermion doublet case in the region of large
$m_{E}$ and small $m_{\textrm{DM}}$, due to the possibility of producing the doublet through the $W$ boson, which enhances the cross section. However, we do not expect any difference from what is shown in \reffig{fig:real_sing}(b),
as the limit is strong enough to exclude this region in Model~1 as well.
Thus, no difference can be observed between Model~1 and Model~2, and the reader can refer to
Figs.~\ref{fig:real_sing} and \ref{fig:g2_real_s} for Model~2 as well.
\subsection{Real scalar with mixing singlet and doublet VL fermions}
As was discussed in \refsec{sec:realsca}, when the singlet and doublet fermion are both included in the theory,
they can mix through the Higgs boson field vev. This introduces an additional explicit source of chiral-symmetry violation in the \gmtwo\ loop,
which can boost its value as now both $c_L$ and $c_R$ differ from zero in \refeq{chiralint}.
For the same reason, however, this model, which we dubbed \textbf{Model~3},
is also subject to strong constraints from EWPOs.
\begin{figure}[t]
\centering
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_sigsip_G2LDSDM.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_mFC2_v1_G2LDSDM.pdf}
}%
\caption{(a) The [$m_{\textrm{DM}}$, $\Re(c^1_L c^{1\ast}_R)^{1/2}$] plane for Model~3 (real scalar field and mixing singlet and doublet VL fermions). The color code is the same as in \reffig{fig:real_sing}(a). (b) The parameter space of Model~3 in agreement with the relic density and the \gmtwo\ anomaly at $2\sigma$ in the
($m_{E_1^p}$, $m_{\textrm{DM}}$) plane.
Gray dots are excluded by a combination of electroweak precision data, the ATLAS and CMS 2-lepton + MET searches
at 13\tev, and the constraints from $\textrm{BR}(h\rightarrow \gamma\gamma)$ at ATLAS\cite{ATLAS-CONF-2017-045}.
The projected reach of ATLAS 2-lepton searches with 300\invfb\ probes the points shown as green dots;
new data from XENON-IT will test the points shown as royal-blue crosses;
and improved electroweak precision at TLEP will test the points marked by black triangles.
The points shown as red squares are possibly outside of foreseeable reach.}
\label{fig:real_mixing}
\end{figure}
We present in \reffig{fig:real_mixing}(a) the parameter space of Model~3 in the $[m_{\textrm{DM}}$, $\Re(c^1_L c^{1\ast}_R)^{1/2}]$
plane, without for the moment applying the limits from EWPOs and the LHC. The color code is the same as in \reffig{fig:real_sing}(a).
The \gmtwo\ anomaly can be accommodated for very large dark matter mass,
well into the TeV range, thanks to the above-mentioned boost provided by the chirality-flip term involving $c_L c_R^{\ast}$.
For the same reason, the new Yukawa couplings are also allowed to span a broader range,
with the sum of them that can be as small as $\sim 0.2$.
We show the points of the parameter space favored by \abund\ and \gmtwo\ in the ($m_{E_1^p}$, $m_{\textrm{DM}}$) plane
in \reffig{fig:real_mixing}(b). After applying the remaining constraints, we mark with gray dots the points excluded by a combination of the ATLAS and CMS 2-lepton + MET searches (mostly points on the bottom left of the picture), ATLAS $R_{\gamma\gamma}$ constraint (a handful of points that are also excluded by the 2-lepton searches), and EWPOs (mostly points on the top right).
Electroweak precision bounds are able to exclude solutions with large fermion mass since large singlet/doublet mixing is required to
fit the \gmtwo\ constraint at $2\sigma$.
More specifically, the BSM contributions to the $Z\mu\bar{\mu}$ vertex imply $\Re(c^1_L c^{1\ast}_R)^{1/2}\lesssim 0.01$,
unless the ratio $Y_S/Y_D\sim\mathcal{O}(1)$. In that case the limit weakens to $\Re(c^1_L c^{1\ast}_R)^{1/2}\lesssim 0.1$.
On the other hand, the corrections to the $W$ mass, which arise from BSM contributions to the muon lifetime and the oblique parameters,
test two distinctive regions of the parameter space: the small mass regime, with $m_s<100\gev$ and small fermion mixing, where the corrections to muon decay are dominant; and the large mass regime, in which the large mixing induces large splitting of the doublet fermion masses,
which subsequently increases the parameter $T$.
The points that are not excluded by LEP or the recent LHC constraints are in reach of
the high-luminosity LHC or future experiments sensitive to corrections to the $Z\mu\bar{\mu}$ effective coupling.
The points in reach of the LHC with 300\invfb\ are shown as green diamonds, whereas black triangles mark the points in reach of future precision experiments. Note that points characterized by a non-negligible portal coupling, $\lam_{12}\gsim 0.1$, will be tested in complementarity with the next release from XENON-1T data, and we show these points in \reffig{fig:real_mixing}(b) as royal-blue crosses.
Finally, we highlight with red squares the points that appear to be beyond the reach of all of the
projected measurements considered in this work.
We point out that these points are almost all characterized by the scalar and lightest fermion mass
being very close to each other. This is not enforced by any of the symmetries of the Lagrangian considered in \refsec{sec:realsca},
so that we can conclude that Model~3 requires a certain amount of fine tuning to evade all future bounds.
\subsection{Complex singlet scalar with VL fermions}
\begin{figure}[t]
\centering
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_sigsip_G2SSDMc.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mFC_Yuk_cont_G2SSDMc.pdf}
}%
\caption{(a) The ($m_{\textrm{DM}}$, $c_R^{(s)}$) plane for Model~1a (complex scalar field and singlet VL fermions). The color code is the same as in \reffig{fig:real_sing}(a). (b) Region of Model~1a favored by a combination of the relic density and \gmtwo\ constraints in the plane ($m_{\widetilde{E}}$, $c_R^{(s)}$). The gray area is excluded by the LHC 2-lepton + MET searches. Projected reach at the LHC with 300\invfb, and future precision experiments at GigaZ and TLEP, are shown as dashed lines.}
\label{fig:compl_sing}
\end{figure}
In \reffig{fig:compl_sing}(a) we present the parameter space of \textbf{Model~1a} in the ($m_{\textrm{DM}}$, $c_R^{(s)}$) plane (recall that $c_R^{(s)}=(Y_S+Y_{S^{\ast}})/\sqrt{2}$). At this stage the LHC and precision constraints have not been yet applied,
and the color code is the same as in \reffig{fig:real_sing}(a), with the only difference being that we do not explicitly highlight here the
parameter space region belonging to the bulk.
The most striking difference with Model~1 is that in Model~1a one can fit the \gmtwo\ anomaly with lighter dark matter,
as light as our prior range allows, $m_s, m_a\approx 10\gev$. This is due to the presence of two possible dark matter particles in this mass range,
the scalar $s$ and the pseudoscalar $a$. When their masses are not far apart from one another,
the relic density can be effectively diluted in the early Universe thanks to additional bulk processes like
$a\,s\rightarrow \mu^+\mu^-$, or $a\,a\rightarrow \mu^+\mu^-$.
When one applies the constraints from the LHC (precision bounds do not alter the picture much in this model)
the available parameter space is much reduced.
We project the region favored by a combination of the relic density and \gmtwo\ constraints to the plane ($m_{\widetilde{E}}$, $c_R^{(s)}$).
The result is presented in \reffig{fig:compl_sing}(b). The region in gray is excluded by the LHC 2-lepton searches.
Note that, while both LHC 2-lepton searches are quite effecfive in excluding large swaths of parameter space in Model~1b,
there is a larger region of the parameter space that survives the contraints than in Model~1, as the number of free parameters is here larger, and there are more ways to evade the bounds.
We also show with dashed lines of different colors the projected reach of the ATLAS search with
300\invfb, and of future precision experiments at GigaZ and TLEP.
As dark matter particles, the scalars $s$ and $a$ behave symmetrically, with the only difference being that, by construction,
the available range for the coupling of $s$ to the muon, $c_R^{(s)}=(Y_S+Y_{S^{\ast}})/\sqrt{2}$, is slightly larger than the allowed coupling
for $a$, $|c_R^{(a)}|=|Y_S-Y_{S^{\ast}}|/\sqrt{2}$.
In fact, the region with good dark matter in \reffig{fig:compl_sing}(a) features solutions of various types,
$m_s\approx m_a$, $m_s\ll m_a$, $m_a\ll m_s$, and cases in between.
\begin{figure}[t]
\centering
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/Csing_deg.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/Csing_nondeg.pdf}
}%
\caption{The computed \deltagmtwomu\ versus the dark matter mass for the parameter space allowed by dark matter
in Model~1a (complex singlet scalar and singlet VL fermions). (a) The case of scalar masses being close to degenerate, $m_{\textrm{DM}}\equiv m_a\approx m_s$, as a function of the coupling to the muon, $c_R^{(s)}=(Y_S+Y_{S^{\ast}})/\sqrt{2}$.
The new fermion mass is fixed slightly above 100\gev,
and we set the pseudoscalar coupling to $|c_R^{(a)}|=|Y_S-Y_{S^{\ast}}|/\sqrt{2}=1$.
The dark matter becomes under-abundant for $m_{\textrm{DM}}\gsim 80\gev$.
(b) The case $m_s\gg m_a$, for different values of the coupling of $a$ to the muon, $|c_R^{(a)}|$.
This case resembles the behavior of Model~1.}
\label{fig:compl_sing_1d}
\end{figure}
Because of a quite large number of free parameters, however, a measurement of \gmtwo\ is not sufficient in Model~1a to
pinpoint specific features and correlations of some parameters with respect to others.
Thus, we identify two limiting cases that we summarize in \reffig{fig:compl_sing_1d}.
In \reffig{fig:compl_sing_1d}(a) we show the value of \deltagmtwomu\ versus the dark matter mass in the case where the scalar and pseudoscalar are close to being degenerate, $|m_s-m_a|\lesssim$ a few GeV.
The parameter of greatest impact on the \gmtwo\ calculation is in this case the sum of the new Yukawa couplings, or $c_R^{(s)}$.
We show in the figure the dependence of \deltagmtwomu\ on selected values of $c_R^{(s)}$,
when $m_{\widetilde{E}}\approx 100\gev$ to avoid LHC bounds, and $|c_R^{(a)}|$ is set to 1.
One can see that, as $m_s\approx m_a$ approaches $m_{\widetilde{E}}$, the bulk becomes more and more efficient\cite{Bai:2014osa}
until \abund\ drops below the lower bound when $m_{\textrm{DM}}\approx 80\gev$.
At that point, in order to maintain the constraint from $\abund\approx 0.12$ in place, the scalar masses must become more separated.
Note also that for $m_{\widetilde{E}}\approx 100\gev$, a dark matter mass below $\sim 40\gev$ is excluded by the ATLAS 2-lepton search,
independently of the value of $c_R^{(s)}$.
In \reffig{fig:compl_sing_1d}(b) we show the case $m_{\textrm{DM}}=m_a\ll m_s$.
We impose in the plot $m_{\widetilde{E}}\approx m_a+50\gev$, as under this condition one can evade the LHC constraints.
Here the scalar particle $s$ effectively decouples from the \gmtwo\ calculation, thus reproducing the limit of Model~1,
with the difference that the coupling of the scalar $a$ to the muon is expressed in terms of $|c_R^{(a)}|=|Y_S-Y_{S^{\ast}}|/\sqrt{2}$.
Similarly to the equivalent cases in \refsec{sec:result1}, if we consider \textbf{Model~2a},
in which the complex scalar couples to a doublet VL fermion, the differences with Model~1a are not substantial.
However, because of the enlarged production cross section for doublet fermions, the LHC excludes in this case the region
shown on the top right in \reffig{fig:compl_sing}(b), characterized by charged leptons between 400 and 500\gev.
\textbf{Model~3a}, finally, presents a pattern that in the [$m_{\textrm{DM}}$, $\Re(c_L^{(s,a)1}c_R^{(s,a)1\ast})^{1/2}$] plane
would look similar to the one depicted in \reffig{fig:real_mixing}(a), with large regions of the parameter space allowed
by the constraints before the bounds from precision and the LHC are applied.
However, because there are now several Yukawa couplings and two scalar masses that can interplay, it appears that the
large $m_{\textrm{DM}}$ region requires slightly lower values for the mixing angles than in Model~3 and, as a consequence,
in Model~3a the parameter space cannot be easily constrained.
In fact, the ($m_{E_1^p}$, $m_{\textrm{DM}}$)-plane plot equivalent to \reffig{fig:real_mixing}(b)
is not very informative in Model~3a, with no clear correlation emerging in the masses of the surviving points.
For this reason we do not show this figure here, and we are forced to conclude that a complex scalar singlet with mixing
doublet/singlet VL fermion can accommodate \abund\ and the \gmtwo\ anomaly for large ranges of parameters that will possibly
avoid most future constraints, as long as the singlet-doublet mixing is not very large.
\subsection{Doublet scalar with singlet, doublet, or triplet VL fermions\label{sec:doub_sca-results}}
In order to analyze the doublet scalar case, let us first briefly recall its dark matter properties.
Inert doublet scalar dark matter has been analyzed in the literature in several papers
(we refer to, e.g.,\cite{Goudelis:2013uca,Arhrib:2013ela} for recent studies).
When the relic density is driven by the Higgs portal couplings the characteristics are well known.
There are two viable regions for dark matter in the parameter space: one for $m_{\textrm{DM}}\lesssim 100\gev$
and the other in the range from $\sim 700\gev$ to several~TeV.
For the parameter space in between, the dark matter is under-abundant,
as at about 85\gev\ the annihilation channel $s s(a)\rightarrow W^+W^-$ opens up
(in a fashion similar to the higgsino case in supersymmetry).
For the models with no fermion mixing, the TeV-range region does not admit solutions for the \gmtwo\ anomaly, so that we will limit
our analysis to scalar masses below $\sim 100\gev$.
In \reffig{fig:doubl_mass}(a) we present the now familiar plane of the Yukawa coupling to muons versus the dark matter mass
in \textbf{Model~4}, which features a doublet scalar and singlet VL fermions in the spectrum. As before, at this stage of the analysis
we have not applied the bounds from EWPOs and the LHC.
The dark matter in the low-mass region is obtained mostly through the bulk, as values of the portal couplings that
might produce $\abund\approx 0.12$ through interactions with the Higgs have long been excluded in direct detection experiments (with the exception of the Higgs resonance).
\begin{figure}[t]
\centering
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_Yuk_cont_G2LDDMc.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_Yuk_cont_G2DDDMc.pdf}
}\\
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_Yuk_cont_G2DLTTMc.pdf}
}%
\hspace{0.02\textwidth}
\subfloat[]{%
\includegraphics[width=0.47\textwidth]{Plots/mDM_Yuk_cont_G2DLATMc.pdf}
}
\caption{Planes of the Yukawa coupling to muons versus the dark matter mass in models with a scalar doublet.
The region where the \gmtwo\ anomaly can be accommodated at $2\sigma$ is shown in blue, the region where
the relic abundance is correct within $2\sigma$ is shown in cyan, and the combined parameter space is highlighted in green.
(a) Model~4 (doublet scalar and singlet VL fermions), (b) Model~5 (doublet scalar and doublet VL fermions), (c) Model~7
(doublet scalar and triplet VL fermions), (d) Model~8 (doublet scalar and adjoint triplet VL fermions).}
\label{fig:doubl_mass}
\end{figure}
As in the previous cases the \gmtwo\ anomaly can be fitted in the bulk.
Unlike in the complex singlet case, however, solutions with dark matter much lighter than 40\gev\ cannot be found here,
as LEP has excluded weakly-coupled charged particles below $\sim 100\gev$ and all scalars belong to the same doublet.
Close inspection of \refeq{doublet_mass} reveals that, once the charged scalar satisfies that constraint,
also the pseudoscalar becomes heavier than 100\gev\ (recall that $\lam_3+\lam_4+2\lam_5\ll 1$)
and the dark matter sector approaches the limit of Model~1.
A similar plot for \textbf{Model~5}, which features a doublet scalar and doublet VL fermions, is shown in \reffig{fig:doubl_mass}(b).
After a quick look at \refeq{sca_doub_fer_doub} one can see that in this case there is a coupling of the muon to the
charged scalar/neutral fermion loop. Thus, we expect \gmtwo\ to be generally smaller than in Model~4 in the equivalent parameter range, as there is a negative contribution damping its value. Note, in this regard,
that the Higgs-resonance region does not present solutions to
the \gmtwo\ anomaly in Model~5 since, in order to avoid excessively diluting \abund, either the Yukawa couplings should be
there quite small, or the VL fermion mass larger than in other regions of the parameter space.
On the other hand, in \textbf{Model~7}, characterized by a doublet scalar and triplet VL fermions, simultaneous
solutions to the \gmtwo\ anomaly and dark matter exist \textit{only} in the Higgs-resonance region.
In fact, in general, due to the impact
of the large doubly-charged contribution, one obtains \deltagmtwomu\ within $2 \sigma$ for fermion masses that must be
quite large, $m_{\Psi^{\pm}},m_{\Psi^{\pm\pm}}\gg 100\gev$. As a consequence, the bulk annihilation cross section is not large enough to yield $\abund\approx 0.12$. However, in the Higgs-resonance region, the relic abundance is obtained via portal couplings, so that
a solution that can accommodate the \gmtwo\ anomaly can be easily found for a wide range of Yukawa coupling and fermion mass values.
Finally, we illustrate the case of \textbf{Model~8}, characterized by a doublet scalar and adjoint triplet VL fermions,
in \reffig{fig:doubl_mass}(d).
As one can see from the plot, there is no parameter space here that can accommodate the measured value of
\gmtwo\ and the relic density at the same time. As a matter of fact, in Model~8 the bulk annihilation
channel $s s(a)\rightarrow \nu_{\mu}\nu_{\mu}$ is so efficient that it effectively places an upper bound on the
new Yukawa coupling, $Y_A\lesssim 0.8-1$, if one wants to satisfy $\abund\approx 0.12$.
As a consequence, \deltagmtwomu\ is never large enough in the region with
$\abund\approx 0.12$.
We briefly come back here to the issue of a breakdown of perturbativity of the Yukawa couplings at some high scale, which is less severe in the models with a scalar doublet. For instance, values of $Y_T$ as large as 1.3 do not generate a Landau Pole below the Planck scale in the fermion triplet case, indicating that such a scenario can be considered as UV-complete. Conversely, for fermion singlets and doublets the lowest $Y_{S/D}$ consistent with the
\gmtwo\ anomaly requires some extension of the corresponding simplified model at the scale of $\sim 10^{9}\gev$.
\begin{figure}[t]
\centering
\includegraphics[width=0.55\textwidth]{Plots/mDM_mFC_COMBO.pdf}
\caption{The impact of LHC 13\tev\ on the parameter space in agreement with dark matter and the \gmtwo\ anomaly in Models~4 (squares), 5 (circles), and 7 (triangles). The points allowed are shown in three different shades of green, while those excluded in three different shades of gray.}
\label{fig:doubs_LHC}
\end{figure}
The impact of LHC 13\tev\ and electroweak precision constraints on the parameter space in agreement with dark matter and the
\gmtwo\ anomaly for Models~4-8 is shown in \reffig{fig:doubs_LHC}. In all scenarios,
as long as the charged fermion is situated around 100\gev\ a compressed region can be observed,
which survives all of the constraints. It can only be minimally tested by the CMS soft-lepton analysis,
as the mass difference between the charged fermion and dark matter is in general too large for the search to be effective.
Outside of the compressed region, across the Higgs resonance, the mass of the charged VL fermions
becomes larger to suppress bulk annihilation. In Model~4 the LHC 2-lepton search places a lower bound on the fermions mass
of about 160\gev. It is much weaker than the corresponding bound for Model~1, as in Model~4 the decay
$E'\to S^+\bar{\nu}_{\mu}$ is possible, which cuts drastically the efficiency of the search due to a reduced branching ratio
to the 2-lepton final state.
As before, we have also calculated the effect of the future LHC reach with 300\invfb\ on the models.
Most of the currently allowed regions with fermion mass larger than $\sim 100\gev$ will be strongly
reduced at the end of the current LHC run, although it does not appear that any of them can be probed in its absolute
entirety even with large luminosity.
We summarize the findings of this subsection in \reffig{fig:g2_doubs}, where we present the value of \deltagmtwomu\
versus the scalar dark matter mass in every model for a fixed value of the new Yukawa coupling, $Y=2$.
The only exception is Model~8 for which, as we saw in \reffig{fig:doubl_mass}(d),
there exist an upper bound on the Yukawa coupling due to the relic abundance.
To avoid the bounds from the LHC, in \reffig{fig:g2_doubs} we have set the charged fermion mass just above 100\gev,
while the pseudoscalar and charged scalar masses are fixed case by case to the typical values observed in the scans.
As the mass of the scalar $s$ approaches the Higgs resonance, however, we move the fermion mass up to larger values, to mimic the behavior of the scans. As a consequence, \deltagmtwomu\ drops.
\begin{figure}[t]
\centering
\includegraphics[width=0.60\textwidth]{Plots/DoubletS.pdf}
\caption{The computed \deltagmtwomu\ as a function of the dark matter mass $m_{\textrm{DM}}=m_s$
and Yukawa coupling to the muon in the models with a doublet scalar, discussed in \refsec{sec:doub_sca-results}.
The charged fermion mass is fixed at about 100\gev\ outside of the Higgs resonance to evade the LHC bounds, but it is progressively
pushed to larger values on the resonance region. The pseudoscalar and charged scalar mass are fixed case by case to the typical values observed in the scans.
Gray solid line: singlet VL fermions; magenta dashed line: doublet VL fermions; blue dot-dashed line: triplet VL fermions; orange dotted line: adjoint triplet VL fermions.}
\label{fig:g2_doubs}
\end{figure}
Note that in Model~5 (magenta dashed) $Y_D\approx 2$ barely allows the model to sit inside the $2\sigma$ region for \gmtwo.
As we discussed above, since in the Higgs-resonance either the allowed Yukawa coupling for $\abund\approx 0.12$ is much smaller than 2,
or the fermion mass must be larger than 100\gev, it follows that in the Higgs-resonance there is no common
parameter space for \gmtwo\ and dark matter.
Conversely in Model~7 (blue dot-dashed), for $Y_T\approx 2$ the model sits generally
above the $2\sigma$ region for \gmtwo. Only the significant drop in the Yukawa coupling necessary to get $\abund\approx 0.12$
in the Higgs resonance can bring its value back into the allowed region.
We finally comment on the numerical results we get for \textbf{Model~9}, characterized
by the mixing of the adjoint triplet fermions and the doublet fermions. As we mentioned when we introduced \refeq{adj_mix},
several substantial contributions to \gmtwo\ arise in this model,
as the neutral scalar/charged fermion and pseudoscalar/charged fermion contributions sum up, and one also has the positive contribution from the mixing heavy neutrinos and charged scalar. As a consequence, solutions to the \gmtwo\ anomaly
can be potentially found in the large dark-matter mass region, $m_{\textrm{DM}}\gsim 800\gev$.
However, since the Yukawa coupling is always quite limited in size,
the solutions we found in our scans are all characterized by large mixing angles, and inevitably fail to pass the constraints from EWPOs.
Thus, up to the possibility of having missed some fine-tuned corners of the parameter space, we conclude that there is no simultaneous solution for \gmtwo\ and dark matter in Model~9.
\section{Summary and conclusions\label{sec:summary}}
In this paper we have drawn some predictions for future measurements of \gmtwo\ under the hypothesis that
the anomaly measured at BNL will be confirmed and that the same underlying BSM physics is responsible for
the relic abundance of dark matter in the Universe.
To investigate these scenarios, we have
constructed a set of renormalizable, SU(2)$\times$U(1) invariant extensions of the SM,
each comprising inert $\mathbb{Z}_2$-odd scalar fields and one or more VL pair of colorless fermions
that communicate to the SM muons through Yukawa-type interactions.
Our new sectors are classified according to their transformation properties under the SM gauge group: real singlet,
complex singlet, and doublet scalars, with all possible types of VL fermions allowed by the gauge symmetry. All
models have been systematically confronted with a variety of experimental constraints:
LEP mass bounds, direct LHC searches, electroweak precision observables, and direct searches for dark matter.
In general, the presence of a muon portal introduces a well known $t$-channel bulk mechanism for the dark matter relic density that
extends the widely studied Higgs portal and allows one to evade strong bounds from direct detection experiments.
In the case of a real singlet scalar dark matter particle, we find that before applying the LHC bounds
both relic density and \deltagmtwomu\ can be accommodated
for $m_{\textrm{DM}}\approx 40-160\gev$, provided VL fermions are lighter than 350\gev\ and the Yukawa coupling exceeds $\sim1.2$. The same pattern is observed for singlet and doublet fermions, since in both cases only the charged component contributes to the anomalous magnetic moment of the muon. When LHC bounds are applied, the parameter space is in large part excluded by the ATLAS 2-lepton + missing $E_T$ search, except for the region where the mass difference between the dark matter scalar and fermion drops below $\sim 70\gev$.
This latter region is extensively tested by the CMS 2 soft leptons + missing $E_T$ search,
which excludes all the points with Yukawa coupling smaller than $\sim1.5$.
Interestingly, future high-precision experiments like GigaZ and TLEP have the potential to probe the remaining untested region entirely,
as the new sector generates small but non-zero corrections to the $Z\mu\bar{\mu}$ vertex.
If the singlet scalar is complex, the region where \gmtwo\ and relic density are satisfied extends down to around 10\gev\ before the LHC bounds are applied, as additional annihilation channels are open due to the presence of a pseudoscalar particle in the spectrum.
The lower bound on the allowed Yukawa coupling is reduced to $\sim 0.5$, since there are two Yukawa couplings summing up.
For the same reason, fermions up to $\sim 500\gev$ are allowed since there are two contributions to \gmtwo.
For both the real and complex singlet scalar, we have additionally allowed the singlet and doublet VL fermions to mix
through interactions with the SM Higgs, thus introducing a source of chiral-symmetry violation that,
by being proportional to the mass of the heavy leptons, can boost \deltagmtwomu.
The anomaly can thus be accommodated for masses up to $\sim 3\tev$. The same effect, however,
generates large contributions to the EWPOs that, for the large fermion mixing, exclude part of the parameter space.
In particular, we find that in the real scalar case with mixing VL fermions the viable part of the parameter space
can be probed almost entirely by a combination of the LHC, dark matter direct detection, and future electroweak precision experiments.
The parameter space is more constrained by the relic density in cases with an SU(2) scalar doublet.
Typical masses range from $m_{\textrm{DM}}\approx 40\gev$ to the Higgs-resonance, $m_{\textrm{DM}}\approx m_h/2$.
Most of the parameter space is almost entirely tested by LHC 2-lepton searches, except for the region of compressed spectra, when the new fermions and scalars are almost degenerate.
Specific properties arise in the case with SU(2) triplet fermions where,
thanks to the well known presence of a doubly charged lepton in the spectrum, which can enhance the calculation of \deltagmtwomu, the parameter space is confined to Higgs resonance.
Overall, our study shows that scenarios with one type of BSM scalar and fermions, which in general can accommodate \gmtwo\ for a
relatively large range of masses and Yukawa couplings, become strongly constrained when the relic density is added to the set of assumptions. That makes them very predictive in case a positive measurement is confirmed at Fermilab or J-PARC.
That is in general not true, however, for scenarios with singlet-doublet mixing, since the number of free parameters is large enough to accommodate both \gmtwo\ and \abund\ and evade other experimental constraints.
For these scenarios, increased precision measurements of
$Z$-physics observables in future electron-positron colliders will be able to disentangle some of the degeneracies.
\bigskip
\noindent \textbf{Acknowledgments}
\medskip
\noindent We would like to thank Luc Darm\' e for valuable input on the interface of \texttt{SARAH} with \texttt{MultiNest},
Florian Staub for helpful correspondence regarding \texttt{SARAH}, Joachim Brod and Wei-Chih Huang for discussions.
KK is supported in part by the DFG Research Unit FOR 1873 ``Quark Flavour Physics and Effective Field
Theories''.
The work of EMS is supported by the Alexander von Humboldt Foundation.
The use of the CIS computer cluster at the National Centre for Nuclear Research in Warsaw is gratefully acknowledged.
\bibliographystyle{JHEP}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 9,308 |
est une doubleuse japonais et chanteuse d'Hokkaido née le 23 juillet 1995. Elle est affiliée avec l'Agence IAM. Elle est connue pour ses rôles tels que Mari Ohara dans Love Live! Sunshine!! et Jashin-chan dans Dropkick sur mon diable !, en plus d'être une idole du groupe Aqours.
Carrière
Aina Suzuki espérait travailler dans le doublage d'anime depuis ses années d'école primaire, mais pensait que sa voix n'était peut-être pas assez bonne. Un tournant s'est produit lorsque, dans sa année de lycée, elle est devenue finaliste (et l'une des 3 meilleures personnes du pays) du Grand Prix All-Japan Anisong. À cette époque, son désir de devenir chanteuse d'anime s'intensifie et elle en fait son objectif. Elle a déménagé à Tokyo dès qu'elle a obtenu son diplôme d'études secondaires. Elle a révélé plus tard que, si elle avait remporté le Grand Prix Anisong, elle aurait fait ses débuts l'année suivante (en 2014) et aurait pu participer à un tournoi qui se tenait à la Yokohama Arena ; cela a été révélé en février 2017, après le succès d' Aqours LoveLive.
Après son arrivée à Tokyo, Aina est entrée à l'International Media Institute (un centre de formation de doubleurs associé à l'agence IAM). Alors qu'elle s'amusait dans sa formation et la trouvait enrichissante, il y avait encore des moments où elle manquait de confiance en ses capacités vocales. Cependant, après quelques encouragements de Ryō Horikawa (directeur en chef de l'institut), elle a commencé à avoir plus confiance. Cela a ravivé son désir de devenir une chanteuse d'anime et doubleuse après son arrivée à Tokyo.
Elle s'est affiliée à l'agence IAM pour apprendre à la fois des chanteurs et des doubleurs. Elle a fait ses débuts en doublage en 2014. En 2015, elle obtient un rôle dans la franchise Love Live! puis dans la nouvelle série, Love Live! Sunshine!! sous le nom de Mari Ohara, et ses activités en tant que qu'idol du groupe d'Aqours commencèrent.
En mars 2017, elle et les autres membres d'Aqours ont reçu un prix de chant lors des Voice Actor Awards.
Le 22 janvier 2020, son premier album solo, 「ring A ring」, est sorti. Elle a joué le rôle de Kana Hoshisato dans la série animée Hatena Illusion, où elle a également interprété le thème de fin de la série . Elle a lancé son fanclub officiel, "Ai catwalk", le même jour.
Filmographie
Animes
2014 : Akame ga Kill! : Mez
2015 : Castle Town Dandelion : Shiori Sakurada, Mina Shinonome
2015 : YuruYuri San Hai! : Membre A du Club d'athlétisme
2016 : Onigiri : Shizuka Gozen
2016 : Three Leaves, Three Colors : Asako Kondō
2016 : Love Live! Sunshine!! : Mari Ohara
2016 : Sweetness and Lightning : Chiyo
2016 : Crane Game Girls : Newscaster
2016 : Crane Game Girls Galaxy : Tokiko
2017 : Clione no Akari : Kaho Ichinose
2017 : Love Live! Sunshine!! : Mari Ohara
2018 : Magical Girl Site : Rina Shioi
2018 : Alice or Alice : Yamirii
2018 : Dropkick on My Devil! : Jashin-chan
2018 : Release the Spyce : Byakko
2019 : Rainy Cocoa side G : Meru
2019 : The Quintessential Quintuplets : Hongō
2019 : Z/X Code reunion : Shuri Kijino
2020 : Hatena Illusion : Kana Hoshisato
2020 : Dropkick on My Devil! Dash : Jashin-chan
2020 : Monster Girl Doctor : Eris
2020 : Iwa-Kakeru! -Sport Climbing Girls- : Sayo Yotsuba
2021-2023 : Arrête de me chauffer, Nagatoro : Yoshi
2021 : PuraOre! Pride of Orange : Shino Ukita
2021 : Rumble Garanndoll : Yuki Aoba
2022 : Teppen!!!!!!!!!!!!!!! Laughing 'til You Cry : Mone Ishiya
2022 : Dropkick on My Devil! X : Jashin-chan
2022 : Tokyo Mew Mew New : Miwa Honjō
2023 : Genjitsu no Yohane: Sunshine in the Mirror : Mari Ohara
OAV/ONA
2016 : Filles Kaiju : Miclas/Miku Ushimaru
2018-2019 : Saint Seiya: Saintia Shō : Equuleus Shō
Films d'animation
2016 : Galactic Armored Fleet Majestic Prince: Wings to the Future : Ahn Medikum
2019 : Love Live! Sunshine!! The School Idol Movie: Over the Rainbow : Mari Ohara
Jeux
2015 : Onigiri Hyakkiyagyō : Shizuka Gozen
2015 : Princess Maker : Cassandra
2015 : Xuccess Heaven : Isa Kotobuki
2015 : Toys Drive : Mabel Small
2015 : Shooting Girl : Nanami Fuwa, Tekkou M. Misa, Miyo Asato
2016 : Love Live! School Idol Festival : Mari Ohara
2016 : Onigiri: Nihon wo Tabisuru RPG : Shizuka Gozen
2016 : Mon Musume☆wa〜Remu : Micuras
2016 : Megami Meguri : Konohana Sakuyahime
2016 : Magic Library Qurare : Moreau
2016 : Girls' Frontline : Luger P08 Handgun
2017 : Knights Chronicle : Lena, Olive, Meril
2017 : Q & Q Answers : Wizard of Oz
2017 : Yuki Yuna is a Hero Hana Yui no Kirameki : Kōri Chikage
2018 : Grand Chase: Dimensional Chaser : Lime Serenity
2018 : Granblue Fantasy: Love Live! Sunshine!! Aqours Sky-High! : Mari Ohara
2019 : Tenka San Bun : Princess Cai Yan
2019 : Shadowverse CCG : Mari Ohara
2019 : Love Live! School Idol Festival ALL STARS : Mari Ohara
2022 : Azur Lane : IJN Sakawa
Drama CD
2015 : Shiden Aratame no Maki : Kabosu
2015 : Saint Seiya Seintia Shō : Shoko
2016 : Nogi Wakaba wa Yusha de Aru Vol. 1 : Kōri Chikage
2016 : Nogi Wakaba wa Yusha de Aru Vol. 2 : Kōri Chikage
2016 : Joshi Shōgakusei wa Hajimemashita P ! : Riri
Manga numérique
2015 : Chocolatier Shitsuren : Matsuri Koyurugi
Web radio
3 avril 2016 – 4 avril 2017 : New Gin Group présente MAO à Suzuki sur JOQR Chō ! A&G+
8 avril 2016 à aujourd'hui : Yumiri à Aina no Mogumogu Communications sur Onsen
9 avril 2016 – 25 septembre 2017 : Les filles A&G battent Queenty sur Cho ! A&G+
Discographie
Albums
Singles
Liens externes
Site officiel
Profil officiel de l'agence
Notes et références
Chanteuse japonaise de pop
Naissance en juillet 1995
Seiyū | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 321 |
package org.apache.flex.compiler.internal.codegen.js.goog;
import static org.hamcrest.core.Is.is;
import static org.junit.Assert.assertThat;
import java.io.File;
import java.util.List;
import org.apache.flex.compiler.driver.IBackend;
import org.apache.flex.compiler.internal.driver.js.goog.GoogBackend;
import org.apache.flex.compiler.internal.test.ASTestBase;
import org.apache.flex.utils.FilenameNormalization;
import org.junit.Test;
/**
* This class tests the production of valid 'goog' JS code from an external
* project.
*
* @author Erik de Bruin
*/
public class TestGoogProject extends ASTestBase
{
private static String projectDirPath = "goog/projects";
@Test
public void test_imports()
{
String testDirPath = projectDirPath + "/imports";
String fileName = "Case";
List<String> compiledFileNames = compileProject(fileName, testDirPath);
assertProjectOut(compiledFileNames, testDirPath);
}
@Override
protected void addSourcePaths(List<File> sourcePaths)
{
sourcePaths.add(new File(FilenameNormalization.normalize("test-files"
+ File.separator + projectDirPath + "/imports")));
super.addSourcePaths(sourcePaths);
}
@Override
protected IBackend createBackend()
{
return new GoogBackend();
}
protected void assertProjectOut(List<String> compiledFileNames,
String testDirPath)
{
if (compiledFileNames.size() == 0)
{
assertThat("No Compiled files", is("Compiled Files"));
return;
}
for (String compiledFileName : compiledFileNames)
{
String compiledFilePath = tempDir.getAbsolutePath()
+ File.separator + testDirPath + File.separator
+ compiledFileName + "_output" + "."
+ backend.getOutputExtension();
String compiledResult = readCodeFile(new File(compiledFilePath));
//System.out.println(compiledResult);
String expectedFilePath = new File("test-files").getAbsolutePath()
+ File.separator + testDirPath + File.separator
+ compiledFileName + "_result" + "."
+ backend.getOutputExtension();
String expectedResult = readCodeFile(new File(expectedFilePath));
assertThat(compiledResult, is(expectedResult));
}
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 9,973 |
{"url":"http:\/\/en.wikibooks.org\/wiki\/User:JMRyan\/Sandbox","text":"# User:JMRyan\/Sandbox\n\n## Example truth table\n\n $\\mathrm{P}\\,\\!$ $\\lnot \\mathrm{P}\\,\\!$ T F F T\n\n## Example derivation\n\n 1 $\\mathrm{P} \\land \\mathrm{Q} \\,\\!$ Premise 2 $\\mathrm{P} \\lor \\mathrm{R} \\rightarrow \\mathrm{S}\\,\\!$ Premise 3 $\\mathrm{S} \\land \\mathrm{Q} \\rightarrow \\mathrm{T}\\,\\!$ Premise 4 $\\mathrm{P}\\,\\!$ 1 KE 5 $\\mathrm{Q}\\,\\!$ 1 KE 6 $\\mathrm{P} \\lor \\mathrm{R}\\,\\!$ 4 DI 7 $\\mathrm{S}\\,\\!$ 2, 6 CE 8 $\\mathrm{S} \\land \\mathrm{Q}\\,\\!$ 5, 7 KI 9 $\\mathrm{T}\\,\\!$ 3, 8 CE\n\n## Example subderivation\n\n 1. $(\\mathrm{P} \\rightarrow \\mathrm{Q}) \\rightarrow\\mathrm{R}\\,\\!$ Premise 2. $\\mathrm{S} \\land \\mathrm{Q}\\,\\!$ Premise\n 3. $\\mathrm{P} \\rightarrow \\mathrm{Q}\\,\\!$ Assumption 4. $\\mathrm{Q}\\,\\!$ 2 KE\n 5 $\\mathrm{P} \\rightarrow \\mathrm{Q}\\,\\!$ 3-4 CI 6 $\\mathrm{R}\\,\\!$ 1, 5 CE\n\n## Logical form\n\nWe will not try to explain fully what logical form is. Both natural languages such as English and logical languages such as $\\mathcal{L_S}\\,\\!$ exhibit logical form. A primary purpose of a logical language is to make the logical form explicit by having it correspond directly with the grammar. In the context of $\\mathcal{L_S}\\,\\!$, a logical form is indicated by a metalogical expression containing no sentence letters but containing metalogical variables (in our convention, Greek letters). A single formula can have several logical forms of varying degrees of explicitness or granularity. For example, the formula $((\\mathrm{P^0_0} \\land \\mathrm{Q^0_0}) \\rightarrow \\mathrm{R^0_0})\\,\\!$ has the following three logical forms:\n\n$((\\phi \\land \\psi) \\rightarrow \\chi)\\,\\!$\n$(\\phi \\rightarrow \\psi)\\,\\!$\n$\\phi\\,\\!$\n\nObviously, the first of these is the most explicit or fine-grained.\n\nWe say that a formula is an instance of a logical form. For example, the formula $(\\phi \\rightarrow \\psi)\\,\\!$ has, among many others, the following instances.\n\n$(\\mathrm{P^0_0} \\rightarrow \\mathrm{Q^0_0})\\,\\!$\n$((\\mathrm{P^0_0} \\land \\mathrm{Q^0_0}) \\rightarrow \\mathrm{R^0_0})\\,\\!$\n$((\\mathrm{P^0_0} \\land \\mathrm{Q^0_0}) \\rightarrow (\\mathrm{Q^0_0} \\lor \\mathrm{R^0_0}))\\,\\!$\n\n## Formal semantics\n\nThe formal semantics for a formal language such as $\\mathcal{L_S}\\,\\!$ goes in two parts.\n\n\u2022 Rules for specifying an interpretation. An interpretation assigns semantic values to the non-logical symbols of a formal syntax. The semantics for a formal language will specify what range of vaules can be assigned to which class of non-logical symbols. $\\mathcal{L_S}\\,\\!$ has only one class of non-logical symbols, so the rule here is particularly simple. An interpretation for a sentential language is a valuation, namely an assignment of truth values to sentence letters. In predicate logic, we will encounter interpretations that include other elements in addition to a valuation.\n\u2022 Rules for assigning semantic values to larger expressions of the language. For sentential logic, these rules assign a truth value to larger formulae based on truth values assigned to smaller formulae.For more complex syntaxes (such as for predicate logic), values are assigned in a more complex fashion.\n\nAn extended valuation assigns truth values to the molecular formulae of $\\mathcal{L_S}\\,\\!$ (or similar sentential language) based on a valuation. A valuation for sentence letters is extended by a set of rules to cover all formulae.","date":"2014-07-24 21:36:06","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\": 30, \"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\": 0.6968024969100952, \"perplexity\": 746.2853659686729}, \"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-2014-23\/segments\/1405997891953.98\/warc\/CC-MAIN-20140722025811-00126-ip-10-33-131-23.ec2.internal.warc.gz\"}"} | null | null |
\section{Introduction}\label{sec:introduction}
A two-dimensional word is a generalization of the notion of a word from a one-dimensional string to an array or matrix of symbols. Two-dimensional words are used as the input to two-dimensional automata, whose input heads move through the input word in a variety of ways, depending on the model.
We may define special projection operations on two-dimensional words that produce either the first row or the first column of the given word. In this way, a projection can be thought of as a conversion from a two-dimensional word to a one-dimensional word. Note that projection operations are lossy (i.e., all but the first row/column of the two-dimensional word is lost when a projection operation is applied).
The row projection operation has been studied in the past \cite{Anselmo2011ClassificationTilingRecognizable, Latteux1997ContextSensitiveRecognizable}, with a particular focus on formal language theory. (We summarize previous results in Section~\ref{subsec:prevwork}.) However, no work has yet been done on investigating projections of languages recognized by various two-dimensional automaton models.
Our results are as follows. We show that both the row and column projections of languages recognized by (four-way) two-dimensional automata are exactly context-sensitive. We also show that the column projections of languages recognized by unary three-way two-dimensional automata belong to the class $\NSPACE(O(\log(n)))$. Finally, we study the state complexity of projection languages, focusing on the state complexity of union and diagonal concatenation for projections of languages recognized by two-way two-dimensional automata.
\section{Preliminaries}\label{sec:prelim}
A two-dimensional word is a matrix of symbols from some alphabet $\Sigma$. If a two-dimensional word $w$ has $m$ rows and $n$ columns, then we say that $w$ is of dimension $m \times n$. A two-dimensional language consists of two-dimensional words. There exist two special languages in two dimensions: $\Sigma^{m \times n}$ consists of all words of dimension $m \times n$ for some fixed $m, n \geq 1$, and $\Sigma^{**}$ consists of all two-dimensional words.
The row projection (resp., column projection) of a two-dimensional language $L$ is the one-dimensional language consisting of the first rows (resp., first columns) of all two-dimensional words in $L$. We formalize these definitions in terms of individual two-dimensional words. In the following pair of definitions, we assume we have an $m \times n$ two-dimensional word
\begin{equation*}
w =
\begin{bmatrix}
a_{1,1} & \cdots & a_{1,n} \\
\vdots & \ddots & \vdots \\
a_{m,1} & \cdots & a_{m,n}
\end{bmatrix}
.
\end{equation*}
\begin{definition}[Row projection]
Given a two-dimensional word $w \in \Sigma^{m \times n}$, the row projection of $w$ is the one-dimensional word
\begin{equation*}
\rowp{w} = a_{1,1} a_{1,2} \cdots a_{1,n},
\end{equation*}
where $a_{1,1}, \dots, a_{1,n} \in \Sigma$. The row projection of a two-dimensional language $L$, denoted $\rowp{L}$, is produced by taking the row projections of all words $w \in L$.
\end{definition}
\begin{definition}[Column projection]
Given a two-dimensional word $w \in \Sigma^{m \times n}$, the column projection of $w$ is the one-dimensional word
\begin{equation*}
\colp{w} = a_{1,1} a_{2,1} \cdots a_{m,1},
\end{equation*}
where $a_{1,1}, \dots, a_{m,1} \in \Sigma$. The column projection of a two-dimensional language $L$, denoted $\colp{L}$, is produced by taking the column projections of all words $w \in L$.
\end{definition}
Note that one may view the column projection operation as taking the ``transpose" of the first column of a two-dimensional word in order to produce a one-dimensional string. The row projection operation has been considered in previous papers, where it was called the ``frontier" of a word or language \cite{Latteux1997ContextSensitiveRecognizable}.
Two-dimensional words are used as the input to two-dimensional automata. When we provide such a word as input, we surround the outer border of the word with a special boundary symbol \#. (For example, the upper-left boundary symbol is at position $(0,0)$ and the lower-right boundary symbol is at position $(m+1, n+1)$ in the word.) The boundary symbol prevents the input head of the automaton from leaving the input word.
The formal definition of a two-dimensional automaton is as follows:
\begin{definition}[Two-dimensional automaton]\label{def:2DFA}
A two-dimensional
automaton is a tuple $(Q, \Sigma, \delta, q_{0}, q_{\rm accept})$, where $Q$ is a finite set of states, $\Sigma$ is the input alphabet (with $\# \not\in \Sigma$ acting as a boundary symbol), $\delta: (Q \setminus \{q_{\rm accept}\}) \times (\Sigma \cup \{\#\}) \to Q \times \{U, D, L, R\}$ is the partial transition function, and $q_{0}, q_{\rm accept} \in Q$ are the initial and accepting states, respectively.
\end{definition}
The specific model in Definition~\ref{def:2DFA} is sometimes referred to as a ``four-way two-dimensional automaton". In this paper, we also consider three-way and two-way variants of two-dimensional automata. In the three-way case, the transition function is restricted to use only the directions $\{D, L, R\}$. Likewise, in the two-way case, the transition function uses only the directions $\{D, R\}$. We may optionally include a direction $N$, which corresponds to ``no move" and does not change the recognition power of the model. We abbreviate each automaton model as \textsf{2(D/N)FA-kW(-1$\Sigma$)}, where \textsf{D/N} denotes deterministic/nondeterministic, \textsf{k} denotes the directions of movement, and \textsf{1$\Sigma$} denotes a unary alphabet.
In later sections, we will use the notation $L_{\textsf{C}}$ to denote the set of languages recognized by some automaton model \textsf{C}.
\subsection{Previous Work}\label{subsec:prevwork}
A number of survey articles and other works have been written about both two-dimensional languages \cite{GiammarresiRestivo19972DLanguages, Morita20042DLanguages} and two-dimensional automaton models \cite{Inoue19912DAutomataSurvey, Rosenfeld1979PictureLanguages, Smith2019TwoDimensionalAutomata}. Previous work on projection operations has taken two perspectives: language-theoretic and automata-theoretic.
\paragraph{Language-theoretic.}
One of the earliest results on two-dimensional row projection, due to Latteux and Simplot \cite{Latteux1997ContextSensitiveRecognizable}, showed that a one-dimensional language $F$ is context-sensitive if and only if there exists a two-dimensional language $L \in \textsf{REC}$ such that $F = \rowp{L}$. The class $\textsf{REC}$ denotes the class of tiling-recognizable two-dimensional languages, or languages whose words can be defined by a finite set of $2 \times 2$ tiles \cite{GiammarresiRestivo1992RecognizablePictureLanguages}.
Anselmo et al.\ \cite{Anselmo2011ClassificationTilingRecognizable} later extended this direction of research to give equivalent characterizations for unambiguous and deterministic context-sensitive one-dimensional languages; namely, $F$ is unambiguous (resp., deterministic) context-sensitive if and only if there exists $L \in \textsf{UREC}$ (resp., $L \in \textsf{Row-UREC}_{t}$) such that $F = \rowp{L}$. The classes \textsf{UREC} and $\textsf{Row-UREC}_{t}$ are subclasses of $\textsf{REC}$, where \textsf{UREC} consists of languages defined by an unambiguous tiling system \cite{GiammarresiRestivo1992RecognizablePictureLanguages} and $\textsf{Row-UREC}_{t}$ consists of languages that are ``top-to-bottom row-unambiguous"; Anselmo et al.\ give a formal definition of the class $\textsf{Row-UREC}_{t}$ in an earlier paper \cite{Anselmo2010DeterministicUnambiguousFamilies}.
Some classes smaller than $\textsf{Row-UREC}_{t}$ (namely, the class of deterministic recognizable languages $\textsf{DREC}$ \cite{Anselmo2010DeterministicUnambiguousFamilies}) have no known characterization in terms of one-dimensional language classes.
\paragraph{Automata-theoretic.}
A (four-way) two-dimensional automaton can recognize whether or not an input word has either an exponential or a doubly-exponential side length \cite{KariMoore2004RectanglesAndSquares}. It is well-known that the language of unary strings of exponential length is context-sensitive but not context-free \cite{HopcroftUllman1979IntroAutomataTheory}. This fact implies that, if $L$ is a language recognized by a four-way two-dimensional automaton, then both $\rowp{L}$ and $\colp{L}$ may be non-context-free, even in the unary case.
Restricting ourselves to the three-way model, we obtain results that differ based on the projection operation under consideration. Let $L$ be a unary language. If $L$ is recognized by a nondeterministic three-way two-dimensional automaton, then $\rowp{L}$ is regular. On the other hand, if $L$ is recognized by a deterministic three-way two-dimensional automaton, then $\colp{L}$ need not be regular \cite{SmithSalomaa20192D3WProperties}. These results apply also for general alphabets. We can improve the bound by showing that $\colp{L}$ may be non-context-free for three-way two-dimensional automata, since the language $L_{\text{composite}}$ used in the proof of the non-regularity result is context-sensitive in both the unary and general-alphabet cases \cite{Hartmanis1968RecognitionPrimesAutomata, Salomaa1969TheoryOfAutomata, Salomaa1973FormalLanguages}.
Finally, for the two-way model, we know that if any language $L$ is recognized by a nondeterministic two-way two-dimensional automaton, then both $\rowp{L}$ and $\colp{L}$ are regular \cite{SmithSalomaa20192D3WProperties}. This applies also to deterministic and unary two-way two-dimensional automata.
\section{Recognition Power and Space Complexity}\label{sec:recognition}
Before we proceed further, we recall a few elementary definitions. These definitions may be found in any standard textbook on the theory of computation; e.g., Sipser~\cite{Sipser1997Computation}.
Recall that a linear-bounded automaton is a nondeterministic Turing machine whose computation is restricted only to the cells of its input tape that originally contained input symbols. A configuration of a linear-bounded automaton $\mathcal{M}$ is a sequence of tape symbols of $\mathcal{M}$, where the currently-scanned symbol is distinguished by adding the current state $q$ as a subscript to the symbol. An accepting computation history of $\mathcal{M}$ on an input string $w$ is a sequence of configurations $C_{0}, C_{1}, \dots, C_{k}$ that $\mathcal{M}$ enters as it performs its computation on $w$, where $C_{0}$ is the initial configuration of $\mathcal{M}$ on $w$, $C_{i+1}$ is obtained from $C_{i}$ in one computation step of $\mathcal{M}$ for all $0 \leq i \leq k - 1$, and $C_{k}$ is an accepting configuration.
Finally, a computation table of $\mathcal{M}$ on an input word $w$ is a two-dimensional word where the rows of the word are configurations $C_{0}, C_{1}, \dots, C_{k}$ appearing in the computation history of $\mathcal{M}$ on $w$.
From previous work, we know that $\rowp{L}$ is context-sensitive when $L \in \textsf{REC}$ \cite{Latteux1997ContextSensitiveRecognizable}. It is known that $L_{\textsf{2DFA-4W}} \subset L_{\textsf{2NFA-4W}} \subseteq \textsf{REC}$ \cite{BlumHewitt19672DAutomata, Inoue1992CharacterizationRecognizable}, so $\rowp{L}$ is also context-sensitive when $L \in L_{\textsf{2DFA-4W}}$. The following theorem proves the other direction of this inclusion.
\begin{theorem}\label{thm:CSLin2DFA4W}
Let $K$ be a context-sensitive language. Then there exists $L \in L_{\textsf{2DFA-4W}}$ such that $K = \rowp{L}$.
\begin{proof}
Let $\mathcal{M}$ be a linear-bounded automaton recognizing the language $K$.
We construct a deterministic four-way two-dimensional automaton $\mathcal{A}$ that checks whether the rows of its input word $w$ are configurations representing an accepting computation history of $\mathcal{M}$\footnote{Since the row projection of $w$ cannot contain state information, an initial configuration of $\mathcal{M}$, $a_{1, q_{0}} a_{2} \dots a_{m}$, is encoded on the first row as the string $a_{1} a_{2} \dots a_{m}$. The computation of $\mathcal{A}$ implicitly assumes that this string represents the initial configuration.}.
Given a two-dimensional word $w$ over an alphabet $\Sigma$ as input, where $w$ is of dimension $m \times n$, $\mathcal{A}$ checks each of the following properties:
\begin{enumerate}
\item The first row of $w$ contains only alphabet symbols from $\Sigma$.
\item The last row of $w$ contains, as a subscript, an accepting state of $\mathcal{M}$.
\item\label{itm:prop3} For each $i$, where $1 \leq i \leq m - 1$, the configuration $C_{i}$ represented by the $(i + 1)$st row can be obtained in one computation step of $\mathcal{M}$ from the preceding configuration $C_{i-1}$ represented by the $i$th row.
For this property, $\mathcal{A}$ must check the following:
\begin{enumerate}
\item Any tape symbol in $C_{i}$ different from the corresponding symbol in $C_{i-1}$ was first scanned by the state in $C_{i-1}$; and
\item Each tape symbol in $C_{i}$ different from the corresponding symbol in $C_{i-1}$ corresponds to one valid computation step of $\mathcal{M}$.
\end{enumerate}
\end{enumerate}
At the beginning of its computation, $\mathcal{A}$ assumes that $\mathcal{M}$ is scanning the leftmost symbol in the first row of $w$ from its initial state. Then, according to Property~\ref{itm:prop3}, $\mathcal{A}$ checks that the configuration represented by the second row of $w$ can be obtained in one computation step of $\mathcal{M}$ under this assumption.
The automaton $\mathcal{A}$ checks Property~\ref{itm:prop3} in the following way. For each $1 \leq i \leq m - 1$, the input head of $\mathcal{A}$ traverses the $i$th and $(i+1)$st rows in a down-and-up motion from the left boundary to the right boundary. Upon reaching a boundary, the input head returns to the input word and checks the next pair of rows. This traversal procedure is illustrated in Figure~\ref{fig:inputheadmovement}. Each time the input head moves downward or upward within a column, it either compares the symbols in the $i$th and $(i+1)$st rows to verify that they match or, if it is at a position where the current computation step of $\mathcal{M}$ applies, it checks that the computation step is valid according to the transition relation of $\mathcal{M}$.
If each of the preceding properties holds, then $w$ encodes a computation table corresponding to an accepting computation of $\mathcal{M}$ and $\mathcal{A}$ accepts $w$.
Since linear-bounded automata recognize all context-sensitive languages, and since $\rowp{L(\mathcal{A})}$ is the input string to $\mathcal{M}$, the result follows.
\end{proof}
\end{theorem}
\begin{figure}
\centering
\begin{tikzpicture}
\matrix[matrix of nodes,nodes={inner sep=4pt,text width=.75cm,align=center,minimum height=.75cm}]{
\node(a0){\#}; & \node(a1){\#}; & \node(a2){\#}; & \node(a3){\#}; & \node(a4){\#}; & \node(a5){\#}; & \node(a6){\#}; \\
\node(a00){\#}; & \node(a01){\texttt{d}}; & \node(a02){\texttt{a}}; & \node(a03){\texttt{b}}; & \node(a04){\texttt{c}}; & \node(a05){\texttt{a}}; & \node(a06){\#}; \\
\node(a10){\#}; & \node(a11){\texttt{b}}; & \node(a12){\texttt{a}$_{q_{1}}$}; & \node(a13){\texttt{b}}; & \node(a14){\texttt{c}}; & \node(a15){\texttt{a}}; & \node(a16){\#}; \\
\node(a20){\#}; & \node(a21){\texttt{b}}; & \node(a22){\texttt{d}}; & \node(a23){\texttt{b}$_{q_{2}}$}; & \node(a24){\texttt{c}}; & \node(a25){\texttt{a}}; & \node(a26){\#}; \\
\node(a30){\#}; & \node(a31){\texttt{b}}; & \node(a32){\texttt{d}$_{q_{1}}$}; & \node(a33){\texttt{c}}; & \node(a34){\texttt{c}}; & \node(a35){\texttt{a}}; & \node(a36){\#}; \\
};
\draw[->] (a01)+(0mm, -2.5mm) -- +(0mm, -5.5mm);
\draw[->] (a11)+(3.5mm, 0mm) -- +(6.5mm, 0mm);
\draw[->] (a12)+(0mm, 2.5mm) -- +(0mm, 5.5mm);
\draw[->] (a02)+(3.5mm, 0mm) -- +(6.5mm, 0mm);
\draw[->] (a03)+(0mm, -2.5mm) -- +(0mm, -5.5mm);
\draw[->] (a13)+(3.5mm, 0mm) -- +(6.5mm, 0mm);
\draw[->] (a14)+(0mm, 2.5mm) -- +(0mm, 5.5mm);
\draw[->] (a04)+(3.5mm, 0mm) -- +(6.5mm, 0mm);
\draw[->] (a05)+(0mm, -2.5mm) -- +(0mm, -5.5mm);
\draw[->] (a15)+(3.5mm, 0mm) -- +(6.5mm, 0mm);
\draw[->] (a16)+(0mm, -2.5mm) -- +(0mm, -5.5mm);
\draw[->] (a26)+(-3.5mm, 0mm) -- +(-6.5mm, 0mm);
\end{tikzpicture}
\caption{An illustration of the movement of the input head of the automaton $\mathcal{A}$, constructed in Theorem~\ref{thm:CSLin2DFA4W}.}
\label{fig:inputheadmovement}
\end{figure}
The proof of Theorem~\ref{thm:CSLin2DFA4W} also works for nondeterministic two-dimensional automata. Moreover, it is straightforward to show that $\colp{L}$ is context-sensitive when $L \in L_{\textsf{2DFA-4W}}$, and so Theorem~\ref{thm:CSLin2DFA4W} can similarly be adapted to apply to column projection languages. These observations, taken together, lead to the following characterization.
\begin{corollary}\label{cor:4WautomataCSL}
Both the row and column projections of languages recognized by four-way two-dimensional automata consist exactly of the class of context-sensitive languages.
\end{corollary}
\subsection{Three-Way Two-Dimensional Automata}\label{subsec:recognition3W}
Recall from Section~\ref{subsec:prevwork} that the row projection of any language accepted by a three-way two-dimensional automaton $\mathcal{A}$ is regular. Since $\textsf{REG} \in \DSPACE(O(1))$ \cite{Shepherdson1959TwoWayReduction}, we immediately get that $\rowp{L(\mathcal{A})} \in \DSPACE(O(1))$ as well.
We further noted in the same section that the column projection of a language in $L_{\textsf{2NFA-3W-1$\Sigma$}}$ may be non-context-free, depending on the choice of language. Here, we investigate the space complexity of column projection languages for $L_{\textsf{2NFA-3W-1$\Sigma$}}$.
In what follows, we use the notation $\rowsubword_{i}[r, s]$ to denote the subword occurrence of the $i$th row starting at index $r$ and ending at index $r + s$; that is, a subword of length $s + 1$. Since we are considering unary languages, all symbols of $\rowsubword_{i}[r, s]$ are identical and independent of the value $i$. Thus, by ``subword occurrence", we mean the cells of the $i$th row at indices $r$ through $r + s$ inclusive.
The following technical lemma states that every string $w$ in the column projection of a language in $L_{\textsf{2NFA-3W-1$\Sigma$}}$ is a projection of a two-dimensional word $z$, where the number of columns of $z$ is at most some constant multiple of the length of $w$. The proof, intuitively speaking, shows that when we have a two-dimensional word containing a large number of columns with no downward moves, we can remove some of these columns and simulate the same computation of the three-way two-dimensional automaton.
\begin{lemma}\label{lem:reduceworddimension}
Let $\mathcal{A}$ be a unary three-way two-dimensional automaton with $k$ states, and consider a word $w \in \colp{L(\mathcal{A})}$. Then there exists a two-dimensional word $z$ with $|w|$ rows and at most $(|w| + 3) \cdot (k^{2^{2k}} + 2)$ columns accepted by $\mathcal{A}$.
\begin{proof}
Let $H = k^{2^{2k}}$. Consider a two-dimensional word $z \in L(\mathcal{A})$ of dimension $|w| \times n_{1}$, where
\begin{equation}\label{eq:n1}
n_{1} > (|w| + 3) \cdot (H + 2).
\end{equation}
Let $C_{z}$ be an accepting nondeterministic computation of $\mathcal{A}$ on input word $z$. Without loss of generality, we may assume that $C_{z}$ accepts at the bottom border of $z$.
By the inequality in Equation~\ref{eq:n1}, the input word $z$ must have $k^{2k} + 1$ consecutive columns such that the computation $C_{z}$ does not make a downward move in any such column. Furthermore, we may assume that these consecutive columns do not include either the first $H$ columns or the last $H$ columns of $z$. That is, there exists $H \leq j \leq (n_{1} - 2H)$ such that the computation $C_{z}$ does not make a downward move in any of the subword occurrences
\begin{equation*}
\rowsubword_{i}[j, H], \ \ i = \{1, \dots, |w|\}.
\end{equation*}
Let $Q$ be the set of states of $\mathcal{A}$ and define $\overline{Q} = \{\overline{q} \mid q \in Q\}$ to be a disjoint copy of states in $Q$. For each column $x \in \{j, j + 1, \dots, j + H\}$, define a function $f_{x}: Q \to 2^{Q \cup \overline{Q}}$ by setting, for all $p \in Q$,
\begin{itemize}
\item $q \in f_{x}(p)$ if, for some $i$, the computation $C_{z}$ on the $i$th row in column $x$ and state $p$ exits the subword occurrence $\rowsubword_{i}[j, H]$ to the left in state $q$; and
\item $\overline{q} \in f_{x}(p)$ if, for some $i$, the computation $C_{z}$ on the $i$th row in column $x$ and state $p$ exits the subword occurrence $\rowsubword_{i}[j, H]$ to the right in state $q$.
\end{itemize}
Note that the computation of $C_{z}$ may visit the subword occurrence multiple times. By our definition, $q \in f_{x}(p)$ if, at some point, $C_{z}$ is in the $x$th column in state $p$ and, when $C_{z}$ next exits $\rowsubword_{i}[j, H]$, it exits to the left in state $q$.
Note also that the accepting computation must exit each subword occurrence $\rowsubword_{i}[j, H]$ either to the left or to the right since, by our choice of $j$, the computation $C_{z}$ makes no downward moves in any of the columns $j, \dots, (j + H)$.
Since the number of functions from $Q$ to $2^{Q \cup \overline{Q}}$ is $H = k^{2^{2k}}$, there exist columns $x_{1}$ and $x_{2}$, $j \leq x_{1} < x_{2} \leq (j + H)$, such that $f_{x_{1}} = f_{x_{2}}$. Moreover, since the computation $C_{z}$ makes no downward moves in any of the columns $j, \dots, (j + H)$, there exists an accepting computation of $\mathcal{A}$ on the two-dimensional word $z'$ obtained by removing the columns $x_{1}, \dots, (x_{2} - 1)$ from $z$.
The above observation relies on our earlier assumption that the designated columns $j, \dots, (j + H)$ are at distance at least $H$ from the left and right borders of the word. For example, consider a situation where $\overline{q} \in f_{x_{2}}(p)$; that is, where the computation starting in column $x_{2}$ and state $p$ exits the subword occurrence to the right in state $q$. When simulating the same computation on the modified word $z'$ starting in column $x_{1}$, the computation could, at some point, move to the left of column $j$. Since $j \geq H$, this guarantees that the computation would not reach the left border.
Altogether, the two-dimensional word $z'$ has $x_{2} - x_{1}$ fewer columns than the original word $z$. By repeated application of the previous argument, we see that $\mathcal{A}$ must accept a two-dimensional word of dimension $|w| \times n_{2}$, where $n_{2} \leq H$.
\end{proof}
\end{lemma}
An application of Lemma~\ref{lem:reduceworddimension} allows us to obtain our main space complexity result for column projections of languages recognized by unary three-way two-dimensional automata.
\begin{theorem}\label{thm:3WunaryautomataNLOGSPACE}
Let $\mathcal{A}$ be a unary three-way two-dimensional automaton. Then $\colp{L(\mathcal{A})} \in \NSPACE(O(\log(n)))$.
\begin{proof}
Suppose $\mathcal{A}$ has $k$ states. We describe the operation of a nondeterministic logspace Turing machine $\mathcal{M}$ recognizing $\colp{L(\mathcal{A})}$.
On input word $w$, $\mathcal{M}$ first writes to its work tape a binary representation of a nondeterministically-chosen natural number $n_{1} \leq (|w| + 3) \cdot (k^{2^{2k}} + 2)$. Since $k$ is constant, this binary representation can be written in space $O(\log(|w|))$.
The machine $\mathcal{M}$ then simulates a nondeterministic computation of $\mathcal{A}$ on a two-dimensional input word $z$ with $|w|$ rows and $n_{1}$ columns. The input head of $\mathcal{M}$ keeps track of the current row of $z$, while a binary counter stored on the work tape of $\mathcal{M}$ keeps track of the current column of $z$. The work tape also contains the originally-guessed value $n_{1}$ so that $\mathcal{M}$ is able to determine when its simulated computation encounters the right border of the input word.
By Lemma~\ref{lem:reduceworddimension}, we know that if $w \in \colp{L(\mathcal{A})}$, then $w$ must be a column projection of a two-dimensional word with at most $(|w| + 3) \cdot (k^{2^{2k}} + 2)$ columns that is accepted by $\mathcal{A}$.
\end{proof}
\end{theorem}
Since the language class \CSL\ coincides with the space complexity class $\NSPACE(O(n))$ \cite{Kuroda1965ClassesOfLanguages}, one consequence of Corollary~\ref{cor:4WautomataCSL} is that the row and column projections of languages recognized by four-way two-dimensional automata consist exactly of languages in $\NSPACE(O(n))$. Theorem~\ref{thm:3WunaryautomataNLOGSPACE} gives a significantly improved space complexity upper bound for column projections of languages recognized by unary three-way two-dimensional automata.
\section{State Complexity}\label{sec:statecomplexity}
Since projections of languages in $L_{\textsf{2DFA-2W}}$ and $L_{\textsf{2NFA-2W}}$ are known to be always regular, it is possible to consider questions of state complexity involving these projection languages.
Although they seem never to have appeared anywhere in the literature, it is straightforward to prove the following closure results for Boolean operations over two-way two-dimensional automata.
\begin{lemma}\label{lem:2DFA2Wunionintersection}
The class $L_{\textsf{2DFA-2W}}$ is not closed under union or intersection.
\begin{proof}
Take $\Sigma = \{\texttt{0}, \texttt{1}\}$. Define two languages $L_{1}$ and $L_{2}$ as follows:
\begin{align*}
L_{1} &= \{w \in \Sigma^{2 \times 2} \mid w[0,0] = \texttt{1}, w[0,1] = \texttt{1}\}; \\
L_{2} &= \{w \in \Sigma^{2 \times 2} \mid w[0,0] = \texttt{1}, w[1,0] = \texttt{1}\}.
\end{align*}
That is, $L_{1}$ is the language of $2 \times 2$ two-dimensional words with two \texttt{1}s in the first two positions of its first row, and $L_{2}$ is the language of $2 \times 2$ two-dimensional words with two \texttt{1}s in the first two positions of its first column.
Clearly, a deterministic two-way two-dimensional automaton can recognize words in $L_{1}$ by scanning the symbols at positions $(0,0)$ and $(0,1)$ and verifying that they are both \texttt{1}s. The same model can recognize words from $L_{2}$ in a similar manner.
However, no deterministic two-way two-dimensional automaton can recognize the language $L_{1} \cup L_{2}$. Suppose such an automaton $\mathcal{A}$ can recognize the language $L_{1} \cup L_{2}$, and consider the computation of $\mathcal{A}$ on a $2 \times 2$ word $w \not\in L_{1} \cup L_{2}$ where $w[0,0] = \texttt{1}$ and all other symbols are \texttt{0}. This computation will reject $w$, but the input head will only scan one of the positions $(0,1)$ or $(1,0)$. Without loss of generality, suppose the unscanned position is $(1,0)$. Then the automaton would also reject a $2 \times 2$ word $w' \in L_{1} \cup L_{2}$ where $w'[0,0] = w'[1,0] = \texttt{1}$ and all other symbols are \texttt{0}.
For the same reason, no deterministic two-way two-dimensional automaton can recognize the language $L_{1} \cap L_{2}$. Consider a $2 \times 2$ word $x \in L_{1} \cap L_{2}$. Such a word has the symbol \texttt{1} at each of the positions $(0,0)$, $(0,1)$, and $(1,0)$, but no deterministic two-way two-dimensional automaton can scan all three of these positions. Given a $2 \times 2$ word $x' \not\in L_{1} \cap L_{2}$, where $x'[0,0] = x'[0,1] = \texttt{1}$ and $x'[1,0] = \texttt{0}$, a deterministic two-way two-dimensional automaton making one rightward move cannot distinguish between $x$ and $x'$.
\end{proof}
\end{lemma}
\begin{lemma}\label{lem:2NFA2Wunionintersection}
The class $L_{\textsf{2NFA-2W}}$ is closed under union, but is not closed under intersection or complement.
\begin{proof}
Let $\mathcal{A}$ be a nondeterministic two-way two-dimensional automaton, and let $L$ and $L'$ be languages recognized by this model. Then $\mathcal{A}$ can recognize the language $L \cup L'$ by making a nondeterministic selection between $L$ and $L'$ at the beginning of its computation, and checking whether its input word $w$ belongs to the chosen language.
Intersection is not closed for this model for the same reason as given in the proof of Lemma~\ref{lem:2DFA2Wunionintersection}.
As a consequence of this model being closed under union but not intersection, we necessarily cannot have closure under complement.
\end{proof}
\end{lemma}
Moreover, the present authors previously investigated closure properties of concatenation operations over two-way two-dimensional automata~\cite{SmithSalomaa20202DConcatenationPreprint}. In this section, therefore, we will focus on the state complexity of projections of union and concatenation operations for nondeterministic two-way two-dimensional automata.
\subsection{Union of \textsf{2NFA-2W}\ Languages}\label{subsec:statecomplexityunion2W}
Before we proceed, we require a slight modification to the definition of a two-way two-dimensional automaton that we introduced in Section~\ref{sec:prelim}.
For the remainder of this section, when we refer to a ``two-way two-dimensional automaton", we use the following definition.
\begin{definition}[IBR-accepting two-way two-dimensional automaton]
An IBR-accepting two-way two-dimensional automaton $\mathcal{A}$ is a tuple $(Q, \Sigma, \delta, q_{0}, q_{\text{accept}})$ as in Definition~\ref{def:2DFA}, where,
when the input head reads a boundary marker \# for the first time, $\mathcal{A}$ either enters $q_{\text{accept}}$ in the next transition or the transition is undefined.
\end{definition}
The abbreviation ``IBR-accepting" refers to the automaton ``immediately-bottom-right accepting", or accepting only once the input head reaches the bottom or right border of the input word. The two-way model is the only model for which we can make this modification; neither three- nor four-way models can be made to halt immediately upon reading a boundary marker.
\begin{remark}
The accepting state of an IBR-accepting two-way two-dimensional automaton, $q_{\text{accept}}$, is a ``dummy" state used only as the target of accepting transitions on the boundary symbol \#.
Thus, by the ``size" of such an automaton $\mathcal{A}$ we mean the size of the set $Q - \{q_{\text{accept}}\}$. This convention ensures that an IBR-accepting two-way two-dimensional automaton recognizing single-row words has the same size as the corresponding one-dimensional automaton accepting the same string language.
\end{remark}
The following result shows that we may convert between the usual and IBR-accepting types of two-way two-dimensional automata without incurring a penalty on the number of states.
\begin{proposition}[\cite{SmithSalomaa20202DConcatenationPreprint}]\label{prop:IBRacceptingstatecomplexity}
Given a two-way two-dimensional automaton $\mathcal{A}$ with $n$ states, there exists an equivalent IBR-accepting two-way two-dimensional automaton $\mathcal{A}'$ with $n$ states.
\begin{proof}[Proof Sketch]
If $\mathcal{A}$ reads a boundary marker, then its input head can never reenter the input word. After reading a boundary marker in state $q_{i}$, say, we can decide whether $q_{\text{accept}}$ is reachable from $q_{i}$ after following some number of transitions of $\mathcal{A}$. Thus, we may take $\mathcal{A}'$ to be the same as $\mathcal{A}$ where the transition upon reading the boundary marker \# goes directly to $q_{\text{accept}}$ if that state is reachable or is undefined otherwise.
\end{proof}
\end{proposition}
Using a construction from a previous paper investigating projections of nondeterministic two-way two-dimensional automaton languages~\cite{SmithSalomaa20192D3WProperties}, we may obtain an upper bound on the nondeterministic state complexity of projection languages for this model.
\begin{proposition}\label{prop:2NFA2Wrowprojectionupper}
Let $\mathcal{A}$ be a nondeterministic two-way two-dimensional automaton with $n$ states. Then both $\rowp{L(\mathcal{A})}$ and $\colp{L(\mathcal{A})}$ are recognized by a nondeterministic one-dimensional automaton with $2n$ states.
\begin{proof}[Proof Sketch]
Given a nondeterministic two-way two-dimensional automaton $\mathcal{A}$, we may construct a nondeterministic one-dimensional automaton $\mathcal{B}$ recognizing the language $\rowp{L(\mathcal{A})}$ that simulates rightward moves of $\mathcal{A}$ and keeps track of whether a downward move is made during the computation of $\mathcal{A}$. We may remember downward moves by doubling the number of states of $\mathcal{A}$. Using an analogous construction, we obtain the same result for $\colp{L(\mathcal{A})}$.
\end{proof}
\end{proposition}
We can show that the following lower bound applies for the same model.
\begin{lemma}\label{lem:2NFA2Wrowprojectionlower}
There exists a nondeterministic two-way two-dimensional automaton $\mathcal{A}$ with $n$ states such that any nondeterministic one-dimensional automaton recognizing $\rowp{L(\mathcal{A})}$ requires at least $2n - 1$ states.
\begin{proof}
Define $\mathcal{A}$ as follows: the alphabet is $\Sigma = \{\texttt{0}, \texttt{1}\}$, the set of states is $Q = \{q_{0}, q_{1}, \dots, q_{n-1}\}$ (and additionally $q_{\text{accept}}$), the initial state is $q_{0}$, the accepting state is $q_{\text{accept}}$, and the transition function $\delta$ consists of the following:
\begin{itemize}
\item $\delta(q_{i}, \texttt{0}) = (q_{i+1}, R)$ for all $0 \leq i \leq n-2$;
\item $\delta(q_{n-1}, \texttt{0}) = \{(q_{0}, R), (q_{n-1}, D)\}$; and
\item $\delta(q_{0}, \#) = (q_{\text{accept}}, N)$.
\end{itemize}
Each rightward-moving transition counts modulo $n$, and the only downward-moving transition occurs in a column position congruent to $-1 \bmod n$. Moreover, the downward-moving transition does not change the state (i.e., the column count is preserved). Note also that $\mathcal{A}$ makes no transitions upon reading the symbol \texttt{1}; this is because, after reading $n - 1$ copies of \texttt{0} and making a downward move, the first row can contain any symbols after that column position so long as the number of total columns remains a multiple of $n$. Combining these observations, we see that the row projection of $L(\mathcal{A})$ is
\begin{equation*}
L_{\text{pr}} = \texttt{0}^{n-1} (\texttt{0} + \texttt{1}) ((\texttt{0} + \texttt{1})^{n})^{*} + \epsilon.
\end{equation*}
To show that the nondeterministic state complexity of $L_{\text{pr}}$ is at least $2n - 1$, we use the following extended fooling set \cite{HolzerKutrib2003NondeterministicDescriptionalComplexity}:
\begin{equation*}
S = \{(x, y) \mid xy = \texttt{0}^{n - 1} \texttt{1}^{n + 1}, |y| \geq 2\}.
\end{equation*}
The set $S$ contains $2n - 1$ elements and, by its definition, for any pair $(x, y) \in S$, $xy = \texttt{0}^{n - 1}\texttt{1}^{n + 1} \in L_{\text{pr}}$.
Consider two distinct pairs $(x, y)$ and $(x', y')$. Without loss of generality, assume $x$ is a proper prefix of $x'$.
If $|x'| - |x| \neq n$, then $|xy'|$ is not a multiple of $n$, and $xy' \not\in L_{\text{pr}}$.
Otherwise, $|x'| - |x| = n$. In this case, since $|x'y'| = 2n$ and $|y'| \geq 2$, we have that $|x'| \leq 2n - 2$. Thus, $|x| \leq n - 2$, and so $x = \texttt{0}^{i}$ for some $0 \leq i \leq n - 2$. However, this means that $xy' \not\in L_{\text{pr}}$, because in this case $y'$ consists only of the symbol \texttt{1}.
\end{proof}
\end{lemma}
Using the previous results, we can obtain a state complexity bound for the projection of the union of two languages recognized by nondeterministic two-way two-dimensional automata.
\begin{theorem}\label{thm:2NFA2Wstatecomplexityunion}
(i) If $\mathcal{A}$ and $\mathcal{B}$ are nondeterministic two-way two-dimensional automata with $m$ and $n$ states, respectively, then $\rowp{L(\mathcal{A}) \cup L(\mathcal{B})}$ is recognized by a nondeterministic one-dimensional automaton with $2(m + n + 1)$ states.
(ii) There exist nondeterministic two-way two-dimensional automata $\mathcal{A}$ and $\mathcal{B}$ with $n$ and $m$ states, respectively, such that any nondeterministic one-dimensional automaton recognizing $\rowp{L(\mathcal{A}) \cup L(\mathcal{B})}$ requires at least $2(m + n - 1)$ states.
\begin{proof}
We prove (i) by construction. Without loss of generality, assume the state sets of $\mathcal{A}$ and $\mathcal{B}$ are disjoint. Then a nondeterministic two-way two-dimensional automaton $\mathcal{C}$ recognizing the language $L(\mathcal{A}) \cup L(\mathcal{B})$ can be constructed in the following way:
\begin{itemize}
\item The state set of $\mathcal{C}$ contains all
non-accepting states of $\mathcal{A}$ and $\mathcal{B}$.
\item There exists a new initial state $q_{0_{\mathcal{C}}}$ that simulates outgoing transitions from the original initial states $q_{0_{\mathcal{A}}}$ and $q_{0_{\mathcal{B}}}$.
\item There exists a joint accepting state $q_{\text{accept}_{\mathcal{C}}}$.
\item The transition function $\delta_{\mathcal{C}}$ includes all transitions of $\delta_{\mathcal{A}}$ and $\delta_{\mathcal{B}}$.
\end{itemize}
Since the state sets of $\mathcal{A}$ and $\mathcal{B}$ are disjoint, $\mathcal{C}$ accepts some input $w$ if and only if $w$ is accepted by either $\mathcal{A}$ or $\mathcal{B}$. By our construction, $\mathcal{C}$ consists of $m + n + 1$ states. Since $\mathcal{C}$ must remember whether or not a downward move is made during the computation of $\mathcal{A}$ (or, similarly, during the computation of $\mathcal{B}$), we must double the number of states of $\mathcal{C}$; this is essentially the same construction as that used by Proposition~\ref{prop:2NFA2Wrowprojectionupper}. Therefore,
$\rowp{L(\mathcal{A}) \cup L(\mathcal{B})}$ is recognized by a nondeterministic one-dimensional automaton with $2(m + n + 1)$ states.
We now prove (ii). Let $\mathcal{A}$ be the $n$-state nondeterministic two-way two-dimensional automaton from the proof of Lemma~\ref{lem:2NFA2Wrowprojectionlower}, and let $\mathcal{B}$ be a ``copy" of $\mathcal{A}$ with $m$ states; specifically, $\mathcal{B}$ is an automaton of the same type as $\mathcal{A}$ over the alphabet $\Sigma' = \{\texttt{2}, \texttt{3}\}$ where the set of states is $Q' = \{q_{0}, q_{1}, \dots, q_{m-1}\}$ (and additionally $q_{\text{accept}}$); the transition function $\delta'$ is identical to $\delta$ with \texttt{0}, \texttt{1}, and $n$ replaced by \texttt{2}, \texttt{3}, and $m$, respectively; and all other aspects are the same.
Let $L_{\text{pr}} = \rowp{L(\mathcal{A}) \cup L(\mathcal{B})}$. A fooling set for $L_{\text{pr}}$ is
\begin{equation*}
S = \{(x, y) \mid xy = \texttt{0}^{n - 1} \texttt{1}^{n + 1}, |y| \geq 2\} \cup \{(x, y) \mid xy = \texttt{2}^{m - 1} \texttt{3}^{m + 1}, |y| \geq 2\}.
\end{equation*}
The set $S$ contains $2(m + n - 1)$ elements. Moreover, $S$ is clearly a fooling set, since mixing a pair over the alphabet $\{\texttt{0}, \texttt{1}\}$ and a pair over the alphabet $\{\texttt{2}, \texttt{3}\}$ always produces strings not in $L_{\text{pr}}$.
\end{proof}
\end{theorem}
Since two-way two-dimensional automata operate symmetrically with respect to rows and columns, there also exist nondeterministic state complexity bounds for column projections analogous to those established in Theorem~\ref{thm:2NFA2Wstatecomplexityunion}.
\subsection{Diagonal Concatenation of \textsf{2NFA-2W}\ Languages}\label{subsec:statecomplexityconcat2W}
Given two-dimensional words $w$ and $v$ of dimension $m \times n$ and $m' \times n'$ respectively, the diagonal concatenation of $w$ and $v$, denoted $w \oslash v$, produces a two-dimensional language consisting of words of dimension $(m + m') \times (n + n')$ where $w$ is in the top-left corner, $v$ is in the bottom-right corner, and
words $x \in \Sigma^{m \times n'}$ and $y \in \Sigma^{m' \times n}$ are placed in the ``top-right" and ``bottom-left" corners of $w \oslash v$, respectively. We assume that the symbols in $x$ and $y$ come from the same alphabet $\Sigma$ as the symbols in $w$ and $v$.
The diagonal concatenation language is formed by adding to the corners all possible words $x$ and $y$ over $\Sigma$.
An example word from such a language is depicted in Figure~\ref{fig:2Ddiagonalconcatenation}.
\begin{figure}[t]
\[\arraycolsep=1.4pt\def0.8{0.8}
w \oslash v =
\begin{array}{cccccccc}
\# & \# & & \# & \# & & \# & \# \\
\# & w_{1,1} & \cdots & w_{1,n} & x_{1,1} & \cdots & x_{1,n'} & \# \\
& \vdots & & \vdots & \vdots & & \vdots & \\
\# & w_{m,1} & \cdots & w_{m,n} & x_{m,1} & \cdots & x_{m,n'} & \# \\
\# & y_{1,1} & \cdots & y_{1,n} & v_{1,1} & \cdots & v_{1,n'} & \# \\
& \vdots & & \vdots & \vdots & & \vdots & \\
\# & y_{m',1} & \cdots & y_{m',n} & v_{m',1} & \cdots & v_{m',n'}& \# \\
\# & \# & & \# & \# & & \# & \#
\end{array}
\]
\caption{Diagonal concatenation of two-dimensional words}
\label{fig:2Ddiagonalconcatenation}
\end{figure}
Nondeterministic two-way two-dimensional automata are known to be closed under diagonal concatenation over a general alphabet and, moreover, this is the only
concatenation operation under which two-way two-dimensional automaton languages over general alphabets are closed
\cite{SmithSalomaa20202DConcatenationPreprint}. Thus, the natural question arises: given a pair of nondeterministic two-way two-dimensional automata $\mathcal{A}$ and $\mathcal{B}$ recognizing languages $L(\mathcal{A})$ and $L(\mathcal{B})$, respectively, how large must such an automaton be to recognize $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$?
We begin by making an elementary observation. In one dimension, an $\epsilon$-NFA extends an ordinary NFA by allowing $\epsilon$-transitions; i.e., ``stay-in-place" moves. The following result is well-known:
\begin{lemma}[Wood \cite{Wood1987TheoryComputation}]\label{lem:epsilonNFA}
Any $n$-state $\epsilon$-NFA has an equivalent $n$-state NFA without $\epsilon$-transitions.
\end{lemma}
Moreover, for a pair of nondeterministic one-dimensional automata with $m'$ and $n'$ states recognizing languages $L_{1}$ and $L_{2}$, respectively, a total of $m' + n'$ states are necessary and sufficient to recognize the concatenation language $L_{1} \cdot L_{2}$ in the general alphabet case, while $m' + n' - 1$ states are necessary in the unary case \cite{HolzerKutrib2003NondeterministicDescriptionalComplexity}.
\begin{theorem}\label{thm:2NFA2Wstatecomplexitydiagconcat}
(i) If $\mathcal{A}$ and $\mathcal{B}$ are nondeterministic two-way two-dimensional automata with $m$ and $n$ states, respectively, then $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$ is recognized by a nondeterministic one-dimensional automaton with $2m + n$ states.
(ii) There exist nondeterministic two-way two-dimensional automata $\mathcal{A}$ and $\mathcal{B}$ with $m$ and $n$ states, respectively, such that any nondeterministic one-dimensional automaton recognizing $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$ requires at least $m + n - 1$ states.
\begin{proof}
We prove (i) by constructing a nondeterministic one-dimensional automaton $\mathcal{C}$ to recognize the language $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$. The following procedure allows $\mathcal{C}$ to simulate the computation of $\mathcal{A}$ and $\mathcal{B}$ on a word in the language $L(\mathcal{A}) \oslash L(\mathcal{B})$:
\begin{enumerate}
\item The input head of $\mathcal{C}$ begins by simulating rightward moves of the input head of $\mathcal{A}$. If the input head of $\mathcal{A}$ makes a downward move, $\mathcal{C}$ remembers that a downward move occurred and replaces it with a ``stay-in-place" move.
\item At some point during its computation, $\mathcal{C}$ nondeterministically switches to simulating moves of $\mathcal{B}$. Again, the input head of $\mathcal{C}$ only simulates rightward moves, and replaces downward moves with ``stay-in-place" moves.
\end{enumerate}
By Lemma~\ref{lem:epsilonNFA}, ``stay-in-place" moves can be used without affecting the number of states. However, by a construction similar to that used in Proposition~\ref{prop:2NFA2Wrowprojectionupper}, the requirement in Step 1 to remember whether a downward move occurred doubles the number of states needed to simulate the computation of $\mathcal{A}$. Remembering downward moves is not required when simulating the computation of $\mathcal{B}$. Furthermore, in Step 2, the input head of $\mathcal{C}$ ignores the alphabet symbols it is reading. Since the simulation only needs to check that $\mathcal{B}$ accepts a two-dimensional word with the correct number of columns, the exact symbols being read at this stage may be ignored.
If the computation of $\mathcal{C}$ accepts, then the computation of $\mathcal{A}$ and $\mathcal{B}$ must have also accepted, and therefore $\mathcal{C}$ recognizes words in the language $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$. Moreover, $2m + n$ states are sufficient for $\mathcal{C}$ to perform its computation in this way.
We now prove (ii). Let $\mathcal{A}'$ (respectively, $\mathcal{B}'$) be an $m$-state (respectively, $n$-state) unary nondeterministic one-dimensional automaton such that the concatenation of $L(\mathcal{A}')$ and $L(\mathcal{B}')$ requires $m + n - 1$ states \cite{HolzerKutrib2003NondeterministicDescriptionalComplexity}. The language $L(\mathcal{A}')$ can be recognized by an $m$-state nondeterministic two-way two-dimensional automaton $\mathcal{A}$ that recognizes words consisting of one row. Similarly, $L(\mathcal{B}')$ can be recognized by an $n$-state nondeterministic two-way two-dimensional automaton $\mathcal{B}$. In this case, the languages $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$ and $L(\mathcal{A}') \cdot L(\mathcal{B}')$ are equal. It follows that $m + n - 1$ states are necessary for any nondeterministic one-dimensional automaton to recognize $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$.
\end{proof}
\end{theorem}
Again, there exist nondeterministic state complexity bounds for column projections analogous to those established in Theorem~\ref{thm:2NFA2Wstatecomplexitydiagconcat}.
\section{Conclusion}\label{sec:conclusion}
In this paper, we established results linking one-dimensional language classes to two-dimensional projection languages; namely, that both the row and column projections of languages $L \in L_{\textsf{2DFA-4W}}$ or $L_{\textsf{2NFA-4W}}$ are exactly context-sensitive. This improves on the
previously-known non-context-free lower bound, which remains for other two-dimensional automaton models.
We also proved space complexity results for projection languages. While both the row and column projections of languages $L \in L_{\textsf{2DFA-4W}}$ or $L_{\textsf{2NFA-4W}}$ belong to the class $\NSPACE(O(n))$, the column projection of languages $L \in L_{\textsf{2DFA-3W-1$\Sigma$}}$ or $L_{\textsf{2NFA-3W-1$\Sigma$}}$ belongs to the class $\NSPACE(O(\log(n)))$.
Finally, we investigated the state complexity of projection languages. We showed that, given a pair of nondeterministic two-way two-dimensional automata $\mathcal{A}$ and $\mathcal{B}$ with $m$ and $n$ states, respectively, between $2(m + n - 1)$ and $2(m + n + 1)$ states are needed to recognize $\rowp{L(\mathcal{A}) \cup L(\mathcal{B})}$ and between $m + n - 1$ and $2m + n$ states are needed to recognize $\rowp{L(\mathcal{A}) \oslash L(\mathcal{B})}$.
These bounds apply also to the column projections of such languages.
We conclude by giving a selection of open problems arising from work done in this paper.
\begin{enumerate}
\item\label{itm:prob1} Which class of one-dimensional languages corresponds to $L_{\textsf{2DFA-3W}}$/$L_{\textsf{2NFA-3W}}$ (or their unary equivalents) under the operation of column projection?
\item\label{itm:prob2} Which class of one-dimensional languages corresponds to $L_{\textsf{2DFA-4W-1$\Sigma$}}$/$L_{\textsf{2NFA-4W-1$\Sigma$}}$ under the operations of row and column projection?
\item\label{itm:prob3} If a two-dimensional automaton $\mathcal{A}$ with $n$ states recognizes a language $L$, how many states are necessary/sufficient for a one-dimensional automaton $\mathcal{A}'$ to recognize the language $\rowp{L}$/$\colp{L}$?
\end{enumerate}
Problems~\ref{itm:prob1} and \ref{itm:prob2} are likely difficult; it may be more reasonable to obtain an improved upper bound on the related question of space complexity for problem~\ref{itm:prob2}, say $\DSPACE(O(n))$. Moreover, for problem~\ref{itm:prob3}, we can obtain a trivial lower bound of $n$ states by constructing an $n$-state nondeterministic three/four-way two-dimensional automaton $\mathcal{A}$ that accepts only words of dimension $1 \times k$, $k \geq 1$, and taking $\mathcal{A}'$ to be the minimal nondeterministic two-way one-dimensional automaton recognizing the language $\rowp{L(\mathcal{A})}$.
\bibliographystyle{plain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 7,108 |
In Nederland verouderde term, nu meestal als Gezondheidspromotie bekend.
In Vlaanderen onderdeel van het takenpakket van een Centrum voor leerlingenbegeleiding.
Daarnaast is de term ook synoniem geworden van "objectieve" informatie over geneeskunde.
Publicaties, niet in het minst op het internet, geven veel gezondheidsinformatie. Soms is die informatie echter verouderd, of gekleurd door (subjectieve) persoonlijke ervaringen, en dus niet veralgemeenbaar. Ook is ze soms -al dan niet opzettelijk- aangestuurd door belangengroepen zoals de farmaceutische industrie of patiëntenverenigingen. Daarom startte de Vlaamse gemeenschap met een eigen website waar wetenschappelijk verantwoorde informatie wordt gebracht, onder toezicht van universitaire wetenschappers, onder impuls van Patrik Vankrunkelsven.
externe link
gezondheid en wetenschap
geneeskunde | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,983 |
Monday, June 10, 2013 12:23 pm PDT
Did Neil Patrick Harris Say The N-Word At The Tony Awards? — VIDEO
Neil Patrick Harris hosted the Tony Awards last night (June 9, 2013), which doesn't sound very exciting — let's face it, no one watches the Tonys — except, during the opening number, NPH may or may not have dropped the N-word. Yes, that N-word.
Sunday, May 26, 2013 8:40 pm PDT
The Week In Not Half Bad: Billboard Awards, Cannes Film Festival & More
With the 66th Cannes Film Festival and the 2013 Billboard Music Awards, stars dressed their very bestest and tried to put their ugly in a closet (but as usual, the ugly celebrities came dancing out of the closet, but that's a tale for another time). Anywho, here are the hottest celebrities from the past week-ish.
The Week In Ugly: Snaggle Toes At Cannes & More Fun Fugliness
From the 2013 Cannes Film Festival's worst dressed, to the fugly celebs at the Billboard Awards, this week was filled with ugly celebrities, and we ain't mad at that. Enjoy!
Monday, May 20, 2013 3:35 pm PDT
Justin Bieber's Billboard Awards Speech — Little Biebs Has Grown Into A Big, Douchey Douche Lord
Last night, June 19, 2013, Justin Bieber attended the Billboard Music Awards, and was presented with the first-ever Milestone Award… because The Biebs has been on the pop planet since 2009, and four years is, like, a really, really big milestone.
Sunday, November 18, 2012 4:03 am PST
Jennifer Aniston & Justin Theroux: America's Most Boring Couple Gets All Matchy-Matchy Penguin Time
Just when you think Jennifer Aniston and Justin Theroux couldn't possibly get more "blah" … they wear these matchy-matchy black and white ensembles to some boring event at the Beverly Hilton. (In case you're just dying to know, the humdrum event in question was the 26th Annual American Cinematheque Awards on November 15, 2012 – bet you're so glad we told you, right?). | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,264 |
{"url":"https:\/\/pdfslide.us\/documents\/ibetelgeuse-an-augmented-reality-browser-for-iphone-11-augmented-reality-in-augmented.html","text":"# iBetelgeuse: an Augmented Reality Browser for iPhone \u00b7 PDF file 1.1 Augmented reality In augmented reality, the real world is augmented with arti\ufb01cial data by means of an augmented\n\n\u2022 View\n17\n\n0\n\nEmbed Size (px)\n\n### Text of iBetelgeuse: an Augmented Reality Browser for iPhone \u00b7 PDF file 1.1 Augmented reality In...\n\n\u2022 iBetelgeuse: an Augmented Reality Browser for iPhone\n\nDennis Stevense (1358448) Peter van der Tak (1358464)\n\nBachelor\u2019s Project (IN3405) Bachelor of Computer Science\n\nFaculty of Electrical Engineering, Mathematics and Computer Science Delft University of Technology\n\nFinalist IT Group\n\nJuly 5, 2010\n\n\u2022 Attachments\n\n1. Opdrachtomschrijving (in Dutch)\n\n2. Plan van aanpak (in Dutch)\n\n3. Research Report\n\nPresentation\n\ndate July 12, 2010\u201414:00\n\nlocation Finalist Rotterdam Groothandelsgebouw A4.191 Stationsplein 45 Rotterdam\n\nCommittee\n\n\u2022 Kees Pronk, c.pronk@tudelft.nl (Delft University of Technology)\n\n\u2022 Gerd Gross, h.g.gross@tudelft.nl (Delft University of Technology)\n\n\u2022 Okke van \u2019t Verlaat, okke@finalist.com (Finalist IT Group)\n\n\u2022 Jacques Bouman, jacques@finalist.com (Finalist IT Group)\n\n\u2022 Abstract\n\nAugmented reality is the concept of taking a representation of the real world, adding something to it and displaying it to the user. Applications for smartphones\u2014so called augmented reality browsers\u2014 typically take the image of the integrated camera as a representation of the real world, and project textual or graphical objects on top of this image to create the augmented reality. The user can now look \u2018through\u2019 their phone as if taking a picture to look at the augmented world.\n\nThis report describes iBetelgeuse; a novel augmented reality browser for iPhone, designed to be compatible with the Gamaray browser for Android. iBetelgeuse was developed for Finalist IT Group to improve the availability of their current and future augmented reality applications, and is the result of our Bachelor\u2019s project. iBetelgeuse supports most features other browsers also support, but focuses on interaction and responsiveness. Like Gamaray, it supports interaction with objects in the virtual world by tapping them, and allows dynamic worlds to be displayed by means of a web service. Unlike Gamaray and most other browsers it is highly responsive to changes in device orientation, which leads to a better user experience.\n\nThe project was performed using Scrum; a framework for agile software development. Scrum suc- cessfully guided us through the development process, which resulted in an ever working product as we progressed. The first few weeks were dedicated to orientation and research, which proved to be very useful.\n\niBetelgeuse has a clean architecture and thoroughly tested implementation, fit for maintenance and extension. It employs various algorithms that are quite complex and that require some mathematical background and thorough reading of this document to be understood, but apart from those algorithms the implementation is generally easy to understand and well documented.\n\nAlthough iBetelgeuse is a fully functional product\u2014currently being reviewed by Apple for publishing in the iPhone App Store\u2014there are still enough areas that can be improved. Our most important recommendations revolve around changes affecting the user experience, although some aspects of the implementation can also be improved, and new features can be added.\n\nOur recommendations for the application of iBetelgeuse, Gamaray, and their web services are, in short, that the interface between the web service and browser should be extended to give the web service more control over what is displayed on the client. We suggest to use a KML based format to replace the currently used GDDF format.\n\n\u2022 Preface\n\nBefore you lies the report of our final project of the Bachelor of Computer Science program of Delft University of Technology. We have carried out our project by way of a ten-week internship at Finalist IT Group in Rotterdam, which started April 26, 2010. Finalist had the wish to bring an existing open source augmented reality browser (called Gamaray) for the Google Android platform to the Apple iPhone platform. We have been very happy to make that wish come true. The end result is called \u2018iBetelgeuse\u2019.\n\nThis report can be read in various ways. Most chapters can be read individually, depending on the interest of the reader. However, it is recommended to read at least the introduction on page 4 and the chapter about the final product on page 6 to get an idea of what iBetelgeuse is about. Terminology used in this report can be found in the glossary on page 61.\n\nBefore starting, however, we would like to express our gratitude to the following parties:\n\n\u2022 Gerd Gross and Bernard Sodoyer of Delft University of Technology, for their feedback and support;\n\n\u2022 Okke van \u2019t Verlaat and Jacques Bouman of Finalist IT Group, for giving us the opportunity to work on this project, for their feedback and for their continuous trust in us; and\n\n\u2022 everybody at Finalist, for the pleasant environment in which we have been able to do our Bache- lor\u2019s project.\n\nRotterdam, July 5, 2010\n\nDennis Stevense Peter van der Tak\n\n1\n\n\u2022 Contents\n\nPreface 1\n\nContents 2\n\n1 Introduction 4 1.1 Augmented reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Finalist IT Group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 iBetelgeuse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Report structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5\n\n2 Final product 6 2.1 Features and overlays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Built-in QR scanner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Good responsiveness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 App Store product description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7\n\n3 Development process 8 3.1 Scrum and agile software development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Sprint zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Sprint 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.4 Sprint 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.5 Sprint 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.6 Final sprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13\n\n4 Implementation details 14 4.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Resource loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4.3 Coordinate spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.4 Spatial state determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 4.5 Feature rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4.6 Radar rendering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 4.7 QR scanning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32\n\n5 Product quality 33 5.1 Functionality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.2 Usability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34\n\n2\n\n\u2022 5.4 Reliability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.5 Maintainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 5.6 Portability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35\n\n6 Possible improvements 36 6.1 Refactoring ARMainController . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.2 Tweaking filtering parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 6.3 Compensating for user-induced acceleration . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.4 Splitting the filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.5 Adding a distance indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.6 Improving feature display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.7 Improving dimension refreshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.8 Adding calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.9 Updating for iOS 4 and iPhone 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.10 Testing in different places and environments . . . . . . . . . . . . . . . . . . . . . . . . . . 38 6.11 Precomputing feature locations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38\n\n7 Conclusion 40\n\n8 Recommendations 41 8.1 Augmented reality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 8.2 Mobile devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 8.3 Augmented reality format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41\n\nA Proof-of-concept 43\n\nB Product backlog 45 B.1 A\n\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nTechnology\nDocuments\nTechnology\nDocuments\nDocuments\nDocuments\nDocuments\nTechnology\nSoftware\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nTechnology\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments\nDocuments","date":"2022-05-28 13:41:40","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, 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{"url":"https:\/\/www.physicsforums.com\/threads\/inductor-in-d-c-circuits.134475\/","text":"# Inductor in d.c circuits\n\n1. Oct 2, 2006\n\n### Amith2006\n\n1) A bulb is connected in series with an inductor and a 6 volt D.C supply. A soft iron core is inserted into the coil quickly. It is said that there is a momentary increase in the intensity of the bulb because at that particular instant the induced e.m.f is greater than the e.m.f of the source because self inductance increases and hence induced e.m.f increases. Is it true?\n\n2. Oct 2, 2006\n\n### Staff: Mentor\n\nHmmm. My first reaction is that it is not true, since the inductance does not matter in a DC circuit, and since a moving non-magnetized core does not induce an EMF in a coil that is stand-alone. But you should write out whatever EMF term they are referring to in order to be sure....\n\n3. Oct 3, 2006\n\n### Amith2006\n\nNow, if the d.c source is replaced by an a.c source then will it be true?\n\n4. Oct 3, 2006\n\n### Staff: Mentor\n\nDepends on the value of the final inductor and the AC frequency. Let's say that the AC reactive impedance of the inductor matches the real resistance of the light bulb at the AC frequency of the source. What will be the effects of the inductor? Remember that current lags the voltage drop across the inductor by some amount here.... What does that do to the power available to the light bulb? What about the extreme case where the inductive reactance far exceeds the resistance of the light bulb?\n\n5. Oct 8, 2006\n\n### Amith2006\n\nSuppose the a.c source has a rms voltage of 6 volts and frequency of 100 Hz, what would be the effect on the intensity of the bulb? The self inductance of the inductor is not given. Is it possible to answer this question without it?\n\n6. Oct 8, 2006\n\n### NoTime\n\nHmmm\nThat is certainly true for a stand alone coil.\nAnd inductance is unimportant in a steady state DC circuit.\n\nHowever, if you instantaneously created an iron core in the operating coil then it will increase inductance and cause a momentary dimming of the bulb, just like switching an inductor into the circuit.\n\nOTOH, when inserting a core into an operating coil it's going to get magnetized as it aproaches the coil.\nThe energy used to move the core has to go somewhere.\n\nSince the coil should pull the core in like any solenoid then I would think there ought to be a momentary dimming followed by brightening as the core is stoped.\n\nIf the core is pushed, exceeding the acceleration the coil might impart to the core, then I might think you would just get brightening.\n\nThe exact answer isn't clear to me.\n\n7. Oct 8, 2006\n\n### NoTime\n\nSure, the exact value of the inductace is not important.\nJust pick some values and plug them into the equation and see what happens to current, thus brightness.\n\n8. Oct 9, 2006\n\n### Amith2006\n\nThat was nice discussion.Thanks.\n\n9. Oct 10, 2006\n\n### SGT\n\nThe answers are wrong! According to Faraday\u00b4s law, the voltage through an inductor is proportional to the derivative of the magnectic flux.\n$$v(t)=\\frac{d\\phi}{dt}$$\nIn a linear, time invariant inductor $$\\phi(t) = Li(t)$$, so the only way to make a voltage to appear is to make the current time varying. $$v(t) = L\\frac{di}{dt}$$\nWhen you introduce a ferromagnectic core into the coil, the flux is varied, so a voltage appears at the terminals of the inductor. If the variation is big enough the induced emf may be greater than the voltage of the battery.\nOf course, after the nucleus is inserted there is no more field variation and the coil will behave as a small resistor.\n\nedited to add: the answer from NoTime is correct.\n\nLast edited by a moderator: Oct 10, 2006\n10. Oct 10, 2006\n\n### Staff: Mentor\n\nHey, good point. I didn't think of the solenoid effect on the core. Thanks for that!\n\n11. Oct 11, 2006\n\n### SGT\n\nNo, If you insert the core quick enough, there will be an alteration in the magnectic field (see my previous post). This alteration in the magnectic field will give origin to a voltage that will oppose the applied dc voltage. So, you are right in saying that there will be a momentary dimming. But the increasing induced voltage may overcome the dc and produce a net negative voltage in excess of that supplied by the source.\nSince a bulb has no polarity, it will glow more strongly with this negative voltage.\nBut when the core is stopped, there will be no more variation in the field, so no induced voltage and the lamp will glow as before the insertion of the core.\n\n12. Oct 11, 2006\n\n### NoTime\n\nIn this particular statement, I was considering the coil pulling the core in only and stoping it (the core will oscilate a bit here). No external force application.\nNow the core entering the coil should increase the coils inductance thus lowering the current temporarily, a back EMF effect as you note, dimming the bulb.\nHowever, as the now moving core tries to leave the coil\nthat back EMF should now become a forward EMF.\n\n13. Oct 11, 2006\n\n### Staff: Mentor\n\nQuiz question -- what happens to the bulb current if you yank the core out of the inductor?\n\n14. Oct 12, 2006\n\n### NoTime\n\nFrankly, I'm not entirely certain, either for pushing it in or yanking it out.\nI suspect it depends on magnetic field diffusion into the core.\nLooking on the web, small steel core might have a diffusion time of 100ms or so.\nPractically speaking I think the core might act like a diamagnetic material if moved fast enough.\n\nSo I'll say the bulb will dim.\n\n15. Oct 13, 2006\n\n### SGT\n\nIn any case, pushing or pulling, the field will oppose the movement, so in a first moment the lamp will dim. After that, the polarity of the induced voltage will reverse and the lamp willgo brighter if the movement is fast enough.","date":"2017-01-19 02:29:39","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\": 0.42700815200805664, \"perplexity\": 1048.9462845370983}, \"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-2017-04\/segments\/1484560280425.43\/warc\/CC-MAIN-20170116095120-00269-ip-10-171-10-70.ec2.internal.warc.gz\"}"} | null | null |
**** Prime Minister Hon. Peter O'Neill thanks Members of Parliament and coalition partners ****
Prime Minister Hon. Peter O'Neill took the time to thank the members of parliament and the political parties that make up the coalition government for the continuous support to the People National Congress led government.
Speaking during the launch of the 5 year Nipa Kutubu district development plan at Nipa in the Southern Highlands on Wednesday, the Prime Minister said that on behalf of the People National Congress and the people of Southern Highlands, he needs to thank the Members of Parliament and the coalition partners for their support to the government that is changing the face of this country with good policies.
He said his government is different from all past government because the current government has good policies that was working and changing the face of the country.
He said previous government has made a lot of promises by the current government did not just promise but was implementing all the promises through the key development pillars, fulfilling election promises.
He said his government's policies of free education, free health, building the infrastructure, addressing the law and order issues and empowering the small to medium enterprises are true policies that was working throughout the country and impacting the lives of the people.
Prime Minister Hon. Peter O'Neill said the government will continue to support the good policies through the annual national budget to build a strong and healthy society. "This government is not just making empty promises. This parliament is the most hard working parliament this country has ever produced.
"I was in parliament for the last three terms but I have seen all kinds of leaders who makes a lot of promises. But now we can see a lot of changes is taking place because we have a stable government," Prime Minister Hon. Peter O'Neill said.
He said past governments have not fulfilled their promises because millions in trust accounts in Port Moresby have been mismanaged but the current government has changed that trend by diverting those funds to the districts and the provinces so that the leaders can be held accountable.
He said for 40 years the country has been begging for money for overseas like the world Banks, IMF and Australia as if the country was poor because we have not managed the sufficient resources we had well.
He said although it is difficult to change the problems and promises of 40 years but the government has started somewhere to change the trend and scenario were have had lived with. He said it was time for action and not making empty promises. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
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Q: which is the best technique for responsive flutter creating responsive widget kinda isMobile?Fontsize 12 : fontsize 24 or use sizer package,what is the best responsive method for web,tablet,mobile?
A: flutter documentation did give some solution but , not effective for all purposes
AspectRatio
CustomSingleChildLayout
CustomMultiChildLayout
FittedBox
FractionallySizedBox
LayoutBuilder
MediaQuery
MediaQueryData
OrientationBuilder
if we using one by one , all methods have it's own defects .
mobile side and tablet side it will work , but in the case of windows and web , it won't.
if we combine these methods , also get some responsive issue , because of all methods are depend on the device height ,device width ,device aspectRatio , device Offset ,
also so much plugins are available but they have defects too , in the case of flutter_screenutil it depend on width , height . so if changes in one of the property it won't count. that means it won't change layout in web
so i am using this way combine 4 methods together
flutter_screenutil , LayoutBuilder , MediaQuery , AspectRatio
by using this way we can achieve,maintain the 3 layouts in one code
please use wisely according to your use case
A: the best place to find FLUTTER solutions/documentations is the official flutter/dart websites.
For this question:
Creating responsive and adaptive apps
| {
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} | 4,030 |
\section{Introduction}
Since the appearance of the seminal paper of Eisert, Wilkens and Lewenstein \cite{EisertWL}, \cite{EisertW} the theory of quantum games has been a subject of intensive research \cite{Meyer}$\div$\cite{Nawaz6}. Particular attention has been paid to the problem of non-classical Nash equilibria \cite{Nash}. Once the set of admissible strategies is selected, their existence and position depend on the degree of entanglement of initial state of the game as well as the form of payoff matrix.
The simplest and natural assumption concerning the set of acceptable strategies is to admit all unitary ones. Our aim here is to show that, once such an assumption is adopted, there exists no pure Nash equilibrium (except a trivial one) if the gate operator yields the maximally entangled initial state. The proof is based on simple group-theoretical considerations; neither the explicit form of gate operator nor that of payoff matrix are necessary.
\section{ELW games}
Let us remaind shortly the main elements of ELW quantization of classical games \cite{EisertWL}, \cite{EisertW}. We start with classical two-players two strategies game defined by the payoff matrix
\begin{center}\begin{tabular}{|c|c|c|}\hline
\cline{1-3}
A $\setminus$ B & C & D\\ \cline{1-3}
C & (r,r) & (s,t)\\ \cline{1-3}
D & (t,s) & (p,p)\\
\hline
\end{tabular}\\
\end{center}
On the quantum level one introduces two two-dimensional Hilbert spaces $H$, one for each player; the total space of the states of the game is $H\otimes H$. The basic vectors in each Hilbert space are denoted by
\eq{\ket{C}=\left( \begin{array}{c}
1\\
0
\end{array}\right ), \qquad \ket{D}=\left ( \begin{array}{c}
0 \\ 1 \end{array}\right ).}
The strategies of Alice and Bob are represented by unitary matrices $U_A$ and $U_B$. The final state of the game reads
\eq{\ket{\Psi_f}=\naw{J^+\naw{U_A\otimes U_B}J}\ket{C}\otimes\ket{C}}
where $J$ is a reversible two-bit gate introducing quantum entanglement.
Given $\ket{\Psi_f}$ one can compute the expected payoffs of both players. For example, the Alice payoff reads
\eq{\$_A=rP_{CC}+pP_{DD}+tP_{DC}+SP_{CD}}
with $P_{\sigma\sigma'}\equiv\modu{\av{\sigma\sigma'|\Psi_{f}}}^2$, $\sigma,\sigma'=C,D$.\\
The key point is the choice of gate operator $J$. One demands the classical strategies to be included into the quantum game; this yields
\eq{J=\exp\naw{-\frac{i\gamma}{2}\sigma_2\otimes\sigma_2}}
with $\gamma\in\av{0,\frac{\pi}{2}}$.
The properties of the game depend on:\\
(i) the choice of payoff matrix\\
(ii) the value of the $\gamma$ parameter\\
(iii) the choice of the subset $S\subset SU(2)$ of admissible strategies $U_{A,B}$.
In particular, if classical payoffs obey $t>r>p>s$, the Prisoner Dilemma emerges on the classical level. Eisert et al. \cite{EisertWL} have shown that for $\gamma=\frac{\pi}{2}$, with the proper choice of $S$, new, genuinely quantum Nash equilibrium appears (which is also Pareto optimal) allowing the players to escape the dilemma.
The existence of quantum Nash equilibrium depends strongly on the choice of the subset $S$. In fact, it can be shown \cite{BenjaminHay}, \cite{BenjaminHay1}, \cite{Landsburg1}, \cite{Bolonek} that for $S=SU(2)$ (i.e. all unitary strategies are admitted) and maximal entanglement, $\gamma=\frac{\pi}{2}$, to any strategy of one player there exists an appropriate counter-strategy of the second one; as a result no nontrivial Nash equilibrium exists.\\
As mentioned above, the value $\gamma=\frac{\pi}{2}$ corresponds to the maximal entanglement of the initial state
\eq{\ket{\Psi_i}=J\naw{\ket{C}\otimes\ket{C}}.\label{a}}
Then the ELW game with all unitary strategies allowed has a number of specific properties. Apart from the existence of cunterstrategy to any given strategy it admits quaternionic description \cite{Landsburg1}, \cite{Landsburg2}, \cite{Bolonek} as well as the the one in terms of real Hilbert space \cite {Bolonek}. All these properties are related to the fact that the stability subgroup of the initial state is $SU(2)$ \cite{Bolonek}.
Let us now consider the classical game between two players, each having $N$ startegies at his/her disposal. The payoff matrix for each player is now $N\times N$ matrix. The game can be quantized following the ELW method. To each player we ascribe the $N$-dimensional Hilbert space $H$. Let $\poisson{\ket{e_i}}^N_{i=1}$ be an orthonormal basis in $H$. We put $\av{e_i|C}=\delta_{i1}$ and adopt eqs. (\ref{a}) as a definition of initial state for general $N$-strategies games; $J$ is appropriately chosen gate operator. The final state which, together with the payoff matrix, allows to compute the expected payoffs of players reads, in analogy with eq.(2),
\eq{\ket{\Psi_f}=J^+\naw{U_A\otimes U_B}J\naw{\ket{C}\otimes\ket{C}}}
where now $U_A,U_B\in SU(N)$ are the strategies of Alice and Bob; we make again the natural assumption that $S=SU(N)$ is the set of allowed strategies.
The main point is again the choice of the gate operator $J$ \cite{Bolonek1}. As in the $N=2$ case we assume that the classical strategies are included into quantum scheme. Moreover, to leave as much freedom as possible for the choice of $J$ it is further assumed that the matrices representing classical strategies commute. As a result, $J$ depends on some, in general arbitrary, parameters $\gamma_i$,
\eq{J=J\naw{\underline{\gamma}};}
actually, the number of $\gamma$ parameters is $N \choose 2$ and, allowing some unitary rotation of the vector $\ket{C}$, one can represent $J$ as an exponent of linear combination of symmetrized tensor products of the Cartan subalgebra elements \cite{Bolonek1}. The explicit form of $J\naw{\gamma}$ will be not needed in what follows.
\section{Nonexistence of Nash equilibria in the maximally entangled case}
Let us assume that the parameters $\gamma$ are adjusted in such a way that the initial state (\ref{a}) is maximally entangled. We put
\eq{\ket{\Psi_i}=J\naw{\underline{\gamma}}\naw{\ket{C}\otimes\ket{C}}\equiv F_{ij}\ket{e_i}\otimes\ket{e_j}\label{c}}
where the summation over repeated indices is understood. The matrix $F$ is symmetric as we are considering symmetric game. The corresponding density matrix reads
\eq{\rho_i= \ket{\Psi_i}\bra{\Psi_i}.}
The state described by $\rho_i$ is maximally entangled if the reduced density matrices are proportional to the unit matrix \cite{Plenio}
\eq{Tr_A\rho_i=\frac{1}{N}I,\qquad Tr_B\rho_i=\frac{1}{N}I.\label{b}}
Eqs. (\ref{b}) imply
\eq{FF^+=\frac{1}{N}I}
i.e. the matrix $\tilde{F}\equiv\sqrt{N}F$ is unitary. \\
Let us apply the unitary transformation $U_A\otimes U_B$ to $\ket{\Psi_i}$;
\eq{\naw{U_A\otimes U_B}\ket{\Psi_i}=\naw{U_AFU^T_B}_{ij}\ket{e_i}\otimes\ket{e_j}.}
By virtue of (\ref{c}) the invariance of the initial state implies
\eq{U_A\tilde{F}U^T_B=\tilde{F}.\label{d}}
The general solution to eq. (\ref{d}) reads
\eq{\begin{split}
& U_A=U\\
&U_B=\tilde{F}\overline{U}\tilde{F}^+.
\end{split}}
where $U\in SU(N)$ is arbitrary.
We conclude that the stability subgroup of $\ket{\Psi_i}$ is, up to an automorphism, the diagonal subgroup of $SU(N)\times SU(N)$.
The Lie algebra of this subgroup induces the symmetric Cartan decomposition of $ su(N)\bigoplus su(N)$.\newline The coset manifold $SU\naw{N}\times SU\naw{N}/diag\naw{SU\naw{N}\times SU\naw{N}}$ is isomorphic, as a manifold (but not as a group!), to the $SU(N)$ manifold. This allows us to write out a useful decomposition of any element of $SU(N)\times SU(N)$. Explicitly, let $U_1,U_2,V\in SU(N)$ be arbitrary; then (cf. Ref. \cite{Bolonek})
\eq{\naw{U_1,U_2}=\naw{V,U_2\tilde{F}\overline{U}^+_1\overline{V}\tilde{F^+}}\naw{V^+U_1,\tilde{F}\overline{V}^+\overline{U}_1\tilde{F}^+}.\label{e}}
The above equation has the following interpretation. Assume Alice chose an arbitrary strategy $V\in SU(N)$. Let $\naw{U_1,U_2}$ be a pair of strategies leading to the expected payoff desired by Bob. By noting that the second term on the RHS of eq. (\ref{e}) belongs to the stability group of $\ket{\Psi_i}$ we conclude that $U_2\tilde{F}\overline{U}^+_1\overline{V}\tilde{F}^+$ is the relevant counterstartegy to the Alice strategy $V$. \\
As a result, there is no equilibrium in pure strategies unless among $N^2$ classical strategy pairs there exists one leading to an optimal outcome for both Alice and Bob \cite{Landsburg1}. In this sense the pure-strategy equilibria are trivial.
\subsection*{Acknowledgement}
I would like to thank Professor Piotr Kosi\'nski (Department of Computer Science, Faculty of Physics and Applied Informatics, University of L\'od\'z, Poland) for helpful discussion and useful remarks.
This research is supported by the NCN Grant no. DEC-2012/05/D/ST2/00754.
| {
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Officials said Martin Francisco, 17, died Sunday morning after he was injured in an apartment fire Saturday evening. When firefighters arrived at the apartment complex at 2636 Wimpole Avenue Saturday evening, they saw thick smoke billowing from a broken window of a ground floor unit. Crews had break into the apartment to get inside, where they found Francisco lying unconscious near the front door.
Crews took Francisco to the University of Tennessee Medical Center where he died Sunday morning. Francisco is the first person killed in a fire in the City of Knoxville in 2015.
Firefighters contained the damage to a back bedroom of the two-bedroom unit.
Officials are investigating what caused the fire. | {
"redpajama_set_name": "RedPajamaC4"
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Punctuation serves an important purpose in written text. When you speak, you place emphasis or pause to indicate different meanings. For the written word, there are punctuation marks such as commas and semicolons, as well as bold and italic text for things that need to stand out. Being able to properly format your essay title to reflect the right punctuation is very important. Your teacher likely has some rules on this, but if you need a general guide for what is appropriate, then keep reading.
Here are a few ways that you can punctuate the title of your project. It will usually be in bold face, or large font size, or both. Do not use italics or quotations around the words. Always center-align your title and subtitle. If your title is a question, you can include a question mark at the end. If your essay has a subtitle, put a colon at the end of your title and then add the subtitle on the next line beneath it. Even if both your title and subtitle are rather short, it's best to use two lines.
For the other titles or headings in your paper, they should be bolded type but not in a larger size than the rest of the body. Make them left-aligned and either place it at the beginning of a paragraph with a period or on its own line without a period.
Depending on the assignment, you may have many sections or subsections within it, and those need proper punctuation as well. For example, you may have section 6, then 6.1, 6.2 etc. and be organized in an orderly way. As always, check with your professor if you aren't sure about the correct way of formatting something. Since your professor is the one who will be giving your grade, he or she knows best what will get you the most marks for this particular homework.
Punctuating your school work titles is not that difficult with so few rules to remember. As long as you are consistent in the punctuation, it will look professional. | {
"redpajama_set_name": "RedPajamaC4"
} | 6,247 |
Q: Laravel, Confirm Mail without Login we have the following problem:
We send after a successfully Registration to all User a Mail confirmation Mail. But when they try to click on it, they need to be logged in. We would like that the user don't need to login. Which kind of adjustment do we need to do in our Code?
public function emailConfirmation()
{
$token = request('token');
if(Auth::check())
{
$checkToken = User::where('email','=',Auth::user()->email)
->where('confirm_token','=',$token)->first();
if($checkToken)
{
$updatestatus = User::where('email','=',Auth::user()->email)->update(['is_mail_confirmation' => '1']);
$status = true;
$messages = trans('profile.thankyou_message_confirm_mail');
}
else
{
$status = false;
$messages = trans('profile.token_not_match');
}
}
else
{
$status = false;
$messages = trans('profile.without_login_message_confirm_mail');
}
return view('main.confirm',compact('status','messages'));
}
A: I Would suggest you to include the email too in the confirmation link ie. confirmation should be example.com/confirm?token=PR1234&email=abc@gmail.com
but that's not necessary if you token will be always unique so you can ignore the email check.
$token = request('token');
$email = request('email');
//if(Auth::check())
//{
$checkToken = User::where('email','=', $email)
->where('confirm_token','=',$token)->first();
if($checkToken)
{
$updatestatus = User::where('email','=', $email)->update(['is_mail_confirmation' => '1']);
$status = true;
$messages = trans('profile.thankyou_message_confirm_mail');
}
else
{
$status = false;
$messages = trans('profile.token_not_match');
}
//}
//else
//{
//$status = false;
//$messages = trans('profile.without_login_message_confirm_mail');
//}
As a side-note if you happen to support uncommon symbols like ! # $ % * + - in your system don't forget to urlencode() the email before you add it in the confirmation link.
Also as @Tarek suggested make sure this method doesn't touch any auth middleware because the user isn't logged in.
A: You just need two things:
*
*Don't check for authentication in your emailConfirmation action code.
*In the controller that containing the emailConfirmation action make a constructor in which you will except emailConfirmation from authentication like the following:
.
public function __construct() {
$this->middleware(['auth'])->except('emailConfirmation');
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,105 |
Q: Select all data from Pandas DataFrame between two dates I have DataFrame in which there is a column with event dates (dates are not unique). I need to select all the data that is in this period. I try next:
start_day = datetime.date(datetime.strptime(start_day, '%d.%m.%Y')) #change user data to date format
end_day = datetime.date(datetime.strptime(end_day, '%d.%m.%Y'))
df = df[df['Transaction_date'].between(start_day, end_day)]
The type of column Transaction_date is datetime64[ns].
When I run the code with the request for the period 01/01/2020 to 31/01/2020 - part of the data for the specified period is lost (information is displayed only for 21 days, it should be for 31 days).
I see that the Data Frame is contained data for the entire requested period.
Can you help me please, where is my mistake?
A: I used the following test DataFrame:
Transaction_date Value
0 2019-12-31 10
1 2020-01-10 10
2 2020-01-15 10
3 2020-01-20 10
4 2020-01-25 10
5 2020-01-28 10
6 2020-01-29 10
7 2020-01-30 10
8 2020-01-31 10
9 2020-02-01 10
10 2020-02-01 10
Start / end dates are:
start_day = '01.01.2020'
end_day = '31.01.2020'
The code is:
# Convert start / end dates to datetime
start_day = pd.to_datetime(start_day)
end_day = pd.to_datetime(end_day)
I noticed that you use datetime module, which I think is a bad practice.
To this end use dedicated pandasonic function (to_datetime).
It is even clever enough to recognize many of commonly used date formats,
so there is no need to specify it on your own.
To get the actual result, run:
df[df['Transaction_date'].between(start_day, end_day)]
The result is:
Transaction_date Value
1 2020-01-10 10
2 2020-01-15 10
3 2020-01-20 10
4 2020-01-25 10
5 2020-01-28 10
6 2020-01-29 10
7 2020-01-30 10
8 2020-01-31 10
So as you can see:
*
*The date from 2019 has been eliminated.
*The output contains only January dates, to the very end.
*Dates from the beginning of February have also been eliminated.
Repeat my example on your computer. Maybe the source of your problem
(that the result dous not contain all dates from January) is somewhere
else?
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,455 |
ABOUT THE BOOK
"The Tao that can be spoken of is not the real Way," reads a famous line from the _Tao-te ching._ But although the Tao cannot be described by words, words can allow us to catch a fleeting glimpse of that mysterious energy of the universe which is the source of life. The readings in this book are a beginner's entrée into the vast treasury of writings from the sacred Chinese tradition, consisting of original translations of excerpts from the Taoist canon. Brief introductions and notes on the translation accompany the selections from the classics; books of devotional and mystical Taoism; texts of internal alchemy; stories of Taoist immortals, magicians, and sorcerers; ethical tracts; chants and rituals; and teachings on meditation and methods of longevity.
EVA WONG is an independent scholar and a practitioner of the Taoist arts of the Pre-Celestial Way and Complete Reality lineages. She has written and translated many books on Taoism and related topics, including _A Master Course in Feng-Shui; Tales of the Taoist Immortals;_ and _Taoism: An Essential Guide._
Sign up to learn more about our books and receive special offers from Shambhala Publications.
Or visit us online to sign up at shambhala.com/eshambhala.
_Teachings_ OF THE TAO
_Readings from the Taoist Spiritual Tradition_
SELECTED AND TRANSLATED BY
_Eva Wong_
SHAMBHALA
Boston & London
2013
SHAMBHALA PUBLICATIONS, INC.
Horticultural Hall
300 Massachusetts Avenue
Boston, Massachusetts 02115
© _1997 by Eva Wong_
All rights reserved. No part of this book may be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher.
_Library of Congress Cataloging-in-Publication Data_
Teachings of the Tao: readings from the Taoist spiritual tradition / selected and translated by Eva Wong.
p. cm.
eISBN 978-0-8348-2887-2
ISBN 1-57062-245-0 (alk. paper)
I. Tao. 2. Taoism. 3. Spiritual life—Taoism. I. Wong, Eva, 1951–
B127.T3T43 1997 96-9728
299′.5144—dc20 CIP
BVG 01
_Contents_
Introduction
1. The Ways of the Earth and Sky: The Shamanic Origins of Taoism
_Ch'u-t'zu_ (Songs from the Land of Ch'u)
2. The Path of Wu-wei: The Classics of Taoism
_Tao-te ching_
_Chuang-tzu_
_Lieh-tzu_
3. Honoring the Sacred: Devotional Taoism
_T'ai-p'ing ching ch'ao_ (Essentials of the Classic of Peace and Balance)
_Pei-tou yen-sheng ching_ (The North Star Scripture of Longevity)
4. The Tao Within: Mystical Taoism
_Shang-ch'ing huang-t'ing nei-ching yü-ching_ (The Yellow Court Jade Classic of the Internal Images of the High Pure Realm)
_Shang-ch'ing chin-ch'üeh ti-chün wu-tou san-yüan t'u-chüeh_ (The Lord of the Golden Tower of the High Pure Realm's Instructions on [Visualizing] the Five Bushels and the Three Ones)
5. In Search of Immortality: Taoist Internal Alchemy
_Tsan-tung-chi_ (The Triplex Unity)
_Wu-jen p'ien_ (Understanding Reality)
6. In the Playing Fields of Power: Taoist Magic and Sorcery
Stories of Taoist Immortals, Magicians, and Sorcerers
_Feng-shen yen-yi_ (Investiture of the Gods)
7. The Tao in Everyday Life: Taoist Ethics
_Chih-sun-tzu chung-ch'ieh ching_ (Master Red Pine's Book of Discipline)
8. Encountering the Sacred: The Taoist Ceremonies
The Fa-lu (Lighting the Stove) Chants
_Chai-chieh-lu_ (Correct Procedures of Purification and Preparation for Festival Services)
9. The Arts of Longevity: Cultivating the Mind
_Shang-ch'ing t'ai-shang ti-chün chiu-chen chung-ching_ (Scripture of the High Pure Realm's Highest Celestial Lord's Nine True Forms)
_Tung-hsüan ling-pao ting-kuan ching_ (The Mysterious Grotto Sacred Spirit Scripture on Concentrated Observation)
_Seven Taoist Masters_
10. The Arts of Longevity: Cultivating the Body
_Yi-men ch'ang-seng pi-shu_ (Chen Hsi-yi's Secret Methods of Longevity)
_Chang San-feng t'ai-chi lien-tan pi-chüeh_ (Chang San-feng's Secret T'ai-chi Method for Cultivating the Elixir)
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_Introduction_
"THE TAO THAT CAN BE SPOKEN OF IS not the real way. That which can be named is only transient. Run straight into it and you will not see its head. Follow it from behind and you will not see its back." Anyone who writes about Taoism is challenged by these statements from the _Tao-te ching_. However, although the Tao cannot be described by words, words can allow us to catch a fleeting glimpse of that mysterious energy of the universe which is the source of life.
The Taoist spiritual tradition is a vast ocean. Flowing into it are the indigenous beliefs of the early Chinese, the personal vision of the sages, the theories and findings of the natural and medical sciences, and influences from Buddhism and Hinduism. However, despite influences from India and Central Asia, Taoism is deeply rooted in the history and culture of China. It is a tradition that goes back several thousand years to the beginnings of Chinese civilization.
When I was growing up in Hong Kong, I received a Western education at school and a traditional Chinese education at home. I was told by my elders that it was important to know the history and the traditions of my people, and that persons who are not in touch with their tradition are like weeds blown by the wind. To me, it has always been an honor and a privilege to be taught the wisdom of my ancestors. As my understanding of Chinese history and philosophy deepened, I realized that it was in Taoism, not Buddhism or Confucianism, that the sacred and spiritual traditions of China are preserved. Confucianism may have shaped Chinese cultural behavior, but Taoism has shaped the soul and the spirit of the Chinese people.
Before I moved to the United States, I assumed naively that most Chinese were brought up with a sense of their history and their ancestral traditions. But after I settled in the U.S., I found that for many Chinese Americans, tradition only went as far as their grandparents who left China to emigrate to the New World. Now, after several generations of assimilation, many Chinese Americans want to be reconnected with the roots of their culture, especially the sacred and spiritual traditions. As they are unable to read classical Chinese, their only access to the wisdom of their ancestors is through translations. I dedicate this book to them and hope that it will help them in the journey back to their origins.
While living in the U.S., I met many Westerners who wish to experience the Taoist spiritual tradition as participants rather than study it as detached observers. I also dedicate this book to them and hope that it will help them explore and understand the spiritual tradition of a culture which is so different from their own.
The readings in this book are chosen to represent a wide range of Taoist knowledge and wisdom. They are selected from the Taoist canon and post-canon collections unless otherwise stated.
**_The Texts of Taoism and the Taoist Canon_**
The Taoist canon is the official collection of the scriptures of Taoism. The current edition of the canon consists of 1,473 volumes of texts. The earliest attempt at categorizing the Taoist texts occurred in the fifth century CE. Lu Hsiu-ching, a Taoist scholar and priest, divided the Taoist texts into seven groups. He named the three major groups of the Taoist scriptures Tung-chen (Cavern of the Realized), Tung-hsüan (Cavern of the Mysterious), and Tung-shen (Cavern of the Spirit), and the four minor sections T'ai-hsüan (Great Mystery), T'ai-p'ing (Great Balance), T'ai-ch'ing (Great Pure), and Cheng-i (Orthodox Classics).
In Lu's system, the Tung-chen section contained the books of the Shang-ch'ing (High Pure) School. These texts first appeared in the Eastern Chin dynasty (317–420 CE). Legend says that the earliest Shang-ch'ing texts were revealed to Yang Hsi by Lady Wei, a Taoist mystic and founder of the Shang-ch'ing movement. The Tung-hsüan section contained the Ling-pao (Sacred Spirit) scriptures. These were collected by Ko Hsüan, a relative of Ko Hung, the distinguished alchemist of the fourth century CE. The Ling-pao texts are a collection of rituals, liturgies, and talismans. The third group, the Tung-shen section, contained the books known as the _San-huang ching_ (Scriptures of the Three Lords). They are primarily magical formulae and invocations, and were reputed to have come from the Era of the Three Kingdoms (220–265 CE). During the early T'ang dynasty (ca. seventh century CE), the books of the _San-huang ching_ were burned. In later compilations of the canon, their place was taken by _Tao-te ching_ and its commentaries.
The T'ai-hsüan texts were reputed to have been transmitted by Lao-tzu to Wen-tzu. They include the _Tao-te ching_ , the _Chuang-tzu_ , the _Lieh-tzu_ , and the _Hsi-hsing ching_ (Scripture of Western Ascension). Most of the texts in this section are treatises on stilling the mind, cultivating longevity, and living a simple and unencumbered life. However, a twist of fate in the T'ang dynasty took these books away from the T'ai-hsüan section and placed them in the Tung-chen group. The T'ai-p'ing texts consist of the volumes of a monumental work called the _T'ai-p'ing ching_ (Classic of Peace and Balance). When Lu Hsiu-ching compiled his catalog of Taoist books in the fifth century CE, the _T'ai-p'ing ching_ was more voluminous than it is now. The question of its authorship is still debated, but it is most likely a text of the Eastern Han dynasty (25–220 CE). It discusses the ideals of a utopian kingdom and contains talismans of healing and deliverance from disasters. The T'ai-ch'ing texts formed the earliest collection of treatises on ingesting minerals and herbs to attain immortality. The movement associated with these techniques of attaining longevity is called the External Pill ( _wai-tan_ ) or External Alchemy school because it advocates the use of external substances in rejuvenating the body. The last entry in Lu Hsiu-ching's catalog of Taoist texts is the _Cheng-i meng-wei lu_ (Protocols of the Classic Orthodox Practice). These are the texts of the Celestial Masters sect ( _t'ien-shih tao_ ) founded by Chang Tao-ling in the third century CE.
The next compilation of the books of Taoism occurred during the T'ang dynasty (618–906 CE). The first official edition of the Taoist canon was completed and printed in 748 CE and was named _K'ai-yüan pao-tsang_ (The Precious Scriptures Collected in the Reign of Emperor K'ai-yüan). Unfortunately, this edition of the Taoist canon perished in the chaos that surrounded the fall of the T'ang dynasty.
During the Northern Sung dynasty (960–1126 CE), a distinguished Taoist scholar and practitioner named Chang Chün-fang gathered the remnants of the Taoist canon of the T'ang dynasty and collated the texts into the categories first named by Lu Hsiu-ching. Moreover, he selected the best of the Taoist texts and edited them into a Taoist encyclopedia called the _Yun-chi ch'i-ch'ien_ (The Seven Bamboo Strips of the Cloud-Hidden Satchel). Not interested in the liturgical form of Taoism, Chang Chün-fang omitted the rituals and ceremonies of the _Cheng-i men-wei_ scriptures from his encyclopedia.
The Taoist canon of the Sung dynasty did not survive the violent end of that dynasty. What was left of a vast collection was rescued by the students of Ch'iu Ch'ang-ch'un, one of the Seven Masters of the Complete Reality school, during the Chin dynasty of the Manchus (1115–1234 CE). They edited the texts into the _Yüan-tu tao-tsang_ (The Taoist Canon Collected in the Reign of Emperor Yüan-tu). Unfortunately, this canon was destroyed during the Yüan dynasty (1271–1368 CE) in a burning of Taoist texts by militant Buddhists.
It was not until the reign of Emperor Cheng T'ung (1436–1449 CE) in the Ming dynasty (1368–1644 CE) that an edict was issued to compile all the existing Taoist books of the time into a canon. This was the C _heng-t'ung tao-tsang_ , the Taoist canon that we have today.
The _Cheng-t'ung Taoist Canon_ was organized around the structure of Lu Hsiu-ching's fifth-century collection. In the Tung-chen section are the scriptures of Shang-ch'ing Taoism and some Ling-pao talismans and ceremonies. Interestingly, Chang Po-tuan's classic of internal alchemy, the _Wu-jen p'ien_ (Understanding Reality) and its commentaries are included in this section, as is the _Huang-ti yin-fu ching_ (The Yellow Emperor's Classic of Yin Convergence). The Tung-hsüan section consists of mostly Ling-pao scriptures and some Shang-ch'ing texts. However, the Shang-ch'ing classic, _Huang-t'ing nei–ching yü-ching_ (The Yellow Court Jade Classic of Internal Images) is placed in this section. We do not know why this important Shang-ch'ing text was placed in a section that contains predominantly Ling-pao texts. The Tung-shen section contains some Ling-pao texts, the most famous of them being the _Pei-tou yen-sheng ching_ (North Star Scripture of Longevity). The _Tao-te ching_ , the _Chuang-tzu_ , and their commentaries are also placed in the Tung-shen section, as are various texts attributed to or were inspired by Lao-tzu.
The T'ai-hsüan section mostly consists of texts of internal alchemy, including the classic _Tsan-tung-chi_ (The Triplex Unity). The _Huang-ti nei-ching_ (The Yellow Emperor's Classic of the Internals) is also included here. In this section is also the great encyclopedia of Taoist knowledge, the _Yun-chi ch'i-ch'ien_ (Seven Bamboo Strips of the Cloud-Hidden Satchel) as well as Shao K'ang-chieh's classic work on divination, the _Wang-chi ching_ (Treatise on the Celestial Pathways). Many formulae of the External Pill school, or external alchemy, are also collected here. The T'ai-p'ing section contains primarily the _T'ai-p'ing ching_ (Classic of Peace and Balance) and some Ling-pao talismans and ceremonies. Interestingly, the poetry of Wang Ch'ung-yang, one of the greatest proponents of the Complete Reality school of Taoism, is collected here, as are the writings of his disciples, Sun Pu-erh and Ch'iu Ch'ang-ch'un, two of the Seven Taoist Masters. In the T'ai-ch'ing section are writings of philosophers who are generally not classified as Taoists. In this section are the works of Mo-tzu the philosopher of universal love, Sun-tzu the military strategist, Han-fei-tzu the legalist, and Kung-sun Lung the sophist. The classic text of Taoist ethics, the _T'ai-shang kan-ying p'ien_ (Lao-tzu's Treatise on the Response of the Tao), is also collected here, as is the encyclopedic work of Ko Hung titled _Pao-p'u-tzu_ (The Sage Who Embraces Simplicity). Cheng-i, the last section of the _Cheng-t'ung Taoist Canon_ , consists of mostly the scriptures, ceremonies, and talismans of the Cheng-i Meng-wei, or Celestial Teachers' Way of Taoism. For reasons unknown, some Shang-ch'ing scriptures are also included in this section.
A hundred years or so after the _Cheng-t'ung Taoist Canon_ was printed, a supplement was added during the reign of the Ming emperor Wan Li (1573–1619 CE). This supplement is known as the _Wan-li Taoist Canon_. Both canons have been preserved to this day. Most of the Taoist books written after the compilation of the Taoist canon in the Ming dynasty have been collected by Hsiao T'ien-shih, a Taoist scholar in Taiwan, and are published in a series of books titled _Tao-tsang ching-hua_ (The Essential Texts of Taoism). Needless to say, Hsiao T'ien-shih's collection is not exhaustive, and there are many Taoist texts that are not included in any canon, old or new.
The Taoist canon is distinct from the sacred scriptures of other spiritual traditions in that it is an "open" canon. New texts are being added to it continuously. Perhaps the Taoist canon is open-ended because Taoists are practical people who, being more concerned with the workability of practices than with orthodoxy of theology or philosophy, never entertained the idea of a closed system of knowledge. Or maybe it is because they acknowledged that the Tao cannot be understood by words and conceptual thinking, and therefore human attempts at understanding the Tao would never be complete.
The readings in this book represent approaches to the Tao as well as expressions of Taoist spirituality. In preparing this book, I have tried to let the texts speak for themselves. Other than a brief introduction to each text and occasional translator's notes, there are no commentaries or discussions of the texts. Readers who want more information on the various aspects of Taoism can refer to my book _The Shambhala Guide to Taoism_ , where the history, theories, and practices of Taoism are presented in detail.
1
_The Ways of the Earth and Sky_
THE SHAMANIC ORIGINS OF TAOISM
THE TAOIST SPIRITUAL TRADITION IS rooted in the shamanic beliefs of early China. The giants of Taoist thinking, Lao-tzu and Chuang-tzu, were natives of the feudal state of Ch'u in the Eastern Chou dynasty (770–1221 BCE), where shamanism had a strong influence on the beliefs and cultural practices of the people. The shamanic culture of Ch'u is best illustrated by a collection of poetry titled the _Ch'u-tz'u_ (Songs of the Land of Ch'u). The sacredness of nature, the ecstatic union of the shaman and the nature spirits, and the flight to the celestial realm are the themes of these poems. Now, three thousand years later, these themes are still a part of the spiritual tradition of Taoism.
**_The_ Ch'u-tz'u ( _Songs of the Land of Ch'u_ )**
The poems of the _Ch'u-tz'u_ were either shamanic songs or were inspired by shamanic experiences. Most of the poems were written by Ch'ü Yüan, a native of Ch'u and one of the greatest poets of early China.
In Ch'u culture, nature was sacred. The people's connection with nature was not one of distant respect but of passionate love. The Ch'u shaman's relationship with the spirits of nature was like that of a lover, and the dances and ceremonies were humanity's attempts to "seduce" the sacred powers.
The section in the _Ch'u-tz'u_ titled "Nine Songs" best illustrates the shamanic tradition of Ch'u. These songs were sung in the sacred ceremonies that honor the spirits of nature. In the ceremony, one shaman, called the spirit-shaman ( _shen-wu_ ), usually took on the persona of the spirit, and another shaman, who was the leader of the ceremony, played the part of the mortal. Unfortunately, the original text of "Nine Songs" does not indicate which stanzas were sung by which shaman, and this has caused much confusion in understanding the songs and translating them. However, if we listen to the mood and style of the text, it is possible to identify the verses sung by the spirit-shaman and those sung by the leader of the ceremony.
In the translation that follows, I have delineated the parts performed by the singers. I think this brings out the feel of the "Nine Songs" as they were originally performed. As you read these selections, note the usage of plants and herbs in the ceremonies, and the power of music and song in renewing the bond between humanity and the sacred powers.
_The Nine Songs_
1. SONG TO THE GREAT UNITY, LORD OF THE EAST
_Sung by the shaman leading the ceremony_ :
It is a beautiful day.
It is an auspicious hour.
We stand silently in awe before the altar of the Great Lord on high.
Long swords of jade are in our hands;
Pendants of jade hang from our belts;
Our ornaments jingle as they clash against each other.
Look, the sacred altar is laden with jade and jeweled bowls,
And on it are fragrant flowers and grasses.
We offer meats wrapped in leaves,
And serve them on mats of orchids.
We offer cinnamon wine and sauces of hot peppers.
Together we lift our drumsticks
And begin to beat a rhythm.
Slowly and solemnly we start our singing;
Then, as we hear the pipes and zithers,
Everyone joins in a loud and shrill song.
The sacred shamaness is in her colorful robe;
She begins to dance.
The air is filled with sweet fragrance.
Now the strings play faster;
The five notes are sounding in harmony.
Great One, enjoy and be merry with us.
2. SONG TO THE LORD-WITHIN-THE-CLOUDS
_Sung by the shaman leading the ceremony_ :
We bathe and wash our hair in water scented with orchid leaves;
We put on our robes, decked out like flowers of many colors.
The Lord-within-the-Clouds comes down to us,
His sacred light shining with eternal brilliance.
Now he rests in his palace,
Shining together with the sun and moon.
Now he flies his dragon-chariot,
Dressed in majestic splendor.
Now he stays for a while;
Now he flies swiftly and wanders in the sky.
Bright One, you have come to us,
But suddenly you are off again in the clouds.
You look at our lands from high;
Your travels take you over many places.
Where will you go now?
I sigh when I think of you,
And my heart grieves that you cannot be with me.
3. SONG TO THE LORD OF THE RIVER
_Sung by the shamaness leading the ceremony_ :
You hesitate and do not come to me;
What is it that keeps you from leaving your island?
_Sung by the Lord of the River (spirit-shaman)_ :
I am attractive and beautiful;
I come to you in my cinnamon bark canoe.
I glide softly on the waters without a ripple,
For I have asked the waves of the river to be still.
_Sung by the shamaness leading the ceremony_ :
I long for you and yet you do not come.
Sadly I play my flute.
Whom do I think of but you?
_Sung by the Lord of the River (spirit-shaman)_ :
I fly north on my dragon;
Then I turn toward the Tung-t'ing Lake.
My boat is decorated with care:
The hull is lined with sweet clover;
The sails are made of fig leaves;
The oars are made of iris stems;
And I have orchids for my banners.
Gazing at the sea strand in the distance,
I step across the great river and display my magical powers.
_Sung by the shamaness leading the ceremony_ :
You have shown your power and yet you do not come;
My attendants are crying for my sake.
Tears run freely down my cheeks,
And I am sick with longing for you.
With my oars of cinnamon bark and orchid leaves,
I plow my way through ice and snow.
My efforts are like gathering figs in the water,
And plucking lotuses from treetops.
When feelings of love are not deep,
You will easily be separated from me.
Fast as waters running through stony shallows,
You fly away on your dragon.
Faithless love and untrusting friendship
Only cause pain and sorrow.
You broke your promise to me,
And made the excuse that you did not have time.
I race along the banks of the river in the morning;
In the evening I stop to rest at the island in the north.
Birds roost on the roof of the hut;
Water laps on the shores.
I throw my jade ring into the river;
I abandon my jade pendant to the flowing waters;
I gather sweet grass on the fragrant island
And think of giving them to your attendants.
Lost opportunities are hard to recover,
And I can only stay and play a little longer.
4. SONG TO THE LADY OF THE RIVER
_Sung by the shaman leading the ceremony_ :
The Lady descends to the northern banks.
When I strain my eyes and cannot see her,
My heart breaks with sorrow.
The gentle autumn wind is blowing;
Waves ripple through the waters of Tung-t'ing Lake,
And leaves on the trees are falling.
I climb onto the white tops of the marsh grass
And gaze longingly.
My love and I have agreed to meet here,
And I wait eagerly as the evening light falls.
But why are the birds resting on the duckweeds?
And why are the fishing nets hanging from the trees?
The Yüan River has angelicas of flavoring oil;
The Li River has orchids.
I think of you all the time,
But I am afraid to say it.
Trembling with anticipation, I gaze toward the distance
And listen to the murmur of the waters.
Why are the deer feeding in the courtyards?
Why are dragons lying in shallow water?
In the morning I drive my horses by the river,
In the evening I cross to the western bank.
I hear my love calling my name;
I will follow her chariot to the farthest places.
I have built a hut in the waters
And covered the roof with lotus leaves.
I have decorated the walls with iris;
I have put purple shells in the courtyard
And adorned the hall with fragrant pepper.
The beams are made of cinnamon wood,
And the rafters are made of orchids.
I have hung lintels over the doorway
And decorated our bedchamber with peonies.
I have used sweet clover to make window screens
And have woven together fig leaves for hangings.
I have used white jade to hold down our sleeping mats;
I have scattered stone-orchids to scent the floor;
I have placed white flags over the lotus thatch
And bound them with stalks.
I have planted many fragrant herbs in the courtyard;
And I have scented the gateway with exquisite perfumes.
Even the spirits of Doubting Mountain will come to welcome you,
Rushing here like a host of windborne clouds.
I have torn the sleeves off my robe and thrown them into the river;
I have taken off my tunic and abandoned it by the swells.
I have plucked sweet grass from the island
To send them to you, who are far away.
Opportunities are hard to come by,
And I can only stay and play a little longer.
5. SONG TO THE GREAT LORD OF DESTINY
_Sung by the Great Lord of Destiny (spirit-shaman)_ :
Open wide the gates of the sky.
I come riding on the black clouds.
I order the whirlwind to be my herald
And call the rainstorm to wash away the dust.
_Sung by the shaman who is leading the ceremony_ :
Great One, you hover and descend to me;
I will climb and follow you
Over the heights of Kong-sang Mountain.
_Sung by the Great Lord of Destiny (spirit-shaman)_ :
This world and all its people;
Their lives, long or short, are in my hands.
_Sung by the shaman leading the ceremony_ :
Serenely and majestically you soar in the sky;
You ride on the clear vapor of the sky and earth,
And on the breath of yin and yang.
Speedily I will go with you to far-off places,
Leading the lord of the sky to the great mountains.
_Sung by the Great Lord of Destiny_ ( _spirit-shaman)_ :
My long robes flutter in the wind;
My jade pendants, in brilliant color, dazzle in the light.
Ah, the changes of yin and yang in the universe;
None of the mortals know what I can do.
_Sung by the shaman leading the ceremony_ :
I have plucked the jadelike flower of the hemp
To give to the one who is far away.
I am getting old, and if we do not stay together,
I am afraid that we will become strangers.
Driving your dragon-chariot with thundering wheels,
You fly high in the sky.
But here I stand on the ground, holding a stick of cinnamon;
My longing for you causing me pain.
What can I do with my sorrow?
I only hope that we will be together forever.
But each life has its destiny.
Meetings or partings, who can decide what will happen?
6. SONG TO THE PROTECTOR OF THE YOUNG ONES
_Sung by the Protector of the Young Ones (spirit-shaman)_ :
Autumn orchid and parsley flowers
Grow in rows below my hall.
Green leaves and white flowers
Send their fragrance strongly to me.
People have always wanted children and grandchildren;
Why do you fuss over them?
_Sung by the shamaness leading the ceremony_ :
The autumn orchids bloom luxuriantly,
Their leaves green and flowers purple.
The hall is filled with beautiful ladies;
You suddenly turned your seductive gaze to me.
You came without a word,
And you left without goodbye.
Riding on the whirlwind, with clouds as your banners,
You are gone.
No pain is greater than parting with life,
And no greater happiness is there than finding a friend.
Wearing a robe of lotus and a belt of sweet clover,
Swiftly you came, and swiftly you left.
At night you rest near the kingdom of the sky.
Are you waiting for someone at the edge of the clouds?
I long to bathe with you in the celestial pool
And watch you dry your hair in the rising sun.
I keep looking and looking, but you do not come.
What can I do but turn to face the wind
And break into a loud song.
Riding on a chariot covered with peacock feathers,
With banners of brilliant green,
You climb into the nine realms of the sky to touch the stars.
You lift your long sword high to protect your beautiful children.
Only you are the true judge of all the people.
7. SONG TO THE LORD OF THE EAST
_Sung by the Lord of the East (spirit-shaman)_ :
Slowly I rise from the east,
My light shining on the wooden gate of my house.
Driving my horses slowly forward,
Night gives way to the pale light of dawn.
_Sung by a group of shamans_ :
The Sacred One drives his dragon-chariot,
Borne on the breath of thunder;
His banners of clouds fluttering in the wind.
I sigh as I rise to the sky above;
My heart is hesitant, and I do not wish to leave my home below.
Your colors at dawn are so enticing.
All who see you are intoxicated and forget to return home.
We tighten the strings of our zithers
And beat our drums together;
We strike the bells and shake the bell-stand;
And we play our pipes and flutes.
We are beautiful and virtuous;
We whirl around, sometimes slow and sometimes fast.
As we sing, everyone breaks into a dance
To the notes of the music and the beat of the rhythm.
The Sacred One has come.
Your many spirit attendants will darken your light.
_Sung by the Lord of the East (spirit-shaman)_ :
I dress myself in a shirt of blue and a skirt of white
And soar into the sky.
I aim my long arrow and shoot at the Sky Wolf.
Grasping my bow, I descend back to earth.
I lift the handle of the Dipper to ladle cinnamon wine;
Holding the reins of my horses, I urge them across the sky;
And in the darkness of night I make my journey back to the east.
8. SONG TO THE EARL OF THE RIVER
_Sung by shaman leading the ceremony_ :
I travel with you to play in the nine rivers.
The gusty winds whip up the breakers.
We ride on a water-chariot with lotus leaves as canopy.
Two dragons draw the chariot,
And two serpents accompany us at our side.
We climb to the top of the Kun-lun Mountains,
And look in the four directions.
My heart flutters and leaps in ecstasy.
The sky will darken soon;
But wanting to stay longer,
I forget about going home.
I gaze at the distant shores,
And my heart is filled with longing.
Your chamber is made of fish scales and your hall of dragon skin;
You have filled your palace with pearls and purple shells.
Why do you have to live in the water,
And travel on the backs of great turtles to catch brightly striped fish?
Come with me instead to play on the sandy islands.
We'll roll around with the floods that come our way.
You and I shake hands goodbye as you continue east.
Let me accompany you as far as the southern bank.
The waves swell up to welcome you,
While shoals of fishes accompany me back home.
9. SONG TO THE MOUNTAIN SPIRIT
_Sung by a group of shamans_ :
There appears to be someone deep in the mountains,
Wearing a cloak of fig leaves and a belt of rabbit fur.
You look at me with penetrating eyes and a friendly smile.
Lady, I know you desire my good looks.
You are driving two leopards and leading two striped lynxes.
Your chariot is made of magnolia,
And your banners are woven with cinnamon sticks.
You are dressed in a cloak of stone-orchids;
The folds are gathered neatly with a belt of stalks.
You pluck sweet grass to give to the one you love.
Here I am in the dense bamboo forest;
The trees are so thick that I can't even see the sky.
The mountain trails are dangerous;
That is why I am late.
Alone, I stand on top of the mountain;
The dense clouds floating down below.
The east wind comes in;
The rains will be here soon.
I am so happy to be with you that
I forget about going home.
I am getting old;
What chances will be left for me to feel the goodness of life?
Alone, I gather mushrooms in the mountains.
I can only see the scattered rocks
And arrowroots creeping through them.
Are you thinking of me although you do not have the time to come?
I long for you, and in sorrow I forget that I have to go.
Wanderer in the mountains, you are like the sweet grass;
You drink from the rock spring
And rest beneath the pine and fir.
Are you really thinking of me?
I cannot be certain.
The thunder rumbles;
The rain darkens the sky;
Monkeys and apes scream mournful cries;
The wind moans loudly and the leaves whistle.
I think of you, and my heart is filled with sadness.
**NOTES ON THE TRANSLATION**
I have titled song number 3 "Song to the Lord of the River" and number 4 "Song to the Lady of the River." I disagree with David Hawkes's interpretation (in the _Ch'u-tz'u: Songs of the South_ ) that song number 3 is addressed to a goddess. The deity in question here is the Shang-chün. _Chün_ is traditionally a respected title for a male. It can be translated as "gentleman" or "husband," and it is typically not used to address a female. Songs number 3 and 4 also form a pair. The chief singer of the Song to the Lord of the River is a shamaness; it is she who longs for her beloved, the male river spirit. On the other hand, the chief singer of the Song to the Lady of the River is a shaman, and he is longing for his lover, the female river spirit.
I have titled song number 6 "Song to the Protector of the Young Ones." I also disagree with Hawkes's interpretation that this song addresses a "lesser" lord of destiny and that some lines do not belong here. The word _hsiao_ can mean "young" or "less." The other two words, _ssu-ming_ , can either mean "giver of life" or "controller of destiny." When interpreted as "giver of life to the young ones," the spirit invoked in the song is not a controller of destiny who has lesser powers than the one in song number 5, but is a totally different kind of power: one who grants life to the young ones. Read this way, the entire poem forms a cohesive unit and no lines are out of place. Personally, I think this rendering is more consistent with Ch'u culture. Children were a blessing, and fertility was much desired among the southern tribes. Unlike the desolate north, the southern lands could support its population, and a family with many children was considered a "rich" family. Thus, I feel that the Song to the Protector of the Young Ones is better understood as a song asking the sacred power to grant fertility.
Many songs describe various species of plants used in the shamanic dance. In the translation I have reduced the use of botanical names and have used common plant names that the general reader is more familiar with.
2
_The Path of Wu-wei_
THE CLASSICS OF TAOISM
THE _LAO-TZU_ ( _TAO-TE CHING_ ), _Chuang-tzu_ , and _Lieh-tzu_ are called the Three Classics of Taoism. Although they were written over two thousand years ago, their wisdom is timeless, and their teachings are remarkably relevant to our times. I have chosen sections from these three books to highlight three major themes in the teachings of Taoism: the nature of the Tao, sagehood, and cultivating life. All three books address similar issues, but they speak differently, as if each has a character and life of its own. The _Lao-tzu_ , or _Tao-te ching_ , is poetic in style and serious in its approach. The _Chuang-tzu_ is prose and is wild and idiosyncratic. The _Lieh-tzu_ tells stories and is humorous. Serious wisdom, crazy wisdom, and humorous wisdom, these books contain some of the best philosophy and literature that the Chinese culture has ever produced.
**Tao-te ching**
The _Tao-te ching_ was originally titled _Lao-tzu_. Although it was named _Tao-te ching_ by Taoist scholar Wang Pi (226–249 CE), who felt that the book dealt with the nature of the Tao and the matter of virtue ( _te_ ), the _Lao-tzu_ did not receive that official title until the reign of Emperor Hsüan Tsung (739–782 CE) in the T'ang dynasty.
Who wrote the _Tao-te ching_? There are several theories. Some scholars maintain that the book was written by several people, one of whom was indeed a historical person named Li Erh, now known as Lao-tzu. Other parts of the book were written either by students of Lao-tzu or by thinkers who were sympathetic to his teachings. Others say that Lao-tzu the person was a fictitious character and that the book represents the teachings of a loosely knit group of thinkers who held similar ideas. When the book was put together, it was titled _Lao-tzu_ because it contained the "teachings of the old wise ones" ( _lao_ means "old," and _tzu_ means "wise one"). There is, however, a general agreement that the book was the work of more than one person.
Most people agree that the _Tao-te ching_ was written over a period of time, but there is no consensus as to when. Some date it to the Spring and Autumn Period (770–476 BCE) of the Eastern Chou dynasty (770–221 BCE), placing the historical Lao-tzu as a contemporary of Confucius. Others argue that because its style differs from the Confucian classics like the _Analects_ , it could not have been written during the time of Confucius. Personally, I agree with the earlier dating for several reasons. First, Ssu-ma Ch'ien, the Grand Historian, noted that Lao-tzu was a native of Ch'u who lived in the time of Confucius and that the two men had met and discussed matters of ceremonies and rituals. I find this believable since Confucius was interested in the ancient rituals and collected them in the _Li-chi_ (Book of Rites), and Lao-tzu was a librarian of the imperial archives. Thus, it is likely that Confucius could have approached Lao-tzu and consulted him on matters of rituals and rites. Second, just because the _Tao-te ching_ and the Confucian classics differ in style does not mean that the two works could not be contemporary, especially if we consider the _Tao-te ching_ to be a work of a southern culture of Ch'u and the _Analects_ to be a work from the northern states of Ch'i and Lu. (Ch'u, Ch'i, and Lu were feudal states of the Eastern Chou dynasty.) In fact, recent Chinese scholars have pointed to the similarity of style between the _Tao-te ching_ and the _Ch'u-tz'u_. Thus, it is reasonable that some parts of the _Tao-te ching_ could have been written as early as the sixth century BCE, with subsequent additions dating as late as the fourth century BCE. But regardless of who wrote it and when it was written, the _Tao-te ching_ is one of the most important classics of Taoism. Its teachings are timeless, and its wisdom transcends culture and history.
The translations that follow are made from the Standard Text found in the Taoist canon.
_From the_ Tao-te Ching
ON THE TAO
1
The Tao that can be spoken of is not the real way.
That which can be named is only transient.
The nameless was there before the sky and the earth were born.
The named is the mother of the ten thousand things.
In nothingness you will see its wonders;
In things you will see its boundaries.
These two come from the same origin, although they have different names.
They emerged from somewhere deep and mysterious.
This deep and mysterious place
Is the gateway to all wonders.
4
The Tao is empty.
However, if you use it, it can never be exhausted.
Deep and bottomless,
It may be the ancestor of all things.
It blunts what is sharp,
Unties what is tangled,
Softens what is dazzling,
And merges with the dust.
Deep and hidden,
It appears to last forever.
I do not know whose son it is;
Looks like it was here before the rulers of the sky existed.
14
Try to look at it and you will not see it;
Therefore we call it "unfathomable."
Try to listen to it and you will not hear it;
Therefore we call it "rare."
Try to touch it and you will not feel it;
Therefore we call it "ungraspable."
These three cannot be penetrated further,
For they cannot be separated.
Up high it is not bright;
Down below it is not dark.
Infinite and limitless, we cannot name it,
Because it always reverts to nothingness.
A shape without a shape,
A form without an object,
It is elusive and fleeting.
Run straight into it and you will not see its head;
Follow it from behind and you will not see its back.
Use the way of the ancients to master the situations of the present.
To know the origin of the universe
Is to understand the structure of the Tao.
25
There was something undifferentiated but complete.
Born before sky and earth,
Soundless and formless,
It stands on its own ground and is unchanging.
It moves like a circle and never stops.
It can be the mother of the universe.
I do not know its name,
So I call it the Tao.
If forced to name it, I'll call it Great.
It is great because it moves through everything.
It reaches far, yet it returns to where it started.
Therefore the Tao is great;
The sky is great;
Earth is great;
And the ruler of humanity is also great.
There are four great things in world, and the ruler of humanity is one of them.
Humanity follows the way of earth;
Earth follows the way of the sky;
The sky follows the way of the Tao;
And the Tao follows its own natural way.
34
The Great Tao flows everywhere.
Its course can go left or right.
The ten thousand things depend on it for growth,
And it does not refuse them.
It accomplishes its work and does not claim credit.
It clothes and feeds all things but does not control them.
Always without desire, it can be called small.
The ten thousand things come under its embrace,
But it does not dominate them.
Therefore it can be called great.
Because it does not consider itself as great,
It can accomplish that which is great.
ON SAGEHOOD AND CULTIVATING LIFE
10
Can you unite your spirit with the One and not let it leave?
In concentrating on your breath, can you make it soft like an infant's?
Can you purify your thoughts and clarify your mind
So that they are spotless?
Can you love your country and people without effort?
In opening and closing the celestial gate,
Can you become the female?
In understanding everything in the universe,
Can you do it without using knowledge?
Give birth to them and nourish them,
But do not possess them.
Help them know that they are not dependent on you.
Guide them but do not control them
This is the most profound virtue.
12
The five colors can confuse your sight.
The five sounds can dull your hearing.
The five flavors can injure your sense of taste.
Racing and hunting can drive you mad.
Material goods that are hard to get will hinder your movement.
Therefore enlightened people care about their stomach and not their senses.
They discard one and take the other.
44
Fame or your body, which do you want more?
Your body or your wealth, which do you value more?
Gain or loss, which do you want more?
If you have a lot of desire, you will probably be extravagant.
The more you hoard, the more you will lose.
Know contentment and you will not be disgraced;
Know when to stop, and you will not meet with danger.
In this way, you will be around for a long time.
52
There was a beginning of the world
That may be regarded as the mother of the world.
Attain the mother, and you will know her children.
Hold on to the mother, and you will not meet with harm all your life.
Block the openings;
Close the doors;
And all your life you won't have to toil.
Open the holes,
Meddle in the worldly affairs,
And all your life you will not be saved.
To be able to discern the small is clarity;
To be able to hold on to the soft is strength.
Use the light
To return to brightness.
In this way, you will not invite harm.
This is called practicing that which is permanent.
One who embraces virtue fully
Is like an infant.
Poisonous snakes and insects will not sting him;
Fierce beasts will not claw him;
Birds of prey will not strike him.
His bones are weak, his tendons are soft,
But his grasp is strong.
He does not know the union of male and female,
And yet his organ is aroused.
This is because his procreative energy is at its height.
He can cry all day without getting hoarse.
This is because he is in perfect harmony.
To know harmony is to be at one with the permanent;
To know the permanent is to be clear.
To be greedy of life is a sign of misfortune.
If you direct your breath with your mind you will be forcing things.
When things reach their prime, they will begin to get old.
This is not the Tao.
What is not the Tao will meet with an early end.
**Chuang-tzu**
The _Chuang-tzu_ is a collection of essays in thirty-three chapters divided into three sections: the Inner Chapters ( _nei-p'ien_ ), the Outer Chapters ( _wai-p'ien_ ), and the Miscellaneous Chapters ( _tsa-p'ien_ ). Like many ancient texts, the _Chuang-tzu_ that we have today is incomplete. The current _Chuang-tzu_ was probably put together in the early fourth century CE. During the T'ang dynasty, the _Chuang-tzu_ 's status was elevated when it became one of the three Classics of Taoism, together with the _Tao-te ching_ and the _Lieh-tzu._
The writings in the _Chuang-tzu_ span over four hundred years of thought, from the fourth century BCE in the Warring States Period (475–221 BCE) of Eastern Chou to the third century CE in the Eastern Han. It is now believed that the Inner Chapters, written between 250 and 300 BCE, are the oldest sections of the book. These chapters were probably written by one person, most likely Chuang-tzu himself. Parts of the Outer Chapters and Miscellaneous Chapters are essays written by various authors sometime between 221 and 25 BCE, during the Ch'in and Han dynasties. Other parts could have been written as late as the Wei and Chin dynasties (between 220–420 CE). Some of the authors were students of Chuang-tzu, while others were Taoist philosophers who lived several hundred years after his time.
The first excerpt is from chapter 2 of the Inner Chapters. The second excerpt, chapter 15, is from the Outer Chapters.
_On the Tao_
From the _Chuang-tzu_ , chapter 2: Discussion on All Things Being Equal
Tzu-ch'i of the southern suburb sat leaning on a table and looked up at the sky. His breathing was slow, as if his mind had wandered off somewhere.
Yen-ch'eng Tzu-yu, who was standing by his side, asked, "What's going on? Can the body become like a withering tree and the wind be like dead ashes? Can the man who sits leaning on the table today be different from the one who sat in the same place yesterday?"
Tzu-ch'i replied, "Yen, you've asked a good question. Today my spirit left my body. Do you understand that? You've heard voices of people, but you haven't heard the voices of the earth. And if you've heard the voices of the earth, you haven't heard the voices of the sky!"
Tzu-yu said, "What does this mean?"
Tzu-ch'i then said, "The Great Earth blows out a vapor and it is called wind. If it doesn't blow, nothing happens. However, when it does, the ten thousand hollows and holes will howl wildly. Haven't you heard their persistent cries? In the high mountains and low hills are deep forests. In these forests are trees whose trunks are so wide that a hundred men can circle them. These trees have openings like noses, mouths, ears, jugs, cups, grain mortars, deep pools, and shallow ponds. When the wind blows, they roar like waves and whistle like arrows shot from bows. Some scream, some make sounds like heavy breathing, some cry, some wail, some laugh, and some sigh. Those in the lead lightly let out an "eeee" and those following behind echo loudly with "yuu." If the wind is gentle, the harmony is faint, but in a strong gale the chorus is deafening. When the wind stops, all the hollows are empty and silent again. Haven't you seen that kind of tossing and swaying going on in the forests?"
Tzu-yu said, "Oh, so the voices of earth are the sounds from the hollows, and the sounds of people are those coming from flutes and pipes. Then, may I ask, what are the voices of the sky?"
Tzu-ch'i replied, "Blowing into the hollows of the ten thousand myriad things in different ways, so that each of them can make its own sound and takes what it needs—this is voice of the sky. But who is directing them to make these sounds?"
Great understanding is broad, and lesser understanding is picky. Great words carry strength and little words are petty and quarrelsome. When people go to sleep, their spirits wander off. When they awake, their bodies are uncomfortable. This is because they get tangled up with everything they contact. Every day they use their minds to scheme. Some brag about themselves, some set up traps for others, and some hide their malicious intentions. Their small fears make them edgy and suspicious. Their big fears make them lose their minds. Some shoot off their arguments like arrows and delight in bickering over right and wrong. Others hold on to their opinions tightly, certain that they are correct. Thus, they fade and die like autumn and winter, decaying day by day. They are so stuck in their condition that it will be hard to get them to turn back. They are so blocked up that not even one whiff of air can come out. Old and withering, their minds are near death, and nothing can restore them to life.
Rapture, anger, sadness, happiness, worry, regret, rashness, stubbornness, modesty, carelessness, bluntness, and pretense are music from empty hollows, bursting out like mushrooms from the damp ground. Day and night they replace each other, springing up in front of us, and we don't even know where they come from!
Let them be, let them be! They're with us morning and evening. We can't exist without them, and they have nothing to latch on to without us. It is the way things are. I don't know how they came about. If they have a true master, then I have not seen it. I can see the actions, but I cannot discern the form. This is because it exists and yet it has no form.
The hundred joints, the nine openings, the six organs all come with my body. Which part do I value most? You say that I should favor all of them. Or is there one that I should like most? Are they all merely servants? If so, then why do they behave in so orderly a fashion? Do they take turns playing ruler and subject? Is there a true lord among them? But whether I know who it is or not, it should not affect the truth of the matter.
_On Sagehood and Cultivating Life_
From the _Chuang-tzu_ , Chapter 15: Constraining the Will
So it is said, the life of the sage follows the celestial way, and in death he dissolves and merges with all things. In stillness he is at one with the virtue of yin; in movement he flows with yang. He does not bring fortune and does not cause misfortune. He only responds when external circumstances call for it. He only acts when pushed. He only rises up when there is no other alternative. He throws away the whys and wherefores, and follows the celestial way. Therefore, he does not meet with disaster. Nor is he burdened by material things. He is not slandered by people nor punished by the spirits. He floats with life and rests with death. He does not worry and does not scheme. He is like light that does not dazzle. Completely trustworthy, he does not need to make promises. His sleep is dreamless and his waking hours are free from worry. His spirit is pure and his soul is not tired. In emptiness, nothingness, and simplicity, he is in harmony with the celestial way.
Therefore, it is said that grief and happiness pervert virtue, joy and anger obstruct the Tao, and delight and repulsion work against virtue. When the mind is without worry or joy, virtue is complete. When it is at one and unchanging, stillness is complete. When it does not oppose anything, emptiness is complete. When it does not interact with things, simplicity is complete. When it does not resent things, purity is complete.
Thus, it is said that if the body works too hard and does not rest, it will weaken. If the generative energy is used without restraint, it will be exhausted. If it is exhausted, you will be tired. It is the nature of water that if it is not mixed with other things, it will remain clear. If it is not stirred, it will remain still. Dam it and it will not flow. If it stops flowing, it will no longer be clear. Such is the nature of the celestial way. So it is said, be pure and simple and do not be mixed up. To be still, unified, and unchanging, to be simple and nonintrusive, moving with the celestial path—this is the way of cultivating the spirit.
**NOTES ON THE TRANSLATION**
Although Burton Watson's translation of the _Chuang-tzu_ is considered the standard reference, I have translated some words and phrases differently. My choice of words is based on suggestions made by commentators of the _Chuang-tzu._ In "Discussion on All Things Being Equal," I have used the phrase "my spirit left my body" instead of "I lost myself" (Watson's version) to translate the three Chinese words that are literally "I," "lost," and "me." In the language of Taoism of the time, "I" and "me" in the phrase do not refer to the same subject. "I" refers to mind or spirit, and "me" refers to the body. Thus, I think that the entire phrase may be better rendered as "my spirit left my body." This is more consistent with some Chinese commentaries that suggest that Tzu-ch'i was describing a meditative or trancelike state.
I have also translated the word _yang_ as "life" instead of "light." In a Taoist text, _yang_ is better rendered as "life," especially in a context where Chuang-tzu was talking about caring for health and sanity in troubled times.
**Lieh-tzu: A Taoist Guide to Practical Living**
The _Lieh-tzu_ is a collection of stories and philosophical musings. It contains materials written over a period of six hundred years (between 300 BCE and 300 CE). There were twenty sections in the original collection, and these were condensed into the eight sections we have today.
During the hundred years or so after it was compiled, the _Lieh-tzu_ did not receive the kind of attention that was given to the _Tao-te ching_ and the _Chuang-tzu._ Most scholars believed that its teachings were similar to those of the _Chuang-tzu_ , which was sufficient for gaining an understanding of Taoism of the Warring States and early Han periods. If not for the efforts of a scholar of the Eastern Chin (317–420 CE) who edited and wrote a commentary on it, the _Lieh-tzu_ probably would have disappeared into oblivion.
Although the _Lieh-tzu_ was written by more than one person and the text that we have today is incomplete, it contains some of the best presentations of the teachings of Taoism. Its down-to-earth, humorous, and amusing discussion of the Tao, human nature, and issues that are remarkably relevant to our times make it one of the most accessible Taoist texts ever written.
The following excerpts are from my book _Lieh-tzu_ : _A Taoist Guide to Practical Living._ In this book I attempted to present the teachings of the _Lieh-tzu_ by bringing out the "intention" or "voice" of the text. While books are meant to be read, voices are meant to be listened to. In the _Lieh-tzu_ I tried to let the text speak as if the philosopher were talking directly to the reader. It is not a translation in the strict sense because I have elaborated on some parts and amalgamated others. Some hard-to-pronounce Chinese names have been omitted to facilitate the continuity of listening to the text. I hope that this method of presenting the _Lieh-tzu_ conveys the feel of listening to one of the greatest teachers of Taoism.
_On the Tao_
From the _Lieh-tzu_ , Part One: The Gifts of Heaven
THAT WHICH IS NOT BORN GIVES BIRTH TO EVERYTHING
Lieh-tzu was a humble and sincere person. His thoughts and actions tell us he was "uncommonly common." He was unassuming and never displayed his learning. He lived a simple and quiet life and did not compete with others for recognition. Therefore, although he had lived in the kingdom of Cheng for forty years, people in positions of power saw him only as a common citizen. Throughout his life, Lieh-tzu never made a name for himself.
Without the burdens and problems associated with fame and fortune, Lieh-tzu could live leisurely and be free to do what he liked and go where he wanted. To Lieh-tzu, being an unknown citizen was better than being a person of power and responsibility. In a time when politicians played games of intrigue, Lieh-tzu felt it was better to remain silent and be truthful to oneself.
Of course, there are certain things that even a wise sage cannot escape. But, not being bound by custom and social convention, Lieh-tzu was able to deal with adversity much better than anyone else. One year, a famine occurred in Cheng, and Lieh-tzu decided to move to the kingdom of Wei to see if he could make a living there. Moreover, he thought this would give him an opportunity to travel to an unknown country and broaden his learning.
While Lieh-tzu was preparing to leave, a group of his students came to him. They were worried that their teacher might leave them for a long time. They knew Lieh-tzu did not follow any routine, and, if the mood suited him, he might wander for months or years before returning. Therefore, they wanted their teacher to give them some words of wisdom before he departed.
Lieh-tzu was not a person given to casual chatting. After his students begged him tirelessly for half a day, he finally said, "Think about this. Old man sky never says a word, but we can see that everything has its place in the universe. Nature has a lot to teach us. All you need is to open your eyes and look. The changes you see in nature follow a course. The four seasons behave in a regulated way. In truth, all human matters follow the same principles as the workings of the sky and earth. What more is there for me to say?"
His students were not satisfied and continued to pester him with questions. One student said, "Sir, even if you feel there is nothing for you to say, you can at least tell us what your teacher Hu-tzu taught you." Lieh-tzu was silent for a while. Then he smiled and said, "Actually, my teacher Hu-tzu did not say much. He told us to let everything go according to its natural way. However, I did remember a few things he mentioned to some of my fellow students. I'll share them with you now."
Here is what Master Hu-tzu taught:
There are many things in the universe that we don't understand. For example, some plants and animals require help from others to grow and survive, while others don't. We humans rely on plants and animals for food. We also need some of our community to farm the land and raise the livestock to sustain the rest of us. On the other hand, cacti can grow in the most hostile conditions and they do not need much support to survive. In general, those that are less dependent on the external environment for support will find it easier to survive than those that do. They will not die when their supporting environment disappears.
However, we should not look down on those who need to depend on others for survival. We should let them grow naturally in their own way, for their mode of living has its place in maintaining the balance of the universe. If we tried to change their way of life, we would upset the balance of things, and the order of the universe would be disturbed.
All things have their place in the universe, whether it is active or passive, moving or not moving. They fulfill their function in the world simply by being what they are. Everything plays a part in the process of creating, nourishing, transforming, and destroying. The creation of one thing is the destruction of another, and the destruction of one thing is the creation of another. In this way, life carries on in the universe. In every moment there is birth and death and there is coming and going. This process never stops. . . .
If we understand that birth and death are part of the natural order of things, we will know that our lives cannot be controlled by our own efforts, and coming and going are not our own doing. At birth, we take a shape and form; in growth, we undergo development and change; and when our course has run out, we dissolve and return to where we were before we were born.
If we know the order of things, we will understand that when intelligence and wisdom have reached their zenith, they will begin to fade and decay. The rise and fall of shapes, colors, thoughts, and feelings are not subject to control. Because we don't know whence they come or where they go, we can only say that everything that is born comes from the not-born.
From _Lieh-tzu_ , Part Six: Effort and Destiny
EFFORT ARGUES WITH DESTINY
One day Effort said to Destiny, "My achievements are greater than yours."
Destiny did not agree. He challenged Effort immediately. "What have you done to make your achievements surpass mine?"
Effort said, "Whether someone lives long or dies young, is rich or poor, will succeed or fail depends on me."
Destiny said at once, "Old P'eng's intelligence did not match the emperors Yao's and Shun's, but he lived a long and healthy life. On the other hand, Yen-hui, Confucius's best student, died when he was eighteen. Confucius's virtue far surpassed the feudal lords', but compared to them he was destitute and poor. The emperor Shang-t'sou was cruel and immoral but lived a prosperous and long life. On the other hand, his ministers who were virtuous met with violent deaths. There was a man who sacrificed his own fortune to allow his brother a chance to be employed by the lord of Cheng. He remained poor and unknown for the rest of his life. Then there was another man who had neither virtue nor ability who became the lord of Ch'i. How about Po-yi and Shu-ch'i, who starved to death in the mountains because they would not compromise their integrity and honor to serve an enemy lord? What can you say about corrupt officials who are rich, or honest, hard-working people who are poor?"
Effort had not expected this barrage of evidence against his assertion. He frowned, but Destiny continued, "If you are as effective as you say, then why don't you make the hard-working people rich? Why don't you give virtuous people a long and prosperous life? Why are the intelligent and able people not employed, and why do stupid people occupy important places in government?"
Effort had no more to say in the face of these challenges, so sheepishly he said to Destiny, "You are right. I do not have much effect after all. But I daresay a lot of things happen the way they do because you've been up to mischief, twisting people's destiny around and enjoying it!"
Destiny then said, "I cannot force the directions of things. I merely open doors for them to go through. If something is going straight, I let it follow the straight path; if something takes a turn I do not hinder it. No one, not you or I, can direct the path of things. Long life or short, rich or poor, success or failure, fortune or misfortune, all come about by themselves. How can I direct events or even know where things would end up?"
_On Sagehood and Cultivating Life_
From _Lieh-tzu_ , Part Two: The Yellow Emperor
RIDING ON THE WIND,
FLOATING WITH THE CLOUDS
Lieh-tzu had the immortal Old Shang for a teacher and the sage Pai-kao-tzu as a friend. After he had finished his training, he came home riding on the wind and floating on the clouds.
A man named Yin-sheng heard about Lieh-tzu's feat and wanted to learn this skill of riding on the wind. So he went to Lieh-tzu and asked to be his student. So intent was Yin-sheng on learning this skill that he stayed at Lieh-tzu's home and kept pestering the teacher with questions. This went on for several months, but Lieh-tzu only ignored him.
Yin-sheng began to get impatient and then angry that Lieh-tzu was not teaching him. One day, he left in a huff.
When Yin-sheng got home, he calmed down and realized he had been stupid and impulsive, so he went to Lieh-tzu and asked to be his student again. Lieh-tzu simply said, "Why did you come and then leave and then return?"
Yin-sheng said, "When I first came to ask you to teach me, you ignored me. So I got annoyed and left. Then I realized I was too impatient and reckless, so I came back to ask you to accept me as a student again."
Lieh-tzu said, "I had thought you were intelligent, but now I can see you are quite stupid. Listen to what I went through when I learned from my teachers."
Lieh-tzu said:
"When I asked Old Shang to be my master and Pai-kao-tzu to be my friend, I decided to work hard to discipline my body and mind. After three years, I was afraid to have notions of right and wrong and I did not dare to speak words that might offend or please. It was only then that my master glanced at me and acknowledged my presence. Five years later, I thought freely of right and wrong, and spoke freely of approval or disapproval. My master gave me a smile. Seven years later, my thoughts came naturally without any conceptions of right and wrong, and words came naturally without any intention of pleasing or offending. For the first time, my master invited me to sit by his side. Nine years later, no matter what came to my mind or what came out of my mouth, there was nothing that was right or wrong, pleasing or offending. I did not even entertain the idea that Old Shang was my master and Pai-kao-tzu was my friend.
"It was then I became aware that there was no barrier between what was inside and what was outside. My body was illuminated by a bright light. I heard with my eyes and saw with my ears. I used my nose as mouth and my mouth as nose. I experienced the world with the totality of my senses as my spirit gathered and my form dissolved. There was no distinction between muscles and bones. My body stopped being heavy and I felt like a floating leaf. Without knowing it, I was being carried by the wind. Drifting here and there, I did not know whether I rode on the wind or the wind rode on me."
He then looked at Yin-sheng and said, "You had only been here for less than an hour and you got dissatisfied that you were not taught. Look at your condition. The parts of your body do not cooperate; the vapors of the sky and earth do not enter your body; your joints and bones are so heavy that you can't even move. And you want to learn how to ride on the wind?"
When Yin-sheng heard these words he was ashamed and did not ask again about riding on the wind.
From _Lieh-tzu_ , Part Seven: Yang-chu
LIFE—TEMPORARILY STAYING IN THE WORLD;
DEATH—TEMPORARILY LEAVING
Yang-chu said:
"If you live to be a hundred, it is considered a long life. However, only one in a thousand persons is that lucky. But if we take a person who has lived a hundred years and look at the time he has spent in his life, we will realize that a hundred years is not a long life. Out of these years, childhood and old age take up at least half the time. In addition, half the day he is asleep. Not to mention the hours during the day that he has idled away. What does that leave him? Moreover, if you take out the times when he is ill, sad, confused, suffering, and not feeling good, there isn't much time left that he can enjoy or be free.
"Some people think they can find satisfaction in good food, fine clothes, lively music, and sexual pleasure. However, when they have all these things, they are not satisfied. They realize happiness is not simply having their material needs met. Thus, society has set up a system of rewards that go beyond material goods. These include titles, social recognition, status, and political power, all wrapped up in a package called self-fulfillment. Attracted by these prizes and goaded on by social pressure, people spend their short lives tiring body and mind to chase after these goals. Perhaps this gives them the feeling that they have achieved something in their lives, but in reality they have sacrificed a lot in life. They can no longer see, hear, act, feel, or think from their hearts. Everything they do is dictated by whether it can get them social gains. In the end, they've spent their lives following other people's demands and never lived a life of their own. How different is this from the life of a slave or a prisoner?
"The ancients understood that life is only a temporary sojourn in this world, and death is a temporary leave. In our short time here, we should listen to our own voices and follow our own hearts. Why not be free and live your own life? Why follow other people's rules and live to please others? When something enjoyable comes your way, you should enjoy it fully. Don't be imprisoned by name or title, for social conventions can lead you away from the natural order of things. It doesn't matter whether you will be remembered in generations ahead, because you will not be there to see it.
"Why spend your life letting other people manipulate you just to get a name and reputation? Why not let your life be guided by your own heart and live without the burdens of fame and recognition?"
3
_Honoring the Sacred Powers_
DEVOTIONAL TAOISM
THE TAO IS THE SOURCE OF LIFE OF ALL things, and this sacred power is sometimes manifested as deities and spirits. In the Taoist spiritual tradition, devotion is a way of honoring the sacred power that gave us life and nourished us. Also, through devotion, a bond is created between humanity and the sacred, and as long as this bond is maintained, there will be peace and harmony in the universe.
The readings in this chapter are from two of the most famous texts of Taoist devotional literature: the _T'ai-p'ing ching ch'ao_ (Essentials of the Classic of Peace and Balance) and the _Pei-tou yen-sheng ching_ (The North Star Scripture of Longevity). The excerpt from the _T'ai-p'ing ching ch'ao_ gives us a glimpse of how Lao-tzu is portrayed as the chief deity of the Taoist religion. The _Pei-tou yen-sheng ching_ is a liturgy that honors the celestial deities of the Northern Bushel Stars (the Big Dipper), who are the rulers of health, longevity, and human destiny.
**T'ai-p'ing ching ch'ao ( _Essentials of the Classic of Peace and Balance_ )**
The _T'ai-p'ing ching ch'ao_ consists of excerpts from the _T'ai-p'ing ching_ , the book from the Eastern Han dynasty (25–220 CE) that launched the movement of devotional Taoism. Much of the original _T'ai-p'ing ching_ is lost, and the version collected in the Taoist canon today is only a small fraction of the original work. The _T'ai-p'ing ching ch'ao_ was compiled by a Taoist of the T'ang dynasty. The editor took what he thought were the best parts of the _T'ai-p'ing ching_ and compiled them into one book. It is in the _T'ai-p'ing ching ch'ao_ that several missing sections of the _T'ai-p'ing ching_ are preserved. The story of the birth of Lao-tzu and his deification (translated below) would have been lost if the editor of the _T'ai-p'ing ching ch'ao_ had not included it in his book.
_The Birth of Lao-tzu_
From _T'ai-p'ing ching ch'ao_ , Chapter 1
The Great Lord of Longevity is named the Great Balance of the One True Wonderful Vapor, the Latter Sacred Lord of the Nine Mysteries of the High Pure Golden Tower of Heaven. His name is Li and he is descended from the Great High One. He is the fetus of the Great Void of the Jade Emperor. During the time of the Lord of the Great Mystery and Completeness, in the fifteenth year of the reign of the Great Emperor, when _ping-tzu_ was the Ruling Star of the year, his vapor was conceived. In the first year, named _chia-shen_ , of the reign of the Emperor of Peace, his shape took form. During the seventh year of the High Harmony, named _keng-yin_ , on the third day, named _chia-tzu_ , at the hour of _mao_ , when virtue and body were in union and the stars were aligned, he was conceived in the Jade Kingdom of the Mysterious North, in the spirit realm of the celestial bodies, on the mountain of Peng-lai that was shaped part human and part bird, in the valley of the _li_ trees.
There was a virgin who was the mother of the High Mysteries who lived in the Chamber of the Nine Mysteries, deep within the shady (yin) valley. When the Mysterious Virgin conceived, she saw in a dream the infant's body wrapped in the clouds, the sun, and the moon. The six breaths resonated with his spirit. She felt the movement of yang and knew that she carried within her womb an enlightened being.
On the morning of his birthday, three suns rose from the east. After he suckled, magic water came out of the mouths of nine dragons. That is why the people of that spirit valley gave it the name "bright landscape."
By the beginning of his third year, his body had attained the true form, and his speech radiated a golden splendor. At five, he frequently gazed at the sun and smiled, and looked at the moon and sighed. Up above he observed the growth of the breath of yang. Down below he saw the way of yin and waning. Therefore he cared for his spirit and harmonized his soul. He held on to the fetus to keep his spirit sacred. He gathered generative energy to fill his blood. He strengthened his marrow to build his tendons.
At seven he learned to swallow the rays of light, eat the mist, and chew the tendrils of the sun. At the age of twenty-seven, his complexion radiated a golden glow. Leaving the mundane world and distancing himself from desire, he pledged to save the world. His spirit moved the Lords of the Great Primal Beginning and he was given the teachings of the Three Completenesses. He practiced the teachings of the Three Caverns and his deeds were seen in the nine directions. At thirty-seven, he could use his humility and simplicity to file down sharpness. At forty-seven, he could use his throat to gather the harmonious light. At fifty-seven, his saliva became the mysterious nectar and his works of merit traveled everywhere unhindered. At sixty-seven, he gave a treatise to the Latter Sacred Lord, who was also the Lord who had received the Tao before sky and earth were created. He is named the Latter Sacred Lord because that was how it was recorded. The Earlier Sacred and Latter Sacred are really the same [sic].
He then ascended to the Palace of the High Pure and wandered in the Houses of T'ai-chi. He rules the skies and the ten realms below. He is given jurisdiction over the millions of mortal beings. He watches over the sky, rivers, seas, plains, valleys, mountains, and woods. There is none that will not obey him. He is the judge of the nine levels and ten layers. Therefore he is called the Nine Mysteries.
At seventy, his longevity became limitless. He could hide and appear with ease. He has mastered the arts of immortality and compiled the methods and formulae of longevity.
**NOTES ON THE TRANSLATION**
Taoist religious terms can be intimidating to people who are not familiar with them, so some of the terminology from the selection is explained below.
The One True Wonderful Vapor is also known as the Breath of the Tao, the Primordial Vapor, and the Undifferentiated Vapor. These are all names of the Tao, the origin and underlying reality of all things. In the _T'ai-p'ing ching_ the term also refers to the ideal state of existence, when everything was in the embrace of the Tao.
Taoist celestial space is divided into nine layers, called the Nine Mysteries. The Ninth Mystery is the highest layer of the celestial realm. In the _T'ai-p'ing ching_ , the High Pure Golden Tower of Sky is the entrance to Shang-ch'ing, the domain of the highest deities. The Golden Tower is sometimes called the Mysterious Gate. Later, the High Pure (Shang-ch'ing) Realm was replaced by the Jade Pure (Yüch'ing) Realm as the highest level of the celestial domain.
The passage of time in the Chinese calendar is reckoned by a system called the Ten Celestial Stems and Twelve Terrestrial Branches. The Ten Celestial Stems are _chia, i, ping, ting_ , _wu, chi_ , _keng, hsin, jen_ , and _kuei_. The Twelve Terrestrial Branches are _tzu, ch'ou, yin, mao, ch'en, ssu, wu, wei, shen, yu_ , _hsü_ , and _hai_. Each year, month, and day can be designated by a pair of stem and branch. Thus, in the text, _ping-tzu_ and _keng-yin_ identify the year, and _chia-tzu_ identifies the day. The Ruling Star of a year is also named after the stem-branch combination. The Ruling Star of the year is a controller of events of that year. It is also the Guardian Star of all persons born in that year. The day is divided into twelve two-hour units, and each unit is named after a Terrestrial Branch.
The Jade Kingdom of the Mysterious North is the realm of the North Pole Star and the Constellation of the Northern Bushel (the Big Dipper). The highest deities are said to reside in these stars.
The fetus of the Great Void refers to the spirit or seed of immortality. It also means the "son of the Mother (the Tao)." In the text, it is taken to mean that Lao-tzu's mother is the Tao itself.
Finally, the nine levels and ten layers refer to the nine steps of the celestial realm and the ten levels of the underworld. The Taoist underworld, at least in the period when the _T'ai-p'ing ching_ was written, was not a hell. It resembles a shaman's otherworld where the Taoist journeyed in spirit to rescue a sick person's soul or obtain power from the Guardians of the Tao.
**Pei-tou yen-sheng ching**
**( _The North Star Scripture of Longevity_ )**
The full title of this scripture is _T'ai-shang hsüan-ling pei-tou pen-ming yen-sheng chen-ching_. Translated, it means "the True Scripture of the North Star, the Governor of Longevity and Destiny, as revealed by the Sacred Spirit of the Great One." Although the text says that the scripture was revealed by Lao-tzu to the Celestial Teacher Chang Tao-ling, it is now generally agreed that the book was written sometime during the end of the T'ang and the beginning of the Sung dynasty.
The _Pei-tou yen-sheng ching_ is a liturgy. It is meant to be chanted in a service accompanied by rituals or read aloud at home by devotees. The _Pei-tou yen-sheng ching_ is also one of the most popular liturgies of Taoism. This liturgy is typically chanted on the first and fifteenth day of the lunar month and on the Festival of the Northern Bushel Stars, which falls on the first nine days of the ninth lunar month. Because the North Star and the Northern Bushel Stars are associated with longevity, the _Pei-tou yen-sheng ching_ is also chanted as a birthday blessing.
_From the_ Pei-tou yen-sheng ching
PROLOGUE
On the seventh day of the first month in the first year of the Realm of Everlasting Life, the Patriarch Lao-tzu was in the Palace of T'ai-chi in the Realm of T'ai-ch'ing (Great Purity). He looked at sentient beings and saw that for millennia they had been sunk into the depths of suffering, doomed to repeat countless cycles of rebirth. Whether born human, whether born on Chinese soil, in foreign lands, or in underdeveloped countries, whether born rich or poor, everyone lived on borrowed time. Many souls had fallen into the underworld, wandering without peace, their destruction brought about by their evil deeds. They were imprisoned in the world of the dead and suffered greater torment than they could bear. They would never find human existence again and would be reborn as beasts, birds, and insects. Having left the path of humanity, it would be difficult for them to return to it. However, despite all this, they still did not awaken. They were locked into the cycles of rebirth because they had been ignorant in their previous lifetimes.
Lao-tzu, out of great compassion, took on human form and descended to the mortal realm to teach humanity. In the capital city of the Kingdom of Shu, the guardian of the earth rose from the ground and built a jade platform. The Patriarch Lao-tzu ascended the platform and transmitted the Scripture of the North Star to the Celestial Master, telling him to let this scripture be known far and wide, so that people might be delivered from their sufferings.
THE MAIN SECTION
The Patriarch Lao-tzu said to the Celestial Master:
"It is difficult to be born in human form. It is even more difficult to be born in the central lands. Even if you have that opportunity, to encounter the true teaching is rare. Many are lost in delusion. Many stray into evil paths. Many are deeply rooted in their unethical ways. Many are dishonest and dishonorable. Many kill and rape. Many delight in casual pleasures. Many are greedy and jealous. Many souls are lost in the underworld. Many have lost their chance to exist in human form. Humanity does not understand karma. They do not know the true way. They are confused and lost. Seeing the suffering of humanity, I am moved by compassion to give them these teachings. I will let them know that all life comes from the Tao. If they understand this, then they will attain longevity. Their seed will not die. They will continue to exist in human form. They will not be born in lands where the teachings of the Tao are unknown. They will not lose the essence of being human. Moreover, they will cultivate the Tao in themselves and gradually enter the path of immortality. They will be liberated from the cycles of rebirth. They will transcend earthly existence and merge with the Tao. This is why I want to give you this great and wonderful vehicle, so that you can deliver humanity, and let them return to their true nature.
"On their birthday, they should abstain from meat, conduct a ceremony, and make offerings to the Northern Bushel deities, the Three Lords and Five Emperors, the Nine Officers and the Four Magistrates. At this time they can ask for blessings and deliverance from catastrophes. They can present petitions and sincerely ask for forgiveness. They should offer fragrant flowers and five kinds of fresh fruits. Following the ways of the sky and earth, they should make the offerings seriously and formally, purifying the environment where the ceremony is held. Whether the ceremony is conducted in a temple or at home, the effects of their actions will be felt. If they perform the ceremony they will receive merit. Remember, do not forget this and do not be tardy.
"Chanting the names of the Northern Bushel deities can deliver you from disaster. It can ward off evil and give you prosperity and longevity. It can help you accumulate good deeds. If you feel that a disaster is imminent, light incense and chant the North Star Mantra, and it will give you peace of mind. I shall now transmit this chant to you:
The seven sacred deities of the Northern Bushel
Can deliver us from the three disasters;
The seven sacred deities of the Northern Bushel
Can deliver us from the four destructive forces;
The seven sacred deities of the Northern Bushel
Can deliver us from catastrophes of the five elements;
The seven sacred deities of the Northern Bushel
Can deliver us from the six harms;
The seven sacred deities of the Northern Bushel
Can deliver us from the seven injuries;
The seven sacred deities of the Northern Bushel
Can deliver us from the eight obstacles;
The seven sacred deities of the Northern Bushel
Can deliver us from the nine baleful stars;
The seven sacred deities of the Northern Bushel
Can dissolve the disharmony between husband and wife;
The seven sacred deities of the Northern Bushel
Can dissolve the conflicts between men and women;
The seven sacred deities of the Northern Bushel
Can protect you from problems in pregnancy and birth;
The seven sacred deities of the Northern Bushel
Can deliver you from the cycles of rebirth;
The seven sacred deities of the Northern Bushel
Can ward off the disaster of epidemics;
The seven sacred deities of the Northern Bushel
Can ward off the disaster of illness;
The seven sacred deities of the Northern Bushel
Can ward off evil spirits;
The seven sacred deities of the Northern Bushel
Can ward off the attacks of tigers and wolves;
The seven sacred deities of the Northern Bushel
Can ward off the attacks of poisonous insects and snakes;
The seven sacred deities of the Northern Bushel
Can ward off the attacks of thieves and robbers;
The seven sacred deities of the Northern Bushel
Can protect you from accidental punishment;
The seven sacred deities of the Northern Bushel
Can protect you from accidental death;
The seven sacred deities of the Northern Bushel
Can protect you from misfortune coming from curses;
The seven sacred deities of the Northern Bushel
Can protect you from disasters coming from the skies;
The seven sacred deities of the Northern Bushel
Can protect you from disasters on the ground;
The seven sacred deities of the Northern Bushel
Can protect you from disasters coming from wars;
The seven sacred deities of the Northern Bushel
Can protect you from disasters of fire and water.
The lords of the seven stars
Are compassionate and understanding.
They deliver us from all disasters
And liberate us from suffering.
If you are beset with problems,
Chant these lines and it will give you peace.
You will be filled with great fortune
And will be in harmony with the five elements.
Your three souls will be healthy and stable,
And evil will stay away forever.
The true breath will descend from the five directions,
And many great fortunes will come to you.
"The names of the true lords of the stars are seldom uttered or heard. If you chant them, the Tao will grow strong and deep in you. It is good karma that led you to know them. If you chant their names, you will accumulate merits beyond measure. When honest men and women chant this scripture, their wisdom and original nature will develop. The heart of Tao will be opened. They will leave the path of delusion and enter the Gate of the Rare Mystery. They will return to the true way and enter the immortal realm.
"Therefore, during the festivals of the Lords of the Three Realms and the eight celebrations, your birthday, and the days in which the deities of the Seven Stars descend to earth, you should prepare an altar, chant this scripture, perform the ceremony, and abstain from meat. Follow the procedures carefully and your prosperity will know no measure. In every lifetime the sacred truth will not abandon you. You will not enter paths of evil. Those who possess this scripture can also regularly chant the names of the Lords of the Seven Stars. In this way, they will accumulate merit and fortune will descend on them.
"This is the sacred mantra:
The North Star group has nine luminous bodies.
In the center of the sky is the great sacred star:
Upward it points toward the golden gate,
Downward it envelops the Kun-lun mountains.
It regulates the movement of all things
And rules the universe.
The Great Pivot,
The Star Craving Wolf,
The Great Gate Star,
The Star of Prosperity,
The Scholar Star,
The Star of Virtue,
The Warrior Star,
The Destroyer of Enemies,
The Jade Emperor's star on high,
Which is the purple throne of the great lord.
The celestial circle of the macrocosm
Is present in the microcosm of a grain of dust.
Is there any disaster that it cannot avert?
Is there any prosperity that it cannot grant?
Let the true vapor of the ancient emperor
Come to protect my body.
All the constellations rotate around the Celestial Pivot,
Day and night without stopping.
We, the unworthy, who live in the mortal realm,
Are drawn toward the Tao and ask for enlightenment.
We are willing to abide by the solemnity of the ritual
So that we may attain immortality.
The Three Altar Stars: Energy of the Void,
The Scholar and Warrior Stars that give me balance—
From them I am born;
From them I receive nourishment;
They protect my human form."
**NOTES ON THE TRANSLATION**
The three disasters are catastrophes that come from the sky, the earth, and water. The four destructive forces are the _sha_ (mischievous and harmful spirits) coming from the four directions: north, south, east, and west. The catastrophes of the five elements are accidents involving metal, wood, water, fire, and earth.
The six harms come from the six senses: eyes, ears, nose, tongue, body, and mind. Because of desire, the six senses are attached to objects. Attachment to objects of desire drains internal energy, leading to the loss of health and longevity.
The seven injuries come from excessive responses of the seven emotions: happiness, anger, sorrow, fear, elatedness, likes, and dislikes. The seven emotions are linked to the seven souls, or _p'o_. Indulgence in these emotions will lead to the loss of the seven _p'o_. This affects mental stability since insanity is often described as the dissolution of the seven _p'o_. It also affects physical health because emotional outbursts and fluctuation of moods are harmful to the internal organs and the circulation of internal energy.
When the three disasters are mentioned with the nine catastrophes, they refer to the three blockages in the cavities along the spinal column. The three disasters are sometimes called "the three poisons" because the three blockages can hinder the circulation of energy and cause illness. The nine catastrophes are the nine closures in the cavities along the spinal column. The closures can drain energy away from an individual, block the flow of energy in the body, and cause illness.
4
_The Tao Within_
MYSTICAL TAOISM
THE GOAL OF THE MYSTIC IS TO BE united with the greater or cosmic part of the self. Shang-ch'ing Taoism, which emerged in China in the third and fourth centuries CE, is a form of mystical Taoism where the cosmic part of the self is the Tao. The primordial energy of the Tao is present in both the macrocosm of nature and the microcosm of the human body. By visualizing the images of the deities and journeying to their realms in the sun, moon, and stars, the Shang-ch'ing mystics achieved an ecstatic union with the greater power that is resident in the universe and within themselves. These two aspects of the Taoist mystical experience are illustrated by the two most important texts of Shang-ch'ing Taoism: the _Shang-ch'ing Huang-t'ing nei-ching yü-ching_ (The Yellow Court Jade Classic of the Internal Images of the High Pure Realm), and the _Shang-ch'ing chin-Ch'üeh ti-chün wu-tou san-yüan t'u-chüeh_ (The Lord of the Golden Tower of the High Pure Realm's Illustrated Instructions on [Visualizing] the Five Bushels and the Three Ones).
**Shang-ch'ing huang-t'ing nei-ching yü-ching**
**( _The Yellow Court Jade Classic of the Internal Images of the High Pure Realm_ )**
The _Shang-ch'ing huang-t'ing nei-ching yü-ching_ is regarded as _the_ representative scripture of Shang-ch'ing Taoism. Reputed to have been revealed by the deities to Lady Wei Hua-ts'un in 288 CE, the scripture was passed on to Yang Hsi, who transmitted it to Hsü Hui and Hsü Mi. When Lu Hsiu-ching compiled the Taoist books into the Three Caverns in 471 CE, the _Huang-t'ing nei-ching yü-ching_ became a part of the Taoist canon.
This scripture is a revealed text. Revealed texts are meant to carry an authority greater than texts written by mortals. One can tell whether a scripture is a revealed text by looking at its preface or the first few lines. Revealed texts always name the deity who transmitted the text to the writer. This is typically followed by statements of why the text is important.
There are two _Huang-t'ing chings_ : the _Huang-t'ing nei-ching yü-ching_ (The Yellow Court Jade Classic of Internal Images) and the _Huang-t'ing wai-ching yü-ching_ (The Yellow Court Jade Classic of External Images). The former is an esoteric text and the latter is an exoteric text. In spiritual literature, esoteric texts are written for initiates and exoteric texts are written for the general public. That the contents of the _Wai-ching_ are almost entirely contained in the _Nei-ching_ suggests that the former is probably an introductory text while the latter contains secret teachings available only to the initiated.
Personally, I find the _Nei-ching_ very much like an instruction manual and the _Wai-ching_ more like a description of the internal universe of the human body. My own training in internal alchemy has helped me to decode much of the information contained in the _Nei-ching_. The phrases of the _Nei-ching_ text are stylistically similar to instruction mnemonics ( _k'ou-chüeh_ ) that my Taoist teachers have given me.
_The Origin and Transmission of the_ Huang-t'ing nei-ching yü-ching
PREFACE
The Great Lord of Fu-sang ordered the immortal King of the Yang Valley to transmit to Lady Wei the _Huang-t'ing nei-ching yü-ching_. It is called the Great High's Harmonious Writ of the Heart. It is called the Golden Book of the Great Lord. It is called the Jade Scroll of the Lord of the East.
After purifying yourself for ninety days, recite it ten thousand times. It will harmonize the three human spirits ( _hun_ ), refine the seven souls ( _p'o_ ), eradicate the three monsters, and sooth and harmonize the five viscera. Your complexion will glow with color; you will be like an infant; the hundred illnesses cannot harm you, and disasters cannot overwhelm you.
After you have recited it ten thousand times, you will naturally see the spirits and deities in the cavern, and will be able to look internally at the intestines and stomach and see the five viscera. At that time, an enlightened being of the Yellow Court, the Jade Lady of the Center, will teach you how to live forever. These are the teachings of immortality.
You who have the mark of an immortal, receive my text. This text displays the one true form of the immortal spirit's abode where the sacred fetus dwells. To those who recite this text, the immortal spirit's dwelling place will be bright and strong, the true fetus will be safe and still, the sacred nectar will flow smoothly, the hundred gates will be bright and clear, the blood and marrow will be plentiful, the intestines and stomach will be empty yet full, there will be luster in the five viscera, the ears and eyes will be intelligent, broken teeth will become new, and the white hair will become black. Because I can eradicate evil and confusion, this is why I have been given the true names of the spirits of the six orbs.
When form is full and the spirit is strong, you will not die even if you want to. This is why the Inner Chapters of the _Huang-ting ching_ contains the teachings of immortality.
CHAPTER I: THE HIGH PURE (SHANG-CH'ING) REALM
Before the Purple Cloud of the Emperor of the Void in the High Pure Realm, the Lord of the Jade Dawn of the Great Way secluded himself in the Chamber of the Pearl Medicine and wrote these seven-word phrases:
Spreading the five forms and transforming them into the ten thousand spirits:
This is described in the Inner Chapters of the _Huang-ting ching_.
The harmonious music in the center is played in the three registers to accompany the dance of the immortal fetus.
Nine vapors shine brightly from the highest places.
From the child's spirit brow a purple haze is born.
This Jade Text is extraordinary and exquisite.
Recite it ten thousand times and you will rise to the three celestial realms.
A thousand disasters will go away and a hundred illnesses will be cured.
You will not be afraid of fierce tigers and brutal wolves;
Old age will be taken away and you will live forever.
_The Guardian Spirits of the Body_
CHAPTER 7: ATTAINING THE TAO
Attaining the Tao is not difficult if you are sincere.
The Mud Ball cavity and the hundred joints all have spirits.
Black and white, the spirit of hairs is called Great Beginning;
Root of vitality, the spirit of the brain is called Mud Ball;
High up and bright, the spirit of the eyes is called Mysterious Infant;
Protruding like a piece of jade, the spirit of the nose is called Hard Numinous Spirit;
Empty yet closed, the spirit of the eye is called Quiet Field;
Connected to life itself, the spirit of the tongue is called Judge of Principles;
Tough and sharp, the spirit of teeth is called a Thousand Varieties.
The spirit of the face is governed by the Mud Ball.
The Nine Cavities of the Mud Ball all have chambers.
The circle with the one-inch square is located here.
Swallow the Purple Robe and fly to the Palace of Multiplicities.
Contemplate this once and your longevity will have no end.
Everything is inside the brain.
All the spirits are seated, facing outward.
Keep them in your mind and they will naturally respond.
CHAPTER 8: SPIRIT OF THE HEART
The spirit of the heart, the Beginning of the elixir, is called Holding the Numinous Spirit;
The spirit of the lungs, a grand cover, is called Complete Emptiness;
The spirit of the liver, with the dragon's vapor, is called Containing Brightness;
Like burning wood, it directs the smoke to separate the muddy from the clear.
The spirit of the kidneys, mysterious and dark, is called Nourishing the Infant;
The spirit of the spleen, which is always present, is called Restrainer of the human spirits;
The spirit of the gallbladder, like a shining dragon, is called Strong Brilliance.
The spirits of six bowels and five viscera are integral to vitality.
Follow their path of celestial movements in your mind.
Keep them inside day and night and you will naturally live a long life.
**NOTES ON THE TRANSLATION**
There is a lot of symbolism in the text. To explain and interpret each term would be beyond the scope of this book. However, some Chinese words have no simple English equivalents and need some clarification on how they are translated. I have translated the Chinese word _shen_ as spirit, _ling_ as numinous spirit, and _him_ as human spirit. Some writers have rendered all three Chinese words as spirit. If these words do not appear together in the same segment of text, it is viable to translate any one of them as spirit. However, in the _Huang-t'ing ching_ , all three words— _shen_ , _ling_ , and _him_ —often appear together, and it would be confusing if all of them were translated the same.
I chose to translate _shen_ as spirit because traditionally the Chinese meaning for shen is a spirit that is an entity. I feel that the _shen_ in the Taoist scriptures have this nature. They are immortal, though they are guardian spirits inside us. I have translated _ling_ as "numinous spirit" because _ling_ has the connotation of "brightness and intelligence". For _hun_ , I have used the term "human spirit" to distinguish it from the immortal spirit, for the _hun_ is intimately tied to a mortal being. It resides in the human body when the individual is alive; it leaves the body at death, and depending on one's religious belief, it may wander in the underworld or enter another body to be reborn. In Taoism, the _shen_ are spirits that protect and judge us, the _ling_ are spirits that teach us, and the _hun_ are spirits that are wayward and mischievous. I hope that translating the three words in this manner will clarify their Taoist meanings.
**_The_ Shang-ch'ing chin-ch'üeh ti-chün wu-tou san-yüan t'u-chüeh**
**( _The Lord of the Golden Tower of the High Pure Realm's Illustrated Instructions on [Visualizing] the Five Bushels and the Three Ones_ )**
This is one of the many Shang-ch'ing scriptures collected in the Taoist canon said to be transmitted by the deity Lord Chou, whose full title is Tzu-yang Chen-jen Chou-chün (The Immortal Lord Chou of the Purple Light).
The text contains instructions for visualizing the deities and merging with them in their celestial palaces. The excerpt below describes the procedure for visualizations performed at the spring equinox. The complete text in the Taoist canon contains procedures for the summer solstice, autumn equinox, and winter solstice, as well as various days of the month.
_Flying to the Stars_
At the beginning of midnight at spring equinox, sit with your eyes closed and face east. Keep me within your body along with the Three Palaces, the Three Ones, and the Three Officials. Together with the Seven, and me in the center, ride the smoke of the purple vapor and step up to the Northern Bushel's (Big Dipper's) Bright Star. The Bright Daylight Star is the Eastern Deity of the Bushel. In this way, you will be transported to the center of the stars. Sit and inhale the purple vapor thirty times. Soon you will see the Eastern High Palace of the Bright Daylight Star. Inside the Palace is the Child of the Green Mystery who will give you the True Light. First, keep the big web of purple vapor below the North Star in front of me. Then hold on to the Three Ones.
These are the oral instructions from the deities.
The Deity Lord Chou said: Hold on to the seven figures and the mantle of the Bushel or the Seven Stars and rise with them to the Brilliant Daylight. Traveling with my lord in the center on the star mantle, turn the head of the handle so that the First Star is pointing forward. Inhale the purple vapor thirty times, keeping me in the purple haze while you are inhaling. Now visualize the Three Ones and the Three Officials. When you have finished inhaling, you should see seven figures revolving around in the purple haze as they descend into the Three Palaces. After a period of time, recite this petition in your mind:
The Thrice Honored Truly Highest Lord Above of the Great Mystery, Brilliant Daylight;
Ruler of spring when the thousand children open the gates to complete the elixir;
Ruler of the summer's pearly vapor mixed with the smoke of the feminine generative energy;
Ruler of the autumn's celestial splendor, the six constellations and the North Pole;
Ruler of the winter when the ten thousand evils block and rape the five earths— _keng, jen, wu, chi_.
Let the Celestial Barriers crumble and dissolve when I turn to face them;
Refine my seven souls and my three human spirits;
Give life to my five viscera;
Let me attain the real, fly to the High Pure Realm's floating images of the Seven Beginnings, live long, and follow my nature.
After my long cry to the thousand spirits,
Let me rest and keep within me the four seasons.
This is my sole wish.
**NOTES ON THE TRANSLATION**
Again there is quite a bit of esoteric symbolism here, and to explain each symbol would be beyond the scope of this book. To be consistent with the _Huang-t'ing nei-ching yü-ching_ , I have translated _hun_ as human spirit although it is the only "spirit" mentioned in this text. I have also translated the words _yin ching_ as "feminine generative energy" because in the text it is paired with the "pearly vapor," which is male generative energy.
_From the text_ Shang-ch'ing chin-Ch'üeh ti-chün wu-tou san-yüan t'u-chüeh ( _The Lord of the Golden Tower of the High Pure Realm's Illustrated Instructions on [Visualizing] the Five Bushels and the Three Ones). The Shang-ch'ing adept sits at the right, and the seven celestial lords of the Northern Bushel are in the center. The figure on the left is the young attendant who brings messages from the celestial lords to the practitioner_.
The pronoun "me" in the expression "keeping me within" refers to the guardian deity, the numinous spirit, and the energy of life inside us. The text consists of words spoken by the deity to the practitioner. Thus, 'you," the practitioner, need to keep "me," the deity, within. If "you" lose "me," you will lose the connection to life.
_Keng, jen, wu, chi_ , are four Celestial Stems. For a discussion of the Celestial Stems, please refer to the Notes on the Translation in chapter 3. The text here mentions five and lists four because the first stem, _chia_ , is "hidden" ( _tun_ ). This is common knowledge to Taoist practitioners, although it is somewhat confusing to people unfamiliar with divinational arcana in Taoism. The scope of this book does not allow me to explain the meaning "hiding the _chia_ stem" in detail. Briefly, there are two accepted meanings. One is that _chia_ , as a Celestial Stem and stellar body, is hidden because it can take on many possible positions. Its location cannot be determined when the rest of the Stems are fitted into the _pa-k'ua_ (eight trigrams). The second meaning is that _chia_ refers to a dark or invisible star, which embodies the primal darkness or the essence of yin energy. Like the dark side of the moon, it is hidden and cannot be seen.
5
_In Search of Immortality_
TAOIST INTERNAL ALCHEMY
SKY AND EARTH ARE AGELESS BECAUSE they are constantly renewed by the breath of the Tao, the source of life. If humans can cultivate the breath of the Tao and circulate it in the body, they too can become immortal and be at one with the sky and earth. Cultivating and circulating the energy of the Tao require transforming body and mind so that the energy within is as pristine as that of the primordial vapor of the Tao. This process of transformation is likened to refining metals, and the methods of purifying body and mind are known as "alchemy."
The selections in this chapter are from two classics of Taoist alchemy: the _Tsan-tung-chi_ (Triplex Unity), and the _Wu-jen p'ien_ (Understanding Reality).
**Tsan-tung-chi ( _Triplex Unity_ )**
The _Tsan-tung-chi_ is regarded by Taoists as the ancestor of all alchemical literature and is reputed to have been written by Wei Po-yang, the father of Taoist alchemy. The oldest sections of the book have been dated to 142 CE. The phrase _tsan-tung-chi_ can be interpreted in several ways. Briefly, _tsan_ means combining, _tung_ means similar, and _chi_ means bringing together. Literally, the phrase means "to compound together three similar substances." Some commentators of the _Tsan-tung-chi_ have interpreted the three substances to be the three internal energies: _ching_ (generative energy), _ch'i_ (vital or breath), and _shen_ (spirit). Others have chosen to describe them as lead, mercury, and cinnabar. Yet others have described them as the Three Ones, who are the guardians of the three energy fields (called _tan-t'iens_ ) in the body. The Three have also been referred to as the three realms of existence: sky, earth, and humanity (or heaven, earth, and man). The diverse interpretations of the title of the book suggest that the _Tsan-tung-chi_ has many levels of meaning. It is simultaneously a theory of the human body, a set of guidelines for spiritual transformation, and a manual for cultivating health.
Historians and scholars now agree that the _Tsan-tung-chi_ in the Taoist canon is probably the work of several authors. Some parts of the _Tsan-tung-chi_ are written in the poetic style of four beats to the line and some with five beats. Other parts are written in prose. It is now generally accepted that the middle section of the book was written by Wei Po-yang himself in the second century CE. Some parts were added by his students, and some sections were probably written by practitioners of Taoist alchemy as late as the sixth century CE.
My translation of the _Tsan-tung-chi_ is from the version collected in the Cheng-t'ung Taoist canon (ca. 1440s). I have kept the partitions used by the major commentators. Richard Bertschinger's _The Secret of Everlasting Life_ presents the _Tsan-tung-chi_ in a different order. Bertschinger's translation is from the _Ku-wen tsan-tung-chi_ (The Old Text of the Triplex Unity). Although the _Ku-wen_ text was once regarded as a secret version that is older than the _Tsan-tung-chi_ of the Taoist canon, scholars have now determined that the _Ku-wen_ text was actually written during the reign of Emperor Chang Te (1506–1521 CE) of the Ming dynasty. This means the _Kun-wen_ text actually postdates the one collected in the Taoist Canon.
Regardless of when it was written and who contributed to its authorship, the _Tsan-tung-chi_ is a remarkable work. Today, fifteen hundred years after Wei Po-yang first set down his theory and practice of transforming body and mind, the _Tsan-tung-chi_ is still acknowledged by Taoists as the definitive manual of spiritual transformation.
_Cultivating Mind_
From Part One
Nourish yourself internally.
In peace, stillness, and complete emptiness,
The hidden light of the origin will glow
To illuminate the entire body.
Close and block the mouth
To strengthen the numinous pearl.
Let the three lights sink below
To incubate the young pearl.
Look for it and you cannot see it.
Yet it is close by and easy to get.
As the Yellow Center gradually penetrates everything,
Luster and glow will spread to the muscles and skin.
Start your cultivation correctly and you will be able to see it to completion.
The trunk will stand firm and the branches will take hold.
The One is concealed and hidden;
The people of the world have never known it.
Great virtue does not act;
It does not seek or want.
Lesser virtue acts;
And it is used endlessly.
Great obstruction is called "having";
No obstruction is called "nothingness."
Nothingness can carry you up
To where the sacred virtue resides.
This is the method of the "dual-entrance cavity"
In which gold and energy (ch'i) work together.
_Cultivating Body_
From Part Two
The mirror of yang makes fire,
But if there is no sun, it will not give light.
If not for the moon and the stars,
How can the watery fluid be collected?
If two energies that are distant from each other
Can respond and communicate,
How much more can those that are close, inside your body,
And held within your chest?
Match yin and yang to the sun and moon,
And use fire and water to activate each other.
The three treasures—ears, eyes, and mouth—
Close and block them and let nothing through.
The enlightened being is immersed in the depths,
Floating and wandering, keeping the direction within.
Sight and hearing are devious and crooked.
Opening and closing must be synchronized.
In the pivot and axle of the self,
Movement and stillness must never be exhausted.
Guard the energy of _li_ (fire) within.
Do not tax the intelligent energy of _k'an_ (water).
Close the mouth and stop talking;
To speak rarely is to flow with the undifferentiated whole.
These are the three important principles:
Relax your body and situate yourself in an empty room;
Abandon the will, and return to the void and nothingness.
When there are no thoughts, you will find the constant.
Let difficulties prod you forward.
Focus the mind and do not let it wander.
Embrace the spirit when you sleep.
Attend to its care and beware of its neglect.
Your complexion will be moistened until it is shining;
The bones and joints will grow firm and strong.
When all the toxins are discharged,
The true yang will stand up alone.
Cultivate without stopping,
And the mass of energy will move like cloud and rain.
Flowing like spring showers,
Dripping like melting ice,
From the head falling down to the feet,
And from there rising up again,
Coming and going, swirling the limitless,
And stirring everything throughout.
Those on the path of the return know the Tao.
Weakness is the handle of virtue.
Plow and pull out the weeds of impurity.
Do it meticulously and you will attain harmony.
For in the mud lies a clear path,
And in the long darkness a light will finally shine through.
People of the world love little tricks.
They do not probe the depths of the Tao.
They abandon the correct way and follow the devious paths.
They want the quick way but they do not get through.
Like the blind leaning on a staff,
Like the deaf who hear ringing in the ears,
They go under the water to hunt for birds and rabbits;
They climb the mountains to look for fish and dragon;
They plant wheat and hope to harvest millet;
They swing a compass to draw a square;
They exhaust their strength and weary the spirit,
And at the end of their lives there is no attainment.
If you want to know how to feed on internal energy,
The procedure is not really that complicated.
_The Alchemical Process_
From Part Two
Strive to nourish your inner nature;
Lengthen your life and turn back time.
Consider the final outcome;
And think about what came before.
We are endowed with a body
Whose form is fundamentally empty.
The primordial generative energy spreads like a cloud,
Held up by vapor in the Beginning.
Yin and yang are the bases of things,
Coming to reside within as _hun_ (human spirit) and _p'o_ (soul).
The yang spirit of the sun is the human spirit,
The yin spirit of the moon is the soul.
Joining together, the human spirit and the soul
Live with each other in the same home.
The inner nature rules within,
Setting up its position in the castle.
Feelings rule the camp outside,
Building and strengthening the city wall.
When the city and its walls are complete,
The people will be secure.
At the appointed time,
Feelings are united with _ch'ien_ (sky) and _k'un_ (earth).
When _ch'ien_ moves, it becomes erect;
The vapor spreads as the generative energy flows.
When _k'un_ is still, it contracts;
Becoming the furnace in the lodge of the Tao.
Apply firmness, then withdraw;
Transform it into softness to provide stimulation.
The Nine is circulated, the Seven is cycled in reverse;
The Eight returns, and the Six stays within.
Male is white, female is red.
Gold and water embrace each other.
Water stabilizes fire,
And the cycle of the five elements is started.
The highest good is like water;
It is clear without a blemish.
The true form of the Tao
And its Oneness is hard to describe.
It changes and spreads,
The parts settling by themselves.
It resembles a chicken's egg,
Where black and white are bound together.
It is about one inch wide
When it first begins.
Then the four limbs and five viscera,
The tendons and bones become complete.
After ten months,
It slips out of the womb.
The bones are soft and curled,
And its flesh is slippery like polished lead.
_Immortality_
From Part Three
The sages and wise ones
Carried the mystery and embraced the ultimate reality.
They refined the Nine Cauldrons,
Covered their traces, and hid from the world.
They conserved their generative energy, nourished the spirit,
And understood the value of the Three Primal Ones.
The sweet nectar moistened their skin and flesh,
Their tendons and bones were soft and strong.
They expelled all the toxins from the body,
And constantly preserved their true energy.
Having accumulated these effects over a long time,
Their bodies were transformed, and they became immortals.
**NOTES ON THE TRANSLATION**
There are many symbols in the _Tsan-tung-chi_. This kind of symbolic reference is quite common in the texts of internal alchemy. To explain the meaning of each line in the text is beyond the scope of this book. Readers who want to know more about the language of Taoist alchemy can refer to my books _The Shambhala Guide to Taoism_ and _Harmonizing Yin and Yang: The Dragon-Tiger Classic_ (forthcoming).
I have retained the Chinese words of _ch'ien_ , _k'un, k'an_ , and _li_ in the translation instead of substituting them with the English _sky_ , _earth_ , _water_ , and _fire_ because these Chinese terms have unique meanings. Thus, for example, _k'an_ is not simply water, but water of the _pa-k'ua_ , which is different from water of the five elements.
Although the _Tsan-tung-chi_ was written as a manual, it is not to be taken casually as a "how to" book. Even if you are familiar with Taoist alchemy, you should not use it as a manual without supervision and guidance from a teacher.
**_The_ Wu-jen p'ien ( _Understanding Reality_ )**
The _Wu-jen p'ien_ was written by Chang Po-tuan, who was one of the greatest theorists and adepts of Taoist alchemy in the Northern Sung dynasty (960–1126 CE).
The alchemical procedures described in the _Wu-jen p'ien_ are similar to those outlined in the _Tsan-tung-chi_ , except for one major difference. For Wei Po-yang and the alchemists of his time, the ingestion of minerals (external alchemy) was perfectly compatible with using internal methods to transform body and mind (internal alchemy). On the other hand, Chang Po-tuan believed that all the ingredients of alchemical transformation are found in the body and that there is no need to ingest minerals and herbs.
_The Process of Internal Alchemy_
From Part One
3
If you want to attain immortality, make sure it is celestial immortality.
Only the Golden Elixir (Pill) is the best.
When the two come together, feelings and inner nature merge.
Where the five elements gather, the dragon and tiger copulate.
With earth yang ( _wu_ ) and earth yin ( _chi_ ) as go-betweens,
Husband and wife happily join together.
Wait for the work to complete and then present yourself before the jade tower,
Borne on the flying phoenix in the light of the nine mists.
4
This wonderful method is the most real of the real.
It solely depends on oneself and not on others.
Know the inversion of _li_ (fire) and _k'an_ (water) within.
Who knows if it is floating or sinking, or who is host or guest?
If you want to hold the mercury within the cinnabar and keep both of them inside the golden cauldron,
First put into the jade pond the silver within the water.
In the spiritual work, it does not take a whole day to pump the fires,
Before the disk of the sun appears in the jade pool.
6
Everyone originally has the medicine of longevity within.
However, they have lost their understanding and thrown it away.
When the sweet dew descends, sky and earth will be joined.
The place where the yellow sprouts grow is where _k'an_ and _li_ interact.
A frog in a well will say there is no dragon's cave.
How can a quail know about a phoenix's nest?
When the elixir is mature, gold will naturally fill the room.
Why need to look for plants or burn reeds?
9
The essence of yin generative energy in the yang is not strong.
Cultivate only one aspect and it will get increasingly weak.
Tiring the body with massage and breath control is not the way;
Swallowing vapor and ingesting mist are crazy;
Everyone idly seeks the lead and mercury;
When will they ever see the tiger and dragon subdued?
I advise you to find the place where your body was born.
Going back to the origin and returning to the source is the great medicine.
13
If you do not know how to invert the mysterious,
How can you plant the lotus in the fire?
Lead the white tiger home and nurture it
To produce a bright pearl as round as the moon.
Relax beside the medicine furnace and watch the fires.
Let the spiritual breath follow its natural way.
When all the toxins are expelled, the elixir will be complete;
Leaping out of the cage, you will live for ten thousand years.
From Part Two
1
First use _ch'ien_ (sky) and _k'un_ (earth) as your cauldron;
Then take the medicine of the raven and rabbit and cook them.
When these two things return to the Yellow Way,
How can the golden elixir not be liberated?
2
Position the furnace and set up the cauldron according to _ch'ien_ and _k'un_.
Refine the essence of the sun and moon to stabilize the human spirit and soul.
Gathering and dispersing, the heated vapor is transformed.
I do not dare to talk about these mysterious wonders casually.
3
Stop wasting your effort at the alchemical stove.
To refine the medicine, you need to find the crescent moon furnace.
In there the natural true fire is born.
Who needs purple coal and bellows?
16
Take the solid center of _k'an_ (water)
To change the yin in the belly of _li_ (fire).
From there it is transformed into the perfect body of _ch'ien_.
To remain hidden or to fly and leap, it is all up to the mind.
17
The mercuric dragon of _chen_ (thunder) comes from its home in _li_ ;
The lead tiger of _tui_ (lake) is born in the position of _k'an_.
The two things come from the child giving birth to the mother.
Most important of all, the five elements need to enter the center.
39
If you want the valley spirit to never die,
You must rely on the mysterious female to build the foundation.
When the true generative energy has returned to the yellow golden room,
The bright pearl will never leave.
43
The black within the white is the mother of the elixir.
The female enclosed inside the male is the sacred fetus.
When the Great One is in the furnace, you need to guard it with care.
The jewels gathered in the three _tan-t'iens_ (fields of energy) are the reflections of the three Altar Stars.
47
If you want to know how to refine, nourish, and circulate the elixir,
You need to plant the seed in your own garden.
No need to huff and puff with force and effort,
Because when the elixir is complete, it will naturally leave its spiritual womb.
54
When the medicine meets the energy, its form emerges.
Imperceptible and inaudible, the Tao merges with nature.
When the numinous pill is swallowed into the belly,
This is the first time you'll know that your destiny is not determined in the celestial realm.
From Part Three
2
The internal medicine is the same as the external medicine.
When you understand the internal, you will understand the external.
In balancing and compounding the elixir, the substances are the same.
Incubation functions in two ways:
Inside there is the natural real fire
And the bright red flame in the furnace;
Outside, increasing and decreasing the heat of the external furnace require diligence.
Nothing is more wonderful than the true seed.
7
The seven reverse cycles return the cinnabar to the origin;
The nine circulations return the golden nectar to the true reality.
Stop counting the hours from three to nine and one to nine.
However, the five elements need to be in accurate order.
Everything is dependent on the silver mercury
Flowing everywhere at all times.
When the numerics of yin and yang are met, it will naturally join with the spirit.
The going out and coming in are not separated from the mysterious female.
12
Cultivate more than eight hundred virtuous deeds;
Accumulate fully three thousand hidden merits.
Equally helping all things, friend or foe;
Only then can you do what the immortals originally did.
Tigers, rhinos, swords, and soldiers will not harm you.
You will not be drawn into the mundane mortal realm.
When the sacred writ descends, you will be ready to present yourself before the celestial realm,
Riding calmly on a chariot pulled by a phoenix.
**NOTES ON THE TRANSLATION**
Again, there is much symbolic language here and they are similar to those in the _Tsan-tung-chi_. As in the translation of the _Tsan-tung-chi_ , I have retained the Chinese names _ch'ien, k'un, k'an_ , and _li_ for the same reasons. Again, if you wish to know more about Taoist alchemy, you can refer to my books _The Shambhala Guide to Taoism_ and _Harmonizing Yin and Yang: The Dragon-Tiger Classic_ (forthcoming).
6
_In the Playing Fields of Power_
TAOIST MAGIC AND SORCERY
TAOIST MAGICIANS AND SORCERERS ARE "artists of power." They are individuals who have penetrated the mysteries of the Tao and have entered into an intimate relationship with both the natural and supernatural forces. Standing between ordinary reality and the subtle world of spirits, deities, and the natural elements, they give us a glimpse of the power of the Tao that we are normally unaware of in our everyday lives.
**_Stories of Taoist Immortals, Magicians, and Sorcerers_**
Stories of Taoist immortals, magicians, and sorcerers are very much a part of Chinese culture. When I was growing up in Hong Kong, my grandmother and my aunt told me many such stories.
The story of Tung-fang Shuo (The Seeker in the East) is based on the _Shen-hsien chuan_ (Biographies of the Immortals) and the legends of Emperor Wu-ti of the Western Han dynasty (206 BCE–8 CE). The story of Chang Tao-ling, the founder of the Celestial Teachers sect and the father of devotional Taoism, is reconstructed from the _Shen-hsien chuan_ , popular stories, and a Chinese opera script.
As you read the stories, you will notice that Taoist immortals are individuals who are endowed with both wisdom and power. Many Taoist immortals were magicians, diviners, and sorcerers, and possessed the same skills as the shamans did in the prehistoric times.
_Tung-fang Shuo (Seeker in the East_ )
When Tung-fang Shuo was a boy, he once left home and did not return until a year later. His family was worried, and when he came home, his brother said, "Where have you been? You were away for almost a year."
Tung-fang Shuo replied, "I was playing on the beach and got sprayed by the salt water. So I went to the Deep Spring to wash the salt off my clothes. I left home early in the morning, and it's only lunchtime now. Why do you say that I've been away for a year?"
His brother exclaimed, "The Deep Spring is ten thousand miles from here! It would take a normal person more than a year to get there and back. You must be joking!"
When Tung-fang Shuo was twenty-two years old, he wrote a letter to Wu-ti, the Han emperor. In the letter he said, "I was orphaned at an early age and was brought up by my brother. I mastered the classics when I was twelve. At fifteen I became an expert in the martial arts. At sixteen I became a master poet and memorized twenty thousand lines of song. At nineteen I mastered the science of warfare and the art of diplomacy. Now, at twenty-two, I stand head and shoulders above everyone. My body is strong and graceful. My mind is agile and cunning. I am honest and trustworthy, brave and honorable. I am someone whom your majesty should have in your service!"
_Tung-fang Shuo washing in the Deep Spring_.
Many people would have been offended by Tung-fang Shuo's manner of presenting himself, but the emperor saw that Tung-fang Shuo was no ordinary person. He not only employed the young man in his service but made Tung-fang Shuo his personal advisor.
The emperor valued Tung-fang Shuo's friendship and lavished him with gifts. He even sent Tung-fang Shuo a beautiful woman to be his wife. However, every time the emperor sent gifts of silks and gold to his friend, Tung-fang Shuo turned all the gifts over to his wife. People made fun of his strange behavior and joked, "Either he really loves his wife or he is afraid of her!" But Tung-fang Shuo was not offended. He only laughed and said, "I am a hermit who escapes worldly matters by hiding in the palace!"
Often Tung-fang Shuo would get drunk and sing in a loud voice:
The world is too muddy,
Therefore I hide behind the gates of the Palace.
The Palace is a place where I can cultivate my life,
Why do I need to be a hermit in the deep mountains?
Before Tung-fang Shuo was about to leave the mortal realm, he made a remark to the emperor, "No one knows where I came from and where I will go. Only the astronomer who keeps a record of the stars knows about my true identity."
One day, Tung-fang Shuo was nowhere to be seen. The emperor was worried about his friend. Suddenly, remembering what Tung-fang Shuo had said a few days previously, he summoned the court astronomer and asked about Tung-fang Shuo.
The court astronomer was bewildered. He said, "Your majesty, I honestly do not know Tung-fang Shuo's true identity."
The emperor was a very clever man. He sensed that Tung-fang Shuo's identity must be related to the patterns of stars in the sky. Otherwise, he would not have mentioned that only the keeper of the record of the stars would know his identity.
Turning to the astronomer, the emperor asked, "In your observation of the stars in the last forty years, did you notice anything out of the ordinary?"
The astronomer replied, "My lord, I did notice that forty years ago a star mysteriously disappeared and then a few days ago reappeared again."
The emperor finally understood. He sighed and said, "In the eighteen years that Tung-fang Shuo was with me, I did not even know that he was a sky immortal. What a pity!"
_Chang Tao-ling_ ( _The Celestial Teacher_ )
Chang Tao-ling stood over seven feet tall and had bushy eyebrows, a large round forehead, and a hawk-beak nose. On the sole of his right foot were seven black dots arranged in the pattern of the seven stars of the Northern Bushel (Big Dipper). He had long, powerful arms that came down to his knees, and he walked with a gait that had the strength of the tiger and the speed of the dragon.
Just before Chang Tao-ling was conceived, his mother dreamed that she saw a giant descending from the North Pole Star. The lord of the North Star came toward her and gave her a flower. When she awoke the next morning, she smelled wisps of fragrance in her room and discovered that she had conceived a child. The fragrance lasted throughout the ten months while she carried the baby in her womb.
On the day Chang Tao-ling was born, a yellow cloud covered the house and purple mist hovered about his mother's bedchamber. When he came out of his mother's womb, music and fragrance filled the air, and the room was flooded with light that matched the brilliance of the sun and moon.
Chang Tao-ling was exceptionally intelligent. At seven he understood the teachings of Lao-tzu's _Tao-te ching_. By twelve he had mastered the _I-ching_ and the classics of divination. As a young man, Chang Tao-ling served his community as a provincial administrator but he continued to study the arts of the Tao.
One day, while he was meditating in his retreat, a white tiger came to his side. In its mouth was a scroll of sacred scripture. Chang Tao-ling knew that it was time for him to leave the world of politics to pursue the Tao.
He resigned his position of civil administrator and became a hermit in the mountains. When the emperor heard about Chang Tao-ling's retirement, he offered him the title Imperial Teacher and begged him to return to the service of the government. Three times the emperor invited him, and each time Chang Tao-ling refused.
When Chang Tao-ling realized that he would not be left in peace, he moved to the remote and mountainous region of Szechuan. There where the streams ran deep and the waterfalls cascaded down precipitous cliffs, Chang Tao-ling selected a cave where he could meditate, learn the arts of immortality, and attain the Tao.
Chang Tao-ling stayed in his cave for many years until one day he heard the cry of a white crane. He knew it was a sign that he would attain enlightenment soon. A year later, when Chang Tao-ling was stoking the fires of the furnace to incubate the Dragon-Tiger Elixir, a red shaft of light appeared and illuminated the cavern. Another year later, a white tiger and a green dragon came into the cave and sat by the side of the cauldron to protect the elixir. Finally, three years after Chang Tao-ling had heard the call of the white crane, the elixir was completed and Chang Tao-ling became an immortal.
Chang Tao-ling left his cave and traveled throughout the river valleys and mountains of Szechuan. On one of his journeys he met Lao-tzu, who taught him how to fly to the stars and tunnel under the earth. When Lao-tzu departed, he gave Chang Tao-ling a scroll of talismans that had the power to heal the sick and a magic sword that could drive away malevolent spirits.
As time went on, Chang Tao-ling's skill in the arts of sorcery matured. Soon he could make himself invisible or change himself into any shape he wished. He could hear and see over great distances and could call down rain and snow. He could heal the sick and drive away evil spirits. His fame spread far and wide, and people called him the Celestial Teacher, for they believed that he was an immortal from the celestial realm.
One time, six evil spirits were wreaking havoc in Szechuan. Lao-tzu appeared to Chang Tao-ling and told him to return to Szechuan to capture the spirits and bring them to judgment. Chang Tao-ling secluded himself for one thousand days to prepare for this encounter.
When the six lords of evil heard that Chang Tao-ling was preparing to fight them, they gathered a large army of ghosts, ghouls, zombies, and other evil creatures. Meanwhile, Chang Tao-ling also made his preparations. He selected a green mound outside the city of Cheng-tu and built a tower with an altar in the middle. On the altar he placed objects of power, such as magical mirrors, bells, and talismans.
At the hour of _tzu_ (11:00 P.M.) Chang Tao-ling ascended the tower and invoked the wind, rain, and thunder to beat upon the army of the evil spirits. Chang Tao-ling also drew talismans of power and called on the celestial deities to fight the evil forces. The lords of evil sent flaming spears and arrows to hit Chang Tao-ling, but none of them could harm him. As the spears and arrows came toward him, Chang Tao-ling waved his sword of power, and the weapons were transformed into lotus flowers.
The lords of evil then sent an army of hungry ghosts to attack Chang Tao-ling, but when they reached the altar, Chang Tao-ling drew a talisman, and all the ghosts fell on their knees and begged for compassion. Then the lords of evil sent an army of ghouls, vampires, and zombies to attack Chang Tao-ling. When these creatures came near the altar, Chang Tao-ling rang his magical bells, and the undead clutched their ears and fell to the ground, never to rise again.
Seeing that their minions had failed, the six lords of evil came forward themselves to attack Chang Tao-ling. Chang Tao-ling grasped his sword and drew the Great Seal of Power. The sword emitted a stream of bright light, which was transformed into a net. The net descended onto the six evil spirits and formed a cage around them. When the six lords of evil saw Chang Tao-ling striding toward them with his sword of power, they begged for mercy and forgiveness. Chang Tao-ling said to them, "You have brought illness and suffering to many people, and for these evil deeds you must be punished. But, as the Celestial Way is compassionate, I shall not kill you. I shall, however, punish you by keeping you locked inside the depths of a mountain. In this way you will not harm people again."
When the people saw that the six lords of evil were captured by Chang Tao-ling, they came to thank him and asked him to teach them his magic. Chang Tao-ling did not want to turn them away, so he told them to organize themselves into groups to help people who were in need. He also told the people that the most effective way to fight evil was to do good deeds. If everyone did only what was good, evil could not take hold.
To his close followers, Chang Tao-ling taught the magic of talismans and told them to always use the power of sorcery for good and never for evil. On the day he ascended to the celestial realm, he left the sword of power and the Great Seal to his son and entrusted him to teach and lead the followers of the Celestial Teachers' Way.
**Feng-shen Yen-yi ( _Investiture of the Gods_ )**
The _Feng-shen yen-yi_ was written in the Ming dynasty (1368–1644 CE) by novelist and Taoist practitioner Lu Hsihsing. The book is a fantasy novel set against the background of the fall of the Shang dynasty (1766–1121 BCE) and the founding of the Chou dynasty (1122–221 BCE). Like its more famous contemporary works _Journey to the West_ and _Heroes of the Marsh_ , it depicts the classic struggle of good against evil and the triumph of the good at the end.
The cast of characters in the _Feng-shen yen-yi_ includes folk deities, Taoist immortals, Buddhist arhats, nature spirits, animal spirits, shamans, sorcerers, superheroes, kings, princes, ministers, and commoners. As the novel says, "Everyone in the world was involved in this gigantic struggle; few did not take sides."
The following excerpt describes how Kiang Tzu-ya, a Taoist sorcerer and chief advisor to the duke of Chou (later King Wen, the first emperor of the Chou dynasty), used his magical powers to summon the elements to defeat the army of the evil king of Shang.
_Kiang Tzu-ya Summons the Elements_
Tzu-ya instructed his assistant to build a mound about three feet high. When it was completed, Tzu-ya climbed to the top of the mound and undid the knot in his hair. With a sword in his hand, he faced east toward the direction of the Kun-lun Mountains, and prostrated. Then he walked the steps of the Big Dipper and began his magic ritual, uttering incantations and scattering talismanic water.
Soon, a strong wind blew and whistled through the forest. Dust churned up from the ground and nothing could be seen. The sky darkened and the earth rumbled. In the distance, the waves crashed onto the shore and the mountains shook. Bells and chimes on the prayer flags clanged against each other. All who stood nearby were unable to open their eyes.
Far away, in the enemy camp, the weather was warm and there were only small gusts of wind. The commanding generals said among themselves, "This is a good sign. Even the weather is on our side. Our emperor has the favor of the celestial lords, for they have sent this refreshing wind to cool us on our march."
However, as the armies of the evil emperor approached Tzu-ya's camp, the situation changed. Tzu-ya summoned a cold wind, and for three days it blew continuously. The imperial soldiers began to whisper to each other, "We are living in unfortunate times. It is said that the weather will become unpredictable when there are problems in the country."
An hour later, a few snowflakes fluttered around. The imperial soldiers began to complain, "We are dressed in summer uniforms. How can we survive in this cold?"
Not long after that, the snow became heavy, and the soldiers could hardly see what was in front of them. Now and then, they could hear avalanches crashing down the mountain slopes. The land became a wall of pure white. Wolves howled, their cries coming out of nowhere. The snow soon became ankle-deep, then knee-deep. The progress of the imperial army came to a halt.
The commanding general looked at his lieutenants and said, "I have never seen snow this heavy in the middle of summer." The general, an old man, was having a hard time enduring the cold. All the soldiers were huddled in heaps, stricken with cold. There was nothing that their commanders could do to keep them moving.
Meanwhile, in Tzu-ya's camp, everyone was prepared for the snow. The soldiers stood in their ranks, grateful that they were wearing padded jackets and straw hats. Everyone was awed by Tzu-ya's power.
Tzu-ya then asked his assistant, "How deep is the snow?"
The young man replied, "In the higher places it is about two feet, but in the valleys the drifts must be at least four or five feet."
Tzu-ya returned to the mound, undid the topknot from his hair, drew talismans in the air with his sword, and chanted. At once, the snow clouds disappeared and a bright sun shone. The ice and snow melted and a torrent of water rushed down the mountain sides into the valley. Just when the water has formed a lake in the valley, Tzu-ya changed his incantations. He drew another talisman and whipped up a cold wind. The sun disappeared behind ominous black clouds and the water froze immediately.
When Tzu-ya looked at the direction where the imperial army was stranded, he saw broken flags and banners. Turning to his assistant he said, "Lead twenty strong men into the enemy camp and capture the commanders."
7
_The Tao in Everyday Life_
TAOIST ETHICS
ALTHOUGH ENLIGHTENMENT AND THE attainment of immortality are the highest goals of Taoism, the importance of everyday living in the mortal world is not neglected in Taoist practice. After all, it is in our mortal lifetime that we prepare ourselves for the return to the Tao. Taoist ethics are intimately tied to traditional Chinese views of right action. Walking in the "ways of goodness" will ensure that we will live a peaceful, prosperous, healthy, and long life. It is also a responsibility that every human being should have during his or her lifetime in the mortal realm.
**Chih-sun-tzu chung-chieh ching**
**( _Master Red Pine's Book of Discipline_ )**
The _Chih-sun tzu chung-chieh ching_ was written during the Six Dynasties (between the fifth and sixth centuries CE). The text uses a conversation between the Yellow Emperor and the sage Master Red Pine to present the ethics of right thinking and right action. In Taoist legend, Master Red Pine was a shaman and rainmaker during the time of the Yellow Emperor. A teacher of humanity, Master Red Pine has appeared from time to time to teach mortals.
_From the_ Chih-sun tzu chung-chieh ching
The Yellow Emperor bowed and addressed Chih-sun Tzu, "I see tens of thousands of people born, each person having a different destiny. Some are rich and some are poor; some live a long life and some die young. Some spend their lives in prison locked up in chains; some are plagued with illness; some die suddenly without becoming ill; and some enjoy longevity and prosperity. Please explain to me why there is such inequality in people's fortunes?"
Chih-sun Tzu said, "Everyone is born under the guardianship of stars. Some stars have great influence over our lives and some have less influence. These stars determine whether someone will be born as a human or animal, whether the individual will live long or die young, whether he or she will rise or fall in fortune, be rich or poor, and live or die. Those who do charitable deeds will be blessed with the spirit of goodness. Fortune and virtue will follow them. Evil will not come near them. The spirits will protect them. People will respect them. Disaster will not befall them. Those who do bad deeds will be visited by the spirit of evil. Misfortune will follow them. Blessings will leave them. The baleful stars will shine on them. People will hate them. Disasters will gather around them.
"In our everyday life, if we think and act against the sky and the earth, punishment will not come lightly. If we do bad deeds, the spirit in us will report to the stars and our longevity will be decreased. The celestial vapor will leave and the terrestrial vapor will suffocate us. This is what it means to meet with misfortune."
The Yellow Emperor then asked, "How long can humans live?"
Chih-sun Tzu replied, "When we tumble out of our mother's womb onto the ground, the celestial lords gave us a life span of forty-three thousand and eight hundred days. This comes to one hundred and twenty years. There is one birthday each year. Thus, humans are given a chance to experience one hundred and twenty birthdays. Those who have broken the laws of the sky and the earth will have birthdays taken from them or will have their lives terminated."
The Yellow Emperor asked again, "How about those who return to the celestial realm in their mother's womb, or those who die in infancy? These people did not have the chance to commit wrongdoings. How could they have offended the sky and earth?"
Chih-sun Tzu said, "When ancestors have done bad deeds, retribution will be carried over to their descendants. This is why the ancient sages have left their teachings in the sacred scriptures to advise people to do good deeds and know what is evil. In this way their children and grandchildren will reap the benefits of fortune.
"Humanity is born in the midst of the sky and earth and is the product of the vapor of yin and yang. The sky is high but it responds to what happens below. The earth is humble but it elicits responses from the sky. Without a word, the sky moves the four seasons. Without a word, the earth creates the ten thousand things and humanity. When our emotions and desires are stirred, the powers in the sky and the earth will know it. Therefore it is said that the celestial realm knows four things. It knows who complains and who is ungrateful to the earth and the sky. When the sky gave us life, _ch'ien_ and _k'un_ are in our father and mother, the sun and moon are in our eyes, and the stars are in our cavities. Movement of wind and the strength of fire give us the warm vapor of life. When we die, we return to the earth.
"In the sky the Three Altars Stars, the Northern Bushel, and the Pole Star govern longevity and prosperity. The T'ai-i star is situated on top of the head. It monitors our actions and takes away our longevity if we do bad deeds. If one year of life is taken, the star on top of the head will become dim. The individual will feel weak and be plagued with small illnesses. If ten years are taken away, parts of the star will gradually disappear, and the individual will always be ill. If twenty years are taken away, the light of the star will be damaged beyond repair, and the individual will be bedridden permanently or be imprisoned. If thirty years are taken away, the star will disintegrate and fall from the sky like a shooting star. Not only will the individual die before his or her time, but the punishment will carry over to the descendants until the family line is extinguished.
"People do not know that they have committed wrongdoings. They only say that their lives are short. The sky does not deceive. It shows us omens day and night—in the moon and sun, in thunder and lightning, in snow and in rainbows, in the eclipses of the sun and moon, and in the shooting stars. These phenomena all carry messages from the celestial realm. Earth does not deceive us either. Its response affects all things. Floods, landslides, earthquakes, ferocious winds, tornadoes, locusts, drought, famine, and poisonous gas are all messages from earth. The spirits do not deceive. Fortune and misfortune, disaster and blessing, are their messages. The ruler of the country cannot deceive us. Signs from the stars, disasters and destruction in the world, the people's loyalty—all these events tell us about the ruler.
"People's action, speech, and intention elicit responses from the sky and the earth. The sages tell us that the great sky follows virtue and does not favor anyone. Therefore we should heed its warnings and those of the great ones and the sages. The celestial lords know who has done good deeds and who has done bad ones. People cannot hide acts of murder, for the spirits of the underworld can see into their hearts and intention. When people have committed a hundred wrongs, the spirits of the underworld will drink their essence. If they have committed a thousand wrongs, earth will take away their human form and bind them with chains. This is retribution from both the yin and yang domains. The celestial realm has established a set of rules and ethics. If people break these rules, the deities, the spirits of the underworld, and the powers of the sky and earth will punish them."
The Yellow Emperor then asked, "Can you tell me more about how the immortals view good and evil, and how fortune and blessings are given?"
Chih-sun-tzu replied, "Practice daily the methods of cultivating your body, your life, and your inner nature. Do good deeds, and always think and act in kindness. If you stay away from three acts of evil every day, then within three years, the celestial lords will send the stars of fortune to visit you, and you will be rewarded with fortune. If you do bad deeds, think evil things, and teach others evil ways, within three years, disaster will come to you. You will lose your health, your wealth, and you will die.
"When harmful vapor spreads on earth, things will go badly for people. The appearance of ugly, evil things in the sky is the result of the nine wrongs on earth. Thus, it is said that the cure for evil is goodness, and evil is the bane of the good. Those who are kind should be the teachers of those who are evil. The presence of evil in the world tells us that we need more people who are good. The existence of blessing means that retribution is thwarted by acts of goodness. On the other hand, retribution is what remains of evil after goodness has been accounted for.
"Sometimes good people meet with disaster. This is because retribution was handed down to them by their ancestors. Those who do good deeds do not need to pick auspicious days for special events. Whenever good deeds are done, there will be blessings even in the midst of disaster. The hundred spirits and guardian deities will make sure that misfortune does not occur. However, for those who do evil deeds all their lives, even if they pick auspicious days for special events, there will be disaster on the days of blessing. The evil spirits will harm them. The spirits who give blessings will avoid them. If people do charitable deeds frequently, the celestial lords will naturally reward them with prosperity and longevity. The relationship between good deeds and rewards is like the effect of a thing on its shadow. Therefore, if you do not want to meet with misfortune or harm, you must not offend the sky and the earth. You must know how to cultivate yourself and affect your destiny."
8
_Encountering the Sacred_
THE TAOIST CEREMONIES
IN SPIRITUAL TRADITIONS, CEREMONIES create a sacred time and space for humanity to meet the powers of the universe. Many Taoist ceremonies are rooted in ancient Chinese rites that predate the emergence of Taoism as a philosophy and a spiritual tradition. However, they are also enriched by two thousand years of Taoist spiritual practice.
All Taoist ceremonies are preceded by purification rituals that prepare the ceremonial grounds and the participants for the event. The first selections in this chapter, the Fa-lu Chants, are recited by participants before the main part of a ceremony is performed. The second selection, from the _Chai-chieh lu_ (Correct Procedures of Purification and Preparation for Festival Services), describes the kinds of purification rites that accompany the Taoist ceremonies.
**_The Fa-lu (Lighting the Stove) Chants_**
The Fa-lu Chants are invocations recited at the beginning of a liturgy. They are used to induce the participants into the appropriate state of mind and remind them of the purpose and meaning of the ceremony—to bring humanity closer to the Tao.
Before the main body of a liturgy is chanted or a ceremony is performed, the ceremonial grounds (temple, shrine, and altar) and the hearts, minds, and bodies of the participants must be purified. The purification rituals and the chanting are a covenant made between humanity and the celestial deities, who are guardians of the Tao. As people make a solemn promise to purify themselves and to embrace the principles of the Tao, the deities renew their promise to protect, guide, and teach. Together, the sacred powers and humanity ensure that the universe is forever filled with the life-giving breath of the Tao.
_Lighting the Stove_
The smoke rises from the stove.
The breath of the Tao lingers.
With dedication I offer this fragrant incense.
Let its scent surround the universe.
Let it spread to the ten directions.
Let all the spirits reveal their golden light.
_Dedication of Incense_
The Tao is approached from the heart.
As the smoke rises, let my heart ascend to the Tao.
Before the fragrant incense and jade pure stove,
I stand single-minded before the celestial lords.
Let the true spirit descend.
Let the immortals come.
This I sincerely petition.
Let my vision reach the nine celestial realms.
_Purification of the Mind_
The stars of the Great Altar constellation
Are forever rotating and changing.
They save us from evil and disaster;
They protect us and guard our bodies.
Let my thoughts be intelligent and pure.
Let my heart's spirit be peaceful and calm.
Let my three souls live forever.
Let the spirit-soul never stray from me.
_Purification of the Mouth_
May the guardian jewel of speech
Expel the impure air in us.
May the guardian of our tongue
Direct us to say what is upright.
Let our health be enhanced,
And let the spirit be cultivated.
May the guardian of our teeth
Help us to retain the good and reject the evil.
May the guardian of the throat let out the tiger's roar.
May the guardian of vital energy nourish the sweet nectar.
May the guardian of the mind hasten the completion of the golden elixir,
And help us to understand the mystery of the origin.
May the guardian of thought cultivate the sweet saliva,
So that the breath of the Tao will stay with me forever.
_Purification of the Body_
Every day I cleanse my body.
Watching the moon I cultivate my form.
The immortals lift me up.
The fair lady hovers over my being.
The twenty-eight constellations
Are united with me.
The Celestial Lord Ling-pao
Protects my soul.
He guards the spirit and soul of sentient beings,
And ensures that the internal organs are bright and whole.
Let the Green Dragon and the White Tiger
Array their power around me.
Let the Red Raven and the Black Tortoise
Protect my true spirit.
_Purification of the Sky and the Earth_
When sky and earth follow the natural way,
The impure breath will disappear.
The mysterious emptiness of the cavern
Will illuminate the great oneness.
May the powerful spirits of the eight directions
Guide me to follow the natural course.
May the Celestial Lord Ling-pao protect my life.
Let my petitions reach the nine levels of the sky.
Let the guardians of the celestial realms
And the ancient mystery of the great cavern
Smite the evil spirits, bind the unlawful beings,
And destroy the ten thousand monsters.
The sacred writ of the central mountain,
Is the jade word from the great beginning.
Chant this once,
And the monsters will flee and life will be preserved.
Do this systematically in the five mountains.
Let it be heard across the eight seas.
The demon lord will be unable to move,
And the internal domain will be guarded.
The forces of destruction will be dispersed,
And the Breath of the Tao will exist forever.
_Revealing the Golden Light_
The great mysterious origin of the sky and earth,
Is the root of the ten thousand breaths.
It gives me life, saves me from a million retributions,
And instructs me in the ways of the spirit.
Inside and outside the three realms
Only the Tao is supreme.
Its essence emanates a golden light.
It covers my body;
It cannot be seen;
It cannot be heard;
It embodies the sky and the earth;
And nourishes and teaches all sentient beings.
Chant it ten thousand times,
And the body will glow with light.
The guardians of the three realms will watch over me;
The five emperors will welcome me;
The ten thousand spirits will prostrate before me;
And the thunder lord will bend to my will.
Ghosts and evil spirits will lose their courage;
Evil nymphs and creatures will lose their shape.
Rumblings are heard within,
As voice of the spirit of thunder resonates.
As copulation occurs in the cavern,
The five vapors fill the air.
Let the golden light quickly appear
To protect the enlightened being.
**Chai-chieh lu ( _Correct Procedures of Purification and Preparation for Festival Services_ )**
The _Chai-chieh lu_ is a collection of purification rites ( _chai_ ) and proper codes ( _chieh_ ) of behavior required of Taoists participating in sacred ceremonies. Its anonymous author was most likely a Taoist priest of the T'ang dynasty (618–906 CE).
The excerpts below are taken from four sections in the _Chai-chieh lu_. The Introductory section discusses the nature of purification and the meaning of _chai_. In Taoist practice, _chai_ is the rite of purification that cleanses the ceremonial grounds and prepares the participants for the sacred festivals.
The excerpt from the section "The Six Tung-hsüan Ling-pao Purifications and Ten Vows" describes ten Taoist vows of discipline and six types of purification rites. It is interesting that in addition to ethical behaviors such as compassion for others and abstinence from killing and stealing, one of the ten vows calls for conserving water and planting trees. This ecological ethic is quite remarkable. It shows that in Taoist spirituality, the respect for nature is never far away.
The excerpt from "The Six Kinds of Chai" describes six purification rites associated with six kinds of sacred ceremonies. Note that the Shang-ch'ing Purification mentioned here is not associated with specific rituals or ceremonies of Shang-ch'ing Taoism, the mystical sect that emerged in the third and fourth centuries. Rather, they refer to general purification rites observed in the preparation of all sacred ceremonies.
In the last excerpt, "The Nine Diets of Purification," the reader is given a feel for what the Taoist dietary regulations are like. They range from a diet of millet and grains to feeding on the Breath of the Tao. Each diet is associated with a level of spiritual development, and practitioners are advised to follow a certain diet only when they are ready. Even so, only the few who have reached the highest levels of spiritual attainment observe the rites of purification every day.
_From the_ Chai-chieh lu
FROM THE INTRODUCTION
There are three kinds of _chai_ , or purifications. In the first kind of purification, offerings are made to atone for wrongdoings and to accumulate merits. The second kind of purification is fasting or abstaining from rich foods. It clears the mind, cleanses the body, and prepares the participants for the sacred ceremonies. This rite can be performed by individuals who take the Middle Path [the path of performing the sacred ceremonies]. The third kind of purification is emptying the mind of desire. It purifies the spirit and dissolves negative attitudes. It cultivates wisdom and curbs anxiety. When there are no thoughts, one will turn to the Tao. When there is no desire or craving, one will be content. When there are no negative attitudes and no scheming, the mind is centered and is at one with the Tao.
THE SIX TUNG-HSÜAN LING-PAO (PRECIOUS JEWELS OF THE MYSTERIOUS CAVERN) PURIFICATIONS AND TEN VOWS
There are five abstinences in the Taoist religion. First, do not kill. Second, do not get intoxicated. Third, do not speak falsely. Fourth, do not steal. Fifth, do not indulge in sensual pleasure. There are ten ways of goodness. First, honor your parents. Second, be dedicated in everything you do. Third, be kind and compassionate to all things. Fourth, be tolerant and forgiving. Fifth, speak out against things that are wrong. Sixth, be selfless and help others. Seventh, value the life of all sentient beings and respect nature. Eighth, help conserve water, plant trees, and build bridges. Ninth, always think of the welfare of others. Tenth, recite the scriptures of the Three Treasures, keep the vows, and make offerings of incense and flowers. An individual who observes the five abstinences and follows the ten good ways will be protected by the celestial spirits. Remember, good things are planted by your actions.
THE SIX KINDS OF CHAI (PURIFICATIONS FOR CEREMONIES)
The _Ti-yi tao-men ta-lun_ (The Great Book of the Practices of Taoism) states that there are three rites of Shang-ch'ing purification. First, the participants must spend time in solitude, eat without company, reduce activity to slow the breath, and cleanse the body. Second, the altars must be purified in a solemn manner. Third, the participants must calm their emotions and clear the mind of desire and negative thoughts.
There are six rites of Ling-pao purifications. The first, the Golden Register Purification rites, are used for petitions made on behalf of the nation. The second, the Yellow Register Purification rites, are for petitions asking for deliverance from suffering. The third set of Ling-pao purification rites, called Understanding the Truth, is for ceremonies of repentance made on behalf of the dead. The fourth is the Three Agents Purification rite, and it is used to petition the Lords of the Three Realms (Sky, Earth, and Water) for forgiveness. The fifth is the Eight Festival Purification rite, and it is used to ask for forgiveness of past wrongdoings. The sixth is the Common Purification rite, and it is used for ceremonies of intercession on behalf of the common citizen.
The Tung-shen (Cavern Spirit) Purification rite is a short ritual used to cleanse the ceremonial ground of worldly dust and prepare it for visits from the spirits.
The T'ai-i (Ancient Beginning) Purification rite is used for solemn and stately occasions.
There is also a purification rite that prepares individuals for receiving instruction. These rites emphasize simplicity and humility.
The rite of purification through suffering emphasizes hard work and service to others.
THE NINE DIETS OF PURIFICATION
The _Hsüan-men ta-lun_ (Great Discourse on Taoist Practices) states that there are nine diets of purification.
The first is a diet of grain, the second vegetarianism, the third fasting, the fourth eating the essence of energy, the fifth eating yellow sprouts, the sixth swallowing light, the seventh ingesting vapor and mist, the eighth absorbing the primordial vapor, and the ninth feeding like a fetus in the womb.
A diet of grain consists of millet and wheat. Vegetarianism is a diet of leafy vegetables and fungus. Fasting is abstaining from eating. Eating the essence of energy is drinking talismanic water and ingesting minerals. Eating yellow sprouts means absorbing the essence of the clouds. Swallowing light is swallowing the light of the sun, moon, and Northern Bushel (Big Dipper) stars. Eating vapor and mist is absorbing the vapor of the Great Harmony from the four directions. Eating the primordial vapor is absorbing the vapor of the three celestial realms and the essence of the Great Harmony from the Great Void. To feed like a fetus is to be nourished by the original essence that was present at conception and be nurtured by the pristine energy that envelops the fetus in the womb.
9
_The Arts of Longevity_
CULTIVATING THE MIND
PRACTITIONERS OF TAOIST SPIRITUALITY use meditation as the primary method to cultivate the mind for health, longevity, and spiritual transformation.
The translations in this section are chosen to give the reader a feel for the different kinds of Taoist meditation. Please do not use them as meditation manuals. The practice of Taoist meditation requires formal instruction and supervision from a qualified teacher. Unguided practice can lead to injuries, and the author and publisher are not responsible for any complications that result from using these texts as manuals.
**Shang-ch'ing t'ai-shang ti-chün chiu-chen chung-ching ( _Scripture of the High Pure Realm's Highest Celestial Lord's Nine True Forms_ )**
This text describes a form of meditation that was practiced by the Shang-ch'ing mystics. According to Shang-ch'ing Taoism, this meditation manual was transmitted by the Immortal Chih-sun-tzu (Master Red Pine) to the Shang-ch'ing patriarch and immortal Chou-chün (the Lord Chou).
The text describes the procedures for visualizing the nine true forms of the Lord of the High Pure Realm. The goal of Shang-ch'ing meditation is to keep the guardian deities within by visualizing them and holding onto their images. If the guardians stay within the body, health and longevity are assured. If the guardians leave, the practitioner will become ill or even die.
_From_ Shang-ch'ing t'ai-shang ti-chün chiu-chen chung-ching
FROM "METHOD OF THE FIRST TRUE FORM"
Slow the breath, close the eyes, and visualize the image of the Lord of Celestial Essence sitting in your heart. He is called the Great Spirit. Next, visualize a purple vapor coming from the mouth of the Great Spirit spreading outward from the heart. The vapor ascends like a straight pole to the _ni-wan_ (Mud Ball) cavity in the head.
FROM "METHOD OF THE SECOND TRUE FORM"
In your mind visualize the image of the Lord of the Jade Stone sending a pearl into your throat down to the stomach. The pearl is transformed into a white vapor that spreads to the hundred joints. Next, visualize a white vapor coming out of the mouth of the Great Spirit to hover around your bones. The vapor floats around the nine external and internal levels like clouds, mist, and smoke.
FROM "METHOD OF THE THIRD TRUE FORM"
Go into your room, clasp your hands together, and put them on your crossed legs. Slow the breath, close your eyes, and visualize the Lord of the Original Beginning floating around in the bloodstream and the generative fluids in the body. Next, visualize a yellow vapor coming out his mouth to wrap around all the openings in the nine levels, so that there is no separation between the internal and external environment.
FROM "METHOD OF THE FOURTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your crossed legs. Slow down the breath, close your eyes, and visualize the Bright and Clear Great Lord entering to sit inside the liver. Next, visualize a blue vapor coming out of his mouth to fill the liver and the nine levels.
FROM "METHOD OF THE FIFTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your crossed legs. Slow down the breath, close your eyes, and visualize, keeping in your mind the image of the Bright Lord entering the spleen. Next, visualize a green vapor coming out of his mouth to fill the spleen. Let the vapor rise up the nine levels into the _ni-wan_ cavity, where it hovers and vibrates inside and outside the grotto.
FROM "METHOD OF THE SIXTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your legs. Slow down the breath, close your eyes, and visualize the Lord of the Upper Realm, named Primal Jade, entering to sit in the lungs. Next, visualize a vapor of five colors coming from his mouth, to fill the lungs and ascending the nine levels to the _ni-wan_ cavity where it hovers around inside and outside.
FROM "METHOD OF THE SEVENTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your legs. Slow down the breath, close your eyes, and visualize the image of the Lord of the Mysterious Yang entering the two kidneys. Next, visualize a red vapor coming out of his mouth filling the kidneys and rising up the nine levels into the _ni-wan_ cavity, where it hovers around inside and outside.
FROM "METHOD OF THE EIGHTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your legs. Slow down the breath, close your eyes, and visualize the Lord of the Internal Environment entering to sit in the gallbladder. Next, visualize a vapor of five colors coming out of his mouth to fill the gallbladder and rising up the nine levels into the _ni-wan_ cavity, where it hovers inside and outside like clouds and mist.
FROM "METHOD OF THE NINTH TRUE FORM"
Go into your room, clasp your hands together, and put them on your legs. Slow down the breath, close your eyes, and visualize the Lord High Emperor inside the purple chamber of the _ni-wan_ cavity. Next, visualize a purple vapor filling the mouth and rising through the nine levels. Then visualize the purple vapor coming out of his mouth to hover around your teeth before rising through the nine levels. This vapor circulates in the body thirty-six times, floating and vibrating as if the sun were inside.
**NOTES ON THE TRANSLATION**
The _ni-wan_ cavity is in the forehead and is the meeting point of many energy pathways. It is also the point where the spirit is gathered, nurtured, and liberated. In Shang-ch'ing practice, the _ni-wan_ is the location where the spirit leaves and reenters the body after its journey to the other realms.
The nine levels are technically known as the Nine Levels of the Celestial Domain. They are the nine chambers inside the head that the vapor or internal energy must penetrate before it can reach the _ni-wan_ cavity.
**Tung-hsüan ling-pao ting-kuan ching ( _The Mysterious Grotto Sacred Spirit Scripture on Concentrated Observation_ )**
This is a treatise on the form of Taoist meditation known as Concentrated Observation ( _ting-kuan_ ) or Internal Observation ( _nei-kuan_ ). The method calls for stilling the mind, eradicating thoughts, and becoming nonattached to the outside world. Written in the Sung dynasty, this text shows the influence of T'ien-tai Buddhism, especially the meditation practiced by this Buddhist sect.
According to the theory of Concentrated Observation, all things originate from the activity of the mind. Therefore, by stopping thinking, the practitioners will come to realize that all things are empty. In emptiness, illusions are dissolved and the underlying reality of the Tao is experienced.
Despite the Buddhist influence, Taoist _ting-kuan_ meditation is not identical to Buddhist insight meditation. When you read the text below, you will notice that this form of Taoist meditation goes beyond stilling the mind. It uses _vi-passana_ (insight) and T'ien-tai techniques to build the initial foundations, but in the higher levels, the practitioner undergoes transformations in body and mind that are alchemical in nature. The realization that all things are empty is only the first step in the transformation of the body to vapor, the vapor to spirit, and the union of the spirit with the Tao.
The _Tung-hsüan ling-pao ting-kuan ching_ is translated in full below. When you read the text, notice the absence of visualization and mantras and the emphasis on emptying the mind. The practitioner does not focus on any part of the body, nor is he or she required to adopt specific body postures while meditating.
_Tung-hsüan ling-pao ting-kuan ching_
The Celestial Lord said to Immortal Tso-hsüan:
If you want to cultivate the Tao, you must let go of worldly things. Disconnect yourself from everything in the outside world so that nothing will disturb your mind. Then you can practice meditation in peace.
Quiet observation begins in the mind. If a thought arises, you must immediately stop it so that you can keep your stillness. Then get rid of all illusions, desires, and wandering thoughts. Needless to say, you must maintain this stillness day and night. Extinguish the active mind but keep the reflective mind. Focus the empty mind but do not let it become static. Do not get stuck in one routine but always keep the mind still.
It is difficult for beginning practitioners to stop thinking. If you cannot extinguish your thoughts, you should stop meditating before you make mistakes. Otherwise, thoughts rising and falling will battle each other and send ripples of repercussion through your body.
With time, your practice will stabilize. When not one thought arises, you will erase the karma of a thousand lifetimes. When you attain stillness in your meditation, you should carry this state of mind to everyday activities such as walking, standing, sitting, and sleeping. In the midst of events and excitement, be relaxed and composed. Whether things are happening or not, your mind should be empty. It should be as if it does not exist. You should hold on to stillness and softness and not let the inner direction be distracted from oneness.
If you are impatient and want to rush things along, you will eventually become ill. Your temper will explode and you will be crazy. This is why you should be patient. Your mind should be still but relaxed. Do not hurry. Let everything go according to its pace. If you can control your thoughts so that nothing will arise, if you can let go and not let the mind wander, and if you can be relaxed and not be bothered by things in the world, you will have no worries. This is true stillness. If things work against you, you will not be frustrated. If you are buffeted by great forces, you will remain relaxed. Use nonaction as the true dwelling and action as response. All forms should be like reflections on the surface of a polished mirror. Let compassion guide your ways, and you will enter stillness.
It is not up to human effort to determine whether enlightenment will come soon or late. Keep your stillness and do not be impatient for enlightenment. Impatience injures original nature, and when you are injured, enlightenment cannot occur. When you are still and do not force things to happen, enlightenment will come naturally. This is true enlightenment.
It is folly if you attain enlightenment and do not make use of it. If you can keep your stillness in enlightenment, this is doubly wonderful. If in stillness thoughts arise and monsters come to tempt you, let your mind deal with them naturally. If you see a host of celestial lords and immortals, you are seeing the images of your true form.
Let no thoughts arise from the beginning. This is called being open and not looking back. Let no thoughts arise at the end. This is called not having a past. Let the old habits diminish and do not accumulate new ones. Let nothing contaminate or obstruct you. Shed the dust and throw off the cage. Practice this long enough, and you will naturally attain the Tao.
Those who attain the Tao go through seven stages. First, the mind will become still easily and the dust of the world will not cling to the senses. Second, the hundred illnesses are kept at bay and mind and body are light and fresh. Third, depleted energy is restored and lost years are recovered. Fourth, the life span is increased and the practitioner becomes an immortal. Fifth, the body is transformed into vapor and the individual becomes a completely realized being. Sixth, vapor is transformed into spirit and the individual becomes a spirit being. Seventh, the spirit merges with the Tao and the practitioner becomes a being above all beings.
With continued practice, inner strength develops, and the light within will become bright. When the Tao is fully realized, original nature will be round and complete. If you practice this for a long time, the body will be at one with itself, all impurities will be purged, all forms will become nothingness, and original nature will emerge. This is called realizing the Tao. The principle of seeking the Tao is nothing but this.
Thoughts arise from the stirring of images. Fire emerges from attachment. These all disturb original nature. When this happens, we lose our connection with the Origin, the Tao. Know that stopping the mind stops desire. Understand that stirrings in the mind create worries. If you know that the mind is originally empty, you will know the gate to all mysteries.
**Seven Taoist Masters**
This excerpt illustrates the style of meditation practiced by the northern branch of the Complete Reality school, specifically the Lung-men sect. This branch of the Complete Reality school focuses on cultivating mind before body.
It is said that of all the Taoist sects, the northern branch of the Complete Reality school is most similar to Zen Buddhism. In the following excerpt, you will notice that like Zen meditation, Northern Complete Reality meditation requires the practitioner to empty the mind of thoughts. Furthermore, like Zen meditation, there are no visual or auditory aids.
However, the form of meditation practiced by the Complete Reality school is not identical to Zen meditation. Compete Reality Taoism is an internal-alchemical school, and its practice is designed to cultivate both body and mind. When you read the following excerpt, notice the details of posture and the use of _ch'i-kung_ techniques, such as knocking the teeth together and swallowing saliva, in this form of meditation.
_From_ Seven Taoist Masters, _Chapter 8_
Ma Tan-yang and Sun Pu-erh asked about meditation. Wang Ch'ung-yang said, "In meditation all thoughts must cease. When the ego is dead, the spirit emerges. When you sit, sit on a cushion. Loosen your clothing. At the hour of tzu (11:00 P.M.), cross your legs gently and sit facing east. Clasp your hands together and place them in front of your body. Your back should be straight. Strike your teeth together and swallow your saliva. Place the tongue against the palate of your mouth. You should be alert in listening, but do not be attached to sounds. Let your eyes drop, but do not close them. Focus on the light that you see in front of you and concentrate on the lower _tan-t'ien_. In meditation it is very important to stop thinking. If thoughts arise, the spirit will not be pure, and your efforts of cultivation will come to nothing. In addition, you should drop all feelings. Once feelings arise, the heart will not be still, and the attainment of the Tao is impossible."
Wang Ch'ung-yang continued, "Sit on a cushion and you will be able to sit long and not feel tired. Loosen your clothing so the movement of internal energy will not be constricted. The hour of tzu is when the first ray of yang appears. Face east because the breath of life flows in from the east at the hour of the first yang. Clasp your hands in the _t'ai-chi_ symbol, because it symbolizes emptiness of form. Sit with your back straight, because only with a vertical spine can the energy rise to the head. Close your mouth and place the tongue against the palate so that the internal energy cannot dissipate. The ear is associated with generative energy. Being attached to sound will dissipate this energy. Do not close your eyes, for they let the light in to shine on your spirit. If you close your eyes, the spirit will be dimmed. If you open them too wide, the spirit will escape. Therefore you should lower the lids but not close them. Concentrate on the lower _tan-t'ien_ as if to reflect the light of your eyes onto it because here is the mystery of all things. Minimize speech, as this conserves vital energy. Rest your ears, as this conserves generative energy. Dissolve thoughts to conserve spirit energy. When all these energies are not dissipated, then you will attain immortality."
10
_The Arts of Longevity_
CULTIVATING THE BODY
CULTIVATING THE BODY IS AN IMPORTANT part of Taoist spirituality. Without a healthy body, enlightenment, or union with the Tao, is not possible. Moreover, a long and healthy life gives us time to prepare ourselves to return to the Tao when we leave the mortal realm.
The readings in this chapter present some prominent Taoist techniques of cultivating the body and improving physical health. Please do not use them as manuals. Unguided practice of these techniques can be harmful, and the author and publisher are not responsible for any complications that result from using these readings as manuals.
**Yi-men ch'ang-seng pi-shu**
**( _Chen Hsi-yi's Secret Methods of Longevity_ )**
The _Yi-men ch'ang-seng pi-shu_ is a collection of techniques practiced by the Taoist sects of Hua-shan. These sects all claim the Sung-dynasty (960–1279 CE) hermit Chen Hsi-yi as their patriarch. _Yi-men_ means the "School of Hsi-yi." Compiled during the Wan-li (1573–1619 CE) years of the Ming dynasty by a Taoist hermit named Chou Fu-ching, the book postdated both the Cheng-t'ung and Wan-li Taoist canons. However, it is included in Hsiao T'ien-shih's _Tao-tsang ching-hua_ (The Essential Works of the Taoist Canon), a contemporary collection of canonical and postcanonical Taoist scriptures.
In the _Yi-men ch'ang-seng pi-shu_ are descriptions of ch'i-kung postures, Taoist calisthenics, massage, breath-control techniques, and meditation. Of all the texts collected in the book, the _Chih-feng sui_ (Red Phoenix Calisthenics) is the most famous. Reputed to be transmitted by Chen Hsi-yi himself, the book is profusely illustrated. It describes sitting, standing, and sleeping ch'i-kung postures, calisthenics, and techniques for control and regulation of the breath.
The illustrations that follow are from the _Chih-feng sui_. They depict techniques of massage, Taoist calisthenics, breath control and regulation, and sleeping ch'i-kung. Accompanying each picture is a description of the method and the health benefits.
_Massage and kneading techniques from the_ Chi-feng sui _(Red Phoenix Calisthenics). "Roll the knuckles over the areas left and right of the gate [Life Gate] thirty-six times_.
_Massage and kneading techniques from the_ Chi-feng sui. _"Using both hands_ , _rub and apply pressure to the area around the kidneys thirty-six times. The more this is repeated_ , _the better the effect."_
_Massage and kneading techniques from the_ Chi-feng sui. _"Knock the teeth together thirty-six times to gather the spirit_. _Take both hands and hold the_ kun-lun ( _spine_ ). _Hit the Heavenly Drum twenty four times." The Heavenly Drum is the flat part of the skull on two sides of the Jade Pillow cavity_ , _where the spine enters the skull_.
_Taoist calisthenics from the_ Chi-feng sui. _"Position both arms in front of the chest. Expel air five times. Then stretch the arms upward above the head. Repeat this cycle nine times."_
_Techniques of regulating and directing breath from the_ Chi-feng sui: _the Tiger Posture of Hsin-men. "Stop the breath, lower the head, and hold_ _the fists like a tiger ready to strike. The arms should be powerful as if they are lifting a thousand catties [a Chinese measurement of weight]. Gradually straighten up. Do not let the breath out but swallow it back when you have straightened. The breath enters the belly to let the energy of the spirit rise. The belly should feel like thunder rumbling. Do this five or seven times. The energy in the meridians will be regulated_ , _the spirit will be clear, and a hundred illnesses will leave."_
_Techniques of regulating and directing breath from the_ Chi-feng sui: _the Ape Posture of Fei Ch'ang-fang. "Stop the breath and hold your hands like an ape hanging from a tree. Then close the fingers of one hand to imitate an ape picking a fruit. Shift the weight completely off one leg. Turn the body around and gather the energy of the spirit. Swallow deep into the belly until perspiration appears."_
_Sleeping ch'i-kung postures from the_ Chi-feng sui: _Mao Hsüanhan's Posture of Subduing and Overcoming the Dragon and Tiger_. _"The original vapor in the heart is known as the body of the dragon. The generative energy in the circle of the middle is called the original nature of the tiger. When the dragon returns to the water_ , _emotions are dissolved, and the tiger hides in the mountain. The two families are in harmony, and your name will be listed among the immortals."_
_Sleeping ch'i-kung postures from the_ Chi-feng sui: _Enlightened Being Mah-i's Method of Regulating the True Vapor. "Regulate the true vapor and the five breaths will return to the origin. The mind is at rest and thoughts are not wayward. The two substances [mind and life] dwell forever in the positions of_ wu _and_ ssu _[the yin and yang in the center of the heart]. The tiger and the dragon copulate to produce the great round pill."_
**Chang San-feng t'ai-chi lien-tan pi-chüeh**
**( _Chang San-feng's Secret T'ai-chi Method for Cultivating the Elixir_ )**
Chang San-feng is best known as the patriarch of the Wu-tang-shan sect and the originator of _t'ai-chi ch'uan_ , an exercise for cultivating health and longevity. T'ai-chi ch'uan is also considered to be an internal martial art, because while cultivating body and mind, practitioners can also develop self-defense skills.
It is said that Chang San-feng originally devised a set of thirteen movements, which was later expanded to one hundred and eight by his students. Therefore, in the literature of t'ai-chi ch'uan we find many references to the Thirteen Postures, although the complete t'ai-chi set today consists of one hundred and eight moves.
For Chang San-feng, t'ai-chi ch'uan is not to be confused with t'ai-chi. While the _ch'uan_ is a set of movements, t'ai-chi is a state of spiritual development. Thus, the movements of t'ai-chi ch'uan are a means to attain the state of t'ai-chi, which is the balance of the yin and yang energies in the body.
Chang San-feng wrote several treatises on t'ai-chi ch'uan, ch'i-kung, and meditation. These texts and his students' commentaries are collected in a book titled _Chang San-feng t'ai-chi lien-tan pi-chüeh_ (Chang San-feng's Secret T'ai-chi Method for Cultivating the Elixir). This text is not listed in the Ming dynasty Taoist canons, but it is published in the series of Taoist texts edited by Taoist scholar Hsiao T'ien-shih of Taiwan. It appears as volume 5, part 2, in the _Tao-tsang ching-hua_ (The Essential Works of the Taoist Canon).
The following excerpts are chosen to illustrate how t'ai-chi ch'uan, an internal martial art, can be used to cultivate physical health and mental clarity.
_Understanding the Work of the Thirteen Postures_
Use the mind to move the ch'i to let it sink. Then the ch'i can be absorbed into the bones. Use ch'i to move the body, letting it happen naturally. Then ch'i will follow the mind with ease. Let the spirit be directed upward, and nothing will feel cumbersome.
What is meant by being suspended by the top of the head? It means that intention and ch'i should be lively and movement should be agile, rounded, and light. What is meant by alternating the substantial and insubstantial? It means that each movement should be grounded in relaxation and stillness and fully directed toward one point.
When you stand, the body should be balanced and comfortable. The feet and arms should be ready to respond to the eight directions. Move the ch'i like a pearl circulating nine times. The energy should flow in the body without obstruction. The movement should be as strong as steel tempered a hundred times. The foundation should be impregnable. Move with the stealth of a ghost. Be focused like a cat stalking a mouse. Be still like a great mountain. Move like a flowing river. Hold your force like a pulled bow. Let the force out like a speeding arrow. In its indirect path maintain straightness. Hold your force and only let it out after the opponent has made his move.
Force should come from the spine. The feet should move according to the body's movement. Let go and then hold on. Coming and going should be like a cascade. Alternate advance and retreat. Only in softness can you be firm. Only when you can breathe can your movement be agile.
Cultivate the ch'i and let it rise. Then there will be no problems. Let the force be indirect and hidden, and there will be plenty to spare. Let the mind be the commander. Let the ch'i be the herald. Let the spine be the pivot. In the beginning, aim to expand. Later, aim to contract. Then you can hide your action.
Thus, it is said, "Start first with the mind. Then follow with the body." Relax the abdomen. Draw the ch'i into the bones. Calm the spirit and still the body. Let this be planted in your mind. In every movement there is stillness, and in every stillness there is movement. Moving forward and backward, let the ch'i run along your back, drawing it into the spinal column. Internally, the spirit is stable. Externally, the composure is leisurely. Walk like a cat. Move like pulling silk. Focus and attention are in the spirit, not in the breath. If it is in the breath, there will be problems. If there is effortful breathing there is no strength. However, when there is no breathing, the breath is pure and strong. Then the ch'i will be like a wheel and the spine will be like the axle.
_Ten Important Things to Do in Your Practice_
1. Clean the face regularly.
2. Rub the eyes regularly.
3. Flick the ears regularly.
4. Knock the teeth together regularly.
5. Always keep the back warm.
6. Always protect the chest.
7. Massage the abdomen regularly.
8. Rub the feet together regularly.
9. Swallow the saliva regularly.
10. Always maintain flexibility in the waist and spine.
_Ten Things to Avoid in Your Practice_
1. Getting up too early.
2. Getting chilled in a shady room.
3. Sitting on wet ground.
4. Getting chilled in wet clothes.
5. Becoming too hot.
6. Perspiring in a breeze.
7. Sleeping with lights on.
8. Having sexual intercourse at the hour of _tzu_ (11:00 P.M to 1:00 A.M.).
9. Immersing muscles and tendons in cold water.
10. Putting hot food in the stomach.
_Eighteen Injuries to Be Avoided_
1. Watch too long and the generative energy will be damaged.
2. Listen too long and the spirit will be damaged.
3. Lie down too long and the vital energy (ch'i) will be damaged.
4. Sit too long and the meridians will be harmed.
5. Stand too long and the bones will be damaged.
6. Walk too much and the tendons will be damaged.
7. Anger harms the liver.
8. Scheming harms the spleen.
9. Worrying harms the heart.
10. Excessive sadness harms the lungs.
11. Overeating harms the stomach.
12. Excessive fear harms the kidneys.
13. Too much laughter harms the abdomen.
14. Too much talking harms the spinal fluid.
15. Sleep too much and the saliva will be damaged.
16. Perspire too much and the yang energy will be harmed.
17. Cry too often and the blood will be harmed.
18. Too much sex will harm the marrow.
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\section{Introduction}
We begin by quoting the introduction from the groundbreaking paper \cite{EH86} of Eisenbud and Harris:
\medskip
\begin{itemize}
\item[]
``One of the most potent methods in the theory of (complex projective algebraic)
curves and their linear systems since the work of Castelnuovo has been
degeneration to singular curves...
Most problems of interest about curves are, or can be, formulated in terms of
(families of) linear series. Thus, in order to use degenerations to reducible curves for
studying smooth curves, it is necessary to understand what happens to linear series
in the course of such a degeneration, and in particular, to understand what structure
on a reducible curve plays the part of a linear series.''
\end{itemize}
This has been very successful in practice and has led to important advances in the study of
algebraic curves (see \cite{HM} for an overview); we mention for example Brill-Noether theory~\cite{EH86, Bi},
the geometry of the moduli space of curves~\cite{HM82, EH87}, and Weierstrass points and their
monodromy~\cite{EH87bis, EM, EH4}.
In view of the Deligne-Mumford compactification of $\mathcal M_g$ and
the stable reduction theorem~\cite{DM}, it is
particularly natural to consider degeneration of smooth curves to stable (or more generally semistable) curves.
Eisenbud and Harris were able to settle a number of longstanding open problems with their theory of limit linear series on such curves,
and the theory has undergone numerous developments and improvements in the last 25 years.
However, the theory of limit linear series only applies, for the most part, to a rather restricted class of
reducible curves, namely those of {\em compact type} (i.e., nodal curves whose dual graph is a tree).
\medskip
In \cite{bakersp}, the second author introduced a new framework for degenerating linear series on curves, degenerating linear series on a regular semistable family of curves to a linear series on the {\em dual graph} of the special fiber.
This theory, which is closely related to tropical geometry and also to the theory of Berkovich analytic spaces, is more or less orthogonal to the Eisenbud-Harris theory, in that it works best for special fibers which are
{\em maximally degenerate}, meaning that the dual graph has first Betti number equal to the genus of
the generic fiber. Specializing linear series to the dual graph provides no information whatsoever when the special fiber is of compact type. Intriguingly, both the Eisenbud-Harris theory and the second author's theory from \cite{bakersp} lead to
simple proofs of the celebrated Brill-Noether theorem of Griffiths-Harris (see \cite{EH86,CDPR}).
\medskip
The aim of the present paper is to introduce a theoretical framework suitable for generalizing both the Eisenbud-Harris theory of limit linear series and the second author's theory of specialization from curves to graphs.
The main new object of study is what we call a {\em metrized complex
of algebraic curves} over an algebraically closed field $\kappa$; this is, roughly speaking, a finite metric graph $\Gamma$ together with a collection of marked complete nonsingular algebraic curves $C_v$ over $\kappa$, one for each vertex $v$ (with a marked point on $C_v$ for each edge of $\Gamma$ incident to $v$).
We define divisors, linear equivalence of divisors, and rank of divisors on metrized complexes of curves and establish a
Riemann-Roch theorem for metrized complexes of curves which combines the classical Riemann-Roch theorem over
$\kappa$ with its graph-theoretic and tropical analogues proved in \cite{AC,BN, GK, MZ}.
For a curve $X$ defined over a non-Archimedean field $\mathbb K$, together with a strongly semistable model $\fX$ for $X$
over the valuation ring $R$ of $\mathbb K$, we define a corresponding metrized complex $\mathfrak{C}\fX$ of curves over the residue
field $\kappa$ of $\mathbb K$ and a specialization map $\tau^{\mathfrak{C}\fX}_*$
from divisors on $X$ to divisors on $\mathfrak{C}\fX$ preserving degrees and linear equivalence.
We then establish generalizations of the specialization lemma from \cite{bakersp} and its weighted graph analogue
from \cite{AC}, showing that the rank of a divisor cannot go down under specialization from $X$ to $\mathfrak{C}\fX$.
As an application, we establish a concrete link between specialization of divisors from curves to metrized complexes
and the Eisenbud-Harris theory of limit linear series. Using this link, we formulate a generalization of the notion of
limit linear series to curves which are not necessarily of compact type and prove, among other things, that any degeneration of a $\mathfrak g^r_d$ in a regular family of semistable curves is a limit $\mathfrak g^r_d$ on the special fiber.
\medskip
As mentioned above, the specialization theory from \cite{bakersp} works best in the case where the
family is maximally degenerate; in other cases, the dual graph of the family forgets too much information.
This loss of information was partially remedied in \cite{AC} by looking at vertex-weighted graphs, where the
weight attached to a vertex is the genus of the corresponding irreducible component of the special fiber.
The theory of metrized complexes of curves offers a richer solution in which one keeps track of the (normalization
of the) irreducible components $C_v$ of the special fiber themselves, and not just their genera. From the point of view of non-Archimedean geometry, this corresponds to retracting divisors on $X$ to the skeleton
$\Gamma_{\fX}$, a metric graph canonically embedded in the Berkovich analytic space $X^{\operatorname{an}}$, but also keeping track, for points retracting to a vertex of $\Gamma_{\fX}$, of the tangent direction in which the vertex is
approached. This is quite natural from the valuation-theoretic point of view: the metric graph $\Gamma_{\fX}$ associated to a strongly semistable model $\fX$ is a canonical subset of the Berkovich analytic space $X^{\operatorname{an}}$, and the curve
$C_v$ over $\kappa$ is naturally identified (for each $v \in V$) with the fiber over $v$ of the canonical retraction map $X^{\operatorname{ad}} \to X^{\operatorname{an}}$ (which sends a continuous valuation of arbitrary rank in the Huber adic space $X^{\operatorname{ad}}$ to its canonical rank-1 generalization), c.f. \cite[Remark 2.6]{Te}.
Though we could possibly (with quite a bit of additional effort) have formulated many of our theorems and proofs without
mentioning Berkovich spaces, it would have resulted in a significant loss of elegance and clarity, and in any case
Berkovich's theory seems ideally suited for the point of view taken here. We do not, however, require any non-trivial
facts from Huber's theory of adic spaces, so we will not mention them again even though they are certainly lurking in the
background.
\medskip
There are a number of connections between the ideas in the present paper and tropical geometry; these will be explored
in more detail in future work. For example, the theory of morphisms between metrized complexes of curves
studied in \cite{ABBR} sheds interesting new light on the question of which morphisms
between tropical curves are liftable. The theory developed in \cite{BPR} shows that there is a close connection between
metrized complexes of curves and ``exploded tropicalizations'' in the sense of \cite[Definition 2.9]{Pay}; we plan to say more about this in the future as well. As noted by Payne in \cite{Pay}, exploded tropicalizations can be thought of as an
algebraic analogue of the ``exploded torus fibrations'' studied by Parker from a symplectic viewpoint \cite{Par}.
It could be interesting to explore connections between {\it loc.~cit.} and the present work.
\medskip
The ideas in the present paper also have Diophantine applications to the study of rational points on curves over number fields (specifically, to the method of Coleman-Chabauty).
Indeed, Eric Katz and David Zureick-Brown have recently proved a result
similar to Theorem~\ref{thm:MCClifford} below (Clifford's theorem for metrized complexes), and they use this result
to answer a question of M.~Stoll. A special case of the main result in \cite{KZB} is the following. Let $X$ be a smooth projective geometrically irreducible curve of genus $g \geq 2$ over ${\mathbf Q}$ and assume that the Mordell-Weil rank $r$ of the Jacobian of $X$ is less than $g$.
Fix a prime number $p > 2r+2$ and let $\fX$ be a proper (not necessarily semistable) regular model for $X$ over
${\mathbf Z}_p$. Then (letting $\bar{\fX}^{{\rm sm}}$ denote the smooth locus of $\bar{\fX}$)
\[
\# X({\mathbf Q}) \leq \bar{\fX}^{{\rm sm}}({\mathbf F}_p) + 2r.
\]
We discuss the theorem of Katz and Zureick-Brown in more detail in Section~\ref{ChabautySection} below,
explaining how limit linear series on metrized complexes of curves can be used to illuminate their proof and put it into a broader context.
\subsection{Notation}
\label{section:Notation}
We set the following notation, which will be used
throughout this paper.
\begin{notation}
\item[$G$]
a finite edge-weighted graph with vertex set $V$ and edge set $E$
\item[$\Gamma$]
a compact metric graph (geometric realization of an edge-weighted graph $G$)
\item[$\mathbb K$]
a complete and algebraically closed non-trivially valued non-Archimedean field
\item[$R$]
the valuation ring of $\mathbb K$
\item[$\k$]
the residue field of $\mathbb K$
\item[$X$]
a smooth, proper, connected algebraic curve defined over $\mathbb K$
\item[$X^{\mathrm{an}}$]
the Berkovich analytification of $X/\mathbb K$
\item[$\mathfrak X$]
a proper and flat semistable $R$-model for $X$, usually assumed to be strongly semistable
\item[$C_v$]
a smooth, proper, connected algebraic curve over $\k$ (one for each vertex $v\in V$)
\item[$\mathfrak{C}$]
a metrized complex of algebraic curves over $\k$
\item[$|\mathfrak{C}|$]
the geometric realization of $\mathfrak{C}$
\item[$\mathfrak{C} \mathfrak X$]
the metrized complex associated to a strongly semistable $R$-model $\mathfrak X$ of $X$
\item[$X_0$]
a nodal curve defined over $\k$
\item[$X_v$]
an irreducible component of $X_0$
\item[$\mathfrak{C} X_0$]
the regularization of the nodal curve $X_0$
\item[$\operatorname{Div}(\mathfrak{C})$]
the group of divisors on the metrized complex $\mathfrak{C}$
\item[$\mathcal D$]
a divisor on $\mathfrak{C}$
\item[$\mathcal E$]
an effective divisor on $\mathfrak{C}$
\item[$\mathfrak f$]
a rational function on $\mathfrak{C}$
\item[$D_v$]
a divisor on $C_v$
\item[$E_v$]
an effective divisor on $C_v$
\item[$f_\Gamma$]
a rational function on $\Gamma$, usually the $\Gamma$-part of a rational function $\mathfrak f$ on $\mathfrak{C}$
\item[$f_v$]
a rational function on $C_v$, usually the $C_v$-part of a rational function $\mathfrak f$ on $\mathfrak{C}$
\item[$\mathrm{slp}_e(f_\Gamma)$]
the outgoing slope of $f_\Gamma$ along an edge (or tangent direction) $e$
\item[$r_\mathfrak{C}$]
the rank function on $\operatorname{Div}(\mathfrak{C})$
\item[$r_{\mathfrak{C},\mathcal F}$]
the restricted rank function with respect to a collection $\mathcal F = \{ F_v \}_{v\in V}$ of subspaces of $\k(C_v)$
\item[$\tau$]
the retraction map from $X^{\rm an}$ to the skeleton $\Gamma_{\mathfrak X}$ of $\mathfrak X$
\item[$\tau^{\mathfrak{C}\fX}_*$]
the specialization map from $\operatorname{Div}(X)$ to $\operatorname{Div}(\mathfrak{C}\fX)$
\item[$\mathcal A_v$]
the marked points of $C_v$ in the metrized complex $\mathfrak{C}$
\item[$x^e_v$]
the point of $\mathcal A_v$ corresponding to the edge (or tangent direction) $e$
\item[$A_v$]
the sum in $\operatorname{Div}(C_v)$ of the points of $\mathcal A_v$
\end{notation}
\subsection{Overview}
\label{section:overview}
We now discuss the contents of this paper in more detail.
\medskip
An {\em edge-weighted graph} $G$ is a connected multigraph, possibly with loop edges, having vertex set $V$ and
edge set $E$, and endowed with a weight (or length) function $\ell : E \to \mathbb{R}_{> 0}$.
A {\em metric graph} $\Gamma$ is the geometric realization of an edge-weighted graph $G$ in which each edge $e$ of
$G$ is identified with a line segment of length $\ell(e)$. We call $G$ a {\em model} for $\Gamma$.
Subdividing an edge of $G$ in a length-preserving fashion changes the model but not the underlying metric graph.
\medskip
Let $\kappa$ be an algebraically closed field.\footnote{To simplify the presentation, we restrict to algebraically
closed fields.
In \S{2.3} of the January 2013 arXiv version of this paper,
we indicate how the theory can be developed over an arbitrary field $\kappa$.}
A {\em metrized complex $\mathfrak{C}$ of $\kappa$-curves} consists of the
following data:
\begin{itemize}
\item A connected finite graph $G$ with vertex set $V$ and edge set $E$.
\item A metric graph $\Gamma$ having $G$ as a model (or equivalently, a length function $\ell : E \to \mathbb{R}_{>0}$).
\item For each vertex $v$ of $G$, a complete, nonsingular, irreducible curve $C_v$ over $\kappa$.
\item For each vertex $v$ of $G$, a bijection $e \mapsto x^e_v$ between the edges of $G$ incident to $v$ (with loop edges counted twice) and a subset
$\mathcal A_v = \{ x^e_v \}_{e \ni v}$ of $C_v(\kappa)$.
\end{itemize}
\medskip
\begin{figure}[!tb]
\includegraphics[width=6cm]{georeal.pdf}
\caption{The geometric realization of a metrized complex of genus four.}
\label{fig:mcsmall}
\end{figure}
The {\em geometric realization} $|\mathfrak{C}|$ of $\mathfrak{C}$ is defined to be the union of the edges of $G$
and the collection of curves $C_v$, with each endpoint $v$ of an edge $e$ identified with the corresponding marked point $x^e_v$.
See Figure~\ref{fig:mcsmall}.
When we think of $|\mathfrak{C}|$ as a set, we identify it with the disjoint union of $\Gamma \backslash V$ and $\bigcup_{v \in V} C_v(\kappa)$.
Thus, when we write $x \in |\mathfrak{C}|$, we mean that $x$ is either a non-vertex point of $\Gamma$ (a {\em graphical point} of $\mathfrak{C}$)
or a point of $C_v(\kappa)$ for some $v \in V$ (a {\em geometric point} of $\mathfrak{C}$).
\medskip
The {\em genus} of a metrized complex of curves $\mathfrak{C}$, denoted $g(\mathfrak{C})$, is by definition
$g(\mathfrak{C})=g(\Gamma)+\sum_{v\in V}g_v$, where $g_v$ is the genus of $C_v$ and $g(\Gamma)$ is the first Betti number of $\Gamma$.
\medskip
Given a metrized complex $\mathfrak{C}$ of $\kappa$-curves, there is an associated semistable curve
$X_0$ over $\kappa$ obtained by
gluing the curves $C_v$ along the points $x^e_v$ (one intersection for each edge $e$ of $G$) and
forgetting the metric structure on $\Gamma$. Conversely, given a semistable curve $X_0$ over $\kappa$ together with a positive real number for each node (which we call a ``length function''), one obtains an associated metrized complex of $\kappa$-curves by letting $G$ be the dual graph of $X_0$, $\Gamma$ the metric graph associated to $G$ and the given length function, $C_v$ the normalization of the irreducible component $X_v$ of $X_0$ corresponding to $v$,
and $\mathcal A_v$ the preimage in $C_v$ of the set of nodes of $X_0$ belonging to $X_v$.
\medskip
Let $\mathbb K$ be a complete and algebraically closed non-Archimedean field with residue field $\kappa$ and
let $X/\mathbb K$ be a smooth, proper, connected algebraic curve.
There is a metrized complex $\mathfrak{C} = \mathfrak{C}\fX$ canonically associated to any strongly semistable model $\fX$ of $X$ over the valuation ring $R$ of $\mathbb K$: the special fiber $\bar{\fX}$ of $\fX$ is a semistable curve over
$\kappa$, and one defines the length of an edge $e$ of the dual graph of $\bar{\fX}$ to be the {\em modulus} of the open annulus ${\rm red}^{-1}(z)$, where $z$ is the singular point of $\bar{\fX}$ corresponding to $e$ and ${\rm red} : X(\mathbb K) \to \bar{\fX}(\kappa)$ is the canonical reduction map.
Equivalently, there is a local analytic equation for $z$ of the form $xy=\varpi$ with $\varpi$ in the maximal ideal of $R$, and the length of $e$ is ${\rm val}(\varpi)$.
The corresponding metric graph $\Gamma = \Gamma_{\fX}$ is called the {\em skeleton} of $\fX$,
and there is a canonical retraction map $\tau = \tau_{\fX}: X^{\operatorname{an}} \onto \Gamma_{\fX}$, where $X^{\operatorname{an}}$ denotes the Berkovich analytification of $X$.
By restricting to $X(\mathbb K)$ and then extending by linearity, we obtain a specialization map
$\tau_* : \operatorname{Div}(X) \to \operatorname{Div}(\Gamma_{\fX})$.
\medskip
If $R$ is a discrete valuation ring and the fibered surface $\fX/R$ is regular, then one can use intersection-theoretic
methods to define and study specialization of divisors from curves to graphs.
For example, in \cite{bakersp}, using intersection theory, a specialization homomorphism $\rho : \operatorname{Div}(X) \to \operatorname{Div}(G)$ was defined, where $G$ is the dual graph of $\bar{\fX}$, with the property that $\rho(D)$ and $\tau_*(D)$ are linearly equivalent as divisors on $\Gamma_{\fX}$ for all $D \in \operatorname{Div}(X)$. In the present paper, we focus exclusively on $\tau_*$ and its
generalization to metrized complexes of curves, though in principle all of our results can be translated (when $R$
is a discrete valuation ring and $\fX$ is regular) into results about this alternative specialization map.
\medskip
A {\em divisor} on a metrized complex of curves $\mathfrak{C}$ is an element $\mathcal D$ of the free abelian group on $|\mathfrak{C}|$.
Thus a divisor on $\mathfrak{C}$ can be written uniquely as $\mathcal D = \sum_{x \in |\mathfrak{C}|} a_x (x)$ where $a_x \in \mathbb{Z}$, all but finitely many of the $a_x$ are zero,
and the sum is over all points of $\Gamma \backslash V$ as well as $C_v(\kappa)$ for $v \in V$.
The {\em degree} of $\mathcal D$ is defined to be $\sum a_x$.
\medskip
To a divisor on $\mathfrak{C}$, we can naturally associate a divisor $D_\Gamma$ on $\Gamma$, called the {\em $\Gamma$-part} of $\mathcal D$, as well as, for each $v \in V$, a
divisor $D_v$ on $C_v$ (called the {\em $C_v$-part} of $\mathcal D$).
The divisor $D_v$ is simply the restriction of $\mathcal D$ to $C_v$, i.e. $D_v = \sum_{x \in C_v(\kappa)} \mathcal D(x)(x)$, and $D_\Gamma$ is defined as
\[
D_\Gamma = \sum_{x \in \Gamma \backslash V} \mathcal D(x) (x) + \sum_{v \in V} \deg(D_v) (v),
\]
where $\mathcal D(x)$ denotes the coefficient of $x$ in $\mathcal D$.
In particular, the degree of $\mathcal D$ equals the degree of $D_\Gamma$.
One could equivalently define a divisor on $\mathfrak{C}$ to be an element of the form
$\mathcal D = D_\Gamma \oplus \sum_v D_v$ of $\operatorname{Div}(\Gamma)\oplus (\oplus_v \operatorname{Div}(C_v))$
such that $\deg(D_v) = D_\Gamma(v)$ for all $v$ in $V$.
\medskip
The specialization map $\tau_*$ can be enhanced in a canonical way to a map from divisors on $X$ to divisors on $\mathfrak{C}\fX$.
The fiber $\tau^{-1}(v)$ of the retraction map $\tau : X(\mathbb K) \to \Gamma$ over a vertex $v \in V$ can be
canonically identified with ${\rm red}^{-1}(C_v^{\rm sm}(\kappa))$, the fiber of the reduction map $\mathrm{red} : X(\mathbb K) \to
\bar{\fX}(\kappa)$ over the smooth locus $C_v(\kappa) \setminus \mathcal A_v$ of $C_v$.
We define $\tau^{\mathfrak{C}\fX} : X(\mathbb K) \to \mathfrak{C}\fX$ by setting
\[
\tau^{\mathfrak{C}\fX} (P) = \left\{
\begin{array}{ll}
\tau(P) & \tau(P) \not\in V \\
{\rm red}(P) & \tau(P) \in V \\
\end{array}
\right.
\]
and we extend this by linearity to a map $\tau_*^{\mathfrak{C}\fX} : \operatorname{Div}(X) \to \operatorname{Div}(\mathfrak{C}\fX)$.
\medskip
Intuitively speaking, for points $P$ of $X(\mathbb K)$ which reduce to smooth points of $\bar{\fX}$,
the map $\tau^{\mathfrak{C}\fX}$
keeps track of the reduced point ${\rm red}({P}) \in \bar{\fX}^{\rm sm}(\kappa)$,
while if $P$ reduces to a singular point of $\bar{\fX}$ then $\tau^{\mathfrak{C}\fX}$ instead keeps track of the retraction of $P$ to the skeleton of the open annulus $\mathrm{red}^{-1}(P)$, which is canonically identified with the relative interior of the corresponding edge of $\Gamma_{\fX}$.
\medskip
A {\em nonzero rational function} $\mathfrak f$ on a metrized complex of curves $\mathfrak{C}$ is the data of a rational function $f_\Gamma$ on $\Gamma$ and nonzero rational functions $f_v$ on $C_v$ for each $v\in V$. (We do {\em not} impose any compatibility
conditions on the rational functions $f_\Gamma$ and $f_v$.)
We call $f_\Gamma$ the {\em $\Gamma$-part} of $\mathfrak f$ and $f_v$ the {\em $C_v$-part} of $\mathfrak f$.
\medskip
The {\em divisor} of a nonzero rational function $\mathfrak f$ on $\mathfrak{C}$ is defined to be
\[
\div(\mathfrak f) := \sum_{x \in |\mathfrak{C}|} \mathrm{ord}_x(\mathfrak f) (x),
\]
where $\mathrm{ord}_x(\mathfrak f)$ is defined as follows:
\begin{itemize}
\item If $x \in \Gamma \backslash V$, then $\mathrm{ord}_x(\mathfrak f) = \mathrm{ord}_x(f_\Gamma)$, where
$\mathrm{ord}_x(f_\Gamma)$ is the sum of the slopes of $f_\Gamma$ in all tangent directions emanating from $x$.
\item If $x \in C_v(\kappa) \backslash \mathcal A_v$, then $\mathrm{ord}_x(\mathfrak f) = \mathrm{ord}_x(f_v)$.
\item If $x = x^e_v \in \mathcal A_v$, then $\mathrm{ord}_x(\mathfrak f) = \mathrm{ord}_x(f_v) + \mathrm{slp}_e(f_\Gamma)$, where
$\mathrm{slp}_e(f_\Gamma)$ is the outgoing slope of $f_\Gamma$ at $v$ in the direction of $e$.
\end{itemize}
If $D_\Gamma$ (resp. $D_v$) denotes the $\Gamma$-part (resp. the $C_v$-part) of $\div(\mathfrak f)$, then
\[ D_\Gamma = \div(f_{\Gamma}) = \sum_{u\in \Gamma} \mathrm{ord}_u(f_\Gamma)\,(u)\qquad \textrm{and}
\qquad D_v = \div(f_v) + \div_v(f_\Gamma), \qquad \textrm{where}
\]
\begin{equation}
\label{eq:divf2}
\div_v(f_\Gamma) := \sum_{e \ni v} \mathrm{slp}_e(f_\Gamma)(x^e_v).
\end{equation}
Divisors of the form $\div(\mathfrak f)$ are called {\em principal}, and the principal divisors form a subgroup of
$\operatorname{Div}^0(\mathfrak{C})$, the group of divisors of degree zero on $\mathfrak{C}$.
Two divisors in $\operatorname{Div}(\mathfrak{C})$ are called {\em linearly equivalent} if they differ by a principal divisor.
\medskip
Linear equivalence of divisors on $\mathfrak{C}$ can be understood quite intuitively in terms of ``chip-firing moves''. To state this formally, for each vertex $v$ of $G$, let $A_v$ be the sum of the $\deg_G(v)$ points in $\mathcal A_v$ and let
$\ell_v$ be the minimum length of an edge $e$ incident to $v$. Also, for an edge $e$ having $v$ as an endpoint and a positive real number $\varepsilon < \ell(e)$, let $p^e_{v, \varepsilon}$ be the unique point of $e$ at distance $\varepsilon$ from $v$.
Then it is not hard to show that linear equivalence of divisors on $\mathfrak{C}$ is the equivalence relation generated by the following three kinds of ``moves'':
\begin{enumerate}
\item (Firing on $C_v$) Choose a vertex $v$ and replace the divisor $D_v$ with a linearly equivalent divisor $D'_v$ on $C_v$.
\item (Firing a vertex) Choose a vertex $v$ and a positive real number $\varepsilon < \ell_v$ and replace $D_v$ with
$D_v - A_v$ and $D_\Gamma$ with $D_\Gamma - \deg_G(v)(v) + \sum_{e \ni v} (p^e_{\varepsilon})$.
\item (Firing a non-vertex) Choose a non-vertex $p \in \Gamma$ and a positive real number $\varepsilon$ less than the distance from $p$ to the
nearest vertex and replace $D_\Gamma$ by the divisor $D_\Gamma - 2({p}) + (p^+_\varepsilon) + (p^-_\varepsilon)$, where $p^{\pm}_\varepsilon$ are the two points at distance $\varepsilon$ from $p$.
\end{enumerate}
\medskip
The motivation for our definitions of $\tau^{\mathfrak{C}\fX}_*$ and $\div(\mathfrak f)$ come from the following fundamental relation,
a consequence of the non-Archimedean Poincar{\'e}-Lelong formula due to Thuillier (see \S{5} of \cite{BPR}).
Let $f$ be a nonzero rational function
on $X$ and let $\mathfrak f$ be the corresponding nonzero rational function on $\mathfrak{C}\fX$, where $f_{\Gamma}$ is the restriction
to $\Gamma$ of the piecewise linear function $\log|f|$ on $X^{\operatorname{an}}$ and $f_v \in \kappa(C_v)$ for $v \in V$ is the
normalized reduction of $f$ to $C_v$ (cf.~\S\ref{section:ReductionOfRationalFunctions}).
Then
\[
\tau_*^{\mathfrak{C}\fX}(\div(f)) =\div(\mathfrak f).
\]
In particular, we have $\tau_*^{\mathfrak{C}\fX}(\operatorname{Prin}(X)) \subseteq \operatorname{Prin}(\mathfrak{C}\fX)$.
\medskip
A divisor $\mathcal E = \sum_{x \in |\mathfrak{C}|} {a_x (x)}$ on $\mathfrak{C}$ is called {\em effective} if $a_x \geq 0$ for all $x$
(or, equivalently, if the $\Gamma$-part $E_\Gamma$ and the $C_v$-parts $E_v$ of $\mathcal E$ are effective for every $v\in V$). The {\em rank} $r_\mathfrak{C}$ of a divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C})$ is defined to
be the largest integer $k$ such that $\mathcal D - \mathcal E$ is linearly equivalent to an effective divisor
for all effective divisors $\mathcal E$ of degree $k$ on $\mathfrak{C}$ (so in particular
$r_{\mathfrak{C}}(\mathcal D) \geq 0$ if and only if $\mathcal D$ is linearly equivalent to
an effective divisor, and otherwise $r_{\mathfrak{C}}(\mathcal D)=-1$).
\medskip
If $r_X(D)$ denotes the usual rank function $r_X(D) = \dim |D| = h^0(D) - 1$ on $\operatorname{Div}(X)$,
there is an important semicontinuity result relating $r_X$ to $r_{\mathfrak{C}\fX}$:
\begin{thm}[Specialization Theorem]
\label{thm:introSpecialization}
For all $D \in \operatorname{Div}(X)$, we have
\[
r_X(D) \leq r_{\mathfrak{C}\fX}(\tau_*^{\mathfrak{C}\fX}(D)).
\]
\end{thm}
Since $r_{\mathfrak{C}\fX}(\tau_*^{\mathfrak{C}\fX}(D)) \leq r_\Gamma(\tau_*(D))$, Theorem~\ref{thm:introSpecialization}
is a strengthening of the analogous specialization result from \cite{bakersp}.
In conjunction with a simple combinatorial argument, Theorem~\ref{thm:introSpecialization} also refines the specialization lemma for vertex-weighted graphs from \cite{AC}.
\medskip
We also state and prove a version of Theorem~\ref{thm:introSpecialization} in which one has {\em equality} rather than just an inequality.
One can naturally associate to a rank $r$ divisor $D$ on $X$ not only a divisor $\tau^{\mathfrak{C} \fX}_*(D)$ on $\mathfrak{C}\fX$, but also a collection
$\H = \{ H_v \}_{v \in V}$ of $(r+1)$-dimensional subspaces of $\k(C_v)$, where $H_v$ is the reduction to $C_v$ of all functions in $H^0(X, \mathcal L(D))$ (c.f. Section~\ref{section:ReductionOfRationalFunctions} for a discussion of reduction of rational functions).
If $\mathcal F = \{ F_v \}_{v \in V}$, where $F_v$ is any $\kappa$-subspace of the function field $\kappa(C_v)$,
then for $\mathcal D \in \operatorname{Div}(\mathfrak{C})$ we define the {\em $\mathcal F$-restricted rank} of $\mathcal D$, denoted $r_{\mathfrak{C},\mathcal F}(\mathcal D)$, to be the largest integer $k$
such that for any effective divisor $\mathcal E$ of degree $k$ on $\mathfrak{C}$, there is a rational function $\mathfrak f$ on $\mathfrak{C}$ whose $C_v$-parts
$f_v$ belong to $F_v$ for all $v \in V$, and such that $\mathcal D - \mathcal E + \div(\mathfrak f) \geq 0$.
(In terms of the ``chip-firing moves'' described above, one has to be able to make $\mathcal D-\mathcal E$ effective using only type (1) moves corresponding to functions belonging to
one of the spaces $F_v$, together with moves of type (2) or (3).)
The following variant of Theorem~\ref{thm:introSpecialization} will be proved as Theorem~\ref{thm:limitseriesgeneral} below:
\begin{thm}[Specialization Theorem for Restricted Ranks]
With notation as above, the $\H$-restricted rank of the specialization of $D$ is equal to the rank of $D$, i.e.,
$r_{\mathfrak{C},\H}(\tau^{\mathfrak{C} \fX}_*(D)) = r$.
\end{thm}
\medskip
The theory of divisors and linear equivalence on metrized complexes of curves generalizes both the classical theory
for algebraic curves and the corresponding theory for metric graphs and tropical curves found in \cite{GK,MZ}.
The former corresponds to the case where $G$ consists of a single vertex $v$ and no edges and $C=C_v$ is an arbitrary smooth curve. The latter corresponds to the case where the curves $C_v$ have genus zero for all $v \in V$.
Since any two points on a curve of genus zero are linearly equivalent, it is easy to see that the divisor theories and rank functions on $\mathfrak{C}$ and $\Gamma$ are essentially equivalent. More precisely, (i) two divisors $\mathcal D$ and $\mathcal D'$ on $\mathfrak{C}$ are linearly equivalent if and only if their $\Gamma$-parts
$D_\Gamma$ and $D'_\Gamma$ are linearly equivalent on $\Gamma$, and (ii) for every $\mathcal D\in \operatorname{Div}(\mathfrak{C})$
we have $r_\mathfrak{C}(\mathcal D) = r_\Gamma(D_\Gamma)$.
In the presence of higher genus curves among the $C_v$, the divisor theories on $\Gamma$ and $\mathfrak{C}$ can be very different. In addition, different choices of $\mathcal A_v$ can drastically change both the linear equivalence relation and
the rank function.
\medskip
As with the corresponding specialization theory from \cite{bakersp}, the main utility of
Theorem~\ref{thm:introSpecialization} is that the rank function $r_{\mathfrak{C}}$ on a metrized complex of curves
is surprisingly well-behaved; for example, it satisfies an analogue of the Riemann-Roch formula.
In order to state this result, we need to define the canonical class.
A {\em canonical divisor} on $\mathfrak{C}$, denoted $\mathcal K$, is defined to be any divisor linearly equivalent to
$\sum_{v \in V} (K_v + A_v)$, where $K_v$ is a canonical divisor on $C_v$ and $A_v$ is the sum of the $\deg_G(v)$ points in $\mathcal A_v$.
The $\Gamma$-part of $\mathcal K$ is $K^\# = \sum_v \left( \deg_G(v) + 2g_v - 2 \right) (v)$, and the $C_v$-part of $\mathcal K$ is
$K_v + A_v$.
\medskip
The following result generalizes both the classical Riemann-Roch theorem for algebraic curves and the Riemann-Roch theorem for metric graphs:
\begin{thm}[Riemann-Roch for metrized complexes of algebraic curves]\label{thm:introRR-metrizedcomplexes}
Let $\mathfrak{C}$ be a metrized complex of algebraic curves over $\kappa$ and $\mathcal K$ a divisor in the canonical class of $\mathfrak{C}$. For any divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C})$, we have
\[r_\mathfrak{C}(\mathcal D) - r_\mathfrak{C}(\mathcal K -\mathcal D) = \deg(\mathcal D) - g(\mathfrak{C})+1. \]
\end{thm}
The proof of Theorem~\ref{thm:introRR-metrizedcomplexes} makes use of a suitable notion of {\em reduced divisors}
for metrized complexes of curves.
\medskip
Taken together, Theorems \ref{thm:introSpecialization} and \ref{thm:introRR-metrizedcomplexes} have some
interesting consequences. For example, the specialization theorem implies that the specialization to $\mathfrak{C}\fX$ of any
canonical divisor on $X$ has degree $2g-2$ and rank at least $g-1$ (where $g = g(X) = g(\mathfrak{C}\fX)$), while the Riemann-Roch theorem easily implies that any such divisor on $\mathfrak{C}\fX$ belongs to the canonical divisor class. Thus we have:
\begin{cor}
\label{cor:introcanonspec}
For any canonical divisor $K_X$ on $X$, its specialization $\tau^{\mathfrak{C}\fX}_*(K_X)$ belongs to the canonical divisor
class on $\mathfrak{C}\fX$.
\end{cor}
In particular, Corollary~\ref{cor:introcanonspec} implies that $\tau_*(K_X)$ is a canonical divisor on $\Gamma$.
This fact was proved in \cite{bakersp}, for discretely valued $R$, by a completely different argument based on the adjunction formula for arithmetic surfaces.
It does not seem easy to prove the general (not necessarily discretely valued) case using arithmetic intersection theory, since there does not seem to be a satisfactory theory of relative dualizing sheaves and adjunction in the non-Noetherian setting.
\medskip
Our theory of linear series on metrized complexes of curves has close connections with the Eisenbud-Harris theory
of limit linear series for strongly semistable curves of compact type, and suggests a way to generalize the Eisenbud-Harris theory to more general semistable curves.
A proper nodal curve $X_0$ over $\kappa$ is of {\em compact type} if its dual graph $G$ is a tree.
For such curves, Eisenbud and Harris define a notion of (crude) {\em limit $\mathfrak g^r_d$}, which we discuss in detail in
Section~\ref{sec:limitcompact} below.
A {\it crude limit} $\mathfrak g^r_d$ $L$ on $X_0$ is the data of a (not necessarily complete) degree $d$ and rank $r$ linear series $L_v$ on $X_v$ for each vertex $v \in V$ such that if two components $X_u$ and $X_v$ of $X_0$ meet at a node $p$, then for any $ 0\leq i \leq r,$
\begin{equation*}
a^{L_v}_{i}( p ) + a^{L_u}_{r-i}( p ) \, \geq \, d\,,
\end{equation*}
where $a^{L}_i (p)$ denotes the $i^{\rm th}$ term in the vanishing sequence of a linear series $L$ at $p$.
A crude limit series is {\it refined} if all the inequalities in the above definition are equalities.
For simplicity, all limit linear series in the remainder of this introduction will be crude.
\medskip
We can canonically associate to a proper strongly
curve $X_0$ a metrized complex $\mathfrak{C} X_0$ of $\kappa$-curves, called the {\em regularization} of $X_0$, by assigning a length of $1$ to each edge of $G$, and we write $X_v$ for the irreducible component of $X_0$ corresponding to a vertex $v \in V$. (This is the metrized complex associated to any regular smoothing $\fX$ of $X_0$ over any discrete valuation ring $R$ with residue field $\kappa$.)
\begin{thm}
\label{thm:introLLS}
Let $\mathfrak{C} X_0$ be the metrized complex of curves associated to a proper strongly semistable curve $X_0 / \kappa$ of compact
type. Then there is a bijective correspondence between the following:
\begin{itemize}
\item Crude limit $\mathfrak g^r_d$'s on $X_0$.
\item Equivalence classes of pairs $(\H,\mathcal D)$, where $\H = \{ H_v \}$, $H_v$ is an $(r+1)$-dimensional subspace of $\kappa(X_v)$ for each $v \in V$, and
$\mathcal D$ is a divisor of degree $d$ supported on the vertices of $\mathfrak{C} X_0$ with
$r_{\mathfrak{C} X_0,\H}(\mathcal D) = r$. Here we say that $(\H,\mathcal D) \sim (\H', \mathcal D')$ if there is a rational function $\mathfrak f$
on $\mathfrak{C} X_0$ such that $D' = D + \div(\mathfrak f)$ and $H_v = H'_v \cdot f_v$ for all $v \in V$, where $f_v$ denotes the $C_v$-part of $\mathfrak f$.
\end{itemize}
\end{thm}
Theorem~\ref{thm:introLLS}, combined with our Riemann-Roch theorem for metrized complexes of curves, provides an arguably more conceptual proof of the fact (originally established in \cite{EH86}) that limit linear series satisfy
analogues of the classical theorems of Riemann and Clifford.
The point is that $r_{\mathfrak{C} X_0, \H}(\mathcal D) \leq r_{\mathfrak{C} X_0}(\mathcal D)$ for all $\mathcal D \in \operatorname{Div}(\mathfrak{C} X_0)$ and therefore upper
bounds on $r_{\mathfrak{C} X_0}(\mathcal D)$ which follow from Riemann-Roch imply corresponding upper bounds on the restricted rank
$r_{\mathfrak{C} X_0, \H}(\mathcal D)$.
\medskip
Motivated by Theorem~\ref{thm:introLLS}, we propose the following definition.
Let $X_0$ be a proper strongly semistable (but not necessarily compact type)
curve over $\kappa$ with regularization $\mathfrak{C} X_0$.
A {\em limit $\mathfrak g^r_d$} on $X_0$ is an equivalence class of pairs $(\H = \{ H_v \},\mathcal D)$ as above,
where $H_v$ is an $(r+1)$-dimensional subspace of $\kappa(X_v)$ for each $v \in V$,
and $\mathcal D$ is a degree $d$ divisor on $\mathfrak{C} X_0$ with $r_{\mathfrak{C} X_0,\H}(\mathcal D) = r$.
\medskip
As a partial justification for this definition, we prove that if $R$ is a discrete valuation ring with residue field $\kappa$ and
$\fX/R$ is a regular arithmetic surface whose generic fiber $X$ is smooth and whose special fiber $X_0$ is strongly semistable, then for any divisor $D$ on $X$ with $r_X(D)=r$ and $\deg(D) = d$, our specialization machine
gives rise in a natural way to a limit $\mathfrak g^r_d$ on $X_0$
(see Theorem~\ref{thm:regularlimitseries} below for a precise statement, and
Theorem~\ref{thm:limitseriesgeneral} for a more general statement).
\section{Metrized complexes of algebraic curves}
\label{sec:basics}
Let $\kappa$ be an algebraically closed field of arbitrary characteristic and let $\mathfrak{C}$ be a metrized complex of
$\kappa$-curves, as defined in Section~\ref{section:overview}.
\subsection{Divisors and their rank}
If ${\mathcal G}$ is a subgroup of $\mathbb{R}$ containing the lengths of all edges of $G$,
we write $\mathrm{Div}(\mathfrak{C})_{\mathcal G}$ for the subgroup of $\mathrm{Div}(\mathfrak{C})$
consisting of all divisors $\mathcal D$ such that the support of the $\Gamma$-part of $\mathcal D$
consists entirely of
${\mathcal G}$-{\it rational points} of $\Gamma$ (i.e., points of $\Gamma$ whose distances to the vertices of $G$ are in $\mathcal G$).
\medskip
Recall from Section~\ref{section:overview} that the {\em rank} $r_\mathfrak{C}$ of a divisor
$\mathcal D$ on $\mathfrak{C}$ is the largest integer $k$ such that $\mathcal D - \mathcal E$ is linearly equivalent to an effective divisor
for all effective divisors $\mathcal E$ of degree $k$ on $\mathfrak{C}$. If ${\mathcal G}$ is any subgroup of $\mathbb{R}$ containing the lengths of all edges of $G$, one can define an analogous rank function $r_{\mathfrak{C},\mathcal G}$ for divisors in $\operatorname{Div}(\mathfrak{C})_\mathcal G$ by restricting the effective divisors $\mathcal E$ in the above definition to lie in $\operatorname{Div}(\mathfrak{C})_\mathcal G$.
By Corollary~\ref{cor:f-widthG}, $r_{\mathfrak{C},\mathcal G} (\mathcal D)= r_{\mathfrak{C}}(\mathcal D)$ for any divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C})_\mathcal G$, so the restriction in the definition of $r_{\mathfrak{C},\mathcal G}$ does not affect the rank of divisors.
\subsection{Regularization of nodal curves}\label{sec:mcnodal}
Let $X_0$ be a (reduced) connected projective nodal curve over $\k$ with irreducible components $X_{v_1},\dots,X_{v_k}$. We can associate to $X_0$ a metrized complex $\mathfrak{C} X_0$, called the {\it regularization} of $X_0$, as follows. The underlying metric graph $\Gamma_0$ has model the dual graph $G_0=(V_0,E_0)$ of $X_0$. Recall that the vertex set $V_0$ of $G_0$ consists of vertices $v_1,\dots, v_k$ (in bijection with the irreducible components of $X_0$) and the edges of $G_0$ are in bijection with singular points of $X_0$. (Note that $G_0$ might have loop edges.) The length of all the edges in $\Gamma_0$ are equal to one. The $\k$-curve $C_{v_i}$ in $\mathfrak{C} X_0$ is the normalization of $X_i$ for $i=1,\dots,k$. The collection $\mathcal A_{v_i}$ is the set of all $\k$-points of $C_{v_i}$ which lie over a singular point of $X_0$ in $X_{v_i}$. By the definition of the dual graph, these points are in bijection with the edges adjacent to $v_i$ in $G_0$.
\medskip
If $X_0$ is {\it strongly semistable}, so that $G_0$ does not have any loop edge and $C_{v_i} = X_{v_i}$,
the rank function $r_{\mathfrak{C} X_0,\mathbb Z}$ on $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ can be reformulated as follows.
Let $\operatorname{Pic}(X_0)$ be the Picard group of $X_0$, and consider the restriction map $\pi: \operatorname{Pic}(X_0) \rightarrow \oplus_i \operatorname{Pic}(X_{v_i})$. For any line bundle $\mathcal L$ on $X_0$, and $v\in V_0$, denote by $\mathcal L_{v}$ the restriction of $\mathcal L$ to $X_v$.
\medskip
Two line bundles $\mathcal L$ and $\mathcal L'$ in $\operatorname{Pic}(X_0)$ are said to be {\it combinatorially equivalent} if there exists a function $f: V_0 \rightarrow \mathbb Z$ such that
$\mathcal L'_v = \mathcal L_v(\div_{v}(f))$ in $\operatorname{Pic}(X_v)$ for any vertex $v$ of $G_0.$
(In a regular smoothing of $X_0$, c.f. Section~\ref{sec:limitseries} for the definition,
the role of $f$ is to specify a particular twist of
$\mathcal L$ by a divisor supported on the irreducible components of $X_0$.)
In particular, two line bundles $\mathcal L$ and $\mathcal L'$ in $\operatorname{Pic}(X_0)$ with $\pi(\mathcal L) = \pi(\mathcal L')$ are combinatorially equivalent.
In the above definition, $\div_v$ is defined in analogy with (\ref{eq:divf2}) as follows:
$$\div_v(f) = \sum_{u: \{u, v\} \in E_0} (f(u) -f(v))(x^{\{u,v\}}_v)$$ where $x_v^{\{u,v\}}$ is the point of $C_v$ labelled with
the edge $\{u,v\}$.
Note that the function $f: V_0 \rightarrow \mathbb Z$ in the definition of combinatorially equivalent line bundles above is unique up to an additive constant. For such an $f$, we denote by $\mathcal L^f$ any line bundle $\mathcal L'$ in $\operatorname{Pic}(X_0)$ such that $\mathcal L'_v = \mathcal L_v(\div_{v}(f))$ for all $v\in V_0$.
\medskip
For a line bundle $\mathcal L$ on $X_0$, define the {\it combinatorial rank} of $\mathcal L$, denoted $r_{c}(\mathcal L)$, to be the maximum integer $r$ such that for any effective divisor $E = \sum_{v \in V_0} E(v) (v)$ on $G_0$ of degree $r$, there is a line bundle $\mathcal L'$ combinatorially equivalent to $\mathcal L$ with
$$\dim_\k H^0(X_v, \mathcal L'_v) \geq E(v)+1$$
for all $v \in V$.
In particular, if no non-negative integer $r$ with the above property exists, the combinatorial rank of $\mathcal L$ will be equal to $-1$.
The combinatorial rank of $\mathcal L$ clearly depends only on the combinatorial equivalence class of $\mathcal L$.
\medskip
Let $\mathcal D$ be a divisor in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ with $X_v$-part $D_v$. We denote by $\mathcal L(\mathcal D)$ any line bundle on $X_0$ whose restriction to $X_v$ is $\mathcal L(D_v)$ for each vertex $v$ of $G_0$.
\begin{prop} \label{prop:combinrank}
Let $X_0$ be a strongly semistable curve over $\k$ and let $\mathfrak{C} X_0$ be the corresponding metrized complex. Then:
\begin{enumerate}
\item Two divisors $\mathcal D$ and $\mathcal D'$ in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ are linearly equivalent iff $\mathcal L(\mathcal D)$ and $\mathcal L(\mathcal D')$ are combinatorially equivalent.
\item For any divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$, the combinatorial rank of $\mathcal L(\mathcal D)$ is equal to $r_{\mathfrak{C} X_0}(\mathcal D).$
\end{enumerate}
\end{prop}
\begin{proof}
The first part follows by definition. To see the second part, let $r$ be the combinatorial rank of $\mathcal L(\mathcal D)$. It follows from Corollary~\ref{cor:f-widthZ}
that $r_{\mathfrak{C} X_0}(\mathcal D) = r_{\mathfrak{C} X_0,\mathbb Z}(\mathcal D)$. Thus, it will be enough to show that $r_{\mathfrak{C} X_0, \mathbb Z}(\mathcal D)=r$.
\medskip
We first prove that $r_{C X_0,\mathbb Z}(\mathcal D) \geq r$.
Let $\mathcal E$ be an effective divisor in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ with $\Gamma$-part $E_\Gamma$ and $X_v$-part $E_v$.
By the definition of the combinatorial rank, there exists a function $f:V_0 \rightarrow \mathbb Z$ such that
$$\dim_\k H^0(X_v, \mathcal L^f_v) \geq E_\Gamma(v)+1 \qquad \textrm{for any vertex $v$ in $G_0$}.$$
Since $\deg(E_v) = E_\Gamma(v)$, this implies the existence of a global section $f_v$ of $\mathcal L^f_v$
such that $f_v$ has order of vanishing at least $E_v(x)$ at any point $x$ of $X_v$.
\medskip
Let $f_\Gamma$ be the rational function defined by $f$ on $\Gamma$.
(Recall that $f_\Gamma|_{V_0} = f$ and $f$ is integer affine with slope $f(u)-f(v)$ on each edge $\{u,v\}$.)
For the rational function $\mathfrak f$ on $\mathfrak{C} X_0$ defined by $f_\Gamma$ and $\{ f_v \}_{v\in V_0}$, one has $\div(\mathfrak f) +
\mathcal D - \mathcal E \geq 0$. This shows that
$r_{\mathfrak{C} X_0,\mathbb Z}(\mathcal D) \geq r$.
\medskip
We now prove that $r \geq r_{\mathfrak{C} X_0,\mathbb Z}(\mathcal D)$.
Let $\mathcal L = \mathcal L(\mathcal D)$ be a line bundle on $X_0$ defined by $\mathcal D$. Let $E$ be an
effective divisor of degree $r_{\mathfrak{C} X_0,\mathbb Z}(\mathcal D)$ on $G_0$, and let
$\mathcal E$ be any effective divisor in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ with $\Gamma$-part equal to $E$.
Then there exists a rational function $\mathfrak f$ with $\div(\mathfrak f) \in \operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ such that
$\div(\mathfrak f) +\mathcal D -\mathcal E \geq 0$. In particular, the $\Gamma$-part $f_\Gamma$ of
$\mathfrak f$ is linear on each edge of $G_0$ and $\div(f_\Gamma) + D_\Gamma \geq 0$,
which shows that up to an additive constant, the set $F$ of all functions $f_\Gamma$ with these properties is finite.
Let $S_\Gamma$ denote the finite set $\{ \div(f_{\Gamma}) \; | \; f_{\Gamma} \in F \}$.
Let $d_v = E(v)$, and for $D_0 \in S_{\Gamma}$, let $S_{D_0}$ be the subset of
$\prod_{v \in V(G_0)} X_v^{(d_v)}$
defined by all collections of effective divisors $E_v$ of degree $d_v$
such that there exists a rational function $\mathfrak f$ on $\mathfrak{C} X_0$ with $\Gamma$-component $f_\Gamma$ satisfying
$\mathcal D -\mathcal E +\div(\mathfrak f)\geq 0$.
(Here $X^{(n)}$ denotes the $n^{\rm th}$ symmetric product of a curve $X$.)
Now let $S$ be the union over all $D_0 \in S_{\Gamma}$ of $S_{D_0}$.
Then one sees easily that:
\begin{itemize}
\item[(i)] Each $S_{D_0}$ is Zariski-closed in $\prod_v X_v^{(d_v)}$. (Use the fact that $S_{D_0}$ is the projection of a Zariski closed subset of a product of proper curves.)
\item[(ii)] $\bigcup_{D_0 \in S_{\Gamma}} S_{D_0} = \prod_v X_v^{(d_v)}$.
\end{itemize}
Therefore there exists $D_0 \in S_{\Gamma}$ such that $S_{D_0} =\prod_v X_v^{(d_v)}$.
In other words, we can suppose that the $\Gamma$-part $f_\Gamma$
of all the rational functions $\mathfrak f$ giving $\mathcal D -\mathcal E +\div(f)\geq0 $, when the effective divisors $E_v$ vary, is constant (and we have $D_0=\div(f_\Gamma)$).
If we fix a corresponding twist $\mathcal L^{f_\Gamma}$, then
\[
\dim_\k H^0(X_v, \mathcal L^{f_\Gamma}_v) \geq E(v)+1.
\]
Since $E$ was an arbitrary effective divisor of degree
$r_{\mathfrak{C} X_0,\mathbb Z}(\mathcal D)$ on $G_0$, we obtain the desired inequality.
\end{proof}
\section{A Riemann-Roch theorem for metrized complexes of curves}\label{sec:R-R}
Our aim in this section is to formulate and prove a Riemann-Roch theorem for metrized complexes of $\kappa$-curves.
\medskip
Let $\mathfrak{C}$ be a metrized complex of algebraic curves over $\k$.
For each vertex $v \in V$, let $g_v$ be the genus of $C_v$ and let $g(\mathfrak{C}) = g(\Gamma) + \sum_v g_v$
be the genus of $\mathfrak{C}$. For each curve $C_v$, let $K_v$ denote a divisor of degree $2g_v-2$ in the canonical class of
$C_v$. Denote by $A_v$ the divisor in $C_v$ consisting of the sum of the $\deg_G(v)$ points in $\mathcal A_v$.
The {\em canonical class of $\mathfrak{C}$} is defined to be the linear equivalence class of the divisor
$\mathcal K = \sum_{v\in V} (K_v + A_v).$
\begin{remark}\label{rem:canonicalsemi-stable} Let $X_0$ be a strongly semistable curve. The definition of the canonical class $\mathcal K$ in $\mathfrak{C} X_0$ is compatible
in a natural sense with the definition of the dualizing sheaf
(or sheaf of logarithmic $1$-forms) $\omega_{X_0/\kappa}$. Indeed, if $\alpha: X \rightarrow X_0$ denotes the normalization of $X_0$, and $y^e$,$z^e$ denote the points of $X$ above the singular point $x^e$ of $X_0$ for $e\in E(G_0)$, then sections of the sheaf $\omega_{X_0/\kappa}$ on an open set $U$ consist of all the meromorphic 1-forms $\delta$ on $X$ which are regular everywhere on $U$ except for possible simple poles at $y^e,z^e$, with $\mathrm{Res}_{y^e}(\delta)+\mathrm{Res}_{z^e}(\delta) =0$ for all $e$. From this, it is easy to see that the restriction of $\omega_{X_0/\kappa}$ to each component $X_v$ of $X_0$ is the invertible sheaf $\omega_{X_v}(A_v)$ corresponding to $K_v+A_v$ for any canonical divisor $K_v$ on $X_v$.
\end{remark}
\medskip
For a divisor $\mathcal D$ on $\mathfrak{C}$, let $r_\mathfrak{C}(\mathcal D)$ denote the rank of $\mathcal D$ as defined
in Section~\ref{section:overview}.
\begin{thm}[Riemann-Roch for metrized complexes of algebraic curves]\label{thm:RR-metrizedcomplexes}
Let $\mathfrak{C}$ be a metrized complex of $\kappa$-curves and $\mathcal K$ a divisor in the canonical class of $\mathfrak{C}$. For every divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C})$, we have
\[r_\mathfrak{C}(\mathcal D) - r_\mathfrak{C}(\mathcal K -\mathcal D) = \deg(\mathcal D) - g(\mathfrak{C})+1. \]
\end{thm}
Let $X_0$ be a strongly semistable curve of genus $g$ over $\kappa$. For any $\mathcal L \in \operatorname{Pic}(X_0)$, let $r_{c}(\mathcal L)$ be the combinatorial rank of $\mathcal L$ as defined in Section~\ref{sec:basics}. As a corollary of Theorem~\ref{thm:RR-metrizedcomplexes}, Remark~\ref{rem:canonicalsemi-stable}, and Proposition~\ref{prop:combinrank}, we have:
\begin{cor}[Riemann-Roch for strongly semistable curves]
For any $\mathcal L\in \operatorname{Pic}(X_0)$,
$$r_{c}(\mathcal L) - r_{c}(\omega_{X_0/\kappa}\otimes \mathcal L^{-1}) = \deg(\mathcal L) - g(X_0)+1.$$
\end{cor}
The Riemann-Roch theorem has a number of well-known formal consequences which can be transported to our situation. For example, we obtain the following analogue of Clifford's bound for the rank of a special divisor. (A divisor $\mathcal D$ on a metrized complex $\mathfrak{C}$ is called {\em special} if
$K_{\mathfrak{C}} - {\mathcal D}$ is linearly equivalent to an effective divisor.)
\begin{thm}[Clifford's theorem for metrized complexes]
\label{thm:MCClifford}
For any special divisor $\mathcal D$ on a metrized complex $\mathfrak{C}$, $r_\mathfrak{C}(\mathcal D) \leq \deg(\mathcal D)/2$.
\end{thm}
\begin{remark} Our Riemann-Roch theorem seems to be rather different from the classical Riemann-Roch theorem on semistable curves. We refer to~\cite{C-LS} for a discussion of Riemann's and Clifford's theorems for linear series on semistable curves, and for examples showing the failure of Clifford's theorem for $h^0(\mathcal L)$ with $\mathcal L \in \operatorname{Pic}(X_0)$ (even for line bundles in the compactified Picard scheme of $X_0$).
\end{remark}
The rest of this section is devoted to the proof of Theorem~\ref{thm:RR-metrizedcomplexes}.
Our proof follows and extends the original arguments of~\cite{BN} in the proof of Riemann-Roch theorem for graphs.
In particular, we are going to first extend the notion of reduced divisors to the context of metrized complexes of
algebraic curves, and then study the minimal non-special divisors.
\subsection{Reduced divisors: existence and uniqueness}\label{sec:reduced}
Let $v_0$ be a fixed base point of $\Gamma$. We introduce the notion of $v_0$-reduced divisors and show that each equivalence class of divisors on $\mathfrak{C}$ contains a quasi-unique $v_0$-reduced divisor, in a precise sense to be defined immediately preceding Theorem~\ref{thm:reduced.divisors} below.
\medskip
For a closed connected subset $S$ of $\Gamma$ and a point $v \in \partial S$ (the topological boundary of $S$), the number of ``outgoing'' tangent directions at $v$ (i.e., tangent directions emanating outward from $S$) is denoted by $\mathrm{outdeg}_S(v)$; this is also the maximum size of a
collection of internally disjoint segments in $\Gamma \setminus (S -\{v\})$ with one end at $v$. If in addition we have $v \in V$, we denote by $\div_v(\partial S)$ the divisor in $C_v$ associated to the outgoing edges at $v$; this is by definition the sum of all the points $x^e_v$ of $C_v$ indexed by the edges $e$ leaving $S$ at $v$.
In what follows we refer to a closed connected subset $S$ of $\Gamma$ as a {\it cut} in $\Gamma$.
\medskip
Let $\mathcal D$ be a divisor on $\mathfrak{C}$ with $\Gamma$-part $D_\Gamma$ and $C_v$-part $D_v$, and let $S$ be a cut in $\Gamma$.
A boundary point $x \in \partial S$ is called
{\it saturated} with respect to $\mathcal D$ and $S$ if
\begin{itemize}
\item $x \notin V$ and $\mathrm{outdeg}_S(x) \leq D_\Gamma(x)$; or
\item $x=v$ for some $v\in V$ and $D_v- \div_v(\partial S)$ is equivalent to an effective divisor on $C_v$.
\end{itemize}
\noindent Otherwise, $x\in \partial S$ is called {\it non-saturated}. A cut $S$ is said to be saturated if all its boundary points are saturated. (When talking about saturated and non-saturated points, we will sometimes omit the divisor $\mathcal D$ or the set $S$ if they are clear from the context.)
\medskip
The divisor $\mathcal D$ is said to be {\it $v_0$-reduced} if the following three properties are satisfied:
\begin{itemize}
\item[(i)] For all points $x \neq v_0$ of $\Gamma$, $D_\Gamma(x) \geq 0$, i.e., all the coefficients of $D_\Gamma$ are non-negative except possibly at the base point $v_0$.
\item[(ii)] For all points $v \in V \setminus \{v_0\}$ ($=V$ if $v_0$ does not belong to $V$),
there exists an effective divisor $E_v$ linearly equivalent to $D_v$ on $C_v$.
\item[(iii)] For every cut $S$ of $\Gamma$ which does not contain $v_0$, there exists a non-saturated point $x \in \partial S$.
\end{itemize}
\medskip
\begin{remark}
\label{rmk:burningalg}
There is an efficient ``burning algorithm'' for checking whether or not a given divisor $\mathcal D$ on $\mathfrak{C}$ which satisfies (i) is $v_0$-reduced.
The algorithm can be described informally as follows (compare with \cite[\S{2}]{Luo} or \cite[\S{5.1}]{BS}).
Imagine that $\Gamma$ is made of a flammable material, and light a fire at $v_0$. The fire begins spreading across $\Gamma$ in a continuous manner and can only be blocked at a point $x \in \Gamma$ if one of the following holds:
\begin{itemize}
\item $x \notin V$ and the number of burnt directions coming into $x$ exceeds $D_\Gamma(x)$. (One should imagine $D_\Gamma(x)$ firefighters standing at $x$, each of
whom can block fire in one incoming direction.)
\item $x=v$ for some $v\in V$ and $D_v$ minus the sum of the marked points corresponding to burnt directions is not equivalent to any effective divisor on $C_v$.
\end{itemize}
It is straightforward to check, following the same ideas as the proof of \cite[Algorithm 2.5]{Luo}, that $\mathcal D$ is $v_0$-reduced if and only if the fire eventually burns through all of $\Gamma$. We omit the details since we will not need this result in the sequel.
\end{remark}
\medskip
We now show that every divisor $\mathcal D$ on $\mathfrak{C}$ is linearly equivalent to a quasi-unique $v_0$-reduced divisor $\mathcal D^{v_0}$.
The quasi-uniqueness is understood in the following sense: the $\Gamma$-part $D_\Gamma^{v_0}$ of $\mathcal D^{v_0}$ is unique,
and for all $v \in V$, the divisor class $[D_v^{v_0}]$ on $C_v$ defined by the $v$-part of $\mathcal D^{v_0}$ is unique.
\begin{thm} \label{thm:reduced.divisors}
Let $\mathfrak{C}$ be a metrized complex of $\k$-curves and $v_0$ a base point of $\Gamma$. For every divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C})$, there exists a quasi-unique $v_0$-reduced divisor $\mathcal D^{v_0}$ such that $\mathcal D^{v_0} \sim \mathcal D$.
\end{thm}
\begin{proof}
Let $\mathcal T_{\mathcal D}$ be the set of all divisors $\mathcal D'$ linearly equivalent to $\mathcal D$ such that:
\begin{itemize}
\item All the coefficients of the $\Gamma$-part $D'_\Gamma$ of $\mathcal D'$ are non-negative at every point of $\Gamma$ except possibly at $v_0$.
\item For each point $v \in V \setminus \{v_0\}$, the $v$-part $D'_v$ of $\mathcal D'$ has non-negative rank on $C_v$.
\item The coefficient of $v_0$ in $D'_\Gamma$ is maximal with respect to the two properties above.
\end{itemize}
One shows as in~\cite[Proof of Theorem 2]{amini} or \cite[Proof of Proposition 3.1]{BN}
that there is a divisor $\mathcal D'$ linearly equivalent to $\mathcal D$ on $\mathfrak{C}$ with the property that the coefficient of every point $x \in \Gamma \setminus (V \cup \{v_0\})$ is non-negative and the coefficient of $D'_\Gamma$ at each point $v \in V$ (which coincides with the degree of $D'_v$) is at least $g_v$.
(The intuitive idea is to repeatedly fire $v_0$ and then use further chip-firing moves to spread chips wherever needed on $\Gamma$, assuring that each $v \in V$ gets at
least $g_v$ chips and that no $p \in \Gamma$ except for $v_0$ remains in debt.)
By the (classical) Riemann-Roch theorem, each $D'_v$ has non-negative rank on $C_v$, which shows that $\mathcal T_{\mathcal D}$ is non-empty.
\medskip
Define $T_{\mathcal D}$ as the set of all $D'_\Gamma \in \operatorname{Div}(\Gamma)$ for which there exists
${\mathcal D}' \in \mathcal T_{\mathcal D}$ whose $\Gamma$-part is $D'_\Gamma$.
Each divisor $D'_\Gamma \in T_{\mathcal D}$ has degree $\deg(\mathcal D)$, and
all divisors in $T_{\mathcal D}$ have the same coefficient at $v_0$.
Thus the number
$N := \sum_{x \in \Gamma \setminus \{v_0\}} D'_\Gamma(x)$
is independent of the choice of a divisor $D'_\Gamma$ in $T_{\mathcal D}$.
As a consequence, $T_{\mathcal D}$ inherits a natural topology from the topology of $\Gamma$, since it can be embedded as a subset of $\mathrm{Sym}^N\Gamma$, and is compact.
Let $\mathcal A$ be the subset of $\mathbb R^{N}$ defined by
$$\mathcal A := \Bigl\{(x_1,\dots,x_N)\,|\,0\leq x_1\leq x_2\leq \dots\leq x_N\Bigr\},$$
equipped with the total order defined by the lexicographical rule $(x_i)\leq (y_i)$ iff
$x_1=y_1,\dots,x_i =y_i$ and $x_{i+1} < y_{i+1}$. One considers a map $F: T_{\mathcal D} \rightarrow \mathcal A$ defined as follows. For each divisor $D'_\Gamma \in T_{ \mathcal D}$, consider the multiset $A(D'_\Gamma)$ of points in $\Gamma \setminus \{v_0\}$ where each point $v\neq v_0$ appears in this multiset exactly $D'_\Gamma(v)$ times. Define $F(D'_\Gamma)$ to be the point of $\mathcal A$ defined by the multiset of distances $\mathrm{dist}_\Gamma(v,v_0)$ for $v\in A(D'_\Gamma)$, ordered in an increasing way.
It is straightforward to verify that the map $F$ is continuous.
Since $T_{\mathcal D}$ is compact and $F$ is continuous, there exists a divisor $D^{v_0}_\Gamma$ in $T_{\mathcal D}$ such that $F$ takes its minimum value at $D^{v_0}_\Gamma$, i.e., $F(D_\Gamma^{v_0}) = \min_{D'_\Gamma \in T_{\mathcal D}} F(D'_\Gamma)$. Let $\mathcal D^{v_0}$ be an element of $\mathcal T_{\mathcal D}$
whose $\Gamma$-part is $D^{v_0}_\Gamma$.
\medskip
{\bf Claim:} The divisor $\mathcal D^{v_0}\sim \mathcal D$ is $v_0$-reduced.
\medskip
Properties (i) and (ii) above are clearly satisfied. The only point one needs to check is that every cut $S$ which does not contain $v_0$ has a non-saturated point on its boundary. For the sake of contradiction, suppose this is not the case, and let $S$ be a closed connected set violating this condition. This means that the following hold:
\begin{itemize}
\item For all $x \in \partial S \setminus V$, $\mathrm{outdeg}_S(x) \leq D^{v_0}_\Gamma(v)$.
\item For each $v \in \partial S\cap V$, $D^{v_0}_v - \div_v(\partial S)$ has non-negative rank on $C_v$, i.e., there exists a rational function $f_v$ on $C_v$ such that $D^{v_0}_v - \div_v(\partial S) + \div(f_v) \geq 0$.
\end{itemize}
By the definition of $\mathrm{outdeg}_S$, there exists an $\epsilon>0$ such that for each vertex $x \in \partial S$, there are closed segments $I_1^x,\dots,I^x_{\mathrm{outdeg}_S(x)}$ emanating from $x$ with the following properties:
\begin{itemize}
\item For $x \in \partial S$ and $1\leq j\leq \mathrm{outdeg}_S(x)$, the half-open segments $I^x_j \setminus x$ are
disjoint from $S$ and from each other and do not contain $v_0$.
\item Each segment $I_j^x$ has length $\epsilon$, for $x \in \partial S$ and $1\leq j\leq \mathrm{outdeg}_S(x)$.
\end{itemize}
These data give rise to a rational function $f_\Gamma: \Gamma \rightarrow \mathbb R$ which is identically zero on $S$, is linear of slope $-1$ on each interval $I_j^x$ for $x\in \partial S$ and $1\leq j \leq \mathrm{outdeg}_S(x)$, and takes the constant value $-\epsilon$ at all points of $\Gamma \setminus \Bigl(S\cup \bigcup_{x,j } I_j^x\Bigr)$.
Consider the divisor $\mathcal D^*= \mathcal D^{v_0} + \div(\mathfrak f)$ on $\mathfrak{C}$, where $\mathfrak f$ is the rational function on $\mathfrak{C}$ consisting of the rational function $f_\Gamma$ on $\Gamma$ and the rational functions $f_v$ on $C_v$.
Letting $D_\Gamma^*$ be the $\Gamma$-part of $\mathcal D^*$,
one verifies that $\mathcal D^*$ and $D_\Gamma^*$ lie in $\mathcal T_{\mathcal D}$ and $T_{\mathcal D}$, respectively, and that $F(D^*_\Gamma) < F(D^{v_0}_\Gamma)$, contradicting the choice of $D^{v_0}_\Gamma$.
This proves the claim and hence the existence part of the theorem.
\medskip
It remains to prove the quasi-uniqueness. Assume for the sake of contradiction that there are linearly equivalent $v_0$-reduced divisors $\mathcal D$
and $\mathcal D'$ on $\mathfrak{C}$ such that either $D_\Gamma \neq D'_\Gamma$ or $D_v$ and $D'_v$ are not linearly equivalent on $C_v$
for some $v \in V$. Then there exists a non-constant rational function $\mathfrak f$ on $\mathfrak{C}$ such that $\mathcal D' = \mathcal D+\div(\mathfrak f)$.
If $f_\Gamma$ is constant then we obtain an immediate contradiction, so we may assume that $f_\Gamma$ is non-constant.
Without loss of generality, we may assume that $f_\Gamma$ does not take its maximum at $v_0$ (otherwise, we can interchange the role of $\mathcal D$ and $\mathcal D'$). Let $S$ be a connected component of the set of all points where $f_\Gamma$ takes its maximum. Note that $v_0 \notin S$. For all points $x\in \partial S$, the slope of $f_\Gamma$ at any outgoing segment $I_j^x$ emanating from $v$ is at most $-1$.
Since $\mathcal D$ is $v_0$-reduced, there exists a point $x\in \partial S$ such that either $x \notin V$ and $D_\Gamma(x) < \mathrm{outdeg}_S(x)$, or $x =v$ for some $v\in V$ and the divisor $D_v - \div(\partial S)$ has negative rank. In the first case, $D'_\Gamma(x) \leq D_\Gamma(x) - \mathrm{outdeg}_S(x) <0$, contradicting the assumption that the coefficient of $D'_\Gamma$ is non-negative at $x \neq v_0$. In the second case, $D'_v \sim D_v + \sum_{e\in E:\,e\sim v} \mathrm{slp}_e(f_\Gamma) (x^e_v) \leq D_v - \div_v(\partial S)$, which implies that $D'_v$ has negative rank, a contradiction.
\end{proof}
\begin{remark}
One can presumably give an ``iterated Dhar algorithm'' for algorithmically finding a $v_0$-reduced divisor equivalent to a given divisor $\mathcal D$ by combining the ideas
in the proof of Theorem~\ref{thm:reduced.divisors} with the ideas behind \cite[Algorithm 2.12]{Luo}.
\end{remark}
\subsection{Description of minimal non-special divisors}
Let $\mathfrak{C}$ be a metrized complex of algebraic curves. For each $v \in V$,
let $\mathfrak N_v$ be the set of all {\em minimal non-special} divisors on $C_v$:
\[\mathfrak N_v = \{D \in \operatorname{Div}(C_v)\,\, :\,\, \deg(D) =g(C_v)-1 \,\,\textrm{and} \,\, |D| =\emptyset\}.\]
\begin{remark}
Recall from \cite[IV, Example 1.3.4]{HartshorneAG} that a divisor $D$ on a smooth projective curve $C$ of
genus $g$ over $\k$ is called {\em special} if $r(K_C-D) \geq 0$.
By Riemann-Roch, every divisor of degree at most $g-2$ on $C$ is special, and if
$\deg(D)= g-1$ then $D$ is special if and only if $r(D)\geq 0$.
Moreover, every non-special divisor dominates a minimal non-special divisor.
This explains the term ``minimal non-special divisor''.
\end{remark}
Similarly, define the set of minimal non-special divisors on $\mathfrak{C}$ as
\[\mathfrak N = \{\mathcal D \in \operatorname{Div}(\mathfrak{C})\,\, :\,\, \deg(\mathcal D) =g(\mathfrak{C})-1 \,\,\textrm{and} \,\, |\mathcal D| =\emptyset\}.\]
In this section we provide an explicit description of the minimal non-special divisors
on metrized complexes of algebraic curves, generalizing the corresponding description of minimal non-special divisors
on graphs and metric graphs from~\cite{BN, MZ}.
\medskip
An {\em acyclic orientation} on $\Gamma$ is an acyclic orientation on some model of $\Gamma$, i.e., a decomposition of $\Gamma$ into closed directed edges with disjoint interiors such that no directed cycles are formed.
Given an acyclic orientation $\pi$ on $\Gamma$, we denote by ${\rm deg}^+_\pi(x)$ the number of tangent directions emanating from $x$ which are compatible with $\pi$. Note that for all but finitely many points of $\Gamma$, $\deg^+_\pi(x)=1$.
For $v \in V$, we denote by $E^+(v)$ the set of edges incident to $v$ which (locally near $v$) are oriented outward from $v$.
A point $x$ with $\deg^+_\pi(x)=0$ is called a {\em sink}. It is well known and easy to prove that every acyclic orientation contains at least one sink (start at any
point and follow the orientation until you get stuck, which must eventually happen by acyclicity).
\medskip
Given a collection of minimal non-special divisors $D_v \in \mathfrak N_v$ for each $v\in V$, together with an acyclic orientation $\pi$ of $\Gamma$, define a corresponding divisor $\mathcal D^{\pi, \{D_v\}}$ by the formula
\[
D^{\pi, \{D_v\}} = \sum_{x \in \Gamma \backslash V} (\deg^+_\pi(x) - 1) (x) + \sum_{v \in V} \left( A^\pi_v + D_v \right),
\]
where $A^\pi_v$ is the sum of all points $x^e_v \in \mathcal A_v$ for which the $\pi$-orientation on $e$ points away from $v$.
The $\Gamma$-part of $D^{\pi, \{D_v\}}$ is
$$D_\Gamma^\pi := \sum_{x\in \Gamma} (\deg^+_\pi(x)+g_{x}-1) (x)$$
and the $C_v$-part of $D^{\pi, \{D_v\}}$ is $D^\pi_v := A^\pi_v + D_v$.
If $\widetilde G = (\widetilde V, \widetilde E)$ is a (loopless) model of $\Gamma$ such that the orientation $\pi$ of $\Gamma$ is induced by an acyclic orientation $\widetilde G^\pi$ on the edges of $\widetilde G$, then the degree of $\mathcal D^{\pi ,\{D_v\}}$ is given by
\begin{align*}
\deg(\mathcal D^{\pi ,\{D_v\}}) &= \sum_{v\in \widetilde{V}} \bigl( \deg^+_\pi(v)+g_{v}-1 \bigr) \\
&= \Bigl[ \sum_{v\in \widetilde{V}} \bigl(\deg^+_\pi(v) -1\bigr)\Bigr] + \sum_{v\in V} g_v = g(\Gamma)-1+\sum_v g_v = g(\mathfrak{C}) -1.
\end{align*}
A divisor $\mathcal M \in \operatorname{Div}(\mathfrak{C})$ of the form $\mathcal D^{\pi,\{ D_v \}}$ is called a {\it moderator} on $\mathfrak{C}$. (This terminology comes from \cite{MZ}.)
Given a moderator $\mathcal M = \mathcal D^{\pi,\{D_v\}}$, the {\em dual moderator} $\bar{\mathcal M}$ is defined to be $\mathcal D^{\bar{\pi}, \{ K_v - D_v \}}$, where $\bar{\pi}$ is obtained from $\pi$ by reversing the orientation of every oriented segment.
It is easy to see that $\mathcal M + \bar{\mathcal M}$ belongs to the canonical class on $\mathfrak{C}$.
\medskip
The following two lemmas are essentially what we need for the proof of Theorem~\ref{thm:RR-metrizedcomplexes}.
\begin{lemma} \label{lem:non-special1} For any acyclic orientation $\pi$ of $\Gamma$ and any collection $D_v \in \mathfrak N_v$ of minimal non-special divisors on $C_v$, the moderator $\mathcal D^{\pi,\{D_v\}}$ is a minimal non-special divisor on $\mathfrak{C}$.
\end{lemma}
\begin{proof}
Suppose for the sake of contradiction that there is a rational function
$\mathfrak f$ on $\mathfrak{C}$ such that $\mathcal D^{\pi,\{D_v\}} +\div(\mathfrak f) \geq 0$.
Let $\widetilde G = (\widetilde V, \widetilde E)$ be a (loopless) model of $\Gamma$ such that the orientation $\pi$ of $\Gamma$ is induced by an acyclic orientation $\widetilde G^\pi$ on the edges of $\widetilde G$.
Let $S$ be the closed subset of $\Gamma$ consisting of all the points of $\Gamma$ where the $\Gamma$-part $f_\Gamma$ of $\mathfrak f$ takes its maximum value. It is easy to see that $\partial S \subseteq \widetilde V$, since at a hypothetical point $x \in \partial S \setminus \widetilde V$ we would necessarily have
$D^\pi_\Gamma(x)+\div_x(f_\Gamma) <0$, contradicting the assumption on $\mathfrak f$.
Note that since $\partial S \subset \widetilde V$, for any edge $e$ of $\widetilde G$ either $S$ contains $e$ entirely or $S$ does not intersect the interior of $e$. Consider now the restriction of the orientation $\pi$ to the induced subgraph $\widetilde G[\widetilde V \cap S]$.
The resulting directed graph $\widetilde G^\pi[\widetilde V \cap S]$ is acyclic and therefore contains a sink vertex $u$.
\medskip
{\bf Claim:} $u\in \partial S$.
\medskip
It suffices to prove that no sink vertex of the directed graph $\widetilde G^\pi$ belongs to $S$, so assume for the sake of contradiction that
$w \in S$ is a sink vertex of $\widetilde G^\pi$. There are two cases to consider:
\begin{itemize}
\item If $w \in V$, then $D_{w} + \div(f_{w}) \geq D^\pi_{w} + \div_{w}(f_\Gamma) + \div(f_{w}) \geq 0$ (since $f_\Gamma$ achieves its maximum value at $w$ and we supposed that $\mathcal D^{\pi,\{D_v\}} +\div(\mathfrak f) \geq 0$), contradicting the assumption that $D_{w}$ is a minimal non-special divisor on $C_{w}$.
\item If $w \notin V$, then by definition the coefficient of $w$ in $D^\pi_\Gamma$ is at most $-1$, from which it follows that the coefficient of $w$ in $\mathcal D^{\pi,\{D_v\}} +\div(\mathfrak f)$ is negative, a contradiction.
\end{itemize}
This proves the claim.
\medskip
By our choice of $u \in \partial S$ and the definition of $S$, $f_\Gamma$ has strictly negative slope along all outgoing
edges at $u$,
and it has slope zero along all other edges incident to $u$.
This shows in particular that $\mathrm{ord}_{u}(f_\Gamma) \leq - \mathrm{outdeg}_S(u) \leq -\deg^+_\pi(u)$.
There are now two different cases to consider, both of which will lead to a contradiction (and hence complete our proof of the lemma):
\begin{itemize}
\item If $u \in \widetilde V\setminus V$, then $D^\pi_\Gamma(u) + \mathrm{ord}_u(f_\Gamma)\leq \deg^+_\pi(u)-1- \deg^+_\pi(u)<0$, contradicting the choice of the rational function $\mathfrak f$ on $\mathfrak{C}$.
\item If $u \in V$, then for each edge $e$ incident to $u$ we have $\mathrm{slp}_e(f_\Gamma) \leq 0$, with strict inequality if
$e$ is an outgoing edge at $u$ in $\widetilde G^\pi$ (because $u$ is a sink of the oriented graph $\widetilde G^\pi[S\cap \tilde V]$).
By the definition of $D^\pi_u$, we infer that $D^\pi_u + \sum_{e\in \widetilde E: e\sim u} \mathrm{slp}_e(f_\Gamma)(x^e_u) \leq D_u$, which shows that $D^\pi_u + \sum_{e\in \widetilde E: e\sim u} \mathrm{slp}_e(f_\Gamma)(x^e_u) + \div(f_u)$
is not effective, since $D_u$ is minimal non-special. This contradicts our assumptions on $\mathfrak f$.
\end{itemize}
\end{proof}
For $v_0 \in \Gamma$, we denote by $\mathcal{AO}_{v_0}(\Gamma)$ the set of all acyclic orientations of $\Gamma$ with a unique sink at $v_0$, i.e., such that $v_0$ has out-degree zero and all other points of $\Gamma$ have out-degree at least one.
\begin{lemma}\label{lem:reduced}
Let $\mathcal D$ be a $v_0$-reduced divisor on $\mathfrak{C}$. Then $r_\mathfrak{C}(\mathcal D) \geq 0$
if and only if the following two conditions hold:
\begin{itemize}
\item The coefficient $D_\Gamma(v_0)$ of $D_\Gamma$ at $v_0$ is non-negative.
\item If $v_0 \in V$, the divisor $D_{v_0}$ on $C_{v_0}$ has non-negative rank.
\end{itemize}
More precisely, if the above conditions do not both hold, then there exists a moderator $\mathcal M = \mathcal D^{\pi,\{D^*_v\}}$ with $\pi\in \mathcal{AO}_{v_0}(\Gamma)$ such that $\mathcal D \leq \mathcal M$.
\end{lemma}
\begin{proof}
The intuitive idea is that one constructs the moderator $\mathcal M = \mathcal D^{\pi,\{D^*_v\}}$ using the burning algorithm
described in Remark~\ref{rmk:burningalg}. Beginning with a $v_0$-reduced divisor $\mathcal D$,
burn through $\Gamma$ following the algorithm and keep track
of the direction in which the fire spreads; reversing all the arrows defines an acyclic orientation $\pi\in \mathcal{AO}_{v_0}(\Gamma)$.
If $\mathcal M$ is the corresponding
moderator, one checks that $\mathcal D \leq \mathcal M$ outside $v_0$, and if $\mathcal D$ is not effective then $\mathcal D \leq \mathcal M$ everywhere.
A more rigorous version of this argument is as follows.
\medskip
First suppose that $D_\Gamma(v_0) \geq0$, and in the case $v_0 \in V$ that there exists a rational function $f_{v_0}$
on $C_{v_0}$ such that $D_{v_0}+\div(f_{v_0}) \geq 0$. We infer that $D_\Gamma\geq 0$, and since each
$D_v$ for $v\in V \setminus \{v_0\}$ is of non-negative rank, there exists a rational function $f_v$ on $C_v$
such that $D_v + \div(f_v) \geq 0$. Let $\mathfrak f$ be a rational function on $\mathfrak{C}$ consisting of a constant rational
function on $\Gamma$ and $f_v$ on $C_v$ for $v \in V$. We obviously have $\mathcal D+\div(\mathfrak f) \geq 0$,
which implies that $r_\mathfrak{C}(\mathcal D)\geq 0$.
\medskip
For the other direction, assume that
$D_\Gamma(v_0) <0$ if $v_0 \notin V$, and that $D_{v_0}$ has negative rank if $v_0 \in V$.
To show that $r_\mathfrak{C}(\mathcal D)=-1$, by Lemma~\ref{lem:non-special1} it will be enough to show the existence of an acyclic orientation $\pi\in \mathcal{AO}_{v_0}(\Gamma)$ and a set of minimal non-special divisors $D^*_v \in \mathfrak N_v$
such that $\mathcal D \leq \mathcal D^{\pi, \{D^*_v\}}$.
\medskip
Let $\widetilde V$ be the union of $V$ and all the points in the support of $D_\Gamma$. Note that in both cases above, $v_0 \in \widetilde V$.
Let $\widetilde G=(\widetilde V,\widetilde E)$ be the corresponding model of $\Gamma$. We are going to recursively define an orientation $\pi $ of $\widetilde G$ and the collection $\{D^*_v\}$ by handling at each step the orientation of all the edges incident to a vertex $v \in \widetilde V$ and the minimal non-special divisor $D^*_v$ in the case $v \in V$. We start by considering the vertex $v_0 \in \widetilde V$. The orientations of all the edges incident to $v_0$ are defined so that $\deg^+_\pi(v_0) = 0$; in other words, all these oriented edges are incoming at $v_0$. Note that in the case $v_0 \notin V$, we have $D_\Gamma(v_0) \leq -1 = D_\Gamma^\pi(v_0)$.
In the case $v_0 \in V$, since $r(D_{v_0})<0$ it follows from the Riemann-Roch theorem for $C_{v_0}$ that there exists a minimal non-special divisor $D^*_{v_0}$ such that $D_{v_0} \leq D^*_{v_0}$.
\medskip
Suppose that the orientation of all edges adjacent to vertices $v_0, \dots, v_i \in \widetilde V$ has been defined, and that
for all $v_j \in V$ with $j\leq i$, a minimal non-special divisor $D^*_{v}$ on $C_{v}$ has been given.
Let $S_i$ be a connected component of the induced subgraph $\widetilde G[\widetilde V \setminus \{v_0,\dots, v_i\}]$.
Since $\mathcal D$ is $v_0$-reduced and $S_i$ is a cut not containing $v_0$, there exists a point $v_{i+1}$ on the boundary of $S_i$ which is non-saturated. (Note that $v_{i+1}$ also lies in $\widetilde V$.) This means that either:
\begin{itemize}
\item[(1)] $v_{i+1} \in \Gamma \setminus V$ and $\mathrm{outdeg}_{S_{i}}(v_{i+1}) > D_\Gamma(v_{i+1})$; or
\item[(2)] $v_{i+1} \in V$ and $D_v - \div_v(\partial S_{i})$ has negative rank.
\end{itemize}
\medskip
All outgoing edges from $S_i$ adjacent to $v_{i+1}$ have already been oriented (and are outgoing from $v_{i+1}$ by the definition of the orientation $\pi$). Orient all other edges incident to $v_{i+1}$ in such a way that they are all incoming at $v_{i+1}$. Note that
$\deg^+_\pi(v_{i+1}) =\mathrm{outdeg}_{S_{i}}(v_{i+1}),$ and so in Case (1),
$$D_{\Gamma}(v_{i+1}) \leq \deg^+_\pi(v_{i+1})-1.$$
In Case (2), since $r(D_v -\div_v(\partial S_{i} )) =-1$, it follows from the Riemann-Roch theorem for $C_v$ that there exists a minimal non-special divisor $D^*_v$ such that
$$ D_v - \div_v(\partial S_{i}) \leq D^*_v .$$
This shows that $D_v \leq \div_v(\partial S_{i}) + D^*_v$. By the definition of the orientation $\pi$ we must have $D^{*\,\pi}_{v+1} = \div_{v_{i+1}}(\partial S_{i}) + D^*_v$. Therefore, by the definition of the orientation $\pi$ at $v_{i+1}$ and the choice of $D^*_{v_{i+1}}$, we have $D_{v_{i+1}} \leq D^{*\,\pi}_{v_{i+1}}$.
\medskip
Let $\pi$ be the orientation of $\Gamma$ just constructed, and let $\{D^*_v\}_{v\in V}$ be the collection of minimal non-special divisors on $C_v$ defined above. By the definition of $\pi$, the only vertex of $\widetilde V$ with out-degree zero is $v_0$ and thus $\pi$ belongs to $\mathcal{AO}_{v_0}(\Gamma)$. We clearly have $\mathcal D \leq \mathcal D^{\pi,\{D^*_v\}}$ as well, which completes the proof.
\end{proof}
As a corollary of the above lemma, we obtain:
\begin{cor}\label{cor:non-special2}
Any minimal non-special divisor $\mathcal D$ on $\mathfrak{C}$ is linearly equivalent to a moderator.
\end{cor}
\begin{proof} Fix $v_0\in \Gamma$.
Let $\mathcal D$ be a minimal non-special divisor on $\mathfrak{C}$ and let $\mathcal D^{v_0}$ be the $v_0$-reduced divisor linearly equivalent to $\mathcal D$.
By Lemma~\ref{lem:reduced}, there exists a moderator $\mathcal M$ such that $\mathcal D^{v_0} \leq \mathcal M$. The effective divisor $\mathcal M - \mathcal D^{v_0}$ has degree zero, and so must be equal to zero.
\end{proof}
\subsection{Proof of Theorem~\ref{thm:RR-metrizedcomplexes}}
The proof of Theorem~\ref{thm:RR-metrizedcomplexes} can now be completed using (a slight simplification of) the idea behind the proof of
Riemann-Roch theorem for graphs given in \cite{BN}.
The key is the following formula, which provides a useful description of the rank of $\mathcal D$ in terms of minimal non-special divisors.
We denote by $\deg^+(\mathcal D)$ (resp. $\deg^-(\mathcal D)$)
the sum of non-negative (resp. non-positive) coefficients in $\mathcal D$.
(Note that $\deg^+(\mathcal D) + \deg^-(\mathcal D) = \deg(\mathcal D)$).
\begin{prop} \label{prop:magicformula}
For any divisor $\mathcal D$ on $\mathfrak{C}$, we have $$r_\mathfrak{C}(\mathcal D) = \min_{\mathcal N \in \mathfrak N}\,\,
\deg^+(\mathcal D -\mathcal N)-1.$$
\end{prop}
\begin{proof}
Fix $\mathcal N\in \mathfrak N$, and
let $\mathcal E$ be the non-negative part of $\mathcal D-\mathcal N$, which is of degree $\deg^+(\mathcal D -\mathcal N)$.
Then $r_\mathfrak{C}(\mathcal D) \leq \deg^+(\mathcal D -\mathcal N)$, since $\mathcal D -\mathcal E \leq \mathcal N$ and $r(\mathcal N)=-1$
imply that $|\mathcal D-\mathcal E|=\emptyset$.
This shows that $r_\mathfrak{C}(\mathcal D) \leq \min_{\mathcal N \in \mathfrak N} \,\, \deg^+(\mathcal D -\mathcal N)-1 $.
To prove the opposite inequality, let $\mathcal E$ be an effective divisor of degree
$r_\mathfrak{C}(\mathcal D)+1$ such that $|D- \mathcal E| = \emptyset$. By Lemma~\ref{lem:reduced}, there exists $\mathcal N \in \mathfrak N$ such that
$\mathcal D-\mathcal E \leq \mathcal N$, or equivalently, $\mathcal D - \mathcal N \leq \mathcal E$. In particular,
$\deg^+(\mathcal D-\mathcal N)\leq \deg(\mathcal E) = r_\mathfrak{C}(\mathcal D)+1$, which proves the proposition.
\end{proof}
To finish the proof of Theorem~\ref{thm:RR-metrizedcomplexes}, note that
$$\deg^+(\mathcal D- \mathcal N) = \deg(\mathcal D -\mathcal N) - \deg^-(\mathcal D-\mathcal N) =
\deg(\mathcal D) - g+1 + \deg^+(\mathcal N-\mathcal D)$$
and observe that $\mathcal N-\mathcal D = \mathcal K -\mathcal D - (\mathcal K -\mathcal N)$.
If $\mathcal N$ is linearly equivalent to the moderator
$\mathcal M$, c.f. Corollary~\ref{cor:non-special2}, then $\mathcal K -\mathcal N$
is linearly equivalent to the dual moderator $\bar \mathcal M$, and so belongs to $\mathfrak N$.
Thus, by Proposition~\ref{prop:magicformula}, we have
\begin{align*}
r_\mathfrak{C}(\mathcal D)
&= \deg(\mathcal D) - g+1 + \min_{\mathcal N \in \mathfrak N}\,\, \deg^+(\mathcal K - \mathcal D -
(\mathcal K -\mathcal N))-1\\
&= \deg(\mathcal D) - g+1 + \min_{\mathcal N' \in \mathfrak N}\,\, \deg^+(\mathcal K - \mathcal D - \mathcal N')-1 = \deg(\mathcal D) - g+1 +
r_\mathfrak{C}(\mathcal K - \mathcal D).
\end{align*}
\section{The specialization map and specialization inequality} \label{sec:specialization}
Let $\mathbb K$ be a complete and algebraically closed
non-Archimedean field with non-trivial absolute value $|.|$, $R$ the valuation ring of $\mathbb K$, and
$\k$ its (algebraically closed) residue field. Let ${\mathcal G} = {\rm val}(\mathbb K^\times)$ be the value group of $\mathbb K$.
Let $X$ be a smooth, proper, connected curve over $\mathbb K$ and
let $X^{\rm an}$ be the Berkovich analytic space associated to $X$. (We assume the reader is familiar with the theory of Berkovich
analytic curves, see e.g. \cite[Section 5]{BPR} which contains everything we need.)
Our first goal will be to define a metrized complex $\mathfrak{C}\fX$ associated to a strongly semistable $R$-model ${\mathfrak X}$ for $X$.
We then define a specialization homomorphism from $\operatorname{Div}(X)$ to $\operatorname{Div}(\mathfrak{C}\fX)$ and prove a specialization inequality which refines
Lemma 2.8 and Corollary 2.11 from \cite{bakersp}.
Finally, we give some applications to specialization of canonical divisors, Brill-Noether theory, and Weierstrass points as in {\em loc. cit.}
\subsection{The metrized complex associated to a semistable model}
Recall that a connected reduced algebraic curve over $\kappa$ is called
{\em semistable} if all of its singularities are ordinary double points, and is called
{\em strongly semistable} if in addition its irreducible components are all smooth.
A {\em (strongly) semistable model} for $X$ is a flat and integral proper relative curve $\fX$ over $R$
whose generic fiber is isomorphic to $X$ and whose special fiber $\bar{\fX}$ is a (strongly) semistable curve.
\medskip
Given a semistable model $\fX$ for $X$, there is a canonical associated reduction map ${\rm red} : X(\mathbb K) \to \bar{\fX}(\kappa)$ which is defined using the natural bijection between $X(\mathbb K)$ and $\fX(R)$.
This extends naturally to a map ${\rm red} : X^{\operatorname{an}} \to \bar{\fX}$.
\medskip
We define a metrized complex associated to a strongly semistable model $\fX$ for $X$ as follows.
Let $G$ be the dual graph of $\bar{\fX}$, so that vertices of $G$ correspond to irreducible components of
$\bar{\fX}$ and edges of $G$ correspond to intersections between irreducible components.
If $x^e$ is the ordinary double point of $\bar{\fX}$ corresponding to an edge $e$ of $G$,
the {\em formal fiber} $\mathrm{red}^{-1}(x^e)$ is isomorphic to an open annulus ${\mathbf A}$.
We define the {\em length of the edge $e$} to be the length of the skeleton of ${\mathbf A}$,
i.e., the {\em modulus} $\log(b)-\log(a)$ of ${\mathbf A} \cong \{ x \in ({\mathbf A}^1)^{\operatorname{an}} \; | \; a < |T|_x < b \}$.
(The modulus of an open annulus is well-defined independent of the choice of such an analytic isomorphism.)
In this way, we have defined a metric graph $\Gamma = \Gamma_{\fX}$ associated to $\fX$ together with a model $G$.
The irreducible components $C_v$ of $\bar{\fX}$ correspond bijectively to the vertices $v$ of $G$,
and we let ${\mathcal A}_v \subset C_v$ be the finite set of double points of $\bar{\fX}$ contained in $C_v$, so that there is a natural
bijection between ${\mathcal A}_v$ and the edges of $G$ incident to $v$. In this way we have defined a metrized complex
$\mathfrak{C}\fX$ canonically associated to $\fX$.
\medskip
One can show that essentially every metrized complex of curves comes from this construction.
The following result is proved in \cite[Theorem 3.24]{ABBR}.
\begin{thm} \label{thm:graph.to.curve}
Let $\mathfrak{C}$ be a metrized complex of $\kappa$-curves whose edge lengths are
contained in the value group of $\mathbb K$. There exists a
smooth, proper, connected curve $X$ over $\mathbb K$ and a semistable
model $\fX$ for $X$ such that $\mathfrak{C} \cong \mathfrak{C}\fX$.
\end{thm}
\subsection{The metrized complex associated to a semistable vertex set}
It is sometimes useful to define skeleta and metrized complexes in terms of semistable vertex sets rather than semistable models.
(By \cite[Theorem 5.38]{BPR}, there is a bijective correspondence between the latter two objects.)
A {\em semistable vertex set} for $X^{\operatorname{an}}$ is a finite set $V$ of type 2 points of $X^{\operatorname{an}}$ such that the complement of $V$ in $X^{\operatorname{an}}$ is isomorphic
(as a $\mathbb K$-analytic space) to the disjoint union of a finite number of open annuli and an infinite number of open balls. (Such a disjoint union is called
the {\em semistable decomposition} of $X^{\operatorname{an}}$ associated to $V$.)
Any finite set of type 2 points of $X^{\operatorname{an}}$ is contained in a semistable vertex set
(\cite[Proposition 5.27]{BPR}).
The {\em skeleton} $\Gamma = \Sigma(X^{\operatorname{an}},V)$ of $X^{\operatorname{an}}$ with respect to a semistable vertex set $V$ is the union (inside $X^{\operatorname{an}}$) of $V$ and the skeletons of
each of the open annuli in the semistable decomposition associated to $V$.
Using the canonical metric on the skeletons of these open annuli, $\Gamma$ can be naturally viewed as a (finite) {metric graph}
contained in $X^{\operatorname{an}}$ (see \cite[Definition 5.17]{BPR} for more details).
The skeleton $\Gamma$ comes equipped with a natural model $G$ whose vertices are the points of $V$ and whose edges correspond bijectively to the open annuli in the semistable decomposition associated to $V$. A semistable vertex set $V$ is called {\em strongly semistable} if the graph $G$ has no loop edges.
Every semistable vertex set is contained in a strongly semistable vertex set.
\medskip
Given a strongly semistable vertex set $V$ for $X^{\operatorname{an}}$,
there is a canonical corresponding metrized complex $\mathfrak{C} V$ of $\kappa$-curves.
Indeed, we have already defined a metric graph $\Gamma = \Sigma(X^{\operatorname{an}},V)$ corresponding to $V$, together with a corresponding model $G$.
For $v \in V$, let $C_v$ be the unique smooth projective curve over $\kappa$ with function field
$\widetilde{{\mathcal H}(v)}$.
(For $x \in X^{\operatorname{an}}$ of type 2, recall that the residue field $\widetilde{{\mathcal H}(x)}$ of the completed residue field ${\mathcal H}(x)$ of $x$ has transcendence degree one
over $\kappa$.)
It remains to specify, for each $v \in V$, a bijection $\psi_v$ from the edges of $G$ incident to $v$ to a subset
$\mathcal A_v$ of $C_v(\kappa)$. Given such an edge $e$, we define $\psi(e)$ to be the point of $C_v(\kappa)$
corresponding to the tangent direction at $v$ defined by $e$.
(Recall from \cite[Paragraph 5.67]{BPR} that if $x$ is of type 2, there is a canonical bijection between $T_x$ and the set of discrete valuations on
$\widetilde{{\mathcal H}(x)} = \kappa(C_x)$ which are trivial on $\kappa$.)
\begin{remark}
\label{rmk:modelcompatibility}
Passing to a larger semistable vertex set is compatible with linear equivalence of divisors and does not change the rank of divisors. One can thus associate a canonical group $\operatorname{Pic} \mathfrak{C} X^{\operatorname{an}}$ to $X^{\operatorname{an}}$, defined as
$\operatorname{Pic}(\mathfrak{C} V)$ for any semistable vertex set $V$, together with a canonical rank function $r : \operatorname{Pic} \mathfrak{C} X^{\operatorname{an}} \to \mathbb{Z}$.
\end{remark}
One can define in a similar way semistable vertex sets and skeleta for an affine curve $X'$ (see \cite[Definition 5.19]{BPR}).
In this case, one must also allow a finite number of punctured open balls in the semistable decomposition and the skeleton is a topologically finite
but not necessarily finite length metric graph -- it will contain a finite number of infinite rays corresponding to the points of
$X \setminus X'$, where $X$ is the projective completion of $X'$.
\subsection{Specialization of divisors from curves to metrized complexes}
There is a canonical embedding of $\Gamma_{\fX}$ in the
Berkovich analytification $X^{\operatorname{an}}$ of $X$, as well as a canonical retraction map $\tau : X^{\operatorname{an}} \to \Gamma_{\fX}$.
In addition, there is a canonical reduction map ${\rm red} : X^{\operatorname{an}} \to \bar{\fX}$ sending $X(\mathbb K)$
surjectively onto the closed points of $\bar{\fX}$.
The retraction map $\tau$ induces by linearity a specialization map $\tau_* : \operatorname{Div}(X) \to \operatorname{Div}(\Gamma_{\fX})$
which is studied in \cite{bakersp}.
We can promote this to a map $\tau_*^{\mathfrak{C}\fX}$ whose target is the larger group $\operatorname{Div}(\mathfrak{C}\fX)$ as follows.
If $P \in X^{\operatorname{an}}$ satisfies $\tau(P)=v \in V$ then either $P$ is the unique point of
$X^{\operatorname{an}}$ with $\mathrm{red}(P)$ equal to the generic point of $C_v$,
or else $\mathrm{red}(P)$ is a nonsingular closed point of $C_v$. The map $\tau^{\mathfrak{C}\fX}_* : \operatorname{Div}(X) \to \operatorname{Div}(\mathfrak{C}\fX)$ is obtained by linearly extending the map
$\tau^{\mathfrak{C}\fX} : X(\mathbb K) \to \operatorname{Div}(\mathfrak{C}\mathcal X)$ defined by
\[
\tau^{\mathfrak{C}\fX}(P) = \left\{
\begin{array}{ll}
\tau(P) & \tau(P) \not\in V \\
{\rm red}({P}) & \tau(P) \in V. \\
\end{array}
\right.
\]
\subsection{Reduction of rational functions and specialization of principal divisors}
\label{section:ReductionOfRationalFunctions}
In this section, we show that if $\mathcal D$ is a principal divisor on $X$, then $\tau^{\mathfrak{C}\fX}_*(\mathcal D)$ is a principal divisor on $\mathfrak{C}\fX$.
In fact, we show a more precise result (Theorem~\ref{thm:PLspecialization} below).
\medskip
Let $x \in X^{\operatorname{an}}$ be a point of type 2.
Given a nonzero rational function $f$ on $X$, choose $c \in \mathbb K^\times$ such that $|f(x)|=|c|$.
Define $f_x \in \kappa(C_x)^\times$ to be the image of $c^{-1}f$ in
$\widetilde{{\mathcal H}(x)} \cong \kappa(C_x)$.
Although $f_x$ is only well-defined up to multiplication by an element of $\kappa^\times$,
its divisor $\div(f_x)$ is canonical and the resulting map $\operatorname{Prin}(X) \to \operatorname{Prin}(C_x)$ is a homomorphism. We call $f_x$ the {\em normalized reduction} of $f$.
\medskip
If $H$ is a $\mathbb K$-linear subspace of $\mathbb K(X)$, the collection of all possible reductions of nonzero elements of $H$, together with $\{ 0 \}$,
forms a $\k$-vector space $H_x$. For later use we note the following elementary lemma, which says that $\dim H = \dim H_x$:
\begin{lemma}\label{lem:dimensionreduction} Let $X$ be a smooth proper curve over $\mathbb K$, and $x\in X^{\mathrm{an}}$
a point of type 2. The $\k$-vector space $H_x$ defined by the reduction to $\widetilde{\H(x)}$
of an $(r+1)$-dimensional $\mathbb K$-subspace
$H \subset \mathbb K(X)$ has dimension $r+1$.
\end{lemma}
\begin{proof}
The inequality $\dim_\k(H_x) \leq r+1$ follows from the observation that
if $f_0, \dots, f_n$ are linearly dependent in $H$, with $|f_i|=1$ for all $i$, then the reductions
$f_{0,x}, \dots, f_{n,x}$ are linearly dependent in $H_x$.
To prove $\dim_\k(H_x) \geq r+1$, choose a $\mathbb K$-basis $f_0, \dots, f_r$ for $H$ consisting of elements of norm $1$
and let $f_{0,x}, \dots, f_{r,x}$ in $H_x$ be the corresponding reductions.
It is not true that $f_{0,x}, \dots, f_{r,x}$ necessarily form a basis of $H_x$: for example, if $f$ and $g$ are linearly independent functions of norm $1$ and $c$ is any scalar
with $|c|<1$, then $f$ and $f+cg$ are linearly independent but they have the same reduction.
However, by the following procedure one can construct another basis $g_0, \dots, g_r$ of $H$ with $|g_i|=1$ for all $i$
such that the reductions $g_{i,x}$ are linearly independent over $\k$. Define $g_0=f_0$, and recursively define $g_{i+1}$ as follows:
among all the rational functions of the form $f_{i+1} - \sum_{j\leq i} a_j g_j$ with $|a_j|\leq 1$ for all $j$, choose one, call it $h_{i+1}$, whose norm is minimal.
Note that $|f_{i+1} - \sum_{j\leq i} a_j g_j|\leq 1$ so such an element exists by compactness.
Let $c_{i+1}$ be a scalar with $|c_{i+1}|=|h_{i+1}|$ and define $g_{i+1} = c_{i+1}^{-1} h_{i+1}$.
It is clear that the $\{g_i\}$ form a basis of $H$. We claim that the reductions $g_{i,x}$ form a basis of $H_x$.
Indeed, if not then there exists a minimal index $i$ and scalars $b_j$ with $|b_j| \leq 1$ for $j=0, \ldots, i$ such that
$|g_{i+1} - \sum_{j\leq i} b_j g_{j}|<1$. But this implies that
$|f_{i+1} - \sum_{j\leq i} (a_j+c_{i+1}b_j)g_j| < c_{i+1}$,
contradicting the choice of $h_{i+1}$.
\end{proof}
We recall the following useful result from \cite[Theorem 5.69]{BPR}.
\begin{thm}[Slope Formula] \label{thm:PL}
Let $f$ be a nonzero rational function on $X$, let $X'$ be an open affine subset of $X$ on which
$f$ has no zeros or poles, and let $F = -\log |f|: (X')^{\operatorname{an}}\to\mathbb{R}$.
Let $V$ be a semistable vertex set for $X'$, and let $\Sigma = \Sigma(X',V)$ be the corresponding skeleton. Then:
\begin{enumerate}
\item[$(1)$] $F = F\circ\tau_\Sigma$ where $\tau_\Sigma:(X')^{\operatorname{an}}\to\Sigma$ is the retraction.
\item[$(2)$] $F$ is piecewise linear with integer slopes, and $F$ is linear on each edge of $\Sigma$.
\item[$(3)$] If $x$ is a type-$2$ point of $X^{\operatorname{an}}$ and $\vec{\nu}\in T_x$ corresponds to the discrete valuation $\mathrm{ord}_v$ on $\kappa(C_x)$, then
$d_{\vec \nu} F(x) = \mathrm{ord}_v(f_x)$.
\item[$(4)$] $F$ is harmonic at all $x \in {\mathbf H}(X^{\operatorname{an}})$.
\item[$(5)$] Let $x\in X \setminus X'$, let $e$ be the ray in $\Sigma$ whose closure in
$X^{\operatorname{an}}$ contains $x$, let $y\in V$ be the other endpoint of $e$, and
let $\vec{\nu }\in T_y$ be the tangent direction represented by $e$. Then $d_{\vec \nu}
F(y) = \mathrm{ord}_x(f)$.
\end{enumerate}
\end{thm}
To each nonzero rational function $f$ on $X$ and each strongly semistable model $\fX$ for $X$, one can associate a rational function
$\mathfrak f$ on $\mathfrak{C}\fX$ whose $\Gamma$-part $f_{\Gamma}$ is the restriction to
$\Gamma=\Gamma_{\fX}$ of the piecewise linear function $F = \log|f|$ on $X^{\operatorname{an}}$
and whose $C_v$-part is the normalized reduction $f_v$ (which is well-defined up to multiplication by a non-zero scalar).\footnote{We take $F=\log|f|$ instead of $-\log|f|$ because our convention is that $\mathrm{ord}_{u}(F)$ is the sum of the outgoing slopes of $F$ at $u$.
One could equally well take the opposite convention, defining $\mathrm{ord}_{u}(F)$ to be {\em minus} the sum of the
outgoing slopes of $F$ at $u$, and then defining $F$ to be $-\log|f|$. Such a modification would also necessitate a change of sign in our definition of $\div_v(F)$.}
As an application of Theorem~\ref{thm:PL}, we obtain the following important formula:
\begin{thm} \label{thm:PLspecialization}
For every nonzero rational function $f$ on $X$,
\[
\tau_*^{\mathfrak{C}\fX}(\div(f)) = \div(\mathfrak f).
\]
\end{thm}
\begin{proof}
Let $D$ be the support of $\div(f)$ in $X$. We apply Theorem~\ref{thm:PL} to $X' = X \setminus D$, the invertible rational function $f$ on $X'$, and a semistable vertex set $V'$ for $X'$ which contains $V$. Let $\Sigma =\Sigma(X'^{\operatorname{an}},V')$ and $\Gamma = \Sigma(X,V)$. Since $V$ is a semistable vertex set for $X$, the closure of $\Sigma \setminus \Gamma$ in $\Sigma$ is a disjoint union of metric trees $\mathcal T_1,\dots, \mathcal T_s$. For each tree $\mathcal T_i$, denote by $x^i_1,\dots, x^i_{n_i}$ all the points in $D \subset X(\mathbb K)$ which are in the closure of rays in $\mathcal T_i$, and let $\overline{\mathcal T_i} = \mathcal T_i \cup \{x_1^i,\dots,x^i_{n_i}\}$. Denote by $y_i$ the unique point of $\Gamma\cap \overline{\mathcal T_i}$.
In addition, if $y_i \in V$, let $z^i_j = \tau_*^{\mathfrak{C}\fX}(x^i_j) \in C_{y_i}(\kappa)$.
\medskip
For each $i \in \{ 1, \ldots, s \}$, the restriction of $F= \log|f|$ to $\mathcal T_i$ is harmonic at every point of $\overline{\mathcal T_i} \setminus \{y_i, x^i_1,\dots, x^i_{n_i}\}$ by (4). By (5), $\log|f|$ is linear in a sufficiently small neighborhood of $x^i_j$ in $\mathcal T_i$, and has (constant) slope $\mathrm{ord}_{x^i_j}(f)$ along the unique tangent direction in this interval toward the point $y_i$.
We infer that the order of $F|_{\mathcal T_i}$ at $y_i$ is equal to $-\sum_{1\leq j\leq n_i}\mathrm{ord}_{x^i_j}(f)$. By (1), $F$ is constant on any connected component of $X^{\operatorname{an}} \setminus \Sigma$. By (4), the restriction $f_\Gamma$ of $F$ to $\Gamma$ satisfies $\mathrm{ord}_{y_i}(f_\Gamma) = - \mathrm{ord}_{y_i}(F|_{\mathcal T_i}) = \sum_{1\leq j\leq n_i} \mathrm{ord}_{x^i_j}(f)$. Since $f_\Gamma $ is linear on each edge of $\Gamma$ by (2), it follows that $\tau_*(\div(f)) = \div(f_\Gamma)$.
\medskip
Fix $i \in \{ 1, \ldots, s \}$ and suppose that $y_i \in V$. For any tangent direction $\vec \nu \in T_{y_i}$, by (3) we have $d_{\vec \nu} F = - \mathrm{ord}_\nu(f_{y_i})$. Since $F$ is locally constant on $X^{\operatorname{an}} \setminus \Sigma$, we infer that $d_{\vec \nu} F = 0$ for any $\vec \nu \in T_x$ not corresponding to a
direction in $\Sigma$. This shows that $\div(f_{y_i})$ is supported on $\{z^i_1,\dots, z^i_{n_i}\}\cup \mathcal A_{y_i}$. By (3), for any point $\nu$ in $\mathcal A_{y_i}$, corresponding to a tangent direction ${\vec \nu}$, we have $d_{\vec \nu} f_\Gamma + \mathrm{ord}_\nu(f_{y_i}) =0$. This shows that the coefficient of $\nu$ in $\div(\mathfrak f)$ is zero. For a point $\nu \in \{z^i_1,\dots, z^i_{n_i}\}$, let $\overline{\mathcal T}_{i,\nu}$ be the closure in $\Sigma$ of the connected component of $\Sigma \setminus y_i$ which contains all the points $x^i_j$ with $z^i_j = \nu$. By (1) and (4), $F$ is harmonic at any point of $\overline{\mathcal T}_{i,\nu} \setminus (D \cup \{y_i\})$, and is linear of slope $\mathrm{ord}_{x^i
_j}(f)$ in a sufficiently small neighborhood of $x^{i}_j$ in $\mathcal T_{i,\nu}$ along the unique tangent direction in this interval toward the point $y_i$. By (3), we infer that
$\mathrm{ord}_\nu(f_{y_i}) = - d_{\vec \nu}(F) = \sum_{x^i_j: \, z^i_j =\nu} \mathrm{ord}_{x^i_j} (f)$. We conclude that $\tau_*^{\mathfrak{C}\fX}\div(f) = \div(\mathfrak f)$.
\end{proof}
In particular, it follows that $\tau_*^{\mathfrak{C}\fX}(\operatorname{Prin}(X)) \subseteq \operatorname{Prin}(\mathfrak{C}\fX)$.
\subsection{The specialization inequality}
Fix a strongly semistable $R$-model ${\mathfrak X}$ for $X$ and let $\mathfrak{C}\fX$ be the metrized complex associated to $\fX$.
The following is a variant of Lemma 2.8 and Corollary 2.11 from \cite{bakersp}:
\begin{thm}[Specialization Inequality]
\label{lem:BakSpecLem}
For every divisor $D \in \operatorname{Div}(X)$,
\[
r_X(D) \leq r_{\mathcal {C}{\fX}}(\tau^{\mathcal C\fX}_*(D)).
\]
\end{thm}
\begin{proof}
Let $\mathcal D := \tau^{\mathfrak{C}\fX}_*(D)$.
It suffices to prove that if $r_X(D) \geq k$, then $r_{\mathfrak{C}{\fX}}(\mathcal D) \geq k$ as well.
\noindent The base case $k = -1$ is obvious. Now suppose $k = 0$, so that $r_X(D) \geq 0$.
Then there exists an effective divisor $E \in \operatorname{Div}(X)$ with
$D - E \in \operatorname{Prin}(X)$. Since $\tau^{\mathfrak{C}\fX}_*$ is a homomorphism and
takes principal (resp. effective) divisors on $X$ to principal (resp. effective)
divisors on $\mathfrak{C}{\fX}$, we have $\mathcal D = \tau_*^{\mathfrak{C}\fX}(D) \sim \tau_*^{\mathfrak{C}\fX}(E) \geq 0$, so that
$r_{\mathfrak{C}{\fX}}(\mathcal D) \geq 0$ as well.
\medskip
We may therefore assume that $k \geq 1$. For each $v\in V$, let
$\mathcal{R}_v \subset C_v(\k) \setminus \mathcal A_v$ be a subset of size $g_v+1$ and denote by $\mathcal{R}$ the union of the $\mathcal{R}_v$.
By Theorem~\ref{thm:f-width}, $\mathcal{R}$ is a rank-determining set in $\mathfrak{C}$.
Let $\mathcal E$ be an effective divisor of degree $k$ with support in $\mathcal{R}$. For each $x \in {\rm supp}(\mathcal E)$, there exists a point $P \in X(\mathbb K)$ whose reduction is $x$,
so there is an effective divisor $E$ of degree $k$ on $X$ with $\tau^{\mathfrak{C}\fX}_*(E) = \mathcal E$.
By our assumption on the rank of $D$, $r_X(D - E) \geq 0$, and so $r_{\mathfrak{C}{\fX}}(\mathcal D - \mathcal E) \geq 0$.
Since this is true for any effective divisor of degree $k$ with support in $\mathcal{R}$, and since $\mathcal{R}$ is rank-determining, we infer that $r_{\mathfrak{C}\fX}(\mathcal D) \geq k$ as desired.
\end{proof}
\begin{remark}
There are many examples where the inequality in Theorem~\ref{lem:BakSpecLem} can be strict.
For example, if $g_v = 0$ for all $v \in V$ then
$r_{\mathcal {C}{\fX}}(\tau^{\mathcal C\fX}_*(D)) = r_{\Gamma}(\tau_*(D))$
and thus the examples of strict inequality from \cite{bakersp} apply.
At the other extreme, if $C = \bar{\fX}$ is smooth (so that $G$ is a point) then the specialization inequality becomes the well-known semicontinuity statement $h^0(D) \leq h^0(\bar{D})$, where $\bar{D} \in \operatorname{Div}(C)$ is the reduction of $D$, and
it is clear that such an inequality can be strict; for example, take $D=(P)-(Q)$ where
$X$ has genus at least $1$ and $P,Q \in X(\mathbb K)$ are distinct points with the same reduction in $C(\kappa)$.
\end{remark}
\subsection{Refined versions of weighted specialization lemma}
In this section we use the specialization lemma for divisors on metrized complexes to provide a framework for obtaining stronger versions of the weighted specialization lemma from~\cite{AC}.
Our key technical tool for this will be the ``$\eta$-function'' on a metrized complex.
To help motivate the definition, we first study an analogous $\eta$-function which controls the rank of divisors on connected sums.
\subsubsection{The $\eta$-function and the rank of divisors on connected sums}\label{sec:rank-csum}
Suppose the underlying graph of a metrized complex $\mathfrak{C}$ has a bridge edge $e = \{v_1,v_2\}$,
and denote by $\mathfrak{C}_1$ and $\mathfrak{C}_2$ the two metrized complexes obtained by removing the edge $e$ from $\mathfrak{C}$ ($v_i$ is a vertex of $\mathfrak{C}_i$).
Denote by $x_1$ and $x_2$ the points of $\mathfrak{C}_1$ and $\mathfrak{C}_2$, respectively, corresponding to the edge $e$.
We say that $\mathfrak{C}$ is a {\it connected sum} of
$\mathfrak{C}_1$ and $\mathfrak{C}_2$.
There is an addition map $\operatorname{Div}(\mathfrak{C}_1) \oplus \operatorname{Div}(\mathfrak{C}_2) \rightarrow \operatorname{Div}(\mathfrak{C})$
which associates to any pair of divisors $(\mathcal D_1,\mathcal D_2) \in \operatorname{Div}(\mathfrak{C}_1) \oplus \operatorname{Div}(\mathfrak{C}_2)$
the divisor $\mathcal D_1+\mathcal D_2$ on $\mathfrak{C}$ whose restriction to each $\mathfrak{C}_i$ is $\mathcal D_i$.
The following proposition provides a precise description of the $\mathfrak{C}$-rank of $\mathcal D_1 + \mathcal D_2$ in terms of the two rank functions
$r_{\mathfrak{C}_1}(\cdot)$ and $r_{\mathfrak{C}_2}(\cdot)$.
In order to state the result, we introduce a function $\eta = \eta_{x_2,\mathcal D_2}: \mathbb N\cup\{0\} \rightarrow \mathbb Z$
defined by the condition that $\eta(k)$ is the smallest integer $n$ such that
$r_{\mathfrak{C}_2}(\mathcal D_2 + n(x_2)) = k$.
(By the Riemann-Roch theorem for $\mathfrak{C}_2$, $\eta$ is well-defined.)
\begin{prop} \label{prop:ConnectedSumRankForMetrizedComplexes}
With notation as above, we have
\begin{equation}\label{eq:wrank3}
r_{\mathfrak{C}}(\mathcal D) = \min_{k\in \mathbb N\cup\{0\}} \Bigl\{\,k + r_{\mathfrak{C}_1}(\mathcal D_1-\eta(k)(x_1))\,\Bigr\}.
\end{equation}
\end{prop}
\begin{proof}
We prove the equality of the two sides of Equation~\eqref{eq:wrank3} by showing that the inequalities
$\leq$ and $\geq$ both hold. By Theorem~\ref{thm:f-width},
we can assume that all the effective divisors we consider below are supported on geometric points (i.e., on points of the curves $C_v$).
\medskip
\noindent $(\geq)$
Let $r$ be the right-hand term in \eqref{eq:wrank3} and let $\mathcal E$ be an effective divisor of degree $r$ on
$\mathfrak{C}$ supported on geometric points. We need to show the existence of a rational function $\mathfrak f$ on $\mathfrak{C}$ such that $\div(\mathfrak f)+\mathcal D -\mathcal
E\geq 0$. There is a (unique) decomposition of $\mathcal E$ as
$\mathcal E=\mathcal E_1+\mathcal E_2$ with $\mathcal E_1$ and $\mathcal E_2$ effective divisors
of degree $r-k$ and $k$, respectively, having support on geometric points.
By the definition of $\eta$, there exists a rational function $\mathfrak f_2$ on $\mathfrak{C}_2$ such that
$\div(\mathfrak f_2) + \eta(k)(x_2)+ \mathcal D_2 -\mathcal E_2 \geq 0$. By the choice of $r$ as the minimum
in Equation~\eqref{eq:wrank3},
we have $r_{\mathfrak{C}_1}\bigl(\mathcal D_1-\eta(k)(x_1)\bigr)\geq r-k$, so
there exists a rational function $\mathfrak f_1$ on $\mathfrak{C}_1$ such that $\div(\mathfrak f_1) +\mathcal D_1-\eta(k)(x_1)-
\mathcal E_1 \geq 0$.
We can in addition suppose that the $\Gamma_1$-part of $\mathfrak f_1$ takes value zero at $v_1$.
Up to adding a constant to the $\Gamma_1$-part of $\mathfrak f_1$, we can
define a rational function $\mathfrak f$ which restricts to $\mathfrak f_1$ and $\mathfrak f_2$
on $\mathfrak{C}_1$ and $\mathfrak{C}_2$, respectively, and which is linear of slope $-\eta(k)$ on the oriented edge $(v_1,v_2)$ in $\Gamma$.
For this rational function, we clearly have
\begin{align*}
\div(\mathfrak f) + \mathcal D -\mathcal E = \div(\mathfrak f_1)+\mathcal D_1 -\eta(k)&(x_1)-\mathcal E_1 \\
&+ \div(\mathfrak f_2)+\mathcal D_2 + \eta(k)(x_2)-\mathcal E_2 \geq 0.
\end{align*}
\medskip
\noindent $(\leq)$
It will be enough to show that for each $k\in \mathbb N\cup\{0\}$,
the inequality
$$r_\mathfrak{C}(\mathcal D) \leq k + r_{\mathfrak{C}_1}\bigl(\mathcal
D_1-\eta(k)(x_1)\bigr)$$
holds.
Let $\widetilde r = r_\mathfrak{C}(\mathcal D)$.
We can obviously restrict to the case $k\leq \widetilde r$.
For each effective divisor $\mathcal E_2$ of degree $k$ supported on geometric points of $\mathfrak{C}_2$,
let $\mathfrak f_{\mathcal E_2}$ be a rational function on $\mathfrak{C}_2$ with the property that the coefficients of
$\div(\mathfrak f_{\mathcal E_2}) + \mathcal D_2-\mathcal E_2$ outside $x_{2}$ are all non-negative,
and such that in addition, the coefficient of $x_2$ in $\div(\mathfrak f_{\mathcal E_2}) + \mathcal D_2-\mathcal E_2$ is maximized among all
the rational functions with this property.
Denote by $n_{\mathcal E_2}$ the coefficient of $x_2$ in $\div(\mathfrak f_{\mathcal E_2}) + \mathcal D_2-\mathcal E_2$
and let $\bar{\mathcal E}_2$ be an effective divisor of degree $k$ on $\mathfrak{C}_2$, supported on geometric points of $\mathfrak{C}_2$,
for which $n := n_{\bar{\mathcal E}_2}$ is minimal, i.e.,
$$n_{\bar{\mathcal E}_2} = \min\{n_{\mathcal E_2}\,|\,\mathcal E_2\geq 0:\,\deg(\mathcal E_2)=k\}.$$
Note that by the choice of $n$, for an effective divisor $\mathcal E_2$ of degree $k$ supported on geometric points of $\mathfrak{C}_2$
and the rational function $\mathfrak f_{\mathcal E_2}$, we have $\div(\mathfrak f_{\mathcal E_2}) + \mathcal D_2-\mathcal
E_2 -n(x_2) \geq 0$, which shows that $r_{\mathfrak{C}_2}(\mathcal D_2 -n(x_2))\geq k$. By the definition of
$\eta$, it follows that $\eta(k) \leq -n$.
\medskip
By the definition of $\mathfrak f_{\bar{\mathcal E}_2}$, for any rational function $\mathfrak f_2$ on $\mathfrak{C}_2$ with the property
that $\div(\mathfrak f_2)+\mathcal D_2-\bar{\mathcal E}_2$
has non-negative coefficients outside $x_2$,
the coefficient of $x_2$ in $\div(\mathfrak f_2)+\mathcal D_2-\bar {\mathcal E}_2$ is at most $n \leq -\eta(k)$.
Let $\mathcal E_1$ be an effective divisor of degree $\widetilde r - k$ on $\mathfrak{C}_1$ supported on geometric points.
There exists a rational function $\mathfrak f$ on $\mathfrak{C}$ such that $\div(\mathfrak f)+\mathcal D -\mathcal E_1-\bar{\mathcal E}_2\geq 0$.
Let $\mathfrak f_1$ and $\mathfrak f_2$ be the restrictions of
$\mathfrak f$ to $\mathfrak{C}_1$ and $\mathfrak{C}_2$, respectively. By the preceding paragraph, the coefficient of $x_2$ in
$\div(\mathfrak f_2)+\mathcal D_2-\bar{\mathcal E}_2$ is at most $-\eta(k)$. Since the coefficient of $x_2$ in
$\div(\mathfrak f)+\mathcal D -\mathcal E_1-\bar{\mathcal E}_2$ is non-negative, the $\Gamma$-part of $\mathfrak f$ has slope at least
$\eta(k)$ along the tangent direction emanating from $v_2$ which corresponds to $x_2$. Since the coefficients of
$\div(\mathfrak f)$ at the interior points of the edge $\{v_1,v_2\}$ are all non-negative, it follows that the slope of the $\Gamma$-part of $\mathfrak f$
along the tangent direction emanating from $v_1$ on the edge $\{v_1,v_2\}$ is at most $-\eta(k)$,
which by the assumption $\div(\mathfrak f)+\mathcal D -\mathcal E_1-\bar{\mathcal E}_2\geq 0$ implies that the coefficient of
$x_1$ in $\div(\mathfrak f_1)+\mathcal D_1- \mathcal E_1$ must be at least $\eta(k)$. It follows that $\div(\mathfrak f_1)+\mathcal D_1 -\eta(k)(x_1)- \mathcal E_1\geq 0$. Since $\mathcal E_1$ was an arbitrary effective
divisor of degree $\widetilde r-k$ supported on geometric points of $\mathfrak{C}_1$, it follows that $r_{\mathfrak{C}_1}\bigl(\mathcal
D_1-\eta(k)(x_1)\bigr)\geq \widetilde r-k$, and the claim follows.
\end{proof}
\begin{remark}
In the same spirit, consider two metric graphs $\Gamma_1$ and $\Gamma_2$,
and suppose that two distinguished points $v_1\in \Gamma_1$ and $v_2\in \Gamma_2$ are given.
The {\it wedge} or {\it direct sum} of $(\Gamma_1,v_1)$ and $(\Gamma_2,v_2)$, denoted $\widetilde{\Gamma} = \Gamma_1 \vee \Gamma_2$, is the metric graph obtained by identifying the points $v_1$ and $v_2$ in the disjoint union of
$\Gamma_1$ and $\Gamma_2$. Denote by $v \in \widetilde{\Gamma}$ the image of $v_1$ and $v_2$ in $\widetilde \Gamma$.
(By abuse of notation, we will use $v$ to denote both $v_1$ in $\Gamma_1$ and $v_2$ in $\Gamma_2$.)
We refer to $v\in \widetilde \Gamma$ as a {\it cut-vertex} and to $\widetilde \Gamma=\Gamma_1\vee \Gamma_2$
as the decomposition corresponding to the cut-vertex $v$. Note that there is an addition map $\operatorname{Div}(\Gamma_1) \oplus \operatorname{Div}(\Gamma_2) \rightarrow \operatorname{Div}(\widetilde \Gamma)$ which associates to any pair of divisors $D_1$ and $D_2$ in $\operatorname{Div}(\Gamma_1)$ and $\operatorname{Div}(\Gamma_2)$ the divisor,
$D_1+D_2$ on $\widetilde \Gamma$ defined by pointwise addition of coefficients in $D_1$ and $D_2$. Let $r_1(\cdot)$, $r_2(\cdot)$, and
$\widetilde{r}(\cdot) = r_{\Gamma_1 \vee \Gamma_2}(\cdot)$ be
the rank functions in $\Gamma_1, \Gamma_2$, and $\widetilde{\Gamma}$, respectively.
For any non-negative integer $k$, denote by $\eta_{v,D_2}(k)$, or simply $\eta(k)$, the smallest integer $n$ such that
$r_2 \bigl(D_2 + n(v) \bigr) = k$. Then for any divisor $D_1$ in $\operatorname{Div}(\Gamma_1)$, we have (by an entirely similar argument)
\begin{equation}
\label{eq:wrank2}
\widetilde{r}(D_1 + D_2) = \min_{k\in \mathbb N \cup \{0\}}\, \Bigl\{\,k+r_1\bigl(D_1 -\eta(k)\,(v)\bigr)\,\Bigr\}.
\end{equation}
\end{remark}
\begin{remark} The above formalism is very handy for studying metric graphs such as the chain of cycles used in~\cite{CDPR}.
In particular, the lingering lattice paths studied in~\cite{CDPR} in connection with a tropical proof of the Brill-Noether theorem
can be understood in a natural way as values of $\eta$-functions.
The $\eta$-function formalism is also useful for studying limit linear series, see for example the proof of
Theorem~\ref{thm:limitseries} below.
\end{remark}
We now define a partial analogue of the $\eta$-function introduced above for a general metrized complex $\mathfrak{C}$
and provide an analogue of
Proposition~\ref{prop:ConnectedSumRankForMetrizedComplexes}.
\medskip
Consider a divisor $\mathcal D$ on $\mathfrak{C}$ with $C_v$-part $D_v$ for $v \in V$. For every vertex $v$ of $G$, define the function
$\eta_v: \mathbb N\cup\{0\} \rightarrow \mathbb N\cup \{0\}$ as follows. For any $k\geq 0$, $\eta_v(k)$ is the smallest integer $n \geq 0$ such that there exists a divisor
$\widetilde D_v$ of degree $n-\deg(D_v)$ supported on the points of $\mathcal A_v \subset C_v(\kappa)$
such that $r_{C_v}(D_v + \widetilde D_v) = k$. For any effective divisor $E=\sum_{v\in V(G)} E(v)(v)$ on $G$,
define
\begin{equation*}
\eta(E) := \sum_{v\in V(G)} \eta_v(E(v))\,(v).
\end{equation*}
\noindent Note that the definition of $\eta$ depends on the data of the divisors $D_v \in \operatorname{Div}(C_v)$.
\begin{prop}
\label{prop:wrank3}
Let $\mathfrak{C}$ be a metrized complex of algebraic curves over $\kappa$. For any divisor $\mathcal D$ on $\mathfrak{C}$ with $\Gamma$-part $D_\Gamma$, we have
\[ r_\mathfrak{C}(\mathcal D)\,\, \leq\,\, \min_{E \geq 0}\, \Bigl(\,\deg(E) + r_\Gamma(D_\Gamma - \eta(E))\,\Bigr), \]
where the minimum is over all effective divisors $E$ on $G$.
\end{prop}
\begin{proof}
Fix an effective divisor $E$ supported on the vertices of $G$. We need to prove that
$$r_\mathfrak{C}(\mathcal D) \leq \deg(E) + r_\Gamma(D_\Gamma - \eta(E)).$$
For the sake of contradiction, suppose this is not the case, i.e., that
$\deg(E) + r_\Gamma(D_\Gamma - \eta(E)) < r_{\mathfrak{C}}(\mathcal D)$.
Since $r_{\mathfrak{C}}(\mathcal D) - \deg(E) > r_\Gamma(D_\Gamma - \eta(E))$,
Luo's Theorem (which is a special case of Theorem~\ref{thm:f-width}) implies that
there exists a divisor $E^0$ of degree
$r_{\mathfrak{C}}(\mathcal D) - \deg(E)$ supported on $\Gamma \setminus V(G)$ such that
$|D_\Gamma - E^0_\Gamma -\eta(E)| =\emptyset.$
\medskip
Consider all the effective divisors on $\mathfrak{C}$ of the form $E^0 + \sum_{v\in V} E_v$, where each $E_v$ is an effective divisor of degree $E(v)$ on $C_v$.
Note that $E^0 + \sum_{v\in V} E_v$ has degree $r_{\mathfrak{C}}(\mathcal D)$, so that by the definition of the rank function, for any choice of effective divisors $E_v$ on $C_v$ there exists a rational function $\mathfrak f$ on $\mathfrak{C}$
such that $\div(\mathfrak f) + \mathcal D- E^0 -\sum_v E_v \geq 0$.
Denote by $f_\Gamma$ and $f_v$ the different parts of $\mathfrak f$, so in particular we have
$\div(f_\Gamma) + D_\Gamma -E^0 -E \geq 0.$ One can assume
as in the proof of Proposition~\ref{prop:combinrank}
that the slope of $f_\Gamma$ along the edges
incident to each vertex of $G$ is fixed. This shows the existence of the divisor $\widetilde D_v = \div_v(f_\Gamma)$ supported on the points $\mathcal A_v \subset C_v(\kappa)$ such that $D_v + \widetilde D_v$ has rank at least $E(v)=\deg(E_v)$ on $C_v$. By the definition of $\eta_v$,
$\widetilde D_v$ has degree at least $\eta_v(E(v)) -\deg(D_v)$. Since the degree of $\widetilde D_v$
is the sum of the slopes of $f_\Gamma$ along the edges adjacent to $v$, which is by definition
$\mathrm{ord}_v(f_\Gamma)$, for each $v\in V(G)$ we obtain
$\mathrm{ord}_v(f_\Gamma) \geq \eta_v(E(v)) - \deg(D_v)$, i.e.,
$\mathrm{ord}_v(f_\Gamma) + D_\Gamma(v) - \eta_v(E(v)) \geq 0$.
In addition, for each non-vertex point $u \in \Gamma$ we must have
$\mathrm{ord}_u(f_\Gamma) + D_\Gamma(u) - E^0(u) \geq 0$.
This implies that $|D_\Gamma - E^0 -\eta(E)|\neq \emptyset$, a contradiction.
\end{proof}
\subsubsection{Weighted specialization lemma}\label{section:weightedspecialization}
Let $\mathbb K$ be a complete and algebraically closed
non-Archimedean field with non-trivial absolute value $|.|$, $R$ the valuation ring of $\mathbb K$, and
and $\kappa$ its residue field. Let ${\mathcal G} = {\rm val}(\mathbb K^\times)$ be the value group of $\mathbb K$.
Let $X$ be a smooth, proper, and connected $\mathbb K$-curve
and fix a semistable $R$-model ${\mathfrak X}$.
Let $(\Gamma,\omega)$ denote the skeleton of ${\mathfrak X}$
together with the weight function $\omega: V \rightarrow \mathbb N$ defined by
$\omega(v) = g_v$. Let $\mathcal W = \sum_{v \in V} g_v(v)$.
Following~\cite{AC}, we define a metric graph $\Gamma^\#$ by attaching $g_v$ loops of arbitrary positive length at each point $v \in \Gamma$
(see \cite{AC} for a discussion of the intuition behind this construction.)
\medskip
Any divisor $D$ in $\Gamma$ defines a divisor on $\Gamma^\#$ with the same support and coefficients (by viewing $\Gamma$ as a subgraph of $\Gamma^\#$). By an abuse of notation, we will also denote this divisor by $D$.
However, we distinguish the ranks of $D$ in $\Gamma$ and $\Gamma^\#$ by using the notation $r_\Gamma(D)$ for the former and $r_{\Gamma^\#}(D)$ for the latter.
Following~\cite{AC}, the {\em weighted rank} $r^\#$ of $D$ is defined by $r^\#(D):= r_{\Gamma^\#}(D)$. Applying the formalism of the $\eta$-function from the previous subsection, we obtain the following useful formula for $r^\#$:
\begin{cor}
\label{prop:wrank}
For every $D \in \operatorname{Div}(\Gamma)$, we have
\[
r^\#(D) = \min_{0\leq E \leq \mathcal W} \bigl(\deg(E)+ r_\Gamma(D-2E)\bigr).
\]
\end{cor}
\begin{proof} Proceeding by induction, we are reduced to the case
$\deg(\mathcal W)=1$.
This case follows from (\ref{eq:wrank2}) applied to $\Gamma_1=\Gamma$, $\Gamma_2$ a circle, $\widetilde \Gamma = \Gamma_1\vee \Gamma_2 $, $D_1 = D$, and $D_2=0$, since in this case one has $\eta(0) = 0$, $\eta(1)=2$, and $\eta(k) = k+1$ for $k>1$.
\end{proof}
The following result is a generalization to metric graphs $\Gamma$, and to smooth curves $X$ over not necessarily discrete non-Archimedean fields, of
the corresponding statement for graphs which was obtained by different methods in~\cite{AC}.
\begin{thm}[Weighted specialization inequality]
\label{thm:weightedmetricspecialization}
For every divisor $D \in \operatorname{Div}(X)$, we have $r_X(D) \leq r^\#(\tau_*(D))$.
\end{thm}
\begin{proof}
Let $\mathcal D =\tau_*^{\mathfrak{C}\fX}(D)$
and note that the $\Gamma$-part $D_\Gamma$ of $\mathcal D$ is equal to $\tau_*(D)$.
Applying Proposition~\ref{prop:wrank3}, we obtain
\begin{equation}
\label{eq:wrank3cor}
r_{\mathfrak{C}\fX}(\tau_*^{\mathfrak{C}\fX}(D)) \leq \min_{E \geq 0}\, \Bigl(\,\deg(E) + r_\Gamma\bigl(\tau_*(D) - \eta(E)\bigr)\,\Bigr).
\end{equation}
For each vertex $v$ of $G$, define the function $\bar \eta_v : \mathbb N\cup\{0\} \rightarrow \mathbb N\cup\{0\}$ by $\bar\eta_v(k)=2k$ for $k \leq g_v$ and $\bar \eta_v (k) = k+g_v$ for $k \geq g_v$.
If $E$ is an effective divisor supported on vertices of $G$, define
$\bar \eta(E) = \sum_v \bar\eta(E(v))(v)$.
By the definition of $\eta_v$ and Clifford's theorem for the curve $C_v$, for any integer $k\geq 0$ we have $\eta_v(k) \geq \bar \eta_v(k)$.
Combining this with \eqref{eq:wrank3cor}, we get the inequality
\begin{equation}
\label{eq:wrank3corbis}
r_{\mathcal{C}{\fX}}(\tau_*^{\mathcal C\fX}(D)) \leq \min_{E \geq 0}\, \Bigl(\,\deg(E) + r_\Gamma\bigl(\tau_*(D) - \bar \eta(E)\bigr)\,\Bigr).
\end{equation}
Note that for $E(v) > g_v$, we have $\bar \eta_v(E(v)) = g_v+E(v)$ and so, whatever the other coefficients of $E$ are, we have
\begin{align*}
\deg(E) + r_\Gamma\bigl(\tau_*(D)-\bar \eta(E)\bigr) &= \deg(E-(v))+ 1+r_\Gamma\bigl(\tau_*(D)-\bar\eta(E-(v))-(v)\bigr) \\
&\geq \deg(E-(v)) + r_\Gamma(\tau_*(D)-\bar\eta(E-(v))).
\end{align*}
In other words, in taking the minimum in \eqref{eq:wrank3corbis}, one can restrict to effective divisors $E$ with $E(v) \leq g_v$ for all $v$, i.e., $0\leq E \leq \mathcal W$.
Finally, applying \eqref{eq:wrank3corbis}, Theorem~\ref{lem:BakSpecLem}, and Corollary~\ref{prop:wrank},
we obtain the inequality $r_X(D) \leq r^\#(\tau_*(D)).$
\end{proof}
\subsection{Some applications} We give some direct applications of the results of this section.
\subsubsection{Specialization of canonical divisors}
Let $K_X$ be a canonical divisor on the curve $X/\mathbb K$. By Theorem~\ref{lem:BakSpecLem}, we have $r_{\mathfrak{C}\fX}\left( \tau_*^{\mathfrak{C}\fX}(K_X)\right) \geq r(K_X) = g(X)-1 = g(\mathfrak{C}\fX)-1$. By the Riemann-Roch theorem for metrized complexes (Theorem~\ref{thm:RR-metrizedcomplexes}), the divisor $\mathcal \tau_*^{\mathfrak{C}\fX}(K_X) - \mathcal K$ has degree zero and non-negative rank, and thus $\mathcal \tau_*^{\mathfrak{C}\fX}(K_X) \sim \mathcal K$. In particular, we have $\tau_*(K_X) \sim K^\#$.
\begin{remark}
As mentioned in the Introduction, for discretely valued $R$ the fact that $\tau_*(K_X) \sim K^\#$ follows from the adjunction formula for arithmetic surfaces.
But it does not seem straightforward to generalize that argument to the not necessarily discretely valued case.
\end{remark}
\subsubsection{Brill-Noether theory}
The following result is an immediate consequence of Theorem~\ref{thm:graph.to.curve}
combined with Theorem~\ref{lem:BakSpecLem}.
\begin{cor}[Brill-Noether existence theorem]
\label{cor:BNexistence}
Let $\k$ be a field and let $g,r,d$ be nonnegative integers.
If the Brill-Noether number $\rho^r_d(g) := g - (r+1)(g-d+r)$ is nonnegative,
then for every metrized complex $\mathfrak{C}$ of $\k$-curves
with $g(\mathfrak{C}) = g$, there exists a divisor $\mathcal D \in \operatorname{Div}^d_+(\mathfrak{C})$ such that $r_\mathfrak{C}(\mathcal D) \geq r$.
\end{cor}
\begin{remark}
In particular, combining the original Specialization Lemma from \cite{bakersp} with
Theorem~\ref{thm:graph.to.curve} yields a new proof of \cite[Theorem 3.20]{bakersp}, which says that
if $\rho^r_d(g) \geq 0$ then for every metrized graph of genus $g$ there exists
$D \in \operatorname{Div}^d_+(\Gamma)$ such that $r(D) \geq r$. The present proof is more direct in that one does not need the approximation arguments given in Lemma 3.17 and Corollary 3.18 of {\em loc.~cit.}
\end{remark}
\begin{remark}
The notion of Brill-Noether rank on metric graphs introduced in~\cite{LPP} and the corresponding specialization lemma extend to the context of metrized complexes as well. Let $\mathfrak{C}$ be a metrized complex of $\k$-curves, and let $W^r_d(\mathfrak{C}) \subset \operatorname{Pic}^d(\mathfrak{C})$ be the subset of all divisors of degree $d$ and rank at least $r$. Define $w^r_d(\mathfrak{C})$ to be the largest integer $n$ such that for every effective divisor $\mathcal E$ of degree $r+n$ on $\mathfrak{C}$, there exists $\mathcal D \in W^r_d(\mathfrak{C})$ such that $\mathcal D-\mathcal E \geq 0$. If $W^r_d(\mathfrak{C}) =\emptyset$, define $w^r_d(\mathfrak{C}) =-1$.
If $\fX$ is a strongly semistable $R$-model of a proper smooth curve $X/\mathbb K$ such that $\mathfrak{C}\fX = \mathfrak{C}$, and $W^r_d(X) \subset \operatorname{Pic}^d(X)$ denotes the Brill-Noether locus of $X$, then we have the inequality $w^r_d(\mathfrak{C}) \geq \dim\,W^r_d(X)$.
\end{remark}
\subsubsection{Weierstrass points on metrized complexes of $\k$-curves}
Let $\mathfrak{C}$ be a metrized complex of $\k$-curves.
We say that a point $x$ in $\mathfrak{C}$ is a {\em Weierstrass point} if $r_\mathfrak{C}\bigl(g(\mathfrak{C})(x)\bigr) \geq 1$.
By Theorem~\ref{lem:BakSpecLem}, the specialization of a Weierstrass point on $X$ is a Weierstrass point on $\mathfrak{C}$.
And by Theorem~\ref{thm:graph.to.curve} combined with Theorem~\ref{lem:BakSpecLem},
any metrized complex of $\k$-curves of genus at least two has at least one Weierstrass point.
\section{Limit linear series}\label{sec:limitseries}
Our aim in this section is to compare our divisor theory on metrized complexes with the Eisenbud-Harris theory of limit linear series for curves of compact type
\cite{EH86}.
As we will see, our comparison results lead naturally to a generalization of the notion of limit linear series to nodal curves which are
not necessarily of compact type.
Note that since Eisenbud and Harris work over a discrete valuation ring, in order to compare our theory to theirs we will sometimes restrict to this setting; we note, however, that most of our results hold over the valuation ring of an arbitrary non-trivially valued non-Archimedean field.
\subsection{Degeneration of linear series}
We start by reviewing some basic facts and definitions concerning the degeneration of linear series in families.
Let $Y$ be a smooth projective curve over $\k$. Recall that a linear series $L$ of (projective) dimension $r$ and degree $d$, or simply a $\mathfrak g^r_d$, over $Y$ consists of a pair $(\mathcal L, H)$ with $\mathcal L$ an invertible sheaf of degree $d$ on $Y$ and $H$ a subspace of $H^0(Y,\mathcal L)$ of $\kappa$-dimension $r+1$.
\medskip
Let $\phi: \mathcal X \rightarrow B = \operatorname{Spec} R$ be a regular smoothing of a strongly semistable curve $X_0$ over a discrete valuation ring $R$ with fraction field $K$. This means that $\phi$ is proper, $\mathcal X$ is regular, the generic fiber $\mathcal X_\eta$ of $\phi$ is smooth, and the special fiber of $\phi$ is $X_0$. Denote by $G=(V,E)$ the dual graph of $X_0$ and let $\{X_v\}_{v\in V(G)}$ be the set of irreducible components of $X_0$.
\begin{prop} Any line bundle $\mathcal L_\eta$ on $\mathcal X_\eta$ extends to $\mathcal X$. The restriction of any two extensions $\mathcal L_1$ and $\mathcal L_2$ of $\mathcal L_\eta$ to the special fiber $X_0$ are combinatorially equivalent (c.f. Section~\ref{sec:mcnodal}).
\end{prop}
\begin{proof} The first part is a well-known consequence of the regularity of $\mathcal X$ (see for example \cite[Chapter II, 6.5(a) and 6.11]{HartshorneAG}). For the second part, note that any two extensions $\mathcal L_1$ and $\mathcal L_2$ of $\mathcal L_\eta$ differ by a divisor supported on the special fiber $X_0$.
In other words, there exist integers $n_v$ for each vertex $v$ of the dual graph of $X_0$ such that $\mathcal L_1 \simeq \mathcal L_2(\sum_v n_v X_v)$. It is now easy to see that, in the notation of Section~\ref{sec:mcnodal}, $\pi(\mathcal L_1|_{X_0})$ and $\pi(\mathcal L_2|_{X_0})$ differ by the divisor of the function $f_G:V(G) \rightarrow \mathbb Z$ which sends $v$ to $n_v$.
\end{proof}
Consider now a $\mathfrak g^r_d$ $L_\eta=(\mathcal L_\eta, H_\eta)$ on $\mathcal X_\eta$ and choose an extension $\mathcal L$ of $\mathcal L_\eta$ to $\mathcal X$.
Since cohomology commutes with flat base change, there is a natural isomorphism $H^0(X_\eta,\mathcal L_\eta) \cong H^0(X,\mathcal L) \otimes_R K$ and
$H_\eta$ corresponds to a free $R$-submodule H of $H^0(\mathcal X, \mathcal L)$ such that $H \otimes_R K \cong H_\eta$.
The restriction $H_0$ of $H$ to the special fiber $X_0$ is an $(r+1)$-dimensional subspace of $H^0(X_0,\mathcal L_0)$. This shows the existence of the limit of a $\mathfrak g^r_d$ once the extension $\mathcal L$ of $\mathcal L_\eta$ is fixed. However, since the extension is not unique, the limit pair $(\mathcal L_0, H_0)$ is not unique.
If one were to restrict to a single such extension, there would inevitably be a loss of important information; this can be
seen, for example, in the study of limits of ramification points and in the study of limits of smooth hyperelliptic, and more generally, smooth $d$-gonal curves, see for example~\cite{HM82,EH86, EM, Ran}. Some of the difficulties in formulating a good notion of limits for linear series are already manifest in the atypical behavior of linear series on reducible curves, since (as mentioned earlier) they do not satisfy many of the classical theorems which govern the behavior of (global sections of) linear series on irreducible curves.
\medskip
The Eisenbud-Harris theory of limit linear series on curves of compact type provides a way to keep track of the geometry in the limit by choosing an {\it aspect} of the limit for each irreducible component, with some extra conditions relating these different aspects at nodes (see below for a precise definition). We refer to~\cite{O, O2} for recent refinements of the Eisenbud-Harris theory, and to~\cite{E98, EM} for generalizations of this theory to certain curves not of compact type.
\subsection{Limit linear series for curves of compact type}\label{sec:limitcompact}
We recall the definition of limit linear series for curves of compact type, following~\cite{EH86}.
\medskip
We first need to recall the sequence of orders of vanishing of a $\mathfrak g^r_d$ $L=(\mathcal L,H)$ at a point on a smooth projective curve $Y$ over $\kappa$.
For any closed point $p$ on $Y$ and any section $f \in H$, denote by $\mathrm{ord}_p(f)$ the order of vanishing of $f$ at $p$. The orders of vanishing at $p$ of all the sections of $\mathcal L$ in $H$ define a sequence of integers $0 \leq a_0^L( p ) < a_{1}^L( p ) < \dots <a_{r-1}^L( p ) < a_r^L ( p )$. (This sequence is obtained by induction: let $f_r$ be the section in $H$ with the highest order of vanishing, and define $f_{r-i}$ inductively as a section in $H$ with the highest possible order of vanishing at $p$ among
all sections which are linearly independent of the first $i$ sections $f_r,\dots, f_{r-i+1}$. Then $a_i( p ) = \mathrm{ord}_p(f_i)$.)
\medskip
Let $X_0$ be a strongly semistable curve over $\k$, let $G=(V,E)$ be the dual graph of $X_0$, and for any $v\in V$, let $X_v$ be the corresponding irreducible component of $X_0$. When $G$ is a tree, the curve $X_0$ is called of {\it compact type}: in this case, $\operatorname{Pic}^0(X_0)$ is compact.
\noindent (Recall that in general, we have an exact sequence of algebraic groups
$$0 \rightarrow H^1(G, \mathbb \mathbb{Z}) \otimes {\mathbb G}_m \rightarrow \operatorname{Pic}^0(X_0) \rightarrow \prod_{v \in V_0} \operatorname{Pic}^0(X_v) \rightarrow 0.)$$
\medskip
Let $X_0$ be a curve of compact type. A {\it crude limit} $\mathfrak g^r_d$ $L$ over $X_0$ is by definition the data of a $\mathfrak g^r_d$ $L_v = (\mathcal L_v, H_v)$ over $X_v$ for each vertex $v \in V$, called the $X_v$-{\it aspect} of $L$, such that the following property holds: If the two components $X_u$ and $X_v$ of $X_0$ meet at a node $p$ corresponding to
an edge $\{u, v\}$ in $E$, then
\begin{equation}\label{eq:crude}
a^{L_v}_{i}( p ) + a^{L_u}_{r-i}( p ) \, \geq \, d
\end{equation}
for all $ 0\leq i \leq r$.
A crude limit linear series is a {\it refined limit linear series} if all the inequalities in \eqref{eq:crude}
are equalities.
\medskip
We are now going to associate to $L$ a degree $d$ divisor on the regularization of $X_0$ (c.f. Section~\ref{sec:mcnodal} for the definition).
Roughly speaking, this amounts to choosing a divisor of degree $d$ on each $X_v$
in the divisor class of $L_v$.
However, the global divisor on $\mathfrak{C} X_0$ defined by such a collection of divisors does not have degree $d$.
To fix this problem, we need to choose a root $\mathfrak r$ for the tree $G$
and modify the local divisors using the root. This is done as follows.
Let $\Gamma$ be the metric graph associated to $G$ and let $\mathfrak{C} X_0$ be the regularization of $X_0$.
For each vertex $v$ of $G$, let $\overline D_v$ be a divisor of degree $d$ on $X_v$ in the divisor class defining $\mathcal L_v$ (i.e., $\mathcal L(\overline D_v) \simeq \mathcal L_v$). The subspace $H_v\subseteq H^0(X_v, \mathcal L(\overline D_v))$ can be naturally regarded as a subspace of $\k(X_v)$.
Let $\mathfrak r$ be a fixed vertex of $G$ and let $G_\mathfrak r$ denote $G$ considered as a rooted tree
with root $\mathfrak r$.
For any vertex $u \neq \mathfrak r$ in $G$, consider the unique path from $u$ to $\mathfrak r$ in $G$ and let $e_u$ be the edge adjacent to $u$ along this path. Let $x_u$ be the node of $X_u$ corresponding to the edge $e_u$. Consider the divisor $\mathcal D$ of degree $d$ on $\mathfrak{C} X_0$ defined by
\begin{equation}\label{eq:D}
D_\Gamma := \overline D_\mathfrak r + \sum_{u \neq \mathfrak r} D_u, \; \textrm{where} \; D_u := \overline D_u - d( x_u ).
\end{equation}
We will see below that $\mathcal D$ has rank at least $r$ in $\mathfrak{C} X_0$.
In order to derive a more precise characterization of crude limits in terms of a suitable rank function,
we need to introduce a refined notion of rank on a metrized complex which
takes into account the spaces $H_v$.
\subsubsection{A refined notion of rank for divisors on a metrized complex}
Let $\mathfrak{C}$ be a metrized complex of algebraic curves, $\Gamma$ the underlying metric graph with model $G$, and $\{ C_v \}$ the corresponding family of smooth projective curves over $\k$. Suppose we are given, for each $v \in V$, a non-empty $\k$-linear subspace $F_v$ of $\k(C_v)$. We denote by $\mathcal F$ the collection of all $F_v$.
Define the {\em $\mathcal F$-rank} of a divisor $\mathcal D$ on $\mathfrak{C}$, denoted $r_{\mathfrak{C}, \mathcal F}(\mathcal D)$, to be the maximum integer $r$ such that
for any effective divisor $\mathcal E$ of degree $r$, there exists a nonzero rational function $\mathfrak f$ on $\mathfrak{C}$, with $C_v$-parts $f_v \in F_v$ for all $v \in V$, such that $\mathcal D + \div(\mathfrak f) - \mathcal E \geq 0$.
\medskip
The following proposition provides an upper bound for $r_{\mathfrak{C},\mathcal F}$ in terms of the maximal dimension of $F_v$
for $v\in V(G)$.
\begin{prop}\label{prop:basic} Let $s = \max\left( 0, \min_{v\in V(G)} (\dim_\k (F_v)-1) \right).$
Then for any divisor $\mathcal D$ on $\mathfrak{C}$, we have $r_{{\mathfrak{C}},\mathcal F}(\mathcal D) \leq s$.
\end{prop}
\begin{proof}
If $\dim_\k (F_v) =0$ for some $v$, then either $r_{\mathfrak{C},\mathcal F}(\mathcal D) = 0$ (if $\mathcal D \geq 0$) or $r_{\mathfrak{C},\mathcal F}(\mathcal D) = -1$ (otherwise), and the proposition holds. For the sake of contradiction, suppose now that $r_{\mathfrak{C},\mathcal F}(\mathcal D) \geq s+1 \geq 1$. Let $v$ be a vertex with $s = \dim_\k (F_v)-1$. For any effective divisor $E_v$ of degree $s+1$ on $C_v$, there exists a rational function $\mathfrak f$ on $\mathfrak{C}$ with $f_v \in F_v$ such that $\mathcal D - E_v+ \div(\mathfrak f) \geq 0$. Taking $\Gamma$-parts shows that $D_\Gamma -(s+1)(v) + \div(f_\Gamma) \geq 0$.
For a generic choice of $E_v$, we can assume
as in the proof of Proposition~\ref{prop:combinrank}
that the slopes of $f_\Gamma$ on the edges adjacent to $v$ are fixed.
For the divisor $D'_v=D_v +\div_v(f_\Gamma)$, this shows that for any choice of $E_v$
on $C_v$, there exists an element $f_v \in F_v$ with $D'_v -E_v +\div(f_v) \geq 0$. This contradicts
the assumption that $\dim_\k(F_v) = s+1$, since $F_v$ can define a linear system of projective dimension at most $s$ on $C_v$.
\end{proof}
In Section~\ref{sec:rank-csum},
we provided a formula for the rank of a divisor on a metrized complex $\mathfrak{C}$ which is a connected sum of two
metrized complexes $\mathfrak{C}_1$ and $\mathfrak{C}_2$. We now state
a straightforward generalization of Proposition~\ref{prop:ConnectedSumRankForMetrizedComplexes}
to restricted ranks, which will be used in the next section.
Suppose that the underlying graph of $\mathfrak{C}$ has a bridge edge $e=\{v_1,v_2\}$ and let
$\mathfrak{C}_1$ and $\mathfrak{C}_2$ be the two metrized complexes obtained by removing the edge $e$.
Let $\Gamma_1$,
$\Gamma_2$, and $\Gamma$ be the underlying metric graphs of $\mathfrak{C}_1$, $\mathfrak{C}_2$, and $\mathfrak{C}$ respectively (with $v_i$ a vertex of $\Gamma_i$).
Denote by $x_1$ and $x_2$ the points of $\mathfrak{C}_1$ and $\mathfrak{C}_2$, respectively, corresponding to the edge $e$.
Let $\mathcal F$ be a family of spaces of rational functions $F_v$ for vertices $v$ of $\Gamma$,
and denote by $\mathcal F_1$ (resp. $\mathcal F_2$) the collection of those $F_v$ for $v$
a vertex of $\Gamma_1$ (resp. $\Gamma_2$).
\begin{prop}\label{prop:ConnectedSumRankForMetrizedComplexes2}
Let $\mathcal D = \mathcal D_1 + \mathcal D_2$ be the sum of
divisors $\mathcal D_1$ and $\mathcal D_2$ on $\mathfrak{C}_1$ and $\mathfrak{C}_2$, respectively.
For a non-negative integer $k$, define $\eta(k)$ to be the smallest integer $n$ such that
$r_{\mathfrak{C}_1,\mathcal F_1}\bigl(\mathcal D_1 + n(x_1)\bigr) = k$. Then
\begin{equation}
r_{\mathfrak{C},\mathcal F}(\mathcal D) = \min_{k\geq 0} \bigl\{\,k + r_{\mathfrak{C}_2,\mathcal F_2}(\mathcal D_2-\eta(k)(x_2))\,\bigr\}.
\end{equation}
\end{prop}
\subsubsection{Characterization of limit linear series in terms of the refined rank function} We retain the terminology from the previous sections. Let $X_0$ be a curve of compact type, $G=(V,E)$ the dual graph, $\mathfrak{C} X_0$ the regularization of $X_0$, and let $L$ be a collection of $\mathfrak g^r_d$'s $L_v = (\mathcal L_v,H_v)$ on $X_v$, one for each $v \in V$. Fix a root vertex $\mathfrak r \in V$ and divisors $\overline D_v \in \operatorname{Div}(X_v)$ such that $\mathcal L(\overline D_v) \sim \mathcal L_v$, and let $\mathcal D$ be the divisor defined by~\eqref{eq:D}. Denote by $\mathcal H$ the family of all $H_v \subseteq H^0(X_v, \mathcal L(D_v)) \subset \k(X_v)$.
\begin{thm}\label{thm:limitseries} The following two assertions are equivalent:
\begin{itemize}
\item[(i)] $L$ is a crude limit $\mathfrak g^r_d$ on $X_0$.
\item[(ii)] $r_{\mathfrak{C} X_0, \mathcal H} (\mathcal D) = r$.
\end{itemize}
\end{thm}
\begin{proof}
Denote by $\mathfrak r_1, \dots, \mathfrak r_h$ all the children of $\mathfrak r$ in the rooted tree $G_\mathfrak r$.
For each $1\leq i\leq h$, denote by $x_i = x_{\mathfrak r_i}$ and $y_i$ the $\k$-points of
$X_{\mathfrak r_i}$ and $X_\mathfrak r$, respectively,
which correspond to the edge
$\{\mathfrak r,\mathfrak r_i\}$.
\medskip
Proof of ${\rm (i)} \Rightarrow {\rm (ii)}$:
Let $L$ be a crude limit $\mathfrak g^r_d$ and let $s \leq r$ be a non-negative integer.
Let $F_\mathfrak r \subset H_\mathfrak r$ be a subspace of dimension $s+1$, and denote by
$\mathcal F$ the collection of $F_\mathfrak r$ and $H_v$ for $v\neq \mathfrak r$ in $V$. We will prove
that $r_{\mathfrak{C} X_0, \mathcal F}(\mathcal D) = s$. The result then follows by taking $\mathcal F = \mathcal H$.
By Proposition~\ref{prop:basic}, we have $r_{\mathfrak{C} X_0, \mathcal F} (\mathcal D)\leq s$,
so it will be enough to prove the reverse inequality $r_{\mathfrak{C} X_0, \mathcal F} (\mathcal D) \geq s$.
The proof proceeds by induction on $|V|$, and by applying Proposition~\ref{prop:ConnectedSumRankForMetrizedComplexes2}.
For the base case of our induction, we have $|V|=1$, and thus $\mathfrak{C} X_0 = X_\mathfrak r$ and $r_{X_\mathfrak r,
\{F_\mathfrak r\}}(D_\mathfrak r) =s$.
Now suppose that the claim holds for all metrized complexes on at most $|V|-1$ vertices. For each $1\leq i\leq h$, denote by
$G_i$ the rooted tree at $\mathfrak r_i$ obtained by removing the edge $\{\mathfrak r, \mathfrak r_i\}$ from $G$,
and let $\Gamma_i$ be the metric graph obtained from $G_i$ by taking all edge lengths to be $1$.
Let $\mathfrak{C}_i$ be the sub-metrized complex of
$\mathfrak{C} X_0$ with underlying metric graph $\Gamma_i$ and curves
$X_v$ for $v$ a vertex of $G_i$, and denote by $\mathcal D_i$ the restriction of $\mathcal D$ to $\mathfrak{C}_i$, i.e.,
$D_{i,v} = D_v$ for all vertices $v$ of $G_i$. Denote by $\mathcal H_i$ the family of all $H_v$ for $v$ a vertex of $G_i$.
Let $\eta_i$ be the $\eta$-function associated to the bridge edge $\{\mathfrak r, \mathfrak r_i\}$, so that
$\eta_i(k)$ is the smallest integer $n$ such that
$r_{\mathfrak{C}_i,\mathcal H_i}(\mathcal D_i + n(x_{i})) = k$.
Repeatedly applying Proposition~\ref{prop:ConnectedSumRankForMetrizedComplexes2} reduces the calculation of $r_{\mathfrak{C} X_0, \mathcal F}(\mathcal D)$
to the calculation of the restricted ranks of certain divisors
on the metrized complex $X_\mathfrak r$ (with a single vertex $\mathfrak r$ and a unique curve $X_\mathfrak r$)
with respect to the subspace $F_\mathfrak r \subset \k(X_\mathfrak r)$; more precisely,
\[r_{\mathfrak{C} X_0, \mathcal F} (\mathcal D) =
\min_{s_1,\dots, s_h \geq 0} \bigl\{\,s_1+\dots+s_h + r_{X_\mathfrak r, \{F_\mathfrak r\}}
\bigl(D_\mathfrak r - \sum_{i=1}^h \, \eta_i(s_i) (y_{i})\bigr)\,\bigr\}.\]
We are thus led to prove that each term $s_1+\dots+s_h + r_{X_\mathfrak r, \{F_\mathfrak r\}}
\bigl(D_\mathfrak r - \sum_{i=1}^h \, \eta_i(s_i) (y_{i})\bigr)$ in the above formula, for non-negative integers
$s_i$, is bounded below by $s$.
We may clearly assume that $s_1+\dots+s_h \leq s+1$.
\begin{claim}
For each $1\leq i\leq h$, $\eta_i(s_i) \leq d- a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i})$.
\end{claim}
\noindent{\it Proof of the claim.}
By definition, the subspace $F_{\mathfrak r_i}$ of $H_{\mathfrak r_i}$ consisting of all global sections of
$\mathcal L_{\mathfrak r_i}$ having an order of vanishing at least
$a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i})$ at $x_{i}$ has dimension $s_{i}+1$.
Let $\mathcal D'_i$ be the divisor defined on $\mathfrak{C}_i$
by the data of the linear series $L_v=(\mathcal L(\overline D_v), H_v)$, for $v$ a vertex of $G_i$,
and the root $\mathfrak r_i$, as in~\eqref{eq:D}. Note that
$\mathcal D'_i = \mathcal D_i + d(x_i)$.
Let $\mathcal F_i$ be the collection of
$F_{\mathfrak r_i}$ and $H_v$, for $v\neq \mathfrak r_i$ a vertex of $G_i$.
By the induction hypothesis applied to the subcurve of $X_0$ consisting of all curves $X_v$ for $v$ a vertex of $G_i$ and the crude limit linear series
$\{L_v\}_{v\in V(G_i)}$, we have $r_{\mathfrak{C}_i, \mathcal F_i}(\mathcal D'_i) = s_i$.
On the other hand, by the definition of $F_{\mathfrak r_i}$, we have
\[
r_{\mathfrak{C}_i, \mathcal F_i}(\mathcal D'_i) = r_{\mathfrak{C}_i,\mathcal F_i}(\mathcal D'_i - a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i})(x_{i}))
\]
and thus
\begin{align*}
r_{\mathfrak{C}_i,\mathcal F_i}(\mathcal D_i + (d- a_{r-s_i}^{L_{\mathfrak r_i}}(x_i))
(x_{i})) =r_{\mathfrak{C}_i,\mathcal F_i}(\mathcal D'_i - a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i})
(x_{i})) = s_i.
\end{align*}
By the definition of $\eta_i(s_i)$, we infer that $\eta_i(s_i) \leq d- a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i})$,
which proves the claim.
\medskip
To finish the proof of ${\rm (i)} \Rightarrow {\rm (ii)}$, note that since $L$ is a crude limit $\mathfrak g^r_d$, we have
\[a_{s_i}^{L_\mathfrak r}(y_{i}) \geq d- a_{r-s_i}^{L_{\mathfrak r_i}}(x_{i}).\]
This shows that the space of all global sections of $\mathcal L_{\mathfrak r}$ with an order of vanishing at least
$\eta(s_i)$ at $y_{i} $ has codimension at most $s_i$.
The intersection of all these spaces with $F_\mathfrak r$ has dimension at least
$s+1 - \sum_{i=1}^h s_i$, which shows that $r_{X_\mathfrak r, \{F_\mathfrak r\}}
\bigl(D_\mathfrak r - \sum_{i=1}^h \, \eta_i(s_i) (y_{i})\bigr) \geq s - \sum_{i=1}^h s_i$.
\medskip
\noindent Proof of ${\rm (ii)} \Rightarrow {\rm (i)}$:
By Corollary~\ref{cor:f-widthZ}, in calculating $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D)$
we can restrict to effective divisors in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$.
In this case, since $G$ is a tree, we can suppose that all the rational functions on $\Gamma$ which appear
in the calculation of $r_{\mathfrak{C} X_0, \mathcal H}$
arise via linear interpolation from integral functions
$f_G: V \rightarrow \mathbb Z$. Since $G$ is a tree, the data of an integral function $f_G$ on $V$ is equivalent,
up to an additive constant, to an assignment of labels $a_{uv}\in \mathbb Z$
to each oriented edge $uv$ of $G$ such that $a_{uv} = -a_{vu}$ for any $\{u,v\} \in E$. (Set $a_{uv} = f_G(u) -f_G(v)$.)
In what follows, we denote by $p_v$ the unique parent of a vertex $v \neq \mathfrak r$ in the rooted tree
$G_\mathfrak r$.
Suppose now that $r_{\mathfrak{C} X_0,\mathcal H}(\mathcal D) = r$.
We first observe that, for any other choice of a root vertex $\mathfrak r'$,
if $\mathcal D'$ denotes the corresponding divisor on $\mathfrak{C} X_0$ defined as in~\eqref{eq:D} then
the two divisors $\mathcal D$ and $\mathcal D'$ differ by the principal divisor $\div(\mathfrak f)$, where
$\mathfrak f$ is a rational function with $\Gamma$-part $f_G$ and constant $X_v$-part for all $v \in V$.
Thus $r_{\mathfrak{C} X_0,\mathcal H}(\mathcal D') = r$, so
it will be enough to prove the validity of Condition~\eqref{eq:crude} for the root $\mathfrak r$ and a child $u$
of $\mathfrak r$ among $\mathfrak r_1,\dots, \mathfrak r_h$.
Denote by $x_u$ and $y_u$ the $\k$-points of $X_u$ and
$X_\mathfrak r$, respectively, corresponding to the edge $\{\mathfrak r, u\}$, and
let $ 0 \leq i\leq d$. For any effective divisor $\mathcal E = E_\mathfrak r +E_u$, where $E_\mathfrak r$ and $E_u$ are effective divisors of degree $r-i$ and $i$
on $X_\mathfrak r$ and $X_u$, respectively, there must exist a rational function
$\mathfrak f$ with $f_w\in H_w$ for all $w$
such that $\mathcal D - \mathcal E + \div(\mathfrak f) \geq 0$.
For any two adjacent vertices $w$ and $z$ in $G$, let $a_{wz} = f(w) - f(z)$ as above.
Since for any vertex $w\neq \mathfrak r$, $D_w$ has degree zero,
a simple induction starting from the leaves and going towards the root shows that $a_{wp_w} \geq 0$.
This in particular implies that $D_\mathfrak r + \div(f_\mathfrak r) - E_\mathfrak r - a_{u\mathfrak r}(y_u) \geq 0$
and $D_u + \div(f_u) - E_u - (d-a_{u\mathfrak r})(x_u) \geq 0$.
For a generic choice of $E_\mathfrak r $ and $E_u$, we can assume as in the proof of Proposition~\ref{prop:combinrank}
that $a_{u\mathfrak r} = a $ is a constant. In other words,
there exists an integer $0\leq a\leq d$ such that the sublinear
system of $H_\mathfrak r$ (resp., $H_u$)
which consists of those sections with an order of vanishing at least $a$ (resp. $d- a$) at $y_u$ (resp. $x_u$)
has projective dimension at least $r-i$ (resp. $i$). By the definition of the sequences $a^{L_\mathfrak r}(\cdot)$
and $a^{L_u}(\cdot)$, this simply means that
$a^{L_\mathfrak r}_i(y_u) \geq a$ and $a^{L_u}_{r-i}(x_u) \geq d-a$. It follows that
$a^{L_\mathfrak r}_{i}( y_u ) + a^{L_u}_{r-i}( x_u ) \, \geq \, d,$ which is Condition~\eqref{eq:crude}
for the two irreducible components $X_\mathfrak r$ and $X_u$ of $X_0$.
\end{proof}
\begin{cor} Let $\k$ be of characteristic zero. Then $L$ is a refined limit series iff $r_{\mathfrak{C}, \mathcal H}(\overline D) =r$ and all the ramification points of $L_v$ are smooth points of $X_v$ for all $v\in V(G)$.
\end{cor}
\begin{proof}
This is a direct consequence of Theorem~\ref{thm:limitseries} above and the Pl\"ucker formula, c.f. \cite[Proposition 1.1]{EH86}.
\end{proof}
We note that the {\em a priori} dependence of the family $\mathcal H$ on the $X_v$-aspects $L_v$ can be removed, and recovered from the condition on the rank, in the following sense. For any crude limit $\mathfrak g^r_d$ $L$ on $X_0$ with $X_v$-aspect $L_v = (\mathcal L_v, H_v)$, choose a divisor $D_v \in \operatorname{Div}^d(X_v)$ with $\mathcal L_v \simeq \mathcal L(D_v)$. Two divisors $\mathcal D$ and $\mathcal D'$ in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ are called {\em combinatorially equivalent} if they differ by the divisor of a rational function $\mathfrak f$ on $\mathfrak{C} X_0$ with all $f_v$ constant.
The following result is essentially a reformulation of Theorem~\ref{thm:introLLS} from the Introduction and easily implies the result stated there.
\begin{thm}
Let $X_0$ be a curve of compact type and $\mathfrak{C} X_0$ the regularization of $X_0$. Then there is a bijective correspondence between the following:
\begin{itemize}
\item Pairs $(L,\{D_v\})$ consisting of a crude limit $\mathfrak g^r_d$ $L$ on $X_0$ and a collection of divisors $D_v$ on $X_v$ with $L_v\simeq \mathcal L(D_v)$ for any irreducible component $X_v$ of $X_0$; and
\item Pairs $(\H,[\mathcal D])$, where $\H = \{ H_v \}$, $H_v$ is an $(r+1)$-dimensional subspace of $\kappa(X_v)$ for each $v \in V$, and $[\mathcal D]$ is the combinatorial linear equivalence class of a divisor $\mathcal D \in \operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ of degree $d$ on $\mathfrak{C} X_0$ with
$r_{\mathfrak{C} X_0,\H}(\mathcal D) = r$.
\end{itemize}
In particular, the data of a crude limit $\mathfrak g^r_d$ on $X_0$ is equivalent to the data of a pair $(\mathcal H, [\mathcal D])$ with $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D) = r$.
\end{thm}
\begin{proof}
We already know by Theorem~\ref{thm:limitseries} that any crude limit $\mathfrak g^r_d$ gives a pair $(\mathcal H, [\mathcal D])$ with $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D) = r$.
\medskip
Let $\mathcal H$ be a collection of $(r+1)$-dimensional subspaces $H_v \subset \k(X_v)$ for $v \in V$,
and let $\mathcal D$ be a divisor of degree $d$ in $\operatorname{Div}(\mathfrak{C} X_0)_\mathbb Z$ with $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D) = r.$ We show the existence of a $\mathfrak g_d^r$ $\mathcal L_v = (L_v, H_v )$ on $X_v$ for each $v \in V$ such that the collection $L = \{ L_v \}$ defines a crude limit $\mathfrak g^r_d$ on $X_0$, and such that $\mathcal D$ is (combinatorially) linearly equivalent to the divisor $\mathcal D^L$ associated to $L$ by~\eqref{eq:D}.
\medskip
Let $D_\Gamma$ (resp. $D_v$) denote the $\Gamma$-part (resp. $X_v$-part) of $\mathcal D$.
Since $\Gamma$ has genus zero, for any vertex $v$ in $V(G)$ there exists a rational function $f_{\Gamma}$ on $\Gamma$ such that $D_\Gamma +\div(f_{\Gamma}) = d(v)$. Define $\widetilde D_v := D_v + \div_v(f_{\Gamma})$, where $\div_v(f_\Gamma)$ is defined as in
(\ref{eq:divf2}).
We claim that $H_v \subset H^0(X_v, \mathcal L_v)$; this amounts to showing that $\div(f) + \widetilde D_v \geq 0$ for any $f \in H_v$. If we denote by $H'_v$ the subspace of $H_v$ consisting of all rational functions in $H_v$ with this property, it will be enough show that $\dim_\k (H'_v) = r+1$.
\medskip
First, we note that for any rational function $f'_\Gamma$ on $\Gamma$ with $D_\Gamma +\div(f'_\Gamma) \geq 0$, we have $\div_v(f_{\Gamma}) - \div_v(f'_\Gamma) \geq0$. Indeed, $D_\Gamma +\div(f'_\Gamma) \geq 0$ implies that for any edge $e$ adjacent to $v$, the slope of $f_{\Gamma}$ in the tangent direction corresponding to $e$ is bounded above by the sum of the coefficients $D_\Gamma(w)$ of the points $w$ lying on the connected component of $\Gamma \setminus \{v\}$ which contains the edge $e$. This sum is precisely the slope of $f_{\Gamma}$ in the tangent direction corresponding to $e$.
\medskip
For any effective divisor $E$ of degree $r$ on $X_v$, let $\mathcal E$ denote the corresponding divisor on $\mathfrak{C} X_0$. Since $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D) = r$, there exists a rational function $\mathfrak f^E$ such that $\div(\mathfrak f^E) + \mathcal D - \mathcal E \geq 0$.
Since $\div(f^{E}_\Gamma) + D_\Gamma \geq 0$, the preceding remark implies that $\widetilde D_v = D_v+ \div_v(f_{\Gamma}) \geq D_v + \div_v(f^E_\Gamma)$. By the definition of $\div(\mathfrak f)$,
we conclude that $\div(f_v^E) + \widetilde D_v -E \geq 0$, and in particular $f_v^E$ belongs to $H'_v$. Since this holds for any $E$, we infer that the linear series on $X_v$ defined by $H'_v$ has (projective) dimension at least $r$ and so $H'_v$ has dimension at least $r+1$, thus $ H'_v= H_v $. We conclude that $L_v = (\mathcal L_v, H_v)$ is a $\mathfrak g^r_d$ on $X_v$, and thus the collection of $L_v$
for $v \in V$ defines a crude limit $\mathfrak g^r_d$ $L$ on $X_0$.
If $\mathcal D^L$ is the divisor associated to $L$ by~\eqref{eq:D}, it is straightforward to check that $\mathcal D^L$ and $\mathcal D$ differ by the divisor of a rational function $\mathfrak f$ on $\mathfrak{C} X_0$
whose $X_v$-parts are all constant and whose $\Gamma$-part is
the linear interpolation of an integer-valued function $f: V \rightarrow \mathbb Z$.
\end{proof}
\subsection{Limit linear series for metrized complexes.}
Let $\mathfrak{C}$ be a metrized complex of algebraic curves over $\k$, $\Gamma$ the underlying metric graph with model $G=(V,E)$, and $\{ C_v \}$ the corresponding collection of smooth projective curves over $\k$.
\medskip
We define a {\em (crude) limit $\mathfrak g^r_d$} on $\mathfrak{C}$ to be an equivalence class of pairs $(\mathcal H, \mathcal D)$ consisting of a divisor $\mathcal D$ of degree $d$ on $\mathfrak{C}$ and a collection $\mathcal H$ of $(r+1)$-dimensional subspaces $H_v \subset \k(C_v)$, for $v \in V(G)$, such that $r_{\mathfrak{C}, \mathcal H}(\mathcal D) = r$. Two pairs $(\H,\mathcal D)$ and $(\H', \mathcal D')$ are considered equivalent if there is a rational function $\mathfrak f$
on $\mathfrak{C}$ such that $D' = D + \div(\mathfrak f)$ and $H_v = H'_v \cdot f_v$ for all $v \in V$, where $f_v$ denotes the $C_v$-part of $\mathfrak f$.
\begin{remark}
Since $r_{\mathfrak{C}, \H}(\mathcal D) \leq r_\mathfrak{C} (\mathcal D)$ for all $\mathcal H$ as above and all $\mathcal D \in \operatorname{Div}(\mathfrak{C})$, it follows immediately from
Theorem~\ref{thm:RR-metrizedcomplexes} that for any limit $\mathfrak g^r_d$ on $\mathfrak{C}$ we have if $d\geq 2g$ or $r\geq g$, then $r+g \leq d$ (Riemann's inequality), and if $\mathcal D$ is {\em special} then $r \leq d/2$ (Clifford's inequality). For curves of compact type, these inequalities are established (by a completely different proof) in \cite{EH86}.
\end{remark}
\begin{thm}\label{thm:limitseriesgeneral}
Let $X$ be a smooth proper curve over $\mathbb K$, $\fX$ a strongly semistable model for $X$,
and $\mathfrak{C} \fX$ the metrized complex associated to $\fX$.
Let $D$ be a divisor on $X$ and let $L_\eta = (\mathcal L(D), H_\eta)$,
for $H_\eta \subseteq H^0(X, \mathcal L(D)) \subset \mathbb K(X)$, be a $\mathfrak g^r_d$ on $X$.
For any vertex $v \in V$, define $H_v$ as the $\k$-vector space defined by the
reduction to $\k(C_v)$ of all the rational functions in $H_\eta$ (c.f. Section~\ref{section:ReductionOfRationalFunctions}), and let $\mathcal H = \{H_v\}_{v\in V}$.
Then the pair $(\tau^{\mathfrak{C} \fX}_*(D), \mathcal H)$ defines a limit $\mathfrak g^r_d$ on $\mathfrak{C} \fX$.
\end{thm}
\begin{proof}
By Lemma~\ref{lem:dimensionreduction}, all the subspaces $H_v$ have dimension $r+1$ over $\k$.
By Proposition~\ref{prop:basic}, we only have to show that $r_{\mathfrak{C}\fX,\mathcal H} \geq r$.
By Theorem~\ref{thm:f-width},
it suffices to show that for any effective divisor $\mathcal E \in \operatorname{Div}(\mathfrak{C} \fX)$ of degree $r$ supported on a subset $\mathcal{R} = \bigcup_v \mathcal{R}_v$ of $\mathfrak{C}\fX$ with $\mathcal{R}_v \subset C_v(\k)\setminus \mathcal A_v$ of size $g_v+1$,
there exists a rational function $\mathfrak f$ on $\mathfrak{C} \fX$ such that $f_v\in H_v$ for all $v \in V$ and $\div(\mathfrak f) + \tau^{\mathfrak{C}\fX}_*(D) - \mathcal E \geq 0$. For any such $\mathcal E$, there exists an effective divisor of degree $r$ on $X$ such
that $\tau^{\mathfrak{C}\fX}_*(E) = \mathcal E$. Since $L_\eta$ is a $\mathfrak g^r_d$ on $X$, there exists a rational function $f \in H_\eta$ such that $D -E +\div(f) \geq 0$. Let $\mathfrak f$ be the corresponding rational function on $\mathfrak{C}\fX$ (as in the paragraph preceding
Theorem~\ref{thm:PLspecialization}).
We conclude that $\tau^{\mathfrak{C}\fX}_*(D-E+\div(f)) = \tau^{\mathfrak{C}\fX}_*(D) -\mathcal E +\tau^{\mathfrak{C}\fX}_*(\div(f)) = \tau^{\mathfrak{C}\fX}_*(D) -\mathcal E +\div(\mathfrak f) \geq 0$. Since $f_v \in H_v$, this shows that $r_{\mathfrak{C}\fX,\mathcal
H} \geq r$ as desired.
\end{proof}
\medskip
For the regularization $\mathfrak{C} X_0$ of a strongly semistable curve $X_0$ over $\k$, Theorem~\ref{thm:limitseriesgeneral} can be reformulated as follows.
Let $\phi: \mathcal X\rightarrow \operatorname{Spec} R$ be a regular smoothing of $X_0$ over a discrete valuation ring $R$ and let $L_\eta=(\mathcal L_\eta,H_\eta)$ be a $\mathfrak g^r_d$ over the generic fiber $\mathcal X_\eta$ of $\phi$. Consider an extension $\mathcal L$ of $L_\eta$ to $\mathcal X$, and let $\mathcal L_0$ be the restriction of $\mathcal L$ to $X_0$. Let $\mathcal D$ be a divisor on $\mathfrak{C} X_0$ in the linear equivalence class of $\pi(\mathcal L_0)$, where $\pi:\operatorname{Pic}(X_0) \rightarrow \oplus_{v\in V(G)} \operatorname{Pic}(X_v)$ is as in Section~\ref{sec:basics}. There exists a family $\mathcal H=\{H_v\}_{v\in V(G)}$ of $(r+1)$-dimensional subspaces $H_v \subset \k(X_v)$ such that $r_{\mathfrak{C} X_0, \mathcal H}(\mathcal D)=r$. In addition, $H_v$ can be explicitly constructed as follows. For any vertex $v$, choose a rational function $\mathfrak f_{v}$ on $\mathfrak{C} X_0$ such that
the divisor $\mathcal D + \div(f_{G,v})$ is $v$-reduced and let $f_{G,v}: V(G) \rightarrow \mathbb Z$ be the $\Gamma$-part of $\mathfrak f_v$.
Consider the extension $\mathcal L\,\bigl(\,\sum_v f_{G,v}(u) X_u\,\bigr) $ of $\mathcal L_\eta$ to $\mathcal X$ and let $H_{f_{G,v}}$ be the closure of $H_\eta$ in $H^0\bigl(\,\mathcal X, \mathcal L\,\bigl(\,\sum_v f_{G,v}(u) X_u\,\bigr)\,\bigr)$. Define $H_v:=H_{f_{G,v}}|_{X_v}$ and $\tau_*(L_\eta):=(\mathcal D, \mathcal H)$.
Finally, for any $v \in V$ let $\mathcal D^v$ be the $v$-reduced divisor linearly equivalent to $\mathcal D$, and define $d_v:= \mathcal D_\Gamma(v) = \deg(D^v_v)$.
\begin{thm}
\label{thm:regularlimitseries}
Let $X_0$ be a strongly semistable curve over $\k$ and $\mathfrak{C} X_0$ the regularization of $X_0$.
For any regular smoothing $\pi: X\rightarrow \operatorname{Spec} R$ of $X_0$ over a discrete valuation ring $R$, $\tau_*(L_\eta)$ as
defined above is a limit $\mathfrak g^r_d$ on $X_0$. In addition, for each vertex $v\in V(G)$ we have $H_v \subseteq H^0(X_v, \mathcal L(D^v_v))$, so that $(\mathcal L(D^v_v), H_v)$ defines a $\mathfrak g^r_{d_v}$ on the irreducible component $X_v$ of $X_0$.
\end{thm}
We conclude this section with the following strengthening of Theorem~\ref{thm:limitseriesgeneral} which will be used in \S\ref{ChabautySection}.
\begin{thm}\label{thm:limitseriesgeneral2}
Let $X$ be a smooth proper curve over $\mathbb K$, $\fX$ a strongly semistable model for $X$,
and let $\mathfrak{C} \fX$ be the metrized complex associated to $\fX$.
Let $D$ be a divisor on $X$ and set $\mathcal D = \tau^{\mathfrak{C} \fX}_*(D)$.
Let $L_\eta = (\mathcal L(D), H_\eta)$ be a $\mathfrak g^r_d$ on $X$
and let $\mathcal H = \{H_v\}_{v\in V}$ be as in the statement of Theorem~\ref{thm:limitseriesgeneral}.
Let $E^\circ$ be an effective divisor of degree $e$ supported on the smooth locus of
the special fiber of $\fX$, and define $\mathcal E^\circ = \sum_{v \in V} E^\circ_v \in \operatorname{Div}(\mathfrak{C}\fX)$,
where $E^\circ_v$ is the restriction of $E^\circ$ to $C_v$.
Suppose that $H_v \subseteq L(D_v - E^\circ_v)$ for all $v$.
Then the pair $(\mathcal D - \mathcal E^\circ, \mathcal H)$ is a limit $\mathfrak g^r_{d-e}$ on $\mathfrak{C} \fX$.
\end{thm}
\begin{proof}
In the view of Theorem~\ref{thm:f-width}, the proof is similar to the proof of
Theorem~\ref{thm:limitseriesgeneral}, by requiring each subset
$\mathcal{R}_v \subset C_v(\k) \setminus \mathcal A_v$ to be disjoint from the support of $E^\circ_v$.
For any effective divisor $\mathcal E$ of degree $r$ supported on $\mathcal{R} = \bigcup \mathcal{R}_v$,
the proof of Theorem~\ref{thm:limitseriesgeneral} shows that there exists a rational function
$\mathfrak f$ such that $\mathcal D -\mathcal E +\div(\mathfrak f) \geq 0$.
We claim that in fact $\mathcal D - \mathcal E +\div(\mathfrak f) - \mathcal E^\circ \geq 0$, which implies that
$(\mathcal D - \mathcal E^\circ, \H)$ is a limit $\mathfrak g^r_{d-e}$ on $\mathfrak{C}\fX$ as desired.
To see this, let $E^\circ_\Gamma$ be the $\Gamma$-part of $\mathcal E^\circ$ and
note that since $E^\circ_\Gamma = \sum_{v \in V} \deg(E^\circ_v) (v)$ and $\div(f_\Gamma) \geq E_\Gamma - D_\Gamma$
by hypothesis, it suffices to prove that the $C_v$-part of $\div(\mathfrak f)$ is at least the $C_v$-part of
$\mathcal E + \mathcal E^\circ - \mathcal D$ for all $v \in V$, i.e.,
\begin{equation}
\label{eq:limitseriesgeneral2}
\div(\mathfrak f)_v := \div(f_v) + \div_v(f_\Gamma) \geq E_v + E^\circ_v - D_v.
\end{equation}
If $z \in \mathrm{supp}(E^\circ_v)$, then since $\mathrm{supp}(E^\circ_v)$ is disjoint from $\mathcal A_v \supset \mathrm{supp}(\div_v(f_\Gamma))$ we have
$\div(\mathfrak f)_v(z) = \div(f_v)(z)$, and since $\mathrm{supp}(E^\circ_v)$ is disjoint from $\mathcal{R}_v \supset \mathrm{supp}(E_v)$ we have $E_v(z) = 0$.
Thus (\ref{eq:limitseriesgeneral2}) holds in this case since $H_v \subset L(D_v -E^\circ_v)$ implies that
$\div(f_v)(z) \geq E^\circ_v(z) - D_v(z)$.
On the other hand, if $z \not\in \mathrm{supp}(E^\circ_v)$, then $E^\circ_v(z)=0$ and thus (\ref{eq:limitseriesgeneral2}) holds because by assumption we have
$\div(\mathfrak f) \geq \mathcal E - \mathcal D$ and in particular $\div(\mathfrak f)_v(z) \geq E_v(z) - D_v(z)$.
Thus (\ref{eq:limitseriesgeneral2}) is valid for all $z \in C_v(\k)$ as desired.
\end{proof}
\subsection{Remarks on completion and smoothing}
Given a divisor $\mathcal D$ of degree $d$ and rank $r$ on $\mathfrak{C}$, one may ask if there exists a collection $\H = \{ H_i \}$, with $H_i$ an $(r+1)$-dimensional subspace of $\kappa(C_i)$
for all $i$, such that $r_{\mathfrak{C},\H}(\mathcal D) = r$. (Recall that we always have $r_{\mathfrak{C},\H}(\mathcal D) \leq r_{\mathfrak{C}}(\mathcal D)$.) If so, we say that $\mathcal D$ can be {\em completed to a limit $\mathfrak g^r_d$} on $\mathfrak{C}$.
Moreover, Theorem~\ref{thm:limitseriesgeneral} shows that if $X$ is a smooth proper curve over $\mathbb K$, $(D,L_\eta)$ is a $\mathfrak g^r_d$ on $X$,
and $\mathfrak{C} \fX$ is the metrized complex associated to a strongly semistable model $\fX$ for $X$, then the associated pair $(\tau^{\mathfrak{C} \fX}_*(D), \mathcal H)$
(which we call the {\em specialization} of $(\mathcal D,\H)$) is a limit $\mathfrak g^r_d$ on $\mathfrak{C} \fX$.
We say that a limit $\mathfrak g^r_d$ $(\mathcal D,\H)$ on a metrized complex $\mathfrak{C}$ over $\kappa$ is {\em smoothable} if there exists a smooth proper curve $X$ over $\mathbb K$ such that
$\mathfrak{C}=\mathfrak{C}\fX$ for some strongly semistable model $\fX$ of $X$ and $(\mathcal D,\H)$ arises the specialization of a limit $\mathfrak g^r_d$ on $X$.
Note that by \cite[Theorem 3.24]{ABBR}, every ${\rm val}(\mathbb K^*)$-rational metrized complex $\mathfrak{C}$ over $\kappa$ is of the form $\mathfrak{C}=\mathfrak{C}\fX$ for some smooth proper curve $X$ over $\mathbb K$ and some strongly semistable model $\fX$ of $X$, where {\em ${\rm val}(\mathbb K^*)$-rational} means that the edge lengths in $G$ all belong to the value group of $\mathbb K$.
\medskip
In this section, we show by example that not every divisor $\mathcal D$ of degree $d$ and rank $r$ on a metrized complex $\mathfrak{C}$ can be completed to a limit $\mathfrak g^r_d$,
and not every limit $\mathfrak g^r_d$ on a ${\rm val}(\mathbb K^*)$-rational metrized complex $\mathfrak{C}$ is smoothable.
\medskip
\begin{example}[A degree $d$ rank $r$ divisor which cannot be completed to a limit $\mathfrak g^r_d$]
\label{ex:NotCompletable}
Consider the weighted graph $\Gamma$ depicted in
Figure~\ref{fig:nog12} (with arbitrary edge lengths),
and let $\mathfrak{C}$ be a metrized complex whose underlying weighted metric graph is $\Gamma$
(so each $C_{v_i}$ has genus $1$ and $C_v$ has genus $0$).
For any point $p$ in $C_v \simeq \mathbb P^1$, consider the degree $2$ divisor $\mathcal D = 2(p)$.
We claim that $\mathcal D$ has rank $1$ on $\mathfrak{C}$ but cannot be completed to a limit $\mathfrak g^1_2$.
The fact that $\mathcal D$ has rank $1$ is straightforward and left to the reader.
Assume for the sake of contradiction that there exists a limit $\mathfrak g^1_2$
$(\H, \mathcal D)$ on $\mathfrak{C}$. Let $x_1, x_2, x_3$ (resp. $y_1,y_2,y_3$) be the points of
$C_v = \mathbb P^1$ (resp. $C_i := C_{v_i}$) corresponding to the three edges of $\Gamma$. Fix $i \in \{ 1,2,3 \}$, choose a point $q_i \neq y_i$ in $C_i$ and let $\mathcal E = (q_i)$. For any rational function $\mathfrak f$ on $\mathfrak{C}$ such that $\mathcal D - \mathcal E + \div(\mathfrak f) \geq 0$, the fact that $C_i$ has genus one
implies that $\div_{v_i}(f_\Gamma) \geq 2(y_i)$, since there is no rational function on $C_i$ whose divisor is $(q_i)-(y_i)$.
Therefore $\div(f_\Gamma) = 2(v_i) - 2(v)$. Restricting $\mathfrak f$ to $C_v$ gives a rational function $f_i$ on $C_v$ with
$\div(f_i) = 2(x_i) - 2(p)$. Since $(\H, \mathcal D)$ is by assumption a limit $\mathfrak g^1_2$, we must have $f_1,f_2,f_3 \in H_v$.
But a simple calculation shows that the $f_i$ are linearly independent, implying that $\dim_\k (H_v) \geq 3$, a contradiction.
\end{example}
\begin{figure}[!tb]
\scalebox{.48}{\input{nog12.pdf_t}}
\caption{A weighted metric graph underlying a metrized complex possessing a degree $2$ rank $1$ divisor which
cannot be completed to a limit $\mathfrak g^1_2$.}
\label{fig:nog12}
\end{figure}
\begin{remark}
Suppose the residue field $\kappa$ of $\mathbb K$ has characteristic different from $2$.
Then there exists a metrized complex $\mathfrak{C}$ over $\kappa$ (with all curves $C_v$ isomorphic to $\mathbb P^1$)
and a divisor $\mathcal D$ of degree 2 and rank 1 on $\mathfrak{C}$ which cannot be completed to a limit $\mathfrak g^1_2$.
Indeed, any hyperelliptic metric graph which cannot be realized as the skeleton of a hyperelliptic curve over $\mathbb K$ provides an example of this phenomenon
(and one can construct many examples of such metric graphs, using the characterization of those hyperelliptic metric graphs which can be lifted to a hyperelliptic curve over $\mathbb K$ given in~\cite{caporaso-gonality} and~\cite{ABBR}.)
Here is a sketch of the argument. It is not difficult to show that
a limit $\mathfrak g^1_2$ on a metrized complex $\mathfrak{C}$ gives rise, in a natural way,
to a finite harmonic morphism of degree two (in the terminology of~\cite[Definition 2.22]{ABBR})
from $\mathfrak{C}$ to a metrized complex of genus zero . By the lifting result \cite[Corollary 1.5]{ABBR},
such a finite harmonic morphism can be lifted to a
degree two map from a smooth proper curve $X/\mathbb K$ with associated metrized complex $\mathfrak{C}$
to $\mathbb P^1$, which implies that the underlying metric graph of $\mathfrak{C}$ is the skeleton of a hyperelliptic curve over $\mathbb K$.
\end{remark}
\begin{example}[A limit $\mathfrak g^r_d$ which is not smoothable]
\label{ex:NotSmoothable}
This phenomenon occurs already in the compact type case: the original paper of Eisenbud-Harris on limit linear series \cite{EH86}
provides an example (Example 3.2 of {\it loc.~cit.}) of a limit $\mathfrak g^2_4$ which cannot be smoothed; we recall their example here.
The metrized complex $\mathfrak{C}$ in question is associated to a semistable curve $X_0$ with two components meeting transversely at a point $p$; one of the
components is a hyperelliptic curve $Y$ of genus at least $4$ and the other component $Z$ has genus zero. The point $p$ is a ramification point of the
$\mathfrak g^1_2$ on $Y$, and without loss of generality we may assume that $p$ corresponds to the point $0$ on $\mathbb{P}^1 \cong Z$.
The dual graph $G$ of $X_0$ has two vertices $v_Y$ and $v_Z$ connected by a single edge, which may take to be of length one in $\Gamma$.
Now define a divisor $\mathcal D$ on $\mathfrak{C}$ by setting $\mathcal D = 4(\infty)$ for the point
$\infty\in \mathbb P^1 \simeq Z$.
If we define $\H = \{ H_Y,H_Z \}$, where $H_Y = H^0(Y,4(p))$ and $H_Z$ is the span of $1,t^2+t^3,t^4$ (with $t$ a local parameter at $0$ on $\mathbb{P}^1$),
then by \cite[Example 3.2]{EH86} and Theorem~\ref{thm:limitseries} above, the pair
$(\mathcal D,\H)$ defines a limit $\mathfrak g^2_4$ on $\mathfrak{C}$. (It is also not hard to show this directly using our definitions.)
This limit $\mathfrak g^2_4$ cannot be smoothed.
\end{example}
\subsection{Application to bounding the number of rational points on curves}
\label{ChabautySection}
In this section, we explain how limit linear series on
metrized complexes of curves can be used to illuminate the proof of a recent theorem due
to E. Katz and D. Zureick-Brown \cite{KZB} and put it into a broader context.
\medskip
Let $K$ be a number field and suppose $X$ is a smooth, proper,
geometrically integral curve over $K$ of genus $g \geq 2$.
Let $J$ be the Jacobian of $X$, which is an abelian variety of dimension $g$ defined over $K$.
If the Mordell-Weil rank $r$ of $J(K)$ is less than $g$,
Coleman \cite{Co} adapted an old method of Chabauty to prove that if
$p>2g$ is a prime which is unramified in $K$ and $\mathfrak{p}$ is a prime of
good reduction for $X$ lying over $p$, then $\# X(K) \leq \# \bar{X}({\mathbf F}_{\mathfrak p}) + 2g - 2$.
Here $\bar{X}$ denotes the special fiber of a smooth proper model for $X$ over the completion ${\mathcal O}_{\mathfrak p}$ of ${\mathcal O}_K$ at $\mathfrak{p}$ and ${\mathbf F}_{\mathfrak p} = {\mathcal O}_K / \mathfrak{p}$.
Stoll \cite{St} improved this bound by replacing $2g-2$ with $2r$. Lorenzini and Tucker \cite{LT} (see also \cite{MP})
proved the same bound as Coleman without
assuming that $X$ has good reduction at $\mathfrak{p}$; in their bound, $\bar{X}({\mathbf F}_{\mathfrak p})$ is replaced by $\bar{\mathfrak X}^{\rm sm}({\mathbf F}_{\mathfrak p})$
where ${\mathfrak X}$ is a proper regular model for $X$ over ${\mathcal O}_{\mathfrak p}$ and $\bar{\mathfrak X}^{\rm sm}$ is the smooth locus of the special fiber of ${\mathfrak X}$.
Katz and Zureick-Brown combine the improvements of Stoll and Lorenzini-Tucker by proving:
\begin{thm}
\label{thm:Katz-ZB}
Let $K$ be a number field and suppose $X$ is a smooth, proper, geometrically integral curve over $K$ of genus $g \geq 2$.
Suppose the Mordell-Weil rank $r$ of $J(K)$ is less than $g$, and that $p>2g$ is a prime which is unramified in $K$.
Let $\mathfrak{p}$ be a prime of ${\mathcal O}_K$ lying over $p$ and let ${\mathfrak X}$ be a proper regular model for $X$ over ${\mathcal O}_{\mathfrak p}$.
Then
\[
\# X(K) \leq \# \bar{\mathfrak X}^{\rm sm}({\mathbf F}_{\mathfrak p}) + 2r.
\]
\end{thm}
In order to explain the main new idea in the paper of Katz and Zureick-Brown, we first quickly recall the basic arguments used by Coleman, Stoll, and Lorenzini-Tucker.
(See \cite{MP} for a highly readable and more detailed overview.)
Assume first that we are in the setting of Coleman's paper, so that $r < g$, $p>2g$ is a prime which is unramified in $K$, and $X$ has good reduction at the prime ${\mathfrak p}$ lying over $p$.
Fix a rational point $P \in X(K)$ (if there is no such point, we are already done!).
Coleman associates to each regular differential $\omega$ on $X$ over $K_{{\mathfrak p}}$ (the ${\mathfrak p}$-adic completion of $K$)
a ``definite $p$-adic integral'' $\int_P^Q \omega \in K_{{\mathfrak p}}$. If $V_{\rm chab}$ denotes the vector space of all $\omega$ such that
$\int_P^Q \omega = 0$ for all $Q \in X(K)$, Coleman shows that ${\rm dim} V_{\rm chab} \geq g-r > 0$.
Locally, $p$-adic integrals are obtained by formally integrating a power series expansion for $\omega$ with respect to a local parameter.
Using this observation and an elementary Newton polygon argument, Coleman proves that
\[
\# X(K) \leq \sum_{\widetilde{Q} \in \bar{X}({\mathbf F}_{\mathfrak p})} \left( 1 + n_{\widetilde{Q}} \right),
\]
where $n_{\widetilde{Q}}$ is the minimum over all nonzero $\omega$ in $V_{\rm chab}$ of
${\rm ord}_{\widetilde{Q}} \widetilde{\omega}$; here $\widetilde{\omega}$ denotes the reduction of a suitable rescaling $c \omega$ of $\omega$ to $\bar{X}$,
where the scaling factor is chosen so that $c \omega$ is regular and non-vanishing along the special fiber $\bar{X}$.
If we choose any nonzero $\omega \in V_{\rm chab}$,
then the fact that the canonical divisor class on $\bar{X}$ has degree $2g-2$ gives
\[
\sum_{\widetilde{Q} \in \bar{X}({\mathbf F}_{\mathfrak p})} n_{\widetilde{Q}} \leq \sum_{\widetilde{Q} \in \bar{X}({\mathbf F}_{\mathfrak p})} {\rm ord}_{\widetilde{Q}} \widetilde{\omega}
\leq 2g - 2,
\]
which yields Coleman's bound.
\medskip
Stoll observed that one could do better than this by adapting the differential $\omega$ to the point $\widetilde{Q}$ rather than using the
same differential $\omega$ on all residue classes.
Define the {\it Chabauty divisor}
\[
D_{\rm chab} = \sum_{\widetilde{Q} \in \bar{X}({\mathbf F}_{\mathfrak p})} n_{\widetilde{Q}} (\widetilde{Q}).
\]
Then $D_{\rm chab}$ and $K_{\bar{X}} - D_{\rm chab}$ are both equivalent to effective divisors, so by Clifford's inequality (applied to the smooth proper curve $\bar{X}$)
we have $r(D_{\rm chab}) := h^0(D_{\rm chab}) - 1 \leq \frac{1}{2} {\rm deg} (D_{\rm chab})$.
On the other hand, by the semicontinuity of $h^0$ under specialization we have $h^0(D_{\rm chab}) \geq {\rm dim} V_{\rm chab} \geq g-r$.
Combining these inequalities gives
\[
\sum_{\widetilde{Q} \in \bar{X}({\mathbf F}_{\mathfrak p})} n_{\widetilde{Q}} \leq 2r
\]
which leads to Stoll's refinement of Coleman's bound.
\medskip
Lorenzini and Tucker observed that one can generalize Coleman's bound to the case of bad reduction as follows.
Let ${\mathfrak X}$ be a proper regular model for $X$ over ${\mathcal O}_{\mathfrak p}$ and note that points of $X(K)$ specialize to
$\bar{\mathfrak X}^{\rm sm}({\mathbf F}_{\mathfrak p})$.
One obtains by a similar argument the bound
\begin{equation}
\label{eq:LTinequality}
\# X(K) \leq \sum_{\widetilde{Q} \in \bar{\mathfrak X}^{\rm sm}({\mathbf F}_{\mathfrak p})} \left( 1 + n_{\widetilde{Q}} \right),
\end{equation}
where $n_{\widetilde{Q}}$ is the minimum over all nonzero $\omega$ in $V_{\rm chab}$ of
${\rm ord}_{\widetilde{Q}} \widetilde{\omega}$; here $\widetilde{\omega}$ denotes the reduction of (a suitable rescaling of) $\omega$ to the unique irreducible component of the special
fiber of ${\mathfrak X}$ containing $\widetilde{Q}$ and ${\rm dim} V_{\rm chab} \geq g-r > 0$ as before.
Choosing a nonzero $\omega \in V_{\rm chab}$ as in Coleman's bound, the fact that the relative dualizing sheaf for ${\mathfrak X}$ has degree $2g-2$
gives the Lorenzini-Tucker bound.
\medskip
In order to combine the bounds of Stoll and Lorenzini-Tucker, we see that it is natural to form the Chabauty divisor
\[
D_{\rm chab} = \sum_{\widetilde{Q} \in \bar{\mathfrak X}^{\rm sm}({\mathbf F}_{\mathfrak p})} n_{\widetilde{Q}} (\widetilde{Q})
\]
and try to prove, using some version of semicontinuity of $h^0$ and Clifford's inequality, that its degree is at most $2r$.
This is the main technical innovation of Katz and Zureick-Brown, so we state it as a theorem:
\begin{thm}[Katz--Zureick-Brown]
\label{thm:Katz-ZB_Degree_Bound}
The degree of $D_{\rm chab}$ is at most $2r$.
\end{thm}
Combining Theorem~\ref{thm:Katz-ZB_Degree_Bound} with \eqref{eq:LTinequality} yields Theorem~\ref{thm:Katz-ZB}.
As noted by Katz and Zureick-Brown, if one makes a base change from $K_{{\mathfrak p}}$ to an extension field $K'$ over which there is a regular semistable model ${\mathfrak X'}$ for $X$ dominating the base change of ${\mathfrak X}$,
then the corresponding Chabauty divisors satisfy $D'_{\rm chab} \geq D_{\rm chab}$.
(Here $D'_{\rm chab}$ is defined relative to the $K'$-vector space $V'_{\rm chab} = V_{\rm chab} \otimes_K K'$; one does not want to look at the Mordell-Weil group of $J$ over extensions of $K$.)
In order to prove Theorem~\ref{thm:Katz-ZB_Degree_Bound}, we may therefore assume that $\mathfrak X$ is a regular semistable model for $X$ (and also that the residue field of $K'$ is algebraically closed).
\medskip
Let $d={\rm deg}(D_{\rm chab})$.
We now explain how to prove that $d \leq 2r$ when $\mathfrak X$ is a semistable regular model using limit linear series on metrized complexes of curves.
Our proof is different from (and arguably streamlined than) the one given in \cite{KZB}.
\begin{proof}[Proof of Theorem~\ref{thm:Katz-ZB_Degree_Bound}]
Let $s = \dim_{K'} V'_{\rm chab} - 1 \geq g-r-1 \geq 0$. We can identify $V'_{\rm chab}$ with an $(s+1)$-dimensional space $W$ of rational functions on $X$ in the usual way by identifying $H^0(X,\Omega^1_X)$ with
$L(K_X) = \{ f \; : \; {\rm div}(f) + K_X \geq 0 \}$ for a canonical divisor $K_X$ on $X$.
The divisor $D_{\rm chab}$ on $\bar{\mathfrak X}^{\rm sm}$ defines in a natural way a divisor $\mathcal D = \sum_v D_v$ of degree $d$ on the metrized complex $\mathfrak{C}\mathfrak X$ associated to $\mathfrak X$, where $D_v$ is the restriction of $D_{\rm chab}$ to $C_v$.
We promote the divisor $K_{\mathfrak{C}\mathfrak X} - \mathcal D$ to a limit linear series
$\mathcal L = (K_{\mathfrak{C}\mathfrak X} - \mathcal D, \{ H_v \})$ on $\mathfrak{C}\mathfrak X$ by defining $H_v$ to be the reduction of $W$ to $C_v$ for each $v \in V(G)$.
By the definition of $D_{\rm chab}$, each element of $H_v$ vanishes to order at least $n_{\widetilde{Q}}$ at each point $\widetilde{Q}$ in ${\rm supp}(D_v)$.
By Corollary~\ref{cor:introcanonspec} and Theorem~\ref{thm:limitseriesgeneral2}, $\mathcal L$ is a limit $\mathfrak g^{s}_{2g-2-d}$ on $\mathfrak{C}\mathfrak X$.
In particular, we must have $r_{\mathfrak{C}\mathfrak X}(K_{\mathfrak{C}\mathfrak X} - \mathcal D) \geq g-r-1$.
On the other hand, Clifford's inequality for metrized complexes (Theorem~\ref{thm:MCClifford}) implies that
$r_{\mathfrak{C}\mathfrak X}(K_{\mathfrak{C}\mathfrak X} - \mathcal D) \leq \frac{1}{2}(2g-2-d)$.
Combining these inequalities gives $d \leq 2r$ as desired.
\end{proof}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 6,425 |
\section{Introduction} \label{sec:introduction}
We consider the stationary incompressible Newtonian Navier--Stokes equations:
given a bounded Lipschitz domain $\Omega \subset \mathbb{R}^d$, $d \in \{2,
3\}$, find $(u, p) \in \ensuremath{{H}^1(\Omega; \mathbb{R}^d)}\xspace \times Q$ such that
\begin{subequations} \label{eqn:ns}
\begin{alignat}{2}
- \nabla\cdot2\nu\eps{u} + \advect{u}{u} + \nabla p &= f \quad && \text{ in } \Omega, \label{eqn:momentum} \\
\nabla \cdot u &= 0 \quad && \text{ in } \Omega, \\
u &= g \quad && \text{ on } \Gamma_D, \\
2\nu \eps{u} \cdot n &= pn \quad && \text{ on } \Gamma_N,
\end{alignat}
\end{subequations}
where $\eps{u} = \frac{1}{2}(\nabla u + \nabla u^T)$, $\nu >0$ is the kinematic viscosity, $f \in \ensuremath{{L}^2(\Omega; \mathbb{R}^d)}\xspace$, $n$ is the outward-facing unit normal to $\partial
\Omega$, $\Gamma_D$ and $\Gamma_N$ are disjoint with $\Gamma_D \cup \Gamma_N =
\partial \Omega$, and $g \in H^{1/2}(\Gamma_D; \mathbb{R}^d)$. If $|\Gamma_N| > 0$, then
a suitable trial space for the pressure is $Q := \ensuremath{{L}^2(\Omega)}\xspace$; if $|\Gamma_N| = 0$,
then the pressure is only defined up to an additive constant and $Q :=
L^2_0(\Omega)$ is used instead. The Reynolds number, defined as $\Re = \frac{UL}{\nu}$ where $U$ is the characteristic
velocity and $L$ is the characteristic length scale of the flow, is an important dimensionless number governing
the nature of the flow.
The Navier--Stokes
equations are of enormous practical importance in science and
industry, but are very difficult to solve, especially for
large Reynolds number.
The importance of these equations has motivated a great deal of
research on algorithms for their solution; for a general overview of the field,
see the textbooks of Turek \cite{turek1999}, Elman, Silvester \& Wathen
\cite{elman2014}, or Brandt \cite{brandt2011}.
After Newton linearization and a suitable spatial discretization of
\eqref{eqn:ns},
nonsymmetric linear systems of saddle point type must be solved:
\begin{equation} \label{eqn:sp}
\begin{pmatrix}
A & B^T \\
B & 0
\end{pmatrix}
\begin{pmatrix}
\delta u \\ \delta p
\end{pmatrix}
=
\begin{pmatrix}
b \\ c
\end{pmatrix},
\end{equation}
where $A$ is the discrete linearized momentum operator, $B^T$ is the discrete gradient
operator, $B$ is the discrete divergence operator, and $\delta u$ and $\delta p$
are the updates to the coefficients for velocity and pressure respectively. One
strategy to solve these systems is to employ a monolithic multigrid iteration on
the entire system with a suitable coupled relaxation method, such as the algorithms of
Vanka \cite{vanka1986} or Braess \& Sarazin \cite{braess1997}. Vanka iteration
works well for moderate Reynolds numbers \cite{turek1999}, but the iteration
counts have been observed to increase significantly once the Reynolds number
becomes large \cite{benzi2006}.
An alternative approach to solving \eqref{eqn:sp} is to build
preconditioners based on block factorizations
\cite{murphy2000,ipsen2001,benzi2005,elman2014,wathen2015}. This strategy can be grounded
in an insightful
functional analytic framework that guides the development of solvers whose
convergence is independent of parameter values and mesh size $h$, at least in the case where
\eqref{eqn:sp} is symmetric \cite{mardal2011}. Block Gaussian elimination reduces the problem of solving the coupled
linear system to that of solving smaller separate linear systems involving the
matrix $A$ and the Schur complement $S = -B A^{-1} B^T$. If a fast solver is
available for $A$, the main difficulty is solving linear systems involving $S$,
as this matrix is generally dense and cannot be stored explicitly for large
problems. Tractable approximations $\tilde{S}^{-1}$ to $S^{-1}$ must be devised
on a PDE-specific basis.
For the Stokes equations, the Schur complement is spectrally equivalent to the
viscosity-weighted pressure mass matrix \cite{silvester1994}. For the
Navier--Stokes equations this choice yields mesh-independent convergence and is
effective for very small Reynolds numbers, but the convergence deteriorates badly with Reynolds
number \cite{elman1996,elman2014}. The pressure convection-diffusion (PCD)
approach \cite{kay2002} constructs an auxiliary convection-diffusion operator on
the pressure space, and hypothesizes that a certain commutator is small. This
yields an approximation to the Schur complement inverse that involves the
inverse of the Laplacian on the pressure space, the application of the
auxiliary convection-diffusion operator, and the inverse of the pressure mass matrix. The
least-squares commutator (LSC) approach \cite{elman2006} is based on a similar
idea, but derives the commutator algebraically. Both of these
approaches perform well for moderate Reynolds numbers. Numerical experiments
comparing the performance of our approach to these algorithms are provided
in section \ref{sec:numerical}.
In 2006, Benzi \& Olshanskii proposed an augmented Lagrangian approach for
controlling the Schur complement of \eqref{eqn:sp}
\cite{olshanskii2003,benzi2006,olshanskii2008,benzi2011b,fortin1983,kobelkov1995}. The
idea, referred to as grad-div stabilization, is to introduce an additional term in
the equations that does not change the continuous solution, but does modify the
Schur complement. The continuous form of the stabilization replaces
\eqref{eqn:momentum} with
\begin{alignat}{2} \label{eqn:nsal}
- \nabla\cdot2\nu\eps{u} + \advect{u}{u} + \nabla p - \gamma \nabla \nabla \cdot u &= f \quad && \text{ in } \Omega,
\end{alignat}
for $\gamma > 0$.
As $\nabla \cdot u = 0$, the solutions of \eqref{eqn:nsal} and
\eqref{eqn:momentum} are the same. The discrete variant of this approach
replaces \eqref{eqn:sp} with
\begin{equation} \label{eqn:spal}
\begin{pmatrix}
A + \gamma B^T M_p^{-1} B & B^T \\
B & 0
\end{pmatrix}
\begin{pmatrix}
\delta u \\ \delta p
\end{pmatrix}
=
\begin{pmatrix}
b + \gamma B^T M_p^{-1} c \\ c
\end{pmatrix},
\end{equation}
where $M_p$ is the pressure mass matrix. This modified system has the same discrete solutions as \eqref{eqn:sp}, as $B\delta u = 0$.
With either variant, for $\gamma$ not too small, the Schur
complement inverse is well approximated by
\begin{equation} \label{eqn:schur}
S^{-1} \approx -(\nu + \gamma) M_p^{-1},
\end{equation}
where $M_p$ is the pressure mass matrix. This approximation improves
as $\gamma$ increases (section \ref{sec:augmentedlagrangian}). In either case, we denote the discretized augmented
momentum block as $A_\gamma$.
\begin{remark}
The continuous form of the grad-div stabilization has some further
appealing characteristics. For example, it significantly improves
the pressure-robustness of discretizations where the
incompressibility constraint is not enforced pointwise
\cite{olshanskii2003,heister2012,john2017}. It also arises in other
contexts in the numerical analysis of \eqref{eqn:ns}. For example,
Boffi \& Lovadina \cite{boffi1997} showed that the addition of the
term $h^{-1/2} (\nabla \cdot u, \nabla \cdot v)_{\ensuremath{{L}^2(\Omega)}\xspace}$ to the weak
form of the \ensuremath{[\mathbb{P}_2]^2\mathrm{-}\mathbb{P}_0}\xspace discretization of \eqref{eqn:ns} improves its
convergence order. It also arises in the iterated penalty
\cite{temam1968,brenner2008} and artificial compressibility
\cite{chorin1967} methods for the Stokes and Navier--Stokes
equations.
\end{remark}
The tradeoff with either variant of this approach is that developing fast
solvers for $A_\gamma$ becomes significantly more difficult.
The divergence operator has a large kernel (the range of the curl operator) and
hence standard multigrid relaxation methods are ineffective.
A key insight of Benzi \& Olshanskii was that a specialized multigrid algorithm
could be built for $A_\gamma$ \cite{benzi2006,olshanskii2008} by applying the seminal work of Sch\"oberl
\cite{schoberl1999}. The algorithm combines four
ingredients, each of which is crucial to the effectiveness of the method: (i)
the discrete variant of the grad-div stabilization; (ii) streamline-upwind
Petrov-Galerkin (SUPG) stabilization of the advective term; (iii) a multigrid
relaxation that effectively treats errors in the kernel of the discrete
divergence term; (iv) a specialized prolongation operator whose continuity
constant is independent of $\gamma$ and $\nu$. This scheme exhibits outer
iteration counts that grow only very slowly with Reynolds number
\cite{benzi2006}. However, it is described as difficult to implement
\cite{hamilton2010,benzi2011}, and so most of the works that use
grad-div stabilization and the Schur complement approximation \eqref{eqn:schur}
employ either matrix factorization as the inner solver
\cite{deniet2007,urrehman2008,borm2010,he2011,heister2012} or a block-triangular
approximation to $A_\gamma$ \cite{benzi2011,hamilton2010,benzi2011b, he2018}. This block-triangular
approximation decouples linear systems involving $A_\gamma$ into $d$ scalar anisotropic
advection--diffusion problems, which may be solved with algebraic multigrid
techniques. However, this simplicity comes at a price; the scheme is much more
sensitive to the choice of $\gamma$, and its convergence deteriorates somewhat
as the Reynolds number increases \cite{benzi2011}.
The main contribution of this paper is the extension of the robust multigrid scheme for
the inner velocity problem arising in the augmented Lagrangian preconditioner to
three dimensions. The previous work of Benzi \& Olshanskii only considered the
case $d=2$. While the same general strategy applies in three dimensions, the extension
is nontrivial: if the finite elements used in \cite{schoberl1999,benzi2006}
are applied in three dimensions, the prolongation operator involves the
solution of ill-posed local problems. We propose appropriate finite element
discretizations and matching prolongation operators that exhibit Reynolds-robust
iteration counts in three dimensions.
A second contribution is the release of an open-source parallel implementation of the
solver in two and three dimensions, built on Firedrake \cite{rathgeber2016} and PETSc \cite{balay2017}.
This has required substantial modifications to Firedrake, PETSc,
UFL \cite{alnaes2012} and TSFC \cite{homolya2017}, as well as minor
developments in FIAT \cite{kirby2004}. The solver heavily relies on and
extends the solver infrastructure developed in \cite{kirby2018},
enabling easy composition and nesting of preconditioners in PETSc and
Firedrake. To express the local solves involved in the
relaxation and prolongation operator, we have developed a new
preconditioner in PETSc that allows for the simple expression of
general additive subspace correction methods. For example, the same code
that does patchwise relaxation can be used to formulate line
smoothers, plane smoothers, or Vanka iteration, and we expect that it
will be of substantial interest for other applications as well.
The remainder of the paper is laid out as follows. The discretization
and the grad-div stabilization are described in section
\ref{sec:discretization}. The augmented Lagrangian approach is
explained in section \ref{sec:augmentedlagrangian}. The multigrid
cycle for the augmented momentum block is described in section
\ref{sec:solvingmomentum}. Numerical experiments analyzing its
performance and comparing it to PCD and LSC are reported in section
\ref{sec:numerical}. Finally, conclusions and prospects for future
improvements are given in section \ref{sec:conclusions}.
\section{Formulation and discretization} \label{sec:discretization}
For boundary data $g \in H^{1/2}(\Gamma_D)$, let
\begin{equation}
V_g = \{v \in H^1(\Omega; \mathbb{R}^d) : \left. v \right|_{\Gamma_D} = g \}.
\end{equation}
The initial weak form of \eqref{eqn:ns} is: find $(u, p) \in V_g \times Q$ such that
\begin{equation}
\int_\Omega 2\nu\eps{u}: \nabla v \ \mathrm{d}x + \int_\Omega \advect{u}{u} \cdot v \ \mathrm{d}x - \int_\Omega p \nabla \cdot v \ \mathrm{d}x - \int_\Omega q \nabla \cdot u \ \mathrm{d}x = \int_\Omega f \cdot v \ \mathrm{d}x,
\end{equation}
for all $(v, q) \in V_0 \times Q$.
This will be extended before discretization in two ways. The first is a consistent SUPG stabilization; it is well
known that straightforward Galerkin discretizations of advection-dominated problems are
oscillatory \cite{brooks1982,turek1999,quarteroni2008,elman2014}. In addition,
it is widely observed that mesh-dependent SUPG stabilization is highly advantageous for multigrid
smoothers on advection-dominated problems \cite{ramage1999,turek1999}. The strong form
of the momentum residual is given by
\begin{equation}
\mathcal{L}(u, p) = - \nabla \cdot 2\nu\eps{u} + \advect{u}{u} + \nabla p - f
\end{equation}
and the following term is added to the weak form:
\begin{equation}
\int_\Omega \delta(u) \mathcal{L}(u, p) \cdot \big(\advect{v}{u}\big) \ \mathrm{d}x.
\end{equation}
Here $\delta(u)$ is a weighting function that should be small in regions where
the flow is well-resolved and large where stabilization is necessary.
The particular form employed in this work is
\begin{equation}
\delta(u) = \delta_d \left( \frac{4 \|u\|^2}{h^2} + \frac{144\nu^2}{h^4} \right)^{-1/2},
\end{equation}
with $\delta_d = 1$ in two dimensions and $\delta_d = 1/20$ in three dimensions.
To the best of our knowledge this form was first suggested in
\cite[eq.~(3.58)]{shakib1991}. It is important to take account of the dependence of
$\delta$ on the (unknown) solution $u$ when taking the derivatives required by
Newton's method; in this work, these derivatives are calculated automatically
and symbolically by the Unified Form Language \cite{alnaes2012}.
The second modification is the augmented Lagrangian term described
above in \eqref{eqn:nsal} and \eqref{eqn:spal}. If the
continuous variant is employed, the term
\begin{equation} \label{eqn:ctsgraddiv}
\gamma \int_\Omega \nabla \cdot u \, \nabla \cdot v \ \mathrm{d}x
\end{equation}
is added to the weak form, while if the discrete variant is employed, the term
\begin{equation} \label{eqn:disgraddiv}
\gamma \int_\Omega \big(\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u\big) \nabla \cdot v \ \mathrm{d}x
\end{equation}
is added instead, where $\ensuremath{\mathrm{P}_{Q_h}}: L^2(\Omega) \to Q_h$ is the projection operator onto the discrete
pressure space $Q_h$.
The continuous grad-div stabilization changes the discrete solution
computed if the discrete velocity $u_h$ does not satisfy $\nabla \cdot
u_h = 0$ pointwise,
whereas the discrete variant does not.
The effect of the continuous approach is to penalize $\|\nabla \cdot
u_h\|_{L^2(\Omega)}$ and thereby improve the discrete enforcement of the
incompressibility constraint \cite{olshanskii2003,heister2012,john2017}.
Nevertheless, in this work we use the discrete variant \eqref{eqn:disgraddiv}.
The reason for this is that the kernel of $\ensuremath{\mathrm{P}_{Q_h}} \mathrm{div}$ is much more
straightforward to characterize than the kernel of $\mathrm{div}$ if
$Q_h$ is chosen to be the space of piecewise constants:
\begin{equation}
Q_h(\ensuremath{\mathcal{M}}\xspace) = \{q \in L^2(\Omega) : \left.q\right|_K \in \mathbb{P}_0(K) \ \forall K \ \in \ensuremath{\mathcal{M}}\xspace\},
\end{equation}
where $\ensuremath{\mathcal{M}}\xspace$ is a simplicial mesh of the domain $\Omega$.
By the divergence theorem,
$u_h \in \mathrm{ker}(\ensuremath{\mathrm{P}_{Q_h}}
\mathrm{div})$ if and only if for any $K \in \ensuremath{\mathcal{M}}\xspace$, $u_h$ satisfies
\begin{equation}
\int_{\partial K} \! u_h \cdot n \ \mathrm{d}s = 0.
\end{equation}
This characterization will be extremely useful for dealing with errors in the
kernel in the multigrid relaxation, as it ensures that the kernel is spanned
by basis functions with local support \cite[\S VI.8]{brezzi1991}. Note also that this choice of $Q_h$ removes
the dependency of $\mathcal{L}$ on $p$ (as $\nabla p$ is zero on each element),
thereby eliminating any extra contribution to the top-right block of the linearized
system to be solved, thus preserving the symmetry between the top-right and bottom-left
blocks of the matrix.
After these modifications, the final discrete weak form to be solved is:
find $(u, p) \in \big(V_h \cap V_g\big) \times \big(Q_h \cap
Q\big)$ such that
\begin{align}
& \ \int_\Omega 2\nu\eps{u} : \nabla v \ \mathrm{d}x + \int_\Omega \advect{u}{u} \cdot v\ \mathrm{d}x \nonumber
+ \int_\Omega \delta(u) \mathcal{L}(u) \cdot \big(\advect{v}{u}\big) \ \mathrm{d}x \nonumber\\
& + \gamma \int_\Omega \big(\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u\big) \nabla \cdot v \ \mathrm{d}x
- \int_\Omega p \nabla \cdot v \ \mathrm{d}x - \int_\Omega q \nabla \cdot u \ \mathrm{d}x =
\int_\Omega f \cdot v \ \mathrm{d}x, \label{eqn:finalweak}
\end{align}
for all $(v, q) \in \big(V_h \cap V_0\big) \times \big(Q_h \cap Q\big)$, with
the choice of $V_h$ to be discussed below.
\subsection{Choice of velocity space}
\label{sec:velocityspace}
We now turn our attention to choosing an appropriate space for the discrete
velocities. Define the space $V_h(\ensuremath{\mathcal{M}}\xspace)$ used for the velocity as
\begin{equation}
V_h(\ensuremath{\mathcal{M}}\xspace) = \{ v \in H^1(\Omega) : \left.v\right|_K \in \ensuremath{\mathbb{P}_v}\xspace(K) \ \forall \ K \in \ensuremath{\mathcal{M}}\xspace \},
\end{equation}
for some choice of $\ensuremath{\mathbb{P}_v}\xspace(K)$. The first condition on $\ensuremath{\mathbb{P}_v}\xspace(K)$ is that $V_h$ must
be inf-sup stable when combined with $Q_h$ for the pressure. Unfortunately,
both in two and in three dimensions, the $[\mathbb{P}_1]^d-\mathbb{P}_0$ element
combining piecewise linear functions for the velocity space together with
piecewise constants for the pressure does not satisfy the inf-sup condition on general meshes.
This means that the velocity space needs to be enriched, with the resulting
element pairs (e.g.~$\ensuremath{[\mathbb{P}_2]^2\mathrm{-}\mathbb{P}_0}\xspace$ and $\ensuremath{[\mathbb{P}_3]^3\mathrm{-}\mathbb{P}_0}\xspace$) exhibiting a suboptimal
convergence rate.
In \cite{benzi2006} the element pair
$[\mathbb{P}_1\text{iso}\,\mathbb{P}_2]^2\mathrm{-}\mathbb{P}_0$ is
used, which is obtained by considering a $[\mathbb{P}_1]^2$ element on
a once refined mesh for the velocity. This element has the same
number of degrees of freedom as $[\ensuremath{\mathbb{P}_2}\xspace]^2\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$.
Neither $[\ensuremath{\mathbb{P}_2}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ nor $[\mathbb{P}_1\text{iso}\,\ensuremath{\mathbb{P}_2}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$
are inf-sup stable on a single regularly refined tetrahedron,
which as we shall see in
section~\ref{sec:prolongation} is crucial for the effectiveness of the
preconditioner. They are missing degrees of freedom on the facets of the
tetrahedra which are necessary to stabilize the jump of the pressure
field.
Increasing the degree of the velocity space to piecewise cubic
polynomials, i.e.~choosing the element pair
$[\ensuremath{\mathbb{P}_3}\xspace]^3\mathrm{-}\mathbb{P}_0$, introduces additional degrees of
freedom on the facets and results in a stable element pair. However, this
element is extremely expensive while being suboptimal by two orders for the
velocity. Alternatively, Bernardi \& Raugel \cite{bernardi1985, bernardi1985b} suggest enriching the
piecewise linear velocity space with bubble functions on each facet\footnote{The bubble
function on each facet is the product of the barycentric coordinates that are nonzero on that facet.}. While it
is only necessary to add a single bubble function for the normal
component of the velocity on each facet, this adds significant complexity to the implementation
as these functions are not affine equivalent; they require a Piola transform
to preserve the normal orientation. This means that the basis functions
associated with vertices and those associated with facets need to be
pulled-back differently, complicating the implementation. For this reason
we choose instead to enrich the space with facet bubbles for all three components of the velocity,
obtaining the $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element. As can be seen in
Figure~\ref{fig:elements}, this results in an element with significantly fewer
degrees of freedom than $[\ensuremath{\mathbb{P}_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$. We also show the $[\ensuremath{\mathbb{P}_2 \oplus B^F_3}\xspace]^3$ element in
Figure~\ref{fig:elements}; we will demonstrate in
Section~\ref{sec:prolongation} that these elements satisfy a particular property
that is useful in the prolongation.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.24\linewidth]{./images/P1FB.png}
\includegraphics[width=0.24\linewidth]{./images/P2.png}
\includegraphics[width=0.24\linewidth]{./images/P2FB.png}
\includegraphics[width=0.24\linewidth]{./images/P3.png}
\caption{The \ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace, \ensuremath{\mathbb{P}_2}\xspace, \ensuremath{\mathbb{P}_2 \oplus B^F_3}\xspace and \ensuremath{\mathbb{P}_3}\xspace elements.}
\label{fig:elements}
\end{figure}
\begin{remark}
Pressure elements other than $\ensuremath{\mathbb{P}_0}\xspace$ have been considered for the augmented
Lagrangian preconditioner.
Benzi \& Olshanskii \cite[Table 6.2]{benzi2006} also present results for the
$[\mathbb{P}_1\text{iso}\,\mathbb{P}_2]^2\mathrm{-}\mathbb{P}_1$ pair,
where the pressure mass matrix solve in $\ensuremath{\mathrm{P}_{Q_h}}$ is approximated by the inverse of a
diagonal matrix. However, for this element pairing the developed multigrid scheme is not independent of the ratio $\gamma/\nu$ and hence as $\nu$ decreases, $\gamma$ has to be decreased correspondingly.
This in turn leads to worse control of the Schur complement and consequent growth in iteration counts.
\end{remark}
\begin{remark}
Effective smoothers for partial differential equations involving the continuous
term $(\nabla \cdot u, \nabla \cdot v)_{L^2(\Omega)}$ have been proposed in
other contexts \cite{arnold1997,hiptmair1997}; it should be possible to extend these
approaches to the two- and three-dimensional advection-dominated case
considered here, and thereby enable the use of finite elements with
advantageous properties such as optimal convergence rates and exact enforcement
of the incompressibility constraint.
\end{remark}
\section{The augmented Lagrangian method} \label{sec:augmentedlagrangian}
The Schur complement of the matrix in \eqref{eqn:spal} is given by
\begin{equation}
S = -B(A+\gamma B^T M_p^{-1} B)^{-1} B^T.
\end{equation}
From the Sherman–Morrison–Woodbury formula it follows (e.g.~\cite[Theorem 3.2]{bacuta2006}) that
\begin{equation}
S^{-1} = -(BA^{-1} B^T)^{-1} - \gamma M_p^{-1}.
\end{equation}
From this we obtain immediately that
\begin{equation}
\tilde S^{-1} = - (\nu + \gamma) M_p^{-1}
\end{equation}
is a good approximation to $S^{-1}$ as $\gamma\to\infty$ \emph{for fixed mesh
size and viscosity}. To understand the quality of the approximation for
finite $\gamma$ as $\nu$ or $h$ change, we need to consider how $\nu M_p^{-1}$
approximates $(BA^{-1}B^T)^{-1}$.
It is well known that the eigenvalues of a matrix do not characterize the
convergence of GMRES for a linear system \cite{greenbaum1996}. Instead, it is
necessary to bound the field-of-values of the preconditioned system
\cite[Theorem 3.2]{starke1997}, \cite[Corollary 6.2]{eiermann2001}, \cite[\S 1.3]{olshanskii2014}. This
analysis was performed by Benzi \& Olshanskii \cite{benzi2011b} for both the
ideal and the modified augmented Lagrangian preconditioner for the Oseen
problem, using general results of Loghin \& Wathen \cite{loghin2004}. One of
the key ingredients in this analysis is that the momentum operator is coercive
with constant $\nu$. They use this to prove that the choice of
$\gamma \sim \nu^{-1}$ results in an optimal preconditioner (assuming exact
solves of the momentum block). However, it is well known
\cite[p.~300]{girault1986} that the momentum operator of the
Newton linearization of \eqref{eqn:ns} is only coercive for $\nu > \nu_0$ for
some problem-dependent $\nu_0$. Fortin \& Glowinski remark
\cite[p.~85]{fortin1983} that this is typically a very restrictive condition:
for $\nu > \nu_0$ the Stokes approximation itself is adequate. This proof
strategy would therefore require significant extension to apply to the Newton
linearization considered here.
In practice, Benzi \& Olshanskii \cite{benzi2006} observe that a constant choice of $\gamma$ yields
mesh-independent and essentially Reynolds number independent results. As our
multigrid solver for the momentum block is robust with respect to $\gamma$, we simply choose
$\gamma$ large. In the experiments of section \ref{sec:numerical}, we take the value $\gamma = 10^4$,
to match the largest Reynolds number considered.
\section{Solving the augmented momentum block} \label{sec:solvingmomentum}
The key challenge with the augmented Lagrangian strategy is the solution of the
augmented momentum block $A_\gamma$. The grad-div term has a large nullspace,
rendering standard relaxation methods (point-block Jacobi or Gauss--Seidel)
ineffective as $\nu \to 0$. In this
section we explain the specialized multigrid algorithm of Benzi \& Olshanskii,
along with the modifications required to extend the method to three dimensions.
The multigrid method has two components: a $\nu$- and $\gamma$-robust relaxation
method, and a kernel-preserving prolongation operator. In subsections
\ref{sec:relaxation} and \ref{sec:prolongation} we first consider the augmented
Stokes momentum operator without the linearized advection terms, to study in the
simplest possible situation the difficulties arising with the grad-div term. We
then comment on the case with advection in subsection \ref{sec:advection}.
To understand the properties required of the relaxation and
prolongation, it suffices to consider a two-level scheme. We use the
subscripts $h$ and $H$ to denote function spaces, bilinear forms, and
meshes on the fine and coarse levels respectively.
\subsection{Relaxation} \label{sec:relaxation}
The augmented Stokes momentum problem is of the form: find $u \in V_{h,0} := V_h
\cap V_0$ such that
\begin{equation} \label{eqn:bilinearstokes}
a_h(u, v) \coloneqq (2\nu\eps{u}, \nabla v) + \gamma (\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u, \nabla \cdot
v) = (f, v)
\end{equation}
for all $v \in V_{h,0}$.
The viscosity term is symmetric and positive definite; the discrete grad-div term
is positive semidefinite.
As $\nu \to 0$ or $\gamma \to \infty$ this system becomes nearly
singular and standard relaxation methods such as Gauss--Seidel or Jacobi
iterations perform poorly. The essential difficulty is in computing the
component of the solution in the kernel
\begin{equation}
\mathcal{N}_h := \{u \in V_{h,0} : (\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u, \nabla \cdot v) = 0
\ \forall\ v \in V_{h,0}\}
\end{equation}
of the grad-div term.
Sch\"oberl \cite[Theorem~4.1]{schoberl1999b} and Lee et
al.~\cite[Theorem~4.2]{lee2007} consider subspace
correction methods for this class of problem.
The key result of these works is that if a subspace decomposition
\begin{equation}
V_{h,0} = \sum_i V_i
\end{equation}
satisfies the kernel decomposition property
\begin{equation} \label{eqn:kernel-decomposition}
\mathcal{N}_h = \sum_i \left(V_i \cap \mathcal{N}_h \right)
\end{equation}
then the resulting subspace correction method (a block Gauss--Seidel
or Jacobi iteration) is robust with respect to $\nu$ and
$\gamma$. This is why characterizing the kernel of the
grad-div term is crucial, and why the discrete variant is easier
to solve: the kernel $\mathcal{N}_h$ is spanned by basis functions with
local support around each vertex.
More specifically, for each vertex $v_i$ in the mesh \ensuremath{\mathcal{M}}\xspace, its
\emph{star} is the patch of elements sharing $v_i$:
\begin{equation}
K_i \coloneqq \bigcup_{{K \in \ensuremath{\mathcal{M}}\xspace \,: \,v_i \in K}} K.
\end{equation}
The subspace decomposition is then given by
\begin{equation}
V_i \coloneqq \{ \phi_j \in V_{h,0} : \mathrm{supp}(\phi_j) \subset K_i \}.
\end{equation}
We call the resulting patchwise block relaxation method a \emph{star iteration}.
Note that homogeneous Dirichlet conditions are imposed on the boundary of each
star patch.
This relaxation method has been employed for robust multigrid methods in $H(\mathrm{div})$
and $H(\mathrm{curl})$ \cite{arnold2000}.
For the reader's convenience, we briefly summarize the argument of \cite[Section~4.1.2]{schoberl1999b} to see why this decomposition satisfies \eqref{eqn:kernel-decomposition}.
Observe that a discretely divergence-free vector field $u_h\in \mathcal{N}_h$
can be suitably modified in the \emph{interior} of each cell to become
continuously divergence-free by solving a local Stokes problem.
Denote this continuously divergence-free vector field by $\tilde u$ and recall
that then $\tilde u = \nabla \times \phi$ for some vector field $\phi$.
Choosing a partition of unity $\{\rho_i\}_i$ with $\sum_i \rho_i=1$ and
$\mathrm{supp}(\rho_i) \subset K_i$ we define $\phi_i = \rho_i \phi$ and obtain
a decomposition
\begin{equation}
\phi = \sum_i \phi_i.
\end{equation}
For such a partition of unity to exist, every point in the mesh has to be in the
interior of at least one patch. The decomposition of the mesh into
star patches is the smallest decomposition of a finite element mesh that
satisfies this property.
Now let $\Pi_1:V\to V_h$ be a Scott--Zhang interpolation operator using facet averaging \cite{scott1990}.
Then it holds that $\Pi_1(u_h) = u_h$.
Furthermore, define $\Pi_2:V \to V_h$ as in the classical proof for inf-sup stability of the $\ensuremath{[\mathbb{P}_2]^2\mathrm{-}\mathbb{P}_0}\xspace$ element \cite[Proposition~3.1]{boffi2008}:
\begin{equation}
\begin{aligned}
\Pi_2(v)(M) = 0, \quad \text{ for all vertices } M,\\
\int_{F}\Pi_2(v) \ \mathrm{d}s = \int_F v \ \mathrm{d}s, \quad \text{ for all facets } F.
\end{aligned}
\end{equation}
Now define $I(v) = \Pi_1(v) + \Pi_2(v-\Pi_1(v))$, then it holds that
\begin{equation}
\begin{aligned}
I(v_h) &= v_h \quad \text{ for all } v_h\in V_h,\\
\int_F I(v) \ \mathrm{d}s &= \int_F v \ \mathrm{d}s \quad \text{ for all } v\in V.\\
\end{aligned}
\end{equation}
Now define $u_i=I(\nabla \times \phi_i)$ and conclude that
\begin{equation}
\sum_i u_i = \sum_i I (\nabla \times \phi_i) = I(\nabla \times \phi) = I(\tilde u)= u_h.
\end{equation}
Lastly, using the fact that we are considering piecewise constant pressures, $u_i \in V_i\cap \mathcal{N}_h$ follows from
\begin{equation}
\int_{\partial K} u_i \ \mathrm{d}s = \int_{\partial K} \nabla \times \phi_i \ \mathrm{d}s = \int_K \nabla\cdot(\nabla\times\phi_i) \ \mathrm{d}x = 0.
\end{equation}
\subsection{Prolongation} \label{sec:prolongation}
The second key ingredient of the multigrid scheme is the prolongation operator
that maps $V_H$ to $V_h$. To get an intuition for the properties required, let
$E_H: V_H \to V_h$ be the prolongation operator obtained by interpolating a
function $u_H\in V_H$ at the degrees of freedom of $V_h$.
The continuity of $E_H$ in the energy norm induced by the bilinear form $a_h$
defined in \eqref{eqn:bilinearstokes} is a key assumption in Sch\"oberl's proof
of the optimality of a two-level multigrid scheme \cite[Lemma
3.5]{schoberl1999b}. In order for the scheme to be robust, this continuity
constant must be uniform in $\nu$ and $\gamma$. Calculating, we observe that
\begin{equation}
\begin{aligned}
\|u_H \|_{a_H}^2 &= \nu\| \eps{u_H}\|_{L^2}^2 + \gamma \|P_{Q_H} (\nabla \cdot u_H)\|_{L^2}^2\\
\|E_H u_H \|_{a_h}^2 &= \nu \| \eps{E_H u_H}\|_{L^2}^2 + \gamma \|P_{Q_h} (\nabla \cdot (E_Hu_H))\|_{L^2}^2.
\end{aligned}
\end{equation}
The key difficulty lies in the second term of this norm. To see this, observe
that for an element $u_H \in \mathcal{N}_H$ the second term in
$\|u_H\|_{a_H}^2$ vanishes, but since it does not necessarily hold that $E_H u_H \in \mathcal{N}_h$,
the corresponding term in $\|E_Hu_H\|_{a_h}^2$ might be
large.
To avoid this, we must modify the prolongation operator to map fields that are
discretely divergence-free on the coarse grid to fields that are (nearly)
discretely divergence-free on the fine grid.
To begin, we assume that there is a decomposition $Q_h = \tilde Q_H \oplus Q_T$ and a subspace $V_T\subset V_h$ that satisfies $V_T \subset \ker(P_{Q_H}(\nabla\cdot))$.
Sch\"oberl proved that if the pairing $V_T \mathrm{-} Q_T$ satisfies the inf-sup condition and if
\begin{alignat}{2}
(P_{Q_h}(\nabla\cdot(E_H u_H)), \tilde q_H)_{L^2} &= (P_{Q_H} (\nabla\cdot u_H), \tilde q_H)_{L^2} && \quad\forall u_H\in V_H, \tilde q_H \in \tilde Q_H\label{eqn:decomposition-exterior}\\
(P_{Q_h}(\nabla\cdot u_T), \tilde q_H)_{L^2} &= 0 &&\quad \forall u_T\in V_T,\ \tilde q_H \in \tilde Q_H\label{eqn:decomposition-interior}
\end{alignat}
then the prolongation $\tilde E_H$ defined as
\begin{equation} \label{eqn:schoberlprolong}
\tilde E_H u_H = E_H u_h - w_T,
\end{equation}
where $w_T\in V_T$ satisfies
\begin{equation}\label{eqn:local-prolongation-problem}
a_h(w_T, v_T) = a_h(E_H u_H, v_T) \quad \forall v_T \in V_T,
\end{equation}
is continuous in the energy norm. The continuity constant is uniform in $\nu$ and $\gamma$.
In this case, the decomposition of $Q_h$ is chosen as
\begin{alignat}{2}
\tilde Q_H &\coloneqq Q_H \\
Q_T &\coloneqq \{ q_h \in Q_h : P_{Q_H}(q_h) = 0\}
\end{alignat}
and we choose
\begin{equation}
V_T \coloneqq \{ v_h \in V_h : v_h\vert_{\partial K} = 0 \ \forall K \in \ensuremath{\mathcal{M}}\xspace_H\}.
\end{equation}
The idea behind this is the following: \eqref{eqn:decomposition-exterior}
guarantees that prolongation preserves the flux across \emph{coarse grid}
facets. Then a correction term $w_T\in V_T$ that corrects the flux across the fine grid
facets is subtracted. The condition \eqref{eqn:decomposition-interior} guarantees that this
correction does not affect the flux across the coarse facets.
\begin{remark} The
definition of $V_T$ implies that the problem in
\eqref{eqn:local-prolongation-problem} can be solved locally on each coarse
grid element. This is crucial for an efficient implementation.
\end{remark}
\begin{remark}
Decompositions $\tilde Q_H \neq Q_H$ arise in other problems, such as
in Reissner--Mindlin plates \cite[Section 4.2.2]{schoberl1999b}.
\end{remark}
In \cite{schoberl1999, benzi2006} the $[\ensuremath{\mathbb{P}_2}\xspace]^2-\ensuremath{\mathbb{P}_0}\xspace$ element is used. For
this element choice it holds that $V_H\subset V_h$ and hence
\eqref{eqn:decomposition-interior} is satisfied trivially. However, in
three dimensions the pairing $V_T\mathrm{-}Q_T$ resulting from the
choice $[\ensuremath{\mathbb{P}_2}\xspace]^3-\ensuremath{\mathbb{P}_0}\xspace$ is not inf-sup stable. This can easily seen by
counting degrees of freedom: $[\ensuremath{\mathbb{P}_2}\xspace]^3$ only has degrees of freedom on edges and
vertices. Since there are zero vertices and only one edge not entirely on the boundary
of the refined coarse tetrahedron (see Figure~\ref{fig:exploded-tet}), we have $\dim(V_T)=3$. On the other hand, the
pressure space satisfies $\dim(Q_T) = 7$ (one dimension is fixed by the
nullspace). The local solve can therefore not be well-posed.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.5\textwidth]{./images/exploded_tet.png}
\caption{The uniform refinement of a coarse mesh tetrahedron yields eight fine mesh tetrahedra. Only the edge highlighted in blue does not lie
entirely on the boundary of the tetrahedron.}
\label{fig:exploded-tet}
\end{figure}
The choice $[\ensuremath{\mathbb{P}_3}\xspace]^3-\ensuremath{\mathbb{P}_0}\xspace$ alleviates this problem of ill-posedness on the
coarse cell and still satisfies $V_H\subset V_h$. However, as described in
Section~\ref{sec:velocityspace}, this element is quite expensive without
improving accuracy of the solution.
A much cheaper alternative
is offered by the $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element. This does satisfy
the inf-sup condition but
violates $V_H\subset V_h$. The
non-nestedness is demonstrated in Figure~\ref{fig:fb-prolongation}; a coarse
bubble cannot be interpolated exactly by functions in $V_h$. In particular,
the flux across the coarse grid faces is not preserved, hence violating
\eqref{eqn:decomposition-exterior}.
\begin{figure}[htbp]
\centering
\begin{tikzpicture}[scale=4.0]
\draw (0, 0) -- (1, 0);
\draw (1, 0) -- (0, 1);
\draw (0, 1) -- (0, 0);
\draw[dashed] (0.5, 0) -- (0.5, 0.5);
\draw[dashed] (0.5, 0.5) -- (0.0, 0.5);
\draw[dashed] (0.0, 0.5) -- (0.5, 0.0);
\draw[fill=black] (1./3., 1./3.) circle (0.015);
\draw[fill=black] (0, 0) circle (0.015);
\draw[fill=black] (0, 1) circle (0.015);
\draw[fill=black] (1, 0) circle (0.015);
\draw (1./3., 1./3.) circle (0.03);
\draw (2./3., 1./6.) circle (0.03);
\draw (1./6., 2./3.) circle (0.03);
\draw (1./6., 1./6.) circle (0.03);
\draw (1, 0) circle (0.03);
\draw (0, 0) circle (0.03);
\draw (0, 1) circle (0.03);
\draw (0.5, 0) circle (0.03);
\draw (0.5, 0.5) circle (0.03);
\draw (0, 0.5) circle (0.03);
\draw (0.3, 0.9) circle (0.03);
\draw[anchor=west] node at (0.3, 0.9) {\small \ dofs on fine facet};
\draw[fill=black] (0.3, 0.8) circle (0.015);
\draw[anchor=west] node at (0.3, 0.8) {\small \ dofs on coarse facet};
\end{tikzpicture}
\includegraphics[width=0.3\textwidth]{./images/bubble.png}
\includegraphics[width=0.3\textwidth]{./images/bubble_prolong.png}
\caption{Left: Degrees of freedom on the facet of a coarse cell and its refinement. Middle: Bubble function on a coarse facet. Right: Prolongation of a bubble function.}
\label{fig:fb-prolongation}
\end{figure}
A brief calculation shows that every coarse
grid bubble is interpolated by four fine grid bubbles: one with
coefficient $1$, the other three with coefficient $1/2$. From this it follows
immediately that the integral of the prolonged bubble is equal to $(1 + 3
\cdot \frac{1}2)/4 = \frac{5}{8}$ of the integral of the coarse bubble.
Hence, when using a hierarchical basis, since the piecewise linear basis
functions are prolonged exactly we can obtain a prolongation that satisfies
\eqref{eqn:decomposition-exterior} by simply multiplying the coefficients
of the fine grid bubble functions by $8/5$. After this scaling, the local
correction $w_T$ is computed as described above.
For a nodal basis, a change of basis to the hierarchical basis should be
performed.
This modification of the prolongation operator is crucial for the solver to work with the
$[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element. We demonstrate this by showing the
residual of the outer flexible GMRES iteration for the linear solve in the
first Newton step at $\Re=10$ for a lid-driven cavity problem (see section
\ref{ssec:threedimensionalexperiments} for details) in Table~\ref{tab:ksp-failure-without-scaling}.
Without modifying the prolongation of the facet bubbles, we observe no convergence.
\begin{table}[htbp]
\centering
\begin{tabular}{r|c|c}
Iteration & Residual with bubble scaling & Residual without bubble scaling \\\hline
0 & $ 3.499\hphantom{{}\times 10^{+0}}$ & $ 3.499$ \\
1 & $ 1.554\times 10^{-2}$ & $ 3.499 $ \\
2 & $ 1.716\times 10^{-3}$ & $ 3.499 $ \\
3 & $ 1.821\times 10^{-4}$ & $ 3.496 $ \\
4 & $ 1.651\times 10^{-5}$ & $ 3.495 $ \\
\end{tabular}
\caption{Residual of the outer flexible GMRES solver when employing the
$[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element. It is necessary to modify the prolongation operator
to achieve convergence with this element.}
\label{tab:ksp-failure-without-scaling}
\end{table}
Lastly, we consider the $[\ensuremath{\mathbb{P}_2 \oplus B^F_3}\xspace]^3-\ensuremath{\mathbb{P}_0}\xspace$ element. While it is also
non-nested, it turns out that the interpolation is exact \emph{on the facets}
of each coarse cell and hence flux preserving. To see this, observe
that the cubic facet bubble function is only quadratic on the newly introduced
edges of a regularly refined facet, as they are parallel to the edges of the
coarse facet and therefore one of the barycentric coordinates is constant. The coarse bubble function
is therefore prolonged exactly. This means that the $[\ensuremath{\mathbb{P}_2 \oplus B^F_3}\xspace]^3-\ensuremath{\mathbb{P}_0}\xspace$
element can be used with the Sch\"oberl prolongation operator \eqref{eqn:schoberlprolong},
without the modifications necessary for $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ described
above. However, in our preliminary numerical experiments the simpler
prolongation was outweighed by the cost of the larger number of degrees
of degrees of freedom, and hence we use $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ for
the numerical experiments in section \ref{sec:numerical}.
\begin{remark}
Only the prolongation is modified; as in Benzi \& Olshanskii \cite{benzi2006}, the natural operations are used for
restriction and injection.
\end{remark}
\subsection{The advection terms} \label{sec:advection}
So far we have neglected the terms arising from the linearization of the
advection term. Applying a Newton linearization, \eqref{eqn:bilinearstokes}
becomes: find $u \in V_{h,0}$ such that
\begin{equation} \label{eqn:advectnewton}
(2\nu\eps{u}, \nabla v) + (w \cdot \nabla u, v) + (u \cdot \nabla w, v) + \gamma (\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u, \nabla \cdot
v) = (f, v)
\end{equation}
for all $v \in V_{h,0}$, while the Picard linearization yields:
find $u \in V_{h,0}$ such that
\begin{equation} \label{eqn:advectpicard}
(2\nu\eps{u}, \nabla v) + (w \cdot \nabla u, v) + \gamma (\ensuremath{\mathrm{P}_{Q_h}} \nabla \cdot u, \nabla \cdot
v) = (f, v)
\end{equation}
for all $v \in V_{h,0}$. The Picard linearization is easier to solve but
sacrifices quadratic convergence of the nonlinear solver. Several authors have
reported success with geometric multigrid for scalar analogues of
\eqref{eqn:advectpicard} without the grad-div term, using a combination of
line/plane relaxation and SUPG stabilization
\cite{ramage1999,olshanskii2004,wu2006}. Olshanskii and Benzi
\cite{olshanskii2008} and Elman et al.~\cite{elman2003} apply preconditioners built on the Picard
linearization \eqref{eqn:advectpicard} to the Newton linearization
\eqref{eqn:advectnewton}, with good results.
Numerical experiments indicated that the additive star iteration alone
was not effective as a relaxation method for
\eqref{eqn:advectnewton}. (Benzi and Olshanskii \cite{benzi2006} used
a multiplicative star iteration with multiple directional sweeps, but
we wished to avoid this as its performance varies with the core count
in parallel.) We investigated the multiplicative composition of
additive star iterations and plane smoothers, and while this led to a
successful multigrid cycle, the plane smoothers were quite expensive
(involving many 2D solves) and were also difficult to parallelize on
arbitrary unstructured grids where the parallel decomposition does not
divide into planes. While the additive star iteration alone is not
effective as a relaxation for \eqref{eqn:advectnewton}, we found that a
few iterations of GMRES preconditioned by the additive star iteration
was surprisingly effective as a relaxation method, even for low viscosities. This point merits
further analysis and will be considered in future work. This
relaxation method also has the advantage that it is easy to
parallelize, with convergence independent of the parallel
decomposition.
\section{Numerical results} \label{sec:numerical}
\subsection{Algorithm details}
A graphical representation of the entire algorithm is shown in Figure
\ref{fig:solver}.
We employ simple continuation in Reynolds number as a globalization
device, as Newton's method is not globally convergent. Newton's method is globalized
with the $L^2$ line search algorithm of PETSc \cite{brune2015}.
\begin{figure}[htbp]
\centering
\resizebox{\textwidth}{!}{\input{images/solver.tikz}}
\caption{An outline of the algorithm for solving \eqref{eqn:ns}.}
\label{fig:solver}
\end{figure}
We use flexible
GMRES \cite{saad1993} as the outermost solver for the linearized Newton system,
as we employ GMRES in the multigrid relaxation.
If the pressure is only defined up to a
constant, then the appropriate nullspace is passed to the Krylov solver and the
solution is orthogonalized against the nullspace at every iteration.
We use the full block factorization
preconditioner
\begin{equation}
P^{-1} =
\left( \begin{array}{cc}
I & -\tilde{A}_\gamma^{-1} B^T \\
0 & I \\
\end{array} \right)
\left( \begin{array}{cc}
\tilde{A}_\gamma^{-1} & 0 \\
0 & \tilde{S}^{-1} \\
\end{array} \right)
\left( \begin{array}{cc}
I & 0 \\
-B\tilde{A}_\gamma^{-1} & I \\
\end{array} \right)
\end{equation}
with approximate inner solves $\tilde{A}_\gamma^{-1}$ and $\tilde{S}^{-1}$ for the
augmented momentum block and the Schur complement respectively. The diagonal,
upper and lower triangular variants described in \cite{murphy2000,ipsen2001}
also converge well, but these took longer runtimes in preliminary experiments.
We use one application of a full multigrid cycle \cite[Figure
1.2]{brandt2011} using the components described in section
\ref{sec:solvingmomentum} for $\tilde{A}_\gamma^{-1}$. The problem on each level
is constructed by rediscretization; fine grid functions, such as the current
iterate in the Newton scheme, are transferred to the coarse levels via
injection. On each level the SUPG stabilization is performed with parameters
corresponding to the mesh in question. For each relaxation
sweep we perform 6 (in 2D) or 10 (in 3D) GMRES iterations preconditioned by the
additive star iteration; at lower Reynolds numbers this can be reduced, but we
found that these expensive smoothers represented the optimal tradeoff between
inner and outer work at higher Reynolds numbers. The problem on the coarsest level is solved with the SuperLU\_DIST sparse
direct solver \cite{li1999,li2003b}. For scalability, the coarse grid solve is
agglomerated onto a single compute node using PETSc's telescoping facility
\cite{may2016}. As all inner solvers are additive, the convergence of the solver
is independent of the parallel decomposition (up to roundoff).
\subsection{Software implementation}
The solver proposed in the previous section is complex, and relies heavily on
PETSc's capability for the arbitrarily nested composition of solvers
\cite{brown2012}. For the implementation of local patch solves, we have
developed a new subspace correction preconditioner for PETSc that relies on the
\texttt{DMPlex} unstructured mesh component \cite{knepley2005,knepley2009} for
topological subspace construction and provides an extensible callback interface
that allows for the very general specification of additive Schwarz methods. A
detailed description of this preconditioner is in preparation.
\subsection{Solver verification with the method of manufactured solutions}
In order to verify the implementation and the convergence of the
$[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element we employ the method of manufactured
solution.
We start by considering the pressure and velocity field proposed in \cite{shih1989}, which is rescaled
to the $[0, 2]^2$ square.
This results in $u=(u_1, u_2)$ with
\begin{equation}
\begin{aligned}
u_1(x, y) =&\ \frac{1}{4} (x-2)^2 x^2 y \left(y^2-2\right) \\
u_2(x, y) =&\ -\frac{1}{4} x \left(x^2-3 x+2\right) y^2 \left(y^2-4\right) \\
\tilde p(x, y) =&\ \frac{x y \left(3 x^4-15 x^3+10 x^2 y^2-30 x \left(y^2-2\right)+20 \left(y^2-2\right)\right)}{5 \Re}\\
&\ -\frac{1}{128} (x-2)^4 x^4 y^2 \left(y^4-2 y^2+8\right)\\
p(x, y)= &\ \tilde p -\frac14\int_{[0, 2]^2} \tilde p(x,y)\ \mathrm{d}x = \tilde p +\frac{1408}{33075} - \frac{8}{5\Re}.
\end{aligned}
\end{equation}
As we are primarily interested in the three dimensional case, we extend the
vector field into the $z$ dimension via $u(x, y, z) = (u_1(x, y), u_2(x, y), 0)$.
The pressure remains the same as in two dimensions.
To demonstrate that the error convergence is independent of $\gamma$, we run
the solver for values $\gamma=1$ and $\gamma=10^4$. Figure~\ref{fig:mms} shows
the error between the computed velocity and pressure and their known
analytical solutions for $\Re=1$, $\Re=200$ and $\Re=500$. Due to the DG0
discretization we expect, and see, first order convergence of the pressure.
Without stabilization, we expect second order convergence for the
velocity field; however, due to the presence of the SUPG stabilization
this is reduced to linear convergence for coarse meshes. Once the mesh
is fine enough so that $h^{-1} \gtrsim \Re$, second order convergence is recovered.
\begin{figure}[htbp]
\centering
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h,error_v,error_p\\
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0.03125,0.0034906304895967115,0.6896606226331777\\
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0.0625,0.013324556679585035,1.7148196381504333\\
0.03125,0.0034906116893429814,0.6896557435605192\\
0.015625,0.000879529966251674,0.3124295483848757\\}\reonegammaone
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h,error_v,error_p\\
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0.0625,0.03952463294902316,0.026975093770353203\\
0.03125,0.012085756491489108,0.012039184365974821\\
0.015625,0.003257861159774448,0.0057070900679878364\\}\retwohundredgammatenthousand
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h,error_v,error_p\\
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0.03125,0.05728182350093682,0.017976847105105765\\
0.015625,0.01704621605013802,0.006846097701282368\\}\refivehundredgammaone
\begin{tikzpicture}
\begin{loglogaxis}[
width=0.5\linewidth,
xlabel={$h$},
ylabel near ticks,
ylabel={$L^2$-error},
log basis x=2,
title={$\Re = 1$},
]
\addplot+[thick, mark=o, mark options={fill=none}, mark size=4pt] table[x=h, y=error_v] {\reonegammatenthousand};
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\end{tikzpicture}
\begin{tikzpicture}
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width=0.5\linewidth,
xlabel={$h$},
ylabel near ticks,
ylabel={$L^2$-error},
log basis x=2,
title={$\Re = 200$}
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\end{tikzpicture}
\begin{tikzpicture}
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width=0.5\linewidth,
xlabel={$h$},
ylabel near ticks,
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title={$\Re = 500$},
legend cell align=left,
legend style={at={(1.425, 0.5)}, anchor=west},
legend columns=1,
legend style={/tikz/every even column/.append style={column
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{\reonegammaone};
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{\reonegammaone};
\addlegendentry{$h$};
\end{loglogaxis}
\path[use as bounding box] (current bounding box.south west)
rectangle ($(current bounding box.north east) + (0.4605cm, 0)$);
\end{tikzpicture}
\caption{Convergence of the computed velocity and pressure field as the
mesh is refined for a 3D lid-driven cavity test problem.}
\label{fig:mms}
\end{figure}
\subsection{Two-dimensional experiments}
We consider two representative benchmark problems: the regularized lid-driven
cavity and backward-facing step problems, fully described in
\cite[examples 8.1.2 and 8.1.3]{elman2014}. For each experiment, we fix a coarse
grid and vary the number of refinements to vary the size of the problem under
consideration; all refinements are used in the multigrid iteration, to ensure
that the convergence does not deteriorate as more levels are employed. We
employ the $[\ensuremath{\mathbb{P}_2}\xspace]^2\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element for all two dimensional experiments.
To investigate the performance of the solver with Reynolds number, the problem is
first solved for $\Re = 10$, then $\Re = 100$, and then in steps of $100$ until $\Re =
10000$, with the solution for the previous value of \Re used as initial guess
for the next. The Stokes equations are solved using a standard geometric
multigrid algorithm with the pressure mass matrix as Schur complement
approximation and point-block SOR as a smoother to provide the initial guess
used at $\Re = 10$. The augmented Lagrangian parameter is set to $\gamma =
10^4$ in these and all subsequent experiments.
The linear solves are terminated with an absolute tolerance of $10^{-10}$ in
the $\ell_2$-norm and a relative tolerance of $10^{-6}$. The nonlinear solves
are terminated with an absolute tolerance of $10^{-8}$ and a relative tolerance
of $10^{-10}$. As each outer iteration of the Krylov method does a
\emph{fixed} amount of work (i.e.~all subproblems are solved with a fixed
number of iterations, not to a specified tolerance), the solver scales well
with mesh size and Reynolds number if the iteration counts remain approximately
constant.
For comparison, we solve the same problems using the reference implementations
of the PCD and LSC preconditioners in version 3.5 of IFISS \cite{elman2014b}, up
to $\Re = 1000$, as IFISS does not employ stabilization of the advection term.
For both of these preconditioners we use the variant that takes corrections for
the boundary conditions into account and we solve the inner problems in the
Schur complement approximation using an algebraic multigrid solver. We employ
the hybrid strategy suggested by \cite[p. 391]{elman2014} that uses a single
sweep of ILU(0) on the finest level and two iterations of point-damped Jacobi
for pre- and post-smoothing on all coarsened levels. A relative tolerance of
$10^{-6}$ is set for the Krylov solver and an absolute tolerance of $10^{-8}$
for the Newton solver.
We begin by considering the regularized lid-driven cavity problem. The coarse
grid used is the $16 \times 16$ grid of triangles of negative slope. The
results are shown in Table~\ref{tab:ourldc}; we observe only very mild
iteration growth from $\Re=10$ to $\Re=10000$ with the performance improving as
more refinements are taken. Iteration counts using the PCD and LSC
preconditioners are shown in Table~\ref{tab:pcdlscldc}. For both PCD and LSC
iteration counts increase substantially from $\Re = 10$ to $\Re = 1000$.
\begin{table}[htbp]
\centering
\begin{tabular}{cc|ccccc}
\toprule
\# refinements & \# degrees of freedom & \multicolumn{5}{c}{Reynolds number} \\
&& 10 & 100 & 1000 & 5000 & 10000 \\
\midrule
1 & $1.0 \times 10^4$ & 2.50 & 4.33 & 6.00 & 8.00 & 14.00 \\
2 & $4.1 \times 10^4$ & 2.50 & 3.33 & 6.67 & 8.50 & 10.00 \\
3 & $1.6 \times 10^5$ & 2.50 & 3.00 & 5.67 & 8.50 & 9.00 \\
4 & $6.6 \times 10^5$ & 2.50 & 2.67 & 5.00 & 8.00 & 8.50 \\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the
2D regularized lid-driven cavity problem.}
\label{tab:ourldc}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{cc|c@{\hspace{9pt}}c@{\hspace{9pt}}c}
\toprule
$1/h$ & \# degrees of freedom & \multicolumn{3}{c}{Reynolds number} \\
&& 10 & 100 & 1000 \\
\midrule
$2^4$ & $8.34 \times 10^2$ & 22.0/21.5 & 40.4/48.7 & 103.3/130.7 \\
$2^5$ & $3.20 \times 10^3$ & 23.0/22.0 & 41.3/52.7 & 137.7/185.3 \\
$2^6$ & $1.25 \times 10^4$ & 24.5/22.5 & 42.0/49.3 & 157.0/205.7 \\
$2^7$ & $4.97 \times 10^4$ & 25.5/21.0 & 42.7/43.3 & 149.0/207.3 \\
$2^8$ & $1.98 \times 10^5$ & 26.0/23.0 & 44.0/38.0 & 137.0/180.0 \\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the
2D regularized lid-driven cavity problem with PCD/LSC preconditioner.}
\label{tab:pcdlscldc}
\end{table}
For the backward-facing step we observe that the performance is dependent on
the resolution of the coarse grid. We consider two experiments, one starting
with a coarse grid consisting of 6941 vertices and 13880 elements (labeled A)
and one consisting of 30322 vertices and 60642 elements (labeled B). Both
unstructured triangular meshes were generated with Gmsh \cite{geuzaine2009}.
For mesh A, we observe that the iteration counts for large Reynolds
numbers show the solver degrades somewhat as the mesh is
refined, see Table~\ref{tab:ourbfs}. Using the finer coarse grid B alleviates
this problem. The bottom half of Table~\ref{tab:ourbfs} shows that iteration counts only
approximately double as we increase from $\Re=10$ to $\Re=10000$.
\begin{table}[htbp]
\centering
\begin{tabular}{cc|ccccc}
\toprule
\# refinements & \# degrees of freedom & \multicolumn{5}{c}{Reynolds number} \\
&& 10 & 100 & 1000 & 5000 & 10000\\
\midrule
\multicolumn{7}{c}{coarse grid A}\\
\midrule
1 & $2.7 \times 10^5$ & 3.00 & 4.00 & 5.50 & 12.00 & 26.50\\
2 & $1.1 \times 10^6$ & 2.67 & 4.50 & 5.50 & 11.50 & 31.50\\
3 & $4.3 \times 10^6$ & 4.00 & 7.00 & 6.00 & 14.00 & 21.00\\
\midrule
\multicolumn{7}{c}{coarse grid B}\\
\midrule
1 & $1.2 \times 10^6$ & 2.67 & 3.75 & 5.00 & 7.00 & 9.00\\
2 & $4.8 \times 10^6$ & 4.00 & 3.75 & 5.00 & 6.50 & 7.00\\
3 & $1.9 \times 10^7$ & 3.67 & 5.75 & 5.50 & 5.00 & 5.50\\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the
2D backward-facing step problem for two different coarse grids.}
\label{tab:ourbfs}
\end{table}
The results for PCD and LSC on the backwards-facing step are shown in Table
\ref{tab:pcdlscbfs}. The iteration counts approximately treble as we increase
from $\Re = 10$ to $\Re = 1000$.
\begin{table}[htbp]
\centering
\begin{tabular}{cc|c@{\hspace{10pt}}c@{\hspace{10pt}}c}
\toprule
$1/h$ & \# degrees of freedom & \multicolumn{3}{c}{Reynolds number} \\
&& 10 & 100 & 1000 \\
\midrule
$2^4$ & $3.94 \times 10^3$ & 23.0/29.0 & 32.5/47.5 & \texttt{NaNF}/\texttt{NaNF} \\
$2^5$ & $1.52 \times 10^4$ & 23.5/26.0 & 31.0/45.0 & 221.3/329.0 \\
$2^6$ & $5.96 \times 10^4$ & 23.5/25.5 & 30.5/42.8 & 122.7/225.7 \\
$2^7$ & $2.36 \times 10^5$ & 23.5/25.5 & 30.0/40.8 & 85.3/161.3 \\
$2^8$ & $9.38 \times 10^5$ & 23.5/27.0 & 30.0/40.0 & 78.3/128.0 \\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the 2D
backwards-facing step problem with PCD/LSC preconditioner. \texttt{NaNF}
denotes failure due to NaNs occurring in the solve for the velocity block.}
\label{tab:pcdlscbfs}
\end{table}
\subsubsection{Runtime comparison to SIMPLE}
\label{sec:comparison-simple}
To give some measure of the runtime of the solver, we compare it to an
implementation of SIMPLE~\citep[Section 6.7]{patankar1980} in the same software framework. We select the
lid-driven cavity in two dimensions with three refinements ($1.6 \times 10^5$ degrees of freedom) as a representative
problem. The SIMPLE preconditioner is given by
\begin{equation}
P_\text{SIMPLE}^{-1} =
\left( \begin{array}{cc}
I & -\operatorname{diag}(A)^{-1} B^T \\
0 & I \\
\end{array} \right)
\left( \begin{array}{cc}
\tilde{A}^{-1} & 0 \\
0 & \tilde{S}_\text{SIMPLE}^{-1} \\
\end{array} \right)
\left( \begin{array}{cc}
I & 0 \\
-B\tilde{A}^{-1} & I \\
\end{array} \right),
\end{equation}
where
\begin{equation}
\tilde{S}_\text{SIMPLE} = -B^T \operatorname{diag}(A)^{-1} B
\end{equation}
and no grad-div augmentation is employed. $\tilde{A}^{-1}$ is approximated
by one full multigrid cycle of the ML
algebraic multigrid library~\citep{gee2006}; $\tilde{S}_\text{SIMPLE}^{-1}$ is
approximated with one V cycle of ML\footnote{For fairness, we do not use exact inner
solves, since our solver also does not use exact inner solves. Of the
algebraic multigrid libraries available in PETSc, ML performed the best with default settings.}.
\begin{table}[htbp]
\centering
\begin{tabular}{c|c@{\hspace{10pt}}c|c@{\hspace{10pt}}c}
\toprule
Reynolds number & \multicolumn{2}{c|}{Augmented Lagrangian} & \multicolumn{2}{c}{SIMPLE} \\
& Total iterations & Time (min) & Total iterations & Time (min) \\
\midrule
10 & 4 & 0.21 & 515 & 1.06 \\
50 & 6 & 0.30 & 741 & 1.57 \\
100 & 8 & 0.38 & 979 & 2.01 \\
150 & 10 & 0.46 & 1111 & 2.27 \\
200 & 10 & 0.46 & 1185 & 2.48 \\
\bottomrule
\end{tabular}
\caption{Iteration count and runtime comparison against the SIMPLE preconditioner.}
\label{tab:simplealmgcompare}
\end{table}
The results for several continuation steps are shown in Table
\ref{tab:simplealmgcompare}. The computations were performed in serial. Each SIMPLE iteration is approximately 22--26 times
faster than an augmented Lagrangian iteration, but the lower cost per iteration
is outweighed by the greater number of iterations required.
\subsection{Three-dimensional experiments}
\label{ssec:threedimensionalexperiments}
The lid-driven cavity and backward-facing step problems can both
be extended to three dimensions in a natural way.
For the lid-driven cavity, we consider the cube $\Omega =[0,2]^3$ with no-slip boundary conditions on all sides apart from the top boundary $\{y=2\}$.
On the top boundary we enforce $u(x, y, z)=(x^2(2-x)^2z^2(2-z)^2, 0, 0)^T$.
The three dimensional backwards-facing step is given by $\Omega=\left(\left([0, 10]\times [1, 2]\right)\cup \left([1, 10] \times [0, 1]\right)\right) \times [0, 1]$.
We enforce the inflow condition $u(x, y, z) = (4(2-y)(y-1)z(1-z), 0, 0)^T$ on the
left boundary $\{x=0\}$, a natural outflow condition on the right boundary
$\{x=10\}$ and no-slip boundary conditions on the
remaining boundaries.
Two aspects of the solver were modified compared to the version used in two
dimensions. Firstly, we observe that reducing the size of the SUPG
stabilization by a factor of $1/20$ improves convergence significantly.
Secondly, the relative tolerance for the linear solver was relaxed to
$10^{-5}$ and the absolute tolerance for the linear and the nonlinear solver
was relaxed to $10^{-8}$, to save computational time. The three-dimensional
experiments were both run for $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ discretizations of
up to one billion degrees of freedom on ARCHER, the UK national supercomputer.
The runs were terminated at $\Re = 5000$ due to budgetary constraints.
Images of the solutions are shown in Figures \ref{fig:bfs} and \ref{fig:ldc}.
\begin{table}[htbp]
\centering
\begin{tabular}{cc|ccccc}
\toprule
\# refinements & \# degrees of freedom & \multicolumn{5}{c}{Reynolds number} \\
&& 10 & 100 & 1000 & 2500 & 5000 \\
\midrule
1 & $2.1 \times 10^6$ & 4.50 & 4.00 & 5.00 & 4.50 & 4.00 \\
2 & $1.7 \times 10^7$ & 4.50 & 4.33 & 4.50 & 4.00 & 4.00 \\
3 & $1.3 \times 10^8$ & 4.50 & 4.33 & 4.00 & 3.50 & 7.00 \\
4 & $1.1 \times 10^9$ & 4.50 & 3.66 & 3.00 & 5.00 & 5.00 \\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the
3D regularized lid-driven cavity problem.}
\label{tab:ourldc3d}
\end{table}
\begin{table}[htbp]
\centering
\begin{tabular}{cc|ccccc}
\toprule
\# refinements & \# degrees of freedom & \multicolumn{5}{c}{Reynolds number} \\
&& 10 & 100 & 1000 & 2500& 5000 \\
\midrule
1 & $2.1 \times 10^6$ & 4.50 & 4.00 & 4.00 & 4.50 & 7.50 \\
2 & $1.7 \times 10^7$ & 5.00 & 4.00 & 3.33 & 4.00 & 10.00 \\
3 & $1.3 \times 10^8$ & 6.50 & 4.50 & 3.50 & 3.00 & 8.00 \\
4 & $1.0 \times 10^9$ & 7.50 & 3.50 & 2.50 & 3.00 & 6.00 \\
\bottomrule
\end{tabular}
\caption{Average number of outer Krylov iterations per Newton step for the
3D backwards-facing step problem.}
\label{tab:ourbfs3d}
\end{table}
As for the two-dimensional case, we see only very little variation of the
iteration counts with Reynolds number over this range.
To stress the solver further, the lid-driven cavity with 2 refinements
($1.7 \times 10^7$ degrees of freedom)
was run until failure. Iteration counts remain stable until $\Re = 7000$,
then begin to increase, with eventual failure of convergence at $\Re = 7700$.
\begin{figure}[htbp]
\centering
\includegraphics[width=0.6\textwidth]{images/ldc3d.png}
\caption{Interior view of the streamtubes of the 3D lid-driven cavity at $\Re = 5000$. The color
denotes speed.}
\label{fig:bfs}
\end{figure}
\begin{figure}[htbp]
\centering
\includegraphics[width=\textwidth]{images/bfs3dre1000.png}
\caption{Interior view of the streamtubes of the 3D backwards-facing step at $\Re = 1000$. The color
denotes speed.}
\label{fig:ldc}
\end{figure}
\subsubsection{Computational performance}
\label{sec:comp-perf}
Having seen that the algorithmic scalability of the solver is good,
with well-controlled iteration counts, we now consider the
computational performance. In Figures~\ref{fig:ldc3d-scaling} and
\ref{fig:bfs3d-scaling} we show the weak scaling\footnote{A weak
scaling test is where the
number of degrees of freedom per MPI process is held constant while increasing the
number of processes. Perfect scaling corresponds to a constant time
to solution as the problem size is increased.} of the total time to
solution over all continuation steps. Both problems show excellent
scalability from 48 to 24576 MPI processes, with the lid-driven cavity
achieving a scaling efficiency of 80\% and the backwards-facing step
79\%.
We attribute the lack of perfect scalability primarily to load imbalance in our mesh distribution. In both
problems, although the mesh has a well-balanced partition of cells,
for the patch smoother to have perfect load balance the number of
vertices owned by each process must also be equal. The partitioning
scheme used does not take this constraint into account, and we observe
that the number of patches per process varies by a factor of 4 over
the partition for the largest problems. The scaling and computational
performance of the code will be improved in future work.
\begin{figure}[htbp]
\centering
\pgfplotstableread[col sep=comma, row sep=\\]{%
Cores,Time,Dofs\\
48,5.3e1,2134839\\
384,6.9e1,16936779\\
3072,6.1e1,134930451\\
24576,6.6e1,1077196323\\
}\ldctable
\pgfplotstableread[col sep=comma, row sep=\\]{%
Cores,Time,Dofs\\
48,5.5e1,2107839\\
384,6.9e1,16534263\\
3072,5.7e1,130973115\\
24576,6.9e1,1042606515\\
}\bfstable
\begin{subfigure}[l]{0.475\textwidth}
\begin{tikzpicture}
\begin{semilogxaxis}[
width=0.925\linewidth,
height=0.8\linewidth,
log basis x=2,
ymin=0,
ymax=80,
xtick=data,
xticklabels from table={\ldctable}{Cores},
extra x ticks={48, 384, 3072, 24576},
extra x tick labels={$[2.13]$, $[16.9]$,$[135]$,$[1077]$},
extra x tick style={tick label style={yshift=-2.5ex}},
xlabel={Cores\\{}[DoFs $\times 10^6$]},
xlabel style={align=center, style={yshift=-2ex}},
ylabel near ticks,
ylabel style={align=center, text width=4cm},
ylabel={Time to solution over all continuation steps [min]},
]
\addplot+ table[x=Cores,y=Time] {\ldctable};
\end{semilogxaxis}
\end{tikzpicture}
\caption{Weak scaling of the three-dimensional lid-driven cavity.}
\label{fig:ldc3d-scaling}
\end{subfigure}
\hspace{1em}
\begin{subfigure}[r]{0.475\textwidth}
\begin{tikzpicture}
\begin{semilogxaxis}[
width=0.925\linewidth,
height=0.8\linewidth,
log basis x=2,
ymin=0,
ymax=80,
xtick=data,
xticklabels from table={\bfstable}{Cores},
extra x ticks={48, 384, 3072, 24576},
extra x tick labels={$[2.11]$, $[16.5]$,$[131]$,$[1043]$},
extra x tick style={tick label style={yshift=-2.5ex}},
xlabel={Cores\\{}[DoFs $\times 10^6$]},
xlabel style={align=center, style={yshift=-2ex}},
ylabel near ticks,
ylabel style={align=center, text width=4cm},
ylabel={Time to solution over all continuation steps [min]},
]
\addplot+ table[x=Cores,y=Time] {\bfstable};
\end{semilogxaxis}
\end{tikzpicture}
\caption{Weak scaling of the three-dimensional backwards-facing step.}
\label{fig:bfs3d-scaling}
\end{subfigure}
\caption{Weak scaling of time to solution over all continuation
steps for both 3D problems.}
\end{figure}
\section{Conclusions and outlook} \label{sec:conclusions}
In this paper we have extended the multigrid method of Benzi, Olshanskii and
Sch\"oberl for the augmented momentum solve arising in the augmented Lagrangian
preconditioner to three dimensions. The prolongation operator proposed by
Sch\"oberl works for the $[\ensuremath{\mathbb{P}_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ and
$[\ensuremath{\mathbb{P}_2 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ discretizations, while a modification is required
to use the cheaper $[\ensuremath{\mathbb{P}_1 \oplus B^F_3}\xspace]^3\mathrm{-}\ensuremath{\mathbb{P}_0}\xspace$ element. We have developed a
new patchwise preconditioner in PETSc and implemented the resulting scheme in
Firedrake. We have demonstrated iteration counts that grow very slowly with
respect to the Reynolds number in both 2D and 3D for problems of up to a billion
degrees of freedom. The code is freely available as open source.
However, this multigrid method is currently tightly coupled to the use of piecewise
constant elements for the pressure for full robustness, and the discretizations considered here do
not represent the divergence-free constraint exactly, which is highly desirable
\cite{john2017}. The key next step is to develop a Reynolds-robust
preconditioner for these discretizations, such as the Scott--Vogelius element
\cite{scott1985}, the Guzm\'an--Neilan modification of Bernardi--Raugel
\cite{guzman2017}, or a $H(\mathrm{div})$-conforming element
\cite{cockburn2006}. It may also be possible to use this solver as a
preconditioner for other discretisations, in a similar manner to the
modified multigrid schemes studied in \cite{john2001}.
\section*{Code availability}
For reproducibility, we cite archives of the exact software versions
used to produce the results in this paper. All major Firedrake
components have been archived on Zenodo~\citep{zenodo/Firedrake-20190617.0}. An
installation of Firedrake with components matching those used to
produce the results in this paper can by obtained following the
instructions at \url{https://www.firedrakeproject.org/download.html}
with\vspace{0.2cm}
{\small
\begin{verbatim}
export PETSC_CONFIGURE_OPTIONS="--download-superlu --download-superlu_dist \
--with-cxx-dialect=C++11"
python3 firedrake-install --doi 10.5281/zenodo.3247427
\end{verbatim}
}\vspace{0.2cm}
\noindent
The additive Schwarz preconditioner has been incorporated into PETSc
as of version 3.10. The Navier--Stokes solver,
and example files, are available at
\url{https://bitbucket.org/pefarrell/fmwns/}, the version used in the
paper is archived as part of \cite{zenodo/Firedrake-20190617.0}.
\bibliographystyle{siamplain}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 5,155 |
The Young and the RestlessSoapbox
Deconstructing Y&R: Classic soap disaster, hospital drama, and the redemption of Adam Newman
Restless Rant for November 2 - 6:
As stated in last week's Deconstructing Y&R, the drama on the show has been entertaining if you can suspend disbelief. The fire disaster had plenty of soapy goodness. There are a few storylines, however, that have too many unbelievable elements, especially for those who prefer their soaps firmly rooted in reality. Thoughts:
The towering inferno.
The fiery disaster in Newman Towers made for fairly riveting viewing. The action jumped between characters and crises at a good pace, all the classic soap devices were used, such as people being left behind, the catfight, and the 'we're going to die' confession and kiss. There was even some comic relief – I laughed out loud when Jack realized the rescuer who came to free him and Phyllis was none other than Patty Williams! It was also hilarious when Patty casually phoned up Dylan to tell him she was out for the night and could he meet up? She's a gem! That said, they milked the fire story a bit too long, the 'humble hero' stuff with Dylan and Adam got a tad cheesy, and it was ridiculous how some people were coughing and choking while the main players were able to carry on full normal conversations while ensconced in smoke and flames. The reveal that Ian Ward was behind the fire felt predictable – a twist would have been nice – and he got too 'cartoon villain' standing in the flames with his arms outstretched reveling in his creation. Some fans found it offensive:
@CandaceLYoung What kind of sick psycho terrorist burns down a building with kids in it trick or treating, I don't like that stuff at all??
— Ray Louison (@raycent) November 2, 2015
I'll get you out.
The little mini soap opera playing out with Noah/Marisa/Luca at the gala was uncomfortable to watch. Luca came off as arrogant and creepy, Marisa behaved like a damsel in distress being led by one or the other of the men, and Noah just stood there and did nothing when Luca kissed her. Unappealing.
So Stitch needed Ashley to know that he loved her when he thought they were going to die, but Ashley later lied to Abby about it; telling her that Stitch talked about his love for her. It might have been more interesting if Abby had seen them confess their feelings and kiss, but pretended she didn't. Who do you think Stitch will ask for when he starts to wake up?
Chelsea versus Christine.
It's always fun to see someone have a go at self-righteous Christine, but in this case the delight in the scene was diminished by the overkill on redeeming Adam. The message was loud and clear – everyone is supposed to love Adam now; he's a good man, he made mistakes, he loves his father and his father loves him, and all the horrible crap he did in the past is to be forgotten. You got that?! Many didn't want to see Adam be hated for killing Delia, but this is too much the other way. The allure of Adam's character is the whole 'misunderstood dark side' thing he had going on. It would be a shame to take that away and make him into a vanilla leading man type. With that said – who loved seeing Adam dressed as a dirty fireman? Show of hands!
He didn't make it.
The storyline with Sage and Nick wasn't popular to begin with, but now it's just silly. Nick and Sage leave the baby in the NICU to go to a gala, don't answer calls or check for missed calls, and then decide they don't want to see him or hold him after they're told he died? How convenient since he was probably stolen. If so, what if they'd decided they wanted to see him? Yeeps. On the whole, many viewers found they were strangely unmoved by this 'death' of a Newman heir. Did you 'feel' it? Let Soaps.com know in the comments.
Fairview fury.
Paul showed up at Fairview believing Patty had died, and tore a strip off Dr. Anderson – great scenes! Meanwhile, Dr. Anderson had just been dealing with some resistance and questions from Sharon, who seemed to have suddenly realized that things weren't quite right. Here's hoping Sharon only pretended to take those pills and will turn the tables on her sinister doll-faced doctor. Oh, and Dr. Anderson told the obviously not pregnant Sharon that her beautiful baby would be arriving soon. No doubt that will be Christian. Sigh…
Come home.
So Cane wouldn't go home with Lily due to ongoing trust issues, and left Joe to help her 'get the kids home'. Confusing, since the reason Cane was so hot to get over to the gala was because he knew Joe was there with Lily. So he went through a near-death experience for what exactly?
Hollering Hilary.
Many don't 'get' this amnesia bit with Hilary at all. If there had been a time when she loved Neil and hated Devon, and her mind had reverted to that time, it might make sense. However, such a time never existed. She had feelings for Devon when she married Neil. If we are to believe that the treatment she received reversed their roles in her mind, well, it's just too dumb. She isn't confused about anyone else…just those two. Bleh.
This is an opinion piece. Feel free to comment in the section below.
Follow Soaps.com on Twitter and Soaps.com on Facebook.
Photo credit: Sean Smith/JPI
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"redpajama_set_name": "RedPajamaCommonCrawl"
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Karol Pękala (ur. 26 października 1902 w Siołkowej, zm. 14 sierpnia 1968 w Sozopolu) – polski duchowny rzymskokatolicki, biskup pomocniczy tarnowski w latach 1946–1968.
Życiorys
Po studiach w Tarnowie 29 czerwca 1928 otrzymał święcenia prezbiteratu. Był wikariuszem w Nowym Wiśniczu, duszpasterzem Polonii francuskiej, diecezjalnym dyrektorem Akcji Katolickiej w 1933 i dyrektorem Caritasu w 1946. Podczas okupacji prowadził działalność charytatywną.
14 grudnia 1946 został mianowany biskupem pomocniczym diecezji tarnowskiej ze stolicą tytularną Trocmades. Święceń biskupich udzielił mu 16 marca 1947 biskup Jan Stepa. W latach 1959–1962 pełnił funkcję wikariusza kapitulnego diecezji. Zasłużony dla rozwoju działalności charytatywnej Kościoła w Polsce. Uczestniczył w I i IV sesji soboru watykańskiego II.
Odznaczenia
W 1939 prezydent RP Ignacy Mościcki nadał mu Złoty Krzyż Zasługi
Postanowieniem prezydenta RP Andrzeja Dudy w 2020 został pośmiertnie odznaczony Krzyżem Komandorskim Orderu Odrodzenia Polski.
Przypisy
Bibliografia
Linki zewnętrzne
Nota biograficzna Karola Pękali w Archiwum Diecezjalnym w Tarnowie (arch.) [dostęp 2014-09-07]
[dostęp 2010-10-21]
Biskupi tarnowscy
Odznaczeni Krzyżem Komandorskim Orderu Odrodzenia Polski (III Rzeczpospolita)
Odznaczeni Złotym Krzyżem Zasługi (II Rzeczpospolita)
Uczestnicy soboru watykańskiego II
Absolwenci Wyższego Seminarium Duchownego w Tarnowie
Urodzeni w 1902
Zmarli w 1968 | {
"redpajama_set_name": "RedPajamaWikipedia"
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{"url":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/decimal-operations\/","text":"What you\u2019ll learn to do: Use various operations to solve applications involving decimals\n\nHow many candy bars can Greg buy with the change in his piggy bank?\n\nGreg is hosting a movie night for his friends, and he\u2019s buying candy to share. Candy bars cost $0.79 each, and Greg plans to buy as many as possible with the change from his piggy bank. If he has$5.53, how many candy bars can he buy? To maximize his candy-buying power, Greg will need to use mathematical operations on decimals. In this section, you\u2019ll learn\u00a0how to perform familiar operations including addition, subtraction, multiplication, and division when working with decimals.\n\nBefore you get started, take this readiness quiz.","date":"2021-10-27 02:59:55","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\": 0.36163926124572754, \"perplexity\": 3130.5386425741244}, \"config\": {\"markdown_headings\": false, \"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-2021-43\/segments\/1634323588053.38\/warc\/CC-MAIN-20211027022823-20211027052823-00283.warc.gz\"}"} | null | null |
{"url":"https:\/\/www.physicsforums.com\/threads\/i-have-attached-the-problem-part-a-show-that-s-is-a-subspace-of.640244\/","text":"# I have attached the problem.part a) show that S is a subspace of\n\nI have attached the problem.\n\npart a) show that S is a subspace of R4\n\nI have to show the following 3 conditions\n0 vector is in S\nif U and V are in S, then U+V is in S\nIf V is in S, then cV is in S where c is a scalar\n\nif s and t=0 which are real #s, then the 0 vector is in R4, thus S is in R4.\nIf U=[2x-y, x, y, -x]^t and V=[2a-b, a, b, -a]^t then U+V still has four rows, thus S is in R4\nIf V=[2a-b, a, b, -a]^t, then cV still has four rows, thus S is in R4.\n\nIs that the right procedure for part a?\n\n#### Attachments\n\n\u2022 8.3 KB Views: 360\n\nRelated Calculus and Beyond Homework Help News on Phys.org\nvela\nStaff Emeritus\nHomework Helper\n\nI have attached the problem.\n\npart a) show that S is a subspace of R4\n\nI have to show the following 3 conditions\n0 vector is in S\nif U and V are in S, then U+V is in S\nIf V is in S, then cV is in S where c is a scalar\n\nif s and t=0 which are real #s, then the 0 vector is in R4, thus S is in R4.\nIf U=[2x-y, x, y, -x]^t and V=[2a-b, a, b, -a]^t then U+V still has four rows, thus S is in R4\nIf V=[2a-b, a, b, -a]^t, then cV still has four rows, thus S is in R4.\n\nIs that the right procedure for part a?\nNo, it isn't.\n\nIf a vector ##\\vec{x}## is in ##S##, you know that it can be written as\n$$\\vec{x} = \\begin{bmatrix} 2s - t \\\\ s \\\\ t \\\\ -s \\end{bmatrix}$$ for some value of ##s## and ##t##. Conversely, if a vector can be written in that form, it is in S.\n\nAs you noted, if s=t=0, then ##\\vec{x} = 0##. Therefore, you can conclude that 0 is in ##S##. That's what you wanted to show, not that 0 is in \u211d4 nor that ##S## is in \u211d4, which doesn't make sense.\n\n$$\\vec{u} + \\vec{v} = \\begin{bmatrix} 2x - y \\\\ x \\\\ y \\\\ -x \\end{bmatrix} + \\begin{bmatrix} 2a - b \\\\ a \\\\ b \\\\ -a \\end{bmatrix}.$$ Can you show that that sum can be written in the form\n$$\\begin{bmatrix} 2c - d \\\\ c \\\\ d \\\\ -c \\end{bmatrix}$$ for some value of ##c## and ##d##? If you can, then you can conclude that ##\\vec{u}+\\vec{v} \\in S##.\n\nI'll leave the last part for you to figure out on your own.\n\nOkay I defined U=(2x-y, x, y, -x)^t, Where x&y are real\nV=(2a-b, a, b, -a)^t Where a&b are real\nU and V are vectors in the subspace S.\n\nI added U+V=(2x-y+2a-b, x+a, y+b, -x-a)^t = [2(x+a)-(y+b), x+a, y+b, -(x+a)] Which is in the form of S, thus U+V is in S.\n\nIs the above correct so far?\n\nLast condition, if V is in S, then cV must be in S.\ncV=V=(c2a-cb, ca, cb, -ac)^t\nNow, this is where I get stuck again. How does this show that cV is in V? Is it because multiply each component by a scalar c still keeps it in the same form of S?\n\nHallsofIvy\nHomework Helper\n\nOkay I defined U=(2x-y, x, y, -x)^t, Where x&y are real\nV=(2a-b, a, b, -a)^t Where a&b are real\nU and V are vectors in the subspace S.\n\nI added U+V=(2x-y+2a-b, x+a, y+b, -x-a)^t = [2(x+a)-(y+b), x+a, y+b, -(x+a)] Which is in the form of S, thus U+V is in S.\n\nIs the above correct so far?\nYes, that is good.\n\nLast condition, if V is in S, then cV must be in S.\ncV=V=(c2a-cb, ca, cb, -ac)^t\nNow, this is where I get stuck again. How does this show that cV is in V? Is it because multiply each component by a scalar c still keeps it in the same form of S?\nBasic algebra: c2a- cb= 2(ca)- (cb) so (c2a- cb, ca, cb, -ac)= (2x- y, x, y, -x) with x= ca and y= cb.\n\nI just looked in the answer in the back of the book, they seemed to have done it in a much easier way.\n\nThey said S=span{[2 1 0 -1]^t, [-1 0 1 0]}. therefore S is a subspace.\n\nvela\nStaff Emeritus\nHomework Helper\n\nIf you've already proved in your class that the span of a set of vectors is a subspace, then, sure, you can go ahead and use that result.\n\nOkay thanks. Also what is part d) is S=R^4 asking?\n\nIs it asking if S is in R^4?\n\nvela\nStaff Emeritus\nHomework Helper\n\nNo, it's asking if S is exactly the same as \u211d4. Is every vector in S in \u211d4 and is every vector in \u211d4 in S?\n\nHmmm. I think the answer is no.\n\nc1[2 1 0 -1]^t + c2[-1 0 1 0]=[a b c d]^t\n\nWriting this in \"augmented\" matrix form gives (each space denotes a new element in the matrix:\n2 -1 a\n1 0 b\n0 1 c\n-1 0 d\n\nRow reducing this into RREF gives\n1 0 b\/2\n0 1 2b-a\n0 0 c-2b+a\n0 0 d+b\n\nThus S doesn't equal all of R^4 because the system is consistent only if c-2b+a=d+b=0\n\nIs this the right approach?\n\nvela\nStaff Emeritus\nHomework Helper\n\nThat's a valid argument. An aside: note if you solve for everything in terms of b and c, you get\n\\begin{align*}\na &= 2b-c \\\\\nb &= b \\\\\nc &= c \\\\\nd &= -b\n\\end{align*} which should look familiar.\n\nIf you know about dimensions, you could also make an argument on that ground as well. Or you could find a vector in \u211d4 that's not in S. There are a variety of ways to show the two spaces aren't the same.\n\nIs every vector in S in \u211d4 and is every vector in \u211d4 in S?\nIs it true if I say this:\nAll of the vectors in S are in R^4, but not all of the vectors in R^4 are in S because c-2b+a=0 and b+d=0 has to be satisfied.\n\nHallsofIvy\nHomework Helper\n\nOr you could pick a vector, say (1, 1, 0, 0), that doesn't satisfy those equations and show that it is NOT in the subspace.\n\nvela\nStaff Emeritus\nHomework Helper","date":"2020-05-29 21:12:28","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\": 0.932919442653656, \"perplexity\": 1649.0479086107448}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347406365.40\/warc\/CC-MAIN-20200529183529-20200529213529-00092.warc.gz\"}"} | null | null |
package org.infinispan.demo.carmart.session;
import java.util.logging.Logger;
import javax.annotation.PreDestroy;
import javax.enterprise.context.ApplicationScoped;
import org.infinispan.client.hotrod.RemoteCacheManager;
import org.infinispan.client.hotrod.configuration.Configuration;
import org.infinispan.client.hotrod.configuration.ConfigurationBuilder;
import org.infinispan.demo.carmart.session.CacheContainerProvider;
/**
*
* {@link CacheContainerProvider}'s implementation creating a HotRod client.
* JBoss Data Grid server needs to be running and configured properly
* so that HotRod client can remotely connect to it - this is called client-server mode.
*
*
*/
@ApplicationScoped
public class RemoteCacheContainerProvider extends CacheContainerProvider {
private Logger log = Logger.getLogger(this.getClass().getName());
private RemoteCacheManager manager;
public RemoteCacheManager getCacheContainer() {
if (manager == null) {
Configuration configuration = new ConfigurationBuilder().addServers(jdgProperty(DATAGRID_HOST) + ":" + jdgProperty(HOTROD_PORT)).build();
manager = new RemoteCacheManager(configuration, true);
log.info("=== Using RemoteCacheManager (Hot Rod) ===");
}
return manager;
}
@PreDestroy
public void cleanUp() {
manager.stop();
manager = null;
}
}
| {
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News | Philanthropy › Grantmaking
Transferring wealth… into the hands of the community
Residents of Wangaratta, Indigo, Alpine and Mansfield could raise $6.3 million in charitable assets over a decade
Maggie Coggan | 5 February 2020 at 5:24 pm
As baby boomers head into retirement and set off one of the largest intergenerational wealth transfers in history, a community foundation in northeastern Victoria is waging a new campaign to harness some of the incoming wealth for local initiatives.
Wealth projection data, released late last year by Wangaratta-based community foundation Into Our Hands, found if just 1 per cent of the wealth transfer from the region was bequeathed to community foundations, the endowment would build to $25 million in a decade.
It also found that if one in 20 residents in the region left 5 per cent of their estate to a community foundation, $6.3 million would end up in management.
First trialled in the American cities of Nebraska, Ohio, and Wisconsin, legacy gifts have seen over $120 million in endowments raised in 30 years. Sarah Thompson, Into Our Hands CEO, told Pro Bono News there was untapped potential for Australian communities to do the same.
Read more: The power of community philanthropy
"These communities [in the US] flipped their thinking and started to talk about raising money in terms of what could be achieved if some of us or all of us started to give a small portion of our estate or our wealth," Thompson said.
"It started to make the development targets for communities very, very achievable [for what] probably felt like a fairly poor rural community."
She said that kind of money would mean a grant budget annually that was more significant than any other funder in the region, and it would be controlled by community members.
"This is a fund overseen by community people and investment in its own region. It's their assets and the funds are managed by the community," she said.
She also said the northeastern region of Victoria had the "right ingredients" of a stable economy and community members that were willing to take ownership of their issues.
"We are a community of people who want to see changes and a community that has put its own money to fund several initiatives such as renewable energy projects in Yackandandah and Beechworth," she said.
With many residents in the region unfamiliar with community foundations or philanthropy, Thompson said if the campaign was to be effective, that had to change.
"We want to set a region-wide, fairly intensive campaign that saturates the community to bring it up to speed with philanthropic terms and what they mean," she said.
"It's really a public education campaign that would include community workshops and information sessions, radio, print, maybe even some TV advertising."
She also said it was important to target groups of people who weren't regular donors.
"The agriculture and farming sector and family business sector in regional areas hold a lot of wealth, but they're not necessarily ready to give till the end of their life," she said.
She said there was potential for the model to scale, creating widespread impact in communities across the country – particularly in regional communities.
"I really see transfer of wealth as a new tool for community foundations to talk to potential donors about why you would give in this way as opposed to setting up your own private ancillary fund, and what this does for long-term community benefit," she said.
"We're very interested in talking to Philanthropy Australia about how this can be a new way to discuss giving in the community and that regional sense that probably hasn't been tapped into effectively in Australia before."
Maggie Coggan | Journalist | @MaggieCoggan
Maggie Coggan is a journalist at Pro Bono News covering the social sector.
Tags : Community Foundations, place based philanthropy, Wealth Transfer,
New grants program to help the hidden victims of COVID-19
Monday, 27th July 2020 at 4:59 pm
COVID crisis forces a shift in grantmaking
Friday, 24th July 2020 at 11:48 am
Supporting not for profits to build capacity for impact
Andrew Cairns
Thursday, 23rd July 2020 at 7:10 am
Want to help shape Melbourne?
Thursday, 23rd April 2020 at 7:15 am | {
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COLUMBUS, Ohio–The annual Ohio State football photo day will be held at 5 p.m. Wednesday at Ohio Stadium. The event is open to the public for viewing only. No public autograph or photo session will be held.
Fans interested in attending the event will be seated on the South Stands only. All gates with access to the South Stands (SE, SW and South Stands gates) will open at 4:30 p.m. Fans are encouraged to park at the West Campus and Sisson (west bank of the Olentangy River) parking lots. Shuttles run all day every 15 minutes from West Campus to Ohio Stadium. A foot bridge connects the Sisson lot to Ohio Stadium.
Concessions and merchandise will be available in the South Stands. | {
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package com.turn.ttorrent.network.keyProcessors;
import com.turn.ttorrent.common.TorrentLoggerFactory;
import com.turn.ttorrent.network.ConnectionListener;
import com.turn.ttorrent.network.ReadAttachment;
import org.slf4j.Logger;
import java.io.IOException;
import java.nio.channels.SelectableChannel;
import java.nio.channels.SelectionKey;
import java.nio.channels.SocketChannel;
public class ReadableKeyProcessor implements KeyProcessor {
private static final Logger logger = TorrentLoggerFactory.getLogger();
private final String myServerSocketLocalAddress;
public ReadableKeyProcessor(String serverSocketLocalAddress) {
this.myServerSocketLocalAddress = serverSocketLocalAddress;
}
@Override
public void process(SelectionKey key) throws IOException {
SelectableChannel channel = key.channel();
if (!(channel instanceof SocketChannel)) {
logger.warn("incorrect instance of channel. The key is cancelled");
key.cancel();
return;
}
SocketChannel socketChannel = (SocketChannel) channel;
logger.trace("server {} get new data from {}", myServerSocketLocalAddress, socketChannel);
Object attachment = key.attachment();
if (!(attachment instanceof ReadAttachment)) {
logger.warn("incorrect instance of attachment for channel {}", new Object[]{socketChannel.socket()});
socketChannel.close();
return;
}
ConnectionListener connectionListener = ((ReadAttachment) attachment).getConnectionListener();
connectionListener.onNewDataAvailable(socketChannel);
}
@Override
public boolean accept(SelectionKey key) {
return key.isValid() && key.isReadable();
}
}
| {
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The Haines Borough School District is the school district administrating education in both the city of Haines, Alaska, but the Haines Borough as well.
Schools
Haines High School
Haines Junior/Elementary School
Mosquito Lake Elementary School
See also
List of school districts in Alaska
External links
Official site
Education in Haines Borough, Alaska
School districts in Alaska | {
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{"url":"https:\/\/www.physicsforums.com\/threads\/index-gymnastics-maxwells-equations.708504\/","text":"# Index gymnastics-Maxwell's equations\n\n#### WannabeNewton\n\n1. Homework Statement\nLet $X^{ab}$ be an antisymmetric tensor such that $\\nabla^{(a}X^{b)c} = 0$. Show that if $R_{ab} = 0$, then $F_{ab} = R_{abcd}X^{cd}$ satisfies Maxwell's equations $\\nabla^a F_{ab} = 0, \\nabla_{[a}F_{bc]} = 0$ where $R_{abcd}$ is the Riemann curvature tensor and $R_{ab}$ is the Ricci tensor.\n\n3. The Attempt at a Solution\nWell to start with, $\\nabla^a X^{bc} = -\\nabla^b X^{ac} = \\nabla^b X^{ca} = -\\nabla^c X^{ba}$ so $\\nabla^a X^{bc}$ is antisymmetric in all its indices. Thus, $\\nabla^a F_{ab} = R_{abcd}\\nabla^{a}X^{cd} + X^{cd}\\nabla^a R_{abcd} = -R_{b[acd]}\\nabla^{a}X^{cd} -2X^{cd}\\nabla_{[b}R_{c]d} = 0$ since $R_{b[acd]} = 0$ by the first Bianchi identity and $R_{ab} = 0$ by hypothesis.\n\nShowing that $\\nabla_{[a}F_{bc]} = 0$ should be just as easy but for some reason I can't seem to find a way to show it. We have $\\nabla_{a}F_{bc} =\\nabla_{a}X^{de} R_{bcde} + X^{de}\\nabla_{a}R_{bcde}$ so $\\nabla_{[a}F_{bc]} = \\nabla_{[a}X^{de}R_{bc]de}$ since $\\nabla_{[a}R_{bc]de} = 0$ by the second Bianchi identity. One can either try to show that $\\nabla_{[a}X^{de}R_{bc]de} = 0$ directly or (equivalently) show that $\\epsilon^{abcf}\\nabla_{a}X^{de}R_{bcde} = 0$. I know I'm missing something very trivial but I can't seem to proceed from here either way. Thanks in advance for any help!\n\nLast edited:\nRelated Calculus and Beyond Homework Help News on Phys.org\n\n\"Index gymnastics-Maxwell's equations\"\n\n### Physics Forums Values\n\nWe Value Quality\n\u2022 Topics based on mainstream science\n\u2022 Proper English grammar and spelling\nWe Value Civility\n\u2022 Positive and compassionate attitudes\n\u2022 Patience while debating\nWe Value Productivity\n\u2022 Disciplined to remain on-topic\n\u2022 Recognition of own weaknesses\n\u2022 Solo and co-op problem solving","date":"2019-10-23 10:45:57","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\": 0.8281480669975281, \"perplexity\": 593.4239935722563}, \"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-2019-43\/segments\/1570987833089.90\/warc\/CC-MAIN-20191023094558-20191023122058-00074.warc.gz\"}"} | null | null |
Q: Error trying to create a Wordpress database table I am creating a plugin for Wordpress.
I'm trying to create a new table to insert inside the Wordpress database, but i keep getting this error and I can't understand well the reason.
"have an error in your SQL syntax; check the manual that corresponds to your MariaDB server version for the right syntax to use near 'wp_gdax_account_info' at line 1"
Is there a mistake in my code? Does someone know how to solve it?
Thank you in advance.
function jal_install(){ //create table
global $wpdb;
global $table_prefix;
$table_name = $wpdb->prefix . 'gdax_account_info';
$charset_collate = $wpdb->get_charset_collate();
if ($wpdb->get_var('SHOW TABLES LIKE '.$table_name) != $table_name) {
$sql = "CREATE TABLE". $table_name ."(
id INTEGER (10) NOT NULL AUTO_INCREMENT,
chiave VARCHAR(55) NOT NULL,
email VARCHAR(55) NOT NULL,
secret VARCHAR(55) NOT NULL,
pass VARCHAR(55) NOT NULL,
PRIMARY KEY (id)
);".$charset_collate.";";
require_once(ABSPATH . 'wp-admin/includes/upgrade.php');
dbDelta ($sql);
echo "$wpdb->last_error";
add_option("gdax-account-info", "1.0");
}
}
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 3,160 |
\section{Introduction}
Dwarf novae (hereafter DN) are a subtype of primarily non-magnetic cataclysmic variables (hereafter CVs), in which a white dwarf primary accretes matters from a Roche-lobe filling late-type star via the inner (L1) Lagrange point \citep{war03}. An accretion disk can extend to the white dwarf surface via viscous processes between adjacent accretion annuli (e.g., friction and shear) due to a weak magnetic field of the white dwarf in DN (B$<$10$^{6}$\,G). Systems in which the magnetic field of the white dwarf is large enough (10$^{6}<B\leqslant$\,10$^{7}$\,G) such that the accretion disk is disrupted inside the white dwarf magnetosphere and material begins to follow the magnetic field lines are called Intermediate Polars (hereafter IPs). In the following, we assume that the disk outside of the magnetosphere in an IP is equivalent in structure to the disk in a regular non-magnetic DN. The interaction between the ballistic stream leaving the L1 point and the accretion disk forms a region of energy release at the edge of the disk called a hotspot. The combination of an accretion disk and a hotspot (hereafter just called the disk model) has been used as the typical accretion model for CVs \citep[e.g.][]{sma70,war03} and has been quite successful in describing the asymmetrical eclipse profile of several high-inclination CVs during quiescence \citep[e.g.][]{bru96,woo86}. This model can also be used to explain a symmetrical CV eclipse profiles during outburst \citep[e.g.][]{kat03,bak15}, which is caused by the significant flux increase of the disk (i.e., the luminous accretion disk almost overwhelms the relatively faint white dwarf and hotspot).
Several high-inclination CVs in quiescence have been comprehensively studied using this disk model \citep[e.g.][]{coo84,bai91,mca15}. By detecting variations in the mid-eclipse times, substellar objects have been suggested to exist in several DN (e.g., V2051\,Oph \citep{qia15} and EM\,Cyg \citep{dai10a}). In addition, many synthetic light curve analysis methods (e.g., BINSYN program \citep{lin12}, Eclipsing Light Curve Code \citep{oro00} and the cool-disk model \citep{khr11}) have been developed to analyze CV eclipse light curves. The irregular eclipse light curves of quiescent CVs are composed of the occultations of multiple components including the white dwarf, the accretion disk and hotspots \citep[e.g.][]{sma94,fel04,lit14,mca15}. High-inclination CVs only show a single eclipse in one orbit (i.e., the secondary eclipse of the red dwarf is invisible \cite[e.g.][]{krz65,bai88}), since the red dwarf in a CV system is usually regarded to be a very faint component compared with the accretion disk and the white dwarf. This ``single-eclipse" feature implies that CV eclipse light curves cannot reveal full information about the red dwarf companion. Due to the complexity of the quiescent CV eclipse light curves, high time resolution is necessary to decompose all components. However, over 70\% of CVs with short orbital periods ($<$\,3\,hr) are fainter than 17\,mag in quiescence based on the updated CV catalogue (RKcat Edition 7.24 first published in \cite{rk724}). Therefore, the majority of CVs have only low time-resolution photometry comprised of blended flux from many components, which makes modelling these systems difficult. For example, recent discussions concerning two new-found CVs with deep eclipses carried out by \cite{kju15} and \cite{ken16} clearly indicated that the model light curves cannot perfectly fit the observed eclipsing light curves during ingress and outside of eclipse. Assuming a deep eclipse is a common feature of CVs with orbital inclination higher than 80$^{\circ}$, the fraction of low-inclination CVs can be simply estimated to be around 90\%. To determine a general model independent of inclination, it is necessary to consider low-inclination CVs.
The unprecedented light curves from the Kepler K2 mission \citep{how14}, with nearly continuous photometric coverage for 1-3 months at different pointings (Campaigns) along the ecliptic provide an excellent database to study quiescent CV light curves. K2 Campaign 0 (K2-C0) was an engineering test in the early stage of the K2 program and only covered $\sim$\,35 days since the spacecraft was not in fine point during the beginning of the campaign, while K2 Campaign 1 (K2-C1) covered a complete period of 80 days. We focus in this paper on the phased light curves of four systems: 1RXS\,J0632+2536 (hereafter J0632+2536) and TW\,Vir which are both DN, RZ\,Leo which is an unusual IP that also has displayed DN outbursts, making it one of the few systems to be both a magnetic system and a DN, and WD\,1144+011 which is a pre-CV (meaning the secondary is likely not filling its Roche lobe). J0632+2536 was observed in K2-C0, while TW\,Vir, RZ\,Leo and WD\,1144+011 were observed in K2-C1. The phased light curves are investigated in detail using the synthesis methods XRBinary and NMfit described in Section 3. Due to the lack of any eclipse feature, all four objects are likely low-inclination systems. The preset model parameters are discussed in Sections 4 and 5. The details of the white dwarf accretion structure during quiescence and the physical parameters of the stars in each system are further discussed and visualized in Section 6.
\section{Phased Light Curves}
\cite{dai16} used the PyKE suite of software tools developed by the Guest Observer Office \citep{sti12} to extract the K2 light curves of J0632+2536, RZ\,Leo and WD\,1144+011, and derive their orbital periods using traditional period finding techniques (e.g., Lomb-Scargle periodogram \citep{lom76,sca82}, phase dispersion minimization \citep{ste78}) and their corresponding phased light curves. Due to the unstable orbital modulations of TW\,Vir, \cite{dai17} applied a phase-correcting method to obtain its orbital period and the phased data from the quiescent data.
Based on the continuous K2 data, we attempted to model the mean orbital light curves of each system by using an XRBinary light curve synthesis code developed by E. L. Robinson \footnote{\url{http://www.as.utexas.edu/~elr/Robinson/XRbinary.pdf}}. The default phase zero of a light curve generated by XRBinary is inferior conjunction of the Roche-lobe filling secondary (i.e., the accretion disk around the white dwarf is occulted by the red component), which is in accord with the phases specified in eclipsing CVs. Compared with the typical CV eclipse light curve with a narrow and deep white dwarf eclipse \citep[e.g.][]{lit14,mca15}, all four light curves derived by \cite{dai16,dai17} only show wide and shallow modulations with an amplitude of several hundredths up to tenths of a magnitude. Note that the phases of the obtained light curves are arbitrary. The three DN (J0632+2536, RZ\,Leo and TW\,Vir) light curves clearly show double-hump modulations with a nearly constant phase difference of $\sim$0.5 between the two minima dips. This means that the light minima at the lower (primary dip) and higher (secondary dip) flux levels are at phases 0.5 or zero, respectively. In principle, an irradiation effect is significant in CV systems and commonly results in a higher flux level at the phase 0.5 dip than at phase zero. But, phase zero of the double-hump modulation cannot be simply identified from this flux difference due to possible changes caused by hotspots on the disk. Therefore, for each DN with a double-hump modulation discussed in this paper, two phased light curves corresponding to phase zero at the primary and secondary dips respectively, were analyzed to search for a final convergent solution. Since the secondary dip in TW\,Vir cannot be accurately measured due to large scatter in the data, the primary maximum was set to be at the reference phases 0.75 and 0.25, guaranteeing that minima would occur around phases 0.5 and zero. For the pre-CV WD\,1144+011, phase zero was set to be the minimum of the light curve since the light curve shows a single-hump modulation.
The four K2 light curves are expressed in Simple Aperture Photometry (SAP) flux (i.e., electrons per second), while the light curves calculated by XRBinary are given in ergs per second. Hence, the K2 light curves were normalized before the calculations of XRBinary. Since the huge number of data points in the observed light curves (i.e., the number of data points in the K2 light curves observed in long cadence (LC; 30\,min sampling) and in short cadence (SC; 1\,min sampling) are more than 10$^{3}$ and 10$^{5}$, respectively.) can take a long calculation time with XRBinary, the K2 phased light curves are moderately binned with a uniform phase resolution 0.01. \cite{dai17} demonstrated that the orbital modulations of the three CVs are stable, and the large amplitude dispersion of $\sim$0.43\,mag in the phased light curve of RZ\,Leo \citep[Figure 5 of][]{dai16} is only caused by a uniform drift of the system light. Thus, while the phased light curve of TW\,Vir has the highest stability \citep{dai17}, all four binned and normalized K2 light curves represent their orbital modulations.
\section{Synthesis Methods for the Light Curves}
Although the program XRBinary was initially designed for calculating the light curves of low-mass X-ray binary stars (LMXBs) \citep{gom15}, it can also be used to model low-inclination CVs based on the following two reasons. First, XRBinary sets the primary star as a much smaller sphere than all other dimensions in the binary system and is unresolved by any of the grids used in calculating the light curves. Like the neutron star in LMXBs, the white dwarf in both CVs and pre-CVs is very small compared with the companion red dwarf. Second, XRBinary simply assumes that the primary star only emits black body radiation. This is a reasonable assumption for low-inclination CVs and pre-CVs since the flux contribution from the visible white dwarf is approximately constant. XRBinary may not be appropriate for accurately modelling complicated eclipse light curves, but should be able to reproduce low-inclination CV light curves. In fact, XRBinary is a powerful tool to analyze the accretion disk around the central compact star by constructing a complex accretion disk model consisting of a disk, a disk rim, a disk torus and an inner disk. \cite{rat13} have successfully applied XRBinary to reproduce an ellipsoidal light curve of the CV CXOGBS J174444.7-260330 in a low state.
In this paper, a standard CV model (i.e., a semi-detached close binary system with a Roche-lobe filling red dwarf and, in the case of the 3 DN, an accretion disk around the white dwarf) with a set of geometric and physical parameters is applied to model the phased light curves of four low-inclination systems. Based on a complete set of preset parameters, XRBinary calculates a theoretical light curve and a relative measurement of goodness of fit, $\chi^{2}$ (i.e., the variance between the calculated and observed light curves). Taking advantage of the improved Nelder-Mead method (i.e., Multi-directional Search method \citep[MDS][]{nel65,tor89,gen08}), which was successfully applied to fit the O-Cs of AM Her \citep{dai13} and UZ\,For \citep{dai10b}, we developed a new program called NMfit to carry out a search for the best binary model within a given parameter space. After obtaining the best binary model, NMfit sets a series of small deviations around each of the parameters to test the variations in $\chi^{2}$ caused by these deviations. Note that when an adjustable parameter is intentionally set to deviate from its optimal value, the other parameters are fixed. Moreover, this optimisation method ignores degeneracies between parameters, which is a big issue. Since the best binary model means the minimal $\chi^{2}$, the deviations give rise to an increase of $\chi^{2}$. When $\chi^{2}$ increases to 5\% larger than the minimal value, this tested parameter deviation is arbitrarily regarded as the uncertainty. All adjustable parameters are tested one-by-one for estimating their errors. The error estimates based on $\chi^{2}$ are only lower limits to the true uncertainties in the derived parameters, and the true uncertainties could be quite large, since the physics of compact binaries is much more complicated and XRBinary arbitrarily makes many tacit assumptions (e.g. the disk is modelled as an object with sharp, well-defined edges and surfaces, and the disk surface elements emit and absorb like black bodies). The uniform design proposed by \cite{fan80} is used to decide the initial parameter set before the search iterates. A good initial parameter set is crucial for the success of the iterations. In addition, since Phoebe \footnote{The version of Phoebe used for the CV plotting is 2.0a2.} is able to calculate and plot an accretion disk around a compact star \citep{prs16}, it was used to visualize the system configuration based on the best-fitting parameters derived by NMfit and XRBinary.
\section{Model Parameters Preset in XRBinary}
For generating light curves, there are a total of 23 model parameters listed in Table 1, which are divided up into 7 fixed parameters and 16 adjustable parameters. Our assumptions for these parameters are as follows.
1. Although the input and output light curves of XRBinary are normalized, the typical luminosity of the white dwarf can provide an important reference for the system luminosity of the output CV model. Since the mass range for isolated white dwarfs is 0.3\,M$_{\odot}$ to 1.4\,M$_{\odot}$ and over 30\% of white dwarfs are centered on $\sim$\,0.56\,M$_{\odot}$ \citep{ber92,pro98}, the white dwarf masses of all four objects were searched in this mass range. By using the relation L$_{wd}$=4$\pi$R$_{wd}^{2}\,\sigma$\,T$_{wd}^{4}$, the white dwarf radius R$_{wd}$ is solely dependent on the white dwarf luminosity L$_{wd}$ and temperature T$_{wd}$. According to the white dwarf mass-radius relation shown in Fig. 1 \citep[e.g.][]{woo90,pro98}, L$_{wd}$ can only be determined by T$_{wd}$ for a given M$_{wd}$. During the iterations of NMfit, T$_{wd}$ calculated from the adjustable parameter L$_{wd}$ is preset to be a fixed parameter.
2. In order to improve the reliability of the model, a simple disk with minimal free parameters consisting of up to two hotspots (one at the vertical side of the edge of the disk (es) and the other one on the surface of the disk (ss)) is used to describe the low-inclination CV light curves. This CV quiescent disk was assumed to normally extend to the surface of the white dwarf (i.e., R$_{in}$\,=\,R$_{wd}$). A boundary layer was not considered since it dominates the flux at ultraviolet wavelengths rather than at optical wavelengths. A hotspot on the vertical side of the edge of the disk can be completely described by using 3 parameters: a uniform temperature T$_{es}$, the centering phase $\zeta_{esmid}$ and the full width $\zeta_{eswidth}$. Considering that the other hotspot on the disk surface can be visible and modulate the light curves of low-inclination CVs, this hotspot is described by using five parameters: $\zeta_{ssmin}$, $\zeta_{ssmax}$, R$_{ssmin}$, R$_{ssmax}$ and T$_{ratio}$. The first four parameters are the boundaries of the hotspot, which are the angles and radii over which the hotspot extends, respectively. The last parameter T$_{ratio}$ is a fractional change in T$_{disk}$ (i.e., T$_{ratio}$\,=\,T$_{ss}$/T$_{disk}$).
3. A different temperature distribution may exist in different quiescent accretion disks. The temperature distribution is assumed to be a power law in disk radius R$_{disk}$, i.e., T$_{disk}\,\propto\,R_{disk}^{\xi}$. For a steady-state disk, typically $\xi$\,=\,-0.75 \citep{wad98}. However, subsequent papers suggested that accretion disks in CVs have much flatter temperature profiles with $\xi$\,$>$\,-0.75 \citep[e.g.][]{mar99,oro03}. According to the disk instability model \citep[DIM,][]{osa13a,osa13b,osa14}, the quiescent DN disk is an optically thin and cool disk with a flat radial temperature profile. Observations of various quiescent DN (e.g., Z Cha \citep{woo86}, OY Car \citep{woo89}, V2051 Oph \citep{rut16}) confirm that their disk temperature distributions are much flatter than the prediction of T$_{disk}\,\propto\,R_{disk}^{-0.75}$. We initially assume $\xi$\,=\,-0.15, but allow this value to be adjusted by NMfit.
4. The adjustable parameter L$_{d0}$ indicating the disk luminosity is only calculated from the temperature distribution of the disk. This parameter should satisfy a default condition that the temperature at the inner edge of disk (i.e., T$_{in}$) cannot be much larger than 10$^{4}$\,K, since the average temperature of observed quiescent disks is below 10$^{4}$\,K, which is consistent with the typical temperature range of an accretion disk (from several 10$^{3}$\,K to 10$^{4}$\,K) predicted by the limit-cycle oscillation between hot and cold states \citep{las01}.
5. Since both theories and observations suggest that the accretion disk around a white dwarf is geometrically thin \citep[e.g.][]{pri81,fra92,wad98,mar99}, the height of the disk, H$_{disk}$, is assumed to obey a power low with a power index H$_{pow}$=1.1 for all four objects, but H$_{edge}$ is set to be adjustable.
6. Since the components of the model calculated in XRBinary (e.g., two component stars, the disk and hotspots on the disk) are independent, we can freely construct the necessary components to model the observed light curves. Three types of models, as listed in Table 2, were attempted to verify the necessity of a disk around the white dwarf and the hotspots on the disk. Model-0 is a detached binary model without a disk. Model-1 contains an accretion disk with a hotspot at the edge of the disk. Model-2 adds a second hotspot on the disk surface. The relative flux contributions in percentage from the different model components to the synthetic light curves calculated by XRBinary are shown in Fig. 2. Their zero points are listed in Table 3.
\section{Irradiation effect calculated in NMfit}
The irradiation effect is only calculated by XRBinary when setting the parameter ``IRRADIATION" to be ``ON". Since a luminous secondary may weaken the illumination from the vicinity of the white dwarf and the disk, the parameter ``IRRADIATION" is preset to be ``OFF" if the summation of the luminosity of the white dwarf and the disk (i.e., L$_{wd}$+L$_{d}$) is smaller than the luminosity of the secondary L$_{rd}$. Although XRBinary can calculate the heating effect due to the irradiation, the output parameter T$_{rd}$ of XRBinary is simply derived from L$_{rd}$ by using the formula $L_{rd}\,\sim\,4\pi R_{rd}^{2}\,\sigma\,T_{rd}^{4}$. This means that T$_{rd}$ represents the temperature of the secondary averaged over its entire surface, which can be significantly higher than the true night side temperature of the secondary if irradiation in the systems is significant. Here, the night side is the surface of the secondary facing away from the WD and disk, and the day side is the surface facing the WD and disk.
\cite{dav92} found that the size of the irradiation region is usually as large as the entire day side surface of the secondary star. The numerical work by \cite{kir82} suggested that the difference in the effective temperature between the day and night sides of the secondary is very large. Considering that the typical difference may reach close to 10$^{4}$\,K \citep{war03}, irradiation would be easily observed if this tremendous disparity of the effective temperature exists. Therefore, an estimation of the size of the irradiation region on the surface of the secondary can help to understand the flux contribution from the irradiation region in both CV and pre-CV systems. The effective temperature of the secondary at the night side can be specified by the semi-empirical CV donor sequence \citep{kni06,kni11}. The derived T$_{rd}$ can be regarded as a lower limit to the effective temperature of the irradiation region.
Due to orbital rotation, our viewing angle of the irradiated region can change with the orbital phase. Assuming that the irradiation region on the leading side of the star \footnote{The secondary is assumed to be spherical to simplify the calculations of the irradiation effect.} is axisymmetric with the line between the center points of two component stars, the flux ratio should reach a maximum between phases 0.5 and 0.0, i.e., F$_{irr}\,=\,f_{0.5}/f_{0.0}$, where f$_{0.5}$ and f$_{0.0}$ are the irradiation flux at phases 0.5 and 0.0, respectively. The details of the calculations of F$_{irr}$ are described in Appendix A. By investigating the variations in F$_{irr}$ along with a normalized area of the irradiation region (i.e., S$_{irr}\,=\,A_{irr}/A_{star}$, where A$_{irr}$ and A$_{star}$ are the areas of the irradiation region and the whole star, respectively), a relation between F$_{irr}$ and S$_{irr}$ based on the phycial model derived by XRBinary and NMfit can be estimated and used to compare with the observed flux ratio F$_{obs}$ between phases 0.5 and 0.0.
\section{Comparisons with Gaia results}
Since the K2 light curves of the four binary systems are from the broad bandpass listed in Table 1, their K2 magnitudes (hereafter Kp$_{2}$) translated by \cite{dai16} are commonly different from their apparent visual magnitudes. Assuming this magnitude difference to be a systematic error, the calculated magnitudes of the four systems (hereafter CKp$_{2}$) based on the luminosities of the models can be set to be a reference parameter for the comparisons with the results from the Gaia mission \citep{gai16}. Table 4 lists the distances of all four systems based on the absolute stellar parallax in the Gaia database \citep{gai18} \footnote{\url{https://gea.esac.esa.int/archive/documentation/GDR2/Miscellaneous/sec_credit_and_citation_instructions/}}. CKp$_{2}$ can be estimated from the Gaia distance D$_{g}$ derived from the Gaia parallax \citep{lur18}, and the system luminosity L$_{all}$, which is summed for all model components and corresponds to the zero point of the normalized K2 light curves, by using the following formula,
\begin{equation}
CKp_{2}\,=\,2.5\,\log\left[\frac{L_{bol0}}{L_{all}}\right]\,-\,BC_{v}\,+\,5\,\log\left[\frac{D_{g}}{10\,pc}\right],
\end{equation}
where L$_{bol0}\,=\,3.0128\times10^{35}$\,erg/s \footnote{A zero point luminosity corresponds to an absolute bolometric magnitude scale (i.e., M$_{bol}$=0) recommended by the IAU 2015 Resolution B2.}, and BC$_{v}$ is a bolometric correction of main sequence star in the typical Johnson-Cousins V band with the solar log\,g, [Fe/H] and [$\alpha$/Fe]. Note that BC$_{v}$ corresponding to the derived T$_{rd}$ can cause an uncertainty of CKp$_{2}$ for CV and pre-CV systems, since BC$_{v}$ is improperly used for the white dwarf and disk. This calculated uncertainty may explain the discrepancy between CKp$_{2}$ and Kp$_{2}$.
Considering that BC$_{v}$ is a model-dependent quantity with many observational constraints, several numerous tabulations are provided in the literature. All three popular BC$_{v}$ tables respectively proposed by \cite{flo96}, \cite{bes98} and \cite{cas14} were used to calculate CKp$_{2}$ to minimize our errors. The relations of BC$_{v}$ and T$_{eff}$ plotted in Fig. 3 clearly show that the three BC$_{v}$ tabulations significantly differ for cool stars with T$_{eff}\leq$\,4,000\,K. Inspection of Fig. 3 indicates that BC$_{v}$ of RZ\,Leo, TW\,Vir and WD\,1144+011 are obviously different for each table. Consequently, the difference between the three BC$_{v}$ tabulations for the same T$_{eff}$ is regarded as the uncertainty of BC$_{v}$. Compared with the two early BC$_{v}$ tables of \cite{flo96} and \cite{bes98}, the updated BC$_{v}$ given by \cite{cas14} is moderate for cool stars. Therefore, they were used to calculate CKp$_{2}$ for all four systems to compare with the K2 magnitudes at the zero point of the normalized K2 light curves \citep{dai16}. The interpolated BC$_{v}$ and the errors used for calculating CKp$_{2}$ for all four systems are listed in Table 4.
\section{Modelling Results and Discussions}
\subsection{J0632+2536}
This is a poorly studied DN with several DN outbursts in 2009 and 2012 \citep{kor12,mas12,ohs12}. \cite{dai16} showed its double-hump light curve extracted from the K2 data archive and several quiescent spectra with strong double peaked Balmer emission lines obtained from the Large Binocular Telescope (LBT). Based on these spectra and the phased K2 light curve, the secondary of J0632+2536 is thought to be a K5V star and the orbital inclination cannot be lower than 50$^{\circ}$. According to the MK spectral classes \citep{cox00}, the initial temperature and mass of the secondary are set to be 4,410\,K and 0.67\,M$_{\odot}$, respectively. Several high-precision measurements of white dwarf masses in CVs \citep{kni06,kni11,zor11} indicate that the mean CV white dwarf mass is usually larger than that of isolated white dwarfs \citep{ber92,kep07}. Thus, for J0632+2536, which lacks an accurate measurement of the white dwarf mass, a mean CV white dwarf mass of 0.83\,M$_{\odot}$ was preset to be the initial parameter (i.e., M$_{wd}$=0.83\,M$_{\odot}$). Finally, \cite{urb06} used IUE spectra of 53 quiescent DN to show that the temperature of a white dwarf, T$_{wd}$, in a CV with an orbital period above the period gap is approximately 25,793\,K \citep{sio99,urb06}. We assume this value for the temperature of the white dwarf in J0632+2536 since its orbital period of 0.314478\,day \citep{dai16} is above the gap.
A large number of trials calculated using XRBinary and NMfit suggest that a convergent solution using a normal CV configuration cannot be achieved when setting phase zero to the primary dip of the light curve. Hence, phase zero was set to be the secondary dip. Model-1 was used to model the phased light curve of J0632+2536. At first, four parameters (M$_{wd}$, T$_{wd}$, mass ratio q$_{orb}$ and T$_{rd}$) were fixed, and the other nine parameters consisting of the orbital inclination i$_{orb}$ and eight parameters of the accretion disk were set to be adjustable. By using NMfit, a preliminary accretion disk model indicated that the inner radius of the disk is basically close to the white dwarf radius, so we then fixed the parameters $\xi$ and R$_{in}$ for deriving the uncertainties of the other 11 parameters. Since $\xi$ is an insensitive parameter, its uncertainty cannot be obtained. By using Phoebe 2.0, a 2D CV configuration at phase 0.75 shown in Fig. 2 visually indicates that J0632+2536 has a large and thick accretion disk with a small hotspot at the edge of the disk. Since the orbital inclination of J0632+2536 is not high enough for the white dwarf to be occulted by the secondary, the flux contribution from the white dwarf is constant and does not vary with the orbital period, so this constant flux contribution is simply added to the ellipsoidal modulations caused by the secondary. Compared with the small white dwarf, the top panel of Fig. 2 clearly shows that the large and thick accretion disk can be partially eclipsed around phase zero. Moreover, the hotspot at the edge of the disk, which has a temperature of 6,200 ($\pm$100) K and has a phase width of 0.033(2) at phase 0.844(2), only contributes a maximum of 5\% of the flux from the whole system. Since CKp$_{2}$ of J0632+2536 listed in Table 4 is almost equal to the corresponding Kp$_{2}$, the obtained physical model of J0632+2536 is compatible with the Gaia distance. However, the T$_{eff}$ of J0632+2536 shown in the Gaia database is obviously higher than that derived from the LBT spectra \citep{dai16} and the derived T$_{rd}$ listed in Table 5.
The region where the mass transfer stream intersects the accretion disk (i.e., the hotspot at the edge of the disk) is simply assumed to be a rectangle with a uniform temperature T$_{es}$ by XRBinary. A mass transfer rate $\dot{M}_{rd}$ (hereafter, the parameters with the subscript rd related to the secondary star) can be roughly estimated by using the following formula,
\begin{equation}
\dot{M}_{rd}\,\simeq\,\frac{L_{acc}\,R_{out}}{G\,M_{wd}},
\end{equation}
where L$_{acc}$ is the luminosity of the hotspot at the edge of the disk. The mass transfer rate can be estimated to be $\dot{M}_{rd}\sim2.5(\pm0.2)\times10^{-10}\,M_{\odot}$/year, corresponding to a mass loss timescale (i.e., $\tau_{\dot{M}}\,\sim\,M_{rd}/\dot{M}_{rd}$) of 2.8$\times10^{9}\,$year. The top right panel of Fig. 4 indicates that M$_{rd}$\,=\,0.7(1)\,M$_{\odot}$ is closer to the semi-empirical mass-period relation of \cite{war03} than that of \cite{smi98}. Furthermore, the secondary radius R$_{rd}$\,=\,0.81 is consistent with the radius-period relations shown in the bottom right panel of Fig. 4. The thermal (or Kelvin-Helmholtz) timescale of the secondary (i.e., $\tau_{kh}\,\sim\,GM_{rd}^{2}/(L_{rd}R_{rd})$) can be calculated to be 7.6$\times10^{7}$\,year, as listed in Table 6, is smaller than the derived $\tau_{\dot{M}}$. This means that the mass transfer via the L1 point is slow, and the secondary is always able to maintain thermal equilibrium. Therefore, the secondary of J0632+2536 is almost indistinguishable from an isolated main sequence star of the same mass. The derived mass and radius shown in the bottom left panel of Fig. 4 confirm that the secondary of J0632+2536 is a typical K5V star \citep{dai16}. Inspection of the top panel of Fig. 2 indicates that the ellipsoidal modulations of this K5 star dominate the observed double-hump modulations. Although the top left panel of Fig. 4 indicates that T$_{rd}$\,=\,4,540(80)\,K is nearly consistent with a normal K5V star based on the MK spectral classes \citep{cox00}, this derived T$_{rd}$ is around 350\,K higher than the prediction of the semi-empirical CV donor sequence \citep{kni06,kni11}. The most likely explanation for this discrepancy may be due to irradiation of the K5V star. Since the irradiation effect is not calculated by XRBinary as L$_{rd}>L_{wd}+L_{d}$, we investigated its strength in more detail. Based on our best-fitting model, the maximal F$_{irr}$ is around 1.08 as shown in Fig. 5. As long as 20\% of the irradiation region can be occulted by the disk at phase 0.5, the observed flux ratio of J0632+2536 (i.e., F$_{obs}\sim$0.87) can be explained. Due to our derived large disk and moderate orbital inclination, a partial eclipse of the irradiation region at phase 0.5 can be expected.
\subsection{RZ\,Leo}
\cite{dai16} confirmed that RZ\,Leo is a short-period DN with an orbital period of 0.07603\,day similar to that derived by \cite{pat03} and \cite{kat09}. \cite{ish01} and \cite{men99} indicated that the secondary of RZ\,Leo should be a normal red dwarf, possibly a main sequence M0 star. Although this spectral type cannot be supported by the mass ratio of 0.14 derived from its superhump excess of 0.033 \citep{ish01}, we speculated that RZ\,Leo should consist of a massive white dwarf and a normal red dwarf with a small mass of $<$\,0.2\,M$_{\odot}$. Thus, we assumed that the initial M$_{rd}$ used in NMfit is 0.15\,M$_{\odot}$, which means M$_{wd}$\,=\,1.1\,M$_{\odot}$ and T$_{rd}$\,$\sim$\,3,500\,K. \cite{szk17} and \cite{dai16} detected a short white dwarf spin period of $\sim$\,220\,s classifying RZ\,Leo as a member of the IP subtype of CVs. From an Ultraviolet (UV) study, \cite{pal17} determined that the white dwarf had a temperature of 15,014($\pm$638)\,K and contributed 83\% of the UV flux. Since the humps of the model-1 light curve are located exactly at phases 0.25/0.75, model-2 with an extra hotspot on the surface of disk can be used to describe the offset secondary hump of RZ\,Leo. For the phased light curve with phase zero at the primary minimum, a convergent solution was found. However, inspection of the bottom left panel of Fig. 4 shows that the derived secondary mass and radius obviously deviate from the predicted mass-radius relation of the semi-empirical CV donor sequence \citep{kni06,kni11}. Based on the MK spectral classes \citep{cox00}, the derived radius is significantly smaller than that of a normal isolated main sequence star. Furthermore, the mass and radius also conflict with the semi-empirical mass-period and radius-period relations of CV secondary \citep{war03,smi98} shown in the right two panels of Fig. 4.
Instead, we created a model with phase zero at the secondary dip of the light curve. Initially, we fixed the inner accretion disk radius to the radius of the white dwarf. However, a convergent solution could not be found. Instead, an accretion disk model with two hotspots and R$_{in}$ much larger than R$_{wd}$ was found to fit the data reasonable well. R$_{in}>R_{wd}$ can be interpreted as a truncation of the accretion disk far from the WD, consistent with the IP classification of RZ Leo by \cite{szk17} and \cite{dai16} This means that the physical structure of RZ\,Leo may be more complex than the simple disk model calculated by XRBinary, as accretion curtains near the magnetic poles of the white dwarf may be involved. This may be the reason that the best-fitting light curve derived by XRBinary cannot perfectly describe the secondary hump of RZ\,Leo. Based on this disk model, CKp$_{2}$ calculated by using Equation 1 is around 1.5 magnitudes larger than Kp$_{2}$. This discrepancy is likely caused by the lack of an accretion curtain in the disk model. In the future, a complete IP model including the light from an accretion curtain should help correct this difference. In spite of the deviation in the secondary hump and CKp$_{2}$, limits to two key parameters of the disk (R$_{in}$ and $\xi$) can be obtained from the double-humped K2 phased light curve.
According to the typical disk-field interaction models \citep[e.g.][]{pri72,gho78,whi88}, the corotation radius of a magnetic white dwarf, R$_{co}$, can be calculated using,
\begin{equation}
R_{co}\,=\,f_{co}M_{wd}^{1/3}P_{rot}^{2/3},
\end{equation}
where $f_{co}=(GM_{\odot}/4\pi^{2}R_{\odot}^3)^{1/3}$, R$_{co}$ and M$_{wd}$ are in solar units, P$_{rot}$ is the spin period of the magnetic white dwarf in unit of seconds. By using the parameters listed in Table 5 and the spin period of 220\,s \citep{szk17,dai16}, R$_{co}$ of RZ\,Leo can be estimated to be 0.085\,R$_{\odot}$, which is 17 times larger than R$_{wd}$\,=\,0.005\,R$_{\odot}$. Considering that the accretion process in RZ\,Leo is steady \citep{dai17}, R$_{in}$ is required to be almost equal to R$_{co}$. However, R$_{in}$\,=\,0.211(2)\,R$_{\odot}$ is much larger than R$_{co}$. In a typical IP \citep{gho78}, R$_{co}$ is regarded as the inner radius of an unperturbed disk, and the transition region of a truncated disk (i.e., located between R$_{co}$ and R$_{in}$) may be actually invisible in the optical band due to a possible disruption of the accretion flow caused by the magnetosphere of the magnetic white dwarf. Since a hotspot on the disk surface always shows R$_{ssmin}<R_{in}$ during the iterations of NMfit, the parameter of R$_{ssmin}$ is fixed to be equal to R$_{in}$. The high effective temperature of this hotspot indicated by T$_{ratio}$\,=\,7.2 indicates that more than 97\% of the luminosity of the disk is from this slim and extended hotspot. Moreover, this hotspot is regarded to be a plausible second impact region of an inward and overflowing stream striking onto the magnetosphere of the magnetic white dwarf. This region was previously reported in several IP systems (e.g., EX\,Hya in outburst \citep{hel89} and QZ\,Vir in quiescence \citep{sha84}. Note that all three systems are unusual short period (under the gap) IPs.). Compared to this hotspot, the other hotspot at the edge of the disk is much smaller and cooler. Both edge and surface hotspots are located at the phases 0.723(1) and 0.47(2), respectively. This disk configuration derived in quiescence is consistent with the disk of EX\,Hya during outburst, with two hotspots at similar phases \citep{hel89}. This disk configuration may be common for IP systems. A low-luminosity truncated disk with L$_{d}=2.3\times10^{30}\,erg\,s^{-1}$ (i.e., the luminosity contribution of the disk is less than 10\% of the whole CV system) may be a straightforward conclusion for an IP system like RZ\,Leo due to the lack of a hot inner part of the disk. Compared with the other four sources of light in RZ\,Leo (i.e., the two component stars and two hotspots on the disk), the relative flux contributions from this truncated disk shown in Fig. 2 are almost negligible (close to zero).
The best-fitting CV model indicates that RZ\,Leo has a moderate orbital inclination of 61.0$^{\circ}$($\pm$0.9$^{\circ}$) and contains a massive white dwarf and a low mass red dwarf. The mass ratio, q$_{orb}=0.080(6)$ is within the error bar of that estimated from its superhump excess \citep{ish01}. The secondary mass and radius (i.e., M$_{rd}$\,=\,0.101(8)\,M$_{\odot}$ and R$_{rd}$\,=\,0.16\,R$_{odot}$) are not only in accord with an isolated red dwarf later than M5V, but also support the semi-empirical mass-period and radius-period relations of CV secondaries \citep{war03,smi98}. The small mass transfer rate, $\dot{M}_{rd}\simeq\,3.01(\pm0.07)\times10^{-12}\,M_{\odot}$/year calculated by using Equation 2, seems to explain the small and cool hotspot at the edge of the disk shown in the disk model. Recently, \cite{dub18} showed the average mass transfer rates of a sample of $\sim$130 CVs with a parallax distance in the Gaia DR2 catalogue. The estimated mass transfer rate of RZ\,Leo lies well within the region where a stable, cool disk exists within the system. This explains a lack of DN outbursts for RZ\,Leo. $\tau_{\dot{M}}\,\sim\,3.4\times10^{10}$\,year calculated from the mass transfer rate is larger than $\tau_{kh}$ of the secondary. The derived secondary mass and radius further confirm that the secondary of RZ\,Leo is in thermal equilibrium, since they are consistent with the mass-radius relation of the isolated main sequence stars shown in the bottom left panel of Fig. 4. Since T$_{rd}$\,=\,3,710($\pm$30)\,K suggests a slightly earlier spectral type than M5V, this higher T$_{rd}$ may be attributed to irradiation of the companion. Due to L$_{rd}>L_{wd}+L_{d}$, the irradiation effect is not calculated by XRBinary. However, the maximal F$_{irr}\sim$1.54 shown in Fig. 5 indicates a significant irradiation effect in RZ\,Leo. A prominent irradiation effect can be expected in an IP system since the white dwarf primary is not embedded in the truncated thin disk. Furthermore, the small disk of RZ\,Leo implies that the irradiation region is visible at phase 0.5 despite the similar orbital inclination to that of J0632+2536. Although F$_{obs}\sim$\,0.93 does not seem to support a large irradiation effect, the presence of an accretion curtain and a brighter second impact region complicate an accurate calculation of the irradiation effect in RZ\,Leo.
\subsection{TW\,Vir}
By using infrared photometry, the secondary is estimated to be a M3V star with a mass of 0.43\,M$_{\odot}$ and a radius of 0.48\,R$_{\odot}$ \citep{mat85}. According to the MK spectral classes \citep{cox00}, the initial temperature of the secondary was set to be 3,367\,K. Based on the mass ratio of 0.44 \citep{sha83}, the white dwarf mass of TW\,Vir is calculated to be 0.98\,M$_{\odot}$. Since there is not any accurate white dwarf temperature obtained from UV spectra \citep{cor82,szk85,ham07}, and TW\,Vir is a long period (above the gap) system with an orbital period of 0.182682(3)\,day derived from the K2 data \cite{dai17}, we set the same initial white dwarf temperature as that of J0632+2536. As the secondary hump of TW\,Vir is not located at orbital phase 0.25 or 0.75, model-2 is used for the calculations. Two phased light curves corresponding to phase zero at the primary and at the secondary dips were used to derive two disk models, respectively. In these two disk models, three parameters involving the positions of two hotspots on the disk in $\zeta$ direction (i.e., $\zeta_{esmid}$, $\zeta_{ssmin}$ and $\zeta_{ssmax}$) show nearly constant phase differences of 0.5, while all the remaining parameters are almost the same. Therefore, both models are not significantly different and the double-hump modulation of TW\,Vir is mainly caused by the two hotspots on the disk.
Since the $\chi^{2}$ of the model based on the phased light curve with phase zero around the secondary dip is slightly smaller than that with phase zero at the primary dip, the primary hump was set to be phase at 0.75 and the corresponding model is analyzed in the following discussion. The two best-fitting orbital parameters: q$_{orb}$=0.41($\pm$0.05) and i$_{orb}$=44.3$^{\circ}(\pm0.5^{\circ}$) listed in Table 5 are consistent with the previous results derived from the infrared and UV data \citep{cor82,mat85}. The derived mass ratio confirms the previous classification of TW\,Vir as a U\,Gem type DN \citep{oco32}, but the derived orbital inclination is smaller than that obtained by \cite{ham07}. The calculated CKp$_{2}$ listed in Table 4 suggests that the best-fitting model of TW\,Vir is consistent with the Gaia distance. The relative flux contributions from the hotspot at the edge of the disk around phase 0.75 shown in Fig. 2 almost perfectly reproduces the significant primary hump which lasts for over half of an orbit. Although the other hotspot appearing on the outer radius of the disk covers a long phase width of 0.42, the small T$_{ratio}^{ss}$=1.20($\pm$0.02) may explain its small relative flux contributions shown in Fig. 2. Like RZ\,Leo, the relative flux contribution from the disk is close to zero. The derived mass and radius of the secondary fits with the semi-empirical secondary mass-period and radius-period relations \citep{war03,smi98}, indicating that the spectral type of the secondary is close to M2V, which is similar to the result from infrared photometry \citep{mat85}. However, compared with the K5V star of J0632+2536 and the M5V star of RZ\,Leo, the M2V star of TW\,Vir never shows large-amplitude ellipsoidal modulations. Instead, it gives rise to a small amplitude second hump in the phased light curve. By using Equation 2, the estimated $\dot{M}_{rd}$ listed in Table 6 indicates that $\tau_{\dot{M}}\sim9\,\tau_{kh}$, which is common for most CV secondaries \citep{pat84}. A somewhat oversized secondary of TW\,Vir relative to an isolated main sequence star of the same mass is not obtained, implying that $\dot{M}_{rd}$ may be overestimated.
Like J0632+2536, T$_{eff}$\,=\,4850\,K listed in Table 4 is higher than the derived T$_{rd}$\,=\,4,000($\pm$40)\,K. This may imply that the higher T$_{eff}$ derived by Gaia is common for DN due to the possible contributions from hotter components in these systems (e.g., the white dwarf and accretion disk). Since T$_{rd}$ is obviously higher than the effective temperature of a M2V star shown in Fig. 4, we investigated the irradiation effect of the secondary in this system. Note that TW\,Vir is the only object with L$_{rd}<L_{wd}+L_{d}$. Accordingly, the calculation of irradiation was included in XRBinary. However, both light curves calculated with and without irradiation by XRBinary are almost identical. Hence, irradiation in TW\,Vir may be weak, which is also demonstrated by F$_{obs}\sim1$ with two minima in the light curve at almost the same flux level. Since L$_{d}$ calculated from a near-flat temperature distribution with a power index of -0.11($\pm$0.04) is nearly two times L$_{rd}$, and the total contributions of two hotspots are only 16\% of L$_{d}$, the weak irradiation effect of the secondary is overpowered in the light curve. Large variations in the disk luminosity may further weaken the ability to detect irradiation. There are two issues which further complicate our conclusions. The first is that the orbital modulation of TW\,Vir shown in Fig. 2 is only extracted from the part of the quiescent light curve around its superoutburst. The second is that the double-hump modulation does not always maintain stability and the secondary hump has a small amplitude and shows a large scatter in the unbinned light curve \citep{dai17}. Further analysis of its light curves at different times may reveal more details of the irradiation effect in TW\,Vir.
\subsection{WD\,1144+011}
This poorly understood variable star is classified as a DA+dMe binary from a single optical spectrum obtained by \cite{ber92}. For comparison with this spectrum obtained over twenty years ago, a new spectrum was taken on 2017 January 22 by using the BFOSC spectrograph attached to the Xinglong Observatory 2.16\,m telescope (XL 216, \cite{fan16}). This is a better optical spectrum showing some changes from the original one taken in long ago. The details concerning our spectrum are presented in Appendix B. A synthetic analysis based on the single-hump light curve extracted by \cite{dai16} can test the possibility of the existence of a disk around the primary white dwarf of WD\,1144+011. Considering that WD\,1144+011 is a long orbital period system with an orbital period of 9.81\,hr \citep{dai16}, the initial parameters of the white dwarf are set to be the same as those of J0632+2536. Combined with the parameters of a M dwarf, all three models were used to attempt to reproduce the stable single-hump modulation that is apparent in the K2 light curve.
\subsubsection{Model without a disk}
In principle, model-0 can only produce ellipsoidal modulation caused by the orbital motion of the Roche-lobe filling secondary. The asymmetry shown in the single-hump modulation of WD\,1144+011 cannot be explained by a pure ellipsoidal modulation derived from model-0. Moreover, the irradiation effect in WD\,1144+011 calculated by XRBinary cannot resolve this problem, since its long orbital period may imply a bright secondary like J0632+2536 (i.e., L$_{rd}>L_{wd}$). In spite of this, an irradiation region on the surface of the secondary was added to allow for an asymmetrical single-hump modulation (i.e., a bump on the rise to the maximum). We assumed this irradiation region to be a circular bright starspot on the secondary, which can be easily calculated by XRBinary. Since the single-hump modulation of WD\,1144+011 observed in K2-C1 is very stable (lasting at least a complete campaign period of $\sim$\,3\,months \citep{dai16}), a stable region due to irradiation of the secondary may be more plausible to explain this long-term steady modulation than a variable starspot on an active M type dwarf.
In XRBinary, a starspot on the secondary can be described by the four parameters (i.e., $\theta^{sp}$, $\phi^{sp}$, R$^{sp}$ and T$_{ratio}^{sp}$) \footnote{$\theta^{sp}$ and $\phi^{sp}$ are the coordinates of the spot center in the spherical polar coordinate system. $\phi^{sp}$\,=\,0 direction lies in the orbital plane and points in the direction of motion of the secondary in its orbit. $\phi^{sp}$ increases in a right-handed sense about the $\theta^{sp}$\,=\,0 direction. R$^{sp}$ is the angular radius of the spot as seen from the center of the secondary star. T$_{ratio}^{sp}$ is the ratio of the starspot temperature to the local effective temperature of the unspotted star.}. For WD\,1144+011, this ``starspot" is assumed to be a hot spot (i.e., T$_{ratio}^{sp}>$1). All parameters including four component parameters (M$_{wd}$, T$_{wd}$, q$_{orb}$ and T$_{rd}$) and four parameters of the starspot were set to be adjustable in NMfit. The derived M$_{wd}=1.11(8)\,M_{\odot}$ is almost the same as that of TW\,Vir shown in Fig. 1, while T$_{wd}=27,100\,K$ suggests a hotter and brighter white dwarf. Compared with the three DN, WD\,1144+011 is the only object with a slightly cooler M dwarf (T$_{rd}=3,500(\pm100)\,K$) than the predicted mass-temperature relation of the semi-empirical CV donor sequence \citep{kni06,kni11}. This is consistent with T$_{eff}$\,=\,3,657.5\,K shown in the Gaia database. Compared with the higher T$_{eff}$ of the two DN J0632+2536 and TW\,Vir, this compatible T$_{eff}$ can be explained by the lack of a disk around the white dwarf. Since the companion star in WD\,1144+011 is cooler than the secondaries in the other systems discussed here, it has the largest uncertainty in BC$_{v}$, as shown in Fig. 3. This is reflected in the large range of derived CKp$_{2}$ (14.8$\sim$16.2\,mag) which is consistent with the corresponding Kp$_{2}$ value listed in Table 4. Like TW\,Vir, the ellipsoidal modulations caused by the M star never dominates the orbital modulation. The mass and radius of the secondary deviate from all the mass-radius, mass-period and radius-period relations shown in Fig. 4. Note that both semi-empirical mass-period and radius-period relations are only available in the period range of 1.3\,$\sim$\,9\,hr \citep{war03,smi98}. WD\,1144+011 with an orbital period of 9.81\,hr is beyond this period range. The bottom left panel of Fig. 4 shows that the inflation of the secondary is about 38\%. Besides the known inefficient mechanisms of donor bloating (e.g., tidal deformation, rotational deformation and irradiation of the secondary) discussed by \cite{kni11}, the deviation from thermal equilibrium of the secondary caused by the donor mass loss can result in a large donor inflation up to 20\%\,$\sim$\,30\% \citep{pat05,kni06}. However, this mass loss mechanism is still not enough to explain the derived inflated secondary star.
Although both light curves calculated with and without irradiation by XRBinary are almost identical due to L$_{rd}>L_{wd}$, the final $\chi^{2}$ of model-0$^{irr}$ is slightly smaller than that of model-0. Thus, the best-fitting parameters and their uncertainties listed in Table 7 are calculated using model-0$^{irr}$. The reproduced light curves and the corresponding 2D pre-CV configuration are shown in the top left and right panels of Fig. 6, respectively. This detached binary configuration with a low inclination of 14.3$^{\circ}(\pm0.4^{\circ}$) supports the previous classification of WD\,1144+011 as a pre-CV system (i.e., a DA+dMe detached system). Our model also shows that the orbital variation seen in the light curve is dominated by the hot spot on the secondary's surface. Compared with the three DN, the pre-CV WD\,1144+011 is the only object with F$_{obs}$\,=\,1.03 larger than 1. Thus, T$_{ratio}^{sp}=1.097(\pm0.003)$ combined with F$_{obs}$ suggests that the calculated irradiation region may be a good representation of the physical picture of WD\,1144+011. The effective temperature of the ``starspot" can be estimated to be around 3,900\,K based on T$_{ratio}^{sp}$. A relation between F$_{irr}$ and S$_{irr}$ shown in Fig. 5 indicates weak irradiation in WD\,1144+011, similar to J0632+2536, and S$_{irr}\sim$\,0.5 corresponding to F$_{obs}$=1.03 is consistent with the size of the ``starspot" calculated from R$^{sp}=27.7^{\circ}(\pm0.7^{\circ})$. Due to the lack of an accretion disk, this irradiation region is much smaller than the typical size of an irradiation region in a CV \citep{dav92}.
\subsubsection{Model with a disk}
Since an extra light source is imperative to explain the asymmetrical single-hump modulation, the model-1 and model-2 were investigated. All adjustable parameters and their uncertainties are listed in Table 7. $\dot{M}_{rd}$ is estimated for both models, and is given in Table 6. The white dwarf mass of model-1 is smaller than the prediction of the average white dwarf mass in a CV with the same orbital period \citep{rit86,zor11}. T$_{wd}$ from both of the disk models is consistent with T$_{wd}$ from the non-disk model, suggesting that WD\,1144+011 does contain a hot white dwarf. The final $\chi^{2}$ of the two disk models are almost the same as that of the non-disk model-0. All three models imply an oversized secondary with generally consistent masses and radii. The top left panel of Fig. 4 shows that the secondary of model-1 has an extremely high effective temperature which is over twice the average effective temperature of a M dwarf. Although the secondary of model-2 agrees with a G9V star based on the MK spectral classes \citep{cox00}, a spectral type of G9V contradicts with our spectrum. Compared with the Gaia distance of WD\,1144+011 listed in Table 4, both L$_{rd}$ for the model-1 and model-2 are too large. Hence, the consistency of the effective temperature may be only coincidental. In order to recheck the deviations in T$_{rd}$ in model-1 and model-2, T$_{rd}$ was fixed to be 3,500\,K in line with the secondary temperature found using model-0. However, no convergent solution could be obtained. In spite of L$_{rd}>L_{wd}+L_{d}$, irradiation was still included in these models. Like model-0, the light curves calculated with and without irradiation for the two disk models only show small discrepancies around phases 0.5 and 0.0. Both calculated F$_{irr}$ are far larger than F$_{obs}$. This means that the assumed large irradiation of the secondary is not supported by the K2 data. Compared with the pre-CV configuration obtained from model-0, the two models with an accretion disk are not convincing. As such, our modelling based on the K2 phased light curve provides further evidence for the classification of WD\,1144+011 as a detached pre-CV system.
\section{Conclusions}
\subsection{Synthetic codes}
Based on the light curve synthesis code XRBinary derived by E.L. Robinson, NMfit was developed to analyze the light curves of the four low-inclination systems: J0632+2536, RZ\,Leo, TW\,Vir and WD\,1144+011. All parameters of the best-fitting models and their uncertainties are estimated by NMfit. Additionally, Phoebe 2.0 was used to visualize the configuration of each system using each systems best-fitting parameters. Since phase zero is hard to identify in any low-inclination CV system with a double-hump modulation due to the lack of a significant eclipse feature, we tested models which had phase zero located at either the primary or secondary minimum, and chose the model which matched the observed light curve best. Except for WD\,1144+011 which had a single maximum in its phased orbital light curve, the derived CV models of the other three DN indicate that phase zero should be placed at the secondary minimum.
\subsection{Physical Models}
For J0632+2536 and TW\,Vir, the best-fit disk models show that the primary hump is mostly due to the hotspot at the edge of the disk, a key indicator of mass transfer via the L1 point. Another hotspot on the disk surface can explain the phase difference between the two humps of the double-hump modulations. For WD\,1144+011, the bright ``starspot" representing irradiation of the secondary star is responsible for the modulation seen in the optical light curve.
The lack of an accretion curtain in the disk model of RZ\,Leo implies that this model may not be appropriate for a comparison with the measured distance by Gaia. The derived physical models of the other three binary systems are consistent with the results from Gaia DR2. The flat power law index of the disk found in all three DN models ($\xi\sim$\,-0.11) is similar to previous observations \citep[e.g.][]{woo86,woo89,rut16} and supports the theory that a quiescent CV disk deviates from the temperature distribution of a typical steady-state disk. A low-luminosity accretion disk model of RZ\,Leo derived from its K2 light curve further confirms that RZ\,Leo is an IP system with two hotspots on a truncated disk. One of the hotspots on the disk surface contributes a significant fraction of the disk luminosity ($>97\%$ of L$_{d}$), and is located at the inner edge rather than the outer edge of the disk. This may be evidence of an impact region between an inward and overflowing stream and the magnetosphere of the magnetic white dwarf. Compared with RZ\,Leo, the small hotspot of J0632+2536 and two hotspots of TW\,Vir covering large phase ranges are only small contributors to the disk luminosity. Our spectrum of WD\,1144+011 with a relatively flat continuum and H$_{\alpha}$ emission supports its previous classification as a DA+dMe system \citep{ber92}. We note that WD\,1144+011 shows different flux levels in the continuum and emission lines. The model light curve based on the asymmetrical single-hump modulation requires an extra light source (i.e., a weak irradiation region of the secondary rather than a large hotspot at the edge of the disk) to explain the modulation of WD\,1144+011.
\subsection{The Secondaries}
The estimated $\dot{M}_{rd}$ for all four objects are within a range of $10^{-9}\sim10^{-12}\,M_{\odot}$/year. Except for the pre-CV WD\,1144+011 which contains an oversized secondary, the other three DN have secondaries in thermal equilibrium with masses and radii conforming to the semi-empirical CV donor sequence \citep{kni06,kni11} and MK spectral classes \citep{cox00}. The derived effective temperatures of all three DN are significantly higher than predicted. Hence a DN system containing a substantially hotter secondary may be a common feature rather than a peculiarity. This can be attributed to irradiation of the secondary, since T$_{rd}$ calculated from L$_{rd}$ is an average parameter which can be increased by irradiation. Compared with T$_{eff}$ listed in the Gaia catalog, the lower T$_{rd}$ of the two DN J0632+2536 and TW\,Vir may due to contamination from a hot white dwarf and disk. This is further supported by the T$_{rd}$ of the pre-CV WD1144+011, which is almost consistent with the Gaia T$_{eff}$. It should also be noted that the Gaia temperatures are determined from three broad bandpasses \citep{and18} and the DR2 releases notes urge caution in using them \footnote{\url{https://gea.esac.esa.int/archive/documentation/GDR2/pdf/GaiaDR2_documentation_1.0.pdf}}.
Although the double-hump modulation of J0632+2536 can be explained by the partial occultation of the irradiation region on the surface of the secondary due to a large disk and a moderate orbital inclination, investigation of irradiation in the other two DN implies that the effect of irradiation in a CV system is complicated and blended with other modulations. The flux contribution from the secondary of TW\,Vir is the lowest (i.e., L$_{rd}<L_{wd}+L_{d}$) among all four objects. Weak irradiation may exist in the DN TW\,Vir and the pre-CV WD\,1144+011. The former can be further tested by additional light curves obtained when the double-hump variation is evident, while the latter can be further checked by taking a time series of spectra over the course of the complete orbital period of 9.81\,hr.
\acknowledgments
This work was partly supported by CAS Light of West China Program, the Chinese Natural Science Foundation (Nos. 11133007 and 11325315), and the Science Foundation of Yunnan Province (No. 2016FB007). PS acknowledges support from NSF grant AST-1514737. M.R.K is funded through a Newton International Fellowship provided by the Royal Society. We acknowledge the support of the staff of the Xinglong 2.16m telescope. This work was partially supported by the Open Project Program of the Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences. We would like to thank the anonymous referee for their comments and suggestions in improving this paper.
\software{IRAF \citep{tod86,tod93}, XRBinary (v2.4), NMfit (v1.0), Phoebe \citep[v2.0;][]{prs16})}
\clearpage
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Q: Button gets pushed down when decreasing the browsers width I have a div that has three elements in it a label, an input box, and a button. they each have 30 percent for their width, so they should become smaller when resizing the browser, but the button gets pushed down at some point. Here is the code
<!DOCTYPE html>
<html style="height: 100%; margin: 0">
<head>
<title></title>
</head>
<body style="height: 100%; margin: 0">
<div style="width: 30%; height: 20%; background-color:red; text-align: center; ">
<label style="height: 80%; width: 30%; display: inline-block;">Table No: </label>
<input style="height: 80%; width: 30%" type="text" name="">
<button style="height: 80%; width: 30%">Back</button>
</div>
</body>
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how can I prevent the button from getting pushed down?
A: Applying display:flex; or display:inline-flex; (depending your purpose) to your parent <div> will solve your problem. However, I highly recommend you restructuring the layout and considering using media queries for it. In the case of small size screens you can have width:100%; for your parent <div> and for larger screen sizes width:30%; as you have right now. Media queries are a better option for making your website responsive than just relying on CSS percentage.
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\section{Introduction}
Compiler verification is important because of the central role that compilers play in computing infrastructure, and because compiler bugs are easy to make but often difficult to catch.
Most work on compiler verification has been done in the setting of imperative or functional programming; very little has been done for logic programming languages like Prolog.
Compiler verification is an equally interesting problem in the case of logic programming.
Logic programs are often easier to write correctly than programs in other paradigms, because a logic program is very close to
being its own specification. However, the correctness advantages of logic
programming cannot be fully realized without compiler verification.
Compiler correctness is a concern for logic programming given the scale of realistic language implementations;
for example, SWI-Prolog is estimated at over 500,000 lines of code~\cite{OpenHub}.
Certifying compilation ~\cite{necula1998design} is an approach to verification wherein a
compiler outputs a formal proof that the compiled program satisfies
some desired properties. Certifying compilation, unlike
conventional verification, has the advantage that the certificates can
be distributed with the compiled code and checked independently by
third parties, but the flip side is that compiler bugs are not
found until the compiler sees a program that elicits the bug. In
the worst case, bugs might be found by the compiler's users, rather than its
developers.
In most work on certifying compilation ~\cite{necula1998design}, an additional disadvantage is that while type and memory safety are certified, dynamic correctness is not.
In contrast, we certify the dynamic behavior of logic programs, whose semantics we give as a signature in the logical framework LF \cite{Harper93aframework}.
This semantics abstracts away the low-level operational details of Prolog semantics such as order of execution.
This brings the type system into close harmony with our source programs, allowing type correctness to naturally encompass dynamic correctness.
In this work, we develop the Typed Warren Abstract Machine (TWAM), a dependently-typed \emph{certifying abstract machine} suitable as a compilation target for certifying compilers.
Section \ref{sec:dependent-wam} formalizes and proves the following claim that TWAM certifies partial correctness:
\textbf{Theorem 1}(\textit{Soundness}): If a query \verb+?-+$G.$ succeeds, there exists a proof of $G$ in LF.
That is, well-typed TWAM programs satisfy partial correctness with respect to their LF semantics.
Because this theorem says that well-typed TWAM programs implement sound proof search procedures for the LF specification, we also call this theorem \textit{soundness}.
We show that TWAM is a suitable compilation target by implementing a compiler from a simply-typed dialect of Prolog called T-Prolog to the TWAM.
The result is a certifying compiler with a small, domain-specific proof checker as its trusted core: the TWAM typechecker.
We ease the presentation of TWAM by first presenting its simply-typed variant (SWAM) in Section \ref{sec:simple-wam} along with standard progress and preservation theorems, which show type and memory-safety.
We then develop a dependently-typed variant in Section \ref{sec:dependent-wam} whose type system expresses the behavior of a TWAM program as a logic program in the logical framework LF \cite{Harper93aframework}, using an encoding demonstrated in Section \ref{sec:lf-encoding}.
\section{Source Language: T-Prolog}
Our compiler accepts programs for a simply-typed dialect of Prolog which we named T-Prolog.
It is worth noting that the language need not be typed for our approach to work: if we wished to
work in an untyped dialect of Prolog, we could simply add a compiler pass to collect a list of
all the constructors used in a particular Prolog program and construct a single type called \verb+term+ containing
every constructor we need. We choose a simply-typed language over an untyped one because our use of LF in the TWAM
makes this feature easy to implement and because the correspondence with LF is easier to present for a simply-typed
language.
T-Prolog programs obey the following grammar:
\begin{center}
\begin{tabular}{lll}
programs & $P$ &$::= D^*\ Q$\\
query & $Q$ &$::= {\tt ?-}t{\tt.}$\\
declaration & $D$ &$::= D_\tau\ |\ D_c\ |\ D_p$\\
type declaration & $D_\tau$ &$::= {\tt ident:type}$\\
constructor declaration & $D_c$ &$::= {\tt ident:}\ \tau_c$\\
predicate declaration & $D_p$ &$::= {\tt ident:}\ \tau_p\ C^*$\\
constructor types & $\tau_c$ &$::= {\tt type}\ |\ {\tt ident\ \verb+->+\ \tau_c}$\\
predicate types & $\tau_p$ &$::= {\tt prop}\ |\ {\tt ident\ \verb+->+\ \tau_p}$\\
clause & $C$ &$::= t{\tt.}\ |\ t\ {\verb|:-|}\ G^*$\\
goals & $G$ &$::= t{\tt.}\ |\ t{\tt,}\ G^*$\\
terms & $t$ &$::= {\tt Ident}\ |\ {\tt ident(}t{\tt, \ldots, }t{\tt )}$\\
\end{tabular}
\end{center}
As our running example throughout the paper, we consider a series of arithmetic operations on the Peano representation of the natural numbers $\mathit{zero}$ and $\mathit{succ}(n)$.
To start, here is the \verb+plus+ function written in T-Prolog, with the query \verb|2 + 2 = X|.
As in standard Prolog, we will often annotate constructors and predicates with their arities as in {\tt plus/3}.
However, each identifier in T-Prolog has a unique type and thus a unique arity, so annotating identifiers with their arity is not strictly necessary.
\begin{exmp}\label{ex:tprolog-code}
\begin{verbatim}
nat : type.
zero/0 : nat.
succ/1 : nat -> nat.
plus/3 : nat -> nat -> nat -> prop.
plus(zero,X,X).
plus(succ(X),Y,succ(Z)) :-
plus(X,Y,Z).
?- plus(succ(succ(zero)), succ(succ(zero)), X).
\end{verbatim}
\end{exmp}
There is no fundamental difference between \verb+type+ and \verb+prop+ (and in the theory they are identical): we differentiate them in the T-Prolog syntax because we find this notation intuitive and because it makes the language easier to parse.
\subsection{Semantics of T-Prolog}
In order to certify that a compiler preserves the dynamic semantics of T-Prolog programs, we must first ascertain those semantics.
As in typical Prolog, a T-Prolog program is defined as a signature of logical inference rules, and execution proceeds via depth-first proof-search under that signature, trying rules in the typical Prolog order.
Seeing as Prolog evaluation is proof search, the semantics of Prolog are often given operationally in terms of proof-search trees.
This operational treatment has the advantage that it can naturally express non-termination and the order in which rules are tried.
The disadvantage is that, in increasing operational detail, we diverge further from the world of pure logic, increasing the difficulty of verification.
For this reason, while the T-Prolog implementation does evaluate in the same order as Prolog, we do not take the operational search-based semantics of T-Prolog as canonical.
Rather, we take as the meaning of a T-Prolog program the set of formulas provable from its inference rules (Section ~\ref{sec:lf-encoding}), without regard to the order in which the proof steps are performed.
The abstractions made in this semantics are not significantly greater than those already made by a proof-search semantics.
The common insight is that a formal semantics for logic programs should exploit the close relationship to logic, ignoring implementation details that have no logical equivalent.
In both semantics, for example, it is typical to ignore Prolog's cut operator {\tt !}, which has the side effect of skipping any remaining backtracking opportunities for the current predicate, typically used as an optimization.
The cut operation is inherently about search rather than truth, informing the Prolog implementation to ignore some of the available proof rules.
Both the search semantics and provability semantics implicitly assume that all Prolog terms are finite.
The backbone of Prolog proof search is unification, and as usual for unification, finiteness cannot be taken for granted.
Allowing instances such as $X = f(X)$ to unify would result in infinite terms that do not have a logical interpretation.
In typical Prolog implementations, such terms are accepted out of the interest of performance.
In T-Prolog, we apply the standard solution of using an occurs check in unification, causing unification to fail on instances such as $X = f(X)$ whose only solutions are infinite.
This restores the close correspondence with logic, at the cost of decreased performance.
\section{The TWAM Instruction Set}
\label{sec:background-wam}
The TWAM borrows heavily from the Warren Abstract Machine, the abstract machine targeted by most Prolog implementations \cite{warren1983abstract}.
For a thorough, readable description of the WAM, see A\"it-Kaci~\cite{ait1999warren}.
Readers familiar with the WAM may wish to skim this section and observe the differences from the standard WAM, while readers unfamiliar with the WAM will wish to use this section as a primer or even consult A\"it-Kaci's book.
In this section we present our simplified instruction set for the WAM using examples.
Notable simplifications include the usage of continuation-passing style and omission of many optimizations (with the exception of tail-call optimization in Section~\ref{sec:tco}) in order to simplify the formalism.
The description here is informal; the formal semantics are given in Section~\ref{sec:simp-op}.
\paragraph{Prolog and WAM Terminology}
The following terminology will be used extensively in this paper to describe Prolog and the WAM:
a \emph{Prolog term} is an arbitrary combination of \emph{unification variables} $X$ combined with \emph{constructors} such as $\mathit{succ}$ and $\mathit{zero}$. What we call \emph{constructors} are generally called \emph{functors} in Prolog terminology.
We use the phrase unification variable when discussing Prolog source text and instead use \emph{free variable} to discuss WAM state at runtime.
The distinction becomes significant, e.g. because the Prolog source may specify that a parameter to some predicate is a unification variable, but at runtime the argument is a ground term.
We use the word \emph{constructor} only when discussing data and use the word \emph{predicate} to refer both to predicates for which a WAM program implements proof search and to the implementation itself.
We also say that certain WAM instructions are constructors because they construct some Prolog term, or destructors if they perform pattern matching on some Prolog term.
A \emph{structure} is the WAM representation of a constructor applied to its arguments.
A predicate consists of one or more \emph{clauses}, each of which specifies one inference rule and each of which consists of a \emph{head term} along with zero or more \emph{subgoals}.
A user interacts with the Prolog program by making a \emph{query}, which is compiled in the same way as a predicate with one clause with one subgoal.
In our discussion of TWAM programs, we consider programs with arbitrarily many predicates, one of which is designated as the query.
\paragraph{Term Destructors}
The instructions \texttt{get\_var, get\_val}, and \texttt{get\_str} are used the implementation of predicates to destruct the predicate arguments:
\begin{itemize}
\item $\texttt{get\_var}\ r_d, r_s$ reads (gets) $r_s$ into $r_d$.
This is an unconditional register-to-register move and thus its use can be minimized by good register allocators.
This is used to implement clauses where a unification variable is an argument.
\item $\texttt{get\_val}\ r_1, r_2$ reads (gets) $r_1$ and $r_2$ and unifies their values against each other.
This is used to implement clauses where multiple arguments are the same unification variable.
\item $\texttt{get\_str}\ r_s, c$ reads (gets) $r_s$ and unifies it against the constructor $c$.
For our initial examples, we will consider only the case where $c$ has no arguments.
\texttt{get\_str} is effectively an optimized special-case of \texttt{get\_val} where we know the second unificand must be $c$.
This is used to implement clauses where a constructor appears as a predicate argument.
\end{itemize}
For example, the Prolog predicate \texttt{both\_zero(zero, zero)}, which holds exactly when both arguments are zero, could be compiled in all of the following ways, with the naming convention
that the register for argument $i$ is named $A_i$ and the $i$'th temporary is named $X_i$:
\begin{exmp}[Implementing a Predicate]
\label{ex:both-zero}
\begin{center}
\begin{tabular}{ccc}
\begin{minipage}{0.25\linewidth}
\begin{verbatim}
# Implementation 1
get_str A_1, zero/0;
get_str A_2, zero/0;
\end{verbatim}
\end{minipage}
& \begin{minipage}{0.25\linewidth}
\begin{verbatim}
# Implementation 2
get_str A_1, zero/0;
get_val A_1, A_2;
\end{verbatim}
\end{minipage}
&\begin{minipage}{0.25\linewidth}
\begin{verbatim}
# Implementation 3
get_var X_1, A_1;
get_var X_2, A_2;
get_str X_1, zero/0;
get_val X_1, X_2;
\end{verbatim}
\end{minipage}
\end{tabular}
\end{center}
\end{exmp}
Generally speaking, Implementation 1 is most efficient, then Implementation 2, then Implementation 3.
Note that even though the Prolog predicate \texttt{both\_zero(zero, zero)} contains no unification variables, we can still use \texttt{get\_val} in the implementation,
because the unification problems $A_1 = zero, A_2 = zero$ and $A_1 = zero, A_1 = A_2$ are equivalent.
Observe that any instruction that uses unification, such as {\tt get\_val} and {\tt get\_str}, will fail if unification fails.
Should this occur, the runtime automatically backtracks if possible; backtracking is \emph{never} executed explicitly in the text of a TWAM program.
\paragraph{Term Constructors and Jumps}
To implement a query or subgoal that uses the predicate {\tt both\_zero}, we must first construct its arguments, then jump to the implementation:
\begin{itemize}
\item $\texttt{put\_var}\ r_d$ writes (puts) a \emph{new} free variable into $r_d$.
This is used to implement passing a unification variable as an argument.
\item $\texttt{put\_val}\ r_d, r_s$ writes (puts) the value of an \emph{existing} unification variable into $r_d$, assuming it is already in $r_s$.
This is an unconditional register move. Thus it is entirely identical to \texttt{get\_var}.
For this reason, in our theory we will condense these into one instruction $\texttt{mov}\ r_d, r_s$ and only use the names \texttt{get\_var} and \texttt{put\_val} for consistency
with traditional terminology in our examples.
\item $\texttt{put\_str}\ r_d, c$ writes a structure into $r_d$ using constructor $c$.
\texttt{get\_str} is effectively an optimized special-case of \texttt{put\_val} where we are storing not an arbitrary unification variable, but specifically a constant $c$.
This is used to implement passing a constructor as an argument to a predicate.
\item $\texttt{jmp}\ \ell^C$ passes control to the code location (address literal) $\ell^C$.
Arguments are passed through registers.
All code is in continuation passing style, and thus a continuation can be passed in through a register, which is named {\tt ret} by convention.
The queries in Example~\ref{ex:make-query} do not require returning from predicate calls, thus continuations are discussed separately.
\end{itemize}
\begin{exmp}[Making a Query]
\label{ex:make-query}
\begin{center}
\begin{tabular}{cc}
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# both_zero(X, X).
put_var A_1;
put_val A_2, A_1;
jmp both_zero/2;
\end{verbatim}
\end{minipage}&
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# both_zero(X, zero).
put_var A_1;
put_str A_2, zero/0;
jmp both_zero/2;
\end{verbatim}
\end{minipage}
\end{tabular}
\end{center}
\end{exmp}
\paragraph{Constructors with Arguments}
We continue to use the \verb|put_str| and \verb|get_str| instructions to construct and destruct structures that contain arguments.
The difference is that when calling \verb|put_str| or \verb|get_str| with a constructor of arity $n > 0$,
we now initiate a \emph{spine} (terminology ours) consisting of $n$ additional instructions using only the following:
\begin{itemize}
\item When $\texttt{unify\_var}\ r$ is the $i$'th instruction of a spine, it unifies the $i'$th argument of the constructor with a \emph{new} unification variable, at register $r$.
\item When $\texttt{unify\_val}\ r$ is the $i$'th instruction of a spine, it unifies the $i'$th argument of the constructor with an \emph{existing} unification variable, at register $r$.
\end{itemize}
The same instructions are used with both \texttt{put\_str} and \texttt{get\_str} spines.
However, at runtime a spine will execute in one of two modes, \emph{read mode} or \emph{write mode}.
\emph{Read mode} is used to destruct an existing value, meaning we are in the \texttt{get\_str $r_s, c$} and $r_s$ contains a structure whose constructor is $c$.
\emph{Write mode} is used to construct a new value, meaning we are either in $\texttt{put\_str}\ r_d, c$ or we are in $\texttt{get\_str}\ r_s, c$ but the content of $r_s$ is a free variable.
In both modes, each unification instruction processes one constructor argument:
\begin{itemize}
\item Read-mode \texttt{unify\_var} stores the next constructor argument in a register.
\item Read-mode \texttt{unify\_val} unifies the next constructor argument with the content of a register.
\item Write-mode \texttt{unify\_var} allocates a free variable as constructor argument, storing it also in a register.
\item Write-mode \texttt{unify\_val} uses the content of a register as constructor argument.
\end{itemize}
For example, the Prolog predicate \texttt{same\_pos(succ(X), succ(X))} which holds when the arguments are the same positive number, can be implemented and used as follows:
\begin{exmp}[Predicates with Prolog Spines]
\begin{center}
\begin{tabular}{cc}
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# Implementation
get_str A_1, succ/1;
unify_var X_1;
get_str A_2, succ/1;
unify_val X_1;
\end{verbatim}
\end{minipage}&
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# Query same_pos(succ(X),succ(Y))
put_str A_1, succ/1;
unify_var X_1;
put_str A_2, succ/1;
unify_var X_1; # Overwrites X_1
jmp same_pos/2;
\end{verbatim}
\end{minipage}\\[0.5in]
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# Query same_pos(succ(X),succ(X))
put_str A_1, succ/1;
unify_var X_1;
put_str A_2, succ/1;
unify_val X_1; # Reads X_1
jmp same_pos/2;
\end{verbatim}
\end{minipage}&
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# Query same_pos(zero,succ(succ(zero)))
put_str A_1, zero/0;
put_str X_1, zero/0; # Z = 0
put_str X_2, succ/1; # Y = 1
unify_val X_1;
put_str A_2, succ/1; # X = 2
unify_val X_2;
jmp same_pos/2;
\end{verbatim}
\end{minipage}
\end{tabular}\\
\end{center}
\end{exmp}
The last example demonstrates a compilation technique known as \emph{flattening}: The unification problem $X = succ(succ(zero))$ is equivalent to the problem $X = succ(Y), Y = succ(Z), Z = zero$.
This allows us to implement nested structures such as $succ(zero)$ or $succ(succ(succ(zero)))$ by introducing intermediate variables.
Thus each spine need only introduce one structure, and nested structures are reduced to the one-structure case by flattening.
\paragraph{Continuations, Closures, and Halting}
Prolog proof search can be structured using success and failure continuations.~\cite{Elliott91asemi-functional}
When a predicate has multiple clauses, failure continuations are used to remember alternate clauses and implement backtracking.
When a clause has multiple subgoals, success continuations are used to remember the remaining subgoals.
In our system, success continuations can be stored in registers and passed to predicates, typically in a register named {\tt ret}, whereas failure continuations are stored in the trail.
Both success and failure continuations can access an environment value (generally a tuple) through the register {\tt env}.
Tuples are like structures, but can contain closures and cannot be unified.
The entry-point of a TWAM program is a top-level query, which specifies an initial continuation that terminates the program in success.
If all clauses fail, then the runtime will automatically report that the program failed.
\begin{itemize}
\item $\texttt{close}\ r_d, r_e, \ell^C$ places a new closure in $r_d$ containing an environment read from $r_e$.
When that closure is invoked, control will pass to $\ell^C$ and the environment will be placed in a special-purpose register named \texttt{env}.
This is used to construct success continuations.
\item $\texttt{push\_bt}\ r_e, \ell^C$ (push backtracking point) creates a new failure continuation.
When that continuation is invoked, control will pass to $\ell^C$ and the environment will be placed in \texttt{env}.
Note that \texttt{push\_bt} does not take a destination register: a stack of failure continuations is stored implicitly in the machine state,
and they are only ever invoked implicitly, when unification instructions like {\tt get\_val} fail.
\item $\texttt{put\_tuple}\ r_d, n$ begins a \emph{tuple spine} of length $n$ which will put a new tuple in $r_d$.
All following instructions of the tuple spine are \texttt{set\_val}.
\item $\texttt{set\_val}\ r_s$ copies $r_s$ in as the next tuple element.
\item $\texttt{proj}\ r_d, r_s, i$ copies the i'th element of the tuple at $r_s$ into $r_d$.
\item $\texttt{succeed}$ immediately terminates the program and indicates that the initial query has succeeded.
(At this point, the runtime system will print out the solution to the query.)
\end{itemize}
As an example, consider implementing and calling the predicate $X + Y = Z$ with two clauses: {\tt plus(zero,X,X)} and {\tt plus(succ(X),Y,succ(Z)) :- plus(X,Y,Z)}:
\begin{exmp}[Implementing {\tt plus}]
\label{ex:plus-wam}
\centering
\begin{tabular}{cc}
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
# Entry point to plus, implements the
# case plus(zero,X, X) and tries
# plus-succ on failure
plus-zero/3:
put_tuple X_1, 3;
set_val A_1;
set_val A_2;
set_val A_3;
push_bt X_1, plus-succ/3;
get_str A_1, zero/0;
get_val A_2, A_3;
jmp ret;
\end{verbatim}
\end{minipage}&
\begin{minipage}{0.5\linewidth}
\vspace{-0.25in}
\begin{verbatim}
# plus(succ(X), Y, succ(Z)) :- plus(X,Y,Z).
plus-succ/3:
proj A_1, env, 1;
proj A_2, env, 2;
proj A_3, env, 3;
get_str A_1, succ/1;
unify_var A_1;
get_str A_3, succ/1;
unify_var A_3;
jmp plus-zero/3;
\end{verbatim}
\end{minipage}
\end{tabular}
\end{exmp}
\begin{exmp}[Calling {\tt plus}]
\centering
\begin{tabular}{cc}
\begin{minipage}{0.5\linewidth}
\begin{verbatim}
init-cont/0:
succeed;
\end{verbatim}
\end{minipage}
&\begin{minipage}{0.5\linewidth}
\vspace{0.08in}
\begin{verbatim}
# plus(succ(zero), succ(zero), X)
query/0:
put_tuple X_1, 0;
close ret, X_1, init-cont/0;
put_str X_2, zero/0;
put_str A_1, succ/1;
unify_val X_2;
put_str A_2, succ/1;
unify_val X_2;
put_var A_3;
jmp plus-zero/3;
\end{verbatim}
\end{minipage}
\end{tabular}
\end{exmp}
In this example, \texttt{plus-zero/3} is the entry point for addition, and implements the base case.
Because \texttt{plus-zero/3} is not the last case, it constructs a failure continuation which tries the \texttt{plus-succ/3} case if an instruction fails.
This requires remembering the environment, implemented by creating a tuple.
In the example query, the first invocation of \texttt{plus-zero/3} will fail on the \texttt{get\_str} instruction because $A_1$ contains $succ(zero),$ not $zero$,
causing \texttt{plus-succ/3} to run (which will succeed after another call to \texttt{plus-zero}).
\texttt{plus-succ} contains several optimizations.
The final subgoal of a clause can always apply tail-call optimization, so no success continuation is necessary.
Furthermore, it carefully avoids the use of intermediate registers. For example, when reading the argument $succ(X),$ the variable $X$ is written directly into $A_1$ to prepare for the recursive call.
The query $plus(succ(zero),succ(zero),X)$ must specify an initial continuation, which simply reports success.
Because the success continuation is trivial, the empty tuple suffices as its environment.
\paragraph{Runtime State}
The runtime representation of a TWAM program differs from that of a WAM program, following the differences in their instruction sets.
Both languages have a fixed \emph{code section} containing the TWAM program text and a variable-sized \emph{heap}, which maintains all Prolog terms in a union-find data structure to enable fast unification.
The most significant difference is that the TWAM machine state does not have a stack, but instead allocates success continuations on the heap and allows them to be garbage collected.
Failure continuations, however, are stored in a separate area called the \emph{trail} as in standard WAM.
In addition to storing a closure created with \texttt{push\_bt}, the trail automatically keeps track of all state changes which might have to be reverted during backtracking.
Traditional descriptions of the WAM contain a \emph{push-down list} or PDL area, which is used in unification to store a temporary list of unification subproblems.
Because this data structure is used only during unification, we found it easier to express the PDL merely as a part of unification and not as a permanent part of the state.
\paragraph{Differences Between WAM and TWAM Instruction Sets}
The key difference between WAM and TWAM is that the TWAM implements predicate calls and backtracking with success and failure continuations, while WAM implements both by maintaining a custom stack discipline, whose invariants are non-trivial.
The use of CPS significantly simplifies the formalism and unifies several instructions that are distinct in traditional WAM:
\begin{itemize}
\item Environments in TWAM are expressed as tuples with the instructions {\tt put\_tuple}, {\tt set\_val}, and {\tt proj}, which replace {\tt allocate} and {\tt deallocate}.
\item The {\tt jmp} instruction of TWAM unifies {\tt call}, {\tt execute}, and {\tt proceed} from WAM.
\item The {\tt push\_bt} instruction of TWAM replaces {\tt try\_me\_else}, {\tt retry\_me\_else}, and {\tt trust\_me} from WAM.
\item The {\tt succeed} instruction is added in TWAM for stylistic purposes; WAM reuses {\tt proceed} for this purpose.
\item The unification and spinal instructionns of TWAM correspond directly to WAM.
\item TWAM omits several optimizations such as cut and case analysis.
\end{itemize}
\section{The Simply-Typed WAM (SWAM)}
\label{sec:simple-wam}
The core contributions of this work are the design, metatheory, and implementation of a type system for the TWAM strong enough to certify compilation.
The certification guarantees provided by the dependently-typed TWAM in Section \ref{sec:dependent-wam} require significant complexity in the type-system.
In this section, we ease the presentation of that system by first presenting its simply-typed variant, the SWAM.
We prove progress and preservation for SWAM, which constitute a safety property analogous to those of other strongly-typed abstract machines such as the typed assembly language TAL \cite{Morrisett:1999:SFT:319301.319345}.
In Section~\ref{sec:dependent-wam}, this is subsumed by progress and preservation for TWAM, which is strong enough to certify partial dynamic correctness.
\subsection{Typechecking SWAM}
\label{sec:simple-wam-istat}
The text of a SWAM program is structured as a code area $C$ mapping code locations $\ell^C$ to code values $\code[\myG](I)$.
A code value is a single basic block $I$ annotated with a \emph{register file type} (rftype) $\myG$ which indicates, for each register $r_i$, the type expected by $I$. One of those code values is designated as the query (a predicate with one clause and one subgoal), which is the entry point of the program.
The type $\tau$ assigned to each register is either an \emph{atomic type} $a$ representing a Prolog term, a \emph{continuation type} $\neg \Gamma$ representing a closure that expects the registers to obey the types in $\myG$, or a \emph{tuple type} $\cross{\vec\tau}$, where the elements $\vec\tau$ can freely mix atomics and continuations.
Here $\vec{\tau}$ is an abbreviation for the sequence $\tau_1,\ldots,\tau_n$; similar abbreviations will be used extensively throughout the paper.
The main typing judgement in SWAM is $\myG \vdash_{\Sigma;\Xi} I \ok$, which says the basic block $I$ is well-typed assuming the registers obey $\myG$ initially,
and given signatures $\Sigma,\Xi$ which assign types to every constructor $c$ and code location $\ell^C,$ respectively.
We omit the subscripts $\Sigma;\Xi$ on rules where they are not relevant.
Throughout the paper, the notation $\thup{\Gamma}{r}{\tau}$ refers to updating the type of $r$ in $\Gamma$ to be $\tau$.
Analogous notation will be used for register values, etc.
Throughout this section, we alternate between inference rules for typechecking instructions and their descriptions.
\begin{center}
{\footnotesize \begin{tabular}{cccc}
\infer[\textsc{Succeed}]{\GE \succeed;I \ok}{}
&\infer[\textsc{PutVar}]{\GE \putvar{a}{r}; I \ok}
{\hups{\Gamma}{r\colon{}a}\ent I \ok}
&\infer[\textsc{GetVal}]{\GE \getval {r_1}{r_2}; I \ok} { \Gamma(r_1) = a & \Gamma(r_2) = a & \Gamma \ent I \ok}
\end{tabular}}
\end{center}
\begin{center}
\footnotesize\begin{tabular}{cc}
\infer[\textsc{Jmp}]{\GE_{\Sigma;\Xi}\jmp op, I\ok}{\Gamma\vdash_{\Sigma;\Xi} op : \neg\Gamma' & \SE \myG' \leq \myG}
&
\infer[\textsc{Mov}]{\GE \mov{r_d}{r_s}; I \ok}
{\myG(r_s) = \tau & \thup{\Gamma}{r_d}{\tau} \ent I \ok}
\end{tabular}
\end{center}
\begin{center}
{\footnotesize\begin{tabular}{ccc}
\infer[\textsc{PushBT}]{\GE_{\Sigma;\Xi} \branch r_e, \ell^C; I \ok}{\GE I \ok &
\Gamma(r_e) = \tau & \Xi(\ell^C) = \neg\heap{\texttt{env}\colon{}\tau}}
&
\infer[\textsc{Close}]{\GE \close r_d, r_e, \ell^C; I \ok}
{\deduce{\GE \ell^C \colon{} \neg \thup{\myG'}{\texttt{env}}{\tau}} {\Gamma(r_e)= \tau &
\thup{\myG}{r_d}{\neg \myG'} \ent I \ok}}
\end{tabular}}
\end{center}
\begin{itemize}
\item {\tt succeed} always typechecks, and is typically the last instruction of its block.
\item ${\tt put\_var}\ [a]r$ allocates a free variable of type $a$ in $r$, thus updating $r$ to type $a$. We write the annotation $[a]$ in brackets to emphasize that it is used only for typechecking.
\item ${\tt get\_val}\ r_1, r_2$ unifies $r_1$ and $r_2$, so they must have the same (atomic) type.
\item ${\tt jmp}\ op$ transfers control to $op$, which in the general case is either a location $\ell^C$ (used in predicate calls) or register $r$ (used in returns, by convention generally named {\tt ret}).
The judgement $\cdot\vdash\Gamma'\leq\Gamma$ means $\forall r\in\dom{\Gamma'}. \Gamma'(r) = \Gamma(r)$ ($\Gamma'$ may omit some registers of $\myG$).
The judgement $\Gamma\vdash_{\Sigma;\Xi} op\colon{}\tau$ has the rules:
\begin{center}
\begin{tabular}{cc}
$\infer[\textsc{Op-}\ell^C]{\myG\vdash_{\Sigma;\Xi} \ell^C\colon{}\tau}
{\Xi(\ell^C) = \tau}$
& $\infer[\textsc{Op-}r]{\myG\vdash_{\Sigma;\Xi} r\colon{}\tau}
{\myG(r) = \tau}$
\end{tabular}
\end{center}
\item${\tt mov}\ r_d,r_s$ copies $r_s$ into $r_d$.
\item${\tt push\_bt}\ r_e,\ell^C$ installs the failure continuation $\ell^C$ in the trail along with the environment from $r_e$, which will be in {\tt env} upon invocation of $\ell^C$.
\item${\tt close}\ r_d,r_s,\ell^C$ is analogous, but stores the resulting success continuation in $r_d$ before proceeding.
\begin{center}
{\footnotesize\begin{tabular}{cc}
\infer[\textsc{Proj}]{\GE\proj r_d, r_s, i; I \ok}{\myG(r_s) = \cross{\vec\tau} & \thup{\myG}{r_d}{\tau_i}\vdash I\ok & \text{(where $i \leq |\vec\tau|)$}}
&\infer[\textsc{PutTuple}]{\GE\puttuple r_d, n; I \ok}{\GE I:_t (\vec\tau\to \{r_d:\cross{\vec\tau}\}) & \text{(where $n = |\vec\tau|$)}}
\end{tabular}}
\end{center}
\item${\tt proj}\ r_d,r_s,i$ puts the $i$'th element the tuple $r_s$ into $r_d$, typechecking only if $r_d$ has length at least $i$.
Here $\vec\tau$ is a sequence of types, one for each element.
\item${\tt put\_tuple}\ r_d,n$ initiates a \emph{tuple spine} of length $n$ with destination $r_d$.
The remainder of the tuple spine is checked using the auxiliary \emph{tuple spine typing} judgement $\GE I:_t (\tau_1 \to \cdots \to \tau_n \to {\tt Post})$,
where {\tt Post} is a singleton rftype $\{r_d\colon{}\cross{\vec\tau}\}$.
The auxiliary judgement $\GE I:_t (\tau_1 \to \cdots \to \tau_n \to {\tt Post})$ should be read as
``the next $n$ instructions construct tuple elements of type $\tau_i,$ with postcondition ${\tt Post} \leq \myG$, and all remaining instructions typecheck''.
The typing rules for the spine typing judgement are given in Section~\ref{sec:spine-typing}.
\begin{center}
{\begin{tabular}{cc}
\infer[\textsc{GetStr}]{\GE \getstr {c} {r}; I \ok} {\deduce{\GE I:_s(\vec a \to \{\})}{\Sigma(c) = \vec a \to a &
\Gamma(r) = a}}
&
\infer[\textsc{PutStr}]{\GE \putstr {c} {r}; I \ok}
{\deduce{\thup{\Gamma}{r}{a} \ent I:_s (\vec a \to \{\})}
{\Sigma(c) = \vec a \to a}}
\end{tabular}}
\end{center}
\item${\tt get\_str}\ c,r$ and ${\tt put\_str}\ c,r$ both initiate \emph{Prolog spines} which are checked with \emph{Prolog spine typing} judgement $\GE I:_s (a_1 \to \cdots \to a_n \to {\tt Post})$. Unlike tuple spines, Prolog spines contain only atomic types, and in SWAM always have an empty postcondition ${\tt Post} = \{\}$.
Intuitively one might expect ${\tt Post} = \{r : a\}$, for {\tt put\_str}, but we choose to update the type of $r$ at the \emph{beginning} of the spine instead of the end, because this leaves {\tt put\_str} symmetric more symmetric with {\tt get\_str}
(a free variable is stored at $r_d$ until the spine completes to ensure type safety).
\end{itemize}
\subsection{Spine Typing}
\label{sec:spine-typing}
When constructing compound data structures (either tuples or structures), we wish to know that the data structure has the intended number of arguments, each with the intended type.
For this reason, we apply the auxilliary typing judgements for tuple and Prolog spines.
Each spinal instruction produces one element, and so each rule application checks the type of one element.
Consider the rules for the tuple spine judgement $\GE I:_t (\tau_1 \to \cdots \to \tau_n \to {\tt Post})$:
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{TSpine-SetVal}]{\GE\setval r; I :_t (\tau\to J)}{\myG(r) = \tau & \GE I:_t J}
&
\infer[\textsc{TSpine-End}]{\GE I :_t {\tt Post}}
{\Gplus{\tt Post}\ent I \ok}
\end{tabular}
\end{center}
The rule for (TSpine-SetVal) says that each {\tt set\_val} contributes one element.
The rule (TSpine-End) resumes the main typing judgement $\GE I \ok$ when
says that when a tuple is complete, we store the tuple according to {\tt Post} and resume normal typechecking. Specifically, $\Gplus{\myG'}$ is the rftype such that $\Gplus{\myG'}(r) = \myG'(r)$ for $\dom{\myG'}$ and $\Gplus{\myG'}(r) = \myG(r)$ otherwise.
Prolog spines have their own auxilliary judgment, $\GE I:_s (a_1 \to \cdots \to a_n \to {\tt Post})$.
The rule for ending a Prolog spine is analogous to \textsc{(TSpine-End)}.
The elements of a Prolog spine can be produced either by ${\tt unify\_val}\ r$ or ${\tt unify\_var}\ r$.
The ${\tt unify\_val}\ r$ instruction which requires the argument register type to match the constructor argument,
whereas ${\tt unify\_var}\ r$ creates a new unification variable of the correct type, which appears both in $r_d$ and as a constructor argument.
\begin{center}
{\begin{tabular}{cc}
\infer[\textsc{UnifyVal}]{\GE \unifyval r; I:_s (a \to J)}
{\Gamma(r) = a & \GE I:_s J}
&
\infer[\textsc{UnifyVar}]{\GE \unifyvar r; I:_s (a \to J)}
{\thup{\Gamma}{r}{a} \ent I:_s J}
\end{tabular}
}\end{center}
\subsection{State Representation and Invariants}
\label{sec:simp-rep-inv}
Following the traditional description of the WAM, the essential parts of the SWAM \emph{machine state} include the \emph{code section} $C$, \emph{heap} $H$, and \emph{trail} $T$ (backtracking structure). $H$ and $C$ are often considered together as the \emph{store} $S = (C,H)$.
Locations in the code section are written $\ell^C$ and locations in the heap are written $\ell^H$.
Where both are acceptable we write $\ell$. The notation $S(\ell)$ denotes either $H(\ell^H)$ or $C(\ell^C)$ as appropriate.
We additionally have an explicit representation of the \emph{register file} $R$ and we represent the instruction pointer as the sequence $I$ of remaining instructions in the current basic block.
Machines also support three spinal execution modes: read spines, write spines, and tuple (write) spines.
In short, machine states are described by the syntax:
\[m ::= (T,S,R,I)\ |\ \mread(T,S,R,I,\vec\ell^H)\ |\ \mwrite(T,S,R,I,c,\ell^H,\vec\ell^H)\ |\ \twrite(T,S,R,I,r,n,\vec\ell^H)\]
We first consider the following typing invariant for normal states $(T,S,R,I)$ in depth and then revisit the additional invariants for spinal states:
\[\infer[\textsc{Mach}]{\cdot \ent_{\Sigma;\Xi} (T,S,R,I) \ok}
{\deduce{\SE S:(\Xi;\Psi) \hskip 0.1in \PE R \colon{} \Gamma \hskip 0.1in \GE I \ok}
{S \ent T \ok}}
\]
As in Section~\ref{sec:simple-wam-istat}, all judgments are parameterized by signatures $\Sigma$ and code section types $\Xi,$ which are elided when irrelevant.
The code section is well-typed when each basic block is well-typed according to the rules of Section \ref{sec:simple-wam-istat}.
The code section is allowed to be mutually recursive:
\[\infer[\textsc{Code-Sec}]{\cdot\ent_{\Sigma;\Xi} \heap{v^C_1, \ldots v^C_n} \colon{} \Xi}
{\cdot\ent_{\Sigma;\Xi} v^C_1 \colon{} \tau_1\ \cdots\ \cdot\ent_{\Sigma;\Xi} v^C_n \colon{} \tau_n & \text{(where $\Xi = \heap{v^C_1 \colon{} \tau_1, \ldots, v^C_n \colon{} \tau_n}$)}}\]
Heap types are written $\Psi$ and are analogous to rftypes.
As in rftypes we write $\thup{\Psi}{\ell^H}{\tau}$ when updating the type of $\ell^H$.
We also write $\thext{\Psi}{\ell^H}{\tau}$ when adding a \emph{fresh} location $\ell^H$ with type $\tau$, or
$\heap{}$ for an empty heap or empty heap type.
We prohibit cycles in the heap because it simplifies implementing SWAM and simplifies the dependent type system of Section \ref{sec:dependent-wam} even further.
Specifically, a typing derivation $\mathcal{D} : (\SE H : \Psi)$ serves as a witness that $H$ is acyclic,
because $\mathcal{D}$ implicitly specifies a topological sorting on $H$: the rules below state that each value may
only refer to preceding values.
However, $\Psi$ need not assign a type to all values in H, so long as those values without types are never accessed.
This technicality is useful when reasoning about backtracking as in Lemma~\ref{lem:trail-up}.
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Heap-Nil}]{\SE H\colon{}\heap{}}{}
&\infer[\textsc{Heap-Cons}]{\SE H\colon{}\thext{\Psi}{\ell^H}{\tau}}
{\SE H\colon{}\Psi & H(\ell^H) = v^H & \PE v^H\colon{}\tau & \ell^H \notin\dom{\Psi}}
\end{tabular}
\end{center}
Values are divided into \emph{heap values} $v^H$ which are arbitrarily large and \emph{word values} $w$ which are fixed size.
In SWAM, words are always heap locations $w ::= \ell^H$.
The heap values $v^H$ follow the syntax:
\[v^H ::= \cwsh\ |\ \free{}[a]\ |\ \bound{\ell^H}\ |\ \close(w_{env}, \ell^C)\ |\ \langle{}w_1,\ldots,w_n\rangle\]
The values $\cwsh$ and $\free{}[a]$ introduce structures and free variables in Prolog terms, respectively.
The type annotation $a$ in $\free{}[a]$ is merely a convenience for the metatheory and not used at runtime (i.e. SWAM and TWAM support type erasure).
Combined with pointers $\bound{\ell^H}$, these values provide a union-find data structure within the heap, used by SWAM's unification algorithm. The $\bound{\ell^H}$ pointers are merely an artifact of that algorithm and are semantically equivalent to $\ell^H$.
In addition to Prolog terms, the heap contains closures $\close(w_{env}, \ell^C)$ where the machine word $w_{env}$ is the environment for executing $\ell^C$, as well as tuples $\langle w_1, \ldots, w_n\rangle$.
The typing invariants for heap values are:
\begin{center}
\begin{tabular}{ll}
\infer[\textsc{HV-Close}]{\PE \close(w_{env}, \ell^C) \colon{}\neg \myG}
{\PE w_{env} \colon{} \tau & \PE\ell^C\colon{}\neg\thup{\myG}{\texttt{env}}{\tau}}
&\infer[\textsc{HV-Tup}]{\PE\langle w_1,\ldots,w_n\rangle\colon{}\cross{\tau_1,\ldots,\tau_n}}
{\PE w_1 : \tau_1&\cdots&\PE w_n : \tau_n}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{lll}
\infer[\textsc{HV-Bound}]{\PE \bound{\ell^H}\colon{}a}{\PE \ell^H\colon{}a}
&\infer[\textsc{HV-Str}]{\PE_{\Sigma;\Xi} \cwsh\colon{}a}
{\Sigma(c) = \vec a \to a & \PE \ell_i^H\colon{}a_i}
&\infer[\textsc{HV-Free}]{\PE \free{}[a] \colon{}a}{}
\end{tabular}
\end{center}
\paragraph{Register Typing}
A register file $R$ simply maps registers $r_i$ to word values $w_i$ and is well-typed when all $w_i$ are well-typed.
Because the only word values in SWAM are heap locations, it suffices to consult the heap type $\Psi$:
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{RF}]{\PE \heap{r_1 \hook w_1, \ldots, r_n \hook w_n} : \heap{r_1 :\tau_1, \ldots, r_n : \tau_n}}
{\PE w_1 : \tau_1 & \cdots & \PE w_n : \tau_n}&
\infer[\textsc{WV-}\ell^H]{\PE \ell^H \colon{} \tau}{\Psi(\ell^H) = \tau}
\end{tabular}
\end{center}
\paragraph{Trail Typing}
When Prolog backtracks because a clause failed, it must revert all changes made by the failed clause.
The only such change is the binding of free variables during unification,
thus it suffices to record bindings when they occur and revert them during backtracking.
The \emph{trail} is the data structure that records these variables.
In traditional presentations of the WAM, the trail contains variable addresses only and separate \emph{choice point} records in the call stack contain the failure continuation.
For our presentation, it simplified the formalism to store the continuation inline.
The trail is given as a list of \emph{trail frames} $(t, w_{env}, \ell^C)$ where $t$ is a list of heap locations (in the theory, annotated with types as in $\ell^H:a$), where we write the list of $t_i$ as $t_1::\cdots::t_n::\epsilon$. The environment is $w_{env}$ and $\ell^C$ is the failure continuation. The function $\unwind(S,t)$ describes the process of backtracking one trail frame, i.e. $\unwind(S,(\ell^H:a)::t) = \unwind( \hup{S}{\ell^H}{\free{}[a]},t)$ and $\unwind(S, \epsilon) = S$.
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Trail-Nil}]{S \ent \epsilon \ok}{}
&\infer[\textsc{Trail-Cons}]{S \ent_{\Sigma;\Xi}(t,w_{env},\ell^C)::T \ok}
{\deduce
{\ent S'\colon{}(\Xi,\Psi')\hskip 0.1in \Psi' \ent w_{env}\colon{}\tau
\hskip 0.1in \Psi'\ent\ell^C\colon{}\neg\heap{\texttt{env}\colon{}\tau}}
{\unwind(S,t)= S' & S' \ent T \ok}}
\end{tabular}
\end{center}
\paragraph{Special Mode Invariants}
When the machine is in read or write mode, it maintains additional data. Read mode maintains a list of arguments not yet read, while the write modes maintain lists of arguments written so far with destination registers or locations. Prolog write mode also tracks the constructor being applied while tuple write mode tracks the number of elements left to be written in the tuple. In each case additional invariants are required, as given in the judgements $\PE\vec\ell^H \reads \vec a$, $\PE (\vec \ell^H, \ell^H,c) \writes (\vec a_2\to \{\})$ and $\PE (n,r,\vec\ell^H) \writes (\vec \tau_2 \to \{r\colon{}\cross{\vec\tau_1 \vec \tau_2}\})$.
In each case the invariants ensure that the type of the constructor or tuple in question is consistent with both the values computed so far and the remaining spinal instructions.
\begin{center}{\footnotesize
\begin{tabular}{cc}
\infer[\textsc{Mach-Read}]{\cdot \ent_{\Sigma;\Xi} \mread(T,S,R,I, \vec \ell^H) \ok}
{\deduce{\PE R\colon{}\Gamma\hskip 0.1in\GE I:_sJ\hskip 0.1in \PE\vec\ell^H\reads J}
{S\ent T\ok & \ent S\colon{}(\Xi;\Psi)}}&
\infer[\textsc{Reads}]{\PE\vec\ell^H\reads(\vec a\to \{\})}
{\PE\ell^H_i\colon{}a_i}
\end{tabular}}
\end{center}
\begin{center}{\footnotesize
\begin{tabular}{cc}
\infer[\textsc{Mach-Write}]{\cdot \ent_{\Sigma;\Xi} \mwrite(T,S,R,I,c,\ell^H, \vec \ell^H) \ok}
{\deduce{ \PE R\colon{}\Gamma\hskip 0.1in\GE I:_s J \hskip 0.1in \PE (\vec \ell^H, \ell,c) \writes J}
{S \ent T \ok&\SE S\colon{}(\Xi;\Psi)}}&
\infer[\textsc{Writes}]{\PE_{\Sigma;\Xi} (\vec\ell^H,\ell^H,c) \writes (\vec a_2\to \{\})}
{\Sigma(c) = \vec a_1 \to \vec a_2 \to a & \PE \vec\ell^H\colon{}\vec a_1 & \Psi(\ell^H) = a}
\end{tabular}}
\end{center}
\begin{center}{\footnotesize
\begin{tabular}{cc}
\infer[\textsc{Mach-TWrite}]{\cdot \ent_{\Sigma;\Xi} \twrite(T,S,R,I, \vec w,r,n) \ok}
{\deduce{\PE R\colon{}\Gamma\hskip 0.1in\GE I:_t J \hskip 0.1in \PE (\vec w, r, n) \writes J }
{S\ent T\ok&\ent S:(\Xi;\Psi)}}&
\infer[\textsc{TWrites}]{\PE (n,r,\vec\ell^H) \writes (\vec \tau_2 \to \{r\colon{}\cross{\vec\tau_1 \vec \tau_2}\})}
{\PE \vec \ell^H \colon{} \vec \tau_1 & |\vec \tau_2| = n}
\end{tabular}}
\end{center}
\subsection{Operational Semantics}
The dynamic semantics of SWAM are given as a small-step operational semantics.
We begin with an informal example trace executing the query \verb|?- plus(X,zero,succ(zero))| using the \verb|plus| function of Example \ref{ex:plus-wam} before
developing the semantics formally.
For each line we describe any
changes to the machine state, i.e. the heap, trail, register file, and instruction pointer. As with the WAM, the TWAM
supports special execution modes for spines: \emph{read mode} and \emph{write mode}. When the program enters read mode,
we annotate that line with the list $\ell^H{}s$ of variables being read, and when the program enters write mode we annotate it
with the constructor $c$ being applied, the destination location $\ell^H$ and the argument locations $\vec\ell^H$. The final instruction
of a write-mode spine is best thought of two evalution steps, one of which constructs the last argument of the constructor and one of which
combines the arguments into a term.
\newcommand{\hspace{0.1in}}{\hspace{0.1in}}
\newcommand{\hspace{0.2in}}{\hspace{0.2in}}
{\footnotesize
\begin{longtable}{ll}
Code & Change\\
\multicolumn{2}{l}{{\tt \# Query} ${\tt plus}(X,{\tt zero},{\tt succ(zero)})$}\\
\multicolumn{2}{l}{{\tt query}$~\mapsto\code[\heap{}]($}\\
\hspace{0.1in}{\tt put\_var}$\ r_1;$ &$H \leftarrow \hext{H}{\ell_1}{\free{}[{\tt nat}]}$, $R \leftarrow \hup{R}{r_1}{\ell_1}$\\
\hspace{0.1in}{\tt put\_str}$\ r_2$, {\tt zero/0}; &$H \leftarrow \hext{H}{\ell_2}{\free{}[{\tt nat}]}, R \leftarrow \hup{R}{r_2}{\ell_2}, c={\tt zero}$\\
&$\ell = \ell_2, \vec\ell = \langle\rangle,$\\
&$H \leftarrow \hup{H}{\ell}{c\langle\vec\ell\rangle}$\\
\hspace{0.1in}{\tt put\_str}$\ r_3$, {\tt succ/1}; &$H \leftarrow \hext{H}{\ell_3}{\free{}[{\tt nat}]}, R \leftarrow \hup{R}{r_3}{\ell_3}, c={\tt succ}$\\
&$\ell = \ell_3, \vec\ell = \langle\rangle$\\
\hspace{0.2in}{\tt unify\_val}$\ r_2;$ &$\vec\ell \leftarrow \langle\ell_2\rangle, H \leftarrow \hup{H}{\ell}{c\langle\vec\ell\rangle}$\\
\hspace{0.1in}{\tt put\_tuple}$\ r_4,0;$ &$H \leftarrow \hext{H}{\ell_4}{\langle\rangle},R\leftarrow\hup{R}{r_4}{\ell_4}$\\
\hspace{0.1in}{\tt close}\ {\tt ret}$,r_4,{\tt success/0};$ &$H \leftarrow \hext{H}{\ell_5}{\close(\ell_4,{\tt success})},R\leftarrow\hup{R}{\tt ret}{\ell_5}$\\
\hspace{0.1in}{\tt jmp\ }\verb|plus-zero/3|$;$ &$I \leftarrow C({\verb|plus-zero|})$ \\
)&\\
~\\
\multicolumn{2}{l}{{\tt plus-zero/3}$~\mapsto\code[{r_2:{\tt nat}, r_2:{\tt nat},r_3:{\tt nat},r_4:\neg\heap{}}]($}\\
\hspace{0.1in}{\tt put\_tuple} $r_4,4;$ &$\vec\ell=\langle\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_2;$ &$\vec\ell=\langle\ell_1\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_2;$ &$\vec\ell=\langle\ell_1,\ell_2\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_3;$ &$\vec\ell=\langle\ell_1,\ell_2,\ell_3\rangle$\\
\hspace{0.2in} {\tt set\_val} ${\tt ret};$ &$\vec\ell=\langle\ell_1,\ell_2,\ell_3,\ell_5\rangle$\\
&$H \leftarrow \hext{H}{\ell_6}{\langle\vec\ell\rangle},R\leftarrow\hup{R}{r_4}{\ell_6}$\\
\hspace{0.1in}{\tt push\_bt} $r_4, {\verb|plus-succ/3|};$ &$T \leftarrow (\ell_6, {\verb|plus-succ/3|}, {\tt nil})::{\tt nil}$\\
\hspace{0.1in}{\tt get\_str} $r_2, {\tt zero/0};$ &$c={\tt zero}, l = \ell_1, \vec\ell = \langle\rangle$\\
&$H \leftarrow \hup{H}{\ell_1}{\tt zero}, T \leftarrow (\ell_6,{\verb|plus-succ/3|}, \ell_1)::\langle\rangle$\\
\multicolumn{2}{l}{\tt\# This instruction fails, backtrack to plus-succ/3}\\
\hspace{0.1in}{\tt get\_val}$\ r_2, r_3;$ &$T \leftarrow {\tt nil}, I \leftarrow {\verb|plus-succ/3|}, H \leftarrow \hup{H}{\ell_1}{\free{}[\tt nat]}$\\
\hspace{0.1in}{\tt jmp\ ret};\\
)&\\
~\\
\multicolumn{2}{l}{{\tt plus-succ/3}$~\mapsto \code[\{{\tt env}:\cross{{\tt nat},{\tt nat},{\tt nat},\neg\heap{}}\}]$ (}\\
\hspace{0.1in}{\tt proj} $r_1, {\tt env}, 1;$& $R\leftarrow \hup{R}{r_1}{\ell_1}$\\
\hspace{0.1in}{\tt proj} $r_2, {\tt env}, 2;$& $R\leftarrow \hup{R}{r_2}{\ell_2}$\\
\hspace{0.1in}{\tt proj} $r_3, {\tt env}, 3;$& $R\leftarrow \hup{R}{r_3}{\ell_3}$\\
\hspace{0.1in}{\tt proj\ ret}$, {\tt env}, 4;$&$R\leftarrow \hup{R}{{\tt ret}}{\ell_5}$\\
\multicolumn{2}{l}{\# Here we are replacing a free variable with a concrete term}\\
\hspace{0.1in}{\tt get\_str} ${\tt succ/1}, r_2;$ &$\ell=\ell_1, \vec\ell=\langle\rangle$\\
\hspace{0.2in}{\tt unify\_var} $r_2;$ &$H \leftarrow \hext{H}{\ell_4}{\free{}[{\tt nat}]},R \leftarrow \hup{R}{r_2}{\ell_4},\vec\ell= \langle\ell_4\rangle$\\
&$H \leftarrow \hup{H}{\ell_1}{{\tt succ}\ \vec\ell},$\\
\hspace{0.1in}{\tt get\_str} ${\tt succ/1}, r_3;$ &$\vec\ell = \langle\ell_2\rangle$\\
\hspace{0.2in}{\tt unify\_var} $r_3;$ &$R \leftarrow \hup{R}{r_3}{\ell_2},$\\
&$H \leftarrow \hup{H}{\ell_1}{{\tt succ}\ \vec\ell},$\\
\hspace{0.1in}{\tt jmp }\verb|plus-zero/3|$;$ &$I \leftarrow C(\verb|plus-zero|)$\\
)&\\
~\\
\multicolumn{2}{l}{{\tt plus-zero/3}$~\mapsto \code[\{r_2:{\tt nat}, r_2:{\tt nat},r_3:{\tt nat},r_4:\neg\heap{}\}]($}\\
\hspace{0.1in}{\tt put\_tuple} $r_4,4;$ &$\vec\ell=\langle\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_2;$ &$\vec\ell=\langle\ell_1\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_2;$ &$\vec\ell=\langle\ell_1,\ell_2\rangle$\\
\hspace{0.2in} {\tt set\_val} $r_3;$ &$\vec\ell=\langle\ell_1,\ell_2,\ell_3\rangle$\\
\hspace{0.2in} {\tt set\_val} {\tt ret}; &$\vec\ell=\langle\ell_1,\ell_2,\ell_3,\ell_5\rangle$\\
&$H \leftarrow \hext{H}{\ell_7}{\langle\vec\ell\rangle},R \leftarrow \hup{R}{r_4}{\ell_6}$\\
\hspace{0.1in}{\tt push\_bt} $r_4, {\verb|plus-succ/3|};$ &$T \leftarrow(\ell_7,{\verb|plus-succ|},\langle\rangle) :: {\tt nil}$\\
\hspace{0.1in}{\tt get\_str} $r_2, {\tt zero/0};$ &$\ell=\ell_4, \vec\ell=\langle\rangle, c = {\tt zero}$\\
&$H \leftarrow \hup{H}{\ell_4}{c\langle\vec\ell\rangle}$\\
\hspace{0.1in}{\tt get\_val} $r_2, r_3;$ &\\
\hspace{0.1in}{\tt jmp} $r_4$; &$I \leftarrow C(R(r_4)) = C({\tt success})$\\
)&\\
~&\\
\multicolumn{2}{l}{\tt {success/0} $\mapsto\code[\heap{}]$ (}\\
\hspace{0.1in}{\tt succeed;}&\\
)&\\
\end{longtable}
\normalsize
\subsection{Formal Operational Semantics}
\label{sec:simp-op}
The small-step operational semantics consists of three main judgements:
$m\step m', m\done,$ and $m\fails,$ where $m\fails$ indicates a negative result to a Prolog query, not a stuck state.
There are also numerous auxilliary judgements for unification, backtracking, trail management, etc.
We begin with conceptually simple cases and proceed to conceptually complex ones.
The simplest instructions are {\tt mov} and {\succeed}, requiring no auxilliary judgements:
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Mov}\step]{(T,S,R,\mov{r_d}{r_s}; I) \step (T,S,\hup{R}{r_d}{w},I)}{R(r_s) = w}&
\infer[\done]{(T,S,R,\succeed) \done}{}
\end{tabular}
\end{center}
\subsubsection{Operands}
The $\jmp{op}$ instruction takes at \emph{operand} which allows us to jump either to a literal location or a success continuation stored in a register.
The \emph{operand evaluation} judgement $R \ent op\eval w$ resolves an operand $op$ into a word $w$ by consulting the registers $R$ if necessary.
If the operand is a code location, {\tt jmp} simply transfers control, else if the operand is a closure, {\tt jmp} also loads the stored environment.
\begin{center}{\footnotesize
\begin{tabular}{cc}
\infer[\textsc{Jmp-}\ell^C]{(T,S,R,\jmp op; I) \step (T,S,R,I')}
{R \ent op \eval \ell^C & S(\ell^C) = \code[\Gamma]I'}&
\infer[\textsc{Jmp-}\ell^H]{(T,S,R,\jmp op; I) \step (T,S,\hup{R}{\texttt{env}}{w_{env}},I')}
{R \ent op \eval \ell^H & S(\ell^H) = \close(w_{env}, \ell^C)
&S(\ell^C) = \code[\Gamma](I')}
\end{tabular}
\begin{tabular}{cc}
\infer[\ell^C\eval]{R\ent \ell^C\eval\ell^C}{}&
\infer[r\eval]{R\ent r\eval w}{R(r) = w}
\end{tabular}}
\end{center}
\subsubsection{Environments}
Environment tuples are constructed with the {\tt twrite} spinal mode.
This mode begins after {\tt put\_tuple} and ends when the count of remaining tuple elements reaches 0.
When the spine completes, the resulting tuple is stored in the destination register specified by the initial {\tt put\_tuple}.
As before, $\epsilon$ denotes an empty sequence. We also use the notation $\vec{w}::w$ even when adding an element $w$ to the end of a sequence $\vec{w}$.
Reading tuple elements with {\tt proj} does not require entering a spine.
\[\infer[\textsc{PutTuple}\step]{(T,S,R,\puttuple{r, n}; I) \step
\twrite(T,S,R,I,r,n,\epsilon)}{}\]
\[\infer[\textsc{SetVal}\step]{\twrite(T, S,R, \setval r_s; I,r_d,n,\vec w) \step
\twrite(T,S,R,I,r_d,n-1,(\vec w::w))}{R(r_s) = w & n > 0}\]
\vspace{0in}
\[\infer[\textsc{TWrite}\step]{\twrite(T,S,R,I,r,0,\vec w) \step (T,\hext{S}{\ell^H}{\args{\vec w}},\hup{R}{r}{\ell^H},I)}{}\]
\[\infer[\textsc{Proj}\step]{(T,S,R,\proj r_d, r_s, i; I) \step (T,S,\hup{R}{r_d}{w_i},I)}
{R(r_s)=\ell^H & S(\ell^H) = \args{w_1,\ldots,w_i,\ldots,w_n}}\]
\subsubsection{Continuations and Backtracking}
\label{sec:cont-bt}
The instructions {\tt close} and {\tt push\_bt} allocate new success and failure continuations, respectively.
The {\tt close} instruction puts the continuation in a register $r_d$ for use by a future {\tt jmp},
whereas {\tt push\_bt} puts the failure continuation in the trail.
As shown in Section \ref{sec:trailing}, the trail maintains an invariant that the location of every free variable
bound since the last {\tt push\_bt} is stored in the current trail frame, which is necessary when backtracking.
Because we have just created a new failure continuation, after a {\tt push\_bt} our new trail frame contains the empty list $\epsilon$.
Backtracking is handled automatically when unification fails, thus there is no need to make the failure continuation accessible via a register.
\[\infer[\textsc{Close}\step]{(T,S,R,\close r_d, r_e, \ell^C; I) \step (T,\hext{S}{\ell^H}{\close(w_{env},\ell^C)},\hup{R}{r}{\ell^H},I)}
{R(r_e) = w_{env}}\]
\[\infer[\textsc{PushBT}\step]{(T,S,R,\branch r_e, \ell^C; I) \step ((\epsilon,w_{env},\ell^C)::T,S,R,I)}
{R(r_e) = w_{env}}\]
The trail invariant is essential to the correctness of the $\bt$ operation, which succeeds when there is failure continuation on the trail, or signals query failure when the trail is empty.
Trail unwinding has its inverse in trail updating, which adds a recently-bound variable to the trail (or safely skips it if there are no failure continuations left).
\begin{center}{\small
\begin{tabular}{cc}
\infer[\textsc{BT-Cons}]{\bt(S,(t,w,\ell^C)::T) = (T,S',\heap{\texttt{env} \hook w},I)}
{\unwind(S,t) = S' & C(\ell^C) = \code[\heap{\texttt{env}:\tau}](I)}&
\infer[\textsc{BT-Nil}]{\bt(S,\epsilon) = \bot}{}\\[0.08in]
$\unwind(S,(\ell^H:a)::t) = \unwind( \hup{S}{\ell^H}{\free{}[a]},t)$ & $\unwind(S, \epsilon) = S$\\[0.08in]
$\uptrail(\ell^H:a,(t,w_{env},\ell^C)::T) = ((\ell^H:a)::t,w_{env},\ell^C)::T$&$\uptrail((\ell^H:a),\epsilon) = \epsilon$
\end{tabular}}
\end{center}
\subsubsection{Unification, Occurs Checks, and Trailing}
\label{sec:trailing}
The {\tt get\_val} instruction unifies two arbitrary Prolog terms stored at $r_1$ and $r_2$.
It does so using the auxilliary judgement $\unify(S,T,\ell^H_1,\ell^H_2) = (S',T')$, which computes the resulting store where $\ell^H_1$ and $\ell^H_2$ are unified, or $\bot$ if unification fails.
It also must compute an updated trail, because unification binds free variables, and backtracking must be able to undo those changes.
\[\infer[\textsc{GetVal}\step]{(T, S,R, \getval{r_1}{r_2}; I) \step (T', S',R,I)}
{R(r_1) = \ell^H_1 & R(r_2) = \ell^H_2 & \unify(S,T,\ell^H_1,\ell^H_2) = (S',T')}\]
The judgement $\unify(S,T,\ell^H_1,\ell^H_2) = (S',T')$ is defined by mutual recursion with the judgement $\unifyargs(S,T,\vec \ell^H, \vec \ell'^H)=(S',T')$ which simply unifies every $\ell_i^H$ with the corresponding $\ell_i'^H$.
These lists $\vec\ell^H$ and $\vec\ell'^H$ correspond to the push-down list (PDL) in other presentations of the WAM.
An additional judgement $\edn(S,\ell^H)$ follows chains of $\bound{\ell^H}$ pointers to their ends.
Because the typing invariant for heaps ensures absence of cycles, this is guaranteed to terminate.
The basic unification algorithm says to recurse if both unificands are structures, or if either is a free variable, then bind it to the other unificand.
However, unification must also maintain the invariant that the heap is free of cycles, thus we employ an occurs check in our algorithm,
writing $\ell_1^H \in_S \ell_2^H$ when $\ell_1^H$ occurs in $\ell_2^H$ (occurs check failure) and $\ell_1^H \notin_S \ell_2^H$ otherwise (occurs check success).\footnote{Typing constraints ensure that at runtime, the occurs check is only ever invoked on Prolog terms. However, the occurs check is also of broader use in the metatheory proofs, and there it is convenient to define the occurs check on closures and tuples as well, such as in Lemma~\ref{lem:heap-str}.}
Additionally, we employ the $\uptrail$ function to maintain the trail invariants when binding free variables.
{\footnotesize\begin{center}
\begin{tabular}{c}
\infer[\in{}c\langle\rangle]{\ell^H_1 \in_S \ell^H_2}{S(\ell^H_2) = c\args{\ell'^H_1,\ldots,\ell'^H_n} & \ell^H_1 \in_S \ell'^H_i\ (\exists i \in [n])}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\in=]{\ell^H_1 \in_S \ell^H_2}{\ell^H_1 = \ell^H_2}&
\infer[\in\bound{}]{\ell^H_1 \in_S \ell^H_2}{S(\ell^H_2) = \bound{\ell'^H_2} & \ell^H_1 \in_S \ell'^H_2}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\notin\free{}]{\ell^H_1 \notin_S \ell^H_2}{\ell^H_1 \neq \ell^H_2 & S(\ell^H_2)=\free{}[a]}&
\infer[\notin\bound{}]{\ell^H_1 \notin_S \ell^H_2}{S(\ell^H_2) = \bound{\ell'^H_2} & \ell^H_1 \notin_S \ell'^H_2}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{c}
\infer[\notin{}c\langle\rangle]{\ell^H_1 \notin_S \ell^H_2}{S(\ell^H_2) = c\args{\ell'^H_1,\ldots,\ell'^H_n} & \ell^H_1 \notin_S \ell'^H_i\ (\forall i \in [n])}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\in\langle\rangle]{\ell^H_1 \in_S \ell^H_2}{S(\ell^H_2) = \args{\ell'^H_1,\ldots,\ell'^H_n} & \ell^H_1 \in_S \ell'^H_i\ (\exists i \in [n])}&
\infer[\notin\langle\rangle]{\ell^H_1 \notin_S \ell^H_2}{S(\ell^H_2) = \args{\ell'^H_1,\ldots,\ell'^H_n} & \ell^H_1 \notin_S \ell'^H_i\ (\forall i \in [n])}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\in\close]{\ell^H_1 \in_S \ell^H_2}{S(\ell^H_2) = \close(\ell'^H_2,\ell^C) & \ell^H_1 \in_S \ell'^H_2}&
\infer[\notin\close]{\ell^H_1 \notin_S \ell^H_2}{S(\ell^H_2) = \close(\ell'^H_2,\ell^C) & \ell^H_1 \notin_S \ell'^H_2}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\edn~\free{}]{\edn(S,\ell^H) = \ell^H}{S(\ell^H) = \free{}[a]}&
\infer[\edn~c\langle\rangle]{\edn(S,\ell^H) = \ell^H}{S(\ell^H) = \cwsh}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{c}
\infer[\edn~\bound{}]{\edn(S,\ell^H) = \ell''^H}{S(\ell^H) = \bound{\ell'^H} & \edn(S,\ell'^H) = \ell''^H}\\
\infer[{\tt unify}=]{\unify(S,T,\ell_1^H,\ell_2^H) = (S,T)}
{\edn(\ell_1^H) = \ell^H & \edn(\ell_2^H) = \ell^H}
\infer[{\tt unify}~\free{}]{\unify(S,T,\ell_1^H,\ell_2^H) = (\hup{S}{\ell'^H_2}{\bound{\ell_1^H}},T')}
{\deduce{{\ell'}_2^H \notin_S \ell_1\hskip 0.1in \uptrail(T,({\ell'}^H_2:a))=T'}
{\edn(S,\ell_1^H) = \ell'^H_1 & \edn(S,\ell^H_2) = {\ell'}^H_2 & S(\ell'^H_2) = \free{}[a]}}\\
\infer[{\tt unify}~c\langle\rangle]{\unify(S,T,\ell_1^H,\ell_2^H) = (S',T')}
{\deduce{\edn(S,\ell_2^H) = \ell'^H_2\hskip 0.1in\unifyargs(S,T,\vec \ell^H, \vec \ell'^H) =(S',T')}
{S(\ell'^H_1) = \func{c}{\vec \ell^H} & S(\ell'^H_2) = \func{c}{\vec \ell'^H} & \edn(S,\ell_1^H) = \ell'^H_1}}\\
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{UA-Cons}]{\unifyargs(S,T,(\ell^H_1::\cdots::\ell_n^H),(\ell'^H_1::\cdots::\ell'^H_n)) = (S'',T'')}
{\deduce{\unifyargs(S',T',(\ell^H_2::\cdots::\ell^H_n),(\ell'^H_2::\dots::\ell'^H_n)) = (S'',T'')}{\unify(S,T,\ell^H_1,\ell^H_2) = (S',T')}}
&\infer[\textsc{UA-Nil}]{\unifyargs(S,T,\epsilon,\epsilon) = (S,T)}{}
\end{tabular}
\end{center}}
The failure cases for unification are straightforward, but they are given here for completeness:
\begin{center}\footnotesize\begin{tabular}{cc}
\infer[\textsc{U}\bot1]{\unify(S,T,\ell^H_1,\ell^H_2) = \bot}
{\deduce{\edn(S,\ell^H_1) = \ell'^H_1 \hskip 0.1in\edn(S,\ell^H_2) = \ell'^H_2}
{S(\ell'^H_1) = \free{}[a] & \ell'^H_1 \in_S \ell^H_2}}&
\infer[\textsc{U}\bot2]{\unify(S,T,\ell^H_1,\ell^H_2) = \bot}
{\deduce{\edn(S,\ell^H_1) = \ell'^H_1 \hskip 0.1in\edn(S,\ell^H_2) = \ell'^H_2}
{S(\ell'^H_2) = \free{}[a] & \ell'^H_2 \in_S \ell^H_1}}\\
\infer[\textsc{U}\bot3]{\unify(S,T,\ell^H_1,\ell^H_2) = \bot}
{\deduce{\edn(S,\ell^H_1) = \ell'^H_1 \hskip 0.1in\edn(S,\ell^H_2) = \ell'^H_2}
{S(\ell'^H_1) = \func{c}{\vec w} & S(\ell'^H_2) = \func{c'}{\vec w'} & c \neq c'}}
&
\infer[\textsc{U}\bot4]{\unify(S,T,\ell^H_1,\ell^H_2) = \bot}
{\deduce{\edn(S,\ell^H_1) = \ell'^H_1 \hskip 0.1in \edn(S,\ell^H_2) = \ell'^H_2 \hskip 0.1in S(\ell'^H_1) = \func{c}{\vec \ell^H} }
{\unifyargs(S,T,\vec \ell^H, \vec \ell'^H) = \bot & S(\ell'^H_2) = \func{c}{\vec \ell'^H}}}\\
\infer[\textsc{UA}\bot1]{\unifyargs(S,T,(\ell^H::\vec \ell^H),(\ell'^H::\vec \ell'^H)) = \bot}
{\unify(S,T,\ell^H,\ell'^H) = \bot}&
\infer[\textsc{UA}\bot2]{\unifyargs(S,T,(\ell^H::\vec \ell^H),(\ell'^H::\vec \ell'^H)) = \bot}
{\deduce{\unify(S,T,\ell^H,\ell'^H) = (S',T')}{\unifyargs(S',T',\vec\ell^H,\vec\ell'^H) = \bot}}
\end{tabular}
\end{center}
Lastly, if unification fails, due to the above failure rules, {\tt get\_val} tries backtracking.
If the trail is non-empty, it backtracks successfully, else execution stops and the query has failed.
\[\infer[\textsc{GetVal-BT}]{(T, S,R, \getval{r_1}{r_2}; I) \step m'}
{R(r_1) = \ell^H_1 & R(r_2) = \ell^H_2 & \unify(S,T,\ell^H_1,\ell^H_2) = \bot & \bt(S,T) = m'}\]
\[\infer[\textsc{GetVal-}\bot]{(T, S,R, \getval{r_1}{r_2}; I) \fails}
{R(r_1) = \ell^H_1 & R(r_2) = \ell^H_2 & \unify(S,T,\ell^H_1,\ell^H_2) = \bot &
\bt(S,T) =\bot}\]
\subsubsection{Term Constructors and Occurs Checks}
The {\tt put\_var} instruction immediately allocates a free variable.
Structures are constructed with a write spine, initiated by {\tt put\_str}.
For symmetry with {\tt get\_str}, we first allocate a free variable and replace it with a structure when the spine completes.
Within a write spine, {\tt unify\_var} allocates free variables while {\tt unify\_val} copies a value into the structure.
In the typical case, a write spine finishes when enough arguments have been computed (one for each constructor argument, i.e. $\arity(c)$) by replacing the free variable with a complete structure.
However, the formalism technically allows us to refer to the destination $r$ within its own write spine.
To prevent a cycle, we perform an occurs check ($\ell^H \notin_S \ell_i^H$) and backtrack on failure.
The choice to use an occurs check here was made for its resulting proof simplicity.
For implementation purposes, an equally correct and more efficient choice is to enforce a syntactic restriction that prohibits references to $r$ within its own write spine.
\vspace{0in}
\[\infer[\textsc{PutVar}\step]{(T,S,R,\putvar{a}{r};I) \step (T,\hext{S}{\ell^H}{\free{}[a]},\hups{R}{r \hook \ell^H},I)}{}\]
\[\infer[\textsc{PutStr}\step]{(T,S,R,\putstr{c}{r}; I) \step
\mwrite(T,
\hext{S}{\ell^H}{\free{}[a]},\hup{R}{r}{\ell^H},I,c,\ell^H,\epsilon)}{\Sigma(c) = \vec a \to a}\]
\vspace{0.0in}
\[\infer[\textsc{UnifyVar}\step\textsc{W}]{\deduce{\mwrite(T, \hext{S}{\ell^H}{\free{}[a]},\hup{R}{r_s}{\ell^H},I,c,\ell^H_d,(\vec \ell^H::\ell^H))}{\mwrite(T,S,R,\unifyvar[a] r_s; I,c,\ell^H_d,\vec \ell^H) \step}}{}\]
\vspace{0.0in}
\[\infer[\textsc{UnifyVal}\step\textsc{W}]{\mwrite(T, S,R,\unifyval r_s; I,c,\ell^H_d,\vec \ell^H) \step
\mwrite(T,S,R,I,c,\ell^H_d,(\vec \ell^H::\ell^H))}{R(r_s) = \ell^H}\]
\[\infer[\textsc{Write}\step]{\mwrite(T,S,R,I,\ell^H,c,\vec \ell^H) \step
(T,\hup{S}{\ell^H}{c\args{\vec \ell^H}},R,I)}
{ S(\ell^H) = \free{}[a] & \ell^H \notin_S \ell^H_i & |{\vec \ell^H}| = \arity(c) }\]
\[\infer[\textsc{Write-BT}]{\mwrite(T,S,R,I,\ell^H,c,\vec \ell^H) \step m'}
{\ell^H \in_S \ell^H_i & |{\vec \ell^H}| = \arity(c) & \bt(S,T) = m'}\]
\[\infer[\textsc{Write-}\bot]{\mwrite(T,S,R,I,\ell^H,c,\vec \ell^H) \fails}
{\ell^H \in_S \ell^H_i & |{\vec \ell^H}| = \arity(c) & \bt(S,T) = \bot}\]
\subsubsection{Term Destructor {\tt get\_str}}
The instruction ${\tt get\_str}\ c,r$ starts a spine which unifies the content of register $r$ with a structure $\cwsh$ where each $w_i$ is provided by the $i$'th spinal instruction.
In the case where $r$ contains a free variable, this amounts to building a new structure, and thus the {\tt write} case of {\tt get\_str} simply reuses the {\tt write} spines of {\tt put\_str}.
\[\infer[\textsc{GetStr}\step\textsc{W}]{(T,S,R,\getstr {c}{r}; I) \step
\mwrite(T, S,R,I,c,\ell'^H,\epsilon)}
{R(r) = \ell^H & \edn(S,\ell^H) = \ell'^H & S(\ell'^H) = \free{}[a]}\]
When $r$ contains a structure, we perform structure-to-structure unification.
This can fail in two ways: either the head constructor $c$ does not match or one of the argument positions does not unify.
The first conditon is checked during {\tt get\_str} itself, the other during the ensuing spinal instructions.
In both cases, errors are handled by backtracking if possible:
\[\infer[\textsc{GetStr}\step\textsc{R}]{(T, S,R,\getstr{c}{r}; I) \step
\mread(T, S,R,I,\vec \ell^H)}
{R(r) = \ell^H & \edn(S,\ell^H) = \ell'_H & S(\ell'^H) = c\args{\ell^H_1,\ldots,\ell^H_n}}\]
\[\infer[\textsc{GetStr-BT}]{(T,S,R,\getstr {c}{r}; I) \step m'}
{\deduce{S(\ell'^H)=c'\ells \hskip 0.1in c \neq c' \hskip 0.1in \bt(S,T) = m'}{R(r)= \ell^H &\edn(S,\ell^H) = \ell'^H}}\]
\[\infer[\textsc{GetStr-}\bot]{(T,S,R,\getstr {c}{r}; I) \fails}
{\deduce{S(\ell'^H)=c'\ells \hskip 0.1in c \neq c' \hskip 0.1in \bt(S,T) = \bot}{R(r)= \ell^H & \edn(S,\ell^H) = \ell'^H}}
\]
\vspace{-0.05in}
\[\infer[\textsc{UnifyVar}\step\textsc{R}]{\mread(T,S,R,\unifyvar [a]r;I, (\ell^H::\vec \ell^H)) \step
\mread(T,S,\hup{R}{r}{\ell^H},I,\vec \ell^H)}{~\hskip 0.1in}\]
\[\infer[\textsc{UnifyVal}\step\textsc{R}]{\mread(T, S,R,\unifyval r; I, (\ell^H::\vec \ell^H)) \step
\mread(T',S',R,I, \vec \ell^H)}
{R(r) = \ell'^H & \unify(S,T,\ell^H,\ell'^H) = (S',T')}\]
\[\infer[\textsc{UnifyVal-BT}]{\mread(T,S,R,\unifyval r; I, (\ell^H::\vec \ell^H)) \step m'}
{R(r) = \ell'^H & \unify(S,T,\ell^H,\ell'^H) = \bot & \bt(T) = m'}\]
\[\infer[\textsc{UnifyVal-}\bot]{\mread(T,S,R,\unifyval r; I, (\ell^H::\vec \ell^H)) \fails}
{R(r) = \ell'^H & \unify(S,T,\ell^H,\ell'^H) = \bot & \bt(T) = \bot}\]
\subsection{Metatheory}
\label{sec:simple-metatheory}
In both the SWAM and dependently-typed TWAM, the main metatheorems are progress and preservation.
\begin{thm*}[Progress] If $\SE m \ok$ then either $m \done$ or $m \fails$ or $m \step m'$.\end{thm*}
\begin{thm*}[Preservation] If $\SE m \ok$ and $m \step m'$ then $\SE m' \ok$.\end{thm*}
Where $m \fails$ mean that a Prolog query terminated normally, but the query had no solution.
In Section \ref{sec:dep-met}, the progress and preservation results for the TWAM will be strong enough to enable certifying compilation.
In the SWAM, progress and preservation amount to type and memory-safety.
Because the theorem of Section \ref{sec:dep-met} subsumes progress and preservation for SWAM,
we restrict ourselves here to the commonalities and present the differences in Section \ref{sec:dep-met}.
For the sake of readability, both this section and Section \ref{sec:dep-met} give proof sketches where the reader might find a detailed proof tedious.
For the sake of exhaustiveness, an extended proof for the dependent system is given in the electronic appendix, however.
The metatheory for SWAM begins with standard preliminary lemmas such as canonical forms and weakening.
This is followed with the heart of the metatheory: our treatment of the occurs check and unification.
The key lemma Heap Update (Lemma~\ref{lem:heap-update}) shows that binding free variables preserves the acyclic heap invariant when the occurs check passes,
which gives us preservation for unification and thus every instruction that depends on unification.
\subsubsection{Preliminaries}
\begin{lem}[Canonical Forms]
\label{lem:scf}
Canonical forms consists of a subclaim for each relevant class of values.
\begin{itemize}
\item \emph{Code Values:} If $\PE v^C : \tau$ then $\tau = \neg \Gamma$ and $v^C = \code[\Gamma](I)$
\item \emph{Word Values:} If $\PE_{\Sigma;\Xi} w : \tau$ and $(C,H) : (\Xi;\Psi)$ then $w$ has form $\ell^H$ or $\ell^C$ where $\ell^H \in\dom{H}$ or $\ell^C\in\dom{C}$.
\item \emph{Heap Values:} If $\PE v^H : \tau$ then
\begin{itemize}
\item Either $\tau = \cross{\vec \tau}$ and $v = \args{\vec w}$ and $\PE \vec w : \vec \tau$
\item Or $\tau = a$ and either $v = \bound{w}$ or $v = \free{}[a]$ or $v = \func{c}{\vec w}$ where $\PE \vec w : \vec{a}$ and $\Sigma(c)=\vec{a}\to a$.
\item Or $\tau = \neg \Gamma$ and $v = \close(w,\ell^C)$ where $\PE w :\neg\myG({\tt env})$.
\end{itemize}
\end{itemize}
\end{lem}
\begin{proof}
Each claim is by inversion on the typing rules.
\end{proof}
\begin{lem}[Weak Unicity of Heap Value Typing] For any value $v$, at most one of the following holds:
\begin{enumerate}
\item $\PE v : a$
\item $\PE v : \cross{\vec \tau}$
\item $\PE v : \neg \myG$
\end{enumerate}
\end{lem}
\begin{proof}
By cases on $\PE v : \tau$.
Each rule requires $v$ to have a specific form.
If $\PE v : a$ then $v = \free{}[a],\bound{\ell^H},$ or $\cwsh$.
In each case the only rules that apply produce type $a$ (the type annotation enforces unicity for $\free{}[a])$.
If $\PE v : \cross{\vec \tau}$ then $v = \args{\vec w}$ and the only rule that applies produces type $\cross{\vec\tau}$.
Otherwise $\PE v : \neg\myG$ and the rules force $v = \code[\myG]$ or $v = \closure(w_{env}, \ell^C)$.
In either case the only rule that applies produces $\PE v : \neg\myG$, because the type is restricted by either the annotation $\myG$ or by $\Xi(\ell^C)$.
\end{proof}
\begin{lem}[Weakening]
\label{lem:sweak}
In SWAM we need weakening for word and heap value typing and occurs check:
\begin{itemize}
\item \emph{Word Values:} If $\PE w : \tau$ then $\thext{\Psi}{\ell_H}{\tau'} \vdash w : \tau.$
\item \emph{Occurs Check:} For fresh $\ell^H,$
(a) If $\ell^H_1 \in_H \ell^H_2,$ then $\ell^H_1 \in_{\hext{H}{\ell^H}{v}} \ell^H_2$ and
(b) If $\ell^H_1 \notin_H \ell^H_2,$ then $\ell^H_1 \notin_{\hext{H}{\ell^H}{v}} \ell^H_2$.
\item\emph{Heap Typing:} For all fresh $\ell^H$ and even ill-typed $v^H$, if $\SE H:\Psi$ then $\SE \hext{H}{\ell^H}{v^H}:\Psi$.
\end{itemize}
\begin{proof} By induction on the derivation $\PE w : \tau$, $\ell^H_1 \in_H \ell^H_2$, $\ell^H_1 \notin_H \ell^H_2$, or $\SE H:\Psi$ respectively, using the fact that for fresh $\ell^H,$ $\hext{H}{\ell^H}{v}(\ell'^H) = H(\ell'^H)$ for all $\ell'^H \in \dom{H}$. Heap Typing weakening uses the fact that $\SE H:\{\}$ for all $H$, i.e. heaps may contain inaccessible values not assigned types by $\Psi$.\end{proof}
\end{lem}
\begin{lem}[Register File Subtyping]\label{lem:reg-sub} If $\GE I \ok$ and $\SE \Gamma \leq \Gamma'$ then $\Gamma' \ent I \ok$. \end{lem}
\begin{proof}
By induction on the derivation $\GE I \ok$.
\end{proof}
\subsubsection{Occurs Check}
The following theory of occurs checks is used in the theory of unification.
\begin{lem}[Occurs is a total function]
\label{lem:occ-tot}
If $\SE H : \Psi$ and $\SPE \ell^H_2:a$ then:
\begin{itemize}
\item\emph{Total:} For all $\ell^H_1,$ either $\ell^H_1 \in_H \ell^H_2$ or $\ell^H_1 \notin_H \ell^H_2$.
\item\emph{Function:} If $\ell^H_1 \notin_H \ell^H_2$ is derivable, then $\ell^H_1 \in_H \ell^H_2$ is not derivable.
\end{itemize}
\end{lem}
\begin{proof}
Totality is by induction on typing derivation of $\SE H : \Psi$, appealing to Lemmas~\ref{lem:sweak} and \ref{lem:scf}. Functionhood is by induction on the derivation $\ell^H_1 \notin_H \ell^H_2$.
In the cases $H(\ell^H_2) = \free{}[a]$, $H(\ell^H_2) = \bound{w},$ and $\close(w_{env},\ell^C),$ clearly no rules apply for $\ell^H_1 \in_H \ell^H_2$. Consider the case $\cwsh$ (the tuple case is symmetric):
\case{\infer[\notin{}c\langle\rangle]{\ell^H_1 \notin_H \ell^H_2}{H(\ell^H_2) = c\args{\ell'^H_1,\ldots,\ell'^H_n} & \ell^H_1 \notin_H \ell'^H_i (\forall 1 \leq i \leq n)}}
By the IH, $\forall i.$($\ell^H_1 \in_H \ell'^H_i$ is not derivable), so $\neg \exists i.( \ell^H_1 \in_H \ell'^H_i$ is derivable). But because
$H(\ell_2) = \cwsh$, the only rule that might apply requires $\exists i. (\ell_1 \in_H \ell'_i$ is derivable).
\end{proof}
\begin{lem}[Transitivity of Occurs]\label{lem:occ-trans} If $\SE H : \Psi, \ell^H_1 \in_H \ell^H_2, $ and $\ell^H_2 \in_H \ell^H_3,$ then $\ell^H_1 \in_H \ell^H_3$.\end{lem}
\begin{proof}
By induction on the derivation $\ell^H_2 \in_H \ell^H_3$.
\end{proof}
\begin{lem}[Occurs Strengthening] If $\SE H : \Psi, \ell^H_2 \in \dom{H}, \ell'^H \notin \dom{H},$ and
$\ell^H_1 \notin_{\hext{H}{\ell'^H}{v'}} \ell^H_2$ then $\ell^H_1 \notin_H \ell^H_2$. \end{lem}
\begin{proof}
By induction on the derivation $\ell^H_1 \notin_{\hext{H}{\ell'^H}{v'}} \ell^H_2$, appealing to Lemma~\ref{lem:scf}.
\end{proof}
\subsubsection{Heap Modification}
The simply-typed metatheory culminates in the treatment of heap modification.
We begin with a strengthening lemma:
\begin{lem}[Heap Value Strengthening]
\label{lem:heap-str}
If $\thext{\Psi}{\ell^H_1}{\tau_1} \vdash v_2:\tau_2$ and $\ell^H_1 \notin_H \ell^H_2$, then $\PE v_2:\tau_2 $.\end{lem}
\begin{proof}
By cases on $\thext{\Psi}{\ell^H_1}{\tau_1} \vdash v_2:\tau_2$.
The case $\cwsh$ is representative:
\case{\infer[\textsc{HV-Str}]{\thext{\Psi}{\ell^H_1}{\tau_1} \vdash \cwsh : \tau_2 }{\Sigma(c) = \vec a \to \tau_2 & \Sigma;\thext{\Psi}{\ell^H_1}{\tau_1} \vdash \ell'^H_i : a_i }}
Then for each $\ell'^H_i$ the typing derivation has form \infer[\textsc{WV-}\ell^H]{\thext{\Psi}{\ell^H_1}{\tau_1} \vdash \ell'^H_i : \sing(M_i : a_i) }{\thext{\Psi}{\ell^H_1}{\tau_1}(\ell'^H_i) = \sing(M_i: a_i)}.
Note $\ell'^H_i \neq \ell^H_1$. Otherwise we would have
\[\infer[\in{}c\langle\rangle]{\ell^H_1 \in_H \ell^H_2}{\infer[\in=]{\ell^H_1 \in_H \ell'^H_i (\exists i)}{\ell'^H_i = \ell^H_1} & H(\ell^H_2)=c\langle \ell'^H_1,\ldots\ell'^H_n\rangle}\]
Which would contradict $\ell^H_1 \notin_H \ell^H_2$ because occurs is a function (Lemma~\ref{lem:occ-tot}). Because $\ell^H_1 \neq \ell'^H_i$ and $\ell'^H_i \in \dom{\thext{\Psi}{\ell^H_1}{\tau_1}}$ we have
$\ell'^H_i \in \dom{\Psi}$ and
\[\infer[\textsc{HV-Str}]{\SPE \func{c}{\ell^H_1, \ldots, \ell^H_n} : \tau_2 }{\Sigma(c)= a_1 \cdots \to a_n \to \tau_2 & \infer[\textsc{WV-}\ell^H]{\SPE \ell'^H_i : a_i }{\Psi(\ell'^H_i) = \sing(M_i : a_i) &(\forall i)}}\]
\end{proof}
\begin{lem}[Heap Update]\label{lem:heap-update} If $\SE H \colon \Psi$ and $\Psi(\ell^H_1) = a$ then
\begin{align*}
(a)&\ \text{If $\Psi(\ell^H_2) = a$ and $\ell^H_1 \notin_H \ell^H_2,$ (the occurs check passes)}&\text{then $\SE \hup{H}{\ell^H_1}{\bound{\ell^H_2}} \colon \Psi.$}\\
(b)&\ \text{If for all $i$, $\Psi(\ell'^H_i) = a_i$ and $\ell^H_1 \notin_H \ell'^H_i$ and $\Sigma(c) = \vec a \to a$,}&\text{then $\SE \hup{H}{\ell^H_1}{\func{c}{\ell'^H_1,\ldots,\ell'^H_n}} \colon \Psi.$}
\end{align*} \end{lem}
The simple statement of Heap Update belies the complexity of its proof.
Recall that heaps and heap types are unordered (identified up to permutation),
while heap typing derivations are ordered, serving as a witness that the heap is acyclic.
The proof of Heap Update must show that no cycles are introduced,
which requires exhibiting a new acyclic ordering in,
e.g. the derivation of $\SE \hup{H}{\ell^H_1}{\bound{\ell^H_2}} \colon \Psi.$
\paragraph{Heap Typing Proof Terms}
In the interest of rigor, we introduce proof term notation for heap typing derivations,
which allows us to give a concise, explicit construction of the topological orderings required by Heap Update.
The reader may wish to skip this section on a first reading, as it introduces significant proof machinery that is not needed elsewhere.
Recall the typing rules for heaps:
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{HT-Nil}]{\SE H\colon{}\heap{}}{}
&\infer[\textsc{HT-Cons}]{\SE H\colon{}\thext{\Psi}{\ell^H}{\tau}}
{\SE H\colon{}\Psi & H(\ell^H) = v^H & \PE v^H\colon{}\tau & \ell^H \notin\dom{\Psi}}
\end{tabular}
\end{center}
These rules result in list-structured proof terms:
\[\mathcal{D} ::= nil_H\ |\ \mathcal{D};d_{\ell^H}\]
We write $\mathcal{D}:(\SE H:\Psi)$ when $\mathcal{D}$ is a proof term of $\SE H:\Psi$.
In this notation $nil_H$ is the proof term for HT-Nil applied to heap $H$
and $\mathcal{D};d_{\ell^H}$ is the proof term for HT-Cons applied to subderivations
$\mathcal{D}:(\SE H\colon{}\Psi)$ and $d_{\ell^H}:(\PE v^H\colon{}\tau)$ and it is a proof of $\SE H\colon{}\thext{\Psi}{\ell^H}{\tau}$.
To state the key lemma precisely, we exploit several functions over proof terms.
The notation $\pred(\mathcal{D}, \ell^H)$ denotes the set of heap locations assigned types by $\mathcal{D}$ that appear before $\ell^H$ within $\mathcal{D}$ and $\succ(\ell^H)$ denotes the set of locations that appear after it.
The notation $\elems(\mathcal{D})$ denotes all locations assigned types by $\mathcal{D}$.
They can be defined recursively by:
\begin{align*}
\elems(nil_H) = \emptyset &&\elems(\mathcal{D};d_{\ell^H}) =\{\ell^H\} \cup \elems(\mathcal{D})&&\\
\pred(nil_H, \ell^H) = \emptyset &&\pred((\mathcal{D};d_{\ell^H}), \ell^H) = \elems(\mathcal{D})&& \pred((\mathcal{D};d_{\ell'^H}), \ell^H)=\pred(\mathcal{D}, \ell^H)\\
\succ(nil_H, \ell^H) = \emptyset &&\succ((\mathcal{D};d_{\ell^H}), \ell^H) = \emptyset && \succ((\mathcal{D};d_{\ell'^H}), \ell^H)=\succ(\mathcal{D},\ell^H) \cup \{\ell'^H\}
\end{align*}
We now have the machinery to state a subclaim which entails both claims of Heap Update.
\begin{subclaim}[Heap Reordering]
If $\mathcal{D}\colon{}(\SE H:\Psi), H(\ell^H_1)=\free{}[a], \ell^H_1 \in
\dom{\Psi}, \ell^H_2 \in \dom{\Psi}, \ell^H_1 \notin_H \ell^H_2$ then exists
$\mathcal{D'}\colon{}(\SE H:\Psi)$ where $\succ(\mathcal{D'},
\ell^H_1) \subseteq \succ(\mathcal{D}, \ell^H_1)$ and
$\pred(\mathcal{D'}, \ell^H_2) \subseteq \pred(\mathcal{D}, \ell^H_2)$
and $\ell^H_2 \in \pred(\mathcal{D'}, \ell^H_1)$
\end{subclaim}
\begin{proof}
By lexicographic induction on $|\mathcal{D}|$ and $|\succ(\mathcal{D}, \ell^H_1)|$.
We give an explicit construction of the proof term $\mathcal{D}'$ as a function of $\mathcal{D},\ell^H_1,$ and $\ell^H_2$ in functional pseudocode, then show the construction obeys the desired properties in each case.
Here $str(d_{\ell^H})$ and $weak(d_{\ell^H})$ refer to the typing derivations that result from appeals to the heap value strengthening and weakening lemmas, respectively (Lemmas~\ref{lem:heap-str} and \ref{lem:sweak}).
\newcommand{\mathcal{D}}{\mathcal{D}}
\newcommand{\Rightarrow}{\Rightarrow}
\newcommand{\tt str}{\tt str}
\newcommand{\tt weak}{\tt weak}
\newcommand{\hspace{0.2in}}{\hspace{0.2in}}
\begin{tabular}{ll}
Case & $\mathcal{D}'(\mathcal{D},\ell_1,\ell_2)=$\\\hline
&${\tt case}~\mathcal{D}~{\tt of}$\\
1 &\ \ ${\tt nil}~\Rightarrow~\mathcal{D}$\\
2 &${\tt|\ nil'}, d_\ell~\Rightarrow~\mathcal{D}$\\
3 &${\tt|\ }\mathcal{D}_1;d_{\ell};d_{\ell 1}~\Rightarrow~\mathcal{D}$\\
4 &${\tt|\ }\mathcal{D}_1;d_{\ell 1};d_{\ell 2}~\Rightarrow~\mathcal{D}_1;\tt str(d_{\ell 2});\tt weak(d_{\ell 1})$\\
5 &${\tt|\ }\mathcal{D}_1;d_{\ell};d_{\ell 2}~{\tt where}~\ell\neq \ell_1~\Rightarrow$\\
&\hspace{0.1in}{${\tt if}~(\ell_1' \notin \ell_2)~{\tt then}$}\\
5a &\hspace{0.2in}{$\mathcal{D}'((\mathcal{D}_1;\tt str(d_{\ell 2})),\ell_1,\ell_2);\tt weak(d_{\ell})$}\\
&\hspace{0.1in}{} ${\tt else}$\\
5b &\hspace{0.2in}{${\tt let}~\mathcal{D}_2=\mathcal{D}'((\mathcal{D}_1;d_{\ell}),\ell_1,\ell)~{\tt in}$}\\
&\hspace{0.2in}{$\mathcal{D}'((\mathcal{D}_2;d_{\ell 2}),\ell_1,\ell_2)$}\\
&${\tt|\ }\mathcal{D}_1;d_\ell;d_{\ell'}~{\tt where}~ \ell'\neq \ell_1,\ell'\neq \ell_2~\Rightarrow$\\
&\hspace{0.1in} $\mathcal{D}'((\mathcal{D}_1;d_\ell),\ell_1,\ell_2);d_{\ell'}$\\
\end{tabular}
\begin{itemize}
\item Cases 1 and 2 hold vacuously because our preconditions only hold for $|\mathcal{D}| \geq 2$.
\item Case 3: In this case $\ell^H_2 \in \pred(\mathcal{D}, \ell^H_1)$ (either $\ell'^H = \ell^H_2$
or $\ell_2^H$ appears elsewhere in $H$), so there is no work to be done.
\item Case 4: By the assumption that $\ell^H_1 \notin_H \ell^H_2$, we can apply Lemma~\ref{lem:heap-str}, yielding $\SE \hext{H'}{\ell^H_2}{v_2} : \thext{\Psi'}{\ell^H_2}{\tau_2}$.
By Lemma~\ref{lem:sweak}, $\thext{\Psi'}{\ell^H_1}{v_1} \vdash v_1 : \tau_1,$ so $\SE \hexts{H'}{\ell^H_2 \hook v_2, \ell^H_1 \hook v_1} : \hexts{\Psi'}{\ell^H_2 : \tau_2, \ell^H_1 : \tau_1}$, which satisfies the requirements.
\item Case 5: By Lemma~\ref{lem:occ-tot}, either $\ell'^H \in_H \ell^H_2$ or $\ell'^H \notin_H \ell^H_2$.
\item Case 5a: By Lemma~\ref{lem:heap-str}, $\hext{H}{\ell^H_2}{v_2} : \hext{\Psi}{\ell^H_2}{\tau_2}$ so we can apply the IH on $\hext{H'}{\ell^H_2}{v_2}$ giving a derivation $\mathcal{D}_1$. The result follows in combination with Lemma~\ref{lem:sweak} on $\ell^H$.
\item Case 5b:
By Lemma~\ref{lem:occ-tot}, $\ell^H_1 \in_H \ell'^H$ or $\ell^H_1 \notin_H \ell'^H$. In this case $\ell^H_1 \notin_H \ell'^H$.
Otherwise by Lemma~\ref{lem:occ-trans}
$\ell^H_1 \in_H \ell^H_2$, but we assumed $\ell^H_1 \notin_H \ell^H_2$ and this is a contradition because occurs is a function (Lemma~\ref{lem:occ-tot}).
Thus we can apply the IH on $\hext{H'}{\ell'^H}{v'}$ (because $|\hext{H'}{\ell'^H}{v'}| < |H|$) to swap $\ell^H_1$ with $\ell'^H$ resulting in a derivation $\mathcal{D}_2$.
The IH tells us $|\succ(\mathcal{D}_2, \ell^H_1)| < |\succ(\mathcal{D}, \ell^H_1)|$,
allowing us to apply the IH a second time on the derivation $\mathcal{D}_2;d_2$.
The second IH implies the result.
\item Case 6: This case is direct by the IH.
\end{itemize}
\end{proof}
Given Heap Reordering, the first claim of Heap Update follows directly with the following derivation
for $\bound{\ell^H_2}$
\[\infer[\textsc{HV-Bound}]{\Psi'\ent \bound{\ell^H_2} : \tau}
{\infer[\textsc{WV-}\ell^H]{\Psi'\ent \ell^H_2 : \tau}
{\Psi'(\ell^H_2)=\tau}}\]
where $\Psi'$ is the heap type assigned by $\mathcal{D}'$ to the prefix of $\ell^H_2$, which must
contain $\ell^H_1$.
The second claim follows by iterating Heap Reordering, and because Heap Reordering preserves the
predecessors of $\ell^H_1$.
\subsubsection{Trails}
\begin{lem}[Trail Update]\label{lem:trail-up} Introducing and binding free variables both preserve the validity of the trail:
\begin{align*}
(a)&\text{If $S \ent T \ok$ and $S(\ell^H)=\free{}[a]$ then $\hup{S}{\ell^H}{w}\ent \uptrail(\ell^H:a,T) \ok$.}\\
(b)&\text{If $S \ent T \ok$ and $\ell^H$ is fresh then $\hext{S}{\ell^H}{\free{}[a]} \ent T \ok$}.
\end{align*}
\end{lem}
First consider the typing rule for nonempty trails:
\[\infer[\textsc{Trail-Cons}]{S \ent(t,w_{env},\ell^C)::T' \ok}
{\SE S' \colon{}(\Xi,\Psi') \hskip 0.1in \Psi' \ent w_{env} \colon{} \tau
&\unwind(S,t)=S' & S' \ent T' \ok
&\Psi' \ent \ell^C\colon{}\neg\heap{\texttt{env}\colon{}\tau}}\]
Trails are well-typed so long as unwinding (as used in backtracking) results in a well-typed state.
Claim (a) says binding a free variable $X$ to a term represented by word value $w$, then adding $X$ to the trail, results in a well-typed trail.
$S(\ell^H)=\free{}[a]$ then $\hup{S}{\ell^H}{w}\ent \uptrail(\ell^H:a,T) \ok$ iff unwinding results in a well-typed store.
Because it unwinds to the same store as does $T,$ this is true by assumption.
Claim (b) is weakening principle for trails, which follows from weakening for stores.
This claim shows that the trail does not need to be modified when a fresh variable is allocated, only when it is bound to a term.
Claim (b) follows from the following subclaim:
\begin{subclaim}$\unwind(\hext{S}{\ell^H}{\free{}[a]},t) = (\hext{S'}{\ell^H}{\free{}[a]})$\end{subclaim}
The subclaim holds by induction on $t$, completing the proof of Lemma~\ref{lem:trail-up}.
\begin{lem}[Backtracking Totality]\label{lem:bt-tot} For all trails $T,$ if $\cdot\ent S:(\Xi;\Psi)$ and $S \ent_{\Sigma;\Xi} T \ok$ then
either $\bt(S,T)=m'$ and $\SE m' \ok$ or $\bt(S,T)=\bot$\end{lem}
\begin{proof}
By cases on $S\ent T \ok$.
\end{proof}
\subsubsection{Dynamic Unification}
Unification uses a simple lemma on pointer following:
\begin{lem}[End Correctness]\label{lem:end-corr} If $\PE \ell^H :a$ and $\SE H : \Psi$
then $\edn(H,\ell^H)=\ell_H'$ and $\PE \ell'^H :a$ and either $H(\ell'^H) = \free{}[a]$
or $H(\ell'^H)=\func{c}{\vec w}$\end{lem}
\begin{proof}
By induction on the derivation $\PE \ell^H:a$.
\end{proof}
Runtime unification is total and results in a well-typed store and trail.
\begin{lem}[Soundness of \unify]\label{lem:unify-sound} If $\SE H: \Psi,
\label{lem:unify-soundness}
\Psi \vdash w_1 : a, \Psi \vdash w_2 : a,$ then $\unify(S,T,w_1,w_2) = \bot$ or
$\unify(S,T,w_1,w_2) = (S', T')$ where $\SE S' : (\Psi;\Xi)$ and $S'\ent T'\ok$\end{lem}
\begin{proof}
We prove the claim by simultaneous induction with the following subclaim:
\begin{claim}
\label{claim:unify-args-soundness}
For all argument lists (push-down lists) $(w_1::\cdots::w_n)$ and $,(w_1'::\cdots::w_n'),$
if for all $i$, $\Psi \vdash w_i : a_i$ and $\Psi \vdash w_i' : a_i$ then $\unifyargs(S,T,(w_1::\cdots::w_n),(w_1'::\cdots::w_n'), \ldots, (w_n,w_n')) = \bot$ or\\
$\unifyargs(S,T,(w_1::\cdots::w_n),(w_1'::\cdots::w_n')) = (S',T')$ where $\SE S' : (\Xi;\Psi)$ and $S'\vdash T'\ok$.
\end{claim}
\begin{proof}
Lemma \ref{lem:unify-soundness} is by induction on the size of the type $\Psi$
and Claim \ref{claim:unify-args-soundness} is by induction on the argument lists $(w_1::\cdots::w_n),(w_1'::\cdots::w_n')$.
The inductive case proceeds by cases on the form of $\edn(S,\ell^H_1)$ and $\edn(S,\ell^H_2)$ using Lemma~\ref{lem:end-corr}.
We present only a few of the success cases here, for the remaining cases are straightforward.
\case{$(\free{}[a], \free{}[a]):$}
Case on $\edn(S,\ell^H_1) = \edn(S,\ell^H_2)$ holds. If it does, we apply the first rule, else by case assumption we have $\edn(S,\ell^H_2) \notin_S \ell^H_1$ and apply the second, then apply Lemma~\ref{lem:heap-update} to get $\hup{S}{\ell^H_1}{\bound{\ell^H_2}} : (\Psi;\Xi)$ and Lemma~\ref{lem:trail-up} to get $\hup{S}{\ell^H_1}{\bound{\ell^H_2}} \ent T' \ok$.
:
{\footnotesize\begin{center}
\begin{tabular}{cc}
\infer[\unify=]{\unify(S,T,\ell^H_1,\ell^H_2) = (S,T)}
{\edn(\ell^H_1) = \ell^H & \edn(\ell^H_2) = \ell^H}&
\infer[\unify\ \free{}]{\unify(S,T,\ell^H_1,\ell^H_2) = (\hup{S}{\ell'^H_2}{\bound{\ell^H_1}},T')}
{\deduce{\Psi(\ell'^H_1) = a \hskip 0.1in \ell'^H_2 \notin_S \ell^H_1\hskip 0.1in \uptrail(T,(\ell'^H_2:a))=T'}
{\edn(S,\ell^H_1) = \ell'^H_1 & \edn(S,\ell^H_2) = \ell'^H_2 & S(\ell'^H_2) = \free{}[a]}}
\end{tabular}
\end{center}}
\case{$(c\langle\ell^H_1,\ldots,\ell^H_n\rangle,c\langle\ell'^H_1,\ldots,\ell'^H_n\rangle)$}
We apply the IH on the subclaim for $\unifyargs$ and the result follows immediately (and similarly if $\unifyargs$ were to fail).
\[\infer[\unify\ c\langle\rangle]{\unify(S,T,\ell^H_1,\ell^H_2) = (S',T')}
{\deduce{\edn(S,\ell^H_2) = \ell'^H_2\hskip 0.1in\unifyargs(S,T,\vec \ell^H, \vec \ell'^H) =(S',T')}
{S(\ell'^H_1) = \func{c}{\vec \ell^H} & S(\ell'^H_2) = \func{c}{\vec \ell'^H} & \edn(S,\ell^H_1) = \ell'^H_1}}\]
\end{proof}
\end{proof}
The essential cases of progress and preservation for the simply-typed system are instructions such as {\tt get\_val} and {\tt unify\_val} that rely on unification.
Those cases of progress and preservation follow from the unification soundness lemma above.
Moreover, progress and preservation for the simply-typed system are subsumed by their dependently-typed equivalents.
Most of the proofs above carry over readily. Any important differences are covered in Section \ref{sec:dep-met}.
\section{Typed Compilation in Proof-Passing Style}
\label{sec:lf-encoding}
Our certification approach is based on specifying the semantics of a T-Prolog program as an LF signature.
Before we can certify the correctness of compilation, we give a mechanical translation from T-Prolog programs to LF signatures (see Figure \ref{lftrans} for example):
\begin{itemize}
\renewcommand\labelitemi{--}
\item A type $a$ in T-Prolog translates to an LF constant $a \colon \type$.
\item A constructor $c \colon \vec a \to a$ translates to an LF constant of the same type.
\item A predicate $p \colon \vec a \to \prop$ translates to an LF constant $p \colon \vec a \to \type$.
\item {A clause $C$ of form $G \verb+ :- + \mathrm{SG}_1, \ldots,
\mathrm{SG}_n.$ translates to an LF constant (of dependent function type) $C\colon\Pi\ \Delta. \Pi\
\vec{\mathrm{SG}}. G$ where $\Delta$ consists of the free variables
of $\Pi\ \vec{SG}.G$.}
\item Executing a query \verb+?-+$G.$ translates to searching for a proof of $G$.
\end{itemize}
\begin{exmp}[T-Prolog Program with its LF Signature]\label{lftrans}
\begin{center}
\begin{tabular}{ll}
\verb+nat:type.+ &\verb+nat:type.+\\
\verb+zero:nat.+ &\verb+zero:nat.+\\
\verb+succ:nat +$\to$\verb+ nat.+ &\verb+succ:nat +$\to$\verb+ nat.+\\
\verb+plus:nat +$\to$\verb+ nat +$\to$\verb+ nat +$\to$\verb+ prop.+ &\verb+Plus:nat +$\to$\verb+ nat +$\to$\verb+ nat +$\to$\verb+ type.+\\
\verb+plus(zero,X,X).+ &\verb+Plus-Z:+$\Pi$\verb+X:nat. plus zero X X.+\\
\verb+plus(succ(X),Y,succ(Z)) :-+ &\verb+Plus-S:+$\Pi$\verb+X:nat. +$\Pi$\verb|Y:nat.| $\Pi$\verb+Z:nat.+\\
\verb+ plus(X,Y,Z).+ &\: \: $\Pi$\verb+D:plus X Y Z. +\\
& \: \: \: \: \verb|plus (succ X) Y (succ Z).|
\end{tabular}
\end{center}
\end{exmp}
Now that we have defined the semantics of a Prolog program in LF, we can describe our certification approach.
The TWAM certification approach can be summed up in the following slogan:
\begin{center}
Proof-Carrying Code + Programming As Proof Search = Proof-Passing Style
\end{center}
Proof-carrying code is the technique of packaging compiled code with a formal proof that the code satisfies
some property. Previous work \cite{necula1998design} has used proof-carrying code to build certifying compilers
which produce proofs that the programs they output are memory-safe. Our insight is that by combining this technique
with the programming-as-proof-search paradigm that underlies logic programming, our compiler can produce proofs of
a much stronger property: partial dynamic correctness.
The programming-as-proof-search paradigm tells us that partial dynamic correctness consists of the following theorem, stated
informally here and formally in Section \ref{sec:dep-met}:
\textbf{Theorem 1: } If a query \verb+?-+$G.$ succeeds, there exists a proof $M$ of $G$ in LF.
Our compiler need only output enough information that the TWAM typechecker can reconstruct the proof of Theorem 1.
This requires statically proving that whenever \textit{any} proof search procedure $p$ would return, the corresponding predicate $P$ would have a proof in LF.
This proof boils down to accumulating facts when unification succeeds and annotating all return points with the resultant LF proof terms.
This \textit{proof-passing} style of programming is essential to the type system of the TWAM.
It is worth noting also that proof-passing style is needed only at compile-time, because TWAM also supports \textit{proof-erasure}.
Thus the only runtime cost of certifying compilation with TWAM is the cost of using SWAM vs. other variants of the WAM;
TWAM introduces no additional overheads compared to SWAM.
\section{Dependently-Typed WAM}
\label{sec:dependent-wam}
The simply-typed system presented in Section \ref{sec:simple-wam} is insufficient to prove that compiled programs implement a given LF signature.
The \verb+succeed+ instruction
\[\infer{\GE \succeed; I \ok}{~\vspace{0.08in}}\]
trivially typechecks in any context, but we wish to prove that a program only succeeds if
a proof $M$ of some query $A$ exists in LF. We begin our dependently-typed development by requiring
exactly that in the typing rule:
\[\infer{\DGE \succeed[M\colon{}A];I \ok}{\DE M \colon{} A}\]
Yet if this was the only change we made, we could never compile meaningful programs because the premise would be too difficult to fulfill.
We make this premise easier to meet by introducing the ability for continuations to accept LF proof terms as arguments.
Because the \verb+succeed[M:A]+ instruction generally occurs in the top-level success continuation for a query, we can make this continuation accept a proof of $M$ as an argument $x$ and supply $x$ as the proof term for \texttt{succeed}, passing the burden of proof onto the caller.
In this way, we can decompose the proof argument for $M$ into one argument for each basic block of the proof search algorithm.
This too is nontrivial: whether the proof $M$ exists for a given query $A$ cannot be known until $A$ is executed at runtime, but certification occurs at compile-time.
In order to reason statically about runtime proof search, the type system must connect LF terms with runtime constructs such as registers and heap values.
Whenever a unification succeeds at runtime (i.e. we learn that we can apply a particular rule), we need some way to say the same terms should be unified in the statics.
Without a mechanism for translating between the runtime values and the static LF terms, we have no mechanism by which to learn new facts during proof search, and thus no way to construct nontrivial LF proofs.
The simplest possible relation between an LF term $M$ and a heap value $v$ is the notion of equality. Since heap values can also contain pointers
and can exhibit sharing structures not visible in the LF term, we might
more accurately think of this equality relation as ``$v$ encodes $M$''.
We add this notion to our type system by introducing
\textit{singleton types} $\sing(M \colon a)$ for values that encode an
LF term $M$ which itself has type $a$. This is the only fundamentally new
value type, though other aspects of the type system will change as well to accommodate
the presence of proofs.
In particular, we introduce a context $\Delta$ that contains the types of all LF variables in scope,
which are introduced either in the parameters of a code value or by the \verb+put_var+ instruction.
Furthermore, we introduce a notion of static unification $M_1 \sqcap M_2$ which allows us to import
knowledge learned from runtime unification into an LF proof.
To see the interaction between runtime and static unification concretely,
consider the zero case of \verb+plus+, which (using the proof terms of Example~\ref{lftrans}) compiles to
\begin{exmp}[TWAM Compilation]
\label{ex:twam-comp}~\\
\begin{tabular}{l}
\verb|plus-zero/3|$~\mapsto~\code[\Pi~X,Y,Z:nat.
\heap{r_1:\sing(X), r_2:\sing(Y), r_3:\sing(Z), r_4:\Pi \_:({\tt Plus~X~Y~Z}).~\neg\heap}]($\\
\hspace{0.1in}{${\tt put\_tuple}~r_4, 4;$}\\
\hspace{0.2in}{${\tt set\_val}~r_1;$}\\
\hspace{0.2in}{${\tt set\_val}~r_2;$}\\
\hspace{0.2in}{${\tt set\_val}~r_3;$}\\
\hspace{0.2in}{${\tt set\_val}~{\tt ret};$}\\
\verb|# plus-succ/3, not shown, has the same three natural number|\\
\verb|# parameters X, Y, Z, so we pass them in when constructing|\\
\verb|# the failure continuation|\\
\hspace{0.1in}{${\tt push\_bt}~r_4, {\tt (\verb|plus-succ/3|~X~Y~Z)};$}\\
~\\
\hspace{0.1in}{${\tt get\_str}~r_1, {\tt zero/0};$}\\
\hspace{0.1in}{${\tt get\_var}~r_2, r_3;$}\\
\hspace{0.1in}{${\tt jmp~(ret~(\verb|Plus-Z|~Y))};$}\\
)
\end{tabular}
\end{exmp}
The syntax \verb+code+$[\Delta.\Gamma](I)$ denotes a code value with body $I$ which expects the register file to
have type $\Gamma$ and where $\Gamma$ may refer to the LF variables in $\Delta$. The line \verb+jmp (r4 (Plus-Z Y))+
is an example of proof passing in action. Here the success continuation \verb|r4| expects a proof of the relevant predicate:
in this case \verb|plus X Y Z|. The \verb+jmp+ instruction constructs a proof \verb+Plus-Z Y+ to satisfy this requirement.
The proof \verb+Plus-Z Y+ has type \verb+plus zero Y Y+, so this code only typechecks
if $X = zero$ and $Y = Z$, which is exactly what we learn when \verb|get_str| and \verb+get_var+ succeed, respectively.
\subsection{Instruction Statics and Dynamics}
\label{sec:istat-dyn}
In this section we detail the type system changes made to support LF terms and singleton types.
The instruction set and dynamic judgements are fundamentally identical to that of the SWAM, but both are augmented with additional annotations as needed by the addition of LF.
For example, because the {\tt put\_var} instruction introduces an LF variable $x$, we now write $\dputvar{r}{x:a.}~I$ instead of $\putvar{a}{r}; I$ to indicate that there is an LF variable $x:a$ in scope for the remaining instructions $I$, a feature we will use to write proof terms.
Complete dynamics for the dependent TWAM are given in the electronic appendix.
In the following sections we detail the judgements that differ significantly from the simply-typed system.
\begin{table}
\begin{tabular}{ccc}
\label{tab:judgements}
Judgement(s) & Meaning & Defined In\\\hline
$\DGE_{\Sigma;\Xi} I \ok$ & Basic Block Well-Typed & \ref{sec:istat-dyn}\\
$\DGE {I :_s}_{\Sigma;\Xi}~J, {I :_t}_{\Sigma;\Xi}~J$ & Spine Well-Typed & \ref{sec:dep-spine-stat}, \ref{sec:dep-env-stat}\\
$\DE M_1\sqcap M_2 = \sigma, \bot$ & Static Unification & \ref{sec:dep-stat-unif}\\
$\DE M_1\in M_2, M_1\notin M_2$ & Static Occurs Check & \ref{sec:dep-stat-unif}\\
$\DGE op :\tau$ & Operand Well-Typed & \ref{sec:word-oper}\\
$\DE M : A$ & LF Term Well-Typed & \cite{Harper93aframework}\\
$\DE A : K$ & LF Type Family Well-Kinded & \cite{Harper93aframework}\\
\hline
$\DGE v :\tau$ & Heap Value Well-Typed & \ref{sec:dep-hvtype}\\
$\DE H :\Psi$ & Heap File Well-Typed & \ref{sec:simp-rep-inv}\\
$\DGE w :\tau$ & Word Value Well-Typed & \ref{sec:word-oper}\\
$\DPE R :\myG$ & Register File Well-Typed & \ref{par:rftype}\\
$\SE (\Delta;\mu) \colon{} H$ & Heap Mapping Unique&\ref{par:con-map}\\
$\DE T \ok$ & Trail Well-Typed &\ref{par:trail-dep-inv}\\
$\DPE \vec \ell^H \reads J_s$ & Prolog Read Spine Invariant& \ref{par:mach-state-inv}\\
$\DPE (\vec \ell^H, \ell^H,c) \writes J_s$ & Prolog Write Spine Invariant& \ref{par:mach-state-inv}\\
$\DPE(n,r,\vec\ell^H)\writes J_t$ & Tuple Spine Invariant& \ref{par:mach-state-inv}\\
$\SE m\ok$ & Machine Well-Typed &\ref{par:mach-state-inv}\\\hline
$R\ent op\eval w$ & Operand Evaluation& \ref{sec:word-oper}\\
$R\ent op\squig w$ & Operand Resolution& \ref{sec:word-oper}\\
$w\eval w'$ & Word Evaluation& \ref{sec:word-oper}\\
$w \path, w \canon$ & Word Canonical Forms &\ref{sec:word-oper}\\
$\edn(S,\ell^H)$ & Pointer Following & \ref{sec:trailing}\\
$\ell^H_1 \in_S \ell^H_2$ & Dynamic Occurs Check & \ref{sec:trailing} \\
$\unify(S,T,\ell^H_1,\ell^H_2)$ & Dynamic Unification & \ref{sec:trailing}\\
$\unifyargs(S,T,\vec \ell^H, \vec \ell'^H)$ & Dynamic Unification & \ref{sec:trailing}\\
$\uptrail(x@\ell^H:a,T)=T'$ & Trail Update & \ref{par:trail-dep-inv}\\
$\unwind(S,\Delta,t) = (\Delta,S)$ & Trail Unwinding & \ref{par:trail-dep-inv}\\
$\bt(S,T)=m,\bot$ & Backtracking & \ref{sec:cont-bt}\\
$m\step m',m\fails,m\done$ & Stepping & \ref{sec:simp-op}\\\hline
\end{tabular}
\caption{Index of Typing and Evaluation Judgements}
\end{table}
A listing is given in Table 1.
\subsubsection{LF Terms}
The typing rule for {\tt succeed} is as given in Section \ref{sec:dependent-wam}:
\[\infer[\textsc{Succeed}]{\DGE \succeed[M\colon{}A];I \ok}{\DE M : A}\]
Here $M$ is an LF term and $A$ is an LF type (we write $A$ for arbitrary LF type families and $a$ for types corresponding specifically to Prolog terms).
Thus we extend the syntax of TWAM with the syntax of LF (here $c$ stands for type family constants and term constants):
\begin{center}
\begin{tabular}{ll}
LF Kinds & $K ::= {\tt type}\ |\ \Pi x:A.K$\\
LF Type Families & $A ::= c\ |\ \Pi x:A.A\ |\ A\ M$\\
LF Terms & $M ::= x\ |\ c\ |\ M\ M\ |\ \Pi x:A.M$\\
\end{tabular}
\end{center}
Note that the TWAM need not be instrumented with LF proof terms at runtime: LF proofs are merely given as type annotations as an aid to establishing the metatheorem of Section~\ref{sec:dep-met}.
LF terms make numerous appearances in TWAM.
For example, because \textsc{Putvar} introduces a free variable at runtime, it introduces an LF variable $x:a$ in the statics as well:
\[\infer[\textsc{Putvar}]{\DGE \dputvar{r}{x:a.}~I \ok}
{\Delta,x\colon{}a;\hups{\Gamma}{r:\sing(x:a)}\ent I \ok}\]
\subsubsection{Words and Operands}
\label{sec:word-oper}
The typing rules \textsc{Jmp} and \textsc{Mov} appear as before:
\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Jmp}]{\DGE_{\Sigma;\Xi}\jmp op, I\ok}{\Xi(\ell^C) = \neg\myG' & \SE \myG' \leq \myG}&
\infer[\textsc{Mov}]{\DGE \mov{r_d}{op}; I \ok}
{\DGE op : \tau & \Delta;\thup{\Gamma}{r_d}{\tau} \ent I \ok}
\end{tabular}
\end{center}
However, both instructions rely on \textit{operands}.
In TWAM, we generalize operands (and word values) so they can accept LF terms as arguments:
\begin{center}
\begin{tabular}{cc}
operands & $op ::= \ell^C\ |\ r\ |\ op\ M\ |\ \lambda x:A.~op$\\
word values & $w ::=\ell^C\ |\ \ell^H\ |\ w\ M\ |\ \lambda x:A.~w$\\
\end{tabular}
\end{center}
With this change we also update the statics and (big-step) dynamics for operands and word values.
The main dynamic judgement is still $R \ent op \eval w$ (Operand Evaluation),
but we add auxilliary judgements $R\ent op\squig w$ (Operand Resolution) and $w\eval w'$ (Word Evaluation).
\begin{center}{\footnotesize
\begin{tabular}{cccc}
\infer[\ell^C\eval]{\ell^C \eval \ell^C}{}
&\infer[\lambda\eval]{(\lambda x:A.~w) \eval (\lambda x:A.~w')}{w \eval w'}
&\infer[\beta\eval]{op\ M \eval w''}{op \eval (\lambda x:A.~w') & [M/x]w' \eval w''}
&\infer[op\ M\eval]{op\ M \eval w\ M}{op \eval w & w \path}
\end{tabular}
\begin{tabular}{cccc}
\infer[op\ M\squig]{R \ent op\ M \squig w\ M}{R \ent op \squig w}&
\infer[\lambda\squig]{R \ent (\lambda x:A.~op) \squig (\lambda x:A.~w)}{R \ent op \squig w}&
\infer[r\squig]{R \ent r \squig w}{R(r) = w}&
\infer[op\eval]{R \ent op \eval w'}{R \ent op \squig w & w \eval w'}
\end{tabular}
\begin{tabular}{ccc}
\infer[op\ r]{\DGE r : \tau}{\myG(r) = \tau}
&\infer[op\ (w\ M)]{\DGE (w\ M) : [M/x] \tau}{\DGE w : \Pi x:A.~\tau & \DE M : A}
&\infer[op\ \lambda]{\DGE (\lambda x:A.~w) : (\Pi x:A.~\tau)}{\DE A : \type & \Delta,x:A;\myG\ent w : \tau}\\
\end{tabular}
\begin{tabular}{lll}
\infer[w\ \ell^H]{\DPE \ell^H : \tau}{\Psi(\ell^H) = \tau}
&\infer[w\ (w\ M)]{\DPE (w\ M) : [M/x] \tau}{\DPE w : \Pi x:A.~\tau & \DE M : A}
&\infer[w\ \lambda]{\DPE (\lambda x:A.~w) : (\Pi x:A.~\tau)}{\DE A : \type & \Delta,x:A;\Psi\ent w : \tau}
\end{tabular}}
\end{center}
In \textsc{Jmp}, the generalization of operands supports proof-passing.
In \textsc{Mov}, it supports tail-call optimization as used in Section~\ref{sec:tco}.
As in LF, we have a notion of canonical forms for words, written $w \canon$, with an auxilliary judgement $w \path$:
\begin{center}
\begin{tabular}{lllll}
&\infer[\ell\path]{\ell \path}{}
&\infer[w\ M\path]{w\ M \path}{w\path}
&\infer[w\canon]{w \canon}{w \path}
&\infer[\lambda\canon]{(\lambda x:A.~w) \canon}{w \canon}
\end{tabular}
\end{center}
To simplify the proofs, the typing invariants for machine states require canonicity.
However, because canonical forms always exist~\cite{Harper93aframework} and involve only static-level computation,
the choice of when to require canonical forms is irrelevant.
\subsubsection{Continuations}
The rules \textsc{Close} and \textsc{BT} also use operands to track LF proof terms in closures,
but those operands are syntactically restricted to $\ell^C\ \vec{M}$ in order to avoid closures within closures,
which would needlessly complicate the dynamics.
Furthermore, we see in \textsc{Close} that the type of continuations has been generalized to $\Pi\vec{x}:\vec{A}.~\neg\myG'$: a continuation can take any number of LF terms, which may freely mix Prolog terms and proof terms.
Here the terms $\vec{M}$ are a static component of the environment, stored in the closure, while the $\vec{x}$ are static arguments supplied by the caller:
\begin{center}
\begin{tabular}{ll}
\infer[\textsc{Close}]{\DGE \close r_d, r_s, (\ell^C\ \vec M); I \ok}
{\deduce{\DGE (\ell^C\ \vec M):\Pi \vec x:\vec A.~\neg
\thup{\myG'}{\texttt{env}}{\tau}} {\Gamma(r_s)= \tau &
\Delta;\thup{\myG}{r_d}{\Pi \vec x:\vec A.~\neg \myG'} \ent I \ok}}
\infer[\textsc{BT}]{\DGE \branch r, (\ell^C\ \vec M);I \ok}{\DGE I \ok &
\Gamma(r) = \tau & \DGE (\ell^C\ \vec M):
\neg\heap{\texttt{env}:\tau}}
\end{tabular}
\end{center}
\subsubsection{Static Unification}
\label{sec:dep-stat-unif}
We arrive now at what is arguably the most novel and surprising technical result of the TWAM type system: Static unification as used in the TWAM type system is not only in harmony with Prolog-style runtime unification, but is strong enough to enable the type-checking of LF proofs.
Without our static unification mechanism, it would in general be impossible to show the proof-terms returned by a clause were well-typed (consider the {\tt jmp} in Example~\ref{ex:twam-comp}).
As before, {\tt get\_val} unifies two Prolog terms stored in registers $r_1, r_2$.
Thanks to the addition of singleton types, the type system now has access to LF terms $M_1, M_2:a$ describing the values of $r_1, r_2$.
The subtlety of static unification lies in the fact that because the exact values of $r_1$ and $r_2$ are unknown until runtime, the terms $M_1$ and $M_2$ cannot be the exact values of $r_1$ and $r_2$.
Rather, they will merely be some terms that \emph{unify} with the eventual values of $r_1$ and $r_2$.
What we find novel and surprising is that this partial knowledge represented by $M_1$ and $M_2$
is simultaneously strong enough to certify proof search, yet consistent with the actual behavior at runtime.
To typecheck {\tt get\_val}, we unify the terms $M_1, M_2$ at compile-time.
We write $\DE M_1\sqcap M_2 = \sigma$ to say they successfully unify with most-general unifier $\sigma$.
We apply the substitution $\sigma$ while typechecking the remaining instructions $I$.
The substitution notation $\sub{\sigma}\Delta$ indicates that $\sigma$ substitutes for an arbitrary set of variables from $\Delta$ (i.e. $\dom{\sigma} \subseteq\dom{\Delta}$) and that the replacees $\dom{\sigma}$ should be removed from $\Delta$ in the process: the need for this variant of substitution arises because the variables of a most-general unifier $\dom{\sigma}$ may appear at arbitrary positions throughout $\Delta$.
The rule \textsc{Getval-F} says it is also possible that we statically detect unification failure, written $\DE M_1\sqcap M_2 =\bot$, in which case the program is vacuously well-typed because unification will certainly fail at runtime, leading to backtracking.
In practice, this rule should not be necessary for useful programs, as it indicates the presence of dead code.
However, it is absolutely essential in the theory to ensure preservation in the presence of predicate calls.
{\small\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Getval-S}]{\DGE \getval {r_1}{r_2}; I \ok} {\deduce{\DE M_1 \sqcap M_2
= \sigma\hskip 0.1in \sub{\sigma}\Delta;[\sigma]\Gamma \ent
[\sigma]I \ok} {\Gamma(r_1) = \sing(M_1:a) & \Gamma(r_2) =
\sing(M_2:a)}}&
\infer[\textsc{Getval-F}]{\DGE \getval {r_1}{r_2}; I \ok}
{\deduce{\Gamma(r_1) = \sing(M_1:a) \hskip 0.1in \Gamma(r_2) = \sing(M_2:a)}{\DE M_1 \sqcap M_2 = \bot}}
\end{tabular}
\end{center}}
All unification in T-Prolog and TWAM is first-order, thus the unification judgements $\DE M_1\sqcap M_2 = \sigma$ and $\DE M_1\sqcap M_2 = \bot$
correspond closely to standard algorithms in the literature \cite{Robinson:1965:MLB:321250.321253}.
As in dynamic unification, unification uses auxilliary occurs-check judgements $x\in M$ and $x\notin M$.
Substitutions in TWAM are capture-avoiding and simultaneous. For example, we write $[M_1/x_1,M_2/x_2]$ for a simulateous subtitution on $x_1$ and $x_2$ or $[\sigma_1,\sigma_2]$ for simultaneous composition of arbitrary substitutions $\sigma_1,\sigma_2$:
{\footnotesize\begin{center}
\begin{tabular}{ccccc}
\infer[\sqcap\cdot]{\DE x \sqcap x = \cdot}{}&
\infer[\sqcap{}x1]{\DE x \sqcap M = [M/x]}{x \not \in M}&
\infer[\sqcap{}x2]{\DE M \sqcap x = [M/x]}{x \not \in M}&
\infer[\notin{}x]{x \notin x'}{x \neq x'}&
\infer[\notin{}x\ \vec{M}]{x \notin c\ \vec M}{x \notin M_i (\forall i)}
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{cc}
\infer[\sqcap{}c]{\DE c\ M_1\ \ldots\ M_n \sqcap c\ M_1'\ \ldots\ M_n' = \sigma_n,\ldots,\sigma_1}
{\deduce[\vdots]
{[\sigma_{n-1},\ldots,\sigma_1]\Delta \ent [\sigma_{n-1},\ldots,\sigma_1]M_n \sqcap [\sigma_{n-1},\ldots,\sigma_1]M_n' = \sigma_n}
{\DE M_1 \sqcap M_1' = \sigma_1}}&\infer[\in{}x]{x \in x}{}\\[0.15in]
\infer[\bot{}c1]{\DE c\ M_1\ \ldots\ M_n \sqcap c\ M_1'\ \ldots\ M_n' = \bot}
{\deduce[\vdots]{[\sigma_{i-1},\ldots,\sigma_1]\Delta \ent [\sigma_{i-1},\ldots,\sigma_1]M_i \sqcap [\sigma_{i-1},\ldots,\sigma_1]M_i' = \bot}{\DE M_1 \sqcap M_1' = \sigma_1}}&\infer[\in{}x\ \vec{M}]{x \in c\ \vec M}{x \in M_i (\exists i)}\\
\end{tabular}
\end{center}
\begin{center}
\begin{tabular}{ccc}
\infer[\bot{}c2]{\DE c\ M_1\ \ldots\ M_n \sqcap c'\ M_1'\ \ldots\ M_m' = \bot}{c \neq c'}&
\infer[\bot{}x1]{\DE x \sqcap M = \bot}{x \in M}&
\infer[\bot{}x2]{\DE M \sqcap x = \bot}{x \in M}
\end{tabular}
\end{center}}
\subsubsection{Spines}
\label{sec:dep-spine-stat}
Recall that a Prolog spine serves to unify some terms $M_1\sqcap M_2$, the distinction being that unlike in {\tt get\_val}, the outermost shape of $M_2$ is known statically.
As above, this unification must be made explicit in the type system.
As before, a spine type expresses a typing precondition on each unificand and a typing postcondition.
Previously the postcondition was trivial, but in our generalized \emph{dependent spine types}, the postcondition says that some unification problem $\DE M_1\sqcap M_2$ has succeeded.
We write dependent spine types as $\Pi
x_1:a_1. \cdots\Pi x_n:a_n.~(M_1 \sqcap M_2)$ to say that $M_1$ and
$M_2$ will be unified if the spine succeeds, where the $x_i$ stand for the unificand subterms associated
with each instruction of the spine.
In \textsc{Putstr}, we temporarily introduce a fresh LF variable $x$ for our new Prolog term, which is then unified with the concrete term resulting from the spine.
In \textsc{Getstr}, the unificand is the existing term stored in $r$.
In \textsc{Unifyvar} we extend $\Delta$ with a fresh unification variable standing for the given argument (because this variable may be needed later in a proof term),
while in \textsc{Unifyval} we do not extend $\Delta$ but rather supply an existing term as the spinal argument.
At the end of the spine, if the terms unify, then the rule $\sqcap\sigma$ applies the unifier $\sigma$ while typechecking $I$,
else $\sqcap\bot$ says typechecking is vacuous because unification will fail at runtime.
As in {\tt get\_val}, if $\sqcap\bot$ applies at compile-time, it indicates the presence of dead code,
but it is of essential use in the preservation proof.
{\small\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Putstr}]{\DGE \putstr {c} {r}; I \ok}
{\deduce{\Delta,x:a;\thup{\Gamma}{r}{\sing(x:a)} \ent I:_s\Pi \vec
x:\vec a.~(x \sqcap c\ \vec x)}{\Sigma(c) = \vec a \to a}}&
\infer[\textsc{Getstr}]{\DGE \getstr {c} {r}; I \ok} {\deduce{\DGE I:_s\Pi \vec
x:\vec a.~(M \sqcap c\ \vec x)}{\Sigma(c) = \vec a \to a &
\Gamma(r) = \sing(M : a)}}\\[0.1in]
\infer[\textsc{Unifyvar}]{\DGE \unifyvar r, x:a.~I:_s\Pi x:a.~J}
{\Delta,x:a;\thup{\Gamma}{r}{\sing(x:a)} \ent I:_sJ}&
\infer[\textsc{Unifyval}]{\DGE \unifyval r, x:a.~I:_s\Pi x:a.~J}
{\Gamma(r) = \sing(M:a) & \DGE [M/x] I:_s[M/x]J}\\[0.1in]
\infer[\sqcap\sigma]{\DGE I:_s M_1 \sqcap M_2}
{\DE M_1 \sqcap M_2 = \sigma & \sub{\sigma}\Delta;[\sigma]\Gamma
\ent [\sigma]I \ok}&
\infer[\sqcap\bot]{\DGE I:_s (M_1 \sqcap M_2)}
{\DE M_1 \sqcap M_2 = \bot}
\end{tabular}
\end{center}}
\subsubsection{Environments}
\label{sec:dep-env-stat}
The typing rules for environment tuples are unchanged, since tuples are orthogonal to Prolog terms and LF in general:
{\begin{center}
\[\infer[\textsc{PutTuple}]{\DGE\puttuple r_d, n; I \ok}{\DGE I:_t (\vec\tau\to \{r_d:\cross{\vec\tau}\})& \text{(where $n = |\vec\tau|$)}}\]
\begin{tabular}{ccc}
\infer[\textsc{Proj}]{\DGE\proj r_d, r_s, i; I \ok}{\myG(r_s) = \cross{\vec\tau} & \thup{\myG}{r_d}{\tau_i}\vdash I\ok & \text{(where $i \leq |\vec\tau|$)}}
&\infer[\textsc{SetVal}]{\DGE\setval r; I :_t (\tau\to J)}{\myG(r) = \tau & \DGE I:_t J}
\end{tabular}
\end{center}}
\subsection{Code and Heap Value Typing Invariants}
\label{sec:dep-hvtype}
In dependent TWAM, code values can accept LF terms as arguments, as reflected in \textsc{Code}.
Furthermore, because heap values can now have dependent types, the heap value typing judgement is now
$\DGE v^H:\tau$, where the added context $\Delta$ contains an LF variable for each free variable on the heap.
The rule \textsc{Close} is generalized to close over LF terms, while the rules $\free{},\bound{},$ and $c\langle\rangle$ are generalized to singleton types.
As with register files, tuples and closures enforce that words are canonical for simplicity:
\begin{center}
\begin{tabular}{l}
\infer[\textsc{Close}]{\DPE \close(w_{env}, \ell^C\ \vec{M}) :\Pi\vec{x}:\vec{A}.~\neg \myG}
{\DPE w_{env} : \tau & \DPE\ell^C\ \vec{M}:\Pi\vec{x}:\vec{A}.~\neg\thup{\myG}{\texttt{env}}{\tau} & w_{env}\canon}\\
\infer[\langle\rangle]{\DPE\langle w_1,\ldots,w_n\rangle:\cross{\tau_1,\ldots,\tau_n}}
{\DPE w_1 : \tau_1&w_1\canon&\cdots&\DPE w_n : \tau_n&w_n\canon}
\end{tabular}
\begin{tabular}{cc}
\infer[\free{}]{\DPE \free{}[x:a] : \sing(x:a)}{\Delta(x) = a}&
\infer[\bound{}]{\DPE \bound{\ell^H} : \sing(M:a)}{\DPE \ell^H : \sing(M:a)}
\end{tabular}
\begin{tabular}{cc}
\infer[c\langle\rangle]{\DPE_{\Sigma;\Xi} c\args{\ell^H_1,\ldots,\ell^H_n} : \sing(c\ \vec M : a)}
{\Sigma(c) = \vec a \to a & \DPE \ell^H_i : \sing(M_i :a_i) }&
\infer[\textsc{Code}]{\cdot \ent \code[\vec x:\vec A.~\myG](\lambda \vec x:\vec A.~I) : \Pi \vec x : \vec A.~\neg \myG}
{(\vec x:\vec A);\GE I \ok}
\end{tabular}
\end{center}
\subsection{Machine Typing Invariants}
The runtime behavior of a TWAM program does not depend on type information, i.e. TWAM is easily executed by first type-erasing it to SWAM and then executing the SWAM program.
However, just as TWAM adds typing and proof term annotations to instructions, our theoretical presentation
of the machine states is annotated with LF variables and proof terms, as well.
\paragraph{LF Contexts and Mappings}
\label{par:con-map}
When we prove soundness for TWAM (Theorem~\ref{dep:sound}) in Section~\ref{sec:dep-met}, we will show that for each successful execution trace, an LF proof term exists \emph{in some context} $\Delta$.
For convenience, we make that context an additional field of the machine state, but this is not strictly necessary because it contains one variable for each free variable in the heap $H$ and could thus be computed as a function of $H$.
For Theorem~\ref{dep:sound} to be meaningful, it is essential that $\Delta$ only contains Prolog terms and not arbitrary LF propositions.
Otherwise, if we wished to find a proof term for some query $A$, we could simply add $A$ to the context with {\tt put\_var} and obtain a trivial ``proof''.
Consider the following example (which assumes we have successfully defined the Riemann Hypothesis in Prolog):
\begin{verbatim}
put_var r1, x:Riemann_hypothesis.
succeed[x:Riemann_hypothesis]
\end{verbatim}
Luckily, we easily enforce that $\Delta$ contains only Prolog terms by adding a syntactic restriction in {\tt put\_var}.
The addition of LF variables affects the heap as well: free variables are now annotated as $\free{}[x:a]$ because they are in correspondence with LF variables $x$.
As a technical device to support our progress and preservation theorems, we maintain the invariant that this correspondence is unique with a mapping
$\mu$ between each variable and its unique location on the heap.
\[\text{LF Mappings} \: \mu ::= \cdot\ |\ x@(\ell^H:a),\mu\]
The syntax $x@(\ell^H:a)$ says the LF variable $x$ has type $a$ and is located
at $\ell^H$. The judgement $\SE (\Delta;\mu) \colon{} H$ says that $\mu$ correctly mediates $\Delta$ and $H$ (i.e. assigns a unique location in $H$ to each variable of $\Delta$):
\begin{center}
\begin{tabular}{cc}
\infer[\mu{}\textsc{-Nil}]{\cdot \ent (\Delta;\mu) : \heap{}}{\Delta=\cdot&\mu=\cdot}&
\infer[\mu{}\textsc{-Skip}]{\cdot \ent (\Delta;\mu) : \hext{H}{\ell^H}{v}}
{\cdot \ent (\Delta;\mu) : H & v \neq \free{}[x:a]} \end{tabular}
\end{center}
\begin{center}
\begin{tabular}{c}
\infer[\mu{}\textsc{-Cons}]{\cdot \ent (\Delta,x:a;\mu::(x@\ell^H:a)) : \hext{H}{\ell^H}{\free{} [x:a]}}
{\cdot \ent (\Delta;\mu) : H}
\end{tabular}
\end{center}
\paragraph{Trails}
\label{par:trail-dep-inv}
Trails are generalized in two straightforward ways.
First, failure continuations are now allowed to close over LF terms.
Second, trail typing annotations $\ell^H:a$ are now generalized to remember the corresponding LF variable name ($x@\ell^H:a$)
so that $\Delta$ can be updated accordingly in unwinding:
{\footnotesize\begin{center}
\begin{tabular}{cc}
\infer[\textsc{Trail-Cons}]{\Delta;S \ent(t,w,\ell^C\ \vec M)::{}T' \ok}
{\deduce
{\SE (\Delta';\mu') : H' \hskip 0.1in \Delta' \ent S' : (\Xi,\Psi')
\hskip 0.1in \Delta';\Psi' \ent \ell^C\ \vec M :\neg\heap{\texttt{env}:\tau}}
{\unwind(S,\Delta,t)=(\Delta';S') & \Delta';S' \ent T' \ok & \Delta';\Psi' \ent w : \tau}}&
\infer[\textsc{Trail-Nil}]{\Delta;S \ent \epsilon \ok}{}
\\[0.1in]
$\unwind(S,\Delta,(x@\ell^H:a)::t) = \unwind(\hup{S}{\ell^H}{\free{}[x:a]},(\Delta,x:a),t)$ & $\unwind(S,\Delta,\epsilon) = (\Delta,S)$\\
$\uptrail(x@\ell^H:a,(t,w_{env},\ell^C)::T) = ((x@\ell^H:a)::t,w_{env},\ell^C)::T$&$\uptrail((x@\ell^H:a),\epsilon) = \epsilon$
\end{tabular}
\end{center}}
\paragraph{Register File Types}
\label{par:rftype}
Register file typing now requires that words are canonical, for the sake of simplicity:
\[\infer[\textsc{RF}]{\DPE \heap{r_1 \hook w_1, \ldots, r_n \hook w_n} : \heap{r_1 :\tau_1, \ldots, r_n : \tau_n}}
{\DPE w_1 : \tau_1 & w_1 \canon & \cdots & \DPE w_n : \tau_n & w_n \canon}\]
\paragraph{Machine States}
\label{par:mach-state-inv}
The machine state typing invariants are updated to use the dependent forms of existing judgements in addition to the new invariant $\SE(\Delta,\mu):H$.
As before, spinal states each appeal to an auxilliary invariant.
\begin{center}{
\begin{tabular}{c}
\infer[\textsc{Mach}]{\cdot \ent (T,\Delta,(C,H),R,I) \ok}
{\deduce{\Delta \ent (C,H) : (\Xi;\Psi) \hskip 0.1in \DPE R : \Gamma \hskip 0.1in \DGE I \ok}
{\Delta;(C,H) \ent T \ok & \cdot \ent (\Delta,\mu) : H}}\\[0.1in]
\infer[\textsc{Mach-TWrite}]{\cdot \ent \twrite(T,\Delta,(C,H),R,I, \vec w,r,n) \ok}
{\deduce{\Delta \ent (C,H) : (\Xi;\Psi) \hskip 0.1in \DGE I:_t J \hskip 0.1in \DPE (\vec w, r, n) \writes J }
{\Delta;(C,H) \ent T \ok & \cdot \ent (\Delta,\mu) : H&\DPE R : \Gamma }}\\[.25cm]
\infer[\textsc{Mach-Read}]{\cdot \ent \mread(T,\Delta,(C,H),R,I, \vec \ell^H) \ok}
{\deduce{\Delta \ent (C,H) : (\Xi;\Psi)
\hskip 0.1in \DGE I:_s J \hskip 0.1in \DPE \vec \ell^H \reads J}
{\Delta;(C,H) \ent T \ok & \cdot \ent
(\Delta,\mu) : H & \DPE R : \Gamma}}\\[0.1in]
\infer[\textsc{Mach-Write}]{\cdot \ent \mwrite(T,\Delta,(C,H),R,I,c,\ell^H, \vec \ell^H)
\ok}
{\deduce{\Delta \ent (C,H) : (\Xi;\Psi)
\hskip 0.1in \DGE I:_s J \hskip 0.1in \DPE (\vec \ell^H, \ell^H,c)
\writes J} {\Delta;(C,H) \ent T \ok & \cdot
\ent (\Delta,\mu) : H & \DPE R : \Gamma}}
\end{tabular}}
\end{center}
However, the auxilliary invariants for Prolog spines have become more complex.
The read spine invariant considers a term sequence $\vec{M}$ for the arguments already read and a second sequence $\vec{M'}$ for those remaining.
The invariant holds if (a) every $x_i$ can still unify with $M'_i$ and (b) every $\ell^H_i$ has the type expected by the spine type.
The write spine invariant requires that (a) the destination $\ell^H$ matches the result type of the constructor $c$, (b) the existing arguments $\vec{\ell^H}$ match the initial argument types, and (c) the remainder of the spine matches the remaining argument types.
\begin{center}{\footnotesize
\[\infer[\textsc{TWrites}]{\DPE (n,r,\vec\ell^H) \writes (\vec \tau_2 \to \{r:\cross{\vec\tau_1 \vec \tau_2})\}}
{\DPE \vec \ell^H : \vec \tau_1 & |\vec \tau_2| = n}\]
\begin{tabular}{cc}
\infer[\textsc{Reads}]{\DPE \vec \ell^H \reads \Pi \vec x:\vec A.(c\ \vec M\ \vec M'
\sqcap c\ \vec M\ \vec x)} {\deduce{\DPE \ell^H_i :
\sing(M'_i:[M'_1,\ldots,M'_{i-1}/x_1,\ldots,x_{i-1}]A_i)}{\DE c\ \vec M\
\vec x \sqcap c\ \vec M\ \vec M' = \sigma}}&
\infer[\textsc{Writes}]{\DPE (\vec \ell^H, \ell^H,c) \writes \Pi \vec x : \vec
a_2. x' \sqcap c\ \vec M\ \vec x}
{\deduce{\Psi(\ell^H) = \sing(x' : a)}{\Sigma(c) = \vec a_1 \to \vec a_2 \to a & \DPE \vec \ell^H :
\sing(\vec M : \vec a_1)} }\\[.25cm]
\end{tabular}}
\end{center}
\subsection{Metatheory}
\label{sec:dep-met}
In the dependent setting, we show our primary result that all TWAM
programs are sound proof search procedures in the following sense:
\begin{thm}[Soundness]\label{dep:sound}
If $\SE m \ok$ and $m \step^* m'$ and $m' \done$ then \\
$m' = (T,\Delta,S,R,\succeed[M:A];I)$ and $\DE M : A$.
\end{thm}
This theorem is an immediate corollary of progress and preservation, by inversion on the typing rule for \verb|succeed|.
Thus it suffices to show progress and preservation and their supporting lemmas.
We present here only the lemmas that are new or significantly different from the simply-typed versions.
A detailed proof for the dependently-typed system is in the electronic appendix.
\subsubsection{Static Occurs Check}
\begin{lem}[Static Occurs Check Totality]
\label{lem:stat-occ-tot}
For all terms $M$ and all variables $x$, either $x \in M$ or $x \notin M$\end{lem}
\begin{proof}
By induction on the structure of $M$.
\end{proof}
\subsubsection{Static Unification}
\begin{lem}[Static Unification Totality]
\label{lem:stat-unif-tot}
For all LF terms $M_1, M_2,$ if
$\DE M_2 : A$ and $\DE M_1 : A$ then $\DE M_1 \sqcap M_2 = \sigma$ or
$\DE M_1 \sqcap M_2 = \bot$.\end{lem}
\begin{proof}
By lexicographic induction on $|\Delta|$ and the structure of $M_1$.
The base cases hold by Lemma~\ref{lem:stat-occ-tot}.
The inductive case $M_1 = c\ \vec M$, $M_2 = c\ \vec M'$ (where $|M| = |M'|$) relies on a subclaim:
\begin{claim}For each $1 \leq i \leq |\vec M|,$ consider $\sigma = [\sigma_{i-1},\ldots,\sigma_1]$. Then $[\sigma]\Delta \ent [\sigma]M_i \sqcap M_i' = \sigma_i$ for some
$\sigma_i$ or $[\sigma]\Delta \ent [\sigma]M_i \sqcap [\sigma]M_i' = \bot$.\end{claim}
\begin{proof} By cases on $i$.
\case{$i=1$} By IH because $M_1$ is structurally smaller than $c\ \vec M$.
\case{$i>1$} By IH: if $\sigma = \cdot$ then $M_i$ is structurally smaller than $c\ \vec M$, else $\sigma = [\vec M''/\vec x]$ where $x_i \in \dom{\Delta}$ and thus $|[\sigma]\Delta| < \Delta$.
\end{proof}
\end{proof}
\begin{lem}[Static Unification Correctness] If $\DE M : A$ and $\DE M' : A$ and $\DE M \sqcap M' = \sigma$, then
\label{lem:static-unif}
\begin{itemize}
\item $[\sigma]M = [\sigma]M'$
\item For all substitutions $\sigma',$ if $[\sigma']M = [\sigma']M'$ then there exists some $\sigma^*$ such that $\sigma' \equiv_{\alpha} \sigma^*,\sigma$.
\end{itemize}\end{lem}
\begin{proof} Analogous to standard results from the literature. \end{proof}
As a technical device for Lemma~\ref{lem:doom} we introduce a judgement $M_1\sqsubset M_2$ meaning ``$M_1$ is a strict substructure of $M_2$'':
\begin{center}
\begin{tabular}{cc}
\infer[\sqsubset\textsc{-Base}]{M_i \sqsubset c\ \vec M}{} &
\infer[\sqsubset\textsc{-Ind}]{M \sqsubset c\ \vec M}{M \sqsubset M_i}
\end{tabular}
\end{center}
The following lemmas support the proof of Lemma~\ref{lem:doom}.
\begin{lem}[Occurs to Substructure]\label{lem:occ-substr}If $x \in M$ and $x \neq M$ then $x \sqsubset M$\end{lem}
\begin{proof}
By induction on the derivation $x \in M$.
\end{proof}
\begin{lem}[Substructure to Occurs]\label{lem:substr-occ}If $x \sqsubset M$ then $x \in M$. \end{lem}
\begin{proof}
By induction on the derivation $x \sqsubset M$.
\end{proof}
\begin{lem}[Substitution Preserves Substructure]\label{lem:subst-substr}If $M_1 \sqsubset M_2$ then $[M/x]M_1 \sqsubset [M/x]M_2$ \end{lem}
\begin{proof}
By induction on the derivation $M_1 \sqsubset M_2$.
\end{proof}
\begin{lem}[Transitivity of Substructure]
\label{lem:substr-trans}
If $M_1 \sqsubset M_2$ and $M_2 \sqsubset M_3$ then $M_1 \sqsubset M_3$.
\end{lem}
\begin{proof}
By induction on the derivation $M_2 \sqsubset M_3$.
\end{proof}
\begin{lem}[Substructures Don't Unify]\label{lem:subst-no-unif} If $\DE M : A, \DE M' : A$ and $M \sqsubset M'$ then $\DE M \sqcap M' = \bot$.
\end{lem}
\begin{proof} By lexicographic induction on $|\Delta|$ and the structure of $M$.
Consider the cases for $M \sqsubset M'$.
The case $x \sqsubset c\ \vec M$ holds by Lemma~\ref{lem:substr-occ}.
\case{\infer[\sqsubset\textsc{-Base}]{c\ \vec M \sqsubset c'\ \vec M'}{\text{(because $c\ \vec M = M'_i$)}}}
If $c' \neq c,$ then unification fails immediately, so assume $c \neq c'$.
Observe $M_i \sqsubset c\ \vec M$ by rule $\sqsubset$\textsc{-Base}. Since $M'_i = c\ \vec M$, we have $M_i \sqsubset M_i'$.
By Lemma~\ref{lem:subst-substr}, for any substitution $\sigma,$ we have $[\sigma]M \sqsubset [\sigma]M'$. Note that when we unify $c\ \vec M$ and
$c\ \vec M'$ we either fail before $M_i$ or attempt to compute $[\sigma]M \sqcap [\sigma]M'$ for some $\sigma$. If we failed already,
the case is done. If we succeeded, then by the IH $[\sigma]\DE [\sigma]M \sqcap [\sigma]M' = \bot$ and we fail here.
\case{\infer[\sqsubset\textsc{-Ind}]{c\ \vec M \sqsubset c'\ \vec M'}{c\ \vec M \sqsubset M'_i}}As in the previous case, AWLOG $c = c'$. Now since $c\ \vec M \sqsubset c\ \vec M'$ then by Lemma~\ref{lem:substr-trans}, $M_i \sqsubset M'_i$ for the $i$ such that $c\ \vec M \sqsubset M_i$. The rest of the case is analogous to the last one.
\end{proof}
\begin{lem}[Unification Lemma of Doom]
\label{lem:doom}
Unifications that fail are doomed to fail forever. That is, if $\Delta,x:A \ent M_1 \sqcap M_2 = \bot$ and $\DE M : A$ then $[M/x]\DE [M/x]M_1 \sqcap [M/x]M_2 = \bot$.
\end{lem}
\begin{proof}
By lexicographic induction on $|\Delta|$ and the unification derivation $\Delta,x:A \ent M_1 \sqcap M_2 =\bot$.
\case{\infer[\bot{}x1]{\Delta,x:A \ent x' \sqcap M_2 = \bot}{x' \neq M_2 & x' \in M_2}}
Case on whether $x = x'$.
\case{$x \neq x'$} In this case, $[M/x]x' = x'$ and $x' \in [M/x]M_2$ so the unification still fails.
\case{$x = x'$} This case reduces to the following claim:
\begin{claim}If $x \in M$ and $\DE M' : A$ and $\Delta,x:A \ent M : A$ then $[M/x]\DE M' \sqcap [M/x] = \bot$. \end{claim}
\begin{proof}
By Lemma~\ref{lem:occ-substr}, $x \sqsubset M$.
By Lemma~\ref{lem:subst-substr}, $M' \sqsubset [M'/x]M$.
By Lemma~\ref{lem:subst-no-unif}, $[M'/x]\DE M' \sqcap [M'/x]M = \bot$.
\end{proof}
\case{\infer[\bot{}x2]{\Delta,x:A \ent M \sqcap x' = \bot}{x' \neq M & x' \in M}}
This case holds by symmetry.
\case{\infer[\bot{}c2]{\Delta,x:A \ent c\ M_1\ \ldots\ M_n \sqcap c'\ M_1'\ \ldots\ M_m' = \bot}{c \neq c'}}
This case holds because substitution preserves head constructors.
\case{\infer[\bot{}c1]{\DE c\ M_1\ \ldots\ M_n \sqcap c\ M_1'\ \ldots\ M_n' = \bot}
{\deduce[\vdots]{[\sigma_{i-1},\ldots,\sigma_1]\Delta \ent [\sigma_{i-1},\ldots,\sigma_1]M_i \sqcap [\sigma_{i-1},\ldots,\sigma_1]M_i' = \bot}{M_1 \sqcap M_1' = \sigma_1}}}
If some $i' < i$ fails to unify, we're done. Otherwise we attempt to unify $ [\sigma]M_i \sqcap [\sigma]M_2$ where $\sigma = \sigma'_{i-1},\ldots,\sigma_1',M/x$.
By Lemma~\ref{lem:static-unif}, $\sigma = \sigma^*, \sigma_{i-1},\ldots,\sigma_1$ so
we can apply the IH to get
and
\[\infer[\bot{}c1]{[M/x]\DE [M/x]c\ M_1\ \ldots\ M_n \sqcap [M/x]c\ M_1'\ \ldots\ M_n' = \bot}
{\deduce[\vdots]{[\sigma'_{i-1},\ldots,\sigma'_1,M/x]\Delta \ent [\sigma'_{i-1},\ldots,\sigma'_1,M/x]M_i \sqcap [\sigma'_{i-1},\ldots,\sigma'_1,M/x]M_i' = \bot}{[M/x]M_1 \sqcap [M/x]M_1' = \sigma'_1}}\]
\end{proof}
\subsubsection{Substitution}
\begin{lem}[Substitution] All appropriate typing judgements support substitution.
\label{lem:subst}
\begin{enumerate}
\item \emph{LF terms:} If $\Delta,x\colon{}A \ent M_1\colon{}A'$, $\DE M_2\colon{}A$ then $[M_2/x]\DE[M_2/x]M_1\colon{}[M_2/x]A$.
\item \emph{Operands:} If $\Delta_1,x\colon{}A;\Delta_2;\myG\ent op\colon{}\tau$, $\Delta_1\ent M\colon{}A$ then $\Delta_1,[M/x]\Delta_2;[M/x]\myG \ent [M/x]op\colon{}[M/x]\tau$.
\item \emph{Word values:} If $\Delta_1,x\colon{}A,\Delta_2;\PE w\colon{}\tau$, $\Delta_1\ent{}M\colon{}A$ then $\Delta_1,[M/x]\Delta_2;[M/x]\PE [M/x] w\colon{}[M/x]\tau$.
\item \emph{Register Files:} If $\Delta_1,x\colon{}A,\Delta_2;\Psi\ent R\colon{}\myG$, $\Delta_1\ent M:A$ then $\Delta_1,[M/x]\Delta_2;[M/x]\Psi \ent [M/x]R \colon{} [M/x]\myG$.
\item \emph{Heap values:} If $\Delta_1,x\colon{}a,\Delta_2;\Psi\ent v^H\colon{}\tau$,$\Delta_1\ent M\colon{}a$, $v^H\neq\free{}[x\colon{}a]$ then \\$\Delta_1,[M/x]\Delta_2;[M/x]\Psi\ent[M/x]v^H\colon{}[M/x]\tau$
\item \emph{Basic blocks:} If $\Delta_1,x\colon{}A,\Delta_2;\Gamma \ent I\ok$, $\Delta_1\ent M\colon{}A$ then $\Delta_1,[M/x]\Delta_2;[M/x]\myG \ent [M/x] I \ok$.
\end{enumerate}
\end{lem}
\begin{proof}
Each claim holds by lexicographic induction on $|\Delta|$ and the structure of the typing derivation.
The first five claims are straightforward. The interesting cases of the final claim are the unification instructions,
because there is a subtle interaction between static and dynamic unification.
The case for $\getval{r_1}{r_2}$ is representative:
\case{{\footnotesize\infer[\textsc{GetVal-S}]{\Delta_1,x:A,\Delta_2;\GE \getval {r_1}{r_2}; I \ok}
{[\sigma]\Delta_1,x:A,\Delta_2;[\sigma]\Gamma \ent [\sigma]I \ok&\Delta_1,x:A,\Delta_2 \ent M_1 \sqcap M_2 = \sigma&\Gamma(r_1) = \sing(M_1 : a) & \Gamma(r_2) = \sing(M_2 : a)}}}
By claim 1, $\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 : a$ and $\Delta_1,[M/x]\Delta_2\ent [M/x]M_2 : a$ so by
Lemma~\ref{lem:stat-unif-tot}, either $\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 \sqcap [M/x]M_2 = \sigma'$ or $\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 \sqcap [M/x]M_2 = \bot$.
\subcase{$\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 \sqcap [M/x]M_2 = \sigma'$}
By Lemma~\ref{lem:static-unif}, $[\sigma']([M/x]M_1) = [\sigma']([M/x]M_2)$ which we
can rewrite as $[\sigma',M/x]M_1 = [\sigma',M/x] M_2$. Also by Lemma~\ref{lem:static-unif}, $\sigma$ is a most general unifier of $M_1$ and $M_2$. Thus there exists $\sigma^*$ such that $\sigma',M/x = \sigma^*,\sigma$ (they need not be syntactically equal, but must be alpha-equivalent). In particular, alpha-vary $\sigma^*$ such that it substitutes for $x$. Then by iterating the IH (we can do this because $|\Delta|$ decreases every time), $[\sigma^*,\sigma](\Delta_1,x:A,\Delta_2);[\sigma^*,\sigma]\Gamma \ent [\sigma^*,\sigma]I \ok$. By the assumption that $\sigma^*,\sigma$ substitutes for $x,$ we have $[\sigma^*,\sigma](\Delta_1,\Delta_2);[\sigma^*,\sigma]\Gamma \ent [\sigma^*,\sigma]I \ok$ which suffices to show the result:
\[\infer[\textsc{GetVal-S}]{\Delta_1,[M/x]\Delta_2;[M/x]\GE \getval{r_1}{r_2}; [M/x]I \ok}
{\deduce{\Delta_1,[M/x]\Delta_2 \ent [M/x]M_1 \sqcap [M/x]M_2 = \sigma^*,\sigma}{([M/x]\myG)(r_1) = \sing([M/x]M_1 : a)}
&\deduce{[\sigma^*,\sigma]\Delta;[\sigma^*,\sigma]\GE [\sigma^*,\sigma]I \ok }{([M/x]\myG)(r_2) = \sing([M/x]M_2 : a)}}\]
\subcase{$\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 \sqcap [M/x]M_2 = \bot$}In this case, since the
unification failed, the result is vacuously well-typed:
\[{\footnotesize\infer[\textsc{GetVal-F}]{\Delta_1,[M/x]\Delta_2;[M/x]\GE \getval{r_1}{r_2}; [M/x]I \ok}
{([M/x]\myG)(r_1) = \sing([M/x]M_1 : a) &
([M/x]\myG)(r_2) = \sing([M/x]M_2 : a) &
\Delta_1,[M/x]\Delta_2\ent [M/x]M_1 \sqcap [M/x]M_2 = \bot}
}\]
\case{\infer{\Delta_1,x:A,\Delta_2;\GE \getval {r_1}{r_2}; I \ok}
{\deduce{\Delta_1,x:A,\Delta_2\ent M_1 \sqcap M_2 = \bot}{\Gamma(r_1) = \sing(M_1 : a) & \Gamma(r_2) = \sing(M_2 : a)}}}
By Lemma~\ref{lem:doom}.
\end{proof}
\subsubsection{Soundness of Unification}
\begin{lem}[Soundness of \unify] If $\DE M_1 \colon{}a$, $\DE M_2 \colon{}a$, $\DE S \colon{} (\Xi;\Psi)$, $\Delta;S\ent T\ok$,
$\SE(\Delta;\mu)\colon{}S$, $\DPE\ell^H_1\colon{}\sing(M_1\colon{}A)$, $\DPE\ell^H_2\colon{}\sing(M_2\colon{}A)$ then
\begin{itemize}
\item If $\DE M_1 \sqcap M_2 = \bot$ then $\unify(\Delta,S,T,\ell^H_1,\ell^H_2) = \bot$
\item If $\DE M_1 \sqcap M_2 = \sigma$ then $\unify(\Delta,S,T,\ell^H_1,\ell^H_2) = (\Delta',S',T')$ where
$\Delta' = [\sigma]\Delta$ and $[\sigma]\DE H' \colon{} [\sigma]\Psi$ and $\Delta',S'\ent T' \ok.$
\end{itemize}
\end{lem}
\begin{proof}
As in SWAM, with the additional use of Lemma~\ref{lem:subst}.
\end{proof}
\subsubsection{Words and Operands}
\begin{lem}[Word Totality]\label{lem:word-tot} If $\DPE w : \tau$ then $w \eval w'$ and $w' \canon$.
\end{lem}
\begin{proof}
By induction on $\size(w)$, defined by $\size(\ell) = 0, \size(w\ M) = 1 + \size(w), \size(\lambda x:A.w) = 1 + \size(w)$,
appealing to Lemma~\ref{lem:subst} and the fact that substitution preserves $\size(M)$.
\end{proof}
\begin{lem}[Operand Resolution]\label{lem:oper-res} For all operands $op$, if $\DGE_{\Xi} op : \tau$
and $\DPE R : \Gamma$ then $R \ent op \squig w$
for some word $w$ and $\DPE_{\Xi} w : \tau$. \end{lem}
\begin{proof}
By induction on $\DGE_{\Xi} op : \tau$ and inversion on register file typing.
\end{proof}
\begin{lem}[Word Preservation]\label{lem:word-pres} If $\DPE w : \tau$ and $w \eval w'$ then $\DPE w' : \tau$.\end{lem}
\begin{proof} By induction on the trace $w \eval w'$ and Lemma~\ref{lem:subst}. \end{proof}
\begin{lem}[Operand Preservation]\label{lem:oper-pres} If $\DPE R : \myG$ and $\DGE op : \tau$ and $R \ent op \eval w$ then $w \canon$ and $\DPE w : \tau$.\end{lem}
\begin{proof}
Follows directly from Lemmas~\ref{lem:oper-res} and \ref{lem:word-pres}.
\end{proof}
\begin{lem}[Operand Canonicalization]\label{lem:oper-canon} If $\DPE R : \myG$ and $\DGE op : \tau$ then $R \ent op \eval w$ and $w \canon$ and $\DPE w : \tau$.
\end{lem}
\begin{proof}
By Lemma~\ref{lem:oper-res}, $R \ent op \eval w'$ and $\DPE w' : \tau$. By Lemma~\ref{lem:word-tot}, $w' \eval w$, so by rule $op\eval$ we have
$R \ent op \eval w$
and by Lemma~\ref{lem:word-pres}, $\DPE w : \tau$.
\end{proof}
\begin{lem}[Word Inversion]\label{lem:word-inv} If $\DPE \ell\ \vec M : \tau$ then $\DPE \ell : \Pi \vec x:\vec A.\tau'$ where $[\vec M/\vec x]\tau'=\tau$
and $\DE M_i : [M_1,\ldots,M_{i-1}/x_1,\ldots,x_{i-1}]A_i$.
\end{lem}
\begin{proof}
By induction on the derivation $\DPE \ell\ \vec M : \tau$.
\end{proof}
\subsubsection{Progress and Preservation}
\begin{thm}[Progress] If $\SE m \ok$ then either $m \done$ or $m \fails$ or $m \step m'$.\end{thm}
\begin{proof}
By cases on $m$ (specifically, cases on $I$), and by Lemmas~\ref{lem:scf}, \ref{lem:bt-tot}, \ref{lem:end-corr}, \ref{lem:unify-sound}, \ref{lem:stat-unif-tot}, \ref{lem:oper-pres}, \ref{lem:oper-canon}, and \ref{lem:word-inv}.
\end{proof}
\begin{thm}[Preservation] If $\SE m \ok$ and $m \step m'$ then $\SE m' \ok$.\end{thm}
\begin{proof}
By cases on $m \step m'$, using the assumptions of $\SE m\ok$.
First consider simulatenously all the cases that end in backtracking.
Those cases hold by Lemma~\ref{lem:bt-tot}.
Thus it suffices to show the cases that do not backtrack.
\case{\infer[\textsc{Jmp-}\ell^H]{(T,\Delta,S,R,\jmp op; I) \step (T,\Delta, S,\hup{R}{r_1}{w},[\vec M\vec M'/\vec x\vec x']I')}
{R \ent op \hook \ell^H\ \vec M & C(\ell^H) = \close(w, \ell^C\ \vec M')}}
By Lemma~\ref{lem:oper-pres}, $\DPE \ell^H\ \vec M : \neg \Gamma'$. By typing assumption, $\ell^C\ \vec M : \Pi \vec x':\vec A'.\neg \hup{\myG''}{r_1}{\tau}$
so by Lemma~\ref{lem:word-inv}, $\DPE \ell^C : \Pi \vec{x}\vec{x'}:\vec A\vec A'.\neg \myG'''$ where $[\vec M'/\vec x']\myG''' = \myG''$. By Lemma~\ref{lem:scf},
$C(\ell^C) = \code[\vec x' \vec x: \vec A' \vec A](\lambda \vec x' \vec x : \vec A' \vec A.I')$ and $\vec x' \vec x:\vec A' \vec A;\heap{r_1 : \tau} \ent I' \ok$.
By Lemmas~\ref{lem:sweak} and \ref{lem:subst}, $\Delta;[\vec M \vec M'/\vec x\vec x']\thup{\Gamma'}{r}{\tau} \ent [\vec M/\vec x]I' \ok$ where $\DPE w : \tau=[\vec M'\vec M/\vec x'\vec x]\tau$. By assumption, $\DE \myG' \leq \myG$, so by Lemma~\ref{lem:reg-sub}, $\Delta;\thup{\Gamma}{r_1}{\tau} \ent [\vec M'\vec M/\vec x'\vec x]I' \ok$. By assumption $w \canon$ so $\DPE \hup{R}{r_1}{w} : \thup{\Gamma}{r_1}{\tau},$ then $\SE m' \ok$.
\case{\infer[\textsc{Jmp-}\ell^C]{(T,\Delta, S,R, \jmp op; I) \step (T,\Delta, S,R,[\vec M/\vec x]I')}
{R \ent op \hook \ell^C\ \vec M & C(\ell^C) = \code[\vec x:\vec A.\Gamma'](\lambda \vec x : \vec A.I')}}
By Lemma~\ref{lem:oper-pres}, $\DPE \ell^H\ \vec M : \neg \Gamma'$. By assumption, $(\vec x : \vec a);\Gamma' \ent I' \ok$ and by Lemmas~\ref{lem:sweak} and \ref{lem:subst}, $\Delta;[\vec M/\vec x]\Gamma' \ent [\vec M/\vec x]I' \ok$.
Since $\DE [\vec M/\vec x]\Gamma' \leq \Gamma$, by Lemma~\ref{lem:reg-sub}, $\DGE [\vec M/\vec x]I' \ok$, so $\SE m' \ok$.
\case{\infer[\textsc{Close}]{(T,\Delta, S,R,\close r_d, r_s, \ell^C\ \vec M; I) \step (T,\Delta, \hext{S}{\ell^H}{\close(w,\ell^C\ \vec M)},\hup{R}{r}{\ell^H},I)}
{R(r_s) = w}}
By assumption and inversion on $\myG(r) = \tau$, we have $\DPE \close(w,\ell^C\ \vec M) : (\Pi \vec x:\vec A.~\neg \Gamma'),$ so
$\DE \hext{S}{\ell^H}{\close[\Gamma'](w,\lambda \vec x:\vec A.I')} : \thext{\Psi}{\ell^H}{\Pi \vec x:\vec A.~\neg \Gamma'}$ and
$\Delta;\thext{\Psi}{\ell^H}{\Pi \vec x:\vec A.~\neg \Gamma'} \ent \hup{R}{r}{\ell^H} : \thup{\Gamma}{r}{\Pi \vec x:\vec A.~\neg \Gamma'}$ and thus, $\SE m' \ok$.
\case{\infer[\textsc{PushBT}\step]{(T,\Delta, S,R,\branch r, \ell^C\ \vec M; I) \step ((\epsilon,w,\ell^C\ \vec M)::T,\Delta, S,R,I)}
{R(r) = w}}
By $\epsilon$ case of $\unwind$, we have $\unwind(\Delta,S,\epsilon) = (\Delta;S)$ so let $\Delta'= \Delta, S'=S,\mu'=\mu$. By Lemma~\ref{lem:scf} and inversion, $\Delta';\Psi'\ent w:\tau$ and $w \canon$ and the rest holds by assumption:
\[\infer[\textsc{Trail-Cons}]{\Delta;S\ent (\epsilon,w,\ell^C\ \vec M)::T \ok}
{\deduce{\Delta';\Psi'\ent w:\tau\hskip 0.1in\Delta';\Psi'\ent \ell^C\ \vec M : \neg\heap{r_1:\tau}\hskip 0.1in w\canon}
{\unwind(\Delta,S,\epsilon)=(\Delta';S')&\Delta';S'\ent T\ok&\SE(\Delta';\mu'):H' &\SE H':\Psi'}}\]
so $\SE m' \ok$ as well by the assumption $\DGE I \ok$.
\case{\infer[\textsc{GetVal}\step]{(T,\Delta, S,R, \getval{r_1}{r_2}; I) \step (T',\Delta', S',R,I)}
{R(r_1) = w_1 & R(r_2) = w_2 & \unify(\Delta,S,T,w_1,w_2)=(\Delta',S',T')}}
By assumption $\DE M_1 \sqcap M_2 = \sigma$ where $\DPE w_1 : \sing(M_1:a)$
and $\DPE w_2 : \sing(M_2 : a)$. By Lemma~\ref{lem:unify-sound}, $\Delta' = [\sigma]\Delta$, $\DE S' : [\sigma]\Psi$ and $\SE (\Delta', [\sigma]\mu) : H'$ and $\Delta';S'\ent T' \ok$. By
substitution, $[\sigma]\Delta;[\sigma]\Psi \ent R : [\sigma]\Gamma$ and
by assumption $[\sigma]\Delta;[\sigma]\Gamma \ent I \ok$ so $\SE m' \ok$.
\case{\infer[\textsc{Mov}\step]{(T,\Delta, S,R, \mov{r_d}{op}; I) \step (T,\Delta, S,\hup{R}{r_d}{w},I)}
{R\ent op \eval w}}
By Lemma~\ref{lem:oper-pres}, $\DPE w : \tau$ and $w \canon$ so $\DPE \hup{R}{r_d}{w} : \thup{\Gamma}{r_d}{\tau}$ and $\SE m' \ok$.
\case{{\small\infer[\textsc{PutVar}\step]{(T,\Delta, S,R, \dputvar{r}{x:a.} I) \step(T,(\Delta,x:a),\hext{S}{\ell^H}{\free{}[x:a]},\hups{R}{r \hook \ell^H},I)}{}}}
Let $\mu' = (x@\ell^H:a,::\mu),$ then have $\SE ((x:a,\Delta), ((x@\ell^H:a)::\mu)) : \hup{H}{\ell^H}{\free{}[x:a]}$ by rule $\mu{}\textsc{-Cons}$.
We also have $\Delta,x:a \ent \hext{S}{\ell^H}{\free{}[x:a]} : \Xi;\thext{\Psi}{\ell^H}{\sing(x:a)}$ and $\Delta,x:a;\thext{\Psi}{\ell^H}{\sing(x:a)} \ent \hup{R}{r}{\ell^H} : \thup{\Gamma}{r}{\sing(x:a)}$. By Lemma~\ref{lem:trail-up}, $\Delta,x:a;\hext{S}{\ell^H}{\free{}[x:a]} \ent T \ok$ which together with the
previous statements gives us $\SE m' \ok$.
\case{\infer[\textsc{GetStr}\step\textsc{W}]{(T,\Delta, S,R,\getstr {c}{r}; I) \step
\mwrite(T,\Delta, S,R,I,c,\ell'^H,\epsilon)}
{R(r) = \ell^H & \edn(S,\ell^H) = \ell'^H & S(\ell'^H) = \free{}[x:a]}}
By assumption, suffices to show $\DPE (\vec \ell^H, r, c) \writes J$. Since
$\vec \ell^H$ is empty, we need only know $\Sigma(c) = \vec a_2 \to a$ where
$J$ accepts $\vec a_2$ which is true by assumption. We also
need $S(\ell'^H) = \free{}[x:a]$ which is true by case.
\case{\infer[\textsc{GetStr}\step\textsc{R}]{(T,\Delta, S,R,\getstr{c}{r}; I) \step
\mread(T,\Delta, S,R,I,\vec w)}
{R(r) = \ell^H & \edn(S,\ell^H) = \ell'^H & S(\ell'^H) = \cwsh}}
Suffices to show $\vec \ell^H \reads J$, and in particular $\DE M_1 \sqcap M_2 = \sigma$. Since $M_1 = x, M_2 = c\ \vec x$ and $x \notin \vec x$ (because $x\fresh$), the unification succeeds with $x \sqcap c\ \vec x = [c\ \vec x/x]$.
\case{{\footnotesize\infer[\textsc{PutStr}\step]{(T,\Delta, S,R,\putstr{c}{r}; I) \step\mwrite(T,(x:a,\Delta),
\hext{S}{\ell^H}{\free{}[x:a]},\hup{R}{r}{\ell^H},I,c,\ell^H,\epsilon)}{\Sigma(c) = \vec a \to a}}}
Similar to the $\mwrite$ case of {\tt getstr}. Define $\mu' = (x@\ell^H:a),\mu,$
then $\SE (((x@\ell^H:a)::\mu),(\Delta,x:a)) : \hext{S}{\ell^H}{\free{}[x:a]}$.
Now $S(\ell^H) = \free{}[x:a]$ as needed, and by assumption, $J$ accepts $\vec a_2$.
\vspace{0.1in}
\case{\infer[\textsc{PutTuple}\step]{(T,\Delta, S,R,\puttuple{r, n}; I) \step
\twrite(T,\Delta, S,R,I,r,n,\epsilon)}{}}
Suffice to show $\DPE (\vec w, r,n) \writes J$ where in this case $\vec w$ is empty and $J = \vec \tau \to \heap{r : \cross{\vec \tau}}$. Since $n = |\tau|,$ we have $\DPE (\epsilon, r, n) \writes \vec \tau \to \heap{r:\cross{\vec \tau}}$.
\case{\infer[\textsc{Proj}\step]{(T,\Delta, S,R,\proj r_d, r_s, i; I) \step (T,\Delta, S,\hup{R}{r_d}{w_i},I)}
{R(r_s) \ell^H & S(\ell^H) = \args{w_1,\ldots,w_i,\ldots,w_n}}}
By inversion and Lemma~\ref{lem:scf}, $R(r_s) = \ell^H$ and $\DPE \ell^H : \cross{\vec \tau}$ so by Lemma~\ref{lem:scf}, $S(\ell^H) = \args{w_1, \ldots,w_i,\ldots,w_n}$ and
$\DPE w_i : \tau_i$. Therefore $\DPE \hup{R}{r_d}{w_i} : \thup{\Gamma}{r_d}{\tau_i}$ so $\SE m \ok$.
\case{\infer[\textsc{SetVal}\step]{\twrite(T,\Delta, S,R, \setval r_s; I,r_d,n,\vec w) \step
\twrite(T,\Delta, S,R,I,r_d,n-1,(\vec w::w))}{R(r_s) = w & n > 0}}
Consider $\vec \tau_1, \vec \tau_2$ from the derivation $\SE (\vec w, r, n) \writes J$. Observe by assumption $\vec \tau_2$ has form $\tau,\vec \tau_2'$.
Now let $\vec \tau_1' = \vec \tau_1, \tau$. This gives us $\DPE (\vec w::w) : \vec \tau_1'$ and $|\vec \tau_2'| = n-1$ and $\vec \tau_1'\vec\tau_2' = \vec\tau_1\vec\tau_2$ so $\DPE ((\vec w::w),r,n-1) \writes (\tau_2' \to \heap{r:\cross{\vec\tau_1'\vec\tau_2'}})$. The rest is by assumption.
\vspace{0.1in}
\case{\infer[\textsc{TWrite}\step]{\twrite(T,\Delta, S,R,I,r,0,\vec w) \step (T,\Delta, \hext{S}{\ell^H}{\args{\vec \ell^H}},\hup{R}{r}{\ell^H},I)}{}}
Since $n=0,$ the instruction typing derivation has form $\DGE I : \heap{r:\cross{\vec\tau}}$
where $\DPE \vec \ell^H : \vec \tau$ (from the derivation $\DPE(\vec \ell^H,r,0) \writes J$). This derivation must contain $\Delta;\thup{\Gamma}{r}{\cross{\vec \tau}} \ent I \ok$. We also have $\DPE \args{\vec w} : \cross{\vec \tau}$
so $\DE \hext{S}{\ell^H}{\args{\vec w}} : (\Xi;\thext{\Psi}{\ell^H}{\cross{\vec\tau}})$ and $\Delta;\thext{\Psi}{\ell^H}{\cross{\vec\tau}} \ent \hup{R}{r}{\ell^H} : \thup{\Gamma}{r}{\cross{\vec \tau}}$ so $\SE m' \ok$.
\vspace{0.1in}
\case{\infer[\textsc{Read}\step]{\mread(T,\Delta, S,R,I,\epsilon) \step (T,\Delta, S,R,I)}{}}
Then $J = c\ \vec M \sqcap c\ \vec M$ which unifies under the empty substitution, so by assumption, $\DGE I \ok$ so $\SE m' \ok$.
\case{
\infer[\textsc{Write}\step]{\mwrite(T,\Delta, S,R,I,\ell^H,c,\vec \ell^H) \step
(T',[c\ \vec M/x]\Delta, \hup{S}{\ell^H}{c\args{\vec \ell^H}},R,[c\ \vec M/x]I)}
{\deduce{|{\vec \ell^H}| = \arity(c) \hskip0.1in \uptrail(T,x@\ell'^H:a) = T'\hskip0.1in\edn(S,\ell^H) = \ell'^H}
{S(\ell'^H) = \free{}[x : a] & \ell'^H \notin c\args{\vec \ell^H}}}}
By Lemma~\ref{lem:trail-up}, $[M/x]\Delta,\hup{S}{\ell'^H}{c\args{\vec \ell^H}}\ent T' \ok$.
Then by assumption, $\DPE \vec \ell^H : \sing(\vec M : \vec a)$ and $\Sigma(c) = \vec a \to a$ so $\DPE\func{c}{\vec \ell^H} :\sing(c\ \vec M : a)$. By assumption and Lemma~\ref{lem:end-corr}, $S(\ell'^H) = \free{}[x : a]$. The typing derivation for $J$ has the form
\[\infer[\sqcap\sigma]{\DGE I:_s (x \sqcap c\ \vec M)}{\DE x \sqcap c\ \vec M = \sigma & [\sigma]\Delta;[\sigma]\Gamma \ent [\sigma]I \ok}\]
By inversion, $\sigma = [c\ \vec M/x]$. Therefore $[c\ \vec M/x]\Delta;[c\ \vec M/x]\Gamma \ent [c\ \vec M/x]I \ok$ so
it suffices to show $\DE \hup{S}{\ell^H}{c\args{\vec \ell^H}} : (\Xi;[c\ \vec M/x]\Psi)$ which it does by Lemma~\ref{lem:heap-update}.
\case{\infer[\textsc{UnifyVar}\step\textsc{R}]{\mread(T,\Delta, S,R,(\unifyvar r, x:a. I), \vec \ell^H) \step
\mread(T,\Delta, S,R,I,(\vec \ell^H::w))}{R(r) = w}}
By inversion, $\Gamma(r) = \sing(M:a)$ so by Lemma~\ref{lem:subst}, $\DGE [M/x]I :_s [M/x]J$ and $\SE m' \ok$.
\case{\infer[\textsc{UnifyVal}\step\textsc{R}]{\mread(T,\Delta, S,R,(\unifyval r, x:a. I), (\ell^H::\vec \ell^H)) \step
\mread(T',\Delta', S',R,I, \vec \ell^H)}
{R(r) = \ell'^H & \unify(\Delta,S,T,\ell^H,\ell'^H) = (\Delta',S',T')}}
By assumption $\DE x \sqcap M = \sigma$ for some $\sigma = [M/x]$. By Lemma~\ref{lem:unify-sound}, $\Delta' \ent S' : (\Xi;\Psi')$ and $\Delta';S'\ent T' \ok$.
By Lemma~\ref{lem:subst}, $\DGE [M/x]I : [M/x]J$.
We now also have $\DE \vec \ell^H \reads \Pi \vec x : \vec A. (c\ \vec M\ M\ \vec x' \sqcap c\ \vec M\ M\ \vec M'')$ as desired, so $\SE m' \ok$.
\vspace{0.1in}
\case{
\infer[\textsc{UnifyVar}\step\textsc{W}]{\deduce{\mwrite(T,(x:a,\Delta), \hext{S}{\ell^H}{\free{}[x:a]},\hup{R}{r}{\ell^H},I,c,\ell^H_d,(\vec \ell^H::\ell^H))}{\mwrite(T,\Delta, S,R,(\unifyvar r, x:a. I),c,\ell^H_d,\vec \ell^H) \step}
}{}}
By Lemma~\ref{lem:trail-up}, $\Delta,x:a;\hext{S}{\ell^H}{\free{}[x:a]}\ent T \ok$. Let $\mu' = ((x@\ell^H:a),::\mu)$. Now $\SE ((\Delta,x:a),((x@\ell^H:a)::\mu)) : \hext{H}{\ell^H}{\free{}[x:a]}$.
Take $\vec a_1, \vec a_2$ from the derivation $\DPE (\vec \ell^H, \ell^H_d, c) \writes \Pi \vec x:\vec \tau.(M_1\sqcap M_2)$. Note $\vec a_2$ has form $a,\vec a_2'$.
Let $\vec a_1' = (\vec a_1::a')$. Now $(\Delta, x:a);\thext{\Psi}{\ell^H}{\free{}[x : a]} \ent (\vec \ell^H, \ell^H) : \vec a_1'$
so $\SE m' \ok$.
\case{{\small\infer[\textsc{UnivyVal}\step\textsc{W}]{\mwrite(T,\Delta, S,R,(\unifyval r, x:a. I),c,\ell^H_d,\vec \ell^H) \step
\mwrite(T,\Delta, S,R,I,c,\ell^H_d,(\vec \ell^H::\ell^H))}{R(r) = \ell^H}}}
Take $\vec a_1, \vec a_2$ from the derivation $\DPE (\vec \ell^H, \ell^H_d, c) \writes \Pi \vec x:\vec \tau.(M_1\sqcap M_2)$. Note $\vec a_2$ has form $a',\vec a_2'$.
Let $\vec a_1' = (\vec a_1,a')$. Now $\DPE (\vec \ell^H, \ell^H) : \vec a_1'$
so $\SE m' \ok$.
\end{proof}
\subsection{Operands, {\tt mov} and Tail Calls}
\label{sec:tco}
Now that we have proven TWAM sound, we illustrate its optimization potential
by describing our implementation of tail-call optimization (TCO), a common and
performance-critical optimization. We take as an example the predicate $f$:
\begin{verbatim}
f : t -> prop.
f(X) :- g(X).
\end{verbatim}
where the definition of $g$ is irrelevant. In our LF translation, this predicate has
one proof term constructor: \verb|F-X:|$\Pi$\verb| X:t.|$\Pi$\verb|D:g X.f X|.
If we compile this program na\"{i}vely, it would produce the following code:
\begin{exmp}[Before Tail-Call Optimization]
\label{ex:before-tco}~\\
\verb+f_main +$\mapsto$\verb+ code[X:nat. {r1:+$\sing(X)$\verb+, r2: +$\Pi D\colon{}f\ X.\ \neg$\verb+{}}(+\\
\verb+ +$\lambda X\colon{}nat.$\\
\verb+ mov f_tail, r2;+\\
\verb+ jmp (g X)+\\
\verb+),+
\verb+# The following code value should not be necessary+\\
\verb+f_tail +$\mapsto$\verb+ code[X:nat, D:g X. {r1:+$\sing(X)$\verb+, r2: +$\Pi D\colon{}f\ X.\ \neg$\verb+{}}(+\\
\verb+ +$\lambda X\colon{}nat, D\colon{}g\ X.$\\
\verb+ jmp (r2 (F-X D))+\\
\verb+)+
\end{exmp}
The problem is that to find a proof of \verb|f X| we must first find a proof \verb|D : g X| and then apply \verb|F-X X D|.
Because \verb|F-X| uses \verb|D| we must apply it after \verb|g| has succeeded,
which means we must apply it in \verb|g|'s success continuation.
This is a problem: \verb|g| is supposed to be a tail call, so its success continuation should be
the one passed to \verb|f|.
Since LF proofs are completely unnecessary at runtime, our ideal solution would be no-op of sorts:
an instruction that allows us to perform simple proof steps in LF, but which can
trivially be deleted after typechecking to avoid any runtime cost. This no-op is easily expressed
as a special case of the \verb+mov+ instruction. The following
\verb+mov+ instruction takes the success continuation and pre-composes an LF term that converts
proofs of \verb|g X| into proofs of \verb|f X| as needed by the continuation.
\begin{exmp}[After Tail-Call Optimization]\label{ex:aften-tco}~\\
\verb+f_main +$\mapsto$\verb+ code[X:t.{r1 :+$\Pi$\verb+D : f X.+$\neg$\verb+{}, r2 : +$\sing($\verb+X+$)$\verb+}](+\\
\verb+ +$\lambda$\verb+X:t.+\\
\verb+ mov r1 (+$\lambda$\verb+ D: g X. r1 (f/X X D));+\\
\verb+ jmp (g X)+\\
\verb+)+
\end{exmp}
\section{Implementation}
The full source code for our compiler implementation is available at \\\verb+http://www.cs.cmu.edu/~bbohrer/pub/twam.zip+, along with
a small test suite. The compiler consists of approximately 5000 lines of Standard ML, and has the following phases:
\begin{itemize}
\item Parsing and Elaboration: T-Prolog is parsed with {\tt ML-Lex} and {\tt ML-Yacc}, then check T-Prolog types.
\item Flattening: Terms with nested constructors are flattened.
\item Main Translation: Generates a variant of TWAM where failure continuations are stored inline.
\item Hoisting: Lifts failure continuations to the top level.
\item Certification: Runs the TWAM typechecker on hoisted code. On failure, signals a compile error.
\item Type Erasure: Trivial conversion from TWAM code to SWAM code.
\item Rechecking: As a sanity check, type-check the SWAM code.If this fails, signals a compiler error.
\item Interpretation: The SWAM code is interpreted, following the operational semantics.
\end{itemize}
The primary goal of this implementation, which it achieved, was to validate the design of TWAM,
especially to show that it is expressive enough to support an interesting source language.
For this reason, we intentionally omitted most optimizations except tail-call optimization, which we deemed too essential to ignore.
That being said, there are a number of avenues available to build a compiler with more competitive performance:
\begin{itemize}
\item Compile to machine code instead of interpreting TWAM code.
\item Replace our trivial register allocator with an efficient (e.g. graph-coloring-based) one.
\item Implement existing WAM optimizations (e.g. optimized switch statements).
\item
Investigate the cost of continuation-passing style.
Implement optimizations to reduce the number of environments allocated, or develop a stack-based system should that be insufficient.
\item Reduce the use of the occurs check by adding a mode system.
\end{itemize}
Among these, the first two options can be implemented with no changes to the instruction set or type system,
and the third can be implemented by adding new instructions without modifying the existing instructions.
The final two optimizations are more fundamental in nature, requiring changes to existing instructions or changes that affect the entire type system.
\section{Conclusion}
We have designed and implemented a typed compiler for T-Prolog by first creating a \textit{certifying abstract machine} for logic programs, called the TWAM.
Our implementation demonstrates that the TWAM is expressive enough to use as a compilation target for real programs,
and that the implementation burden of TWAM is acceptable.
This implementation result supports our primary contributions: the development of the TWAM and its metatheory.
The metatheory shows that TWAM typechecking suffices to enable certifying compilation in theory, and our compiler shows it in practice.
Our work differs from previous work on Prolog compilation because
we are the first to take a typed compilation approach.
We have also produced a working compiler with a formal guarantee, whereas previous efforts stopped before implementing a compiler
\cite{Russinoff92averified,Borger95thewam---definition,Beierle92correctnessproof,Pusch96verificationof}.
Several optimizing compilers have been verified in proof assistants \cite{Leroy06formalcertification,cakeml} and some of them use
proof-producing compilation \cite{JFP14}, but these do not address logic programming languages.
Typed compilation is from our perspective an instance of certifying compilation\cite{necula1998design},
and proof-passing style specifically is a variant that allows us reason about semantic preservation.
Our type system relies on the logical framework LF \cite{Harper93aframework}, and
is inspired by other languages with dependent type systems \cite{Xi98dependenttypes}, though
the languages differ greatly. Our formalisms are inspired by
typed assembly languages, but we make major changes to provide stronger guarantees and support
logic programming \cite{Morrisett:1999:SFT:319301.319345}.
Future work includes developing a production-quality optimizing
compiler and runtime, including any changes to the core TWAM language
to enable greater efficiency. We also wish to extend our abstract
machine to support logic programming languages with advanced type
system features and investigate whether certifying abstract machines
can provide equally strong guarantees for non-logic programming languages.
\bibliographystyle{ACM-Reference-Format}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 3,666 |
Home — Essay Samples — Literature — Books — Desiree's Baby
Essays on Desiree's Baby
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AllBlack people Race Love Woman Racism White American White people Short story
The Rising Culture of Feminism in Desiree's Baby and the Story of an Hour by Kate Chopin
Desiree's Baby The Story of An Hour 1 Page
Feminist Qualities of the Late 1800's The two stories, Desiree's Baby, and The Story of an Hour, by Kate Choplin, both depict the rising culture of feminism that took place during the time period that they were written. The two very opposing stories show different...
The Importance of the Distinction of Social Class and Racial Stability in the South in Desiree's Baby, a Short Story by Kate Chopin
Desiree's Baby 1 Page
It is stories like this one that should have turned the southern racial and social structure on it's head. It should have forced the people who subscribed to these racist principles to ask themselves, how fundamental are the differences between black and white people if...
The Racial Profiling Desiree's Baby
Desiree's Baby Kate Chopin Racial Profiling 1 Page
Have you ever noticed that race plays a major part in some peoples lives? In the story, Desiree's Baby, you will see how race affects a relationship between the mother and father of a mixed baby. The protagonist is a white woman named Desiree who...
The Story of An Hour Essays The Yellow Wallpaper Essays Things Fall Apart Essays To Kill a Mockingbird Essays Brave New World Essays A Modest Proposal Essays All Quiet on The Western Front Essays Between The World and Me Essays Maus Essays As I Lay Dying Essays Fish Cheeks Essays Drown Essays The Divine Comedy Essays The Flowers Essays A Raisin in The Sun Essays Beowulf Essays George Orwell Essays Hamlet Essays Macbeth Essays Othello Essays Poetry Essays Ralph Waldo Emerson Essays Romeo and Juliet Essays Satire Essays The Crucible Essays Character Essays Antigone Essays Allegory Essays Langston Hughes Essays A Streetcar Named Desire Essays A Midsummer Night's Dream Essays A Doll's House Essays A Poison Tree Essays A Noiseless Patient Spider Essays A Man For All Seasons Essays
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The Great Gatsby Essays | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 8,275 |
If you have been betting small, and winning small money on fantasy football then you definitely have to pick free fantasy football picks and fulfill your fantasy of winning a lot of money. These free picks can assist you to choose the ideal amount to bet on the ideal player or team and rejoice jubilantly whenever you win most of your placed bets.
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Although fantasy football is fairly distinctive from professional football such as the NFL or even college football games, the final result ought to be the same, i.e. you should win money against your stake. Winning high amounts against small stakes is extremely difficult but yet achievable if you utilize the knowledge of experts to your favor. Pick these free picks and look at them carefully to check if you decide to do trust such picks. If your gut feeling and study points in the same direction then use these free picks while placing your bet. In the event the experts have predicted accurately, then this small stake is certain to get converted into huge winnings more often than not.
Many sites like GertGambell.net also offer betting systems free of charge and these basically have to be followed spanning a longer period of time in order to benefit from the full benefits by means of increased winnings. You should only download systems from trusted sites and follow them faithfully in order to reap the benefits. You can even cross-check your free picks by visiting other such websites to check if they also offer their picks on similar lines more bonuses.
If you wish to lift up your sagging fortunes and bet like a pro then you surely ought to enlist the help of experts and what better way to acheive it than to get such help totally free? All you need to do is to simply go online and get free fantasy football picks from any reputed site and start winning an increased amount of your placed bets. The predictions available from select sites are really accurate and you could certainly benefit from their expertise. | {
"redpajama_set_name": "RedPajamaC4"
} | 4,030 |
The was a conspiracy that took place in 866 and centered on the destruction of the main gate (Ōtenmon) of the of the Imperial Palace in Kyoto, Japan. This event is known to scholars today primarily based on the depiction of it in the narrative handscroll (emaki) called Ban Dainagon Ekotoba (The Picture-narrative of Great Minister Ban).
Minamoto no Makoto, a member of the powerful Minamoto clan, was accused by his political rival Tomo no Yoshio of having set the fire. However, Makoto had the support of the Daijō-daijin (Chancellor of the Realm) Fujiwara no Yoshifusa, and was cleared of the charges. Soon afterwards, however, a man claiming to have witnessed the event accused Tomo no Yoshio of setting the fire himself, along with his son. Yoshio was exiled to Izu.
This event, and Fujiwara no Yoshifusa's handling of it, served Yoshifusa well, politically. Many of those executed were his political rivals, and he found himself promoted to Regent (Sesshō) soon afterwards.
References
Mills, Douglas E (1985). "Ōtemmon Conspiracy". Kodansha Encyclopedia of Japan. Tokyo: Kodansha Ltd.
866
9th century in Japan | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,528 |
function carregaCicloAscaris() {
// Criando um aliase de scene[0].item
var item = scene[0].item;
// Adicionando o aluno
item.estTomateNormal = new Game.Item("estHngrSdv.png");
item.estTomateNormal.setPosition(940, 590);
item.estTomateNormal.setZorder(11);
item.estTomateNormal.setBrightness(220);
item.estTomateNormal.onMouseOver = function() {
item.estTomateNormal.setBrightness(255);
scene[0].setSubtitle("Ascaridíase");
item.popupFlores.disable();
item.popupFloresTexto.disable();
}
item.estTomateNormal.onMouseOut = function() {
item.estTomateNormal.setBrightness(220);
scene[0].setSubtitle("");
}
item.estTomateNormal.onClick = function() {
somClique();
item.popupLivro.disable();
item.popupLivroTexto.disable();
var currentTime = 0;
var animationInterval = 500; // Intervalo entre cada animacao
item.popupFlores.disable();
item.popupFloresTexto.disable();
// Fadeout unrelated images
scene[0].background.changeBrightness(100, 600);
item.carteiras.changeBrightness(100, 600);
item.mesaProfessor.changeBrightness(100, 600);
item.caixaDeAreia.changeBrightness(100, 600);
item.vasoDeFlores.changeBrightness(100, 600);
item.livro.changeBrightness(100, 600);
item.microscopio.changeBrightness(100, 600);
item.estBananaNormal.changeBrightness(100, 600);
item.estPernNormal.changeBrightness(100, 600);
item.estGatoNormal.changeBrightness(100, 600);
item.setaJanela.changeAlpha(0, 600);
item.setaArmario.changeAlpha(0, 600);
item.estBananaNormal.setInteractive(false);
item.estPernNormal.setInteractive(false);
item.estGatoNormal.setInteractive(false);
item.estTomateNormal.setInteractive(false);
item.setaJanela.setInteractive(false);
item.setaArmario.setInteractive(false);
item.caixaDeAreia.setInteractive(false);
item.vasoDeFlores.setInteractive(false);
item.livro.setInteractive(false);
item.microscopio.setInteractive(false);
item.bananaRegion.setInteractive(false);
setTimeout(function() {
scene[0].setSubtitle("");
item.setaJanela.disable();
item.setaArmario.disable();
}, currentTime += animationInterval);
setTimeout(function() {
item.estTomateNormal.changeAlpha(0, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.estTomateNormal.disable();
item.estTomateCiclo.enable();
item.estTomateCiclo.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateElem1.enable();
item.tomateElem1.changeAlpha(1, 600);
item.tomateNum1.enable();
item.tomateNum1.changeAlpha(1, 600);
item.tomateSetaElem1Est.enable();
item.tomateSetaElem1Est.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateElem2.enable();
item.tomateElem2.changeAlpha(1, 600);
item.tomateNum2.enable();
item.tomateNum2.changeAlpha(1, 600);
item.tomateSetaElem2Est.enable();
item.tomateSetaElem2Est.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateSetaEstElem3a.enable();
item.tomateSetaEstElem3a.changeAlpha(1, 600);
item.tomateElem3a.enable();
item.tomateElem3a.changeAlpha(1, 600);
item.tomateNum3.enable();
item.tomateNum3.changeAlpha(1, 600);
item.tomateSetaElem3aElem3b.enable();
item.tomateSetaElem3aElem3b.changeAlpha(1, 600);
item.tomateSetaElem3aElem3c.enable();
item.tomateSetaElem3aElem3c.changeAlpha(1, 600);
item.tomateSetaElem3aElem3d.enable();
item.tomateSetaElem3aElem3d.changeAlpha(1, 600);
item.tomateElem3b.enable();
item.tomateElem3b.changeAlpha(1, 600);
item.tomateElem3c.enable();
item.tomateElem3c.changeAlpha(1, 600);
item.tomateElem3d.enable();
item.tomateElem3d.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateSetaElem4Est.enable();
item.tomateSetaElem4Est.changeAlpha(1, 600);
item.tomateNum4.enable();
item.tomateNum4.changeAlpha(1, 600);
item.tomateElem4.enable();
item.tomateElem4.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateSetaEstElem5.enable();
item.tomateSetaEstElem5.changeAlpha(1, 600);
item.tomateNum5.enable();
item.tomateNum5.changeAlpha(1, 600);
item.tomateElem5.enable();
item.tomateElem5.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateSetaElem5Elem6.enable();
item.tomateSetaElem5Elem6.changeAlpha(1, 600);
item.tomateElem6.enable();
item.tomateElem6.changeAlpha(1, 600);
item.tomateNum6.enable();
item.tomateNum6.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
item.tomateFechar.enable();
item.tomateFechar.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
enableInteractiveness();
}, currentTime += animationInterval);
}
var itensTomateCiclo = [];
// Imagens ciclo
item.estTomateCiclo = new Game.Image("estHngrClo.png");
item.estTomateCiclo.setPosition(900, 550);
item.estTomateCiclo.setScale(0.5);
item.estTomateCiclo.setZorder(9);
item.estTomateCiclo.setAlpha(0);
item.estTomateCiclo.disable();
itensTomateCiclo.push(item.estTomateCiclo);
item.tomateElem1 = new Game.Item("ovoAscaris.png");
item.tomateElem1.setPosition(450, 250);
item.tomateElem1.setScale(0.58);
item.tomateElem1.setZorder(6);
item.tomateElem1.setAlpha(0);
item.tomateElem1.disable();
item.tomateElem1.onMouseOver = function() {
scene[0].setSubtitle("Ovo de <i>Ascaris lumbricoides</i>");
}
item.tomateElem1.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem1);
item.tomateNum1 = new Game.Text("1", estiloNumeros);
item.tomateNum1.setAnchor(0.5, 0.6);
item.tomateNum1.setPosition(620, 120);
item.tomateNum1.setAlpha(0);
item.tomateNum1.disable();
itensTomateCiclo.push(item.tomateNum1);
item.tomateSetaElem1Est = new Game.Line(450, 250, 830, 440, 4);
item.tomateSetaElem1Est.setColor(0, 0, 0);
item.tomateSetaElem1Est.setZorder(7);
item.tomateSetaElem1Est.setAlpha(0);
item.tomateSetaElem1Est.disable();
itensTomateCiclo.push(item.tomateSetaElem1Est);
item.tomateElem2 = new Game.Item("ascarisFilhote.png");
item.tomateElem2.setPosition(380, 550);
item.tomateElem2.setScale(0.47);
item.tomateElem2.setZorder(6);
item.tomateElem2.setAlpha(0);
item.tomateElem2.disable();
item.tomateElem2.onMouseOver = function() {
scene[0].setSubtitle("Verme jovem de <i>Ascaris lumbricoides</i>");
}
item.tomateElem2.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem2);
item.tomateNum2 = new Game.Text("2", estiloNumeros);
item.tomateNum2.setAnchor(0.5, 0.6);
item.tomateNum2.setPosition(290, 420);
item.tomateNum2.setAlpha(0);
item.tomateNum2.disable();
itensTomateCiclo.push(item.tomateNum2);
item.tomateSetaElem2Est = new Game.Line(380, 550, 897, 721, 4);
item.tomateSetaElem2Est.setColor(0, 0, 0);
item.tomateSetaElem2Est.setZorder(7);
item.tomateSetaElem2Est.setAlpha(0);
item.tomateSetaElem2Est.disable();
itensTomateCiclo.push(item.tomateSetaElem2Est);
item.tomateSetaEstElem3a = new Game.Line(900, 600, 1300, 300, 4);
item.tomateSetaEstElem3a.setColor(0, 0, 0);
item.tomateSetaEstElem3a.setZorder(7);
item.tomateSetaEstElem3a.setAlpha(0);
item.tomateSetaEstElem3a.disable();
itensTomateCiclo.push(item.tomateSetaEstElem3a);
item.tomateElem3a = new Game.Item("circulacao.png");
item.tomateElem3a.setPosition(1300, 300);
item.tomateElem3a.setScale(0.57);
item.tomateElem3a.setZorder(6);
item.tomateElem3a.setAlpha(0);
item.tomateElem3a.disable();
item.tomateElem3a.onMouseOver = function() {
scene[0].setSubtitle("Migração do verme para a circulação sanguínea");
}
item.tomateElem3a.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem3a);
item.tomateNum3 = new Game.Text("3", estiloNumeros);
item.tomateNum3.setAnchor(0.5, 0.6);
item.tomateNum3.setPosition(1430, 180);
item.tomateNum3.setAlpha(0);
item.tomateNum3.disable();
itensTomateCiclo.push(item.tomateNum3);
item.tomateSetaElem3aElem3b = new Game.Line(1300, 300, 1520, 200, 4);
item.tomateSetaElem3aElem3b.setColor(0, 0, 0);
item.tomateSetaElem3aElem3b.addArrowAtEnd();
item.tomateSetaElem3aElem3b.setZorder(7);
item.tomateSetaElem3aElem3b.setAlpha(0);
item.tomateSetaElem3aElem3b.disable();
itensTomateCiclo.push(item.tomateSetaElem3aElem3b);
item.tomateSetaElem3aElem3c = new Game.Line(1300, 300, 1570, 360, 4);
item.tomateSetaElem3aElem3c.setColor(0, 0, 0);
item.tomateSetaElem3aElem3c.addArrowAtEnd();
item.tomateSetaElem3aElem3c.setZorder(7);
item.tomateSetaElem3aElem3c.setAlpha(0);
item.tomateSetaElem3aElem3c.disable();
itensTomateCiclo.push(item.tomateSetaElem3aElem3c);
item.tomateSetaElem3aElem3d = new Game.Line(1300, 300, 1470, 450, 4);
item.tomateSetaElem3aElem3d.setColor(0, 0, 0);
item.tomateSetaElem3aElem3d.addArrowAtEnd();
item.tomateSetaElem3aElem3d.setZorder(7);
item.tomateSetaElem3aElem3d.setAlpha(0);
item.tomateSetaElem3aElem3d.disable();
itensTomateCiclo.push(item.tomateSetaElem3aElem3d);
item.tomateElem3b = new Game.Item("coracao.png");
item.tomateElem3b.setPosition(1630, 170);
item.tomateElem3b.setScale(0.35);
item.tomateElem3b.setZorder(6);
item.tomateElem3b.setAlpha(0);
item.tomateElem3b.disable();
item.tomateElem3b.onMouseOver = function() {
scene[0].setSubtitle("Migração para o coração");
}
item.tomateElem3b.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem3b);
item.tomateElem3c = new Game.Item("figado.png");
item.tomateElem3c.setPosition(1670, 370);
item.tomateElem3c.setScale(0.32);
item.tomateElem3c.setZorder(6);
item.tomateElem3c.setAlpha(0);
item.tomateElem3c.disable();
item.tomateElem3c.onMouseOver = function() {
scene[0].setSubtitle("Migração para o fígado");
}
item.tomateElem3c.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem3c);
item.tomateElem3d = new Game.Item("pulmao.png");
item.tomateElem3d.setPosition(1550, 530);
item.tomateElem3d.setScale(0.35);
item.tomateElem3d.setZorder(6);
item.tomateElem3d.setAlpha(0);
item.tomateElem3d.disable();
item.tomateElem3d.onMouseOver = function() {
scene[0].setSubtitle("Migração para o pulmão");
}
item.tomateElem3d.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem3d);
item.tomateSetaElem4Est = new Game.Line(420, 850, 886, 751, 4);
item.tomateSetaElem4Est.setColor(0, 0, 0);
item.tomateSetaElem4Est.setZorder(7);
item.tomateSetaElem4Est.setAlpha(0);
item.tomateSetaElem4Est.disable();
itensTomateCiclo.push(item.tomateSetaElem4Est);
item.tomateNum4 = new Game.Text("4", estiloNumeros);
item.tomateNum4.setAnchor(0.5, 0.6);
item.tomateNum4.setPosition(540, 720);
item.tomateNum4.setAlpha(0);
item.tomateNum4.disable();
itensTomateCiclo.push(item.tomateNum4);
item.tomateElem4 = new Game.Item("ascarisMF.png");
item.tomateElem4.setPosition(420, 850);
item.tomateElem4.setScale(0.51);
item.tomateElem4.setZorder(6);
item.tomateElem4.setAlpha(0);
item.tomateElem4.disable();
item.tomateElem4.onMouseOver = function() {
scene[0].setSubtitle("Macho e fêmea de vermes adultos de <i>A. lumbricoides</i>");
}
item.tomateElem4.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem4);
item.tomateSetaEstElem5 = new Game.Line(870, 815, 1165, 790, 4);
item.tomateSetaEstElem5.setColor(0, 0, 0);
item.tomateSetaEstElem5.addArrowAtEnd();
item.tomateSetaEstElem5.setZorder(7);
item.tomateSetaEstElem5.setAlpha(0);
item.tomateSetaEstElem5.disable();
itensTomateCiclo.push(item.tomateSetaEstElem5);
item.tomateNum5 = new Game.Text("5", estiloNumeros);
item.tomateNum5.setAnchor(0.5, 0.6);
item.tomateNum5.setPosition(1400, 680);
item.tomateNum5.setAlpha(0);
item.tomateNum5.disable();
itensTomateCiclo.push(item.tomateNum5);
item.tomateElem5 = new Game.Item("fezesSemMosca.png");
item.tomateElem5.setPosition(1300, 800);
item.tomateElem5.setScale(0.44);
item.tomateElem5.setZorder(6);
item.tomateElem5.setAlpha(0);
item.tomateElem5.disable();
item.tomateElem5.onMouseOver = function() {
scene[0].setSubtitle("Fezes contendo ovos de <i>A. lumbricoides</i>");
}
item.tomateElem5.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem5);
item.tomateSetaElem5Elem6 = new Game.Line(1300, 800, 1700, 800, 4);
item.tomateSetaElem5Elem6.setColor(0, 0, 0);
item.tomateSetaElem5Elem6.setZorder(7);
item.tomateSetaElem5Elem6.setAlpha(0);
item.tomateSetaElem5Elem6.disable();
itensTomateCiclo.push(item.tomateSetaElem5Elem6);
item.tomateElem6 = new Game.Item("ovoAscaris.png");
item.tomateElem6.setPosition(1700, 800);
item.tomateElem6.setScale(0.5);
item.tomateElem6.setZorder(6);
item.tomateElem6.setAlpha(0);
item.tomateElem6.disable();
item.tomateElem6.onMouseOver = function() {
scene[0].setSubtitle("Ovo de <i>A. lumbricoides</i>");
}
item.tomateElem6.onMouseOut = function() {
scene[0].setSubtitle("");
}
itensTomateCiclo.push(item.tomateElem6);
item.tomateNum6 = new Game.Text("6", estiloNumeros);
item.tomateNum6.setAnchor(0.5, 0.6);
item.tomateNum6.setPosition(1820, 680);
item.tomateNum6.setAlpha(0);
item.tomateNum6.disable();
itensTomateCiclo.push(item.tomateNum6);
item.tomateFechar = new Game.Item("botaoFechar.png");
item.tomateFechar.setPosition(1840, 70);
item.tomateFechar.setRotation(180);
item.tomateFechar.setBrightness(200);
item.tomateFechar.setScale(0.14);
item.tomateFechar.setZorder(1);
item.tomateFechar.setAlpha(0);
item.tomateFechar.disable();
item.tomateFechar.onMouseOver = function() {
item.tomateFechar.setBrightness(255);
}
item.tomateFechar.onMouseOut = function() {
item.tomateFechar.setBrightness(200);
}
item.tomateFechar.onClick = function(mouse) {
disableInteractiveness();
somClique();
var currentTime = 0;
var animationInterval = 750; // Intervalo entre cada animacao
groupChangeAlpha(itensTomateCiclo, 0, 600);
setTimeout(function() {
groupDisable(itensTomateCiclo);
scene[0].setSubtitle("");
item.tomateFechar.setBrightness(200);
item.estTomateDoente.enable();
item.estTomateDoente.changeAlpha(1, 600);
}, currentTime += animationInterval);
setTimeout(function() {
groupDisable(itensTomateCiclo);
item.tomateBalaoSintoma.enable();
item.tomateBalaoSintoma.changeAlpha(1, 600);
item.tomateTextoSintomas.enable();
item.tomateTextoSintomas.changeAlpha(1, 600);
item.tomateAbaPrevencao.enable();
item.tomateAbaPrevencao.changeAlpha(1, 600);
item.tomateAbaTransmissao.enable();
item.tomateAbaTransmissao.changeAlpha(1, 600);
item.tomateBotaoOK.enable();
item.tomateBotaoOK.changeAlpha(1, 600);
item.tomateBalaoPrevencao.setAlpha(1);
item.tomateBalaoTransmissao.setAlpha(1);
item.tomateAbaSintomas.setAlpha(1);
item.tomateBotaoOKhover.setAlpha(1);
item.tomateTextoPrevencao.setAlpha(1);
item.tomateTextoTransmissao.setAlpha(1);
}, currentTime += animationInterval);
setTimeout(function() {
enableInteractiveness();
}, currentTime += animationInterval);
}
itensTomateCiclo.push(item.tomateFechar);
var itensTomateDoente = [];
item.estTomateDoente = new Game.Image("estHngrDte.png");
item.estTomateDoente.setPosition(960, 550);
item.estTomateDoente.setZorder(11);
item.estTomateDoente.setAlpha(0);
item.estTomateDoente.disable();
itensTomateDoente.push(item.estTomateDoente);
item.tomateBalaoSintoma = new Game.Image("balSintEsq.png");
item.tomateBalaoSintoma.setPosition(730-260, 300);
item.tomateBalaoSintoma.setScale(0.25);
item.tomateBalaoSintoma.setZorder(6);
item.tomateBalaoSintoma.setAlpha(0);
item.tomateBalaoSintoma.disable();
itensTomateDoente.push(item.tomateBalaoSintoma);
item.tomateBalaoPrevencao = new Game.Image("balPrevEsq.png");
item.tomateBalaoPrevencao.setPosition(730-260, 300);
item.tomateBalaoPrevencao.setScale(0.25);
item.tomateBalaoPrevencao.setZorder(6);
item.tomateBalaoPrevencao.disable();
itensTomateDoente.push(item.tomateBalaoPrevencao);
item.tomateBalaoTransmissao = new Game.Image("balTranEsq.png");
item.tomateBalaoTransmissao.setPosition(730-260, 300);
item.tomateBalaoTransmissao.setScale(0.25);
item.tomateBalaoTransmissao.setZorder(6);
item.tomateBalaoTransmissao.disable();
itensTomateDoente.push(item.tomateBalaoTransmissao);
item.tomateAbaSintomas = new Game.Item("abaSint.png");
item.tomateAbaSintomas.setPosition(432-260, 71);
item.tomateAbaSintomas.setScale(0.25);
item.tomateAbaSintomas.setZorder(7);
item.tomateAbaSintomas.disable();
item.tomateAbaSintomas.onClick = function() {
somClique();
item.tomateBalaoSintoma.enable();
item.tomateBalaoPrevencao.disable();
item.tomateBalaoTransmissao.disable();
item.tomateAbaSintomas.disable();
item.tomateAbaPrevencao.enable();
item.tomateAbaTransmissao.enable();
item.tomateTextoSintomas.enable();
item.tomateTextoPrevencao.disable();
item.tomateTextoTransmissao.disable();
}
itensTomateDoente.push(item.tomateAbaSintomas);
item.tomateTextoSintomas = new Game.Text(
"- Ação espoliadora: subnutrição;\n" +
"- Ação tóxica: edema, urticária e convulsões;\n" +
"- Ação mecânica: irritação na pele, obstrução intestinal."
, estiloInfoBalao);
item.tomateTextoSintomas.setPosition(432-130-260, 58+20);
item.tomateTextoSintomas.setAlpha(0);
item.tomateTextoSintomas.disable();
itensTomateDoente.push(item.tomateTextoSintomas);
item.tomateAbaPrevencao = new Game.Item("abaPrev.png");
item.tomateAbaPrevencao.setPosition(432+486-260, 71);
item.tomateAbaPrevencao.setScale(0.25);
item.tomateAbaPrevencao.setZorder(9);
item.tomateAbaPrevencao.setAlpha(0);
item.tomateAbaPrevencao.disable();
item.tomateAbaPrevencao.onClick = function() {
somClique();
item.tomateBalaoSintoma.disable();
item.tomateBalaoPrevencao.enable();
item.tomateBalaoTransmissao.disable();
item.tomateAbaSintomas.enable();
item.tomateAbaPrevencao.disable();
item.tomateAbaTransmissao.enable();
item.tomateTextoSintomas.disable();
item.tomateTextoPrevencao.enable();
item.tomateTextoTransmissao.disable();
}
itensTomateDoente.push(item.tomateAbaPrevencao);
item.tomateTextoPrevencao = new Game.Text(
"- Ingerir água tratada;\n" +
"- Lavar bem frutas e legumes;\n" +
"- Não defecar em locais inapropriados;\n" +
"- Saneamento básico."
, estiloInfoBalao);
item.tomateTextoPrevencao.setPosition(432-130-260, 58+20);
item.tomateTextoPrevencao.disable();
itensTomateDoente.push(item.tomateTextoPrevencao);
item.tomateAbaTransmissao = new Game.Item("abaTran.png");
item.tomateAbaTransmissao.setPosition(432+232-260, 71);
item.tomateAbaTransmissao.setScale(0.25);
item.tomateAbaTransmissao.setZorder(8);
item.tomateAbaTransmissao.setAlpha(0);
item.tomateAbaTransmissao.disable();
item.tomateAbaTransmissao.onClick = function() {
somClique();
item.tomateBalaoSintoma.disable();
item.tomateBalaoPrevencao.disable();
item.tomateBalaoTransmissao.enable();
item.tomateAbaSintomas.enable();
item.tomateAbaPrevencao.enable();
item.tomateAbaTransmissao.disable();
item.tomateTextoSintomas.disable();
item.tomateTextoPrevencao.disable();
item.tomateTextoTransmissao.enable();
}
itensTomateDoente.push(item.tomateAbaTransmissao);
item.tomateTextoTransmissao = new Game.Text(
"- Ingestão de água e alimentos contaminados;\n" +
"- Poeira, aves, insetos (moscas e baratas);\n" +
"- Irrigação de hortas com água contaminada."
, estiloInfoBalao);
item.tomateTextoTransmissao.setPosition(432-130-260, 58+20);
item.tomateTextoTransmissao.disable();
itensTomateDoente.push(item.tomateTextoTransmissao);
item.tomateBotaoOK = new Game.Item("okNormal.png");
item.tomateBotaoOK.setScale(0.25);
item.tomateBotaoOK.setPosition(432+450-260, 71+290);
item.tomateBotaoOK.setAlpha(0);
item.tomateBotaoOK.disable();
item.tomateBotaoOK.onMouseOver = function() {
item.tomateBotaoOK.disable();
item.tomateBotaoOKhover.enable();
}
item.tomateBotaoOK.onClick = function() {
item.tomateBotaoOKhover.onClick();
}
itensTomateDoente.push(item.tomateBotaoOK);
item.tomateBotaoOKhover = new Game.Item("okHover.png");
item.tomateBotaoOKhover.setScale(0.25);
item.tomateBotaoOKhover.setPosition(432+450-260, 71+290);
item.tomateBotaoOKhover.disable();
item.tomateBotaoOKhover.onMouseOut = function() {
item.tomateBotaoOKhover.disable();
item.tomateBotaoOK.enable();
}
item.tomateBotaoOKhover.onClick = function() {
disableInteractiveness();
somClique();
var currentTime = 0;
var animationInterval = 750; // Intervalo entre cada animacao
groupChangeAlpha(itensTomateDoente, 0, 600);
setTimeout(function() {
item.estTomateNormal.enable();
item.estTomateNormal.setBrightness(220);
item.estTomateNormal.changeAlpha(1, 600);
scene[0].background.changeBrightness(210, 600);
item.carteiras.changeBrightness(210, 600);
item.mesaProfessor.changeBrightness(210, 600);
item.caixaDeAreia.changeBrightness(210, 600);
item.vasoDeFlores.changeBrightness(210, 600);
item.livro.changeBrightness(210, 600);
item.microscopio.changeBrightness(210, 600);
item.estBananaNormal.changeBrightness(210, 600);
item.estPernNormal.changeBrightness(210, 600);
item.estGatoNormal.changeBrightness(210, 600);
item.setaJanela.enable();
item.setaArmario.enable();
item.setaJanela.changeAlpha(1, 600);
item.setaArmario.changeAlpha(1, 600);
item.tomateBotaoOKhover.disable();
item.tomateBalaoPrevencao.disable();
item.tomateBalaoTransmissao.disable();
item.tomateAbaSintomas.disable();
item.tomateAbaPrevencao.disable();
item.tomateAbaTransmissao.disable();
item.tomateTextoPrevencao.disable();
item.tomateTextoTransmissao.disable();
}, currentTime += animationInterval);
setTimeout(function() {
item.estBananaNormal.setInteractive(true);
item.estPernNormal.setInteractive(true);
item.estGatoNormal.setInteractive(true);
item.estTomateNormal.setInteractive(true);
item.setaJanela.setInteractive(true);
item.setaArmario.setInteractive(true);
item.caixaDeAreia.setInteractive(true);
item.vasoDeFlores.setInteractive(true);
item.livro.setInteractive(true);
item.microscopio.setInteractive(true);
item.bananaRegion.setInteractive(true);
enableInteractiveness();
}, currentTime += animationInterval);
}
itensTomateDoente.push(item.tomateBotaoOKhover);
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,920 |
{"url":"https:\/\/rdrr.io\/github\/neuroconductor-devel\/DensParcorr\/man\/DensParcorr.html","text":"# DensParcorr: Conduct the Dens-Based approach for partial correlation... In neuroconductor-devel\/DensParcorr: Dens-Based Method for Partial Correlation Estimation in Large Scale Brain Networks\n\n## Description\n\nThis function is to conduct the Dens-based approach for partial correlation estimation in large scale brain network study.\nDensParcorr is the main function in this package. prec2dens and prec2part are sub-functions called by DensParcorr.\n\n## Usage\n\n 1 2 DensParcorr(data,select=FALSE,dens.level=\"plateau\",plateau.thresh=0.01, Parcorr.est=NULL,directory=NULL) \n\n## Arguments\n\n data Input data matrix with dimension of TxM where T is the number of observations and M is the number of nodes. For example, in fMRI data the T is the number of scans. select Whether to conduct the Dens-based selection. If FALSE, output will only contain the estimated partial correlation list and precision matrix list corresponding to the default tuning parameter series ranging from 1e-8 to 0.6. If TRUE, the ouput will include the previous results and the selected partial correlation matrix and percision matrix corresponding to the specified density level. Default is FALSE. dens.level Specify the density level in Dens-based tuning parameter selection method, including the plateau based density selection (dens.level = \"plateau\") and p percentage density selection (dens.level = p, 0\n\n## Details\n\nThis function implements the statistical method proposed in Wang et al. (2016) to estimate partial correlation matrix for studying direct connectivity in large-scale brain network. The method derives partial correlation based on the precision matrix estimated via Constrained L1-minimization Approach (CLIME) (Cai et al., 2011). This function applies the Dens-based tuning parameter selection method in Wang et al. (2016) to help select an appropriate tuning parameter for sparsity control in the network estimation. Below is the breif step of Dens-based approach.\n\nFirst, we specify a series of tuning parameters {\u03bb_n}. Then, based on {\u03bb_n} we esimate a list of precision matices \u03a9(\u03bb_n) and and evaluate the density level of each precision matrix based on the Dens criterion function in equation (5) of Wang et al. (2016). This will provide the users the profile of the density level corresponding to the series of tuning parameters in {\u03bb_n}. Users can use the dens.level option to specify the desired density level in the precision matrix estimation. If dens.level=\"plateau\", the function will select the plateau point \u03bb_{platu} in the density profile based on the plateau.thresh and output the precision matrix \u03a9(\u03bb_{platu}). If dens.level=p and 0<p<1, the function will select the tuning parameter \u03bb_p to achieve p percentage density and output the precision matrix \u03a9(\u03bb_p). Then, the partial correlation matrix will be derived from the precision matrix. Further details can be found in the Reference.\n\nThe density profile and the heatmaps of precision matrices and partial correlation matrices will be saved in directory, and the esimated list of precision matrices and partial correlation matrices will also be saved in directory.\n\nWhen users would like to run the function multiple times on the same input data for different dens.level, it is computationally more efficient to read in the previous output from DensParcorr to Parcorr.est so that the function won't need to re-estimate the partial correlations based on the previous tuning parameters.\n\n## Value\n\nAn R list from DensParcorr containing the following terms:\n\n selected.partial.corr Selected Partial Correlation matrix corresponding to dens.level. Only when select=TRUE. selected.precision Selected Precision matrix corresponding to dens.level. Only when select=TRUE. selected.lambda Selected tuning parameter corresponding to dens.level. Only when select=TRUE. lambda.list The series of tuning parameters used for esimation and density profile. partial.corr.list Estimated Partial Correlation matrix list corresponding to lambda.list. precision.list Estimated Precision matrix list corresponding to lambda.list. Dens Actual density levels for estimated precision matrix list. Dens.Percentage Actual percentage density levels for estimated precision matrix list. selection.method The method used for tuning parameter selection. For percentage Dens selection, this value will include the actual Dens precentage and the nominal Dens percentage. Only when select=TRUE.\n\n## Author(s)\n\nYikai Wang, Jian Kang, Phebe Brenne Kemmer and Ying Guo\nMaintainer: Yikai Wang [email\u00a0protected]\n\n## References\n\nWang, Y., Kang, J., Kemmer P. and Guo, Y. (2016). An efficient and reliable statistical method for estimating functional connectivity in large scale brain networks using partial correlation. Front. Neurosci. 10:123. doi: 10.3389\/fnins.2016.00123\n\nCai, T.T., Liu, W., and Luo, X. (2011). A constrained \\ell_1 minimization approach for sparse precision matrix estimation. Journal of the American Statistical Association 106(494): 594-607.\n\n## Examples\n\n 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 # require(gplots) # require(clime) ## Simulated the data to use. # data = matrix(rnorm(200),ncol=20) ##### Example 1: Estimate the partial correlation matrices for the ##### default series of tuning parameters. # t0 = proc.time()[3] # dens.est = DensParcorr(data,select=FALSE) # proc.time()[3]-t0 ##### Example 2: Estimate the network that reaches 40% density level. # partial.dens.est = DensParcorr(data,dens.level =.4,select=TRUE) ###### Example 3: Now, estimate the 60% density level network based ###### on the same data. To speed up computation, we read in the ###### previous output from Example 2 into Parcorr.est # t0 = proc.time()[3] # partial.dens.est2 = DensParcorr(data, Parcorr.est = partial.dens.est, # dens.level=.6,select=TRUE) # proc.time()[3]-t0 \n\nneuroconductor-devel\/DensParcorr documentation built on Oct. 3, 2017, 8:06 p.m.","date":"2018-08-16 04:51:04","metadata":"{\"extraction_info\": {\"found_math\": true, \"script_math_tex\": 0, \"script_math_asciimath\": 0, \"math_annotations\": 0, \"math_alttext\": 0, \"mathml\": 0, \"mathjax_tag\": 0, \"mathjax_inline_tex\": 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\": 0.635613203048706, \"perplexity\": 2910.8533962830584}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-34\/segments\/1534221210413.14\/warc\/CC-MAIN-20180816034902-20180816054902-00084.warc.gz\"}"} | null | null |
{"url":"http:\/\/ceafel.tecnico.ulisboa.pt\/news\/ceafel-seminar-28\/","text":"# CEAFEL Seminar\n\nOn Friday, 18\/05\/2018, 15:00 \u2014 16:00, in Room P3.10 of Mathematics Building of the IST will take place a seminar by Olga Azenhas\u00a0(Universidade de Coimbra, CMUC) with title\n\n\u201cInvolutions for symmetries of Littlewood-Richardson (LR) coefficients\u201d.\n\nThe action of the dihedral group $\\mathbb Z_2\\times \\mathfrak{ S}_3$ on LR coefficients is considered with the action of $\\mathbb Z_2$ realized by the transposition of a partition. The action of $\\mathbb Z_2\\times\\mathfrak{ S}_3$ carries a linear time action of a subgroup $H$ of index two, and a bijection which goes from $H$ into the other coset is difficult. LR coefficients are preserved in linear time by the action of $H$ whereas the other half symmetries consisting of commutativity and transposition symmetries are hidden. The latter are given by a remaining generator, the reversal involution or Schutzenberger involution, by which one is able to reduce in linear time the LR commuters and LR transposers to each other.\n\nTo pass from symmetries of LR (skew) tableaux to symmetries of companion Gelfand-Tsetlin (GT) patterns we build on the crystal action of the longest permutation in the symmetric group on an LR tableau, and Lascoux\u2019s double crystal graph structure on biwords. This analysis also affords an explicit bijection between two of the interlocking GT patterns in a hive.\n\nThis is based on a joint work with A. Conflitti and R. Mamede.","date":"2018-09-26 07:02:20","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\": 0.8975703716278076, \"perplexity\": 1051.521338809474}, \"config\": {\"markdown_headings\": true, \"markdown_code\": false, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2018-39\/segments\/1537267163704.93\/warc\/CC-MAIN-20180926061824-20180926082224-00174.warc.gz\"}"} | null | null |
@interface CSStatusBarWindow : UIWindow {
UIView *informationBar;
NSInteger informationIndex;
}
- (void)addInformation:(NSString *)value;
- (void)setInformationBarHidden:(BOOL)hidden animated:(BOOL)animated;
- (void)showNextInformation:(BOOL)animated;
- (void)showPreviousInformation:(BOOL)animated;
- (void)showInformationAtIndex:(NSInteger)index animated:(BOOL)animated direction:(UISwipeGestureRecognizerDirection)direction;
- (void)addGitRef;
- (void)addGitDescription;
- (void)addBundleVersion;
- (void)addBundleShortVersionString;
@property (nonatomic, readwrite, getter = isInformationBarHidden) BOOL informationBarHidden;
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 2,260 |
Four Ways in Which Technology Is Transforming Sports
Published on : 12 August 2021 Published by : Paul
From plane propellers to mobile phones and computers, our world has seen mind-blowing technology packaged in varying sizes. These innovations exist in all spheres of human life, from healthcare to transportation, sports, and the delivery of goods and services. So much time is now being saved thanks to technological advancement.
Sporting activities have benefited immensely from the introduction of technology. Fans can now watch live games via mobile gadgets and TVs without being in the same country where the match is being played. Also, players and managers no longer have to haggle with referees over goals and ball outs, time records in races, or point counts in basketball.
Sports technology expert Kate Richardson analyses the uses and benefits of tech innovations in sports.
What Is Sports Technology?
Why Sports Technology?
Sport Technologies at Work
Sports technology refers to artificial scientific creations used to augment human experience in sports. Such creations include chips in a soccer ball, hawk-eye technology, ball sensors and live replays. Sports technology is built on the premise of reducing the referee or judge's margin for error in sports. By employing technological innovations in sports, these officials can make impartial considerations and ultimately make the right decision in dicey situations.
As a kid, you probably played football in the yard and argued for several minutes when your opponent cleared an apparent goal under the guise of goal-line clearance. Or maybe had a tiny margin separate you from the winner of a race, which made you doubtful of the judge's vision. These instances happen in professional sports too. Yet, judges and refs are humans with imperfect vision. To this end, it is essential to assist them to make confident and correct decisions via sports technology.
See also 5 Things to Consider Before Starting a Small Business
It is not precisely clear when technology was first introduced to sports. However, many sources believe that horse racing was the first sport to embrace technology. This was back in the 19th century when photo finishing was created. Photo finish equipment operates by taking photos of athletes at several points within the race to determine their positions. Athletics soon followed suit by introducing wearable chips to athletes clothing.
Now, timing systems, goal-line technology and video assistant refereeing are the modern sports technologies currently in use.
Technology has become an integral aspect of sports, helping athletes to compete fairly and without bias. The following are some of the ways sports organizers are using technological innovations to balance the competitive scale.
Sensors: Sensor tools are the most popular technology in sports. Sensor tools like goal-line technology in football help the referee to verify if the ball crossed the line. This way, match officials can determine the validity of each goal claim. Another example of sensors is in tennis, where the officials use hawk-eye technology to ascertain if the ball has gone out of bounds. Sensors generally transmit the position of the ball at given points during a game.
Live Replays: Live replays are the most notable sports technology in fans' books. Live replays give officials autonomy on the review of critical decisions during gameplay. These replays can be slowed down or switched to different angles to provide the referee with an encompassing view of the tackle, foul or dispute. This innovative technology is used in almost all modern sports games, including cricket, soccer, basketball, and combat sports. It is also the primary component in Video Assistant Refereeing (VAR) which is now widely used in soccer games.
Timing Technology: Ever wondered how athlete-specific times are recorded at IAAF events? The answer lies in timing technology. Usually, the clock begins ticking as the starter pistol goes off and records athlete movements to the hundredth of a second. Sometimes, you may see a mobile timer board near the finish line, which shows the time duration of the race's winner. Timing technology is also used in swimming competitions where swimmers wear inertial sensors and place their hands on a touchpad for personal time records.
RFID and Gear Development: In individual competitions such as marathons and other long-distance races, RFID chips are worn by athletes to track their exact location. These chips have built-in batteries and show when each participant crosses a specific line. As a result, you can tell how far away each athlete is from the finish line. Sports technology is also used in developing sports jerseys, helmets and boots. These gears are technologically enhanced to absorb impact shocks and to improve athlete safety. For instance, Formula One drivers wear fire-resistant clothing while NFL players put on special helmets to prevent concussions.
See also Top Tips for Finding the Best Bookkeeping Service
The benefits of sports technology are not limited to fair competition and athlete safety. It is also useful in analyzing betting tips on these sports. As sports technologies record these facts, bettors are able to access them from archives when considering what odds to pick. Betting companies also use the data generated from sports tech in algorithms when calculating the odds for each event.
In addition, some bookmakers now offer betting markets on whether VAR will be used in a match. Overall, technology has dramatically improved the experience of sports fans, particularly during the covid lockdown. When football clubs faced impending economic doom during the lockdown, sports technology rose to the occasion, offering broadcast revenue to cushion clubs' financial losses.
Several sports were able to go on, with fans watching live games online via streaming apps and broadcast stations. In this way, clubs were able to garner more revenue from merchandise and broadcast rights; fans too managed to stay in touch with the games without visiting stadiums. On the whole, the use of digital media and technology in sports grew in the past twelve months thanks to the pandemic as mankind turned to sports for entertainment. You can read more about technology in sports on this informative site.
History of the Joker Card
What To Do If You Have Been Involved in an Auto Accident? | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 1,516 |
The Social Network (Contains Spoilers)
I think by this point it's pretty safe to say that David Fincher is a dude who really knows what he's doing. He may not have as many Oscars as Scorsese, as many classics as Spielberg or as much money as Cameron, but his repertoire shows that he definitely has it together and is more than capable of creating pieces of cinema that are sure to make heads turn. Se7en, Fight Club, Zodiac – all of these have been incredibly tense and very intellectually challenging films, and The Social Network is no exception to this. Ironically enough, after seeing The Social Network I honestly couldn't wait to write a blog about it and express my opinions of it on a public medium!
The Social Network, I personally think, is one of the most intellectually entertaining films not just of this year, but of recent years as well. Pair that with the fact that, at its centre point, it is a piece about one of the most used, talked about and potentially dangerous inventions of recent years and you have a film that is GOING to cause a stir, no matter what! The partly true, partly fictional story of the Harvard University based creators of the social networking site Facebook (which you'd be hard-pressed to find someone NOT on it now!) sees Jesse Eisenberg playing the role of Mark Zuckerberg, the main geek-brained creator of the infamous networking website. Eisenberg does a fantastic job playing Mark as he is able to deliver all his lines with such a straight face and blank attitude that it's both believable and ironic in equal measures – believable because Eisenberg delivers all the computer jargon with such conviction you'd think he graduated from MIT, and ironic in the way that someone with such a lack of social interaction skills and emotional depth could create the world's largest and most famous social networking site. But that's the irony of the situation to begin with, really – the fact that The Social Network starts with a five minute scene of Mark basically ruining a date by gradually insulting his date more and more because his mind obviously operates on different levels from normal humans goes to show just how socially awkward and emotionally blind Eisenberg's Mark is. Also, as a side note, that first scene of the film where the awkwardly sarcastic Mark and his date Erica Albright (Rooney Mara) are sat around a table was probably the hardest part of the film to write! From this early point, it's clearly established that Mark is not just socially blind, but more a borderline Asperger's patient, which is again why it's ironic he managed to create Facebook.
Whilst Eisenberg does an amazing job as the sarcastically smarter-than-thou Mark, it's Andrew Garfield who truly shines through as Mark's roommate and co-founder of Facebook, Eduardo Saverin. Garfield is genuinely an amazing actor in The Social Network, providing the other half of the entire story that makes up the script of the film. Saverin is the more socially aware, richer go-getter of the two founders which is what starts to provide Eisenberg's Mark with the conflicts he faces, as for someone so socially unaware, he's friends with someone who is more popular, has more money and can intellectually keep up with Mark. The scene where Garfield truly steals the show is at the point where Saverin is given further contracts to sign and realises exactly what his shares in Facebook are after a corporate investment and, even though you don't feel as much of a connection to this jealous and somewhat spiteful portrayal of Eduardo Saverin, you can't help but feel bad for how shunned and cast out he gets.
This is not to say that Saverin was the "bad guy" in any of this, and that's part of the beauty of The Social Network – there are no clearly defined "good" or "bad" characters. Each of the characters is right or wrong about different things in equal measures – at the point where Saverin wants to monetise Facebook through advertising, Eisenberg's Mark doesn't want to. He wants to "not stop the party before 11" as the parallel goes. BUT, as it now turns out, Facebook ended up charging for advertising on their spaces and that is now why Facebook is worth so much money, and has made billionaires of Saverin and Zuckerberg. So in the end, neither of them are exactly right or wrong, which is what makes their characters so compelling throughout the entire film.
Justin Timberlake is a bit questionable in the role of Sean Parker, and I'm having a hard time making my mind up about him. On the one hand, I think Timberlake is doing a good job for himself in becoming a legitimate actor as well as singer, and I think the Social Network will work well for him as a stepping stone to further good roles. However, his particular role in this film I found a little hard to accept as it progressed. At the start of the film, Timberlake obviously does a good job of becoming the Napster Mastermind Sean Parker – a cocky rich guy who dropped out of school, managed to screw around in the Music industry and has gotten plenty of fame and fortune because of it. Let's face it; of course Justin Timberlake would be good at playing that role… But as the film went on, and the character of Sean Parker had to become gradually more genuine and less of a "mogul" type, Timberlake became a little less believable in his character, and that's where he started to falter. So to begin with, Timberlake's character works well and drives the storyline, but towards the end he starts to become less of a steering wheel and more of a regular cog in the works. But he still makes for an interesting character, and I think that Timberlake might actually have some kind of possible career in film ahead of him.
One aspect of The Social Network that was interesting, and in fact of many of Fincher's films, is the way in which the story is told. The Social Network isn't exactly told in a series of flashbacks as the film actually starts back before Zuckerberg created Facebook or even his first attempt at an internet-wide practical joke of Facemash, but more with cut-aways to the legal proceedings that followed after Facebook became something bigger than any of its creators. At the end of the film, the storylines catch up to each other and come to one, single conclusion as the story of the creation of Facebook meets with the courtroom drama that ensued after it. In this way, the delivery of the information that drives the story is evenly spread out, and in some places even comical with the way that it is cut together to tell the story of certain incidents in Facebook's creation. What is also interesting about this form of storytelling is that it keeps you guessing as to how they all got to that point – at one part towards the end, you get the sense that Saverin and Zuckerberg are almost at a point of an understanding again before everything gets far worse, but the point is that it keeps you guessing at times, and that's what gives The Social Network's story its edge.
I should also say that the film's soundtrack is worth a mention at this point. The soundtrack to The Social Network has been written and put together entirely by Nine Inch Nails front man Trent Reznor and legendary rock producer Atticus Ross, so it would definitely make for an interesting listen if you know your music history AND enjoy using Facebook as well, considering that two veritable legends of modern rock music have come together to create this soundtrack.
One thing that The Social Network does make very clear is, ironically enough, the dangers of using Facebook. It's actually quoted in the film "It's addictive. I'm on it like, 5 times a day!" and about how "the internet isn't writing in pencil, it's in pen" and it's repeatedly referenced at how just using Facebook is all about putting all of your personal details up on a public forum for anyone you know to access. It's been recently stated by Eric Schmidt, boss of Google.com, about how the dangers of using Facebook and other social networking sites won't be apparent for a while, but will still be there all the same. Schmidt anticipates that the current generation of Facebook users won't be worried about identity theft, but more about how to escape the online identity they've been creating for themselves all this time. He states "Young people may one day have to change their names in order to escape their previous online activity" and that could end up being very true, and The Social Network does a good job of beginning to subliminally imply this.
Ultimately, there is very little to fault The Social Network on, except for one small part where in one scene they have Prince Albert played by someone who is CLEARLY American and looks nothing like Prince Albert at all. That detail aside, The Social Network is an awesome film with great characters and brilliant casting all round, and I think it has easily made its way into my Top Films of the Year. It will also be interesting to see how Fincher tackles the re-make of The Girl With The Dragon Tattoo next year with Rooney Mara from this film becoming Lisbeth Salander. I'm giving The Social Network 8 out of 10 for sheer impressiveness and intelligence, and I think everyone should make an effort to catch it in cinemas!
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Categories: Films And DVDs . Tags:Andrew Garfield, Atticus Ross, David Fincher, Eduardo Saverin, Eric Schmidt, Facebook, Fight Club, Jesse Eisenberg, Justin Timberlake, Mark Zuckerberg, Nine Inch Nails, Rooney Mara, Se7en, Sean Parker, The Girl With The Dragon Tattoo, The Social Network, Trent Reznor, Zodiac . Author: Drew
Comment by Mindy on October 19, 2010 3:34 am
I like how you comment on the Prince not being British, because you are, haha. I like this review a lot. All I have to say is that Justin Timberlake does a lot of tv and movie work, (especially on SNL) but I didn't find this role convincing either.
The first scene was genius!! (and the girl WAS his girlfriend not date…before he got dumped) I feel like it really did set up his character. I really wonder what parts of the movie were true and which just go far off the truth. The movie was also very funny and made me think of how true some of it is, like when the girl says, "facebook me."
I liked the movie a lot. Great review!!
Despicable Me (Contains Spoilers) Canterbury @ The Joiners 20/10/2010 | {
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Miroslav Šmajda, född 27 november 1988 i Košice, även känd som Max Jason Mai, är en slovakisk sångare. .
Biografi
Miroslav Šmajda (Miro) föddes i dåvarande Tjeckoslovakien. Han skriver låtar själv och spelar även gitarr. Bland hans inspiratörer finns Led Zeppelin, Whitesnake, Alter Bridge, 30 Seconds to Mars, Dream Theater, Metallica, John Mayer, Enigma, Sade, Ennio Morricone och Antonín Dvořák.
Karriär
År 2009 deltog han i den första säsongen av Česko Slovenská Superstar där han slutade på andra plats. Programmet är den tjeckiska och slovakiska versionen av Idols och består av deltagare från båda länderna.
År 2011 deltog han i Slovakiens nationella uttagning till Eurovision Song Contest 2011.
Eurovision 2012
Redan den 16 november 2011 meddelades det att Miro valts ut internt till att representera Slovakien i det kommande årets upplaga av Eurovision Song Contest. Bara två dagar senare meddelades det dock att det ännu inte längre var säkert på grund av att vissa delar av kontraktet ännu inte var klara. Flera månader senare, den 7 mars 2012, blev det klart att han faktiskt skulle representera landet i Baku i Azerbajdzjan med låten "Don't Close Your Eyes" som han själv hade skrivit. Han gjorde sitt framträdande i den andra semifinalen den 24 maj men lyckades inte ta Slovakien till finalen.
Diskografi
Album
2010 - Čo sa týka lásky
2013 - mirosmajda.com
Singlar
"Last Forever"
"Baby"
"Pod vodou"
"Loneliness"
"Don't Close Your Eyes"
"Nostalgie"
Referenser
Externa länkar
Officiell webbplats
Deltagarprofil på eurovision.tv
Födda 1988
Män
Levande personer
Artister som representerat Slovakien i Eurovision Song Contest
Slovakiska sångare
Personer från Košice
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{"url":"https:\/\/computergraphics.stackexchange.com\/tags\/lighting\/hot?filter=month","text":"# Tag Info\n\nIf you are asking whether: $$\\int fr(...) cos\\theta_1Le_1 > \\int fr(...)cos\\theta_1 fr(...)cos\\theta_2 Le_2$$ (simplified terms from the render equation you posted above), I don't think you could prove this. Le_2 could just be much greater than Le_1. For example you could have a set of mirrors which only hit a light source after two bounces. Then ...","date":"2020-05-28 05:10:31","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\": 0.6466579437255859, \"perplexity\": 1106.7072553394357}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": true}, \"remove_buttons\": true, \"remove_image_figures\": true, \"remove_link_clusters\": true, \"table_config\": {\"min_rows\": 2, \"min_cols\": 3, \"format\": \"plain\"}, \"remove_chinese\": true, \"remove_edit_buttons\": true, \"extract_latex\": true}, \"warc_path\": \"s3:\/\/commoncrawl\/crawl-data\/CC-MAIN-2020-24\/segments\/1590347396495.25\/warc\/CC-MAIN-20200528030851-20200528060851-00283.warc.gz\"}"} | null | null |
<?php
// Establish connection to database and retrieve comments.
require_once('Dao.php');
// Retrieve all comments from the database (model) to display on page
try {
$dao = new Dao();
$comments = $dao->getComments();
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echo $e->getMessage(); // only print this during development. We want to log in production.
die(); // stop the page from loading because something is not right.
}
// If we reached this page via comment form submission we need to save the user comment
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if(isset($_POST["commentButton"]))
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var_dump($e); // Don't do this in production!! Gives hackers too much information!
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{"url":"https:\/\/mattermodeling.stackexchange.com\/questions\/3967\/how-to-delete-a-selection-with-avogadro2-ubuntu-20-x?noredirect=1","text":"# How to delete a selection with Avogadro2 (Ubuntu 20.x)?\n\nFor reason that I did not understand Avogadro has been phased out of Ubuntu 20.x and the available package Avogadro2 is instead another branch of the package, which unfortunately does not cover all the features. As it appears impossible to install that older but more powerful version of Avogadro on last Ubuntu, does anyone know if it is still possible to delete selected atoms? I am really surprised such a basic feature has been \"lost\".\n\nBasically, you can click and select atoms (although they do not appear selected for any displaying style but \"ball and stick\"), but then if you press CANCEL the whole model is deleted (all atoms). I was using this feature a lot to manipulate structures via GUI and now I just can't proceed unless I use my older Ubuntu distribution.\n\n\u2022 An answer to an earlier question about using Avogadro2 input generators mentions a method for getting the original Avogadro installed on Ubuntu. I haven't tried it on my Ubuntu version, but on the Windows version of Avogadro2, I can just right click an atom\/bond to delete it if I'm in \"Draw\" mode (the pencil in the toolbar). \u2013\u00a0Tyberius Dec 23 '20 at 15:08\n\u2022 thanks @Tyberius ... I have seen that but I was hoping to avoid to install a Window version via wine ... :-S \u2013\u00a0gluuke Dec 23 '20 at 15:15\n\u2022 in the meantime I have also asked on avogadro forum: discuss.avogadro.cc\/t\/\u2026 \u2013\u00a0gluuke Dec 23 '20 at 15:16\n\u2022 also: please note that similar issues have been risen few times already on avogadro forum and also here for example: reddit.com\/r\/Ubuntu\/comments\/gb55uo\/\u2026 \u2013\u00a0gluuke Dec 23 '20 at 15:19\n\u2022 The main problem was that the selection tool and particularly 'rubber band' selections were only added recently, so there are still a few features missing. Help, is always welcome. :-) \u2013\u00a0Geoff Hutchison Dec 24 '20 at 19:29\n\n## 2 Answers\n\nYes, I saw your post on the forum - not sure why that commit didn't make it in, but I have a pull-request now.\n\nThe long and short is that while the main \"guts\" of Avogadro 2 are finished, there's a lot of small pieces that need to be done (case in point). Help is always welcome - there are plenty of tasks that can be done in a few hours for anyone interested.\n\nIn the meantime I have found a couple of solutions and I am listing them here for other users, as frankly not many packages allow to easily (via mouse) select atoms and delete them.\n\n1. you can use chimera as it offers the same feature via CTRL+mouse: https:\/\/www.cgl.ucsf.edu\/chimera\/data\/downloads\/1.15\/linux_x86_64.html and then menu Actions -> Atoms\/Bonds -> delete.\n\n2. if you still want to use avogadro2 on Linux you can actually delete atoms one-by-one by using right-click in \"Draw\" mode: https:\/\/discuss.avogadro.cc\/t\/delete-some-atoms-in-a-supercell\/341\/2","date":"2021-07-28 13:30:46","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\": 0.32487499713897705, \"perplexity\": 1496.9492501431923}, \"config\": {\"markdown_headings\": true, \"markdown_code\": true, \"boilerplate_config\": {\"ratio_threshold\": 0.18, \"absolute_threshold\": 10, \"end_threshold\": 15, \"enable\": false}, \"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\/1627046153729.44\/warc\/CC-MAIN-20210728123318-20210728153318-00085.warc.gz\"}"} | null | null |
Daniel Larsson (Gotemburgo, Gotia Occidental, 25 de enero de 1987) es un delantero de fútbol profesional sueco que actualmente juega en el Apollon Limassol de Chipre. Su hermano menor, Sam Larsson, es también futbolista profesional. Ha sido cinco veces internacional con .
Carrera en clubes
BK Häcken
Larsson comenzó su carrera profesional en BK Häcken. Algunos clubes importantes de Suecia se dieron cuenta de la calidad de Larsson tras varias actuaciones impresionantes jugando en la Superettan. En 2009 fue traspasado al Malmö FF. En su última temporada en el BK Häcken fue una pieza clave que contribuyó al ascenso a la Allsvenskan al anotar doce goles en la Liga.
Malmö FF
Marcó su primer gol con el Malmö FF el 19 de abril de 2009, en el segundo partido en casa de la temporada contra el Trelleborgs FF. Para la campaña 2009 de la Allsvenskan fue el máximo goleador del club en la liga con once goles, acabando como tercer máximo goleador del Campeonato. Diez de estos goles fueron anotados en la última parte de la temporada junto con Edward Ofere quien anotó diez goles, muchos de ellos con la asistencia de Larsson. En la siguiente campaña, Larsson se convirtió en uno de los jugadores más importantes del Malmö FF en el título ganado por estos. Una vez más, marcó diez goles, y dio diez asistencias. En muchos de ellos Larsson fue aplaudido por el público gracias a su juego de visión, a su trabajo en equipo, la habilidad y el gran ritmo.
Larsson marcó el único gol en el partido de ida de la Champions League 2011-2012 del Malmö para ganar por 1-0 al Glasgow Rangers en el Ibrox Stadium. Terminó como el máximo goleador de nuevo del equipo en la temporada 2011, además de dar nueve asistencias de gol. La Temporada 2012 fue el curso más débil de Larsson en términos de gol desde que llegó al club ya que anotó cuatro goles en treinta partidos. El 7 de noviembre de 2012, se anunció que Larsson se iría en un traslado gratuito al Real Valladolid, equipo de la Primera División Española, cuando su contrato con el Malmö FF terminaba el 1 de enero de 2013.
Real Valladolid
El 7 de noviembre de 2012 el Malmö FF confirmó que Larsson formaría parte del Real Valladolid el 1 de enero de 2013. Al final de la Temporada Larsson jugó un total de dieciocho partidos, convirtiéndose casi en un fijo para Miroslav Đukić aunque su punto débil fue que no logró meter ni un gol. La siguiente campaña, a las órdenes de Juan Ignacio Martínez la comenzó lesionado, perdiéndose los primeros partidos de la temporada. En su reaparición, el 25 de octubre de 2013 en un partido en casa ante el Rayo Vallecano (3:0) anotó su primer gol con la camiseta blanquivioleta. Días después, el 30 de octubre anotaría otro gol ante la Real Sociedad (2:2). Desde su reaparición volvió a ser un fijo para JIM en la posición de extremo y mediapunta y anotó un gol más a lo largo del año. Sin embargo, el club acabó descendiendo a la Liga Adelante en la última jornada tras perder ante el Granada CF (0:1). Larsson, debido a su carácter batallador fue uno de los pocos jugadores que se salvaron de los pitos de la afición debido a la horrorosa campaña de los pucelanos.
Granada CF
El 3 de junio de 2014 el Granada hace público su fichaje a coste cero tras desvincularse del Real Valladolid por el descenso de categoría de este club. Firmó por el Granada desechando ofertas de equipos de la Ligue 1 de Francia y del RCD Español, también de España.
Carrera como internacional
Larsson debutó con la selección de en un partido amistoso contra , como parte de una gira de invierno, el 20 de enero de 2010.
Clubes
Actualizado el 5 de diciembre de 2017.
Palmarés
Títulos nacionales
Referencias
Enlaces externos
Ficha en zerozero
Futbolistas de Suecia
Futbolistas del BK Häcken
Futbolistas del Malmö FF
Futbolistas del Real Valladolid Club de Fútbol en los años 2010
Futbolistas del Granada Club de Fútbol en los años 2010
Futbolistas del Esbjerg fB
Futbolistas del Gaziantepspor
Futbolistas del Akhisar Belediyespor
Futbolistas del Aris Salónica Fútbol Club
Futbolistas del Apollon Limassol
Futbolistas de la selección de fútbol de Suecia en los años 2010
Nacidos en Gotemburgo | {
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Only one of two women (Lk 17:35-17:35)
"There will be two women
Grinding meal together.
One will be taken
And the other left."
ἔσονται δύο ἀλήθουσαι ἐπὶ τὸ αὐτό, ἡ μία παραλημφθήσεται ἡ δὲ ἑτέρα ἀφεθήσεται.
Luke indicated that Jesus said that there would be two women grinding meal together (ἔσονται δύο ἀλήθουσαι ἐπὶ τὸ αὐτό). One will be taken (ἡ μία παραλημφθήσεται) and the other left (ἡ δὲ ἑτέρα ἀφεθήσεται). This is similar to Matthew, chapter 24:41, perhaps indicating a Q source. Jesus said that there would be two women grinding meal together (δύο ἀλήθουσαι ἐν τῷ μύλῳ). Only one would be taken or admitted (μία παραλαμβάνεται), while the other would be left or dismissed (καὶ μία ἀφίεται). Not everyone would like this Parousia or end times. Someone would be left behind. What happens to the people left behind? Just ask Jerry B. Jenkins (1949-) and Tim LaHaye (1926-2016), since they wrote 16 novels from 1995-2007 based on the theological theme of the end times. Jenkins also published 40 children's books on the left behind idea from 1998-2004. What do you believe about the end times?
Bible, Gospel of Luke, Jesus, New Testament admitted, believe, children's books, dismissed., end times, grinding meal, indicated, Jerry B. Jenkins, Jesus, left behind, Luke, Matthew, novels, Only one of two women, Parousia, published, Q source, said, similar, taken, theological theme, Tim LaHaye, women 0 Comments
The oldest son (Lk 15:25-15:25)
"Now his elder son
Was in the field.
When he came,
He approached
The house.
He heard music
And dancing."
ἦν δὲ ὁ υἱὸς αὐτοῦ ὁ πρεσβύτερος ἐν ἀγρῷ· καὶ ὡς ἐρχόμενος ἤγγισεν τῇ οἰκίᾳ, ἤκουσεν συμφωνίας καὶ χορῶν,
This long parable story about the 2 sons can only be found in Luke, not in any of the other gospel stories. Luke indicated that Jesus said that the older or elder son (ἦν δὲ ὁ υἱὸς αὐτοῦ ὁ πρεσβύτερος) was in the field (ἐν ἀγρῷ) when his brother came back. As he approached the house (καὶ ὡς ἐρχόμενος ἤγγισεν τῇ οἰκίᾳ), he heard music (ἤκουσεν συμφωνίας) and dancing (καὶ χορῶν). Interesting enough, Luke once again was the only biblical writer to use these two words in his writings, συμφωνίας that means harmony of instruments or music, and χορῶν that means a dance, or dancing. The older or elder son had worked hard on the farm, while his brother went and spent his fortune on wine, women, and song. He knew nothing about the reconciliation of his brother and father. Are you sometimes out of the loop?
Bible, Gospel of Luke, Jesus, New Testament approached, brother, came, came back, dancing, elder, farm, field, heard, his fortune, house, indicated, Jesus, long parable story, Luke, music, only biblical writer, out of the loop, reconciliation, said, song, spent, The oldest son, unique, Wine, women, words, worked hard 0 Comments
Mary (Lk 10:39-10:39)
"Martha had a sister
Named Mary.
She sat
At the Lord's feet.
Mary listened
To what Jesus
Was saying."
καὶ τῇδε ἦν ἀδελφὴ καλουμένη Μαριάμ, ἣ καὶ παρακαθεσθεῖσα πρὸς τοὺς πόδας τοῦ Κυρίου ἤκουεν τὸν λόγον αὐτοῦ.
Luke uniquely said that Martha had a sister (καὶ τῇδε ἦν ἀδελφὴ) called Mary (καλουμένη Μαριάμ). There were many women called Mary in the gospel stories. This Mary sat down at the Lord's feet (καὶ παρακαθεσθεῖσα πρὸς τοὺς πόδας τοῦ Κυρίου) and listened to his words (ἤκουεν τὸν λόγον αὐτοῦ). This was a common position for the disciples to take. It also was common for women to sit at the feet of men to listen to them. Was she a disciple of Jesus? Notice that Jesus was called the Lord (Κυρίου), not Jesus. Certainly, this Mary was very attuned to the teaching of Jesus. Are you willing to listen to the teaching of Jesus?
Bible, Gospel of Luke, Jesus, New Testament common position, disciple of Jesus, disciples, gospel stories, his words, indicated, Jesus, listen, listened, Lord's feet, Luke, Martha, Mary, men, said, sat, sister, teaching, uniquely, women 0 Comments
They had leftovers (Lk 9:17-9:17)
"They all ate.
They were filled.
What was leftover
Was gathered up.
There were
Twelve baskets
Of broken pieces."
καὶ ἔφαγον καὶ ἐχορτάσθησαν πάντες, καὶ ἤρθη τὸ περισσεῦσαν αὐτοῖς κλασμάτων κόφινοι δώδεκα.
Luke said that they all ate (καὶ ἔφαγον) until they were filled or satisfied (καὶ ἐχορτάσθησαν πάντες). What was leftover was gathered up (καὶ ἤρθη τὸ περισσεῦσαν), so that there were 12 baskets of broken pieces (αὐτοῖς κλασμάτων κόφινοι δώδεκα). This is the only miracle that is recorded in all four gospels, Matthew, chapter 14:20, Mark, chapter 6:42-44, and John, chapter 6:12, plus here, but there were slight differences. All the synoptic gospels have the same wording, so that Mark may be the source. All agree that there were 12 baskets of food left over, symbolic of the 12 tribes of Israel and the 12 apostles. They also agree that it was about 5,000 men. Obviously, there was no exact count taken. Only Matthew added the remark about women and the children. Mark said that they took up 12 full hand baskets of the broken pieces of bread, and the pieces of fish. Those who ate the loaves and fish were about 5,000 men. Certainly, it was a miraculous feeding. Matthew said that everyone ate some food. They were all satisfied or filled, but there was no mention of anything to drink. They took up the leftover broken pieces or fragments of food, so that it filled 12 full baskets, a very symbolic number. Those who ate were about 5,000 men, not counting the women and the children, who would have been on the edges of this large crowd of men. Without a doubt, this was a very big crowd to feed. What is the largest crowd that you ever ate with?
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Mary Magdalene (Lk 8:2-8:2)
"Some women
Who had been cured
Of evil spirits
And infirmities
Were with him also.
Called Magdalene,
Seven demons
Had gone out,
Was with him also."
καὶ γυναῖκές τινες αἳ ἦσαν τεθεραπευμέναι ἀπὸ πνευμάτων πονηρῶν καὶ ἀσθενειῶν, Μαρία ἡ καλουμένη Μαγδαληνή, ἀφ' ἧς δαιμόνια ἑπτὰ ἐξεληλύθει,
Luke uniquely said that some women (καὶ γυναῖκές), who had been cured of evil spirits (τινες αἳ ἦσαν τεθεραπευμέναι ἀπὸ πνευμάτων πονηρῶν) and other infirmities (καὶ ἀσθενειῶν), were with him also. Mary (Μαρία), called Magdalene (ἡ καλουμένη Μαγδαληνή), from whom 7 demons had departed (ἀφ' ἧς δαιμόνια ἑπτὰ ἐξεληλύθει) was with him also. This Mary Magdalene, who traveled with Jesus as one of his followers, probably came from the town of Magdala, a fishing town on the western shore of the Sea of Galilee. She was explicitly mentioned by name 12 times in the canonical gospels, more than most of the other apostles, indicating her importance. She certainly was a key figure in the gospel stories about the death and resurrection of Jesus. Jesus apparently healed her in some way that is not indicated, since Luke said that 7 demons had been driven out of her, a statement that Mark, chapter 16:9, also said. She helped support Jesus' ministry, indicating that she was probably relatively wealthy. This Mary was a central figure in later apocryphal Gnostic Christian writings. She had a very popular following in the Middle Ages as the repentant woman. In the late 20th century, she became more popular with her role in the play of Andrew Lloyd Weber's "Jesus Christ Super Star" (1971) and Dan Brown's novel and movie "Da Vinci Code" (2003 and 2006). What do you think about Mary Magdalene?
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The prophet Anna (Lk 2:36-2:36)
"There was a prophet,
The daughter of Phanuel,
Of the tribe of Asher.
She was of a great age.
She had lived
With her husband
After her marriage."
Καὶ ἦν Ἄννα προφῆτις, θυγάτηρ Φανουήλ, ἐκ φυλῆς Ἀσήρ· αὕτη προβεβηκυῖα ἐν ἡμέραις πολλαῖς, ζήσασα μετὰ ἀνδρὸς ἔτη ἑπτὰ ἀπὸ τῆς παρθενίας αὐτῆς,
Next Luke introduced a female prophet, Anna. There were some female prophets in the biblical literature like Miriam in Exodus, chapter 15:20, the sister of Aaron and Moses, who was called a prophet like her brother Aaron, the first instance of women worshiping God. Deborah, in Judges, chapter 4:4, was a married woman prophet from the northern tribe of Ephraim who led troops into battle. Finally, Huddah in 2 Kings, chapter 22:14-20, was one of the few mentioned female prophets. The elders in Jerusalem consulted her about what to do with a holy book. Her response led to the religious revival under King Josiah (640-609 BCE). Like the other Israelite male and female prophets, Anna interpreted God's will for his people. Luke said that there was a prophet Anna (Καὶ ἦν Ἄννα προφῆτις), the daughter of Phanuel (θυγάτηρ Φανουήλ), of the northern tribe of Asher (ἐκ φυλῆς Ἀσήρ). Her father's name Phanuel was considered to be the fourth of the great archangels with Michael, Raphael, and Gabriel, according to the 3rd century BCE work, the Book of Enoch, but there is no implication here that she was angelic. Thus, she was not a local Judean, but a northern Galilean Jewish person from Asher. She was greatly advanced in years (τη προβεβηκυῖα ἐν ἡμέραις πολλαῖς), since she had lived with her husband seven years after her marriage (ζήσασα μετὰ ἀνδρὸς ἔτη ἑπτὰ ἀπὸ τῆς παρθενίας αὐτῆς). She had become a widow.
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The purification (Lk 2:22-2:22)
"When the time came
For their purification,
According to the law
Of Moses,
They brought him up
To Jerusalem
To present him
Καὶ ὅτε ἐπλήσθησαν αἱ ἡμέραι τοῦ καθαρισμοῦ αὐτῶν κατὰ τὸν νόμον Μωϋσέως, ἀνήγαγον αὐτὸν εἰς Ἱεροσόλυμα παραστῆσαι τῷ Κυρίῳ,
Luke said that when the time or the days were completed (Καὶ ὅτε ἐπλήσθησαν αἱ ἡμέραι) for their purification (τοῦ καθαρισμοῦ αὐτῶν), according to the law of Moses (κατὰ τὸν νόμον Μωϋσέως, Joseph and Mary brought Jesus to Jerusalem (ἀνήγαγον αὐτὸν εἰς Ἱεροσόλυμα) to present him to the Lord (παραστῆσαι τῷ Κυρίῳ). What is this purification and is it different than circumcision. The story of John did not have this purification ritual. Strictly speaking, this was a purification of the mother to take place 40 days after the birth of a child that had made her unclean as described in Leviticus, chapter 12:1-8. The presentation of the child and the father were not part of this purification ritual. There was no law or custom about the presentation of a child, other than the presentation of the first born as in Exodus, chapter 13:2 and 13:16. Women were considered unclean after childbirth because of the blood discharge that took place with birthing. If a male was born, the woman was unclean for 7 days, like menstruation, so that on the 8th day the male child could be circumcised. There were 33 more days of blood purification for the male child. During her unclean period, this new mother could not touch any holy thing, or go into the sanctuary. Thus, the purification ritual took place on the 40th day, a symbolic number based on the 40 years of the Israelites in the desert wilderness.
Bible, Gospel of Luke, Jesus, New Testament birth, birthing, blood discharge, brought, came, child, circumcised, Circumcision, completed, custom, days., described, desert wilderness, different, Exodus, first-born, Israelites, Jerusalem, Jesus, John, Joseph, law, Leviticus, Luke, male, Mary, menstruation, Moses, mother, new mother, present, presentation, purification ritual, ritual, sanctuary, story, symbolic number, the father, the Lord, the purification, time, unclean, unclean period, women, years 0 Comments | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 3,148 |
Sabulodes acidaliata är en fjärilsart som beskrevs av Achille Guenée 1858. Sabulodes acidaliata ingår i släktet Sabulodes och familjen mätare. Inga underarter finns listade.
Källor
Mätare
acidaliata | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 9,034 |
Refresh your skin with Dermablend Dissolver Make Up Remover, a gentle yet extremely powerful cleanser that vanishes even waterproof mascara. Effortlessly melting away dirt, toxins and impurities, the bi-phase formula can be used with or without water and is suitable for all skin types, even sensitive and acne-prone. Lightweight and non-greasy, it will leave skin feeling calm, fresh and ultra-nourished.
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The Leasehold Reform (Ground Rent) Act 2022 (c.1) is an Act of the Parliament of the United Kingdom. It defined the peppercorn rent as a price of one peppercorn per year and prohibited ground rent greater than that price on new leases.
Raising ground rent had prevented purchaser of a leasehold property in England to sell their home as the lenders refused to approve a mortgage. This act is a part of the UK government's programme to reform the leasehold system.
See also
Leasehold Reform Act 1967
Commonhold and Leasehold Reform Act 2002
References
English property law
United Kingdom Acts of Parliament 2022
Housing legislation in the United Kingdom | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 8,951 |
GETTING STARTED ON TWITTER
by Keith Keller | Jul 2, 2015 | MP3s, Twitter Podcasts | 0 comments
A while back now, I developed a series of podcasts with Annemarie Cross all based around "CRACKING" the Twitter code.
Part 1 is all about this idea:
Do you need to promote yourself and your products?
Well Twitter may just be your missing link in your current marketing mix.
First up, there are so many social media and blogging platforms out there. Facebook, Instagram, LinkedIn, YouTube, Google+… who can keep count?
Whether you choose to use Twitter or not is completely up to you but please don't just discount this fantastic platform because 'you don't get it.'
What I've learnt through the people I've mentored though, is that once they start to understand the ins and outs and how Twitter can really benefit them, they see it as a real asset to their business.
Ever had a light bulb moment where things just make sense? I've witnessed thousands of them when it comes to my clients and Twitter.
So, you might be asking: why should I bother with Twitter?
"Twitter Is The Buzz Builder"
It's not Facebook, Google+ or any other platform: people check Twitter for news.
In many instances, you'll see news breaking on Twitter before the news… we're talking from anywhere between a 10 second to 30 time frame. Of course, this means you need to tailor your messages accordingly.
I've heard many people adopt a 'one-stop shop' strategy to all of their social media platforms. In my experience, this doesn't work. Twitter is not Facebook… people aren't interested in seeing you eat an ice cream on the beach or your endless cat videos.
As soon as you switch your mindset to Twitter – this means composing short, direct hooks that'll entice people to click onto a link to your website, the sooner you'll experience real success with Twitter.
Keep in mind, Twitter is intended for short, sharp and direct bites of news/information.
Once people are on your website or blog, that's when you can send people to with your 2,000 word essay or content piece.
In newspaper terms, Twitter acts as your headline.
The podcast below goes into more detail about this:
What next? In the next episode I talk about "LAYING THE FOUNDATIONS" for Twitter success.
Twitter is the ROCKET providing you use it correctly and you've "GOT YOUR MOJO"
"LAYING THE FOUNDATIONS" Crack The Twitter Code ((Part 2)) http://t.co/hIXSoCpwli #CrackTheTwitterCode pic.twitter.com/sqLPF4E5ET
— Keith Keller (@KeithKeller) July 20, 2015
SOME ADDITIONAL RESOURCES TO SHARE
www.KeithKeller.com.au
(Free Twitter Marketing eBook)
www.CrackTheTwitterCode.com
(Twitter Strategy Sessions - via SKYPE)
The complete 10 part podcast series
Strategy sessions can be created around any of these topics
(Download The Transcript Here)
Annemarie Cross (AMC) Now for a really special series, so exciting and we are going to be running this over the next 10 episodes. This special series is for all of you, coaches and consultants, out there listening to the show! Let's focus on how you can promote yourself and your products using Twitter. With one of our global business partners Keith Keller.
Welcome to the show Keith!
Keith Keller (KK) Hi! What a great intro! Thank you very much and how groovy is that music !
AMC: I know, I love that! Selected one with a little bit of guitar because I know you actually love that!
KK: I can feel my 80's "MOJO" coming back!
AMC: So Twitter. When you explain to people that I have got a lovely relationship with that, so what are you going to be talking about in today's show?
KK: Well today, I want to set the all 10 parts up with the idea of "Why Twitter?" because there are 7 social medias sites compelling for your time and 3 blogs platform as well. So if you gonna engage in Twitter I want you to really get it, I really want to you to love it and when you do that you commit you know half an hour day or every few days. It's quite possible that you might not like it but that's okay coz there is 6 others choices. But if you want to include Twitter in your Marketing-Mix, these series of episodes is actually going to shank it down and make it doable. And that's really the big chance that everyone has, isn't it?
AMC: Oh certainly it is! And I love the way you've said you want to chunk it down and really help people to understand how they are using twitter because one of the things that I have identified, and this is something that might be very apparent when you will work with clients, the reason people don't really like Twitter very much is that they don't get it, they haven't taking the time to really learn how it can be benefit for the business. Suddenly we realise the beauty of the relationships that have been built and the connections that have been built out there and when you found it you say okay, I can see how so many people write about this incredible resource.
KK: We all have this experience in life when the light goes on and you go "I just don't know why I haven't done this before". It's so simple!
But look, let me start with the numbers!
AMC: Absolutely!
KK: That's a very very good reason to start twitter. 645 million accounts, lots and lots of people have multiple accounts, that's particular number is not that useful but 115 million active accounts. So, 115 million people around the world are using Twitter regularly. So that's a reason to jump on! So that's a reason to at least take notice. 2.5 million australians now have a Twitter account. It's about 12% if your business is centered around Australia, so there are about 2.5 millions of Aussies using Twitter for news, I will talk about that in a minute. But the big step that we really need to talk about, if your market is North America, specifically the US, then 20% of the US Twitter's users use Twitter "EVERY DAY". That just don't use it occasionally for updates, they're using it for "NEWS". And the big story where a lot of people don't get Twitter and why it's very important to realize the difference: Twitter is not Facebook! Twitter is not updates with your family and friends and cat videos. Twitter is The Information Network. And once you get that, once you know that they are people around the world who log in to twitter, check Twitter on their phone every day to get the news often hours, but hours before the tele. And somehow you are not gonna sit at 10 am or 6pm at night, you can find it on Twitter straight away within 10 seconds sometimes or at least within half an hour. People love that immediacy, that instantness of Twitter. Once you get used it, thinking of ways you can become the go to resource. If you are a life coach or a coach in a specific genre and you have a book about this particular subject, you want to become the go to resource for that and you probably already have.
Twitter is a great way of getting the message out because people are hungry, people want the go, don't they?
AMC: They do, they do. And I think it's good that people spend a little bit of time in learning the differences between each of the social medias platforms because as you've just said with "Twitter Is The Information Network" and people are there scanning Twitter for infos so if you want to become known as an expert in your field by sharing quality content you'll become known as someone who is reliable, who is trustful and who has obviously something good to say. Then you realize that, okay so the content that I gonna sharing on there needs to be very focus on sharing a quality content. And as I said not like on Facebook where we are sharing photos of any of things that you have for breakfast and things like that. Do you find that there are still people who get confused and who are doing things on Twitter that is unfortunately tarnishing their brands?
KK: Well I actually think the biggest stories that people have a "one-stop shop" mentality and use Twitter in the same way that they use Instagram, that they use Google + and in the exact same way that they use Facebook. Each of them is different! Twitter is a very specific animal. It's very cool for life coachers, speakers, writters, people in the public area. And usually the reason that you use it, it's because you've got a message, you've got your mojo, you know exactly what you stand for and you just want to tell as many people as possible because you are so proud that you've written a book, you were on the TV, you've been interviewed on the radio, you've got a speaking guide next week, sometimes all four at once. As we get better and better at what we do, we get those TV interviews, we start our own TV shows, we write a book (etc - etc).
Twitter is just purpose built for that! And a lot of people still using it to share photos of ice creams at the beach… And no one cares about chicken sandwiches and ice creams at the beach! They don't! I'm afraid they just go. But they do care about your knowledge and if you got a specific subject you are very good at then people will follow you to source that information as a great teaser for book launches, for radio show, for podcasts, it's also fantastic for sharing You Tube videos.
AMC: Yeah exactly. And one thing coz for those people who are absolutely new to Twitter, Twitter is a microblog so you really only have a limited amount of spaces to be able to share some that contents, some that information. So it's 140 characters so as you were saying that you can pick a snippet or something that is valuable and share that on Twitter. Then that is going to showcase your knowledge and of course build interests and your reputation in someone who knows what you are talking about in that topic.
KK: I think that is actually the biggest challenge that most people told me."Keith, 10 words? What am I going to say in 10 words? I've just got started." But, if you think that Twitter is the front page of a newspaper, and you think about headline, or as I like to say the chorus of a song, and you have a 10 words hook which is your headline for your article, how to become the go to leader in your field, it's a hook that "Oh I want to read that article" and a mark link which take them to your website, and even the website has got a lovely article with 5000 words and Youtube videos and interviews with you on the radio, but you've only got 10 words hook to makes it work.
This actually is a "SCIENCE" and that is why I love it.
AMC: Oh yeah wonderful and I know that in the upcoming episode in the special series you are going to be sharing others tips and tools and others strategies to really up leverage so we can really bring a message outband and continue to promote our sales and products.
So Keith, what will you be talking about in the next special series episodes ?
KK: Next episode, I want to talk about "laying the foundations". It's very very important that you have your mojo before you start on Twitter. Like you've got a blog, you've got a website, you've got an understanding of what you're standing for. Most importantly if you get on Twitter and you don't, it's just a waste of time. I don't think anything tragic is going to happen, it's just a waste of time but once you have your mojo - you've got a blog, a website, a homebase maybe free teaser like an ebook or videos – you can create miracles really quickly! Because Twitter is just a rocket! So I'm going to talk about laying the foundations in the next episode which is the Part 2!
AMC: Fantastic! Cannot wait to find out more about how we can lay the foundations and really up leverage of all the promotions that you are doing on Twitter back to our website.
Thanks Keith and we catch up again next week!
KK: See you next week!
TRANSCRIPTS & TRANSLATIONS BY SYLVIA LANDEZ?
Sylvia is Keith's French translator. She's from Toulouse, in the south of France, but currently living "somewhere in New Zealand" for 10 months. After a Master in Communication & Marketing, she realized that you don't need to be brave or lucky to travel on your own; but just taking the decision and doing it. So she decided to live her dream: discover a new country, a new language and meet people from around the world.
Fascinated by the power of Social Media throughout her studies, she recognizes that she's drawn her inspiration for her travels from experiences of others travelers shared online by blogs or Facebook / Twitter accounts, and this is the reason why she's sharing her experience online as well.
Meeting Keith thanks to others connections and working with him was an amazing opportunity for her to learn more about the REAL Twitter, improve her skills in Social Media and also share about her vision of using Twitter during her travel.
LinkedIn: https://fr.linkedin.com/pub/sylvia-landez/8a/16/870
Twitter: @slandez @KiaOraKaikoura
Blog: www.KaikouraNewZealand.Blogspot.com
(Download The French Translation Here)
TOP 10 PODCAST HOSTING SITES FOR 2022
WHY TWITTER SPACES REALLY COULD BE THE NEXT BIG THING | {
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\section{Introduction}
Active Brownian particles (ABP) are a widely used model system to study
the statistical physics of swimming micro-organisms \cite{Romanchuk_Schimansky-Geier_review_EPJST,Elgeti_Gompper_Winkler_review,ourRMP}.
In the ABP model, particles undergo Brownian translational and rotational
motion, and in addition possess an ``active'' mechanism of self-propulsion
along a fixed body axis.
The simplest such model is that of active hard spheres (AHS), where particle
interactions are spherically symmetric and only enforce no-overlap conditions.
In particular, no direct interactions between the swimming directions of
AHS exist. Despite this simplification, AHS still show interesting
non-equilibrium phase behavior that allows to investigate many principles
of actively driven systems. They can also be realized to good approximation
in experiments on colloidal ``Janus'' particles \cite{buttinoni2012active,Howse2007,Palacci2014}.
For equilibrium ("passive") fluids, the basic quantity revealing the structural correlations
in the disordered fluid state
is the structure factor $S(q)$, or alternatively the radial pair-distribution
function $g(r)$
\cite{HansenMcDonaldbook}. Since the early days of liquid state physics,
the structure factor
has been measured by scattering experiments and computed by simulations and
integral equation theory. In this respect the hard-sphere system
(including its two-dimensional version of hard disks)
has played a pivotal role to understand fluid structure and to test approximative theories.
The hard-sphere potential does not have an energy scale and therefore,
temperature is irrelevant in determining the phase behavior.
This allows to examine the role of structural correlations in fluids most
clearly.
The
structural properties of active fluids have been much less
studied (but see \cite{Haertel} for a recent exception).
This is a significant gap, because
the homogeneous active fluid can provide a clear-cut
testing ground to extend the well-established concepts of classical
statistical physics to regions far from thermal equilibrium.
In this contribution, we provide reference simulation data for the
static structure factor $S(q)$ and the pair distribution function $g(r)$
of active Brownian hard disks in two spatial dimensions. As stated above,
hard-sphere like interactions are the least arbitrary starting
point to describe sterical repulsion between particles, and in equilibrium
fluids, the approach to start from hard spheres and extend to other types
of interactions has been hugely successful. In active fluids, there might
be a subtle interplay between the softness of repulsion and active driving
\cite{Haertel}, so that it is important to establish the hard-sphere
reference case.
We restrict ourselves to two-dimensional systems for simplicity. To date,
most experiments on Janus colloids are done in quasi-2D settings, and
many simulation studies of the phase behavior of ABP have also been performed
in 2D. Brownian dynamics simulations of strict hard disks are not straightforward
as already known from passive systems
(see e.g. \cite{Hinsen,LowenPRE1994,DeMichele}) so special care is needed for the algorithm used. Here
we choose an event-driven scheme \cite{DeMichele} which is particularly designed
to be efficient for Brownian hard disks.
Sufficiently strong self propulsion induces clustering of ABP, so that for a
large range of densities, ABP systems evolve into inhomogeneous states
of very dense clusters separated by very dilute regions \cite{Marchetti,TailleurCatesReview2015}.
This phenomenon is called motility-induced phase separation (MIPS) as it
shares a number of qualitative features with the liquid--gas phase separation
known from equilibrium fluids.
MIPS has been studied in great detail for various
spherical ABP models with different interactions between the particles \cite{Bialke_review,Zoettl,Siebert},
since recently also including the hard-sphere case (using the same simulation
algorithm as ours) \cite{Levis}.
Here we deliberately restrict our attention to the homogeneous fluid state
outside the spinodal of MIPS.
\section{Methods and Techniques}
The active Brownian hard-disk system obeys the following equations of motion
for the positions $\vec r_j$ and the orientation angles $\theta_j$ of the
particles (relative to a fixed laboratory coordinate frame):
\begin{subequations}
\begin{eqnarray}
d\vec r_j&=&\sqrt{2D_t}\,d\vec W_j+v_0\vec e(\theta_j)\,dt\,,
\qquad|\vec r_j-\vec r_k|\ge\sigma\;\forall j,k\,,
\\
d\theta_j&=&\sqrt{2D_r}\,dW^\theta_j\,.
\end{eqnarray}
\end{subequations}
Here, $j=1,\ldots N$ labels the particles. Brownian translational and
rotational diffusion is described by uncorrelated Wiener processes
$d\vec W_j$ and $dW^\theta_j$; their amplitude is given by the
translational diffusion coefficient $D_t$ and the rotational diffusion
coefficient $D_r$. Self propulsion is modeled by a fixed swimming speed
$v_0$ along the particles orientation, $\vec e(\theta)=(\cos\theta,
\sin\theta)^T$. The hard-sphere interactions translate into no-overlap
conditions $|\vec r_j-\vec r_k|\ge\sigma$ for all particle pairs.
The hard-core diameter $\sigma$ and the translational diffusion coefficient $D_t$
are used to set the units of length and time in the following.
There remain three parameters to specify the state of the system:
the density $n=N/V$, expressed as a dimensionless packing fraction
$\eta=(\pi/4)n\sigma^2$, the self-propulsion velocity $v_0$ (in units
of $D_t/\sigma$), and the rotational diffusion coefficient $D_r$
(in units of $D_t/\sigma^2$).
For three-dimensional passive hard spheres, the Stokes-Einstein relation
fixes $D_r=3D_t/\sigma^2$, assuming Stokes flow in the solvent and stick
boundary conditions on the particle surface. However, for active systems,
the effective rate of change of particle orientations may be significantly
different from this passive value, depending on the swimming mechanism.
We will therefore fix $D_r=1$ as a reference case for most simulations,
and also explore the effect of changes in $D_r$, i.e., changes in the
persistence of active motion.
Given the particle positions, one obtains the static structure factor,
\begin{equation}\label{eq:sq}
S(q)=\frac1N\left\langle\sum_{j,k=1}^N e^{-i\vec q\cdot(\vec r_j-\vec r_k)}
\right\rangle\,,
\end{equation}
where the angular brackets denote an average over the non-equilibrium
stationary state, and $\vec q$ is the wave vector of the density fluctuations
that are probed by $S(q)$. Note that in the homogeneous, isotropic fluid,
$S(q)$ depends on $\vec q$ only through its magnitude $q=|\vec q|$.
The static structure factor is intimately related to the radial distribution
function $g(r)$ defined by
\begin{equation}\label{eq:gr}
g(r)=\frac1{nN}\left\langle\sum_{j\neq k}\delta(\vec r-(\vec r_j-\vec r_k))
\right\rangle\,,
\end{equation}
which quantifies the probability density for finding a particle at distance
$r$ from a given particle, irrespective of their orientations.
Again, $g(r)$ quantifies structural properties of the isotropic homogeneous
fluid, although for ABP systems, the angle-resolved pair distribution
function provides further information \cite{Haertel}.
Simulations were carried out using an event-driven Brownian dynamics (ED-BD)
algorithm \cite{DeMichele}. In the ED-BD simulation, a fixed ``Brownian''
time step $\Delta t$ is introduced, and at each time step, Gaussian trial
displacements $\Delta\vec r_i$ and angle increments $\Delta\theta_i$
are drawn for all the particles. The self-propulsion term is included
by drawing the $\Delta\vec r_i$ from appropriately shifted Gaussians.
To propagate the system to the next time steps, the trial displacements
have to be modified to avoid particle overlaps. This is done by assigning
to the particles pseudo-velocities $\vec v_i=\Delta\vec r_i/\Delta t$,
and by performing event-driven molecular dynamics using these pseudo-velocities
in the time interval $[t,t+\Delta t]$.
This way, the ED-BD algorithm guarantees no-overlap conditions
at any time, and thus incorporates hard-sphere interactions exactly.
In the passive case, the ED-BD algorithm has been shown to accurately
describe the Brownian motion of hard spheres, if the time step is reasonably
small, $\Delta t<0.1\,\sigma^2/D_t$, say \cite{DeMichele}. Note however
that for strong self-propulsion and/or fast reorientational diffusion,
significantly smaller time steps may be required.
The extension
to active particles has been used to study glassy dynamics of dense
AHS systems \cite{Ni2013}, and more recently also MIPS \cite{Levis}.
We performed runs with $N=1000$ and $N=5000$ particles to estimate
finite-size effects. These are found to be small for the structural
quantities we study for state points sufficiently far from the spinodal of MIPS.
Results are shown for the $N=5000$ system. The Brownian time step
was chosen to be $\Delta t = 0.001\,\sigma^2/D_t$, and some runs with
$\Delta t=0.01\,\sigma^2/D_t$ were performed to confirm that no significant
finite-time step effects remain in $S(q)$.
From individual runs with a specific choice of parameters, after an initial
transient time of $t_i=333\,\sigma^2/D_t$ to reach a stationary state,
133 configurations in $[t_i,t_f]$ with $t_f=1000\,\sigma^2/D_t$ were
stored and analyzed to obtain $S(q)$ and $g(r)$. To obtain $S(q)$,
a set of 5000 $\vec q$-vectors compatible with periodic boundary conditions
were used to evaluate Eq.~\eqref{eq:sq}, which were afterwards binned
according to $|\vec q|$. For $g(r)$, bins of width $0.01\,\sigma$ were used
in evaluating Eq.~\eqref{eq:gr}.
\section{Results}
\subsection{Passive Hard Disks}
\begin{figure}
\indent{\includegraphics[width=\linewidth]{structure_schar_mit_bc_vo_0}}
\caption{\label{fig:sq_passive}
Static structure factor $S(q)$ of passive hard-disk systems with
packing fractions $\eta=0.1$, $0.2$, $0.3$, $0.4$, $0.5$, and $0.6$
(top to bottom around $q\sigma=2$).
Solid lines: results from ED-BD simulations.
Dashed lines represent the Baus-Colot expression for $S(q)$.
}
\end{figure}
We begin by recalling the features of the passive reference system.
The only relevant parameter in the passive hard-disk system is the packing
fraction $\eta$.
Hard disks are known to order at high densities, transforming first
from the fluid to a hexatic phase, and later to a crystalline phase.
The nature and phase-transition boundaries of the fluid--hexatic and
the hexatic--solid transitions have only recently become clear in large-scale
simulations \cite{Bernard2011} and experiments \cite{Thorneywork2017}:
in the regime $0.700\le\eta\le0.716$, coexistence between a fluid and
the hexatic phase was found. There is a further continuous transition
to a solid at $\eta\simeq0.720$.
In the following, we will restrict the discussion to packing fractions
$\eta\le0.7$.
The static structure factor of the fluid displays the standard features
known from simple fluids (Fig.~\ref{fig:sq_passive}): with increasing
packing fraction, intermediate-range order in the fluid becomes more
pronounced, and this gives rise to damped oscillations in $S(q)$ that
become increasingly pronounced. The ordering is reflected in a pronounced
first peak of $S(q)$ at $q_*\approx6/\sigma$ (for $\eta=0.6$).
The position of this peak
(or rather, the period of the oscillations) reflects a typical interparticle
distance. The sharpness of the peak is an indicator for how pronounced
ordering is.
For 3D hard spheres, several well known approximation schemes exist
for $S(q)$.
For example, a widely used analytical, albeit approximate, expression is the
Percus-Yevick (PY) structure factor \cite{HansenMcDonaldbook}.
In 2D, no closed analytical form of the PY approximation for $S(q)$
is known.
An empirical expression has been proposed by Baus and Colot \cite{Baus}.
The Baus-Colot expression provides an excellent description of the
data, as shown by the dashed lines in Fig.~\ref{fig:sq_passive}.
\subsection{Active Hard Disks}
\begin{figure}
\indent{\includegraphics[width=\linewidth]{structure_schar_vo_10}}
\caption{\label{fig:sq_lowv0}
Static structure factor $S(q)$ of active Brownian hard disks with
self-propulsion velocity $v_0=10\,D_t/\sigma$ and rotational diffusion
coefficient $D_r=1\,D_t/\sigma^2$, for packing fractions
$\eta=0.1$, $0.2$, $0.3$, $0.4$, $0.5$, $0.6$, and $0.7$.
}
\end{figure}
We now turn to the discussion of the active hard-disk system with rotational
diffusivity $D_r=1$.
For self-propulsion velocities $v_0$ that are below the onset of
motility-induced phase separation (estimated to be around $v_0=12$ in
the present system \cite{Levis}), a similar evolution of $S(q)$
with increasing packing fraction is seen as in the passive system.
This case is shown in Fig.~\ref{fig:sq_lowv0} for $v_0=10$.
In particular the evolution of the first and second peaks in $S(q)$ does
not differ qualitatively from the one in the passive system. For
$\eta=0.7$, the second peak around $q\sigma=12$ exhibits an asymmetric
shape, which we interpret as a precursor of incipient ordering.
It is known that two-dimensional ABP systems crystallize at high densities
(seen, for example, in active hard-core Yukawa systems \cite{Bialke2012}).
For the hard-disk case discussed here, the passive system displays
much stronger signatures of ordering in $S(q)$ at $\eta=0.7$ than the
active system does. This is consistent with the expectation that -- at
least for self-propulsion velocities small enough to prevent MIPS -- the
ordering transition sets in at higher densities in the presence of
active motion.
The main difference of the active $S(q)$ to the passive one
is in the low-$q$ behavior.
At densities comparable to the critical
density of MIPS, a strong increase of $S(q\to0)$ is seen in the active system.
This is
the signature of impending phase separation that is expected from the analogy
with equilibrium systems.
Precursors of this low-$q$ increase are seen at all densities shown
in Fig.~\ref{fig:sq_lowv0}.
The structure factors shown in Fig.~\ref{fig:sq_lowv0} are exemplary for
the active hard-disk fluid. At higher $v_0$, only the low-density regime
remains, because MIPS sets in; our simulations confirm that phase separation
prevails for large $v_0$ up to very high densities. It is therefore,
at least for $D_r\approx1$,
not possible to prepare a homogeneous monodisperse hard-disk fluid for
large $v_0$ and large $\eta$.
\begin{figure}
\indent{\begin{tabular}{ll}
a) & b) \\
\includegraphics[height=0.42\linewidth]{structure_schar_eta_0_2} &
\includegraphics[height=0.42\linewidth]{snaps_eta_0p2}
\end{tabular}}
\caption{\label{fig:sq_lowdens}
a) Low density fluid regime: static structure factor $S(q)$ for active hard disks with $D_r=1\,D_t/\sigma^2$
and at packing fraction $\eta=0.2$. Different curves corresond to
different self-propulsion velocity: $v_0=0\,D_t/\sigma$ to $v_0=100\,D_t/\sigma$ increasing in
steps of $10$ (blue to green). b) Simulation snapshots at the indicated self-propulsion velocities. The self-propulsion
of each particle is directed towards its red side. Note that the total simulation box is significantly larger than the
region depicted here.
}
\end{figure}
To understand the effect of activity on the static structure of the fluid,
it is instructive to discuss cuts in parameter space where the packing
fraction is fixed. Increasing the self-propulsion velocity $v_0$
for a low-density system ($\eta=0.2$ shown in Fig.~\ref{fig:sq_lowdens}a)
causes two prominent changes: first, the main peak of $S(q)$ shifts
to larger $q$ and increases in amplitude (and the subsequent peaks
undergo a similar change).
The increase of the peaks in $S(q)$ signals that structural order in the
more active fluid is more pronounced, while the shift to larger $q$
indicates that the average particle distance is reduced. This is consistent with
a visual inspection of the simulation snapshots illustrated in Fig.~\ref{fig:sq_lowdens}b, which
shows the formation of local areas with both higher ordering and density.
Second, the low-$q$ region of $S(q)$
increases with increasing self-propulsion speed.
This latter effect is attributed to the emergence of
a phase-separated region, as discussed above.
If one defines the isothermal compressibility $\kappa_T$
of the active fluid system in terms of the particle-number fluctuations
by extending the well-known equilibrium relation,
$\kappa_T=S(q\to0)/n k_BT$ (where $k_BT$ is the thermal energy needed to
define an energy scale for the compressibility), to the non-equilibrium
stationary state, the active fluid is much more compressible than the
passive one.
Interestingly, the $S(q)$ appear to approach a limiting curve for large $v_0$:
in Fig.~\ref{fig:sq_lowdens}a, the strongest change is seen upon increasing
$v_0$ from zero to about 10, while a further increase by a factor of $10$ (up
to $v_0=100$) only causes small further changes in the average fluid structure.
Also the MIPS spinodal is nearly vertical in the $v_0$-vs-$\eta$ plane
\cite{Levis},
indicating that there is a regime where self-propulsion effects saturate.
The shift in the peak positions of $S(q)$ indicate that the average
particle distance decreases from about $2\pi/5\,\sigma\approx1.26\,\sigma$ to
about $2\pi/6\,\sigma\approx1.05\sigma$. Hence, the saturation may stem from the
fact that for true hard disks, a further increase in activity cannot
cause particles to stay closer than $\sigma$ on average.
The saturation effect may thus be masked for soft spheres.
\begin{figure}
\indent{\includegraphics[width=\linewidth]{gofr_schar_eta_0_2}}
\caption{\label{fig:gr_lowdens}
Radial distribution function $g(r)$ of an active Brownian hard-disk system
at packing fraction $\eta=0.2$, for self-propulsion velocities $v_0
\in[0,20]$ (in steps of two, from bottom to top at $r=1^+$).
}
\end{figure}
The radial distribution function $g(r)$ provides more intuitive
information on the average structure. At the low density discussed here,
$\eta=0.2$, the equilibrium $g(r)$ is relatively featureless: it shows
a weak enhancement over the ideal-gas value at particle contact, but quickly
decays to unity for larger $r$.
Increasing $v_0$ for the low-density
system leads to a strong enhancement of $g(r)$ near contact, see
Fig.~\ref{fig:gr_lowdens}. This is in line with the interpretation that
the average particle distance decreases with increasing self-propulsion
velocity.
At sufficiently large $v_0$ there emerges a second peak around $r=2\sigma$.
Hence, active particles form small transient clusters. However, no
pronounced peaks are seen at $r\approx n\sigma$ with $n>2$. Thus,
the system does not (yet) form large clusters with a statistically
significant probability, and it also does not form pronounced intermediate-range
order.
The changes in $g(r)$ that are visible in Fig.~\ref{fig:gr_lowdens} can
be contrasted to those found in ABP systems with soft
interactions \cite{Brader15}. There, a comparable change of $v_0$ only
led to a relatively mild change in $g(r)$, and the main effect was a shift
of the nearest-neighbour peak to smaller distances.
An appealing concept is to map activity onto an effective interaction between
the particles. Quite robustly for a number of different ABP models,
activity induces effective attractions that become increasingly strong when
$v_0$ is increased \cite{Brader15,Ginot,Mani,Wittmann}.
For soft-sphere ABP, the interaction range was found to be around $20\%$ of a
particle diameter at moderate densities \cite{Brader15}.
To describe the effects of attractions in passive colloidal systems,
the square-well system (SWS) is a canonical starting point \cite{Bolhuis1994}. In this model,
a hard-sphere repulsion is supplemented by an attraction of fixed strength
$\Gamma$ and range $\delta\sigma$. For the three-dimensional SWS, the static
structure factor $S(q)$ can be obtained analytically within the mean-spherical
approximation for $\delta$ not too large \cite{Dawson2001}. At low density,
the SWS-$S(q)$ displays a change upon increasing the attraction
strength $\Gamma$ that is similar to the one seen for the low-density
AHS in Fig.~\ref{fig:sq_lowdens}: increasing attraction causes increased
structural order, and a shift of the average particle separation to lower
distances. This confirms earlier findings that activity can be mapped
to an effective attraction in describing the fluid structure \cite{Ginot}. The mapping
$v_0\leftrightarrow\Gamma$
is however quite nonlinear, because the saturation effect we find for the AHS
upon increasing $v_0$ is not found in the SWS upon increasing $\Gamma$.
\begin{figure}
\indent{\parbox[t]{\linewidth}{
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{structure_schar_eta_0_6}}}\hfil
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{structure_schar_eta_0_7}}}\\
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{gofr_schar_eta_0_6}}}\hfil
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{gofr_schar_eta_0_7}}}
\parbox[t]{.495\linewidth}{{\includegraphics[width=0.8\linewidth]{snaps_eta_0p6}}}\hfil
\parbox[t]{.495\linewidth}{{\includegraphics[width=0.8\linewidth]{snaps_eta_0p7}}}
}}
\caption{\label{fig:sq_highdens}
High-density fluid regime: static structure factor $S(q)$ (top row),
radial distribution function $g(r)$ (middle row), and snapshots (bottom row) of active hard disks
with packing fraction $\eta=0.6$ (left column) respectively
$\eta=0.7$ (right column). Different curves correspond to different
self-propulsion speeds $v_0=0$, $2$, $4$, $6$, $8$, $10$, $12$
(from blue to green; curves ordered by increasing
first-peak position in $S(q)$ from left to right).
}
\end{figure}
We now turn to the high-density fluid, limited to small enough $v_0$
so that the system remains homogeneous. As the phase diagram confirms
\cite{Levis},
there opens a small window where the system is not yet crystallized
and not yet phase-separated. We discuss two packing fractions for this
case, $\eta=0.6$ and $\eta=0.7$. The latter case represents the upper
end of the equilibrium fluid regime in passive hard disks, and the
structure functions for this system already show precursors of a
phase transition to the hexatic phase.
The $S(q)$ at high densities, Fig.~\ref{fig:sq_highdens},
demonstrate an interesting trend upon increasing $v_0$ that is
absent at low densities: while the main peak of $S(q)$ monotonically
shifts to the right with increasing $v_0$, it first weakens, and then
increases with $v_0$.
The corresponding effect in $g(r)$ is an interplay between a sharpening of
the contact-value peak and an increasing depletion of the region between
the first neighboring shells. However, this structural
change is too subtle to be clearly visible in the simulation snapshots.
The initial decrease in the amplitude of $S(q)$
is much more pronounced at $\eta=0.7$, but already noticable at $\eta=0.6$,
where precursors of hexatic ordering are not yet obvious.
We therefore attribute the non-monotonic change to a genuine change in
the way activity influences the fluid structure, and not to the vicinity of
a phase transition.
The non-monotonic trend revealed in Fig.~\ref{fig:sq_highdens} indicates
that the effect of activity in the high-density hard-disk system is
twofold: first, activity reduces ordering in the dense system.
This is also expected from
simulation studies of glassy dynamics, where a shift of the glass transition
to higher densities with increasing activity was seen \cite{Ni2013}. Similar
trends are confirmed for various other model systems \cite{Berthier2013,Bi2016}
and predicted by theory \cite{mct}. Such a ``fluidization'' of the system
is usually associated with a weakening of the peak amplitudes in $S(q)$.
It is reminiscent of the reentrant melting of glass-forming systems with
short-ranged attraction, where a similar decrease of peak height in $S(q)$
with increasing attraction strength describes the structural changes
of the system \cite{Dawson2001}.
Second, stronger activity in the high-density system restores the effects
that also prevail at lower densities. Here, activity favors structural
order. For the case we study here, the crossover between the two
effects occurs around $v_0=5\,D_t/\sigma$, slightly depending on the packing fraction.
\begin{figure}
\indent{\parbox[t]{\linewidth}{
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{sws1}}}\hfil
\parbox[t]{.495\linewidth}{{\includegraphics[width=\linewidth]{sws55}}}
}}
\caption{\label{fig:swssq}
Static structure factor $S(q)$ of a three-dimensional square-well system
with short-ranged attraction (range $0.1\sigma$), as a function of
attraction strength ($\Gamma=0$, $2$, $4$, $6$, $8$, and $10$; blue to green),
for moderate density (left panel; three-dimensional packing fraction
$\varphi=0.1$) and for high density (right panel; $\varphi=0.55$).
}
\end{figure}
Again, the comparison with the passive square-well system allows to understand
the qualitative mapping of activity to effective interactions.
Specifically, the non-monotonic change in the first peak of $S(q)$ allows
to estimate the range of the effective attraction. For the SWS with an
attraction range of, say, $\delta=20\%$,
the same trend is found at large densities
as it was also found in the low-density state: increasing attraction strength
$\Gamma$ increases the peak height and shifts its position to larger $q$
(recall Fig.~\ref{fig:sq_lowdens}). The situation changes however, if one
considers short-ranged attractions. For, say, $\delta=10\%$, the dense SWS
reproduces a decrease in peak height with increasing $\Gamma$ up to
about $\Gamma=5\,k_BT$, followed by an increase upon further increasing
$\Gamma$. (To exemplify this, Fig.~\ref{fig:swssq} shows the corresponding
$S(q)$ for a three-dimensional $S(q)$, evaluated in the mean-spherical
approximation \cite{Dawson2001}.)
From this similarity in trends one may conclude that indeed, activity in the AHS
can be mapped to an effective attraction, of a range around $10\%$.
The SWS also offers a physical explanation for the different behavior
of $S(q)$ at high densities as compared to low densities: at $\eta\approx0.6$,
the average particle separation is on the order of $10\%$ of a particle
diameter.
If the attraction range and the interparticle separation are comparable,
the effect of increasing attraction strength is to increase disorder,
because some particles will be bounded more strongly, while others can explore
a larger configuration-space volume. Only if the attraction is sufficiently
strong, the energetic increase in order offsets the entropic decrease.
\subsection{Influence of Rotational Persistence}
Activity induces a coupling between $D_r$ and the translational
evolution. Thus, $v_0$ and $D_r$ are both relevant parameters for the
active fluid.
One way to describe ABP that is successful in the low-density limit is
by assigning to the ABP system an effective temperature (or pressure)
\cite{Takatori2014},
based on the notion that a single ABP over long time and length scales
undergoes diffusion with a renormalized diffusivity that in two spatial
dimensions reads
$D_\text{eff}=D_t+(1/2)v_0^2/D_r$.
Here, only a specific combination of $v_0$ and $D_r$ enters.
There are indications that the high-density dynamics of ABP on the contrary
depends on
both these parameters separately \cite{mct,Ni2013,Bi2016},
because at high densities the average distance between ineracting particles
is easily shorter than the persistence length associated to the swimming,
$\ell_p=v_0/D_r$.
It is therefore interesting to see the effect that varying both $v_0$ and $D_r$
has on the stationary static structure.
The relevant dynamical rates of the AHS system thus are:
the rate of passive Brownian diffusion, $\tau_0^{-1}=D_t/\sigma^2$,
the rate of self-propelled motion, $\tau_v^{-1}=v_0/\sigma$,
and the rate of active effective diffusion, $\tau_a^{-1}=v_0\ell_p/\sigma^2$.
From these rates, three dimensionless parameters can be formed to quantify
the amount of ``activity'' in the system. (They are ratios of rates, and
thus called ``P\'eclet'' numbers in analogy to hydrodynamic theory.)
A natural choice from the equations of motion is the
translational P\'eclet number that quantifies the rate of self propulsion
in relation to passive diffusion,
${Pe}_t=\tau_v^{-1}/\tau_0^{-1}=v_0\sigma/D_t$.
The low-density theory suggests to use the rate of active over that of
passive diffusion,
${Pe}=\tau_a^{-1}/\tau_0^{-1}=v_0^2/D_rD_t$;
at high densities one may expect the persistence length to play a crucial
role, and thus the ratio of self-propelled motion relative to active
difusion,
${Pe}_r=\tau_v^{-1}/\tau_a^{-1}$. Note that
${Pe}_r^{-1}=\ell_p/\sigma$ is sometimes also referred to by the symbol
${Pe}$ in the context of MIPS; we stick to the notation introduced in
\cite{Takatori2014} to avoid confusion.
\begin{figure}
\indent{\parbox[t]{\linewidth}{
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_vergleich_N_5000_eta_0_2_vo_10}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{peclet_schar_N_5000_eta_0_2_peclet_100}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_persistenz_10_N_5000_eta_0_2}}}
}}
\caption{\label{fig:sq_lowdens_dr}
Static structure factor of active hard-disks fluid at packing fraction
$\eta=0.2$ with different rotational diffusion coefficients $D_r=0.1$, $1$,
and $10$ (red, green, blue).
Left: comparison at constant self-propulsion velocity
(translational P\'eclet number) ${Pe}_t=v_0\sigma/D_t=10$;
middle: comparison at constant P\'eclet number ${Pe}=v_0^2/D_rD_t=100$;
right: comparison at constant persistence length
(rotational P\'eclet number) ${Pe}_r^{-1}=v_0/\sigma D_r=10$.
}
\end{figure}
We thus compare the static structure factors obtained for the system
at moderate density, $\eta=0.2$, for various rotational diffusion
coefficients, while keeping one of the three parameters (${Pe}_t$,
${Pe}$, or ${Pe}_r^{-1}$) fixed. Varying $D_r$ over two orders of magnitude
shows (Fig.~\ref{fig:sq_lowdens_dr}) that the static structure factors
$S(q)$ are in fact independent on $D_r$ in the regime of moderately
strong self propulsion. The curves for different $D_r$ fall on top of each
other within error bars at fixed ${Pe}_t$, with the exception of a small
increase towards $q\to0$. The latter indicates that the appearance of
MIPS is influenced by both $v_0$ and $D_r$, while the dependence on $D_r$
has no significant structural precursors in the fluid.
At fixed ${Pe}$ (middle panel of Fig.~\ref{fig:sq_lowdens_dr}), an increase
in $D_r$ has a similar effect as increasing $v_0$ regarding the change
in nearest-neighbor structure that is reflected in the change of
the peak positions in $S(q)$. A similar conclusion holds for the evolution
of $S(q)$ with increasing $D_r$ at fixed persistence length (right panel
of the figure). Note that one expects the dynamics for $D_r\to\infty$
at fixed $v_0$
to become identical to that of passive hard spheres, because in this limit
the net effect of self propulsion vanishes. Figure~\ref{fig:sq_lowdens_dr}
suggests that this is true only if the limit is taken such that the
persistence length vanishes sufficiently quickly: only for the case
of fixed ${Pe}_t$, the structure factor approaches the passive one with
increasing $D_r$ at least at low $q$.
\begin{figure}
\indent{\parbox[t]{\linewidth}{
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_vergleich_N_5000_eta_0_6_vo_10_ohne_0_1}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{peclet_schar_N_5000_eta_0_6_peclet_100}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_persistenz_10_N_5000_eta_0_6}}}\\
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_vergleich_N_5000_eta_0_7_vo_10_ohne_0_1}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{peclet_schar_N_5000_eta_0_7_peclet_100}}}\hfil
\parbox[t]{.325\linewidth}{{\includegraphics[width=\linewidth]{sofq_persistenz_10_N_5000_eta_0_7}}}
}}
\caption{\label{fig:sq_highdens_dr}
Static structure factor of active hard-disks fluid at packing fraction
$\eta=0.6$ (top row) respectively $\eta=0.7$ (bottom row)
with different rotational diffusion coefficients $D_r=0.1$, $1$,
and $10$ (red, green, blue), at constant ${Pe}_t=10$ (left), constant ${Pe}=100$ (middle), and constant ${Pe}_r^{-1}=10$ (right).
Results are omitted for the state point (${Pe}_t=10$, $D_r=0.1$), where
the system is already phase separated.
}
\end{figure}
At high densities, the situation is less clear, because phase separation
sets in at very different self-propulsion velocities for different $D_r$.
Static structure factors for $\eta=0.6$ and $\eta=0.7$,
shown in Fig.~\ref{fig:sq_highdens_dr}, confirm the observation made above:
as long as the system remains in the homogeneous fluid state, $D_r$
itself appears to have very little influence on the static structure.
At fixed P\'eclet number or fixed persistence length, the increase of $D_r$
does not render the system more passive-like, but rather induces a change
in $S(q)$ that is similar to the one seen upon increasing $v_0$ at
fixed $D_r$.
\section{Conclusions}
We have obtained static structure factors and radial distribution functions
from simulations of active Brownian hard-disk fluids.
The system remains in the homogeneous fluid phase for all packing fractions
$\eta\lesssim0.7$ and low enough activities, $v_0\lesssim12\,D_t/\sigma$
for $D_r=1\,D_t/\sigma^2$; it also remains a homogeneous fluid for low
densities, $\eta\lesssim0.2$, and all the self-propulsion velocities we have
studied.
The evolution of the static structure factor with density, outside the
region of MIPS, resembles that of the passive fluid at finite $q$.
On the low-density side of the phase-separation spinodal, increasing
activity causes the fluid to exhibit slightly more pronounced ordering
concommittant with a shift of typical interparticle separations to smaller
distances. For the active hard-disk system, the static structure evolves
from the passive one to an essentially $v_0$-independent active one: the
$S(q)$ data with increasing $v_0$ converge to a well-defined limiting curve.
The high-density fluid reveals an interesting non-monotonic change in $S(q)$
with increasing $v_0$. Small self-propulsion velocities destroy the ordering
that is present in the passive dense fluid, but further increasing the
self-propulsion velocity reinstitutes more pronounced ordering at a shorter
average particle separation. This highlights the interplay of a
nearest-neighbor length scale (that determines the fluid structure in
equilibrium) and the length scale introduced by persistent swimming.
It is possible to qualitatively understand the
active-fluid $S(q)$ by analogy to the effects caused by an attractive
interaction in an equilibrium fluid. In particular the non-monotonic evolution
of $S(q)$ at high densities suggests an effective attraction of a range
that is around $10\%$ of the particle diameter. From this, an interplay
between the effective activity-induced attraction width and the interparticle
separation length arises. In the equilibrium fluid, such an interplay
causes non-monotonic changes in the dynamics that lead to a reentrant
melting of the glass \cite{Dawson2001,Pham2002}. Indeed, a similar reentrant
behavior of the glassy dynamics of an active fluid (albeit not an ABP fluid)
has been discussed \cite{szamel2015glassy}. It should, however, be stressed
that the effective-attraction description of $S(q)$ does not acknowledge
the non-equilibrium nature of the active fluid. While changes in
the glassy dynamics of an equilibrum fluid are largely governed by changes
in $S(q)$, the same need not be true for the ABP system.
The fact that activity enhances structural order in the low-density fluid might at first
sight seem surprising: The single-particle dynamics of ABP can be
mapped onto diffusion with an enhanced diffusivity, $D_\text{eff}\ge D_t$.
This mapping suggests a description in terms of an enhanced effective
temperature, and from such a mapping, one would expect the oscillations in
$S(q)$ to become less pronounced.
The qualitative mapping to an effective attraction, instead of an effective
temperature, much better explains the observed changes in $S(q)$.
The effect of rotational diffusivity on the low-density static structure
of the active hard-disk fluid is weak. At high densities, the influence
of $D_r$ is masked by the onset of phase separation, so that the trends
emerging in $S(q)$ are less clear. As already known from studies of MIPS,
it is not possible to maintain the high-density strongly active system
in a homogeneous fluid state. Doing so may be possible in suitably polydisperse
systems (either using size polydispersity or polydispersity in self-propulsion
speed).
Our data can be used as a reference for future theoretical studies which construct approximative closures for the structure based on the
Smoluchowski equation \cite{Haertel,SpeckEPL,FarageBraderArchive}
or for mode-coupling-like dynamical theories that either need static
structure factor data as an input
\cite{FarageBraderArchive,Berthier2013,Szamel}
or can in principle approximate it based on the equilibrium one \cite{mct}.
As a remark, however, the extension of theoretical frameworks to calculate
$S(q)$ and related structural quantities that characterize the
non-equilibrium steady state of active particles is not obvious, even for radially-symmetric pair potentials.
There are two basic reasons for that: first, active Brownian particles possess an internal orientational degree of freedom
which represents the direction of their intrinsic motion. This orientational degree of freedom is irrelevant for spherical
passive systems but similar to molecular liquids with rotational symmetric shape (such as rods).
For these liquid-crystalline systems, it is much more difficult to derive and numerically solve
integral equations closures to access the orientationally averaged structure factor for the particle centers
\cite{Gubbins,Patey,Klapp}. Second, more importantly, active Brownian system are not in equilibrium which brings about
complications in the description of the steady state.
\ack{
We gratefully acknowledge funding from Deutsche Forschungsgemeinschaft (DFG)
within the Special Priority Programme SPP~1726 ``Microswimmers'',
grants VO~1270/7-2 and LO~418/17-2.
}
\section*{References}
| {
"redpajama_set_name": "RedPajamaArXiv"
} | 921 |
@interface WXNewsViewController : UIViewController
@end
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,101 |
Preparative Methods: prepared fresh, or generated in situ, from Magnesium metal and typically 1-3 mol % of a mercury(II) salt such as Mercury(II) Chloride in THF or aromatic hydrocarbon solvent.
Handling, Storage, and Precautions: mercury salts are toxic. Proper disposal is required.
Rivière and Satge20 reported the Mg(Hg)-mediated reductive dimerizations of organogermanes. For example (eq 5), treatment of phenylchlorogermane with Mg(Hg) (THF, 20 °C) affords the diphenyl-1,2-digermane in 75% yield. Similarly, diphenylchlorogermane affords tetraphenyl-1,1,2,2-digermane in 73% yield.
Bickelhaupt and co-workers56 reported the use of bis(bromomagnesio)methane as a reagent for the preparation of 1,3-dimetallacyclobutanes. For example (eq 8), treatment of bis(bromomagnesio)methane (prepared using Mg(Hg) as described above) with Cp2TiCl2 and Dichlorodimethylsilane affords the novel mixed 1,3-dimetallacyclobutane in quantitative yield.
1. Adams, R.; Adams, E. W. OS 1941, 1, 459.
2. Binks, J.; Lloyd, D. JCS(C) 1971, 2641.
3. Nichols, P. P. JOC 1979, 44, 2126.
4. Corey, E. J.; Danheiser, R. L.; Chandrasekaran, S. JOC 1976, 41, 260.
5. Lenior, D. S 1989, 883.
6. McMurry, J. CRV 1989, 89, 1513.
7. Pons, J.-M.; Santelli, M. T 1988, 44, 4295.
8. Chiara, J. L.; Cabri, W.; Hanessian, S. TL 1991, 32, 1125.
9. Szymoniak, J.; Bescancon, J.; Moise, C. T 1992, 48, 3867.
10. Jun, J.-G.; Shin, H. S. SC 1993, 23, 1871.
11. Mangeney, P.; Tejero, T.; Alexakis, A.; Grosjean, F.; Normant, J. S 1988, 255.
12. Cuvinot, D.; Mangeney, P.; Alexakis, A.; Normant, J.-F. JOC 1989, 54, 2420.
13. Betschart, C.; Schmidt, B.; Seebach, D. HCA 1988, 71, 1999.
14. Enholm, E.; Forbes, D. C.; Holub, D. P. SC 1990, 20, 981.
15. Imamoto, T.; Nishimura, S. CL 1990, 1141.
16. Roskamp, E. J.; Pederson, S. F. JACS 1987, 109, 3152.
17. Kalyanam, N.; Rao, G. V. TL 1993, 34, 1647.
18. Takai, K.; Tsubaki, Y.; Tanaka, S.; Beppu, F.; Fujiwara, Y. CL 1990, 203.
19. Shono, T.; Kise, N.; Oike, H.; Yoshimoto, M.; Okazaki, E. TL 1992, 33, 5559.
20. Rivière, P.; Satge, J. Synth. Inorg. Metal-Org. Chem. 1972, 2, 57.
21. George, J.; Chandrasekaran, S. SC 1983, 13, 495.
22. Dijkstra, P. J.; Van Steen, B. J.; Reinhoudt, D. N. JOC 1986, 51, 5127.
23. Sanchez, I. H.; Larraza, M. I.; Rojas, I.; Brena, F. K.; Flores, H. J.; Jankowski, K. H 1985, 23, 3033.
24. Pakusch, J.; Ruechardt, C. CB 1990, 123, 2147.
25. Ho, T.-L.; Wong, C. M. S 1974, 45.
26. Suzuki, H.; Manabe, H.; Enokiya, R.; Hanazaki, Y. CL 1986, 1339.
27. Kano, S.; Tanaka, Y.; Sugino, E.; Hibino, S. S 1980, 695.
28. Ram, S.; Ehrenkaufer, R. E. TL 1984, 25, 3415.
29. Yuste, F.; Saldana, M.; Walls, F. TL 1982, 23, 147.
30. Varma, R. S.; Varma, M.; Kabalka, G. W. TL 1985, 26, 3777.
31. Bellamy, F. D.; Ou, K. TL 1984, 25, 839.
32. Ganem, B.; Osby, J. O. CRV 1986, 86, 763.
33. Wiberg, K. B.; Ubersax, R. W. JOC 1972, 37, 3827.
34. Celina, M.; Lazana, R. L. R.; Luisa, M.; Franco, T. M. B.; Herold, B. J. JCS(F) 1993, 1327.
35. McVicker, G. B. Inorg. Synth 1976, 16, 56.
36. McVicker, G. B. IC 1975, 14, 2087.
37. Green, M. L. H.; Wong, L. L. CC 1989, 571.
38. Hill, A. F.; Honig, H. D.; Stone, F. G. A. JCS(D) 1988, 3031.
39. Morancais, J. L.; Hubert-Pfalzgraf, L. G. Transition Met. Chem. 1984, 9, 130.
40. Jones, R. F.; Fisher, J. R.; Cole-Hamilton, D. J. JCS(D) 1981, 2550.
41. Bickelhaupt, F. AG(E) 1987, 26, 990.
42. Bertini, F.; Grasselli, P.; Zubiani, G.; Cainelli, G. T 1970, 26, 1281.
43. Georges, M.; MacKay, D.; Fraser-Reid, B. JACS 1982, 104, 1101.
44. Cardillo, G.; Orena, M.; Porzi, G.; Sandri, S. JOC 1981, 46, 2439.
45. Gewali, M. B.; Ronald, R. C. JOC 1982, 47, 2792.
46. Welch, S. C.; Rao, A. S. C. P.; Gibbs, C. G.; Wong, R. Y. JOC 1980, 45, 4077.
47. Yoshimura, J.; Sato, K.; Wakai, H.; Funabashi, M. BCJ 1976, 49, 1169.
48. Petasis, N. A.; Bzowej, E. I. JACS 1990, 112, 6392.
49. Okazoe, T.; Takai, K.; Utimoto, K. JACS 1987, 109, 951.
50. Takai, K.; Hotta, Y.; Oshima, K.; Nozaki, H. BCJ 1980, 53, 1698.
51. Hibino, J.; Okazoe, T.; Takai, K.; Nozaki, H. TL 1985, 26, 5581.
52. Lombardo, L. TL 1982, 23, 4293.
53. Piotrowski, A. M.; Malpass, D. B.; Boleslawski, M. P.; Eisch, J. J. JOC 1988, 53, 2829.
54. Van de Heisteeg, B. J. J.; Schat, G.; Tinga, M. A. G. M.; Akkerman, O. S.; Bickelhaupt, F. TL 1986, 27, 6123.
55. Hogenbirk, M.; Van Eikema Hommes, N. J. R.; Schat, G.; Akkerman, O. S.; Bickelhaupt, F.; Klumpp, G. W. TL 1989, 30, 6195.
56. Van de Heisteeg, B. J. J.; Schat, G.; Akkerman, O. S.; Bickelhaupt, F. JOM 1986, 308, 1.
57. Bertini, F.; Grasselli, P.; Zubiani, G.; Cainelli, G. JCS(D) 1970, 3, 144.
58. Wong, H. N. C.; Fok, C. C. M.; Wong, T. H 1987, 26, 1345. | {
"redpajama_set_name": "RedPajamaC4"
} | 303 |
package com.microsoft.azure.management.network.v2018_12_01.implementation;
import com.microsoft.azure.arm.model.implementation.WrapperImpl;
import com.microsoft.azure.management.network.v2018_12_01.P2sVpnServerConfigurations;
import rx.Completable;
import rx.Observable;
import rx.functions.Func1;
import com.microsoft.azure.Page;
import com.microsoft.azure.management.network.v2018_12_01.P2SVpnServerConfiguration;
class P2sVpnServerConfigurationsImpl extends WrapperImpl<P2sVpnServerConfigurationsInner> implements P2sVpnServerConfigurations {
private final NetworkManager manager;
P2sVpnServerConfigurationsImpl(NetworkManager manager) {
super(manager.inner().p2sVpnServerConfigurations());
this.manager = manager;
}
public NetworkManager manager() {
return this.manager;
}
@Override
public P2SVpnServerConfigurationImpl define(String name) {
return wrapModel(name);
}
private P2SVpnServerConfigurationImpl wrapModel(P2SVpnServerConfigurationInner inner) {
return new P2SVpnServerConfigurationImpl(inner, manager());
}
private P2SVpnServerConfigurationImpl wrapModel(String name) {
return new P2SVpnServerConfigurationImpl(name, this.manager());
}
@Override
public Observable<P2SVpnServerConfiguration> listByVirtualWanAsync(final String resourceGroupName, final String virtualWanName) {
P2sVpnServerConfigurationsInner client = this.inner();
return client.listByVirtualWanAsync(resourceGroupName, virtualWanName)
.flatMapIterable(new Func1<Page<P2SVpnServerConfigurationInner>, Iterable<P2SVpnServerConfigurationInner>>() {
@Override
public Iterable<P2SVpnServerConfigurationInner> call(Page<P2SVpnServerConfigurationInner> page) {
return page.items();
}
})
.map(new Func1<P2SVpnServerConfigurationInner, P2SVpnServerConfiguration>() {
@Override
public P2SVpnServerConfiguration call(P2SVpnServerConfigurationInner inner) {
return wrapModel(inner);
}
});
}
@Override
public Observable<P2SVpnServerConfiguration> getAsync(String resourceGroupName, String virtualWanName, String p2SVpnServerConfigurationName) {
P2sVpnServerConfigurationsInner client = this.inner();
return client.getAsync(resourceGroupName, virtualWanName, p2SVpnServerConfigurationName)
.map(new Func1<P2SVpnServerConfigurationInner, P2SVpnServerConfiguration>() {
@Override
public P2SVpnServerConfiguration call(P2SVpnServerConfigurationInner inner) {
return wrapModel(inner);
}
});
}
@Override
public Completable deleteAsync(String resourceGroupName, String virtualWanName, String p2SVpnServerConfigurationName) {
P2sVpnServerConfigurationsInner client = this.inner();
return client.deleteAsync(resourceGroupName, virtualWanName, p2SVpnServerConfigurationName).toCompletable();
}
}
| {
"redpajama_set_name": "RedPajamaGithub"
} | 3,662 |
Today I was tagged by the lovely je ne regrette rein. It's an easy one (thank god). All I have to do is answer these questions and then tag some other bloggers to do the same. Sounds fun.
1. Where was I 10 years ago? Bruce and I were packing up to move from Los Angeles to Las Vegas. We had been together for 2 years and I was still a corporate monkey, selling computer software. I hated it, but knew nothing else. My territory was the southwest west - (Colorado, Utah Nevada, Arizona, New Mexico and Southern California). We were die hard rock-climbers, travelling around the world to climb. My company wanted me to move to another part of my territory to get it going and I got to choose where. Colorado and Utah (great climbing) but too cold. We usually drove to Vegas every other weekend to climb and camp, so we decided to go with that. We rented a rocking house up by Red Rocks and stayed for 8 months. We couldn't do it any longer...too strange. I actually quit my job while I was living there, but I quit from the airport in Boston. Was tired of flying every day, tired of the pressure, tired of the stress, tired of wearing a suit every day, just tired. We moved back to Southern California and that was the start of our studio and my vow never to work full-time again.
2. What is on my to-do list today. We are moving to france in 17 days. Well, we are leaving Los Angeles for Chicago in 17 days and then well fly to france from there. But we have to have everything ready to leave in 17 days. Here's what on the list, knowing that we can't get everything done in one day, some of these keep getting put on the next days list.
- call United airlines to figure out our return ticket...will we return???
3. What would I do if I was a billionaire. Well, I wouldn't get plastic surgery. But I would buy a farmhouse in france and maybe one in Italy and maybe an apartment in Paris, because Bruce loves Paris. I'd buy another road bike and one for Bruce and I'd build an amazing studio for me and an amazing studio for Bruce, at both of our houses. I'd have a beautiful kitchen, because I love to cook, and in that kitchen I would have a Lacanche range. I would love to cook on this range. I would travel all over the world and see new places and meet new people, but I would NEVER fly commercial again, I would charter a plane, because then we could take the dogs with us everywhere and not have to put them in the belly of the plane. I would pay off everything for my Mom, my sister and Bruce's parents. I would pay for my niece and nephews college education. I would use wealth to help animals, the environment and people who live in poverty. I would try and make a difference and would hope to stay a nice person.
4. Five places that I have lived.
out of the laundry basket.
big mistake, but I never seem to learn!
6. snacks that i like.
Dill pickles! You've cut your hair after downing le vin? You might be crazier than I am.
I shudder at the daily routine of selling software while cocooned in fancy dudes and fuselages. You should have gotten a medal for that, or hazard pay.
I let my motehr once cut my bangs after she had a few vodka martinis. The results were as you would expect.
So funny that you were at the Lakes too. And, I think I have also taken a vow to never work again--I just have never done it consciously. I think it is time to do that.
Farmhouse in Italy? I'm so totally there!!!
I am going to do my best while doing what I do best, procrastinating and slipping my gears.
RG- yes dill pickles, love them and yes I do seem to have a couple glasses of wine and then look at my hair and decide I could cut it just a bit...maybe a little off here and a little off there and then I have to call my Diana, who fixes everything. I'm left-handed and hold the scissors upside down and can't even cut a straight line, have no idea why I continue to do it.
Yes, I wore a suit for a long time. The money was amazing and I would bet that if I had not met Bruce I would still be doing it. The only thing good about it was that if allowed us to buy a house in LA, start a new business and now go to france.
LBR - hope your english muffin was yummy! The Lakes - such a funky place, all the houses looked exactly the same, very poltergiest.
justfoodnow - i'll keep you posted on italy!
Becky - i know, we are freaking out a bit...but a good freak out.
LF - you can do it...I know you can! It's very easy, doesn't take a long time. Great to see you yesterday!
It was so cool I can't write about it! Perfect!
Aha! Your first tag!! I've done this one before and if I could come up with better, more impressive replies, I'd answer the questions all over again.
Red vines...ooh yeah, one of my all-time faves!
From October 2008-October 2009 we moved from Los Angeles to rural france (the Aveyron region). Took a year off from our business and fell in love with life in France. We came back to the states sold our business and in October 2010 we moved back to France. After 5 great years in France, we're moving again. This time to Cataluyna Spain. Follow our new adventures. | {
"redpajama_set_name": "RedPajamaC4"
} | 7,515 |
Q: Proof of work-energy theorem for a rigid body Could anyone show me a way to derive the work energy theorem
for a rigid body whose motion is along a fixed axis ( such as of a cylinder rolling on a plane) which states that
states that $W=\frac{1}{2} m V_{c m}^{2}+\frac{1}{2} I \omega^{2}$
using the basic definition that
$W=\int \vec{F} \cdot d r$.
A: Starting with the EOM's:
\begin{align*}
&\textbf{Translation}\\
&m\,\ddot{r}_{cm}=F\\
&\dot{r}_{cm}\,m\,\ddot{r}_{cm}=\dot{r}_{cm}\, F\\
&\frac{m}{2}\frac{d}{dt}\left(\dot{r}^2_{cm}\right)=\frac{d}{dt}{r}_{cm}\, F\\
&\int \frac{m}{2}{d}\left(\dot{r}^2_{cm}\right)=\int {d}{r}_{cm}\, F\\
&\frac{m}{2}\,\left(\dot{r}^2_{cm}\right)=\int {d}{r}_{cm}\, F\\\\
&\textbf{Rotation}\\
&I\,\ddot{\varphi}_{cm}=F\,R\\\\
&\text{analog}\\
&\frac{I}{2}\,\left(\dot{\varphi}\right)^2=\int {d}{\varphi}\, F\,R\\\\
&\text{thus work for the total energy $~T=\frac{m}{2}\,\left(\dot{r}^2_{cm}\right)+\frac{I}{2}\,\left(\dot{\varphi}\right)^2~$is }\\
&\int {d}{r}_{cm}\, F+\int {d}{\varphi}\, F\,R=
\int F\,\left(dr_{cm}+R\,d\varphi\right)=\int F\,dr\\
&\text{with}\\
&dr=dr_{cm}+R\,d\varphi
\end{align*}
Remark:
F is the constraint force between the cylinder and the plane and $~\dot\varphi=\omega$
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,626 |
Decio Vinciguerra, né à Gênes le et mort à Padoue le , est un médecin et ichtyologiste italien qui a été pendant de nombreuses années directeur de l'Aquarium romain.
Biographie
Notes et références
Bibliographie
.
Liens externes
Liste des taxons nommés par Decio Vinciguerra sur wikispecies
Ichtyologiste italien
Naissance à Gênes
Naissance en mai 1856
Décès en octobre 1934
Décès à 78 ans
Décès à Padoue | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 1,732 |
sand batch dryer - SBM Crushers, Raymond Mill, ... Find Details about Rotary Dryer, Silica Sand Rotary Dryer from Rotary Sand Dryer Used in Sand Making Line .
belt sanding machine | eBay - Electronics, Cars, Fashion ... Find great deals on eBay for belt sanding machine and wood sanding machine. Shop with confidence. | {
"redpajama_set_name": "RedPajamaC4"
} | 1,071 |
Q: How can I change hover back-ground-color of ul list items Spent HOURs without success. Remodeling current ecommerce site to be responsive. Construction site: www.abundant-yarns.com. Image below shows backgrounds I want to change. When "Our Services" is clicked, I want the gray active state behind "Our Services" to be the tan color. When hovering over the menu items, I want the blue hover color to be green. Please assist this this task. Thanks
A: .navbar-nav>.open>a, .navbar-nav>.open>a:hover, .navbar-nav>.open>a:focus {
color: #555;
background-color: red;
}
That will allow you to change the gray background on click.
.dropdown-menu>li>a:hover, .dropdown-menu>li>a:focus {
color: #fff;
text-decoration: none;
background-color: black;
background-image: -webkit-gradient(linear,left 0,left 100%,from(#428bca),to(#357ebd));
background-image: -webkit-linear-gradient(top,#428bca,0%,#357ebd,100%);
background-image: -moz-linear-gradient(top,#428bca 0,#357ebd 100%);
background-image: linear-gradient(to bottom,#428bca 0,#357ebd 100%);
background-repeat: repeat-x;
filter:progid:DXImageTransform.Microsoft.gradient(startColorstr='#ff428bca',endColorstr='#ff357ebd',GradientType=0);
}
This will allow you to change the blue hover to whatever you want by adjusting the above rules (namely: background-color).
See if this helps.
I just put random colors in there so you can see the difference. As well, you're overriding Bootstrap core CSS here so remember it will apply globally.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 8,789 |
Sampling and analysis of radioactive liquid wastes and sludges in the Melton Valley and evaporator facility storage tanks at ORNL (Listing Multiple Pages).
This report has 212 pages. Select a thumbnail to view a larger version. Result listing will show up to 100 pages per screen. Displaying: 1 of 3. | {
"redpajama_set_name": "RedPajamaC4"
} | 5,816 |
the
Other Side
of Self
The Eleven Gem Odyssey of Plurality
Susan D. Kalior
M. A. in Education in Counseling
Human Relations and Behavior
B.S. in Sociology
# Table of Contents
Title Page
The Other Side of Self: The Eleven Gem Odyssey of Plurality (Other Side Series, #3)
Prologue
The Mighty "I" | GEM #1 IDENTITY
The Pull of Destiny | GEM #2 MISSIONS
The Tributaries of Life | GEM #3 Currents and Tangents
The Land of Make Believe | GEM #4 Drama
THE SCALE OF SENSITIVITY | GEM #5 Connection
The Bog of Regrets | GEM #6 Folly
THE PLAYGROUND | GEM #7.. Experience
In the Land of Crazy | GEM #8 TRAGEDY
The Long Road Home | GEM #9 SPIN
The Invisible Crowd | GEM #10 PLURALITY
Jumping the Grid | GEM #11 INTERMUNDIAM
Note from the Author
About the Author
The Other Side of Self: The Eleven Gem Odyssey of Plurality
Copyright©2017 by Susan D Kalior
First Printing: July 2017
All rights reserved, including the right to reproduce this work in any form without permission in writing from the publisher, except for brief passages in connection with a review.
Published by Blue Wing Publications, Workshops, and Lectures
Blue Wing Publications, Workshops, and Lectures
sdk@bluewingworkshops.com
www. bluewingworkshops.com
Readers' comments are welcomed.
Other Books by Susan D. Kalior
The Other Side of Life: The Eleven Gem Odyssey of Death
Growing Wings Self Discovery Workbook: Volume One
17 Workshops to a Better Life
Growing Wings Self Discovery Workbook: Volume Two
18 Workshops to a Better Life: Exploring the Multi-Faceted Self
The Simple Guide to Feeling Better
Warriors in the Mist: A Medieval Dark Fantasy
The Dark Side of Light: Book One-INITIATION
The Dark Side of Light: Book Two-CRESCEDO
The Dark Side of Light: Book Three-ETERNITY
The Mark of Chaos
An Angel's Touch
The Golden Disc
To those caring for loved ones with dementia,
we know . . . don't we.
| |
---|---|---
# Prologue
▫
MY FAMILY WAS NEVER conventional. Instead of typical parents going out to dinner and a movie, they astral projected and went on drug free journeys. Instead of having parties powered by alcohol, we had meditation gatherings with wonderful people who brought laughter and depth into our lives.
My father led dream workshops, gave metaphysical lectures, and held energy circles that facilitated deep meditation. My mother was an exceptional astrological counselor. Although the validity of astrology might be questioned, after years of watching the planet's configurations correspond with people's life experiences, I currently believe there is something to it. Anyway, valid or not, my mother helped many understand themselves through that medium.
My brother would slip into trances that brought forth predictions and insights. My sister had a healing touch with her hands. Although she never spoke much about it or actively pursued metaphysical events, she had her share of mystical experiences. In high school my nickname was High Priestess because I was always good at espousing wisdom that made others feel better, as well as analyzing their dreams.
So, it did not surprise me that the last year I spent with my dad before he died was extraordinary and almost impossible to document, but I'll try.
Old age had come calling for him. Caring for himself was no longer an option. I answered with my heart and my bags at his door in the Arizona desert, eager to care for him in the stellar manner in which he'd always cared for me. He was my father, best friend, and hero for most of my life. And even in his condition, a hero once more, plucking me out of a turbulent three-year psycho-spiritual smack down.
My arrival was met with a man only half there. He was in the between worlds of life and death, just as My Fool (my psycho-spiritual mentor who died a while back) was when first we met. Physically, he was a mess, exhibiting signs of dementia, going lame and blind, and in a lot of physical pain. Death was at his door, and he was fine with that.
Being the philosophical sort and a strong proponent of meditation, he walked the most interesting worlds as he released his grip on life. He was somewhat like My Fool, and perhaps why I was drawn to My Fool in the first place. With my dad on the verge of death, and me barely escaping it, we were both ripe for a metaphysical journey. And we were about to have one.
My Fool, though dead, arrived in spirit. He took my dad and me on the quantum physical journey of our lives. While this might be deemed imagination, or an old man's senility with his daughter's wishful thinking, given our beginnings as an open-minded psycho-spiritual adventuring family, these perceptions fall short of the vivid events my father and I experienced that year with My Fool at the helm.
This is hard to fathom, I know, but somehow it happened. Perhaps because my father was in the in-between world. Or perhaps after a long stint of outer world turmoil, I needed to find refuge in my existential heroes. Or maybe I just never say no to journeying into dimensions of existence, that in transcending logic, broaden and brighten my reality.
I invite you to come journey with My Fool, my father, and me on the other side of self into the rich wonderland of plurality, where transcendental experiences enrich the fabric of our lives.
Buckle up now and prepare for an enlightening adventure; it is going to be a thrilling ride!
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# The Mighty "I"
# GEM #1 IDENTITY
We are who we think we aren't,
and we aren't who we think we are.
##
IN THE PEARL WHITE sands of everywhere and nowhere, I fell from my dream into time and awakened in my deceased mother's bed. The ceiling fan whirled fast above me, blowing welcoming breezes upon my face. Summer sunrays streamed through the sliding glass door and gobbled up early morning shadows. I was getting brighter too, rising from the dungeon of my grief.
After six amazing years adventuring in the Pacific Northwest, the three that followed sucked me up, drained me dry, and spit me into a metaphorical meat grinder. My pursuits were met with dead ends, I was weak from mold sickness, and the outpouring of my love and kindness, shockingly, was returned with fast balls to my heart. Even strangers were attacking me. I had somehow become fodder for people's fictional perception of me to support their fictional perceptions of themselves. Life had become like one of those dreams when you are running hard from the monster, but can't get out of slow motion, and the monster is gaining ground.
This would have been manageable if my support system there had not been carried out of my life into their own adventures. But they had. Not only did no one have my back, but I could no longer see my reflection in the eyes of anyone who truly knew me. I don't know why it hadn't occurred to me then to move back to Arizona where my family and friends resided, except that I so loved the Pacific Northwest, the ocean, forests, and rain.
Sometimes we humans get tunnel vision and refuse to quit treading in stagnate waters, and we begin to drown. And I was drowning in a life chapter that had stopped producing pages. Yet, I soldiered on.
I glanced about my mother's room, staring at the pictures on the wall of pensive women in nature, reflective of the current me: contemplative, quiet, and still, just trying to recover from a dramatic overstay in a played out location. Sometimes I am too tenacious for my own good.
I had been caught in what felt like a never ending rip current sucking me farther and farther away, not only from everyone who loved me, but from myself. My energy continued to drain, and I grew fragile.
This is what happens when we have gone too long without a kindly touch or genuine interaction.
I began to understand then how people can let themselves die, or have a mental break and harm others. They are lost and feeling hopeless, like treading dark water in a cold and cruel sea.
I began to feel unreal, like a shell of a person going through the motions. I had fallen away from the clarity, energy, and inner brightness that was always mine. I couldn't understand why I was losing all that. Losing me. I always thought I was fine going it alone, but I was wrong. We all need kindred connections to keep us grounded in our lives. Without that grounding, we fade into all sorts of unpleasant realities.
Exhausted on every imaginable level, I had let go of trying to figure it out, or direct my life, or hang on to who I knew myself to be. I was in a free fall of constant uncertainty, punches coming at me, and no current to pull me out of my demise. I was going down, and I didn't know how to stop it.
Then came the net, the direction, and my salvation. My aged father was flailing, falling fast and hard, just like me, but unwilling to burden his children, he hid his suffering and would not ask for help.
I had needed him too, his kindness, and his love to save me from obscurity, but I was unwilling to invade his space because he seemed content. I, like he, would not ask for help. But when I read between the lines and could see he did need me, I mean really need me (as I was the only of his children in a position to help) I was then quite okay letting him know I needed him too. Apparently, I really am my father's daughter.
So, as life does, it closes and opens doors directing us along our life path. Synchronicity, it is always there, if only we will see.
On a hot July day, I returned to the nest, to my family, to those who knew and loved me. In the month I'd been back, I had seen them all and began to feel real again.
Home sweet home. I stretched my arms out over the soft sage green comforter under me, more contented on top than confined beneath. I wiggled my bare toes with a smile, despite the 110 degree weather, and that the desert wasn't really my thing. My father was here, and I needed him more than the trees and rain. My father always treated me wonderfully, ever giving me room to grow into my true self. He understood me, appreciated me, respected me, and oh how I needed that now!
I could feel my mother too. Here, nestled atop her bed, I felt all cozy and wonderful, as if in her womb. She had been gone a while now, but here in her bedroom, I could feel her mothering energy comfort me still. She was a fiercely nurturing sort, and I basked in the lingering afterglow of her death.
My recently acquired black kitten, Christopher, sprung up on the bed, and started purring and pawing my stomach, enjoying my soft white pajamas. I pet him, thinking how we all really do need each other, animals, and humans alike, even we fiercely independent types.
This was a new experience for me, needing people that is, my people. I had taken them for granted and underestimated how critical they were to my well-being. After a few minutes, Christopher jumped off the bed, mewing for food.
Well, time to rise and shine, and tend my beloved father. My bare feet landed on the cushy blue carpet as my pajama legs dropped over my ankles. "I trust my life story," I murmured out loud. "All I need do is nurture my being, live in the moment, and embrace my day."
Christopher rubbed affectionately against my shin. I crouched down, landing my elbows on the carpet so he could nuzzle my face and lick my cheek, our morning ritual. All my other cats had aged out and died. Christopher and I would begin this next life chapter together, comrades in the journey.
I made my way toward the kitchen for coffee with Christopher prancing alongside my feet.
Although I felt better, lingering still was that feeling of navigating treacherous waters. I was unable to let down my guard, waiting for another sock to the heart, a post-traumatic stress thing, I suppose. I was often short of breath, and seemed to have a chronic clench to my jaw.
I would heal. I just had to work at it. Breathe, Susan. Relax. Let go. Trust life. I had been meditating several times daily to stay calm, but had trouble getting deep enough. Part of the problem was that I kept rehashing the painful memories of my recent past. I had worked too hard and come too far to let that novice lack of control consume me. I needed to get deeper, fast.
I made it to the large blue kitchen. While Christopher ate from a dish of cat food my father had apparently set out, I made my morning coffee. My dad was up at all hours, often lost in other worlds, on missions no one else could see.
I poured my coffee into a sky blue mug, watching the steam rise. I sighed heavily, then took a sip, another, and yet another. So good, that first cup of morning coffee! I needed more of that pleasantness in other areas of my life. I craved a hiatus from the confusing mundane world into the deeper realms where everything made sense. A metaphysical adventure would be the ticket to get me there.
However, the kind of adventure I was imagining, I had always done with My Fool, even after He died. I wasn't sure I could do without Him. I hadn't seen Him once in the three years of my grueling descent. Maybe I never would again. His last departure into Pure Creative Energy felt final.
I headed for the living room sofa, sipping my coffee along the way. I never liked sitting at tables. Just like covers over my body, it always felt so confining. I sank back into the billowy beige sofa, and propped my bare feet on the bulky, square, brown marble top coffee table. As I drank my coffee, I stared at my toes. An upbeat attitude washed over me. I will openly flow with whatever comes next in the Book of Me. Fear be damned.
My dad always seemed fearless. Even these days when I gazed into his tired eyes that bespoke a longing to end the staled experience of his daily life, he seemed fearless. Ever since my mom died, he had lost his will to mingle in the outside world, or bring others into his fray. His words touched only the ears of his children, grandchildren, and the occasional grocery store clerk or banker.
He often awoke at night, acting out his dreams, which generally involved a struggle to get inside his house in which he'd been locked out, or to escape what he believed was a replica of his house, designed by pranksters who had locked him in.
I theorized that this happened when he couldn't quite awaken from a deep sleep (locked out of his house) or because he was going through the mere motions of living, and in a way, wasn't really here any more (thinking his house a replica).
He had other experiences too, like being in worlds where he could see people, but they couldn't see him. Or commonly seeing a woman appear in the loft window where he listened to music. This might be viewed as senility in the public eye, and yes, on one level it was, but what is senility?
Senility by the medical community would be explained by changes in the brain, but who says what comes first? When an aged person's time to die nears, they often begin to release their current reality without realizing it. If they are not focused in this reality, why would they be anchored to it?
Those who have briefly died often report seeing a bright white light and have a positive life changing experience. It has been said this is due to something happening in the brain. But could the near death event be causing the brain change? In this, is dementia necessarily the cause of a diseased brain, or could the time spent in other realities manifest the disease?
My meditative experiences have given me the impression that brain and existential changes often happen simultaneously. Even in the case of brain damage due to an accident, perhaps on a soulic level, the vibratory configuration of that identity called for that experience, and that any consequential skewed thinking or 'hallucinations' are true in another reality.
I had to shake my head, mind-boggling myself. I guess my main point was that in old age, the veils of reality often thin, and a variety of metaphysical experiences can be had. So, my dad's invisible world was real, as are our dream worlds and even our imaginings, perhaps just not real to anyone else.
Christopher jumped up on the sofa and curled up next to me, giving me a rush of warmth. Oh, to feel that peaceful again! My dad and I both needed to sink deep into the core of our being where we could reenergize at our source—Creative Energy. While this would likely renew me in the life of Susan, it would probably help my dad die, and transition to a new existence.
His one good eye was going bad, his once adventurous gait had turned to slow motion limping, and he talked more and more of my mother, how much he missed, loved, and appreciated her.
He cherished his children, knowing they wished him alive, but hanging on was becoming a less tolerable ordeal with each passing day.
He would often get comments from others like, "You have lots of years left. You are healthy!" He actually was quite healthy, save the aforementioned. What they didn't understand is that you don't have to be unhealthy to die.
I swigged down the last of my coffee, and set the empty cup on the marble table. The empty cup, like my dad's body, was just a vessel. What is in it always goes somewhere. The coffee I just drank made a long journey to get into my body, and it will continue its journey long after it runs through me, making its way back into the earth. It never meets its demise and neither do we. Neither does anything. On we go through passages of seeming death and birth in any number of realities. In that, energy itself experiences its own constant transformation.
Still, on a human level, my dad nearing death was a hard thing. Tears pooled in my eyes. I had to let him go. Living with him daily and watching him up close, I had touched upon his deep suffering. Though he was often lucid, he regularly fell into what I term, 'episodes'. One particular midnight he woke me asking where my mother was, that he'd been looking for her everywhere. In his hand, he held her picture. It was heart breaking. Another time, he went rifling through my drawers, very frustrated because he couldn't find the air conditioner. Then there were the hours of constant moaning, groaning, and sighing.
His suffering was sad to me, and evidence of his decline, much like an old leaf drying up on the tree, longing to fall to the earth and decay into the soil from whence its roots sprang. It would be cruel of me to try and keep him here just because I did not want to let him go.
Only for his children would his death be an adjustment, but for me mostly, seeing him every day, he who saved me so many times throughout my life.
Being so sensitive, highly intuitive, and seeing only the best in others, led me into many dangerous situations with sociopaths and the mentally unstable.
In my work world as a therapist, I could handle it because they were there wanting to get better; but outside work, when these sorts got on my tail, shaking them was an ordeal, especially since they weren't always embodied. Sometimes the unembodied hitch on to unstable humans and encourage unsavory behavior. Or sometimes the unembodied are from other worlds, or other dimensions with their own agenda. My dad understood this, and knew how to guide me to ward them off. So, for me, even though he taught me well, his death would be as removing a shell of protection.
I pet Christopher, which started his little purr motor. I would really need the comfort he gave me after my dad was gone. Christopher's head popped up as a fly buzzed by his head. He bopped about on the sofa trying to get it, flipping onto the floor, chasing it about the family room. I laughed and laughed. It felt good to laugh.
I heard my dad's cane tapping on the floor. I looked to the sound. My dad came hobbling toward me, bare-chested, wearing only his white boxer shorts. He was not a modest man, nor really ever seemed to be too affected by human drama, for that matter.
My eyes trailed him until he reached me. "Good morning, dad. How was your night?"
"Exhausting." He plopped down beside me, our shoulders touching. His French brown eyes and English nose gave him an interesting look. The top of his head was bald, but the remaining hair, even at his age, was mostly black. This was my dad, eccentric and outside the norm, and this wasn't an age thing.
"So dad, tell me about your night while I put your glaucoma drops in and your compression socks on."
"Well," he began as I reached for the clear vial of drops on the coffee table. "I had a night experience of being in an upside down world. Everything was upside down."
"Wow!" I exclaimed, popping a drop in his good eye. "I've never heard anyone say that before." I put the vial back on the coffee table. "Go on."
"I also had an experience where I was born an orange baby. Everyone was orange. It was an orange world."
"Orange?" I said with interest as I reached for his compression socks in a little basket under the coffee table.
"I had another experience too, where I was a Roman trying to create Rome, the way it was supposed to be before it went off course. It was to be a place of exceptional law and order, defined by mutual respect, and a unified community with equal rights for all."
I began tugging a white compression sock onto his one foot. "You have had that dream, I mean night experience about Rome before."
Adopting what My Fool once said, my dad called dreams night experiences because the word dream often diminished its importance.
"Yes," he continued, "I also am beginning to see my next incarnation, a black woman in the South Pacific. She will help bring women to their fruition, not by emulating men, but by shining the pure power of feminine energy."
"Wow dad, that sounds truly wonderful." His one sock on, I worked on the other while imagining his next incarnation.
He added, "This life will be on a parallel earth."
"A parallel earth? That sounds like a quantum physics thing."
"Well, it just is what it is. Maybe I am just crazy."
"No, I don't think so. I think that because you are near death, and open to the next adventure, you witness things that those still attached to mundane reality, cannot."
"Maybe." He leaned back, closing his eyes.
I furrowed my brows. "Are you okay?"
"I just need a minute," he murmured.
I gazed upon him, empathing his readiness to die. He'd had so many other worldly and out of body experiences, that the impending journey after death had him a little excited.
Suddenly my dad's breathing became rapid, shallow, and without rhythm.
"Dad?" I touched his shoulder. "What's happening?"
His closed eyes rippled. "I don't know."
I calmed my mind, fearing a heart attack or stroke had assailed him. Watching him with hawk eyes, I went into a meditative state to feel what was happening, rather than guess with my mind.
His eyes opened looking blank, as if he had bleeped out of this reality and was in another world.
"Where are you dad? Are you still here in your house?"
I wondered if he was having that trapped in or out of his house experience again.
I assured him, "You are here in your house dad, the house you own."
He shook his head lightly. "I don't think so."
"Maybe you don't feel like this is your house because, right now, you aren't really here, but in another reality."
"I am in Rome before it developed a brutal reputation."
"Oh," I sighed with interest. I'd had experiences like that too being another person in a different time. Many people have, in dreams or otherwise. This always portended to me a more comprehensive meaning of what a self actually is. If we, or in this case, my dad, can experience being another identity other than Robert, then one's identity perhaps is not the sole definition of "self".
He suddenly leaned forward and stared strangely into me. I gasped. In both his eyes, a familiar miniature face sparkled. My Fool!
"You called?" my dad and Fool's mouths moved simultaneously.
With teary eyes, I inquired, "Why am I seeing you through my dad? Or am I just seeing what I want to see, or . . . what is this?"
My Fool's words came through my dad's lips, "Not only is your father more ready for an inner world journey than even you, but in his current state, he unconsciously allowed me to enter him, comfortable with my brand of energy, so like his own. "
I blurted, "But when you matriculated back into the whole again after our last adventure, I thought it was for good."
"Did you just hear what you said? Again."
"Oh yeah," I muttered, a bit embarrassed.
My dad's lips moved with His words, "Remember my dear, everything always is; there is never really any coming or going, here nor there. When you are attuned to me, you can reach through time and space, and pull the me you have known from the Wall of Remberence. You have been calling for me, whether you realize it or not, but since you were lost in the surface world, I couldn't answer. Now, that you have managed to deepen, well," He grinned, "here I am."
My Fool's twin image in my dad's eyes faded slightly. My dad spoke, "I feel like we have a visitor, a wise being."
Apparently, he hadn't been consciously present to hear me and My Fool talking. I said, "Dad, the visitor is My Fool, you know, the one I wrote about in my last two books."
He shrugged his shoulders casually. "Okay, he can stay."
Channeling energies was not new to my dad, and he could easily kick out unwelcome beings. I was glad, that to him, My Fool was not one of them.
"Dad? Are you still the Roman?"
"Yes," my dad replied. "But I can be in two worlds at once. I know that recently I haven't at times been able to tell the difference between mundane reality and my other worlds, but I can now."
My Fool's images again brightened in my father's eyes. My dad's mouth moved with His words. "Well then, shall we prepare to move inside?"
"Inside?" I questioned.
"Inside your dad's being to commence a journey to the other side of self. He is currently a convenient portal to deep inner worlds."
I got very excited. This is just what I was hoping for and intended to do on my own today. Oh yeah, that's why he's here!" At long last, I could regenerate and refresh myself by having an inner world adventure with My Fool.
My eyes lit. "You said you are here for my dad too, so will he come with us?" I know that sounds weird, but it would be different if he consciously came, or just unconsciously bleeped out of his current identity.
"Will you join us, Robert?" He asked.
"I am in, of course I am in. It will be nice to have company on an inner world adventure."
It was weird hearing my dad and Fool converse through one mouth in different tones, but I loved their symbiotic connection. I smiled, very excited to have my dad come along.
My face lit. "Well then, let's go!"
"First," said My Fool, "Let's stir the old wisdom pot and review its contents. You will need to apply these wisdoms along the way on our journey."
I nodded. "I agree, it will be a nice lead in to our adventure."
He said to my dad, "Would you care to sit in on the review?"
"Of course," my dad affirmed. "I have read Susan's books documenting her time with you, so I would find it of interest."
My Fool, through my dad's hand, placed His palm on my forehead. "Close your eyes."
The moment my eyes closed, I had a zooming sensation in my head.
My Fool announced, "You have arrived."
While my eyes remained physically closed, I metaphysically opened them. Looking about, I seemed to be in what resembled an IMAX theater. White panel movie screens surrounded me. Each panel shown a freeze frame of My Fool in his standard violet sweatshirt, white pants, and jogging shoes with the toe part cut out, headphones on ears, and Walkman on waist. His grey hair, mustache, and short grey beard were just as I remembered. This particular visage gave me such comfort, and I was fairly certain, I saw Him as I wished rather than how he actually was.
My dad appeared next to me. I slanted my eyes to him and blurted, "I love you, dad."
He smiled at me warmly.
My Fool's voice echoed in surround sound, "Focus on the panel before you. When finished with it, move to the next, until each panel has played, and the circle is complete."
The first panel began playing like a movie, starring My Fool lecturing like a professor.
"A self is often viewed as a living individual visible to the human eye, an identity of sorts, possessing a functioning body, brain, harboring emotions, capable of thought, and imbued with its own personality. However, this generally agreed upon definition of a self is akin to glimpsing a book cover without ever exploring the contents.
"Scientists and psychologists are engaged in an ongoing pursuit to probe beyond the physical understanding of what a human being is. Theories emerge, rearrange, change, and re-emerge constantly. Theologians and philosophers have their own theories based on their insights and experiences, or the insight and experiences of others. Still, there is no conclusive evidence to explain the total story of who we are, why we are, and how we came to be.
"Many, desperate to feel safe, or to have a direction, choose a given paradigm, scientific, philosophical, or religious, already postulated on the story of creation and the meaning of life. Fewer choose to embark upon their own journey to the other side of their perceived self into what mostly eludes conscious understanding, far beyond what book learning or preaching could ever explain. And of those few who do, it is generally a short period before conclusions are drawn about what they have experienced, such as, 'God talked to me,' or 'My scientific analysis leads me to the following hypothesis.' "
His image froze in the panel. I guess that meant panel one was done. I glanced at my dad, then we both shifted our focus to the next panel, and it came to life.
My Fool again lectured as a professor, "When we think we know something, that knowing generally is finite. Yet, there is always more to know. This is why our conclusions change over time, often further developed, or proven mistaken, if not outright wrong, by other information or experiences.
"To even glimpse the full story of who we are, why we are, and how we got here involves temporarily releasing all ideas ever postulated. Learning more requires an open mind regarding what we think we know. Imagine what might occur if we stepped into the unknown, naked of beliefs and postulation."
I murmured, "Like dancing in the dark."
That frame froze. My dad looked to me. "That is a good way of putting it. For me, I am doing something I learned from your books. I am opening myself up to Creative Energy unimpeded by my thoughts, a true dancing in the dark, if you will. How can one go wrong to mentally merge with the energy of creation without defining what it is?"
My Fool's surround sound voice echoed in our ears, "Yes, Robert, yes. In the concept of linear time, our 'self' is even more than the sum of all identities we have ever been or will be. Opening to the unknown broadens the aperture of what we define as 'self'."
I smiled. "That is so true. When I meditate by opening to the mysteries of life rather than directing my meditation the way I think it should go, I have had unexpected insights and treasured experiences."
My Fool said in surround sound, "And soon you will have more. Focus on the next panel please."
My dad and I looked to Panel Three. My Fool came to life, continuing his professor-like lecture. "A light bulb burns out, but the energy that ran through it still exists. Our bodies die. What happens to the energy that was in them? Can energy be stomped out? Energy always is, it just transforms when its current structure breaks down. Given that, can energy be less than everything? And given that, what is an identity?"
"The mass of who we are transcends all scientific knowledge, imagination, space and time. While pursuing knowledge is exciting and often quite helpful, in the case of understanding everything, no human can. Not completely. However, collectively, new understandings propel us all into the next chapter of the earth story.
"But if we can also, at times, get past the need to know, we can circumvent getting stuck in intellect. Intellect, at best, is using our mind to figure things out. However, sometimes 'what is' can only be experienced because it is beyond human conception.
"It is not uncommon to have a powerful psycho-spiritual experience and lack words to explain it. In this, we often fumble and come up with a way of explaining that falls short of what we are trying to convey. We usually choose words that support our belief system in describing the experience, which diminishes the purity of the event. These skewed explanations are what lingers on the minds of the listeners and often cemented by followers.
"The followers cannot have the same experiences of the ones who share them because the information conveyed was never wholly accurate. Even if the experience and path to getting to that enlightened state of mind could be explained adequately, it still would not work to that same degree, because the path is different for everyone."
That panel froze and my dad and I looked to the next one.
My Fool lectured, "To experience what is beyond identity, we must begin at our present state of consciousness, then journey inward beyond our identity (who we think we are). Inward is merely moving away from life's reflection as beheld through our identity's eyes. The source of the reflection is the other side of our perceived self. Moving inward, without directing or analyzing the experience, brings us into a pure undefined experience with energy itself, the same energy that pulses in the whole universe."
That panel froze and My Fool's voice sounded around us. "This sort of, as you put it, Susan, dancing in the dark, has led you to experience enlightenment beyond words. You too, Robert. And many others as well. There is no need to explain it, not even to yourselves. It is enough to touch it and know it for even a single moment."
I felt a warm swelling in my heart remembering these times.
The next panel came to life and Professor Fool went on, "After experiencing enlightenment, then upon returning to conscious awareness to our perceived identities, that sense of who we are beyond them, remains. Mundane life feels richer, brighter, and more rewarding. Human living seems less like an obstacle course, and more like an amazing gift to explore individuality. What is it like to experience a separate self with its own emotions and thoughts, and to physiologically behold the touch and sensation of numerous things? What is it like to be creative from a point of identity?"
The frame froze. In surround sound, He directed us, "Next panel please."
Having turned a full circle, we looked to the last panel.
Professor Fool came to life. "It is often our divine intention to move from the experience of Pure Creative Energy to the impression of everything as separate unto itself. In this, we may explore what interaction feels like, and generate new experiences. Even though we feel separate, we never are. Between separation and oneness, there are many dimensions. And that will be the nature of our adventure. So bring your focus back to your physical bodies and we shall proceed."
My dad and I glanced at each other before bouncing our focus back from where we were into our bodies. My dad and I opened our eyes at the same time, and laughed. My dad's eyes again shown My Fool's twin faces.
My Fool stretched out my dad's hand. "Come inside."
I cocked my head. "My dad, come inside my dad?"
My Fool assured, "As I have stated, his vibratory mind state makes for a perfect entrance to the other side of, what is deemed—self."
This wasn't the first time I had done something like this with my dad. We had often been in altered states simultaneously albeit unintentional, yet our experiences would interweave. But we hadn't taken a conscious purposeful inner world journey together, and no less with My Fool!
Elated to do such a thing before he died, I smiled softly, and went into a deep trance. My Fool's incorporeal hand stretched toward me. I took it, and I was in. I appeared between my dad and Fool, who both beat me on the draw.
I glanced at my dad warmly, surprised to see his white boxer shorts had turned purple. My eccentric dad. Interestingly, I was still in my white pajamas.
It was glaringly bright in here. Squinting my eyes, looking ahead, brightness was all I could see.
"Come," My Fool directed, splaying His hand in the direction we were to go.
As we stepped along, I couldn't really feel anything solid beneath my feet. It was rather like walking on bright air with no definable form about us. I felt tense and short of breath, and realized I was somehow falling behind, even though I was walking fast.
My dad and Fool were getting farther and farther away, their backs growing smaller ahead of me. I shouted out, "Wait up!" I was terrified I'd be left behind and miss out on the adventure.
They both looked back and then appeared instantly on either side of me. I looked to My Fool. "How come I can't keep up? I am walking just as fast you both."
My Fool gave me a knowing look. "You are out of alignment with yourself, kind of like double vision. You are split between here and your recent past. First on our agenda is to get you back in alignment for this journey."
My dad nodded. "Agreed."
My Fool said, "To begin, let us walk further along together so you can see of what I speak."
As we began walking, I watched my feet stepping forward. I noticed my steps were out of sync with My Fool's feet to my right and my dad's feet to my left. They walked in unison. My gait was tight and tense as if I were in a big hurry to go nowhere.
My Fool stopped us walking. "Susan."
I looked to him.
He gazed penetratingly deep into my eyes. "You have become stuck in your human self's identity, and the roles you play: martyr, savior, victim, an old pattern for you. You are stuck even though you've taken steps to transcend your identity and merge with your quintessential being."
I nodded tearily. "I need to get unstuck so much!"
"Well then," He said, "To begin, define human identity."
I answered thoughtfully, "Well, as humans, we generally identify ourselves with our bodies. As we grow, our sense of identity grows: our likes and dislikes, our strengths and weaknesses, how we react to events and people, what makes us sad or joyful. All this gives us clues to who we are. Identity to most is really just a projection of how we discern ourselves from others, an interpretation of who we are, tall or short, smart or dumb, creative or practical."
"Go on," He urged.
I dug a little deeper. "The more we understand who we are, the more we can identify with ourselves. If others are similar to us, we identify with them. We make a connection."
"And?" He paused for me to go on.
I continued, "Our self-identification carries on in our dream worlds. We generally are still who we identify ourselves to be in our waking world."
He asked, "Always?"
"No. Sometimes, we dream we are in an unfamiliar body. This can be another identity that is also us, but in another reality, or time period. In a linear perception, one might call it a past life identity that comes into focus, usually because what happened then is redolent of what is happening in our current life.
"For instance, my son once had a dream that his father, who looks different than his current father, was an army general in World War 1, and my son, who also looked different, was under his command, but they were brothers. They were in conflict, and the general (my son's father) left my son to die. The dream reflected my son's upset then, feeling neglected and unloved by his dad. Of course, in this life, they eventually repaired the rift and have a great relationship. But much of what we feel often bleeds through from an old story that we have forgotten."
"Good example," my dad complimented. "I remember you telling me about that."
Feeling rather proud, I went on, "Another example is when we fall in love. We sometimes fall in love with a person we knew from another once upon a time. However, who they are currently is imbued with a new identity with a different personality. We may feel confusion because their behavior isn't what we unconsciously remember. We are conflicted, in love with an identity from another time and place, yet, in a sense, stuck with the new version of that identity before us.
"For instance, we think of our lover as a swashbuckling type, but he currently sticks his head in the metaphorical sand whenever he is challenged. We might get angry at his uncharacteristic behavior according to our unconscious memory. Yet, having had his head whacked off in many other lives, maybe now sticking his head in the sand is due diligence."
My Fool said, "Yes, humans tend to quickly judge the whole show by glimpsing a single frame."
I added, "I think this quick judgment also happens when we unconsciously remember an unsavory past with a person in our current life. We might cast villainous dispersions on another, remembering that person as they were in another time and place. For instance, that identity may have greatly betrayed me, even killed me. But in this new identity, that would never happen given transformational changes and a new mandate for that person in this life."
My dad added, "And we humans, not usually remembering our old identities and the story of us that led up to today, really are dancing in the dark." He paused, then said with a smile, "Or maybe anxiously jumping up and down," he chortled. And so did My Fool.
I laughed too, "Yes, I guess we do that more often than we'd like! These are the things that go beyond current psychology and science. Our struggles are not always from our childhood, or at least not just from our childhood or events that happened to us in this life."
My Fool raised a brow. "And don't forget our other selves in various realities can also affect our current identity."
"Yes," I acknowledged, "I remember that lesson. Sometimes, our other identities are going through something difficult. Without realizing it, we feel the runoff of their emotions."
My dad said, "Identity is funny thing. Do we ever really know who we are?"
"Perhaps not from the human standpoint," answered My Fool. "More importantly, however, is that beyond our own self-identification, untapped potential lies within each of us. If we could open to that, imagine the possibilities."
That thought soothed me. What was my untapped potential? I was looking forward to that discovery.
"Time to get aligned, Susan." My Fool spun me around so quickly, it startled me. I was like a spinning ice skater, whirling so fast I could not be identified.
I glimpsed various faces as I spun, knowing somehow they were all me. It started with the different aspects of me, like the nun, the warrior, the nurturer, maybe twenty or so faces, then it grew into the faces of all the lives I've ever had, or am having (in non-linear time). Then it seemed to expand into all the faces of the earth into the millions, plant and animal identities inclusive. This went on for so long I lost track of time. I had spun so fast, I didn't even feel the spinning anymore. Deep inside myself, I felt like was in the still eye of the storm.
I had a weird thought then, that all these faces were being shaken out of me, because after all, what was me? Is there even a me at all? Or just the idea of a me. I began to notice many unrecognizable life forms. I gasped with a sudden sensation of being all things.
I heard music, Richard Wagner's, The Ring, playing, but not through any instrument. My Fool always said that the music is ever playing everywhere in life, and in fact is often what musicians hear when they compose. We need only alter our state of consciousness to hear it. And I certainly heard it now. Releasing the idea that I am my identity, I felt like I was on a one way swing that flung me into a huge female face.
Having seen her before, she was a goddess of sorts, like the top part of a carousel that umbrellas all the horses beneath, the horses being my numerous selves in various realities. I called her my Great Self. Of course she was not likely a she or a personification at all, just how I beheld her, I mean my Great Self. We all seem to have one, there to love and guide us.
Residing in my Great Self, my stiffness loosened. The stifling blockade I had erected in my recent past, began to dissolve. I choked down tears. No more. I inhaled a deep breath. I consented to allow my human self to feel good and strong and powerful instead of victimized. Tears streamed down my face. My pain drained away like a punctured abscess releasing me from that old torture. And though I still needed to heal, that past no longer had such a hold on me.
I then experienced a strong shift, like a sonic boom breaking the sound barrier. Feeling turned inside out, my identities all about me now basked in Creative Energy. I was in a zero gravitational space, in an undefined form, in a deep quiet place, yet everywhere, calm but stimulated.
I heard clapping and I appeared back with my dad and Fool in the inner world.
My dad smiled. "She's ba..ack."
"Feel better?" My Fool asked with a grin.
I nodded. "So much. I am back, I mean reconnected to my Great Self. I do feel so much better!"
"Good," My dad and Fool proclaimed simultaneously.
My Fool said, "Now, you both need rest so that your physical bodies can sleep peacefully instead of regurgitating thoughts of the day, given your heightened activity here."
I said, "But, isn't it still morning? We have barely begun."
My Fool's eyes sparkled. "Time is different in the inner world."
I cocked my head. "Yes, I had forgotten. It has been awhile since my last adventure with you. Just hard to believe it is already bedtime for our bodies. I know though that once they are in deep sleep, we will feel more enlivened in this realm, just as people do when they dream. Dreams are never just dreams, I know. It is only in our waking world that we demote them as less important than our mundane reality."
My dad nodded in agreement.
Suddenly the scene changed and we were in a young meadow of short green grasses and baby wildflowers.
I looked about. I liked it. The natural world always calmed me. "I really like it here." I commented, "I just wish the meadow was a bit more mature."
My Fool looked at me knowingly. "Give it time, my dear, give it time. Once your physical bodies are in deep sleep, we will continue our adventure." He looked to my dad. "Then Robert, it will be your turn. Rome awaits."
My dad's eyes lit with both excitement and bitterness.
My Fool pointed downward and there appeared two glowing golden mats, reminding me of magical beds. He bade us lay.
We both retired to our mats. I don't know how my dad felt, but a wave of sleepiness washed over me. Before I could close my eyes, something light touched my stomach. I sat up on my elbows and peered at my belly beholding a charm-sized fingerprint. It disappeared and I felt something on my wrist. I held my wrist up gazing at a beautiful gold bracelet with the fingerprint charm on it. I jiggled it admiringly.
"The gem of identity," My Fool commented. "All perceptions of identity are but an aspect of our one true self—Creative Energy. And every I that seems to come knocking on your door or from inside of you, is all just one mighty I."
I nodded with a faint smile, overcome with a great sense of relief to feel all I's as one. Nothing to fight, no one to hate. Struggle faded in unification.
"Rest now, my dear."
Hearing my dad snoring lightly next to me, I closed my eyes, ready for sleep.
I sighed, releasing future worries. I saw myself jumping off a cliff into the unknown to see what would happen. Living life now, moment by moment is all we can really know. So I will dance in the dark, and come what may.
And with that, I drifted to sleep hearing the words My Fool had long uttered, It is I. It is I. It is I; don't you know who I am?
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞You too, are so much more than you could possibly imagine. The identity you have decided is you, is but a fraction of the whole you. It is as a mask we wear for a short while to catalyze needed experiences that generate more Creative Energy. But we all need nourishment and it is hard to get from a mask. So take heart in these times and open to the vaster god/goddess like you without defining what that is. It is simple really, just sit under the stars and imagine you are all of them.
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# The Pull of Destiny
# GEM #2 MISSIONS
Missions give us purpose; and purpose gives us missions.
##
MY DAD AND I AWAKENED in our meadowland to My Fool sprinkling orange sparkles over us.
"Wake up fellow adventures. Today is about Rome."
I stretched and yawned, seeing pleasant sparkles glistening all about me before disappearing. I sat up feeling refreshed. Our physical bodies were still slumbering, which was good because it was so much easier to adventure in this world without distractions from that world. Here, it felt like morning with dawn light slowly brightening the meadow.
My dad sat up, looking about. Then we both rose without the usual grog many feel upon awakening. We could eat here in the inner world, but it wasn't necessary, and neither my dad nor I craved food. We were ready for adventure!
Standing side by side, me in my white pj's and dad in his purple boxing shorts, we looked to My Fool for direction. Behind My Fool, brilliant oranges and shadowy purples cast by the rising sun painted the landscape. A new day. A new chance. A new experience was at hand.
My Fool stared into my dad. "Today is about you, Robert. We will journey deep into your being."
My eyes slid sideways. "Are you ready for this, dad?"
He answered, "More than you could ever know."
My Fool nodded. "Very well. To begin, face each other. Susan, look far into your father's eyes."
I gazed into my dad's rich glossy brown eyes, a father's eyes at first, eyes that had watched over me all my life, like a warrior at the gate, ready to swoop in and save me from circling predators. And he never stopped, no matter how old I was, or how old he was.
Deeper I went, deeper, and deeper still. An electrical type energy buzzed at the crown of my head, turning to a strong tickle, then a zooming sensation, and I was in my dad's world. My dad and Fool were already there. Gazing about, I viewed an expansive landscape marked with sheer, seemingly permeable boundaries encompassing various realities.
My dad had been uncementing himself from the anchors that held his identity and life story in place for some time now, which is likely why the boundaries were so sheer. My inner world would probably show thick boundaries as I yet had much to do in my current identity.
"Come." My Fool's hand stretched out to show us the way. As we started to walk, the various realities began to look like a house of opal mirrors. Each mirror of milky white glistened prism colors about the silhouette of an identity.
My eyes were large with wonder, honored to be exploring the inner workings of my dad's being. Glancing at him, he seemed thoroughly content, as if this adventure was his mission, perhaps the last in the life of Robert.
We walked along, perusing mirrors, continuing our philosophical discussion. I asked occasionally if we could enter this or that mirror to explore my dad, but My Fool kept saying not yet.
After awhile, My Fool stopped abruptly, facing a mirror that reflected a silhouette. The form became clear. It was my dad's current image.
"Gaze into the mirror, Robert. You too, Susan."
I commanded myself to stop thinking and just flow deeper into the experience. As I continued to gaze into the mirror, I went into a trance. I am not sure what my dad was seeing, but I saw his whole life going backwards from an old man to a baby. As this happened, all with whom he engaged became branches of a storyline going back into seeming forever.
I saw my mom and the branch of her family zooming back and back, then my brother's, then my sister's, then mine, for we had all been together for a very long time. Then all the family and friends he ever had were also branches of his storyline. All these branches made my dad's earth journey seem like the biggest tree in the world, but deeper into each story were more stories that transcended human perception; worlds into worlds into worlds, into mind, body, and emotion itself.
Dizzied, my head fell forward, eyes shut.
My dad was sighing and gasping a bit, so I assumed he was experiencing something similar.
My Fool said, "Now, go forward into the seeming future."
I lifted my head and peered into the opal mirror that again reflected my dad as an old man. I allowed myself to see him forward in time. I saw his death, then his journey into seemingly infinite mirrors into infinite worlds. Some worlds seemed minute, then opened up really large blending into everything, and at the same time shrunk until they became nothing.
Huh? I closed my eyes a moment, again, feeling dizzy.
"Go a little longer, Susan," My Fool instructed, "See all of it now in this moment."
Opening my eyes, countless one of a kind pieces flew together, as would a shattered mirror being repaired into one reflection of an indefinable image. The pieces seemed to be identities, and the image seemed to be all identities as one.
My jaw hung open; tears formed in my eyes. I don't know why it affected me so, save my deepened insight into what I already knew. All identities were really one great identity. One Being. One energy.
Tears spilled down my cheeks. My tears fell not from pain, or even joy. What I felt transcended emotion, even though I was crying. It was as if all my struggles in the life of Susan disappeared into the clarity of belonging, of being . . . everyone, and it was all right. Everything was, is, and will be, all right.
I felt a warm hand on my shoulder. I thought it was My Fool, but when I turned my head to the hand's owner, it was my dad. His eyes were clear and strong here in the inner world, void of the confusion his physical eyes so often shown.
"So you see," my dad raised a brow, "you cannot lose me when I die, because . . . we are . . . each other."
A fresh batch of tears bathed my cheeks. I don't know why I couldn't quit crying, not at the idea of losing my dad, but at the clarified idea that all my identities, worries, and fears were as a fiction, and the nightmare was over.
I muttered, "It is I. It is I—"
"Don't you know—" My dad continued.
My Fool finished, "—who I am?"
I kept boo hooing.
My Fool took my hand. "Come, you don't want to stay here too long. The identity of Susan has not yet finished her mission. And Robert, you have a mission now before you."
My dad said, "The Rome Mission."
My Fool nodded. "Yes, Robert."
My tears began to dry as He led me and my dad onward toward a slowly brightening scene. It seemed to be an expansive cliff that overlooked an ancient city. A man was crouched at the cliff's edge. The air around us turned orangish, all the way to the cliff.
We arrived by the crouched man, who was more of a spirit, and stopped to observe. My Fool's palm waved above the cliffs edge, and there appeared a scene in the valley below. "Behold early Rome."
Below us there was an aerial view of structures and roads. Then the city scene changed from outdoors to indoors, resembling a conference room, featuring a dozen regally dressed men seated at a large rectangular table.
My dad gasped a bit, "That is me, the one at the left far end of the table."
The spirit man rose, and looked straight at my dad. I didn't think he could see us, but he blurted, "He is me too. I am his spirit, and one of many who helped conceive Rome. Not so much building and creating the city or system, although there is that, but the greater mission is to construct a vibration of a certain potential Rome can be in its purest form. It shall be a great dawning of an advanced community that catalyzes honor, wisdom, justice, and exalted knowledge for the rest of the world to benefit."
My dad seemed unable to speak, overcome with emotion, acknowledging the spirit man was of his Roman self from so very long ago.
The spirit man crouched again, his palms held out toward the city, sending energy into the third dimensional realm. The scene became a panoramic view of Rome. The view became more and more beautiful, and the people in it glowed.
I felt like we were observing a preview to a movie. We watched as time seemed to progress so subtly it was hard to notice. Things continued to flourish, public welfare, art and theater. Inventions abounded to bring ease to the human race: aqueducts, plumbing systems, and superior architecture. Then as if blight had hit, somehow along the way it took a bad turn from the original intent. Greed and power overcame the once abounding spiritual beauty. The powerful wanted more. They wanted to rule the world. Death and destruction ensued, slavery and cruelty abounded.
The spirit man's head fell into his hands, distressed that it had all gone so wrong. The beauty he had envisioned had been lost in the ugly quest for power for the sake of power alone. His human self in that actual storyline had watched it all happen, at first with dismay, but then, he, like the others, was pulled into the power, and become one of the mongers.
The spirit man wept.
I looked to my dad. My heart sank. His cheeks were awash with tears. My dad never cries, so this Roman thing was really key for him.
My dad said softly, "My mission was difficult, although it appeared at first so easy. But the lust to accumulate power short-circuited the mission."
I said to my dad, "Now I understand why all my life, I have watched you deflect opportunities to gain power and acclaim." It was true, every time my dad was offered something that would boost him up the ladder of success, he declined.
The spirit man looked up at my dad and shook his head. "I am sorry. I tried. I tried and failed. It is so hard as a human to manifest the very best of who we are, the hidden positive potential that has yet to be actualized."
My dad knelt, and gazed into his eyes. "Maybe we can try again. Maybe."
The spirit man nodded, then turned back to gaze upon the horror that Rome had become.
My dad rose, facing My Fool and me. "I'd like to go back some day to the inception of Rome and try again to create the Rome that was meant to be, here from this ethereal realm."
My Fool touched my dad's shoulder. "Do it now."
My dad cocked his head, looking curiously at My Fool.
My Fool explained, "In your many lives, the theme of honor has been explored. You have examined honor from every angle, including dishonor. You are nearly done. You have learned that too much honor is as imbalanced as too little honor. One can easily, stubbornly hurt themselves or even others in the name of honor, so honor has its dark side.
"In your Roman identity, which is ever with you, the mission had changed from bring to balance male and female energies of give and take, reception and creation, to conquering and acquiring power. Many lives sprang from that one, accentuating top heavy male energy. However, those experiences have served their purpose. You have slowly been reintegrating your feminine aspects to balance the scales within you. In your next and last life, in the concept of linear time, you will transcend honor and dishonor altogether in the recreation of a New Rome, restore an equilibrium of male and female energy within you, and thus about you. It is time."
My dad eyes rolled back, trance like. "Yes, honor is a story for the human world. I need but experience honor in balance to finish it, then my rudder is set and my oars are in motion to row me out of that theme into—"
"—the sea of conclusion," My Fool finished.
My dad nodded. "Yes. That."
My Fool said, "In beginning the rebuilding now, you can continue the process when your physical body expires."
"A New Rome," my dad sighed, as if relieved.
My Fool clarified, "The New Rome, you understand, has nothing to do with the current city of Rome. All that Rome was to be when first it was created will be manifested in another story through a black woman born on a Pacific Island in another earth."
My eyes widened at my dad, as he had spoken of this woman just yesterday. Looking to My Fool, I asked, "Why another earth?"
My Fool answered, "The time line is different there. Here, women are becoming empowered, but largely by utilizing the masculine energy inside them. On the other earth, women will become empowered by developing the feminine energy inside them. This will yield quite different results than your current earth focus."
"But how will that help us here?"
"Remember Susan, all earths are connected and affect each other. So, in your father helping to create a New Rome there, it will do much good here."
That might sound confusing, but in recalling what My Fool had told me long ago, that there are many worlds, all interconnected like the ripples in a fan, it did make sense. This woman my dad was to be would reside in another realm every bit as real as this world we all live in and understand as reality.
My dad blurted, "I find it interesting that our after life missions can be so different from one another. For some it is about an idea of heaven, others to be reincarnated into this or that. Even the missions we have in our current lives often have nothing do with tangibles, like becoming president or earning a million dollars. Sometimes our mission is about using Creative Energy to create."
"Yes," said My Fool, "Is the great desire to complete the actual painting on canvas, or is it the Creative Energy itself at work that carries the most importance?"
I said, "In the human world, we tend to focus on results more than the process; and yet the process is everything. Just because we don't achieve what we were trying to achieve doesn't mean we did not achieve something much greater."
My Fool nodded. "Well said."
"So," my dad shrugged his shoulders, "I suppose my drive to have another try at creating a New Rome is more about the process of experiencing creative energy, rather than the rationale that drives the mission."
"Yes," My Fool nodded. "That is it." We will now converge our energies to get you started."
He glanced at me as if asking, 'Are you up for that?'
My receptive eyes confirmed the idea.
"Before we begin," He said to me, "let us stir the pot of wisdom once more and refresh our insight on missions. This way your father can go into it with that mindset."
I nodded lightly. "Let's see." I rolled my eyes up, recalling what I learned, lectured, and written about from my other adventures with My Fool. I began, "Before manifestation of anything, there is vibration. The vibration becomes something, like a painter painting a picture, or a composer creating compositions. All things have a vibration even if they never manifest in our mundane reality."
"Go on," My Fool urged.
"So before the brain becomes physical, one's master intent, or mandate for that life, is already set. References are built into our brain to create certain perceptions that will propel us into needed adventures to complete our life missions. These references are countless bits of information that come forth at the right time as we journey into our lives. For instance, a compelling urge to quit or start school, or to pursue a lover, to take a turn down a road that leads to something amazing, or maybe horrifying. These experiences then give us what we are after in order to fulfill our life mission preconceived before we were born."
"Very good," My Fool's eyes glimmered. "Shall we begin?"
My dad nodded.
Looking at my dad, My Fool jerked his head slightly at the spirit man still sunken in his devastation. "You might want to get him, this self of yours whom you've long shunned."
My father nodded with quivering breath, stepped over to the spirit man, then knelt. The spirit man gazed intently at my dad, then blended into him.
This was all so mind boggling, this matter of selves, dimensions, separation, and oneness.
My Fool reached out to me and my dad, and we three formed a circle, joining hands, eyes closed.
"Fall into the story," My Fool began, "of flowing Creative Energy into the female infant born in the South Pacific. She will spearhead this project. Focus on filling her with all that Rome was to be."
My Fool's voice deepened, "She is the vibration of unity and equality, able to permeate boundaries and foster the reality of oneness. This isn't for most, yet there are numerous beings in her earth world who are ready to begin dissolving the impression of separation to some degree. The energy created from this exalted reality will bleed through to the earth where your bodies currently reside. It will serve as a compass to help guide those lost in the abyss of illusion to the great clarity within."
I smiled, just loving that concept. In our earth, it almost seemed like we humans were advancing so fast in the outer world, we were losing touch with our inner world. We could use some energy that would draw us more inward to gain stability.
"I see her," my dad said, "I see myself as a black baby girl on a boat. I am thrown overboard, but floating on something."
My dad almost choked, unable to speak.
My Fool said, "Keep going, what do you see next?"
My dad's voice trembled, "I am somehow washed ashore and found by a man who seems to be an important leader. His wife can't have children and they want me."
My Fool said, "And there it begins." Now let's build the dream.
Almost immediately, I had the sensation of we three as one energy. It was strange creating not with our minds, but with the energy of 'becoming'. It was like the energy of the baby's brain was being created, and made just so, to be what it was meant to be. And we, the creators, were not our identities, but Creative Energy itself. Not sure what was really happening, but that is how it felt.
Time seemed to fade away, yet the feeling kept intensifying slowly, culminating in a strong release.
My eyes flashed open. My dad and Fool's eyes were open too. My dad was glowing. Perhaps the glow signified that he was already becoming his next identity. I loved thinking of him being reborn rather than dying.
We dropped hands. I noticed we were back in the meadow. My Fool said to my dad, "That was a good beginning. You have taken a step in giving yourself over to the next adventure, and in that, the identity of Robert is a bit more defocused."
I had mixed feelings about that, but I tried not to linger on those thoughts.
My Fool announced, "In your physical world, two days have passed."
"Two days!" I exclaimed. I couldn't believe two whole days had passed. Our physical bodies back home had awoken and continued on by rote, doing what we do, but our deeper selves were able to remain here in this world and keep it our primary focus. Others in the outer world might have viewed us as in a bit of a daze, our minds adrift. But that was okay for a while.
My Fool said, "Your physical bodies are in need of a good night's rest, and regeneration is necessary for you to continue on here. Return your focus there for a bit. Then we can go on with our adventure." He pointed to the two golden mats on the meadow floor, adorned with sunset lighting.
"Will you be near?" I asked.
He laughed a bit. "I am always here, there, and everywhere."
I smiled faintly, finding great comfort in that.
My dad sat on the mat. "Well let's get to it, Sue." He curled up on his pad looking quite comfortable.
I sat on my mat, lying down with a sigh, face up. I was weary and glad to have time to regenerate. I glanced over at my dad. His eyes were already closed.
I exhaled a tired breath, my eyes falling shut. What would tomorrow's mission be? We can never completely predict our future because every second we are changing. As we are always transforming, the future point we envision is only relevant to who we are at the moment. As the change progresses, so does everything else.
Unforeseen things happen, further stimulating various changes, which alter our outlook and hence affect our projected life direction. It's not that our future changes from what we foresee it to be, it is we who change. And if our forecasted future does come to pass, it might manifest differently than expected. For example, we might marry our so-called soul mate, but that liaison might trigger a series of events forcing us to face our inner monster.
Sleep Susan, I told myself, stop thinking. Just one more thought. Even though outside time there is no past, present, or future, everything just is. In time, we live out the story that we as Creative Energy conceived.
I jolted with a gasp when something landed on my belly. I lifted my head and viewed a U-shaped magnet. I sat up, curling my fingers around its curve. An urgent compulsion coursed through me to complete my life's mission that transcended my understanding of what it was. My hand shot straight out before me, almost pulling me off the mat.
My whole body trembled.
My Fool said, "This is the Gem of Missions. When we feel driven, it is the pull of a mission we have designed for ourselves. Our many sub missions are all key to our core mission. No matter what the mission, it is what we somehow need, a gift to ourselves to experience something that will make us more than we were. This experience enriches the fabric of everything."
The magnet disappeared. As my hand drifted down to my leg, I glanced at my gold bracelet. Next to the dangling gold fingerprint keepsake, was a gold u-shaped magnet charm. I smiled feeling good about the way my inner world adventure was going.
My body relaxed as I fell back down upon my mat. I sighed, feeling important to myself.
"Sleep now," My Fool said.
I closed my eyes with one last thought before I drifted off. Our greatest mission is to grow into our individuality. Only then can we feel our oneness. Anyway, that's how I viewed it.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
Everyone's missions play an integral part in our collective becoming. Yours too. Our missions transcend intellect and anything we can imagine. Whether or not we feel anything profound is happening with ourselves, others, or anything, there always always is.
Believe not what you think you see, or surely know what you think you know. Lay aside assumptions of who and what you are and where you are going in life. Sink deep into your center, and you will feel where to go.
You are uniquely special, not to be compared to any other. Have a little faith in your life purpose, what you are meant to be, and the experiences yet to come your way. Each moment in your day is a dot of adventure driven by a quest to fulfill your missions. Watch how the dots connect, and behold the picture that is your life story. Your story. Yours. Put your hand over your heart and feel that now.
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# The Tributaries of Life
# GEM #3 Currents and Tangents
We go off on tangents, and tangents go off on us.
##
ONCE MY PHYSICAL BODY was in deep sleep for some time, I awakened in the inner world on my back. My eyes opened to puffy clouds in a blue sky. I turned my head and peeked through green grass blades about six inches tall. I watched a little red ladybug crawl up a blade.
Sitting up, my eyes drank in the meadow. The green grasses were taller than yesterday, sporting an abundance of bluebells and lily of the valley. Nearby, a small lush green hill presented itself as another new feature. Glancing about, I inhaled a deep breath. I loved the meadow!
Growing up, my technique for calming down was to envision myself in a long white dress with lengthy hair flying as I joyfully scampered amongst the wild meadow flowers.
I felt a slight energy shift, and noticed I was wearing a long white dress. I brushed my hand over the soft cotton on my knee. I think the dress represented my more innocent days, or perhaps the innocence inside me, inside everyone really, no matter how buried. My feet were still bare. I never did like wearing shoes and socks.
I looked to my dad's mat, but startled to see a pair of knees inches from me. Scrolling my eyes up, my dad was looking down at me. "You look rather blissful," he commented.
I stretched. "The meadow does me good, dad."
He shrugged his shoulders. "That is probably why we are here."
"Well, I love it," I rose to face my dad, yet clad in his purple boxer shorts.
He rocked up on his toes, then back down on his heels with a grin. "Are you ready for a new adventure?"
I nodded affectionately, loving this special time with him.
"Shall we?" My Fool sounded.
We both turned to the voice.
My Fool was there in his usual white pants and violet sweatshirt, jogging shoes with the toe part cut out, accompanied by twinkling eyes, headphones and Walkman in place. I always saw Him this way. Always. I think maybe because He was such an expansive being and this visage enabled me to see him more clearly.
I nodded lightly, then cocked my head with an affectionate smile.
Eagerness brimmed on my dad's face." Let's begin."
Here in this world, his mind was bright, and he could walk without impediment, his scoliotic spine, unimpaired. This wasn't true for me, I could still feel my body's woes, but perhaps my father was more immune as he was so near death, in a way, always more here, than there.
We stepped along the meadow grasses, me in the middle. A minute later, I slowed at the onset of a thick energy. My eyes widened and my heart sped as we stepped along through the invisible mass. Suddenly, as the energy seemed to thin out, the scene darkened to pitch black. We all stopped in our tracks.
Against the blackness, bright colored light balls bounced about, catalyzed it seemed by a magnetic energy. Many collided and joined together in various configurations, intensifying their pull. The more balls that joined a mass, the more force that unit had. Eventually, a mass of united balls became a string, seemingly formed from the pull of a current.
The various colored balls banded together in numerous combinations, some multi-colored, some the same color, and others with various hues of one general color. There were many different width and densities. The variety was astounding. Soon there were hundreds, then thousands of light ball currents.
The streams then began to appear as a massive cluster of highways criss-crossing over and under lapping, moving in various directions, in varying speeds.
I shook my head, dizzy.
My Fool said, "Keep watching."
I watched. Sometimes one stream would break apart and join with a new stream that changed the color and consistency.
I commented, "This is kind of like human behavior."
My dad said, "It is kind of like everything."
I laughed, "That's true. Since I study human behavior, I guess my focus is there. Ever since I was little, I was interested in—"
"Susan." My Fool's hands clapped. "Deepen your mind state, lest you go off on a tangent."
I nodded, then closed my eyes for a moment to refocus. Hearing Orf's Carmina Burana playing in the background, it was easy. I don't know if it was really playing, or if I just wanted to hear it, but there it was.
I inhaled a deep breath, releasing my thoughts, and concentrated on truth beyond all beliefs. I sighed deeply and got back on track. Opening my eyes, the darkness had changed to dawn. The massive highway web of light ball streams were still there, yet seemed less daunting in the light.
As I said that, I suddenly noticed how beautiful some of the light streams were. They seemed to flow with a kind of harmony and brightness that surpassed all the other light streams. I pointed to a particularly beautiful one. "Some are so striking."
"Yes," agreed My Fool. "These streams are the currents of life that pull us all in various directions. Those really beautiful streams are how we flow when we feel when in alignment with our master life purpose."
"Is that like our primary life mission?"
"No. We go on missions to fulfill our purpose. The mission of being a great teacher might have the purpose of guiding hundreds of students into their full potential to incite positive world change. Or the mission to explore outer space might have a purpose of finding new worlds to live in."
"Oh," I exhaled. "So our missions are our adventures, but the reason for those missions are our purpose?"
He nodded.
I gazed upon the light streams once more. "So
the less bright streams then, are those of us who haven't quite found our way, or our purpose, and are going off on tangents, and maybe are even stuck in them?"
"Yes." My Fool answered. "Everyone has a master life purpose with various sub purposes. The greatest pull we feel is from our master purpose. However, most are drawn off their path, taking detours along the way. We often need to experience what we don't want, before we can come to know what we are truly after. For example, a woman who is drawn to have many affairs may have a life purpose of knowing emotional intimacy. Or," he looked at me, "a woman who tends to go off on social causes because she is comfortable giving herself away, might have a life purpose of fully developing her individuality."
"I know. I know." I slid my eyes to my dad. "Remember that dad? You always reeled me back in with 'you can fight for a cause, but do not be consumed by it. Walk your path, not someone else's.' "
My dad's eyes widened. "Oh yes, I remember. Even now, you tend to rush to give yourself away, when your real mission, I think, is to take yourself back that you can fulfill your true purpose."
My Fool nodded at me. "Yes, taking yourself back, for you, is balance. Everyone needs something different. The difference is discovered upon sinking into our quintessential selves, then nourishing that quintessence to become who we are meant to be."
I smiled faintly. "It's really then just about becoming who we quintessentially are. That is so beautiful, yet," I sighed, "my martyr pattern is tough to shake." I shook my head. "It's weird how we can go off on tangents even when we are abundantly aware they are not good for us. The tide of emotion just pulls us off track. I will bend over backwards to please him because I need his love. Or I am so mad; I am going to punish her. Or, I am excited, I am going to jump in with both feet, even though I haven't checked the facts.
My Fool said, "It is the way it is supposed to be. Exploring side roads that seem to take us the wrong way will give us the experience required to stay on course later, as well as strengthen the thrust of our master life purpose to actualize."
My dad chimed in, "And to have these side road adventures, I guess we'd have to be completely consumed with the perceptions that will facilitate the experience we seek."
"Yes," My Fool confirmed, "Our minds must become closed to all else. We are going to do what we are going to do and no one can stop us. In this, it is easy to get lost from our true path for extended periods of time."
My dad said, "Overreacting to how people treat us, I think, is one way we get off course, and maybe stay off course."
My Fool elaborated, "Yes, when we have strong, and/or prolonged reactions to others who throw critical, condemning, or even ego boosting energy at us, we can get sucked off our trajectory onto theirs by making them the focus of our lives. Our focus has been stolen, and we have let it happen." He said theatrically, "She hates me; I don't measure up. And the tangent is set."
My dad chimed in with the same theatrical spirit, "I hate him for insulting me, and I never want to see him again. And the tangent is set."
I jumped in, hamming it up, "Gee, I really like what she said about me; maybe I can get more of that from her. And the tangent is set."
My Fool explained, "In all three instances, our focus is derailed from that deeper sense of centered living that only comes when we are aligned to our master life purpose. We play and replay various side bar scenarios, leaving us tired, unhappy, maybe bored, in trouble, or wanting more."
My dad tapped his chin. "I think that quest for more is another way we can go off on tangents, searching out there for what can only be found in there. Never quite feeling that inner brightness and joy of living, many of us go down numerous outer world roads in search of it. In our quest, we might fall into puddles of agony, get pummeled by emotional storms, and become lost in the social wilderness, but never find what we are after. Some even conclude peace can only be had in a paradise after life."
My Fool nodded. "Yes, the search for peace can dishearten us. Yet, sometimes we need to falter, experience destructiveness, and die unnourished, even prematurely. Though that paints a horrid picture, in the long run, for instance, that soul may in a future life, act as a savior for the human race. However, most go in and out of their quintessential flow throughout their lives. When out, the pull to get back in is powerful for it resonates with our quintessence, and will always guide us back to it."
"So," my dad concluded, "this quest for a sense of inner wellness really does seem to be the carrot that draws us forth to have various experiences."
"Yes," agreed My Fool. "The need to feel vibrant and whole sets us on a determined course where our experiences will eventually nourish our individuality into a one of a kind creation. This alignment with our selves as individuals brings us in balance with everything and everyone around us."
I chortled. "Interesting, that individuality, not conformity, leads to unity. When we all try to become like each other, there is unrest, for the essence of who are is denied."
"Yet," My Fool pointed to an intersection of dull light ball streams, "even when we are seemingly off course, the experiences reaped serve to make us wise, catalyzing growth not only in ourselves, but others. For instance," He looked at me. "You stayed in the Northwest seemingly too long, yet you learned about aloneness, the need for human connection, and though your efforts felt futile to you, you spurred growth in many."
I furrowed my brows. "I guess that's true."
"In short, the tangents we take—"
I gasped a bit as numerous paths sprouted all over him like tree branches.
"—are part of our growth. The more we have gone off on tangents, as previously stated, the stronger we are to resist them once we are flowing with our quintessence. We can then bypass all the hullabaloo on the sidelines enticing us off our path. Having learned our lessons, our focus remains steadfast on our own becoming. Once our master life purpose is fully actualized, we then arrive at —".
I finished with Him, "—the sea of conclusion."
He smiled. "You know me well."
I returned the smile.
My dad smiled too. "That is how I feel about me dying. I am concluding my life and preparing for my journey in another reality. Well, with the New Rome and all, I guess I know what that might be now."
My Fool added, "Or who you will be, or are now, and that is just one of your selves. Your black woman life is just one of your many selves that are still in various places and times. You are gathering them now, simultaneously finishing the adventures of all the earths."
My dad cocked his head slightly. "I can sense that. The pull is strong." His voice cracked, "My time is near."
I looked at my dad sadly.
My Fool addressed me, "Now, now, let's not go off on a tangent."
"Yes, I know," I said with trembling voice, my eyes glued to my dad, "Still, I am having a hard time letting you go."
He said, "But Sue, you let your Fool go, and look, here He is."
"Sometimes—" My Fool began.
Looking at Him, the numerous branch like paths that had sprouted all over him were replaced by a bounty of black biting creatures flying toward Him.
He finished, "—our fears, like fear of a loved one dying, can become the tangents that lure us off our path."
The black biting creatures vanished, but a dismal gray light stream started coming at me. I felt the pull of the current, and then my feet were lifting off the ground. Like a magnet pulling me, I started to fly toward the grey stream charging my way. "Oh no!" I shrieked.
My dad said, "Think about it Sue, tangents are the manifestation of grabbing onto an idea that we decide is true. Leaving is good for me, but you are focused on the idea that it will be bad for you, but will it? Be open. If not, then you are letting a current take you off track from the adventure we are trying to have."
"I don't know how not to be sad about you dying," I cried out, losing gravity.
"Shift your focus, Susan," My Fool said calmly, "to here and now, and our next adventure."
I quickly thought about here and now, taking this next adventure with my dad and Fool. I repeated over and over, "I am having an adventure with my dad and Fool." I concentrated with all my heart.
My feet touched down next to them.
I sighed, relieved to be grounded.
My Fool continued his diatribe in a nonplussed manner as if I had never been swept away. "If you want to continue the inner world journey, keep focus on your quintessential being beneath your mind's conjecture and the bubbling up of emotional currents. If instead, you feed your fear, then what you fear is felt right now as if it has already happened."
"I know. I know," I said, a bit breathless. "I think unstable people, or gullible people, like me, are easily prone to being sucked into tangents."
"Yes," My Fool agreed, then pointed to a very small woman, almost like a Barbie doll sitting against a tree with her forehead bowed to her upward bent knees, looking sad. She lifted her head and looked all around as if searching for someone to comfort her.
I said, "She looks kind of lost."
"Observe," My Fool instructed.
A colorful stream of light went zipping by, then circled around as if discovering her. When it stopped, it looked elf-like, reminding me of Rumplestiltskin. It said, "What's wrong lady?"
The woman desperately spewed her pain, "Everything I try to do to be okay, fails. I have no life purpose. I am caught in a whirlpool that has no meaning."
The elf creature said, "Come, I can help you. I have the way to your salvation." He reached out a hand, and she took it. Suddenly they both zoomed off in a streak of colored lights.
"Keep watching," My Fool bade. The elf creature zoomed around collecting stray people who were ailing and lost in their own lives. He became stronger and more colorful with each collection, but the people behind him, with each stop, were turning greyer and dimmer, as if the elf creature was feeding off their loyalty.
My Fool said, "Because they have no direction of their own, they take whatever pops out bright and strong and unquestioningly follow. Sometimes it is an idea coming from another that sucks us into a tangent."
I cocked my head. "I guess that is how people get snagged into dangerous groups, such as terrorists, or self-serving cults that in the long run, hurt their members. It's like people can get so desperate for love and acceptance, or purpose and a life direction that they will believe any charismatic person or encouraging pitch, just to get a few drops of nourishment, meaning, or a feeling of security."
My Fool added, "While some charismatic leaders truly believe in their pitch, many more are power mongers aware of their strategy, such as banning religion, or forbidding boundaries to be crossed, to prevent uprisings."
"Yes," my dad said, almost guiltily. "They have tasted power and it is getting the better of them."
My Fool winked at him. "You and I know a bit about that, don't we?"
My Fool had told me how He as a human, like my dad, had been sucked into the goal of absolute power many times over. I looked to my dad. "Rome?"
My dad nodded with a hard sigh. Then he shook his head, as if shaking off the thought. "No, no, I will not go off on that tangent."
But I started thinking about it, about my dad's tendency to be seduced by power and how I always hid from it, and how I wanted to stay hiding, ever fearing to show my true self to the world.
The creature zoomed again and came to me with questioning eyes inviting me to join him. He must have thought me an easy target. I did have inclinations to sell my soul to anyone's cause, because any yarn of love and peace could attract my attention so much, I wouldn't look behind the illusion at the mal-intent lurking there.
I boinged my defiant eyes at the elf creature with a resounding, NO. That was an old me in younger years of my life, giving myself away, saved only by my dad who had a stronger hold on me. Over the years, in that regard, I had learned to resist those currents that would take me away from myself.
He zoomed away with his long line of colorless followers.
I said, "It seems that while sometimes we are swept away in the flow of other people's judgments, our own judgments often get in the way, like me judging that I will feel lost when my dad dies."
"Oh yes," My Fool turned on His heels, and waved His hand. A wall of squares appeared before us, showing living scenes. One square had two women jumping to conclusions to degrade their cousin behind her back. Another square had a stern mother waggling her finger at her son, chewing him out for something he didn't do. Another square shown a tight-jawed man loading a gun, mumbling, "She will pay for cheating on me." Another square had a woman berating her husband for not making more money.
Staring at the squares, I murmured, "What horrible realities," then said louder, "the judgers exude superiority by demeaning whom they judge."
The two gossiping women looked at me. One said, "Don't judge us. Our cousin is a moocher, and lazy. Come and meet her, you'll see." I just glared back at them, saying aloud to my companions, "They're mean. I have been judged like that and I am about the most self-sacrificing hardest worker there is."
My Fool laughed, "Now you are judging them."
"Yeah," I said, "but they deserve it."
My Fool chortled, "Whether you realize it or not, you are already going off on a tangent with those two women by giving the time of day because of an old event that happened to you."
I shook my head. "You are right, you're right. As long as I know who I am and believe and love my own being, none of that matters."
My dad looked pensive.
I asked, "What are you thinking, dad?"
He said, "Just realizing the magnitude of our surface judgments and how destructive they can be to our personal relationships. I try hard not to do that."
"Dad, you have succeeded. You have always said that we can't always stop others from judging us, but we can stop ourselves from judging others. You taught me, through example, to reserve acting on judgment with our loved ones, unless our opinion is asked, or to show loving concern, but then back off. I think that is why none of your children ever went through a rebellious phase with you. Our whole family has always been close because of that. And when we did ask your opinion, you would give it with the caveat that it may or may not be accurate."
My dad sighed, "I am glad for that."
The wall of scenes disappeared. "Come," My Fool said, turning back to the super highway web of light streams. "Let us continue."
We walked under the web as if walking under a bridge. I was really done with going off on tangents. They all just felt so familiar and overplayed. "I needn't get sucked into currents even if my own toes are being stepped on." I said aloud, mostly to myself, "I must engrain it in my head that when I am challenged, I need only preserve my integrity and inner peace, and not feed those attempting to derail me by engaging with them."
My dad nodded. "Yes, when we resist going off on tangents, the allure of the tangent loses steam. What felt like 'truth' to such a strong degree we would stake our lives on it, can then be seen as unnecessary drama."
"Precisely," My Fool agreed. "When we cling to partial truths as the whole truth, it is as pressing our eyes against binoculars viewing a portion of the scene, yet declaring full panoramic vision. This enables the 'dog with a bone' experience. But with binoculars removed and a broader picture at hand, our conclusions change. When that happens, we are able to release the experience that could only be had by the binocular view."
My head bobbed in agreement.
He went on, "We can then also see that the tangents others take are their business, for they too embark upon their own journey to have the life story they 'need' whether we can understand it or not."
My dad added, "And if the tangents they take affect us negatively, we needn't try to change their minds. We can do for ourselves to feel better."
"For example," I interjected, "If you are snapping at me, I can go do something I enjoy. If you are taking advantage of me, I have the right to withdraw my energy from you, and use it in a manner that nourishes me."
My Fool said, "That's it. Everything comes to balance when we balance ourselves."
I added, "When we are kind to ourselves, we choose to act in ways that nourish us. But when we continuously act out of fear, sorrow, or anger, we are often left bereft. There is, of course, a therapeutic time for these emotions in certain circumstances, but when others who maltreat us become the center of our reality for a prolonged period, then we have gone off on a tangent—theirs."
"Indeed," My Fool nodded. "These tangents, as we touched upon earlier, are often old stories from other times and places that we have already lived. The ladies gossiping about their cousin was upsetting because it touched upon your old story. You could have spent all day stewing about it or possibly reengaged to tell them off. The present situation resembles your old reality making it easy to fall into it, and relive it as if it were happening now."
I grimaced. "I am trying hard to avoid that, I mean not let my past worsen my present by rehashing bad memories that nag at me, sparking the old anger and fear. I, like many, are laboring to release an unsavory past and walk out of the fog to begin a new life chapter."
My Fool smiled softly. "The fog will clear all on its own if you can stay the course with patience and focus, one foot in front of the other, and resist getting distracted. Step by step by step, not looking ahead to miles of the vague unknown, but only at your feet, stepping along, shutting out the voices, whether within or around you, enticing you to fear, hate, and hurt."
I cocked my head. "It's like focusing only on flowing along in the river of our quintessence, even if we don't understand it or know where it will lead us." I paused as a mantra came to my head. "Cut the ties I think I need, and let spirit form the bonds."
My Fool clapped His hands. "Very good!"
Suddenly it seemed we were in a river floating along as if on inner tubes, but we were just on our behinds. The scenery about us was beautiful, chirping birds in trees, sunlight glimmering on the water. It felt so nice to glide along.
My Fool, between me and my dad, declared, "This flowing peacefully along is what it is like if we can resist going off on tangents. Here, we are in the deeper moment, which is always crisp and clear, even euphoric."
We just glided along so peacefully for what felt like enjoyable hours. I determinedly chased away dark thoughts that wanted to crash my party.
Suddenly we picked up speed, and it seemed we were headed for a waterfall. I began to panic. "Oh no, what now!" I cried out.
"Hush," said my Fool.
"Focus," said my dad.
"Go with the flow," said My Fool.
"Be one with the water," said my dad.
"Be one with your self," added My Fool.
I focused real hard on what they said, and muttered, "I am one with the water, one with myself."
Then it seemed we were weightlessly flying. I felt a downward pull, but we seemed to just hover near the crashing water. Reaching the bottom, we floated along on the water as if the waterfall never happened. I opened my eyes in delight. "Wow, it worked!"
Now I was in the middle of my dad and Fool as we floated along almost shoulder to shoulder.
I turned my head to My Fool as He spoke. "Sometimes earth-shaking life events just happen. When they do, trust in your master life purpose, and focus on flowing with your quintessence."
I turned my head to my dad as he added, "You needn't tangle with the rattlesnake, just bid it adieu and be on your way."
My head went back to My Fool as He proclaimed, "You needn't pull those at the bottom of the mountain to the top, nor can you, lest you cheat them of their journey. Just bid them adieu and be on your way."
I twisted my head back to my dad as he said, "You needn't believe anything you hear, save your own song and sing it with joy, no matter what response is forthcoming from others."
Geez it was like being with the Bobbsey Twins. My Fool began to speak. I slid my eyes His way, feeling a bit nauseas, turning my head side to side so often. Why was I turning my head at all? My ears could hear just fine. I always made things harder on myself than necessary.
"Susan, you actually have been learning how to tell the difference between a tangent and your true path."
"Yes." I agreed. "The tangent has a sense of urgency, like I'm being inducted into a way of feeling that seems rash. When actually off on the tangent, it feels more real than anything on earth; it is the be all and end all, but there is a feeling of emptiness trailing behind me, as if there is no real substance to my action, just perceived substance."
"In that," My Fool began. "—you are not in your natural flow." He threw out His hand as if to create something. "This is you when you are not in your natural flow."
Before me was a vision of a hummingbird with beating wings, zooming ahead of the river's flow out of sight. I had to laugh. It looked so funny.
My Fool said, "You tend to want to get a move on with things way ahead of your natural flow."
"I do that, I know I do that."
My dad said, "I used to be that way too, very mission oriented."
My Fool said, "And you are not alone."
Suddenly, I saw a mass of people like me, hummingbird people, similar to type A, in constant accomplishment mode, going at high-speed motion, zooming over the river flow out of sight, miles ahead of where they needed to be. I laughed again.
"It's sad," I sighed, "but also kind of funny. This rushing doesn't really get us anywhere because our flow is what it is, and we still have to go through the growing process and we can't rush growing. So many of us rush through our days trying to get numerous things done. Our focus is on one task to the next and the next, getting a little high off of each thing we achieve. And when we slow down and curb our high speed achieving, we get anxious."
My dad said, "Yes, then there are those who feel like their feet are stuck in mud and every step is a major effort. These people are trying to catch up with time and often fall into depression. Sometimes they quit moving altogether."
I said, "Then there are those who hide in plain sight, not really moving at all, they just put on the appearance so that everyone will leave them alone."
My Fool said, "And there are those who glide through a day, relaxing into whatever comes and remaining cool no matter what befalls them. These people are in the deep moment and not distracted by their thoughts."
I looked at my dad, "Even though you have been mission oriented, I always remember you like this, having air of inner balance."
My Fool cleared his throat. "All speeds are okay, too fast, too slow, too stuck, or flowing just right. All experiences have merit, but we can change course if we choose."
I said, "Well for me, I am ready to leave behind the hummingbird world, beating my wings a thousand times a minute to achieve, achieve, achieve. I am ready to settle into my natural flow and not the million sub currents that whisk me into soap opera drama. I am done with that. No more drama for me if I can help it. I just want to quietly flow with the synchronicity of life. When I flow like this, thoughts born from trying to get a one up on the future or escape from the past, dissipate along with emotionally charged thoughts, fears, and rages that can suck me into tangents."
My Fool said, "However, be grateful for the tangents, for they offered something you needed at the time. The appeal satisfied some longing inside you, or flamed some deep-seated fear. It was what it was, and it did what it did, for a reason. Eventually all these tangents lead us back into our quintessence."
My dad went on, "And when we do get back on course, we can feel relieved and appreciate our sideline experiences in a new light. What once we hated, we now forgive. What once hurt us, we now heal."
"Yes," My Fool concurred. "Ah, peace. And we roll along until another tributary beckons us to have another experience. Depending on the experience and the type of drama it incites, we may decide, Nah, I know about that kind of experience and I am done having it, I will just continue to flow along and enjoy my life. Or we might crave a certain kind of adventure, and say, What the hell, I am jumping in and going that way!"
I said, "I think for me, the trick to avoiding tangents is not to necessarily believe what I feel."
"Or even what you believe," My Fool commented as He tossed something on my head. I could see it in my mind. It was a big arrow with many smaller arrows attached pointing in different directions. He explained, "The gem of currents and tangents. May it remind you to draw wisdom from tangents, and joy from your quintessence."
I lifted my hand to it to feel if it appeared as I saw in my mind. It did. I felt a bit silly with this arrow contraption on my head, but soon we were all laughing as we floated blissfully along. The arrow assembly dissipated into my head, yet appeared as a third charm on my gold bracelet. I held up my wrist to the sun, enjoying the glimmering gold of my three charms.
Inside me, however, I could feel the pull of the arrows. One arrow pulled stronger from a deeper more blissful place. I realized then that 'true north' in life direction can be distinguished by an accompanying inner calm, even in the face of an emergency. The other currents that sweep us off on wild goose chases feel urgent, rash, and can incite agitation. With that, I closed my eyes and enjoyed the serene ride, that was, at least for this moment . . .mine.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞Oh the tangents of our lives! If you are weary of emotional dramas that feel depleting, stop reacting to agitated feelings of urgency to behave rashly and/or close mindedly. These tangents arise as a fallacy in our own thinking, giving power to faulty or destructive beliefs that manifest into a tunnel vision reality, often void of wisdom and love.
When the tangent begins to feel like the only choice you can make, stop and meditate, let it go, clear it out, calm down. Let the waters settle. Breathe in. Breathe out. Focus instead on the quintessential you, flowing in Pure Creative Energy.
The current of the quintessential you will surge through the illusion of obstacles and bypass the side currents of other people's realities that can suck you out of your bliss. Hands reach out to you, Come this way. Go that way. Over here. Over there. Keep focus on your 'true north' yours, and there you will go with an inner calm transcendent of human emotion. Your Great Self is always reaching out to you. Take that hand.
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# The Land of Make Believe
# GEM #4 Drama
We feed the fiction; the fiction feeds us.
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WE ALL FLOWED ALONG so peacefully on our inner world river that I fell into a deep altered state. I was flying at high speed over what seemed like the North Pole, moving so fast that all below me was a blur. Words came to me in a woman's voice and it felt so soothing. She seemed like an exalted version of me, perhaps my Great Self that umbrellas my many selves (my plurality). Our Great Self comes through in many ways in various forms in accordance with what we need and believe at that time, but there is a feeling to it that seems beautiful, wonderful, and wise, always guiding us toward what I could best term as unconditional love and broad understanding.
Her words made a soft imprint on my psyche.
"We invent our lives every day. Each morning we awaken, conscious thoughts come to mind. I hate her; I love him. I enjoy my job; I hate going to work. I fear this; I am confident about that. All these thoughts, shaped by our point of view, are a snapshot of what we decide our reality is that day. We have been deciding what our reality is since childhood, and we will until the day we die."
My speed over the arctic scene slowed as she continued speaking.
"Our ongoing interpretation of what we perceive creates and propels our life story. In short, we each live the story we decide is what we want to believe."
I had an epiphany when she said that. Perhaps everything is more the same than we realize. One person is who she is, but will be viewed differently by everyone depending on the construct of the viewer. Our makeup influences our perception, and hence the way we think. In that, the same person is actually a different person to everyone on earth. So, maybe we seem far more different to each other than we actually are.
As I slowed further, I could see below me a great mass composed of fragments, millions of them, like pieces of a mosaic, jiggling, bubbling almost, sparking sometimes, pieces flying out, and some just floating off. Some areas had a conglomeration of pieces that seemed melded together like melted plastic. I couldn't really define anything specific.
The woman's voice continued, "Individual perception is necessary. If we did not filter out all the stimuli around us and make some sense of it, (even if erroneous) we would not be able to step forward and act upon anything. Without the ability to siphon out and pinpoint the next scene of our story, deciding what is important and what is not; what we need and what we can live without; we would feel overwhelmed by all the choices. Multitudes of data all around us, without a focus, would render us paralyzed to exist in the world. We have no life without inventing a way to perceive it. In many ways, we are a product of our imagination."
With those words, I honed in on one part of the mass. I seemed to be lowering to it without trying.
The woman's voice went on, "Our collective perceptions are our belief system. Our beliefs anchor us to our invented life story, that for whatever reason we need to have. The conflicting and harmonious beliefs of each identity create a global story.
As I neared, I began to see landscapes, and people in various scenes. I wondered if I had to pick one in which to land, but I wasn't sure which to choose.
The voice explained, "You will land naturally in the reflection of the vibration in which you are currently attuned."
With that, I quit trying and let the process occur. The closer I neared a scene, the slower I dropped, like in a film going from high speed, to normal, to slow motion.
The voice sounded so softly in my ears, I kinda loved it. "As you already know, all perceptions touch upon truth. No one perception is absolutely true because there are endless points of view about anything depending upon where we are standing. The bottom line is that no one really knows anything. Selectively choosing what is true and what is not is the product of the human mind."
I thought about that. We really do go off on our perception of truth every moment of the day. We are happy or sad because we have gone off on a perception. We are vengeful or kind because we have gone off on a perception. We love or hate ourselves because we have gone off on a perception.
The woman continued, "While this is all part of each human's life adventure, and rightfully so, if you can keep in mind, Susan, that your whole reality is just you going off on perceptions, then it will be easier to step back and not believe what you think you see. The truth will show itself soon enough."
I really agreed with what she was saying. If a perception is causing us pain, such as nobody loves me, or, it's all over for me, we can think, Well, it seems that way, but maybe it isn't. Basically, don't believe what appears to be. Rash reactions can take us down dark roads.
The woman's voice instructed, "Remember this, Susan, when you land."
I seemed to be coming down in a crowd of people. I cringed, usually not doing so well in a jungle of stimuli. Still, it was better than all the aloneness I felt in my last Northwest years.
The voice said, "When you can admit you don't know anything for sure, your conscious mind can open to life's deeper dimensions where more profound insights can be had. In this, you open to what you don't know and see glimmers of what you can know. In reality, there is no one reality; there only is what is, and that transcends everyone's reality."
As my feet headed toward the crowd getting ready to touch down, I heeded her words. Open up to what I don't know. Do not preconceive the nature of my experience. I held my focus there.
I landed, but I wasn't in a crowd at all. I was standing in a small pile of autumn leaves in a warmer world of browns and oranges. About me were maple trees and a small community nestled amongst them. I was quite surprised at how differently I experienced my reality based on how I was thinking. I may still have been in crowd for all I know, but since I shifted perception, it didn't feel like it.
The woman's voice said, "We humans analyze the world around us to make sense of it. Conclusions are drawn and solidified into a foundation on which to build our lives. The foundation, paradoxically, while meant to bring stability or a sense of sanity, is just a self-created fiction in the sea of truth. Stability isn't really there, we just pretend it is."
Interesting, I thought. We feel safe if we decide we are, but are we ever really?
In perusing my surroundings, two scenes appeared, each with a person guarding a doorway with a sign overhead. One woman had a broom in her hand. Her sign read, "If I keep my house spotless, I am in control of my life, and thus secure."
When others came to the door, she made them pass inspection of cleanliness before they could enter. And in a fast forward bleep of motion, she was inside chasing people out of her house with her broom, swatting their behinds to shame them for being unclean.
Then she would be at the door again, looking relaxed and tense at the same time. As long as she could have complete control over the state of her home, she was okay, yet ever lonely, not understanding why fewer and fewer people wanted to enter her abode. In her effort to feel secure, she wasn't.
Another doorway had a woman in a designer business suit with a baton in her hand. The sign read, "My net worth in business equals my value as a human." She opened her door to presidents and kings, but blocked it with a baton from paupers and ordinary people, bobbing trespassers on the head should they dare try to enter.
Her significant others would come and go in her life, but be treated as if they were a million miles away. She drank alcohol to ease the loss of emotional intimacy. And she ever feared that if her professional life went sour, so would she. In seeking to increase her value, she lost it.
I murmured, "We are never really safe, I guess, never really stable."
The woman's voice sounded, "It is more that we are never really in danger and never unstable, we just create the drama." When she said drama, it bellowed in my head. She added, "The drama of these two women is your drama, for these two women are you."
"Me!" I exclaimed. "My house is a mess half the time, and I am more likely to cavort with the homeless than the rich, and sabotage any hope of financial success because the nun in me deems it a sin."
"Yes, that is you, but these women are your saboteurs, those destructive voices we all hear within us at times. One says, If you can't keep your house clean all the time, you are worthless. The other says, You are irresponsible to let money slip through your hands to aid or cheer others.
I sighed hard, "Yes, I do have aspects of myself that ride me like that, and then they seem to manifest in people I come in contact with, like my last two room mates."
The woman explained, "That happened because in your need for companionship to keep yourself from slipping away, you deemed yourself a failure, evident by everything persistently turning against you. This gave strength to your inner saboteurs."
That made so much sense! I was my own worst enemy. Really, we all are.
"There is more," the woman said.
I grimaced, trying to stay open, not sure I wanted to hear more.
You have a martyr nature, hence when in that focus, you attract persecutors (abusers) into your life. Until you can find and sustain an inner balance of this duality, these dramas will continue to manifest. Balance for you is to give, but not give yourself away, and to disconnect, but only from abusive people and situations."
"Yes, yes. I can see that."
"There is more."
I tried real hard not to tighten my jaw. Truth is just sometimes hard to swallow.
She asked, "Now, what is the common denominator of the two women?"
I said, "Do you mean the two women here, the ones inside me, or the women I lived with?"
She answered, "All of them."
My eyes narrowed in deep thought. Then it came to me. They were all in isolation, as I had been. And still am to some degree, still steering the little lost boat of me to the mothership.
It was then I felt myself back on the river still floating along on my behind as if sitting in an inner tube.
I opened my eyes. I was indeed back on the river, but I was all alone. No dad. No Fool. Did my dad die? I mean physically? Is that why he wasn't here?
I started to panic, and found I was no longer floating but getting swept away by rough waters, falling sideways, face down, and all over the place, feet in the air, sometimes choking on cold water, drenched to the bone, feeling everything as uncomfortably as my physical body would, like we do in dreams. I was still attached to my body after all.
I gasped for air realizing my thinking was causing this mayhem. Calm down, Susan, calm down. I held my focus. The waters began to slow and smooth out.
I focused on my mundane reality, deciding I needed to return for a bit, just to see if my dad's body was still alive.
I focused on home, meaning my body. I felt the shift. I saw my hand washing a pan in the kitchen sink. I was back. I abandoned the pan and raced to my dad's bedroom. Don't die on me, dad, not yet! He wasn't there.
I scampered up the stairs to my dad's loft where he so often meditated. Please don't die today, I'm not ready! I saw the back of the purple armchair he usually sat in, facing a picture window that gave view to the desert. I couldn't tell if he was in it. I walked slowly to the side of the chair, my heart pounding. Would I find him dead? He was there, eyes closed, his chest rising and falling gently. I let out a sigh of relief. He was alive!
Since his body was alive but not in this focus, he was likely still back in the inner world with My Fool. So where were they? Time to go back in. Eying the beige armchair next to my dad, my black kitten Christopher was all curled up in contented slumber. I lifted him gently, then sat, replacing him on my lap. After gazing at me for a moment, he snuggled into the crook of my legs and went back to sleep.
Closing my eyes, I released my thoughts and worries. Trusting in life's synchronicity, I gave myself to it. Breathe in, breathe out. Breathe . . . in. Breathe . . . out. B r e a t h e i n . . . b r e . . .
Deep in my trance, I reappeared in the inner world back in the meadow sitting in a half lotus with my white dress plumped about me, and feeling much better. The meadow scene had developed more. The base of the hill was lush with clusters of deep purple and pink lupines. Butterflies flitted about the tall, elongated flora. I was sitting amongst yellow buttercups where bees hummed and grasshoppers played amongst the grass blades.
A bit further in front of me, bright yellow goldfinches chirped amongst tall grasses, catching bugs. Gazing upward, the azure sky sported an occasional fluffy white cloud. I gave a small smile acknowledging nature's beauty. Now, if only my dad and Fool could be seen.
I heard laughing. My dad and Fool came up over the hill conversing playfully, walking toward me. Look at those two, I thought, like long time buddies. I sprung to my feet and raced to them, blockading their walk. "Where were you! I was so worried. I thought you died dad, I was so upset!"
My Fool's eye twinkled. "Oh, the drama!"
I smirked, feeling a little embarrassed. I had created that whole fiction in my head and lived it out as if it were real, and my Great Self, had just educated me about this very thing. "You're right. I spun my own yarn and believed it."
My Fool said, "Humans need fiction, but the nature of that fiction is primarily up to us. We allow our mind to weave what it will despite substantial evidence, and sometimes no evidence at all."
I furrowed my brows. "That is so true. We live in a bubble of perceptions that define everything."
My Fool blew a slight breeze out of his mouth, and a bubble landed on my nose. Crossing my eyes, I saw a little person in it. Then it rolled off my nose, floating down to the meadow floor. Many bubbles began floating all around us, each housing a little person.
My dad looked about them. "It is all kind of beautiful, isn't it, the roles we play, and the plays we create."
"It is," I nodded, trying to lighten up. "I just wish I could remember to view it that way. I tend to view our fictions as a product of human ignorance; for if we were wise enough, we'd see that our conjured realities are not truth."
My Fool narrowed a knowing eye at me. "Yes, but too much wisdom can circumvent adventure, and the making of a life story, or even a world story. While all our realities are a creation of our imagination, charged with emotion and belief, what we experience is real. Just as what we experience in dreams is real. We awaken and say, "Ah, it was just a dream. Yet, lingering there are the powerful impressions the dream left upon us."
I said, "Yes, but if we are always lost in a fiction, it seems we'd be cut off from our deeper being."
"We are not always in a fiction," He explained. "After awhile something happens." He then popped a bubble in front of me and a little person dropped to the ground, looking rather frightened. "Our reality bubble pops. Sometimes by other people confronting us or convincing us that our perceptions are faulty. Or sometimes the natural world can pop our reality, such as a tornado demolishing our home. Sometimes it is a common natural event that dramatically shifts our reality, such as giving birth, or" He winked at me, "a loved one dying. The drama we were in suddenly feels small and doesn't matter so much, for a larger reality has changed all that."
I watched the little person at my feet, and there were others too whose bubble had burst. They at first seemed startled, or in a way awakened with their personal world enlarged. Eventually, a new bubble formed around them and they lifted in the air again, a bit shinier, brighter, and clearer.
It was almost comical, sad, and inextricably beautiful at the same time: people dropping out of the sky and landing on solid ground; soaking in a more truthful reality; then forming a new fiction, rising again, but enriched.
I could see that in my own recent life quite clearly. My bubble fictions had repeatedly burst with amazing speed. I'd be floating along with cheery hope, then pop, mold sickness. I crashed to the ground. I was slowly dying, and surviving took precedence over writing, my workshops, and lectures—all of it.
I formed a new fiction then, a bubble rising with cheery hope, as I moved to Washington and lived with a friend for companionship and a time to heal. She had a lot of medical and self-esteem problems, and I wound up giving her my all (yes, the martyr again). Once her life improved, she shockingly accused me of using her. Hah? Me? Devastated, that bubble burst.
I formed a new fiction then, a bubble rising with cheery hope, as I moved back to Oregon on the coast with another friend who was bereft in many ways. I again gave her my all, (you'd think I'd have learned my lesson, but yes, the martyr again) Once her life improved, she too turned on me. That bubble burst.
Suddenly all the drama from those years resurfaced and I was very upset.
My Fool's hands clapped loudly in front of my face, startling me. "Come back here."
I stared at him a little shocked, then realized I'd gone off on a tangent. I blushed, embarrassed by how quickly I could regress. "You were saying, we are not always in a fiction."
"Yes, not only do our bubbles pop from time to time, but there are those who mainly live outside the fiction experiencing life's synchronicity, and in that, become beacons of wisdom for all."
I agreed quickly, my mind flashing on some of the greatest peacemakers in history, overthrowing enemies without lifting a finger toward violence. Not buying into the game, they unite the masses as one with a bond of peace and love.
I elaborated. "Yes, India, through Gandhi, largely regained power from Britain this way, Czechoslovakia from the Soviets, and Martin Luther King helped masses of people overcome prejudice, which is just small thinking. In a way, they were all pulling thousands out of an oppressive drama, and freeing them into a new reality."
My Fool added, "However, without the preceding drama, those moments could never be had."
I nodded reluctantly. "I guess drama is important." A warm feeling overcame me as I gazed upon bubbles, bubbles everywhere with a little person in each. Our self-created realities were really quite imaginative, even entertaining, giving us ways 'to be'.
My dad interjected, "Remember, we weave our fictions to give us the experiences we wish to have."
My Fool said, "Yet, the most rewarding time is the time between a bubble burst and a new bubble forming. For instance, in the aftermath of a loved one dying," His eyes slanted to my dad, then back to me, "say, your father, and you are in a meadow, say this one, and you notice a little nest of birds hatching out of their eggs, a scene you and he once shared. Suddenly then, your focus turns to your dad's next reality, and you feel his essence being reborn. Feeling as if you've been touched by your dad's spirit, your sorrow shrinks, and you view the rest of your life as a gift to unwrap and enjoy until it is your turn to hatch into a new reality."
My eyes watered up and a lump formed in my throat. I shook my head, flicking off thoughts of my dad's death. No, now was about now, not then. I'd face then . . . then.
My Fool, knowing my thoughts, nodded. "That's it. Be here now, not in the imagined fiction of the future."
My dad said, "It will be different than you anticipate, Sue. Our futures always are."
I sighed, "I need to keep remembering that everything is as it should be and to ride the wave rather than freak out that it is coming. Drama, I guess, is what I make it. I don't need to keep repeating the same old dramas if I just change my thinking."
My Fool said, "Yes, but whether you realize it or not, your last Northwest years were about more than old dramas which involved people relations. When you moved there, for the first time in your life, you learned about isolation, which was something at the time, you craved. Due to various circumstances, the longer you were there, the more isolated you became, and hence more bereft deep within. In your aloneness, though you weren't actually lonely, you were fading."
My dad said, "I felt you slipping away, Sue. You looked okay on the outside to others, but inwardly you were disappearing, beginning to float away like a helium balloon from your reality and all the characters in your current play."
I felt like I had a wet rock in my throat. It was true, back then I had a great drama going on inside myself, larger than any drama I'd ever had in my life. No one could see that Susan was dying, and seemingly failing in everyth—
I was startled by a stereotypical version of a witch on a broom sweeping past my face.
I looked to My Fool, "What was that?":
"That was you demeaning yourself beginning with the word failing. What happened to you was not a failing. It is simply what happens when any human is alone too long."
"Well, I know that is part of it, but, the martyr thing, I think I failed there."
I jumped as the witch swished by me again on her broomstick.
"Susan, that's not it. Your alienation was what set it all off. And when you were occasionally touched genuinely by another, that warmth trailed through oceans of emptiness and began to pull you back into your identity, into conscious mundane reality."
I blurted, "But if I was at times getting what I needed, why did the two women with whom I lived and was so loyal and helpful and loving to, turn on me? I mean talk about kicking a dog when she's already down."
He answered, elaborating it seemed on what My Great Self was just trying to tell me, "Needing the people connection, yet judging yourself harshly because you needed this, you automatically reverted back to your old pattern of giving yourself away as a gesture of gratefulness, like laboring all day for a sip of water. This martyr like output exuded a kind of disrespect for yourself, and hence attracted abuse."
I nodded, "I can see that."
My Fool shook His head lightly. "Again, that is not the main storyline here. The bigger story is that you disregarded the fact that you need people. You pride yourself on standing independent because you are safer that way. You think needing people is weakness." His eyes slid to my dad. "You know what I am talking about."
My dad grimaced. "Unfortunately, yes."
My Fool said, "In my last human life, I was that way too." He looked at me. "Remember, Susan?"
I replied, "Oh yes, you fought hard against being vulnerable with anyone. You preferred complete control over yourself."
My Fool narrowed a wise eye. "Back to you. This notion of equating independence with strength, and striving to maintain that stance even when the floor fell out from under you, is what took you down. So much so that you forgot to meditate. You had not only fallen away from your outer self and the surface world, but also your inner self and the deeper worlds."
That empty lost feeling grabbed me for a moment. "But, I shouldn't need people because I can feel at one with everything."
My dad said, "That is not the human world. I am learning that same thing, by letting you help me. It has been hard. I felt better when you were calling me to vent your woe. You seemed on such a survival level, and you really needed me."
I said, "I know, I think that is why I wasn't meditating either. I felt so much on a survival level that looking away from the outer world for a second felt too dangerous. I had to be on guard constantly. Every time I let it down, I'd get a punch to the heart. I am not used to living a guarded life. I just don't work that way."
My Fool continued, "You weren't used to being on a survival level for such an extended period and it threw you off. So, not getting what you needed outwardly or inwardly set you further adrift."
I said to My Fool. "You're right, it was different from all the other dramas of my life." I looked at my dad, "You were the only constant in those dark years, even from afar, and even now you are the one who is helping me heal the most. I fear I will slip back without you."
My Fool nodded. "Yes. Part of your anxiety regarding your father's impending death is that you are not ready to feel isolated again. This brings us to the real reason all this happened. You were trying to get somewhere from a location that was out of time. Like when you try to physically do something in a dream. So where you were at on the inside, did not connect with where you were at on the outside."
"Yes," I confirmed, "that is very true. It's like I was staying in a place that was out of alignment with where I needed to be . . .meaning Arizona," I looked to my dad, "with you, so we could have these days together. I was just so stubborn about staying in the landscape I loved, I couldn't even see anything else." I sighed, "I guess, given our quintessential flow always pushes us where we need to be, if we fight it, we feel out of place."
But I was here now, where I needed to be, and just not ready to lose my dad. A pang shot through my heart.
My dad's hand landed on my shoulder, and My Fool's hand the other. Their energy filled me, and my heart stopped hurting. I felt more real, like a blurry picture coming into focus.
I said, "I know I'll be alright because I can always find strength and peace through meditation. I just must remember to do it even if I feel endangered. In that profound place, I can see and experience synchronicity, and hence deep calm." I let out a huge sigh. "I will be okay dad, even when you go."
A butterfly landed on my cheek, and I smiled. I laughed at the tickle, then just as quickly it flitted away to a buttercup by my foot.
My Fool said, "When outside the drama, as in this moment, we can feel our oneness with all around us, as can the flora, fauna, bugs, and beasts. They respond to our fear, anger, or disrespect as a threat, but when we are calm, respectful, and feel oneness with them as if we were them, they too grow calm and seem to greet us the same."
I said, "Basically then, if we could maintain that state of mind, we could by pass unwanted drama.
Before us a thundercloud appeared. All the bubbles were gone. What did this mean? I froze, wondering what horrible thing might happen.
My Fool said, "Notice how you are already anticipating a drama. And that's okay. It's okay to be human."
I scowled.
He added, "Just keep in mind, a drama can't be had unless it is fed."
A roar of thunder sounded and I braced myself further, wondering if some tragedy was befalling my family. Maybe I should get back and see how they are doing.
Dark clouds formed everywhere.
I said, "Am I doing this?"
"Not yet. Sometimes a storm is just a storm, as in the earth is thirsty, but we can make it personal and bigger than it really is."
My dad said, "Enjoy the storm, Sue."
Oh yeah, I do like storms. I relaxed with a small smile, joy creeping in.
A wind picked up, and began blowing ferociously. Hair strands whipped across my face, and my ears filled with a howl. I shouted through the howl. "What does this mean?"
My Fool hollered back through the wailing wind, "It can mean anything you decide that it means!"
I tried very hard to control my thoughts and reminded myself how we humans can glom onto a perception that worsens our experience.
Stay calm. Stay clear, I told myself, knowing that if I let my fear run away with me, I would actually put myself into the hell I feared. I had a vision of me blowing away with the wind into the Netherworld.
I shook my head. I am okay. I am always okay. We are always okay, it is just our perception that makes the drama.
I braced myself this way for about twenty minutes until the winds died down and I began to re enjoy the storm.
My dad threw out his arms. "That was invigorating!"
Then My Fool threw out His arms. "Ain't . . . life . . . great!"
We continued to watch the grey electric sky. A hum of energy hung in the air. Rain started pouring, but we didn't get wet. Not succumbing to fear, but rather enjoying the scene, we experienced it the way we wanted to experience it.
My dad philosophized with arms crossed, looking out at the storm, "It isn't just the drama we create for ourselves that can get out of hand, but our perceptions also can cement the drama between the various characters in our lives. The roles of villain, victim, and hero are often volleyed about in a theatrical game that can last a lifetime with the same players, or even changing out a few. There is a new villain in town, or a hero emerges. As long as we keep feeding the fiction, it never ever ever ends, and if we want to finish it, we can detach from the drama."
"Bravo," My Fool clapped.
My dad was always good at detaching from drama. I think that is one reason he was everyone's rock.
I cocked my head. "You know, if no one fed the drama of dissension but instead kept their sites on personal growth, then conflict would minimize and the world would change for the better."
"Yes," My Fool concurred. "However, although this is the utopia people often hope and pray for, earth is still earth, and the dramas will continue. Despite suffering, in the end these dramas yield great growth and beauty, a result that could not be attained with out the preceding labor."
Scenes in the storm appeared like holographic realities layered over each other, as if playing in different dimensions of the same space. I had to focus on one at a time to behold anything. A war scene, a crime scene, a love scene, a victory scene.
I asked my dad, "Do you see those scenes?"
"Oh yes," my dad affirmed casually.
I glanced at My Fool. "Are you making those scenes appear, or are we just seeing them?"
My Fool said, "You have deepened your mind state, your father too, that is always how one sees more."
I refocused on the layered dramas, shaking my head a bit, "Even though drama can be rather scary and unpredictable, we seem to invite it, hunt for it, get lonely for it, and sometimes jump into it no matter what the cost."
My Fool explained, "This is because, as you have been learning, humans feel alive when acknowledged by others. Drama, which can also be quite lovely, provides that."
I asked, "Do we always create the drama?"
My Fool said, "Sometimes, it isn't that we create the drama, but we need it to get to where we are going. What we do with the drama is the great experiment. Wallow in self-pity and sprout a tragedy, sport the chip on our shoulder and generate conflict, shine unconditional love and feel the world."
My dad sighed long and hard with eyes closed, and murmured to himself, "Keep my ship upright and head into the wind with an open heart to the sea of conclusion."
I could feel what he was really saying. The dementia could at times throw him way off course, and stir up an inner hell. He wanted to stay steady until he sailed right out of this life.
I glanced at My Fool.
He caught my eye. "There is more to it than that."
My dad explained, "I know something is coming. The biggest storm of my life. I just don't know how it will happen."
I touched my dad's shoulder to comfort him.
My Fool urged, "Go on, Robert."
My dad continued, "This upcoming drama is my passage to where I need to go. Waiting for it to happen makes me feel insecure and alone in a struggle to be brave. The event itself is obscure, however."
The storm evaporated and fog took its place.
Looking out to the fog, I saw multiple figures with hands reached out trying to find their way. Others were motionless, seemingly confused on what direction to go. Others still were crouched, some crying, some just looked like they were shutting down. Some periodically cried out, "Help me, I'm lost!"
I shook my head. "I don't like this."
My Fool said, "When in a fog, if we calm down deep within ourselves, a guiding light will appear."
My dad nodded. "For me, music takes me deep. When I give myself over to it, I can usually see beauty in the unfolding drama. And even though I don't know what the upcoming drama is, I know it will carry me to where I truly yearn to go. And this is what I cling to now."
A light streaked through the fog. I was trying hard not to cry from sadness at my dad's plight, or from being moved by the beauty he sought in the face of it.
I rallied myself to stay philosophical. "Instead of being afraid or mad for what is happening to us, we can rejoice that it will bring us into beauty," I paused, "even if in an after life, or in another body."
My Fool's eyes gleamed. "When we greatly expand our life view, we can perceive how all the lines of drama and people playing parts dance together in the greatest symphony ever. Instead of letting the drama maul us, we can feel in rhythm with the greater whole. Any drama is but a stepping-stone in personal growth. When seen as such, it is even easy to have compassion for our foes struggling in their dark realities."
Warmth blossomed in my heart. And in that moment, drama didn't frighten me. In fact, I was beginning to see it as a magic carpet to get us to the next chapter of our lives.
Suddenly the scene was sunny, crisp, and clear. Looking around with a smile, I said, "The way we think is so powerful! When we are enduring a difficult situation and feel like we are sitting in a pile of thorns, shifting our mind state from thorny to smooth really does begin with changing the way we think. This has worked time and time again for me on this whole adventure. As everything seems to happen more instantly here, I can see the manifestation of my thoughts more quickly."
My dad said, "Yes, here it is easier to see that when we stop negative self talk about what seems to be, and start opening our minds to the big picture and our unrealized potential, it can make all the difference in the world."
I concurred. "It's really amazing how much power we actually have to affect our personal reality."
My Fool's eyes glimmered. "Sometimes we just need to stop analyzing our troubles and look to the beauty. Does one need to understand how the stars work to marvel in their exquisiteness? Does one need to understand the nature of water to enjoy a refreshing swim? Everything that exists is out there, in there, there, somehow, someway. What will we do with it? That is up to us."
Words came to me. "Every drama has a gift. Claim it." I sighed, "I am however, done with getting lost in a drama."
My Fool proclaimed, "That is well, however, sometimes we need to get lost in the drama to have it. This is especially true in family drama."
Before I could react, we appeared inside what reminded me of a pomegranate with various sections housing seeds in a variety of arrangements. As we moved from section to section like ghosts, I viewed scenes of my family unit playing out variations of a storyline about being pulled apart and trying to come back together.
One storyline had my brother and sister in a horrible feud where one accidentally hurt the other. Another storyline had my father in duel with another man for my mother, and my dad died. Another storyline had me dying young and it ripped the family apart. Another had me leaving the family to join a convent, but they weren't happy about it because they needed me to help the family survive. In another, my brother did a similar thing as a monk. And in my current life, my mother dying somehow set us all adrift from each other.
My Fool said, "Are you seeing a theme yet?"
I said, "Yes, the family, trying to unite in various lives, keeps getting derailed with one drama or another."
We then appeared back in the meadow, and my dad looked a bit sad. "What's going on, dad?"
"All this talk reminds me of our recent family drama."
I knew exactly what he was talking about. My dad and I had experienced turbulence with a member; a seeming family spat turned into a soap opera drama, so uncharacteristic of not only that member, but our whole family.
My Fool elucidated, "Family dramas are so often misunderstood. Members judge each other by current life references when so much of the drama is actually a multi-dimensional event often rooted in other times and places. For instance, your recent family drama was likely a residual of a different reality where this member really did turn on the family and the family turned on the member. But in your current focus, that reality is not yours, but rather a bleed through of another. In the concept of linear time, it is a choice point of repeating it, or moving on."
"I can see that," I said. "Our current family, for the most part, really seems to have each other's back deep down, being on the same side as a supportive team. Yet, in the course of our lives, a certain event can occur, like this recent one that mimicked an old event from another time and place, reincarnationally speaking. These events can pull us into past realities as if it is our current reality. The next thing we know, we are behaving as we did then, and the rest of the family is dumbstruck because that behavior is so uncharacteristic of us currently."
My dad said, "I agree one hundred percent. It was an unnecessary drama that I helped initiate. I reacted to an attitude and drew a line in the sand out of instinct. This triggered a feud with both sides going off on a seemingly irrational tangent, cementing our perceptions in blood."
I said, "I am just so glad you saw that dad, and stopped it. We are trying to reunite as a family ever since mom died, and that would have taken us once again into an already played out plot from other time and place."
My dad said, "I guess when we get sucked into these old dramas, they seem new at the time because in this life, such scenes had not occurred. And yet, in some way they seem oddly familiar."
My Fool added, "Although all these dramas are custom created to fulfill our needed experience, they also set the stage for all the players to experience what they need as well. The human cast and their interactions with each other in the earth play are as varied and numerous as mathematical possibilities."
I thought about that, and truly it did seem that anything that could happen as a by-product of human interaction, did happen. I said, "I guess, on earth, anything goes."
"Oh yes, " My Fool concurred, "Identities collide and collude with each other in this massive storyline that encompasses the globe, designed to catalyze our 'becoming'. It is not bad, or wrong. Ignorance, as we have discussed, is necessary to facilitate the play."
I added, "Yeah, and when we are ready for help, all the sudden our ears and eyes can see and hear a whole new way of dealing with our challenge. And if another person is offering a hand, we view it as being helped. Not that we weren't, but only because we were ready to help ourselves."
My dad said, "Yes, unsavory natural consequences eventually take their toll on us, whereupon we take stock of things and develop a firm desire to end the drama one way or another."
My Fool narrowed an eye. "But until then . . ."
Suddenly, the air went black and appearing before us was a basketball size red spot. "Every drama," My Fool began, "requires a solitary focus that blacks out all other possibilities and points of view. It is a type of tunnel vision. This is why when someone we love is hell-bent on having a certain experience, there literally is nothing we can do to stop them. If we were to continue staring at the red spot, we too would begin to feel a suction that would pull us into it. Once in it, we live the experience generated by our adamant perception."
For a moment it seemed that a torrent of massive suctioning drew us into the red spot, but then we bleeped back to the meadow where the air was bright and clear again.
I gasped a bit, glad to have not been sucked into the red spot.
My Fool winked at me.
I shook my head. "I know that sucking feeling so well."
My Fool said, "Everyone does because it ensures that the needed experience will be had, even if that experience is seemingly destructive."
My dad shrugged his shoulders. "It is human really, to occasionally act on destructive impulses, such as eating too much or spewing anger on another."
My Fool's hand fell over His heart. "We do what we need to do, and we believe what we need to believe, to give us the drama that will eventually incite the experiences we seek to advance our personal evolution. What is less understood is that the evolution of one is the evolution of all. The other side of self is our plurality. Our plurality is us. And all pluralities are one. While outside time and space everything is happening at once, in time and space there is a feeling of forward momentum, and in that way, the experience of past, present, and future is real.
I gasped with an epiphany. Time doesn't change. We do!"
"Precisely," My Fool confirmed. Seeming progression in behavior is really just a difference in behavior, like an experiment. Humans rely on a perception of forwardness to fully experience their current reality, a sense of getting better. However, even more shadowy players give others opportunities to push through hurdles and have challenging experiences. So then, the villains in our life have given us a great gift in motivating us to grow."
I nodded. "You can't have heroes without villains."
My dad added, "And our past actions that may have hurt others, purposefully or not, gave them the experiences and opportunities, that on some level, they were calling for. So, though we may be mostly good, to some we may appear as shadowy figures of their past."
A few incidents crossed my mind of when I am sure I appeared to be the villain. What is a villain anyway? If others hurt our feelings, we deem them a villain. If we hurt them, aren't we? So much drama!
I exhaled hard, "I am just so glad I know how to pull back from the drama and meditate to gain perspective, which makes the drama seem smaller and sometimes even . . .
My Fool raised a brow. "Silly?"
My dad laughed a bit. "Comedians often glimpse that, the silliness of our behavior, and we can good heartedly laugh at ourselves or others."
"Observe," My Fool said, waving His hand, creating another sparkly scene. I was twenty-two, in my bedroom, curled in a ball on the floor, sobbing my guts out.
I said, "That's me being very dramatic, feeling like it was the end of the world. I had been dating a man who was looking for a wife that would suit the profession he was training for, a minister. I had a bad reaction to an assembly at his church, which to me, demeaned women. I told him I could never go back to that church."
My dad blurted, "I remember that."
"Well," I went on, "he broke up with me, and I cried and cried and cried. Oh, the rejection. But now, it all seems so silly that I wasted one single tear on that event. What I was really crying about was just being rejected as a woman, reflecting my insecurity at that time. Did I want to be a preacher's wife that supported a dogmatic religion? Well, no. I wasn't even in love with the man. We only went out on several dates."
My Fool waved His hand again, and that scene was replaced by another. I was in my dad's bedroom on my knees, bent over, sobbing.
"I remember that one." I said with a sigh, "I was fighting against instituting uniforms at my children's elementary school. I was more for dealing with the problems head on; teaching kids communication skills, and to respect each other, while still preserving their individuality by allowing creative self-expression in their dress. Uniforms were wonderful everywhere else, but forcing them on public school children whose parents do not want, or cannot afford private school, seems mean. Like masking who they are, suppressing their uniqueness, as if it is unwanted."
My Fool said humorously, "Oh the drama! And then again with compassion, "Oh, the drama."
His compassion soaked into me, initiating a feeling of deep self-respect as I continued telling the story. "During the course of my battle, which included sociological studies I conducted that were published in the newspaper, a backlash occurred. There were several editorials written against me, degrading me, and pointedly told me to get out of town. I was crushed, broken. To be publicly decried just for fighting for children to be celebrated as individuals, and for programs like peer mediation to help them work through their problems instead of being punished for having them." I looked to my dad. "Do you remember that dad, the uniform battle and me breaking down?"
My dad smiled. "Yes, I told you that the backlash must mean you were powerful because you were making an impact."
"See, you viewed that as a victory, but I viewed it as rejection."
My Fool winked. "Yes, good little girl that you are."
"I know. I know, but when I look back on it today, I can see my dejection was really unnecessary. I was making an impact so what was I boohooing about? In the end, the school board voted against school uniforms, so that showed me I could stand out in the world, sing my song, and actually survive. The real surprise was that I seem to have been heard." My eyes widened. "I guess adventures into drama can be rewarding."
"However," My Fool added, "sometimes the less adventurous person is the mark of one, in the concept of linear time, nearing the end of the earth journey, done exploring and preparing for Highway Eleven, as you know, is the esoteric entrance and exit of earth. This does not mean those coming are less evolved, and those leaving are more evolved. There are many worlds."
I suddenly felt so tired, and our golden mats appeared. My Fool said, "Rest now. Step outside the drama and regenerate."
My dad stretched out on his mat, and almost instantly fell asleep.
Before I could do the same, My Fool slipped something in my hand. I raised my palm to my face and unfurled my fingers. A little golden charm was there, two masks attached, one happy, one sad. Staring at them, they seemed alive, looking back at me.
My eyes widened, mesmerized.
My Fool said, "Drama is mesmerizing, exciting, and tragic, funny and sweet, all of it. Partake of the drama, but wear it like a mask, as a persona starring in a fascinating play. Your Great Self is outside the fiction, a home base you can always visit in meditation, or in the aftermath of sweeping drama. There, the worth of your identity is a shining star, and your existence is forever."
I whispered those words to myself. I am a shining star and my existence if forever. The golden mask set appeared as a fourth charm on my bracelet. Repeating those words that felt so good, I lay down on my mat, closed my eyes, and slipped into comforting sleep.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
We need drama to move our lives along in our life adventure. Sometimes we cringe when drama charges us like a lion roaring with fangs, seeming larger than it really is. Yet, where would we be without that stimulation?
Interestingly, visions of utopia usually entail a reality where everything is peachy keen and drama free, a commotionless land void of upset. A land of no challenges where drama has gone away forever. But would we be content in such a utopia?
If we were instantly provided with perfect mates, perfect jobs, were all wealthy, stunningly beautiful, and we never got old or died—basically if we were all the same, would we feel any zest for living, any thrill of the hunt, sense of accomplishment, or impetus to personally evolve. Might we not just be plain bored?
Perhaps the idea for utopia is just a wish to experience the sweet relief that washes over our bodies, safe and sound, warm and loved, in the aftermath of a nightmare.
Given that, are nightmares bad? Or do we make them worse than they really are by feeding our ideas of what we deem them to be? We humans tend to attribute punishment and reward to the way of things. The tornado hit my house; I am being punished. The tornado missed my house; god watched over me.
Yet, the inhabitants of the house hit are often rewarded with an outpouring of human compassion that restores hope in humanity. The inhabitants of the house not hit, though relieved, might grapple with survivor's guilt, and a psycho-spiritual crises of senseless destruction of 'why that house and not mine', and is perhaps a less rewarding experience.
Tragedy elicits human kindness. Challenge tests us to our very limits. Bad luck teaches us more than 'lucking out' ever could. It isn't the great times that give us the most, it is the hard times. Even great times can have a dark lining, such as fear of the great time ending, or fear of being knocked off the pedestal, not feeling worthy of the great time, or getting conceited because we have it.
Nothing is ever as it seems. Everyone experiences the positive and negative of any given event. Everything is a double-edged sword because everything is the whole sword, and really, would we want it any other way?
Balance is found in realizing that the more unpleasant aspects of drama are fed by our fears, and sustained by besmirching ourselves or each other, creating sores that eat away at us. We can heal these sores, and clean our reality in the face of such drama by feeding ourselves doses of kindness, mercy, and forgiveness that we share with others. Bestowing faith in all to find their way, we can duck or ride the damning wave to the shores of utopia that every drama offers, until the next drama makes our hearts race with excitement of the next 'what if?'
So when the lion roars, make yourself big and wonderful and take back the night.
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# THE SCALE OF SENSITIVITY
# GEM #5 Connection
In individuality, we seek wholeness;
in wholeness we seek individuality.
##
IN MY DREAM, I WAS on the meadow hill speaking before a large mass of people. A glowing ball hovered over each person's head as an extension of each.
Charged words poured out of me. "We often think we are alone in this life, a mere individual steering our course the best we can through the darkness of uncertainty. This aloneness is as a baby duck getting lost when following its mother and siblings on an outing, desperate to belong again. This aloneness is like being transported from a bustling city to a desolate land, even if the reality is that we are surrounded by multitudes of people. If we can't connect, it is as if others are not even there."
My words seemed to fly out like a gentle storm of powdery energy that absorbed into my listeners. "This uncertainty generates a thrust to connect, join, unify with something or someone, some way, some how. The quest to feel connection masquerades as a need to be loved, to belong, to feel calm, secure, and worthy, to know that we are okay, and all is right with our world.
"Our modes of connection are many: goal collaboration, romance, sex, having children, friendships, belonging to groups, or receiving acclaim. When others are moved by our ideas, emotions, bodies, creativity, or accomplishments, we are elated that we made the connection.
"Sometimes the only way we can connect is to misbehave. The toddler who throws a toy at his mother's head, the woman who makes her lover jealous, the lonely alienated man who commits mass murder, all to convey one message. Notice me. All these acts are done to connect, to make contact, to get attention, to get proof we exist."
I could feel the energy of the crowd thicken as I spoke. "Negative attention can do that, but in general, we prefer others to care for us with all their hearts, because we then feel worthy and really alive. This is true in romance, parenthood, family, friendship, and even in celebrity.
"Romance is the idea that another can love us unconditionally to the death. And when that sentiment is returned, it is the stuff of legendary lovers. This too is true of children who want more than anything to know their parents love them unconditionally, above all others. A family who accepts and supports each other is a prize. Best friends are the ones who always have each other's back. Celebrities often mistake the masses celebrating their shine for personal love, but they do feel loved and thus shine more brightly."
The crowd seemed to drink in my energy, yet gave it back with their great need to hear it.
"Difficulties arise when we try to feel connected from a perception that we are all alone in this world and must fend for ourselves. This can manifest in manipulating and controlling behaviors. If we can manipulate our significant others to do as we need, then we feel that means they love us. In getting others to submit to our dominance, we have made a connection, albeit from a controlling stance. A dictator controlling the masses feels connected to the conquered, and yet is plagued with constant fear of being overthrown and subject to tragic behavior.
"All these modes, though twisted, are still forms of connection. What is a winner without losers, a boss (at work or home) without subordinates, or a tyrant without subjects? The need for constant approval exudes our insecurity, and invites or incites abuse"
The crowd murmured loudly for a few seconds, then simmered down.
I went on, "We also prefer our social world to include us as a member of the tribe rather than hang us out to dry for a difference of opinion. Even rebels and activists aim at being heard and accepted by at least some people. Making a grand statement, or creating change makes us feel connected to life, and that our existence matters."
I heard a few mumbles, "Our existence matters."
I continued, "Even connecting to the natural world can quell our anxiety. In nature, we feel something of our own soul. Religion too. However, an open spirituality that transcends defined religious ideology can connect us to everything. Basically, on some level, we have a need to connect with that which seems larger than our individual self. Even scientists are trying to make this connection by understanding the unknown.
"Drugs, though dangerous and unadvisable, have been used as a bridge to feel connected to a broader consciousness. The high is a short cut to feeling that connection. However, this method poses risks, namely adverse drug reactions, unproductive escape from our troubles, and addiction. Drug free mediation can better serve us in feeling what is perhaps the greatest connection of all, oneness with all existence."
The crowd grew hauntingly quiet, as if thirsty to expose this topic.
"These more lofty connections can save us from feeling alone, abused, overwhelmed, or forgotten. However, we actually always are connected, we just feel like we aren't because of the perceptions that keep our reality in place.
"Even the natural world can be viewed as having separate features; the mountain, the stream, the trees. Yet, in a panoramic view, they are all just part of one landscape. The protons, neutrons, and electrons seem separate, but they all make up the atom. A blackberry bush is always one entity with many leaves, berries, and roots, so the reality of one leaf or one berry being separate from the rest of the bush is not the whole picture. It is separate, and yet it isn't.
"Unlike humans, plants in metaphysical, and to some extent scientific theory, experience connection with other plants as if they are one entity even as they physically compete to survive. Even animals have in studies been shown to experience connection in a variety of ways, such as geese flying in a v formation, or bees making and tending a hive, or the telepathy of monkeys on one island being taught something, and monkeys on the adjacent island learning it.
"So while there are forces at work that lead us to compete, every member of a species seems to draw upon the collective memory of that genus. This helps explain universal phobias, such as spiders, snakes, and heights. Whatever happened to our distant ancestors, no matter what species we are, seems to become a part of our unconscious memories."
I heard a bit of discussion amongst the crowd, and decided I needed to wrap up my speech. "However, while this naturally occurs in almost every form of nature, humans have a brand of intellect whereupon they decipher reality, usually concluding they are alone in the world, because that is what it looks like. We so often exact great schemes to feel connected. But we already are. Those at the greatest peace can sink deep beneath consciousness into their core being. The deeper they go, the more connected they feel to all life, to energy itself. From this mind state, we can see life's symmetry, how everything connects in a brilliant dance of beauty. This was Buddha's great discovery.
"The essence of our deepest possible being then contains all of nature, all forms of life, all molecules and atoms, infinity and eternity, transcending time and space, and the breath of life—all life."
The people in the crowd each welled up in a golden light until they merged as one glorious emanation. I gasped at the beauty of the rich mellow gold that soothed me so. I suddenly had a strange sensation that the crowd was me, my own plurality, all the me's I'd ever been and currently are, and perhaps will be. I'd been talking to my many selves, giving an old lecture really, but it seems there were aspects of me that needed a refresher.
Then I wasn't on the hill, I was on my mat, hearing my dad and Fool conversing next to me. My Fool was saying, "We are all connected."
Then my dad said, "We just feel alone."
Opening my eyes, I sat up, and beheld my beloveds standing over me. My dad was still bare, save his purple boxer shorts. My Fool adjusted His headphones. I could hear Mahler's third symphony eking out. Then suddenly, I heard it everywhere around us as background music.
I rose to face them, the hem of my white dress bunching up a bit from the tall grasses. "I just had the most interesting dream."
My Fool said, "About connection?"
I nodded.
"That is today's adventure." He held out His hand. "Shall we begin?"
I sighed with a smile, "Yes. Connection is my favorite subject."
We all began walking, not that walking was ever necessary, but it did serve as a time to transition into the next experience. In front of us, there appeared the beginnings of a wide road.
My Fool said, "This is the road of empathy and apathy."
I narrowed my eyes, looking ahead as far as I could. There seemed to be measurements on the road marking increments like a giant ruler.
I asked, "What are the markings?"
My Fool answered, "They measure sensitivity levels."
"Oh," I said, examining the road further. The first part was colorful, almost too colorful, and it kind of hurt my eyes. The further down the road I looked, the colors slowly faded until way at the end it appeared grey and bleak looking.
I said, "I am guessing this first part is empathy and the end is apathy."
My Fool said, "Yes, we humans span this road, experiencing various levels of sensitivity and apathy. However, as a collective, we experience it all. In singular identity, of course the more sensitive we are, the more we feel. And of course, the less sensitive we are, the less we feel. Both extremes present monumental challenges." His palm opened to the road, "Shall we?"
I was a bit apprehensive, but stepped on the road in unison with my dad and Fool. Billions of small energy configurations were vibrating around us with such intensity, all I heard was loud painful buzzing. I clamped my head, and my knees buckled. My whole reality was pain, joy, sadness, madness, pleasure, terror, poking at me, poking me to pieces, so much so that I couldn't feel any sense of direction.
I slanted my eyes right to my dad, then left to My Fool. They had somehow managed to equalize the energy, but I was being eaten alive by it. I felt my arms on each side lifted and pulled along the path to the next increment.
I felt better and stood on my own as my dad and Fool dropped my arms. I sighed hard. "That was horrible. I guess that is what some acute forms of mental illness can feel like. My own sensitivity has tortured me at times, but that felt even more unbearable, like a never ending living hell."
My Fool said, "At that level of sensitivity, the energy field emanating from the body is thin, or drastically porous, or even absent in places. The result is a lack of boundary between certain worlds, rendering these people unable to, in most cases, discern the difference between one reality and another, and distinguish their imagination from what is true in their physical reality. To exist as an individual, we must have some ability to block out the reality of other people and worlds."
I said, "That's hard for me."
My dad raised a brow. "At least you can do it."
"Barely." I looked about me. "This area feels very familiar. I am guessing we are in my territory now."
"Yes," My Fool confirmed. "It is much more stable here, albeit often difficult to manage. Of course, there is a long road between where we just left and where we are now, but for the purpose of demonstration, I have condensed things."
My dad confirmed, "This arena here really is you, Sue."
I examined the road, bright and colorful still, but the color seemed more controlled or solid. Butterflies flitted, and toads hopped about flowers and broken glass. The road surface was a patchwork of dirt and rocks, grass and flowers, garbage, pavement, water, fire, and clouds.
I couldn't take my eyes off my surroundings. "This is so weird!"
My Fool looked about. "Those who dwell here are exceptionally sensitive, and highly empathic with a colorful energy field that is more porous and extensive than most. However, it is not broken, nor thin, as is the case with your more feeling neighbors.
"The exceptionally sensitive walk into life feeling more connected to everything and everyone than the average person. This connection manifests as empathy or in other words, unconditional love. These people naturally feel at one with everything. In this, while they often experience the reality of others, they also tend to project their own reality onto everyone.
These sensitives are especially vulnerable to the idiom, Come into my parlor said the spider to the fly, or walking into the lion's den. Assuming that everyone possesses the same loving motivation as they, getting metaphorically bitten is not uncommon.
"The predator welcomes these innocents into their lair and feeds off them. The empathic victims are shocked by these violations, for they could never imagine another with such intent. They are further at risk for abuse by those steeped in separatism, snug within walls of, It's me against you. Out to serve themselves, they consciously or unconsciously exploit the good will of others. I will step on this person and take or destroy what they have that I do not. That makes me feel strong and vindicated. I need to feel strong because inside I feel so helpless and alone."
I hung my head, expelling a pained sigh. "That has happened, all of what you just said, to me so many times. When people treat me poorly after I pure heartedly connect with them, I feel shattered inside. I am shocked. It isn't so much that I want to be liked, but I don't understand why anyone would behave negatively toward me when I give them pure love."
My dad interjected, "Sometimes they are just not ready for it. Sometimes they don't believe you, and think you are a phony. And on occasion, they might be jealous, and have a need to demean you to feel better about themselves."
I said, "I just wish I could shield myself better from that kind of fall out. It just hurts so much. It's like I absorb the energy they are throwing at me. Feeling their reality is unbearable."
My Fool gave a wily smile. "Empaths are quite the sponges!"
As Mahler's third symphony came to a rather whimsical part, I had a little vision of a bunch of sponges flying around absorbing everyone's realities, then getting weighed down by unsavory emotions, not their own. I would have laughed, but it was never funny when that happened to me.
My Fool commented, "This is why empaths need a lot of solitude. Alone, they are not subject to all the energy flying about when in the presence of others, and they can also air themselves out from what they've sponged."
I said, "This is so true. Even when I am around friendly others too long, I absorb their realities, and need time alone to separate my reality from theirs. It's like, I need to reel myself in. I have improved though at envisioning a shield around myself before I go out into public, charged with an attitude of I am not up for grabs.
The road was suddenly dotted with numerous white beings, almost faceless, eyes closed, heads slightly jutted in deep concentration as if they were here, but not here. Energy from their beings emanated far around them, sometimes stretching a ridiculous distance. I noticed then that their whiteness shone slight rainbow colors.
My Fool said, "This is what empaths look like at this level. Though they may question their sanity from time to time, constantly experiencing other people's realities as their own, they can, when aware, stay centered in themselves. And with a little work, they can develop skills to cope with their sensitivity, and function normally in the mundane world."
My mind flooded with memories. "I can relate to questioning my sanity. Once, when I was a child with my mom in a mall parking lot heading for the car, a girl was on the pavement having an epileptic fit with medical people gathered around her. I had felt strange suddenly and went into a state of mind that frightened my mother. I was not being a drama queen, I was feeling the girl's reality, but I didn't know it.
"Another time when I was young, I was in a movie theater with my siblings. I suddenly felt so weird that panic took me. Seconds later, a severely mentally challenged child walked past me down the aisle. I had felt his reality before he passed me by. I have had hundreds of experiences like this all my life. That is also why being around anger upsets me so much, even if it has nothing to do with me. I absorb the anger, and I just want to run and hide."
My Fool added, "This absorption can also happen from afar by tuning into a topic, such as gun violence."
My eyes widened. "Yes, I was writing a fiction book once and researching guns. I suddenly could feel gun violence the world over throughout history, all at once. I was on the floor in a ball crying!"
My dad said, "That's so you, Sue."
I said, "I know. The only way I have been able to detach is by shifting my focus," I looked at My Fool, "as you once taught me long ago. Like changing channels, I need to sometimes tune out all stations but the one that brings beauty and relief. I guess that is a positive about being an empath. The simplest things can bring me great joy. "
My dad said, "It took you a long time to learn how to separate your reality from others, but you have made great progress."
I smiled faintly. "I have come a long way."
My Fool added, "Those on this level also can feel when others are strongly thinking about them. Intuition is acute because their auric emanation (which is a manifestation of their state of being) is more permeable than most, hence not sealing them so strongly into their own realities. Therefore, they can see into not only others, but also other realms more easily. While this insider vision makes them wonderful healers and artisans, they are also susceptible to all the emotional currents of the world, and can be sucked in easily.
I nodded, "I have had to learn to step back and take a beat before succumbing to those currents. I also censor where I go, what I watch, and what I might hear." Suddenly feeling the weight of all I'd learned to shut out, my hands became fists at my side, hiding my thumbs. With a strong exhale, I exclaimed, "I could get out and about more if I could strengthen my shields."
My Fool said, "You could, but it may not be necessary. Your way is your way and it gives passage to many experiences that are meant for you. As incidents arise and it becomes necessary to develop your shielding, then you will, and you have. It is important to release the notion of having to be a 'certain way' and instead embrace who you already are."
I relaxed a bit with that. I found it hard to get it through my head that I don't have to be achieving all the time.
My dad said, "You are not alone, Susan. There are many who struggle in this level of sensitivity. Even famous well known philosophical types have become alcoholics as a result of trying to numb the pain they constantly empath from others. Another pitfall, as you have experienced, is trying to rid yourself of other people's suffering by saving them, all of them, which is impossible."
I sighed hard. "That is so true. I know I will feel better if I can make whomever I am emptying feel better. I have had to back off from that considerably just to survive. I used to feel weak because I was so easily overwhelmed with all I was sensing and feeling." I looked to My Fool. "You taught me that I can still feel that oneness, but from a deeper place. By maintaining a meditative mind state, I can merge with people's quintessence while disengaging from their outward persona."
An instance came to mind.
My Fool, seeing into me, uttered, "Share."
I explained, "Once an acquaintance with a criminal history came to my door. He was high on meth. His rapid speech went on and on with a focus of getting into my house. He had locked himself into my presence inside my energy field. Initially, I tried to reason with him, giving plausible excuses why he couldn't come in. I tried to redirect him where he could go instead. But my situation remained the same. So I gave up reasoning and soul merged with him, not his identity, but far beyond his body and life story. When I did that, he stopped talking, and had a funny look on his face, as if unable to maintain the perception of me as a separate someone he was trying to overpower. He blurted, 'I have to go,' and virtually ran to his car and sped away."
My dad and Fool were grinning and nodding.
I cocked my head. "What?"
My Fool said, "You chose not to participate in his drama. You ducked under the oncoming wave instead of dealing with his identity. When we remain centered in ourselves, we naturally do the balanced thing, which ends better for all concerned."
I smiled back. "I did do that. Staying balanced for me has become my main life goal."
"Balance, however," my dad added, "is an individual thing. What is balanced for you may not be balanced for me. For example, for one who is constantly used, balance might be closing the door in those people's faces."
"Or," My Fool said, "balance sometimes can appear tragic. If, for instance, a crazed person breaks into our home and is charging at us, we might, if we have a firearm, instinctively use it. The intruder then has forced his hand, and has called for the experience of being shot."
I sighed hard. "I agree. We so often blame ourselves for other people's behavior, but what happens to those people, as you have previously stated, is all a part of their set up to have the experiences they need. I really must remember that regarding those I have upset."
My dad put his arm around my shoulders. "It is inevitable, Sue, that we all will, at times, upset each other."
My Fool said, "It is just another way we make connections to play out the unconsciously agreed upon story. It is the way it is supposed to be."
"Yes," I conceded. "I guess, as horrible as it sounds, even if we accidentally killed another, the killed were in that place and time to exact the storyline needed for not only their soulic progression, but their deaths often generate powerful opportunities for those involved to exponentially grow. Is that right?"
"Yes," My Fool concurred, "Everyone has their own soulic agenda, and we cannot alter that course, unless that was already on tap for that identity."
I blew out a hard sigh with apple cheeks, not wanting to go down an unsavory memory lane again. I looked ahead. "I wonder what if feels like further down the road. I mean, I wonder what it would feel like to have less feeling."
My Fool said, "Well, let's see."
We continued walking along as we talked, and I was glad to get further away from all this sensitivity. I began to see people about that seemed more solid, yet had beautiful flaming colors emanating from their beings. They all seemed involved in their various realities. I saw an energy at their feet go into the road.
My Fool said, "People at this level are more grounded. They can have empathy or apathy depending on the situation."
I exclaimed, "I love that!"
I examined the people more closely. Some were standing their ground and making great headway in their lives. Some were even throwing punches at misbehaving invaders. Others were compassionate, helping those around them. And it was kind of funny, but I saw numerous miniature people diving into the road into someone else's peril to rescue them. They would pop out of the road with another person or animal.
My Fool explained, "When those at this level aid others at risk to themselves, they are empathizing with the victim, and at that moment are one with them. That is why people will die for their loved ones and even strangers. Saving another is as saving themselves, even if it kills them. This is the stuff of heroes, not born of an attraction to danger, but from identifying with the one in peril."
My dad blurted, "Every good deed we do is rooted in feeling empathy for another or others."
My Fool elaborated, "Yes. The dog stuck in the tunnel, the cat with no place to live, the urge to save a baby bird, are all about empathy."
I sighed hard. "For me, it is extreme. Killing a fly is just too brutal for me, and if I see one struggling, I have to save it. My heart aches every time I see a dehydrated plant, and though I can pull weeds, it really hurts me to do it. It's hard to live this way."
My dad said, "Remember Sue, the fly, plant, and weed may not suffer the way you think. We only know suffering based on our human reality."
I furrowed my brows. "I really need to remember that. For instance, to the eagle who lost its mate, that loss is experienced in its own way, not my way per se."
"Exactly," my dad confirmed. "I have watched you time and time again assume others are suffering in the way you would under the same circumstance."
I nodded. "So true."
My Fool said, "This projection, for most, also extends to matters of right and wrong, that what is good or bad for us, is good or bad for all."
"Yes, that seems quite common." I scanned my eyes about the people, seeing how their almost blinding boundaries might cause judgmental perceptions. Yet, they also seemed quite able to repel those who would try to thwart them. I blurted. "People here on this level seem to easily guard their boundary."
My Fool said, "Yes, in defending their well being, they can repel, by whatever means necessary, those trying to take advantage or cause harm. They also can do this for their loved ones."
I said, "Like warriors."
"Yes," my dad affirmed, I think because he was one.
I shook my head. "I respect that so much. To be able to confront and repel looks so beautiful to me. I always admired my daughter for being loving and deep, but also staunch in not giving herself away or taking any garbage from anyone." I looked to my dad, "I think she has a bit of you in her!"
My dad's eyes glimmered. "Maybe so."
My Fool turned His palm upward, outstretched ahead of us. "Shall we continue?"
We walked further down the road in this expansive middle section showing varying degrees of people both connecting and detaching on a regular basis, detaching a little more as we journeyed forth. I really did envy them.
Suddenly, it got colder, almost like winter and everything around us was barren.
I said, "Let me guess, we are on the opposite end now, the land of apathy."
"Yes," said My Fool. "These more detached people are deeply embedded in the own identity and have difficulty connecting to anyone."
I added with psychological expertise, "Excessive detachment is indicative of a psychopath or sociopath. Psychopaths are totally wrapped up in their own existence and unable to empathize with anyone. A sociopath can feel for maybe a few or one person. These select people are often a shining reflection of what the sociopaths have cut off in themselves, something akin to their own souls. They will kill for that person or two, and do whatever it takes to keep them in their lives."
My dad added, "This behavior also has shades of mafia culture where the family is everything, but everyone else can be killed without batting an eye."
I said, "For them, and especially the psychopath, desecrating others is a desperate attempt to affirm their own existence." I shook my head and bit my lip. I did not want to empathize with the psychopath because, having done it before, it is very scary. I learned that they are so alone that they try to make their victims cry out with great emotion, usually fear because that is the only way they know how to connect with them. The only way they can feel is to torture, or kill. I said aloud, "Even psychopaths are trying to connect."
My Fool said, "Yes, they can't emotionally connect to anything, not even a pet. They want to feel, but they are unable."
I said, "That is its own kind of horror I suppose."
My dad said, "Every rotten deed we do is rooted in an ability to lovingly connect."
I blurted, "I don't like it here. Can we get off this road?"
My Fool nodded. "Yes, but remember, even the psychopath is just playing a part, having an experience, and at the core of his or her being is us."
I cringed. "That is very hard to stomach." I gulped and took a deep breath, having bumped up against many a socio and psychopath in my life. I blew out air, feeling more solid. "I guess perceiving the so called 'bad' people as us, at least spiritually, can help us cope with the trauma of being victimized. I mean while detaching from them on the physical level, we can still feel homogenized on a spirit plane."
My dad said, "I think so too," then elaborated. "By acknowledging that we are all one, (the religious version being—We are all god's children, we can see that the earth story is a collaboration of everyone and everything interacting, alchemizing into something divine. Though we may have been deeply traumatized, there is a powerful reason for any happening. The religious version would be—God works in mysterious ways."
I said, "I can see that. These trials can lead to intense personal growth and transformation, as well as inciting great change in our social world, such as new laws being created. In the end and from a bird's eye view, as we have said, tragedy begets beauty, eventually."
"It's always both," My Fool declared.
My dad raised a brow. "We are the whole road, remember?"
I gasped a bit as my dad and Fool seemed to be expanding like water balloons. I noticed then, I was too. Our energy fields were growing and merging with each other. Suddenly, we enveloped the whole road. Mahler's third symphony, last movement, picked up in volume exuding glorious vibrations, expressing how I felt in this expanded state.
My Fool said, "The more connected we experience ourselves with others, the more we experience ourselves as Creative Energy housing its creations. This also touches upon what it feels like to be in the core of Creative Energy, where creations are created."
The road felt almost infinite within us, and the possibilities for ranges of experience seemed endless.
My Fool continued, "As we mix all these experiences together, like cake ingredients, we become more than we were, and something else altogether."
I felt billions of beings moving about on the road of us. My heart swelled feeling the worth of each. I reiterated an old wisdom My Fool once taught me. "We all are as valuable as the universe, we just don't usually know it. In not knowing it, we travel many roads and have many experiences in search of it."
The symphony's explosive ending filtered throughout me, increasing my sense of exaltation.
My Fool declared, "Ain't . . life . . . great!"
Suddenly, we were back in the meadow standing in a triangle.
I shook my head a bit to get my bearings, "Life is great, I suppose, it just doesn't always feel that way. But I guess, although closed minds in varying degrees fashion our needed reality, when we release rigid thinking, and open our minds to all possibility, we are more able to feel the company of the world. Life sure feels great then!"
My dad added, "I think this urge to feel better is always, one way or another, a veiled thrust to feel the oneness we knew before we experienced being separate and alone in the world."
"I agree," I said. "I think this too applies to our experience of being in the womb. We likely don't remember being there, but since we were, we have a sense memory of the feeling it evoked. Whatever might emulate it, such as a feeling of belonging, can prove quite comforting. Curling up in a fetal position in the darkest of times is also an attempt to feel safe, secure, and connected to the mother."
My Fool said, "Being out in the world is daunting, and yet the world is ours to explore. However, the real journey before us is into ourselves, it just takes us time to get there. Adventuring inward is not so popular as adventuring into the unknown depths of the ocean or space. It is human nature. It is our way. There is nothing wrong with that. Only when something cries out in us so intensely, do we often fall into ourselves. We simply must or we will perish. That is if we can even see or sense the way in. Those who cannot may commit suicide or become substance addicted, or maybe even commit homicidal acts. Or, at the very least feel depressed or anxious much of the time."
I smiled faintly. "But when we do go inward, everything changes."
My Fool affirmed, "Yes. Even though the journey feels like we are leaving behind everything we cherish, everyone we know, and everything we believe, it is actually a sojourn into the source of all those things. As we wipe away our tears from leaving the outer world reflection in which we have found some measure of comfort born from the feeling of belonging, we might be surprised to feel continually better as we move toward the creative source itself."
My dad's eyes deepened. "In arriving at the core of all being, our loneliness fades, and our anxiety and depression are no more."
Feeling what my dad was saying, I added, "All we ever sought, needed, or wanted is here in our center, where we can see that we have always belonged."
The rhythm of our words seemed like a song as My Fool spoke in turn. "For at the core of everything, there are no veils or divisions, but only one Creative Energy."
My dad said, "And this one Creative Energy, it is not out there or a part of us where we beg for it to love us and protect us."
I continued the thought, "It is in each of us, in the depth of our being where there we merge with the depth of all being."
"The depth of all being," My Fool reiterated. His words seemed to echo and trail off.
Suddenly, my head felt big and small at the same time. I felt single and plural, me and not me. And also very tired.
My Fool pointed to the golden mats. "It is time."
I said, "I can really use a rest right now."
My dad concurred and we both lay down to rest.
As usual, I felt a thump on my stomach. I felt it and sat up, taking an object into my hand. It appeared to be an enlarged atom.
My Fool's voice sounded, "The Gem of Connection. Everything is made of atoms. Everything has energy. The bustling interaction of all can only be had through connection. We are all one."
The atom shrunk to a charm that appeared as the fifth keepsake on my bracelet. "This is to remind you that even if pained by another, that another is a reflection of you, and there is nothing to fear."
I sighed, lying back down on the mat with reassuring thoughts. We are all different, and all the same. Different on the surface, the same at our core. All in all, we are all one.
I suddenly felt an overwhelming love for those closest in my life. Oh how precious are our family and friends! Right down to their eyes and noses and every hair on their heads. When we connect with them, we can feel oneness and Creative Energy dancing between us. Creative Energy is the fuel in us all, the inner core of every seed that drives it to open. We are connected in an invisible maze that links us together as one force of energy. With that, I fell asleep.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
As you sleep this night, put to rest questions of your worth incited by how others treat you. Put to rest ideas that you are alone, or that anyone is better or worse than you.
When you look upon another, think, I know you are me, deep down, we just look different, and act different, because we each have our individual part to play. We sometimes are in conflict because we all feel a little lost and afraid.
We are our friends and our enemies, the loved and the hated, the sky and the earth, one massive energy. Since we are not separate, we are equally significant always. Sensing our oneness allows us to journey through our day, knowing that everything is okay even if challenges present themselves. If we don't get the job, it's okay! If we don't win the guy or gal, it's okay! If we don't look like the socially preferred image, it's okay! When we can, in oneness, touch a person, a pet, a plant, we touch all existence, and that is intoxicatingly beautiful.
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# The Bog of Regrets
# GEM #6 Folly
We remember what we want to forget,
and forget what we want to remember.
##
MY DAD AND FOOL WERE off again working on my father's next incarnation. I'd been instructed to think of all the meaningful things I'd done as a means to end my old pattern of piling guilt on myself just for being human. I had always felt comfortable suffering, the cornerstone of every good martyr. Hiding there in the martyr story, I could dive beneath mundane life, and die young for a cause. I shook my head defiantly. No more.
I gazed about the meadow, now seeming more like autumn with a bit of chill in the air, although I wasn't really cold. I decided to walk while I pondered my meaningful accomplishments. Stepping along the grasses, I went away from the hill where my dad and Fool had gone off.
Okay, let's see. Started out in life quite shy, liking the idea of invisibility. My mother worked me out of that by writing school plays, giving me the starring role, and with the teacher's permission, acting them out with other students for the class. "The Unhappy Poinsettia" and "The Rusty Doorknob" were my second grade debuts.
She told me stories of the groundhog afraid to stick its head out of its burrow to go play with the other groundhogs, but how one day bravery pushed the groundhog out of her hole and soon she had many wonderful friends. Eventually, I did come out of my hidey-hole and became quite popular just by bravely being my own person. However, to this day, my innate shyness haunts me. I just handle it better now. In the past, there were many times I wanted to speak up, but couldn't.
When my son was five, I had him in private swim lessons. The teacher scolded him for defying her instruction, when really he didn't understand what she was asking. I didn't correct it. My mouth just wouldn't open. I was paralyzed. Angry tones paralyze me. When anger is flying about, whether at me, or even if it doesn't involve me, I shut down. I still feel bad about not defending my son.
A few flies started buzzing around my head trying to land on my nose and eyes. Distracted from my memory, I realized I was already thinking of what I hadn't done 'right'. I sighed. This was going to be harder than I thought. I waved my hand hard around my face to ward off the pesky flies.
Okay, back to the meaningful things I'd done. I have long been the one friends come to for advice. I smiled slightly, seeing that the flies had disappeared and butterflies were flitting about my feet instead.
Even as a child, I had a knack to help others feel better. I think it was by my empathy that I could feel their pain and somehow see how they were caught up on an inhibiting idea. Even my friend's mothers sometimes called me to help their children feel better. But one time, I felt smothered by a friend, and I started to ignore her . . .and ouch, my arm. I looked to where I felt a sting. A horse fly bit me!
Oh, of course it bit me, I was getting down on myself again. Interesting, that when we are down on ourselves, whatever is around us seems to join the crusade. As always, the outer world is a reflection of our inner world. I had a bigger case against myself than I thought.
Okay okay, I began walking again. Focus on the brighter things, Susan, not on what I wish I would have done better, like various animals that died because of my folly. My mind flashed with events that I wished I'd done differently. A sad old song I once wrote came to mind. Let's see, how did that go? Have ever felt the world stop spinning, and all you could feel was pain? Did you ever feel there was no end or beginning, and nothing left to lose or gain? Have you ever seen blood on the face of your ghost? Have you ever felt that what wasn't real, was real the most? I fell into the ocean and I drown. And I will never be found.
Suddenly, I couldn't stop thinking of my regrets, the time I accidentally left my dog in the car and he died of heat affixation. Poor dog. I thought of the time I yelled at my mother for trying to direct my life. Poor mother. I thought of the time my baby son crawled in the swimming pool when my head was down fixing his toy, and he almost drowned. Poor son. Saying good-bye to my crying little daughter who wanted so badly to spend a weekend with me instead of going on a family visit with her dad and brother. I had really needed some alone time to care for myself, but I will never forget the look on her face crying so desperately, reaching out for me. I want to go back in time and hold her and love her, and I would almost die to do it.
I teared up, and suddenly couldn't walk. Everything turned foggy, brown, and obscure. I was in a peat bog up to my ankles, sinking slowly. I had done this to myself. Regrets, oh how they come alive when we feed them, like evil little demons set on doing us in for our transgressions, no matter how large or slight, or maybe not even real transgressions, even though we deem them to be.
Although these regrets would abate for huge spans of time, even for years, there they seemed to remain in my subconscious, ultimately resurfacing whenever I became mired in self-doubt. This ever seemed to awaken the martyr and jumpstart that old pattern once more.
Tears rolled down my eyes, and I was mad at myself for not being able to dissipate my regrets once and for all. Wet peat enclosed my knees. No! Everyone has regrets. It's normal, it's human, why is this sinking me? I am guilt free most of the time, I shouldn't be sinking this much, this fast. It came to me then, Thoughts of the past become the present. Yes, that's true. One moment of intense regret is all it takes to pull me down. I huffed a breath and closed my eyes, concentrating. I did the best I could for who I was then and where I was at psychologically. I just wish—
A shrill whine grabbed my attention. My eyes opened. A cluster of apparitions zoomed at my face, smacking into me with a cold snap, giving me a brain freeze headache. I knew at that moment that the ghosts were these memories that haunted me. The wet peat closed in around my chest.
I heard my dad and Fool calling from behind me. I looked over my shoulder, startled to see them so far away, appearing about an inch long. I gazed about me. The bog extended for miles ahead of me, and to my sides as far as the eye could see, and dotted with multitudes of people at various stages of sinking. Some were on rafts, but still unable to get out of the bog.
My Fool suddenly appeared before me as a foot long visage, hovering just above the bog's surface. "You are in the Bog of Regrets created by people's machinations against themselves. These machinations manifest as ghostly energies sucking them into the underworld of their imagination, where they are shamed into punishing themselves. Those on rafts are coping with their regrets, but are still plagued. Those who have gone under have physically died from the stress the regrets caused."
"I hate this!" I cried out, losing emotional control.
My Fool said, "All humans tend to be self-critical, even if only at times. Even braggarts have secret regrets that plague them to no end. When humans brag, they are trying to tell people they are important and therefore worthy of approval because deep down, way deep down, they fear they are not. On the other side, when humans openly berate themselves, they are telling others they are not important and do not expect to be liked. Yet, these appraisals linger on the outskirts of truth."
"I know, I know," I said. "And when humans feel liked, then their regrets have less pull. I need to like myself, which I generally do, just not at this moment." The wet peat engulfed my neck.
I twisted my head back to view my polka dot dad at the shore. My torment was getting me further away from him, which was the last place I wanted to be before he died. This had to stop.
My dad's voice sounded in my brain. I think we all can hear what our loved one's 'would say' at various times in our heads. "Sue, think of all the people you helped find themselves, and the children you made smile, of the animals you were kind to, of the loving talks you've had with your kids. Think how you always share your love so easily with everyone and everything. Cultivating the bees, saving wild birds, and championing the trees. Think. Focus."
My Fool's eyes glimmered in front of me even in His teeny tiny body. It came to me then that even if our greatest regret was that we killed a flea, we could still drown. It is never about what we have done, but what we do with what we have done. We can make little things seem gigantic.
I remember when I was a therapist and people would tell me their deep dark secrets, and when I reacted with, Oh, that is not so bad, and not unusual, the dark secret became light and freed them. With their secret shame out in the open, they began to heal instead of fester in their self-created hell. One client was a secret cross dresser and turns out his wife didn't care. Greatly relieved, he began to enjoy life.
Okay, okay, I have shined some light in this world. I have written books to uplift people's spirits. I have facilitated workshops to ease peoples suffering. I am attentive to my loved ones, and deeply kind to animals and plants.
I began to rise from the bog floating up in the air. Then just like that I was on shore standing before my dad and regular sized Fool.
My dad looked at me warmly.
I shook my head. "Sorry about that." I looked to My Fool. "Can we ever extinguish our regrets?"
"No," He answered, "because they aren't really there."
"Huh?" I cocked my head.
He explained, "Our regrets are just conclusions we draw from our past that serve as glue to keep our storyline in place. And at the same time, they can ensure we do not repeat the past and do better in the future. But—"
My dad finished, "—they are a concoction of our mind."
I added, "A concoction, I guess, that serves a purpose."
My dad looked into me. "When you think of your dog that died in the car, even though his destiny was set and he still exists somewhere, will that, can that ever happen again?"
I said, "No, I am too focused on that possibility now. I am so much more careful with my animals, and I tell the story to everyone so they will be more mindful of not forgetting animals or even children in their cars. I do sense that everything really does happen as a part of the greater synchronicity, but sometimes the regrets loom large anyway."
My Fool said, "Still, you have taken that event and made it constructive."
I said, "I just need to focus on that, I guess."
My dad brushed some peat off my cheek and said, "When you, or anyone replays their regrets, they are allowing a past to keep them from a brighter future."
I scowled. "I guess we can be pretty hard on ourselves."
"And each other," my dad said before glancing at me. Except you, Sue. You always make excuses for others and tend to get fixated on only the good in them."
I furrowed my brows. "Well, there is good in everyone."
"Yes," My Fool nodded, "but you tend to close your eyes in denial of their folly, wanting to see things as you wish rather than how they are."
My dad and Fool suddenly disappeared. I craned my head about. Where were they? The air became engulfed in a soft white glow, almost like being in a cloud. Or maybe I appeared in a soft white glow, I don't know.
Searching for my dad and Fool, I saw an open gate embedded in a diamond wall. The glitter from light rays accentuating all the gems clarity, hurt my eyes. Were they in there? I passed through the gate and entered the diamond world: diamond mountains, diamond trees, diamond ground. Prism colors splashed everywhere. So beautiful!
I scanned the sight, but saw no other around. My chest felt heavy. Anxiety subtly electrified my body, growing stronger. Breathing became difficult. My initial elation had changed to nervousness. Why in the face of such beauty did I feel so bad?
My feet started hurting, feeling the cut of diamonds pushing through my skin. Air was not flowing into my lungs as it should. I turned around with my eye on the gate to make my exit. I fell to my knees and began crawling through the diamond world, feeling punctured by sharp things on the ground, as I edged forward hoping to escape.
I saw my dad and Fool at the gate. After painstaking minutes that seemed too long to cover the ground to reach them, I arrived at their feet. My Fool took my hand and helped me stand, then led me a few steps more out the gate.
"What was that all about?" I asked them.
My Fool explained, "You saw what you wanted to see, and not what was."
"Why would I do that?" I asked,
My dad glanced at My Fool. "I got this one." He looked at me. "Because if you pretend that everything is harmonious, you don't have to face the fact that it isn't."
My Fool pointed to the scene. "Look again."
I looked back. Dying trees were scattered amongst sharp rocks and broken glass that carpeted the ground. The clear-cut mountains against a backdrop of dark smog, left only tree stubs.
I grimaced. "But what is the point of seeing the horrors of the world?"
My Fool's head dipped with eyes penetrating me. "You know the answer. We've been over this before."
I did know the answer. I sighed. "If there is beauty, there is ugly, and when I don't see both, I tend to walk into trouble. I need to accept the duality of opposites that permeate the earth."
My Fool said, "And . . ."
I said, "Beauty and ugliness are the same energy flowing through different channels. Depending on our makeup, what is beautiful to one might be ugly to another and vice versa. A terrorist act is ugly to the victims, but beautiful to the terrorist. Abundant rain is beautiful to some and a sorry sight for others. Watching a surgery might be a sight of admiration to behold, but to me, it is horrifying."
My dad added, "You let your cat nuzzle your face, I find it unacceptable."
My Fool said, "Pollution looks unsightly to most people, but to the actual pollutants, they are finding new life and freedom of expression."
My dad looked at me affectionately. "This doesn't mean that seeing the best in everyone isn't a good thing, however, you are less likely to get upset if you are also open to what could be termed as the worst in people."
I rolled my eyes. "I get it. I get it."
We then seemed back at the meadow, green grass, flowers, and all.
My Fool pointed to something. "Look."
Before us were two block piles. One pile was grey, cracked with maroon dripping like spilt blood. The other pile was prism white with rainbow reflections. He looked to the grey blocks. "Sometimes stories shared about innocent others are given a dark twist, and a lynch mob appears. 'You are guilty,' they proclaim."
He looked to the prism white stack of blocks. "Sometimes stories shared about others are embellished to create heroes we exalt with our minds, even though a hero to one might be viewed as a villain to another."
Then both piles turned clear and appeared the same. My Fool summarized, "We often create what we either want to see or fear to see, and generally act upon it as complete truth."
I shrugged my shoulders. "I guess if we could just view all assumptions as holograms we create, we would be less likely to overreact."
My Fool said, "Like this?"
I felt a whisk of energy and we all appeared in a desert scene. The land glowed like a sunrise. The sands were pinkish light brown, and hills crested on the distant horizon. Hearing a growling roar behind me, I jumped and spun around. A mighty lion charged us, leaping into the air.
My Fool's voice sounded, "It isn't really there. Don't react."
The lion seemed to jump right over our heads and disappear.
I sighed with relief, my heart pounding.
"We make our monsters," My Fool said.
"We make our heroes too," added my dad.
"We give our own meaning to everything," said My Fool.
Having calmed down, I chimed in. "Nothing is ever as it seems, but what of the events that are tangible, like a tsunami, or a murder? I mean they are real, aren't they?"
My Fool smiled. "Everything is real, even if it isn't really there. Illusions and impressions are real to us, but how real is dictated by our perceptions and way of thinking."
Suddenly, we were hanging high in the air, looking down on the desert, viewing a bloody battle. It was so grotesque I had to look away. I felt us rising higher, but it was more than that. We also had a greater view of the width of time. Before the battle, one side was exploited, and the other, the conquerors.
Then we went higher in view and wider in time. It was as if each new perspective was superimposed over the previous smaller one.
Before the exploited side was conquered, they had been exploiting a lower class of their own people. And the side that was exploiting, had also once been exploited. The picture kept getting bigger in view and wider in time. This volleying of both sides exploiting, inciting battles and wars, seemed to span millenniums. People lived and died, and lived again, and died again.
The scene grew even bigger and the width of time more expansive, and millions of people were all interacting almost as reflections of each other, and then I could see that they were. They bounced off each other as light shines through leaves fluttering in the wind, casting glimmers. They actually all looked so beautiful here, exploring the theme of exploitation, learning about themselves and group behavior, about power and powerlessness.
I wasn't quite sure how I could smile at a panorama involving war, but they were all glinting spirits then, and I could see their connection. Like when paper is folded over and over, and singular cuts are made, but when the paper is unfolded, all the cuts are just one beautiful pattern.
I saw these multitudes as one being, experimenting as if they were not. As one being there is no one to hate, no one to blame, for what they do to each other, they do to themselves. Only when the experiment is over can they begin to feel this.
I then saw the whole scene in the expansive future of two provinces working together in harmony. Feeling a bit teary, I murmured, "Chaos leads to peace. From the rubble comes new foundations, stronger than the previous. The horrors of war spark an urgent yearning for serenity, compassion, and a different way of being."
My Fool said, "Remember that when you look at this." He pointed down abruptly and we were back hovering just above the first scene of bloody grotesque battle.
I grimaced even though I knew it was just a scene in a much bigger story.
My dad said, "The moral of the story is that our conclusions, based on what we see, limit our vision of the greater truth. This is our folly. Even so, our folly also generates many good things."
How true, I thought. Much of my upset in life was due to looking at a scene, like this bloody battle, and feeling only the horror, and failing to trail the event to its eventual end to see the beauty. I shook my head lightly. "Small perspectives really do pin us into uncomfortable realities."
My Fool summarized, "Once again, in keeping an open mind instead of drawing cemented conclusions, we can more easily stay centered instead of going off on tangents with affirmative proclamations that cause us to suffer. However, assessing things on a temporary basis, such as, It seems like this; but . . . maybe it isn't, can short-circuit our turmoil."
"Yes," my dad said, "we so often act on our impressions, throwing out the baby with the bathwater, or keeping the dirty water with the baby in the bath. Learning to sift the wheat from the chafe is an art of staying open by realizing any information that comes our way is only a piece of the whole picture, and if we are patient, another piece will eventually show itself."
My Fool said, "And each new piece changes the picture."
As the initial bloody battle scene played below us, I focused on how the whole saga eventually ended in harmony, and it made everything more palatable.
I rambled on, "Realizing we do not understand everything, and that somehow our folly has value even if we can't see it, can be most freeing. That whenever we see something, to know there is more to it, we needn't overreact. I mean, for instance, if I am uncomfortable around a person, it doesn't mean that person is bad or did anything wrong, just that for whatever reason, I am uncomfortable around this person, and that there is more to the story."
I looked to My Fool to see His response. He seemed to be growing taller and wider. My eyes shifted side to side wondering what this meant.
We disappeared from the desert scene and were back in the meadow. I'd never bounced back and forth so much on a single adventure. I gasped as a panoramic vision of life's many scenes formed all around us.
I looked about, twirling slowly on my feet, and inhaled a deep breath.
My dad had been slowly turning around at the scene too.
I was expecting My Fool to chime in, but then noticed He was not with us. I snapped my head to my dad. "Where is He?"
My dad took his finger and pointed out to the surrounding panorama, turning on his heels in a full circle.
I squinted, turning as he did, trying to see what he saw. The scenes then seemed to fade just a bit, and our Fool's face was panoramic, remaining constant as I turned. Not sure how I could see Him that way, but I did.
I heard gentle laughter coming from that face that seemed to defy location. Then My Fool was standing next to me, shaking His head wisely, "We are all of it, but as we push our way through life, few know anything, and no one knows everything, we only think we know. In that, we are subject to folly. Folly is as accidentally wandering into a dangerous neighborhood, and the escapade to get out is what makes the adventure."
My jaw dropped with an epiphany, "What goes wrong is the prize, for it catalyzes growth and understanding. The rewards of living are not in certainty, but born from uncertainty. How we handle the unexpected is the experience that facilitates our becoming."
My Fool grinned approvingly. "An exciting moment, day, year, life. It is always there, and need not be feared. Whether open-minded or closed, what we attract to us is a reflection of the current vibration of our inner self. We may try to attract our soul mate, but our inner state of being will dictate who actually comes forth. That person, though perhaps not our soul mate, will propel our story line just as it was meant to be."
My dad joined My Fool in staring at me.
I rolled my eyes. "I know, I know, I attract controlling warrior types."
My Fool continued, "Those that came at you may have felt like mistakes, but you didn't know how to stop it. You were not supposed to. Experiencing those seeming mistakes, you changed within yourself, and now are capable of attracting those who reflect your inner growth."
I bit my lip. "I can't believe it, but I am actually starting to see that folly isn't really folly. It is just us stepping along in life as we should. And as utterly horrible as all tragedies may seem, there is a synchronicity in all of it, leading to pondering, probing, and reform. While a tragedy can be viewed as a punishment or senseless, it might be well to consider that it was a natural consequence to various energies colliding for a reason that transcends conscious understanding."
My Fool was nodding. "Your sight is deepening as it once was, Susan, before you fell away."
I smiled faintly. I was coming along, and I was feeling better. "I guess when we change our thinking and feeling, it is because it is time to change our thinking and feeling. What we think and feel at any given moment is integral to the experience we are trying to have."
My Fool concurred, "Yes. When it is time to ascend from our pain, we do."
My dad said, "That's like when people say, suddenly the cloud lifted, I don't know why. Or people who have been depressed for many years suddenly hit the jackpot for the depression to lift. It might be a pill, or an event, or there may be no apparent reason why they are suddenly okay."
I inhaled a deep breath, feeling more aligned with myself, another step in recovering from my Northwest struggle. I closed my eyes, just soaking it in, consoling myself.
My Fool said, "Speak Susan. Flow freely."
With eyes closed, words streamed out of me like warm water. "I will get kicked in the teeth. I will stub my toe. I will not get most of what I strive for; but that is okay, because now I will take my kick in teeth as an opportunity to redesign my relationship with myself, or my life direction. I will lovingly address my toe and teeth to do what is necessary to avoid further injury, and take it as a sign to give myself kindly attention.
"I will take my disappointment and realize things did not work out because that was not my path. I will march on and be in the moment, enjoy the sunrise, the stars, and the smile on my loved ones faces, or the kindness of a stranger. I will walk on with a full heart and sense the synchronicity of seeming folly, even if beyond my conscious understanding, as intertwined with everything in one great balancing act.
"Like a mobile that is tugged, the whole mobile moves. And no matter how hard we try to separate ourselves from each other, we all affect one another, and we are all in this life together. What one does, we all feel, and the whole earth is influenced. We are like one giant being with billions of particles moving about, growing and becoming."
I opened my eyes. The warm clarity about me was stunning.
My Fool gazed into me, then into my dad. With a light nod, He said. "It is time."
I heard the mumblings of many people behind us. I turned around. There was a crowd. My dad and Fool had also turned around.
My Fool explained, "These are those who have come here in their dreams, attracted by the topic of our focus and the energy we emanate. They have come to learn how to deal with the Bog of Regrets."
My eyes widened with interest.
My dad looked at me with a questioning eye. "Shall we?"
I shrugged my shoulders. "Why not? I guess it is a good way to further assimilate all I have learned."
My Fool smiled knowingly, then suddenly we three were at the top of the little hill, My Fool sandwiched in the middle. Below us was a sea of astral bodies, some standing, some sitting, and interestingly, some just floating in the air looking our way.
My Fool said, "You begin, Susan."
It was so weird, but white robes appeared on us like in the biblical days. Given the perception of wise beings was often as this, it was likely how the crowd viewed us.
Not a stranger to lecturing, I began speaking. My voice amplified as if through a microphone. "Every time something doesn't go right, we tend to view it as gone wrong and a bad thing, and our stress levels soar, blinding us to what is going smoothly. We become obsessed with our thwarted pursuit of happiness. Our mood darkens, affecting everyone around us."
"Step back." My Fool chimed in. "Observe the bigger picture, and how much skill, energy, and attention it takes to merely live. We are more masterful than we realize."
My dad elaborated, "We strive to maintain our vehicles, electronics, appliances, homes, yards, bodies, relationships, jobs, finances, and our environment.
I jumped in. "Simply maintaining all the machines in our lives can feel burdensome. Home repair might feel never ending."
My Fool spoke up, "Tending our bodies can get tedious: eating too much or too little; eating healthy or foods that make us sick because we are stressed or on the go; problems with digestion and expelling waste, staying clean and germ free. Our bodies challenge us to keep our organs going, brain's sharp, muscles strong, and lungs healthy, and to get needed sleep. We take vitamins, supplements, and medicine, and try to stay hydrated. We try not to abuse our hands with too much use of gadgetry, or hurt our eyes from being addicted to one screen or another. We might even miss some teeth brushings because we are tired, busy, or just don't feel like it. And that is just our bodies."
My dad chimed in, "Then there is making a living, finding a way to pay our bills, save our money, or have fun spending it; sometimes spending it when we should save it, or stealing it when we should earn it, or saving it to the exclusion of having any joy. We deal with debt, working so hard we might drop, or going through hell just to put food on the table. We pay our mortgage, utilities, insurance, medical, upkeep on everything, our entertainment, vacations, our bank bills, take out loans, give loans, compete for the buck whether to make ends meet or to become a mogul of untold proportion. And that is just money matters."
I jumped in, "Then there are relationship challenges with our family, friends, colleagues, those who serve us, and those whom we serve. These relationship challenges extend to our social groups, other groups, and societies, even countries. We compete, collude, and collide, striving to get along, handle conflict, and survive the drama. Our relationships extend to animals and insects, and the mountains, ocean, earth, sky, and even our things. I love my shoes. I love my car. I need my computer, my phone, my music. And that is just our relationships."
My Fool said, "Navigating through a single day requires tremendous juggling and balance. Thoughts are racing through our heads constantly, trying to assess and adapt. What does this mean? What does that mean? Should I do this or that, or nothing? And that is just our minds."
I could feel the crowd aligning with us, like energy fitting together, uniting in one powerful mass.
My dad's words intensified, "Then, we have our emotions. Sometimes they take control and we put our foot in our mouths, act on impulse, or emote with a burst to make a stand for ourselves, or explode with a bang to cause suffering. We deal with anxiety, depression, highs and lows. We quest for love, feed hate, endure jealousy, are fear driven, climb the heights of joy and accomplishment only to be knocked down around the corner. And just when we are about to sink into sad oblivion, something beautiful happens and we are uplifted to new levels of hope. We struggle to feel our worth, and give it to others, or take it if possible. We offer a hand to help another get to where they want to be, and we step on heads to get to where we want to be. And that is just our emotions."
My voice rang out, "How can we possibly navigate through all of this and have everything go as we'd like? In western culture, the popular term floating about the milieu is, "I just want to be happy." That is like saying, "All I want is for everything to go smoothly all the time. But how can it when life is complex involving millions of people, entities, and energies?"
My Fool's voice deepened with an almost haunting tone. "The pursuit of the ever elusive happiness often involves an attempt to control our outer world. I will be happy if . . . my house is always clean; lose weight, my kids get good grades; my mate pays more attention to me, my subordinates make me look good. However, even if we attain what we seek, other issues arise. Our children get good grades. but they are failing socially. Our subordinates are making us look good, but they hate us. We get that new job, but our health is failing. We beat the disease, but we are broke. We find the perfect mate, but the ex-spouse is vicious. We move to the foreign country of our dreams, but we are lonely."
I felt a warm rush of My Fool's energy fill me. It almost seemed His words flowed through my mouth, teaching me as I taught our audience. "Consider that things never go wrong, that our expectations of how we think things should be keeping us from appreciating how things are. Consider that things are always going right; we just aren't seeing it. Connect the dots. Follow the sequence of events. Our car breaks down and we are stranded on the side of the road. A few minutes later, a wrong way driver speeds by. We get fired from our job, making us reconsider that line of work, prompting us to pursue a more tenable occupation. We get dumped by the person who actually thwarts our personal growth."
I felt the warm rush flow back into My Fool as He spoke. "This is life, and trying to force outcomes in the pursuit of happiness, hoping nothing ever goes wrong, will only lead to eventual disappointment. All humans inevitably face challenges that try us to the very fabric of our being, be it the loss of a loved one, living in an impossible circumstance, or living with a daunting handicap."
My dad added, "The quest to feel better is less about trying to control our environment and the people in our lives, and more about controlling ourselves. How is our thinking contributing to our upset? How are our expectations keeping us from achieving enjoyment?"
My Fool held out His palms. In one was a miniature cat, and the other a dog. He commanded the cat to bark, and the dog to meow, but they couldn't. They disappeared and a red ball was in His hand. He threw it up in the air and commanded, "Stay up!" but it didn't. It came down and bopped Him on the head. Laughter rippled through the crowd as the ball rolled down the hill, then vanished.
A child appeared and walked past us wearing a glittery sombrero. My Fool shouted, "Hey, you should be wearing a baseball cap!" The child gave Him a dirty look, then said, "My sombrero." The child vanished and a short teenage boy appeared with eyes closed chanting, "I will be six feet tall." Then he cried because he wasn't. The teen disappeared.
My Fool announced poignantly to the crowd, "Instead of laboring to force wanted outcomes, or pining for them, we could fair better by viewing ourselves as a flower unfolding into who we truly are. Just as a seed that becomes what it is meant to be, a flower, a vine, a cucumber, so do we. We are as a tree growing a bit more here and there in various aspects of our lives, another leaf sprouting, another root sprawling forth to absorb more nutrients. Our story is our story. Why not see what it is?"
My dad chimed in, "We cannot set ourselves apart from the laws of life."
I added to the chime, "Collectively, everything on earth is simultaneously making its way into fruition through hardship."
My Fool's voice filled with power. "In the cycle of our becoming, our seeming folly is nothing more than doing our best at each given moment, for given all the variables at play, we can do no less. Through trial and error, we learn what does and does not work, what to do and not do, and what brings the most reward. And along the way, we discover who we are."
I found myself grinning and a bit teary as I celebrated my own self-discoveries.
As My Fool continued to address the audience, golden sparkles fell over the crowd. "You are each magnificently unique. Celebrate your specialness and revere your 'becoming'. Let your new quest be to naturally bloom, and be open to where that takes you. Live the mystery."
As the sparkles absorbed into the astral crowd, I felt some absorb into me. I had heard Him talk about living the mystery before, but only now did I truly feel it. Just make the most of today, and tomorrow will bring a new adventure that will help me grow.
The crowd started glowing brighter and brighter until they disappeared. Our regular attire returned.
My Fool said. "They feel better and are soon to wake up in their bodies."
Something was happening to me, and I think my dad too as we were both glowing a bit.
My Fool said, "Time to deepen the experience of the words in which you have both just spoken." He narrowed a knowing eye at us, then whirled His hand above His head. A colorful rain-washed energy swirled about us, placing us in a vortex. I felt myself falling away into another world and presumed my dad was too. He to his world, and me to mine.
Mahler's Symphony #5 played, bathing me in its vibration.
Words came. Leave your shame at the door. I gave myself permission to be shameless. That decision was up to me; it had always been up to me.
Soothing darkness replaced light, the darkness of quiet and womb-like security, yet I felt beyond my identity, though my identity was part of me. I was more expansive than Susan, wiser, and eternally balanced. The lights came up and I was outside my human self, who I could see far below me.
My bright human being, riddled with dark spots, was huddled in a ball on the floor, focusing on all the so-called mistakes she ever made, all that she deemed she did not do 'right'. The dark spots were all the judgments she passed on herself. Draped over her back was an invisible heavy shroud of lethargy, weighing her down.
I, as this greater being, told my human self, "Dissolve the dark spots of self-judgment with compassion and love. Let the heavy shroud of lethargy that keeps you from flying free in the world, dissolve."
Susan looked up toward me, sensing I was a higher being giving her divine direction. I was, but I was her higher being, her Great Self, and she was a projection of me, out there bravely having earth experiences that contributed to the Creative Energy that made us all more than we were. I loved her.
I was in my human self again and became determined to allow myself to shine, instead of inviting blight. I am okay. I am all right. I am valuable no matter what. My true self is as big as the universe, shining through my human form. I love me. I embrace me. I forgive me, for there was never anything to forgive. I am human and expected to trip and falter before I can learn to walk and run.
I felt the heavy lethargy on my back begin to crack up, realizing it as the shroud I wore in my last Northwest years. I was shedding the old guilt-laden me that tethered the true me from moving freely into the world, unfettered of the shame I inflict upon myself for virtually every so-called mistake I ever made. Being perfect is not perfect, but an image that makes us feel safe, but also inhuman and in many ways unlovable, unreachable, and untouchable, for we all bump into walls, and can hold each other in our suffering and bring comfort.
I was my Great Self again watching Susan bow her head over her knees with shins flush to the ground, her palms turned upward.
I flashed back into Susan, and gave myself permission to completely heal from this paralyzing self-inflicted disease of regret and shame, fed by the quest to be perfect. I began sobbing, pulling up deep down roots of my attempts to grow a good little girl forbidden to blossom into true womanhood, and the pious nun forbidden to feel joy.
I flashed back to my Great Self looking down upon my hunched human form. I poured love and compassion into Susan, and she let me. As I filled her, the dark spots faded and she began to sparkle.
I kept pouring Creative Energy into her, which manifested as colorful swirls whirling in her and about her, turning lighter and brighter. The energy bath was washing away dark hunks of matter like leeches stuck on her everywhere she went. And when she began to get strong and shine into the world, the leeches would make her weak. Leeching came in the form of how she unconsciously invited people to mistreat her.
I flipped back into Susan. I can be free of what drags me back if I have courage. Courage to fly without the familiar ties of my past, meaning my whole soulic journey on earth within the concept of time and space. I can be anew right now in Pure Creative Energy.
I flipped back into my Great Self watching Susan. Energy wings grew on her back until they were full sized. Her head came up as she rose to her feet. Although a physical being, she had an energy form that was also active. It began flitting from person to person, to beast, bug and flower, flickering the light of love because she had let herself become love, which is simply experiencing oneness with everything.
Back in my human self, I felt the old me fade into the Creative Energy in which it was made. A new Susan was coming into fruition, preparing to live a life quite different than the previous Susan.
Perhaps all the Susans I had been in my life were versions of other Susan's in parallel worlds living out their lives? Maybe we blinked in and out of each others realities, not as separate in our worlds as one might think. Perhaps boundaries have various constancies regulating many flows of penetration.
However it may work, I embraced the Susan to be, releasing the Susan that chronically elevated others above her with acts of nurturing, painstakingly feeding those with depleted egos in need of more self-esteem, and in the end, so often blamed for whatever in them was not ready to heal.
It isn't other people's fault, this undeserved thrashing that commonly came my way. I brought this upon myself every time by giving too much of myself away rather than letting it build up inside me into something that is trying to develop into a new me. The minute I feel an inner boost, I want to spread joy and give it to someone. But I fail to realize I am one of those who needs what I have to offer. I need to feed myself long enough to complete my transformation.
Well, the new Susan was trying to come into being. My new commitment was to make her the priority and harness my energy to finish developing into the new me. I must shoo away the guilts I carry, that like blood suckers drain me dry and keep me the undeserving martyr.
I had a flash of the Susan I was leaving behind. Her destiny was as a cannon ball shot into the world with guilt, physically dying, snuffed out by the energy sucking monster of martyrdom.
Before I came home to my dad, I had been feeling that way for so long, I could not feel my future. It just wasn't there. I was at a choice point. Would I choose the new Susan to finish out my life purpose, or the old Susan to die before my time and pick up the story later in another time and place, or perhaps another Susan in a parallel world? We all feel this at pinnacle times in our lives, this 'do or die'. And it really is just that, if we don't do, we don't transform into the next level of our being, and we die to take that next step in some future reality.
I inhaled a deep breath and felt myself again in the meadow and there was my dad just opening his eyes as I opened mine. We smiled softly at each other, our eyes glossy with tears. We knew we had both just experienced a great healing.
My Fool pointed to our golden mats that had suddenly appeared. "You are overdue for your rest."
I didn't realize how tired I was until He said that. I was drenched with exhaustion. I don't even remember lying down, but I was there on my mat, with closed eyes, seeing a broken heart symbol in my mind.
I felt something added to my bracelet, probably a broken heart charm.
My Fool's voice sounded warmly, "This is the gem of folly. Folly takes us to places beyond what we can see, into the realms where the brightest wisdoms brew. See your folly, and the folly of all, as the most real part of being human. Sacred it is, for in folly we stumble upon love."
With that, I fell asleep.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
Oh behold the human being. So often we deem ourselves the sole bearer of guilt born from our folly, but we are not, and in fact are accompanied by millions. While a self-thrashing might seem in order, our guilt is but a sign that our heart is intact, that compassion still dwells there for those who may have been hit with the fallout of our folly.
Guilt serves its purpose at the time of the scene, instigating us to examine, learn, and redirect our energies to change our future. However, there is always a time to let go. Whatever happened was going to happen no matter what because that is the way it was supposed to be. All the variables at that time, variables often forgotten or not seen, compelled us to act in certain ways, not only for our growth, but for others. If regret has you bound, extend compassion to yourself.
Then there are those of us who will not claim our folly, but instead shame others for its rendering. In this, like a monster behind the door, our denied guilt grows and growls, threatening our destruction. We divert it by setting it loose on those around us even though it eventually chases them away, sometimes forever.
Alone in a world we don't want to be in, there seems no way out. It is hard, but sometimes we have to look into the mirror and scream in beholding what we have become, before we can take off that mask and see the wounded one beneath, drowning in sorrow. That damaged self is literally dying for our compassion, yet we continue to ignore it, and keep trying to pretend it isn't there.
Whether we punish others or ourselves for our folly, the solution is the same. Pour compassion into ourselves with everything we've got. Let it sink into the nooks and crannies, sliding into the cracks and holes, soaking into festering wounds of the past and present so that we can be healed in the future.
All seeming folly is as it should be to incite the experiences necessary for our great adventure to continue. Look now upon your life and see the good that has come, or can come, from your own unsavory life scenes.
We are not so bad, you and I, just gleaming balls of light making our way through the universe, glowing, changing, growing. Every time we change into something new, we are challenged again. We meet new levels of discomfort that often feel like folly, but this seeming folly is just the fuel needed to keep our transformation going. We are always doing the best we can at any given moment, which is more phenomenal than we could ever imagine. In our deepest state of being, our Great Self enfolds us in wings of love and compassion. In that, we begin to feel exalted. We always were, and we will always be.
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# THE PLAYGROUND
# GEM #7.. Experience
Our experience fosters growth,
and growth fosters experience.
##
I WAS QUITE COMFORTABLE upon my golden mat when I awoke in the inner world that morning. What would today's adventure entail? My eyes opened, drinking in a beige canvas ceiling. Hmm. I appeared to be in a tent. I sat up and looked about. No dad. No Fool. I was alone . . . again.
I peeked my head out the opening, craning my neck left to right, viewing a sea of beige tents all about me. Strangely, the outdoors felt like indoors. The meadow floor was astro turf. I scowled and murmured, "Not liking this."
I crawled outside and stood with a stretch and a yawn, letting my arms float down along my long white dress, hands landing on hips. "Dad!" Looking all about, I called out again, not too concerned, "Dad, oh . . . da-d!"
He finally emerged from the tent to my right. With bare feet, in his purple boxer shorts, he stepped toward me. I found it interesting that he began our inner world journey in boxer shorts. In my first journey, my attire slowly wore away as I continued to discover my true self. However, I suppose my dad had already done that before this adventure began, hence his scant attire.
From the same tent My Fool emerged, stepping up next to my dad. They seemed joined at the hip lately and getting closer by the day. I was still a little jealous of being left out of their time together, but I did want the best for my dad in preparing for his next life.
We all converged in a little triangle, facing each other.
"Good morning, Susan," My Fool smiled softly.
My dad tapped his bottom lip, eyes turned upward. "Interesting. Very interesting."
I looked up, a bit startled. Above us was another canvas ceiling, appearing as a larger tent that encased all the tents.
I slanted my eyes to my dad. "I don't think I like this. It feels confining. I want the freedom of the sky."
My dad narrowed an eye. "I think these tents are like our belief systems. They confine us to a certain reality. And the big tent we are all in is like the general belief system of the collective conscious. For instance, we all basically believe we are on a planet called Earth, and have boundaries for countries, and a place for cultures, that a car is a car, and a mountain is a mountain. These joint beliefs glue us together in a specific space and time. We all engage in a confluence of thoughts propelling us each to not only act out a global story, but a personal one as well, hence the millions of individual tents."
Oh, I could tell my dad was spending quality time with My Fool, talking more like Him every day.
"That makes a lot of sense." I frowned "Still, I don't like being bound to a story. I'd rather fly high above all the stories "
My Fool's eyes sparkled with His usual whimsy. "Very well."
Before I could blink, we three were soaring high, Superman style, with My Fool in the middle. We were orbiting a humongous mass of moving kaleidoscopic shapes that encompassed the earth. From here, it was actually quite beautiful, all the people, places, and things, mixing and matching, changing colors and contours. I was feeling rather lonely flying above it all, despite my dad and Fool's company.
Around and around and around we continued to go. I wanted to see what might eventually happen if we remained unbound from earth experiences. Around. Around. Around. If we were in earth time, my hair would be pure grey by now. Would this process lead somewhere or was it a stagnate situation?
My Fool said to my dad comically, "She can be so stubborn."
My dad chortled, "Yeah, tell me about it."
The kaleidoscopic view of earth kept changing into new things, unlike here in this detached realm, removed from all the action. I was beginning to feel envious of those in the mix, engaging in the earth adventure. I was astounded by the beauty and newness of billions of particles ever joining and separating making something new, like all the millions of songs that can be written from notes and half notes and quarter notes, with varying rhythm and tempo. It was a very creative endeavor, this immersion into the earth experience, even though we so often feel lost and alone.
I said, "It is all so awfully pretty, earth life, I mean, viewing it from here, while here feels kind of empty, uneventful, and basically unfulfilling."
I inadvertently glanced at My Fool, and quickly did a double take. He wore the usual superman garb, cape and all, one hand jutting in front of His horizontal body, the other, fisted by His hip. I giggled and giggled. My dad did too.
"Now," My Fool said, "What kind of adventure could even Superman have without touching down somewhere?"
He was right. "None."
"So," My Fool went on. "Fulfillment cannot be had without experiencing events. Humans want to feel safe as you do right now, above all the conflict, and yet, they yearn to grow, lured by a natural curiosity to have new adventures."
I said, "That's true, humans seem to crave experiences. We want a baby so we can experience parenthood. We want to marry someone to experience a close bonding. We want to get a certain job to express our talents."
My Fool added, "So, if you could sky dive, but not feel the movement of falling, or eat but not taste, or get to the top of the mountain without feeling the climb, life would seem fairly hollow."
My dad blurted, "Kind of like how circling around and around without getting involved or having new experiences feels. He looked to me. "Is this what you really want, Sue? It is rather unadventurous, going around and around."
I conceded, "Yes, it's boring."
"What do you want then?" My Fool inquired.
"I guess I want back in. I can't believe I am saying that as I've never been fond of the human experience, the primitive level anyway. Seems like we just keep repeating the same old stories but with a new twist."
Another glance at My Fool revealed Him face up, hands clasped behind His head, in His regular white pants, purple sweatshirt, and jogging shoes with the toe part cut out. He was the most entertaining thing up here, and if I were alone, it would be awful.
"Repetitive, old stories," He began, "are made anew by the various ways we experience them. As each identity is unique, with distinctive perspectives, there are innumerable combinations we can make to generate new experiences. For instance, every person looking out at the ocean will have a distinctive experience based on the context of where they stand in life, who they are as individuals, and how they are relating to everything else. Nothing can ever truly be repeated, for change is constant."
"Nothing stays the same," I murmured. "You taught me about this before, but from here, I can see it more clearly. That mass below us never stops moving."
My dad said, "I find it refreshing, knowing that no matter what, everything is always changing, even if we think it the same, or even if we try to keep it the same."
I sighed, "I have to agree. Feeling stagnate is the worst. Okay, I am ready to go back in."
"Then go," said My Fool.
I focused on the identity of Susan, but nothing happened.
"Why isn't it working?"
"Keep trying."
I focused real hard on Susan for another minute, but I remained an outsider to earth, looking in from afar.
"Why is it so hard?"
My Fool explained, "You are in a gravitational pull outside the earth realm, and moving back into the collective earth soup requires a pull too."
"How do I do it?"
"You must go deeper, much much deeper. Imagine Susan, and all she has experienced. Be in the meat of her being, in the guts of her struggle, and beauty in her heart."
As He spoke, I saw Susan's story on earth as a book of pages flipping one after the other. An essence, like a glowing golden dust, rose from the pages as they turned. I realized then that what really mattered wasn't the story, or even the experiences, but rather what we get out of the experiences. Experiencing love or horror does something to change us. Change is the thing. Change is creation.
The dust from the pages of me rose up and absorbed into me. I suddenly felt a delicious love for earth life, and all the people I ever knew, even the mean ones. We were all trying so hard, which can sometimes make us unsavory, but we were all esoterically stunning.
A shock rippled through me as I was forcefully sucked toward earth like a skydiver, until I plopped into Susan's identity so magnanimously that my eyes burst open in my body at my dad's house. Then I bounced back to the meadow where my dad and Fool were waiting for me. The tents were gone, and the kaleidoscopic wonder I'd witnessed outside the earth realm was now all around me.
My Fool landed a warm hand on my shoulder with a chortle. "Welcome back."
My dad's eyes glimmered. "Earth is a grand journey. I am glad I came."
My Fool's arms splayed outward. "Ain't . . . life . . . great!"
I loved hearing Him say that. It made me feel so hopeful.
I turned slowly around to behold it all, sighing in amazement. It was like looking into a huge circular mirror, our forms made of up pieces, ever moving in our interaction with each other and everything else, and that glowing dust-like energy was everywhere.
My Fool glowed brighter for a moment.
I peered into Him, wondering what was happening, then looked back at the scene around us. The kaleidoscopic pieces were slowly being infused with a brilliant, yet mellow white light. Hard to explain how it could be both, but it was.
I felt an intense, invigorating energy blowing against my back, charging me with what felt like the pure life force. My dad must have felt it too because we both turned around.
Before us was an enormous white spinning vortex like thing, but instead of sucking in, it blew out. I could actually see energy waves, similar to heat waves on hot pavement, radiating outward.
My Fool explained, "This is the portal from which Pure Creative Energy feeds into the earth to bring it what we call life. Through that portal is the source of us standing here."
I slanted my eyes to my dad to view his reaction. His jaw, like mine, was agape.
My Fool scanned his finger about the circular scene. "Everything we see in life is a projection," He pointed to the white whirling mass, "of Creative Energy, which is us in wholeness. We are all, always, everything. Look into the mirror of earth life, however, and we get to have experiences as if we are not."
Then the white whirling mass disappeared, and so did the kaleidoscopic pieces. The meadow was just a meadow once more.
My dad tapped his lip, "To me, experiencing earth life seems like a playground. We sometimes fall off the monkey bars, skin our knees from running too fast, or can't find our way out of the corn maze, but we also get to experiment with almost anything we can imagine."
I shook my head. "It is mind boggling that we grow from forgetting our oneness, thus creating excitement, challenge, conflict, and the impetus to problem solve. Ignorance, interestingly, is not always a bad thing."
"Nor is enlightenment," said My Fool, "but in stride, as a window to what is, behind all that appears to be."
I loved His wording! "We do need moments of enlightenment. I know I have. When we go too long without it, life becomes intolerable."
"Yes," My Fool nodded. "The residual emotion generated from experiences, created by individuals interacting, embeds us in our story, often so deeply that we lose touch with the source of our creation outside the story. When gone too long without that refreshment, we must step off the stage to find it again, for a story itself cannot sustain our spirit."
I was grateful that for most of my life I seemed to emanate through my identity from a deeper place akin to Divinity (something we can all do). "Yes," I concurred, "an actor who never steps off stage can forget who he is. A mother who does nothing but mother will starve the other parts of herself. And if we cannot step back from our various roles (which we often equate with our identity) our malnourished spirit begins to wilt."
My dad's eyes locked into mine. "For me, the classical music collection you brought me all those years ago, takes me deeper so that I can touch what is beyond my perceived identity."
I was happy my dad had soaked in the insights reaped from my previous escapades with My Fool, even though he'd always had quite a few insights of his own. It made our current adventure infinitely more rewarding.
Music sounded in the distance, pleasing my ears. It was the soundtrack from the movie Fantasia, comprised of various compositions and composers. As my ears tuned in, it became louder, playing all around us. Memories of the movie flashed in my head: dancing hippopotamuses, flowers with faces, and Mickey Mouse as the sorcerer's apprentice.
My Fool's palms splayed outward. "Everything has energy. When we sink beneath the surface of perceived separation, we all experience the same energy."
Further scenes from Fantasia bleeped in my head as I realized it was the music that drew all the scenes together into one beautiful motion picture. Energy, like music, weaves us all together too.
My Fool continued, "We are all not only of that same energy, but we are also its creations. Feeling both simultaneously is prevalent in such experiences as deeply appreciating or making peace with someone, or feeling regenerated by the sea, a mountain, or even a flower. Only when we barricade ourselves from such merging, do we feel, for lack of better words, soul sick."
As the music continued in the background, the movie's scenes in my head manifested all around me: Dumbo, the big- eared flying elephant, the centaurs falling in love, the evil demon looming high. That movie really did have it all.
My Fool's glimmering eyes swayed, observing the scenes, perhaps viewing what I did. His words soaked into me. "Everything in seeming existence out there is but a reflection of—"
"—what lies within our vast self," I finished. "You taught me well."
My Fool smiled softly.
I smiled back. "You taught me that in relating to others, we are relating to ourselves. We draw to us the needed characters to experience the play we have written before birth. We might need a scoundrel, a champion, or someone who challenges us, so we summon them. Those summoned also have their own plays going on, and we happened to fit the parts they need in their story."
My dad's eyebrows raised. "In that sense, we really do create our own reality, in a way—together."
Suddenly, all the Fantasia action going on around me turned into scenes of my life, but put to music in all brands of emotion. I glimpsed at my dad, who too, was intently looking about, likely viewing renditions of his own life.
In silence, shoulder to shoulder, we watched our lives as a movie. I am not sure what My Fool was seeing, but He had paused.
Some of my unpleasant life scenes were accompanied by whimsical music and seemed almost laughable, and others that seemed light-hearted were accompanied by profound music, portending there was more going on than met the eye. What amazed me most was seeing all my life scenes woven together into a spectacular show. I suspected this would be true of everyone if they could view their lives as such.
I really loved seeing the chronicles of my life in this manner. I had forgotten why I did what I did so many times, but seeing the logic in my actions helped me feel kinder toward myself, like I'd done all right. I was okay. My life was a beautiful production, starring me. All lives, no matter how wonderful or horrible, star an identity in a profound production. A tear rolled down my cheek as I murmured aloud, "We are all so . . so . . . " I couldn't find the words. There were no words, but what came out of my mouth was, "exquisite."
"Yes," my dad concurred. "We are. We are each on a chosen path that celebrates individuality, yet nourishes the whole."
I smiled, nodding my head.
Suddenly, all my scenes changed to what seemed to be someone else's story, not my dad's, because I knew all his stories.
My Fool said, "Now, Susan, go change a scene you dislike."
I scanned the area and saw a boy bullying another boy.
My Fool said, "Go to them."
My dad's eyes glinted wisely. "Yes Sue, go."
I nodded lightly and went their way. As I neared, the boys seemed more tangible. Standing before them, just as two flesh and blood boys, I tried to mediate peace, but they couldn't hear me. I tried various things, but I couldn't get their attention. I went back to my dad and Fool.
My Fool said, "If you don't have a part in that particular scene, your efforts will be fruitless. This is why when we warn our loved ones of pitfalls, they often don't listen. Exploring these pitfalls is part of the experience that will catalyze them into eventual self-actualization, even if in another life." His hand, palm up, waved in front of us. The scenes around us disappeared, "Let us walk and talk."
We all began walking along the meadow floor as My Fool resumed sharing wisdom. "People will often say, it was a tough mistake to take consequences for, but in the long run it made them a better person, and even sometimes gave them a purpose, such as the parent who accidentally kills their child. That parent might go around speaking at facilities to warn other parents of how easily this can happen, and thus prevent other children from being accidentally killed in a similar manner."
I shook my head as I stepped over a gopher hole. "Still, these sorts of story lines are so hard to bear."
"Yes, but without these hardships or antagonists to challenge us, we'd not be spurred to grow, and so much good would never happen. The greatest joys we feel are those born from experiencing struggle. What would life be like if we could get babies from vending machines, or medals without winning a competition, diplomas without going to school, or snap our fingers and have the project completed."
I shrugged my shoulders. "There would be no satisfaction because the struggle is what makes any end game feel so good. Even when we recover from the flu; life feels wonderful."
Three tall, steep stair steps appeared in front of My Fool. He stretched His legs high, marching up each one with a bit of huff and puff, then sailed down the other side, landing in the meadow grasses. The stairs disappeared as He turned around, waiting for us to catch up. His voice felt like a warm breeze washing over us. "We simply appreciate everything more by doing it the hard way."
"I agree," said my dad as we flanked My Fool once more. "Getting a job because someone just gave it to us is different than working to be eligible, then competing for the position. Being given money feels different than earning it. Getting grocery store vegetables feels different than growing them. Raising our children full time feels different than sending them off to boarding schools."
"It is hard to remember," I slowed my walk as the once sparse trees seemed to be growing taller and thicker by the second, "when we are in our hardship that reward does await. For example, a country's grueling and gruesome fight for independence later empowers them to thrive. If it had been too easy, the result would be far less."
The thick trees now blocked out the sun. Fear lingered on my breath.
My Fool nudged my shoulder. "Don't be so afraid of the unknown, my dear."
I looked down at my feet, because I was.
"The harsher events," My Fool went on, "even in the natural world, are part of a process that leads to something better. Animal kills animal, forests burn, volcanoes destroy, and species go extinct even without human interference. In the people world, tribes of all kinds fight to survive and thrive in accordance with their culture. And yet animals killing animals is survival of the fittest and strengthens the gene pool. Burned down forests, in the long run, pave the way for luscious new growth from the nutrient rich soil. Volcanoes create a variety of landforms and terrain. And when humans take destructive paths, it catalyzes multitudes to make peace and contribute to the healing process."
"Basically," my dad said, "there can't be total peace on earth, for then there would be no earth. Yet, the struggle for peace is what brings the reward."
I nodded. "Well said, dad."
The forest terrain grew darker and more ominous. My dad didn't seem too unnerved by this, but I sure was. I had a glimmer of Sleeping Beauty in the night forest and her terror getting the better of her. I shook my head to shake it off.
I gulped, uneasy, stepping slower still, finding it hard to move on, and I really didn't want to go further. "Yes," I swallowed hard, trying to cage my anxiety, "in the face of downfall, it seems all life has a thrust to push on and begin again."
In my head, I sang, Itsy bitsy spider climbed up the water spout. Down came the rain and washed the spider out. Out came the sun and dried up all the rain, and the itsy bitsy spider climbed up the spout again.
My dad blurted, "The will to survive is astonishing and actually quite moving."
My Fool's voice deepened, "That will is strengthened by the wise teachers and angels among us, some embodied, some not, who help free the ailing with a compassion that stuns the cynical. This ability also lies within each of us, and rises from time to time." A little blue bird landed on My Fool's head and spread its wings.
I raised a brow, beholding the sweet almost comical sight, so welcomed against our ominous surroundings.
My dad chuckled.
My Fool's eyes rolled up. "Hmm," and the bluebird flew away. "Although there must be those whose mission is to contribute to peace on earth, inner peace, as you both know, can be readily achieved by embracing the moment, opening our minds, and focusing on 'what actually is' beyond all beliefs. In this, an almost magical thing begins to happen."
We had all stopped walking as a pleasant energy whirled lightly about us. My Fool's words took me deeper into myself.
"In the deep within, we can experience the synchronistic weaving of positive and negative interactions, and behold the beauty of those creations."
That old familiar buzzing at the top of my head intensified as My Fool's words poured forth a familiar message He'd taught me long ago. Sometimes we need to hear what we already know, like giving it a reboot.
"In the deep within, we begin to feel ourselves as one pure energy, devoid of judgment because there is nothing to judge. Separation is only an impression. We can see that we are all okay. Everything is okay. We are each precious in our own right and nothing can ever change that."
As I distanced myself from the outer terrain, heading for the 'deep within', I felt lighter on my feet and safer in myself.
My Fool went on, "We rise, we fall, we unite and debate, we birth and die, save and kill, and a million, billion other things that are testament to the bounty of Creative Energy's manifestations. But when we learn to tap this energy of 'isness' that transcends all beliefs, we can experience a natural high which mitigates the lows of horror and hardship, and ever heightens creative open-minded thought."
Deeper I went. Deeper.
"Just like breathing, we open and close our minds to keep going. In opening our minds and hearts, we touch oneness, which must be if we are to regenerate in order to continue having experiences. Acts of empathy, prayer, meditation, epiphany, soaking in the energy of the natural world, keep us nourished. We do not get this nourishment when our minds are closed.
The concept of opening and closing showered my mind with visages of so much that opens and closes. Our eyes, our mouths, our heart valves, our hands, books, and on and on. Opening and closing seems to the beat of life.
My Fool said, "Closing is just as important as opening. We can have positive and negative experience in both. For instance, by shutting out other beliefs or ideas that go against what we need, we can feel better. Sometimes a narrow focus, such as a single religion that promotes love and compassion, can help us experience oneness, and hence give us peace and security. Although this is more limiting than opening to the validity of all paths and everyone, religious experience is often a way of touching the source in a more finite way, even though it can backfire if used in acts of destruction, such as a religion that promotes—"
My dad blurted, "—death to the infidels!"
I laughed, popping one eye open to view him. His eyes were open wide. Cueing off him, I opened my other eye. The ominous forest had disappeared, and we were in the meadow once more. I sighed with relief. Sinking into a meditative state, as usual, had changed it all.
"Indeed," said My Fool, chortling a bit Himself. "Further, pulling others into our cemented viewpoints strengthens our belief that we are right. The more certain we are right, the more righteous we become. This righteousness can lead to the formation of communities, which in turn, give us more experiences. Yet, if those experiences begin to hurt us, we can release the beliefs that foster them, and change the story."
I chimed in, "I love it that we have the ability to repel the beliefs that hurt us, especially when others negatively bombard us with their perceptions. I can do this pretty well on a social level. One on one is harder for me. But I just tell myself, as you both have taught me, that if I know who I am, I am strong, and needn't prove myself to anyone. I am living proof of who I am. And if I emanate that fearlessly, I won't be chosen to play unsavory psychological games with others, for it is clear I won't participate. In a way, it is beneath me, and currently an old road I have already milked. On to better things!"
"Bravo," clapped My Fool.
I furrowed my brows. "Well, I still need to work on it."
My dad grinned. "Even so, you have come a long way, Sue."
"I can do it for a while," I swallowed hard, "be brave, that is, and shine my depths into the surface world, but then I seem to slip and shut down all together."
My dad raised a brow. "Ever since you were a little girl you would be so nervous about going to school, painfully shy about moving into the outer world. Sometimes you were so nervously sick, you'd throw up. Remember?"
I nodded, almost shamefully.
"But you pushed on through, time and time again, to face the hard things of life. For you, it has been like going against a current that would keep you from coming into full fruition."
"I know," I said, "this fear I have that, 'they are going to get me,' I think adds a lot to that current I am up against."
My Fool added, "As I have taught you, any ridicule that you fear might come your way is but a reflection of the sender and has nothing to do with you. When you embrace that, 'the other' has no steam to attack you. What you experience then, is between you and yourself."
I sighed, remembering the old lesson. "Heaven on earth is not out there," I placed my hand over my heart, "but in here."
"Precisely," said My Fool. "We needn't physically die to have heavenly experiences, or wait, as in certain beliefs, to go to heaven. Heaven is always here, a breath away in the depth of our being."
My dad added, "This makes all our harsh experiences bearable, even in the face of them. How we experience our reality lies squarely in the depth and width of our outlook."
"It always stuns me," I said, "how our outlooks can change our reality. A job rejection in a negative outlook could lead to depression and a foul attitude, hence affecting the immediate future, or a positive outlook could lead to deciding a better job is around the corner, and catalyze us to get more interviews."
My Fool added, "And which ever way we play it, that is what we needed to live out that chapter of our story. And we will continue to have changing outlooks at appropriate junctures to experience our unique storyline."
I flashed upon a prime example. "Case in point, I once had a client who felt oppressed by men. I took her into deep meditation; she came out wide-eyed exclaiming, 'I have the answer!' "
I replied, "What is it?"
"God is a Woman!" she exclaimed.
While that was a revelation to her that the idea of God as a Man was not accurate, her deeper consciousness was showing her a way beyond conventional thought, and God as a Woman was acceptable to her. However, the idea of a supreme being remained intact. Perhaps later in a meditation, she might experience God as more than a being in the so-called sky with human traits of compassion and wrath, be it a woman or a man. Yet, at that time, her experience was right for her and necessary."
My Fool summarized, "We believe what we need to believe, to make the choices we need to make, to have the story we wish to have."
My face lit. "That's a great summary. I need to memorize that."
Before us appeared split screen scenes that seemed to be about people's life choices: a person in prison, a student at college graduation, a woman in labor, a robbery, a preacher at the pulpit, a man punching a woman, a woman dying for her child, lovers kissing, a woman teaching children to dance, and many many more.
My Fool narrated as my dad and I gazed about the scenes. "Though it feels like every moment our decisions determine the course of our lives, as we grow, our perceptions are altered, even if slightly, thus changing our decision making along the way, keeping us on the path of our choosing before we were born."
My dad said, "It's like free will is always there, but so is destiny, and though they appear different, there are actually two sides of one coin and the same. I chose to quit my job. Yes, but why? Because at that stage of my evolution, I just couldn't take it any more. So in the necessity of quitting, was it even really a choice?"
I jumped in, "I think that decisions we make are generally born of a need to feel better, just as a plant will lean toward the sun if it is positioned in the shade. We are alcoholics if we just don't have the energy, will, or courage to be sober. Is it a choice? When we just can't take being an alcoholic any more, we change. Was that a choice, or necessity?"
My dad elaborated, "When we are at these choice points they often seem almost equal or difficult to choose, however, eventually the one that gives us more of what we 'need' at the moment will be chosen."
My Fool summarized, "We make choices then in accordance to our destiny, which we have a hand in creating, in synchronicity with the rest of creation. We need never fear destiny, for it always yields what we need beyond what is consciously understood."
My face lit again. "I love that!"
He tapped my nose once playfully. "You are such a good little pupil." He narrowed an eye. "I do mean that affectionately, even though the 'good' thing is still a trap for you. A trap, that in escaping, creates the energy configuration that will manifest as a new plateau of experiences in your future."
His words moved me. Our life challenges really are such a blessing.
He went on, "Just as the caterpillar or tree sprig goes through the paces of its transformation, so do we, individually and globally. No two individuals have the same exact journey, as we each have a unique intent for specific life experiences."
My eyes narrowed in remembrance, "You once told me that each identity's intent is as a puzzle piece, and the journey, the manifestation of that puzzle piece. Every living thing has its own journey and part to play. Each and every part synchronistically fits together with all the others. And when complete, finishes that global story, so a new one can begin."
My Fool's voice deepened, "Of course it is never as cut and dried as it seems, for these things occur in layers stacked in various time tables, but this is the simple way of glimpsing our global evolution. It happens this way too in our personal evolution."
I felt a sudden rush of small formations zooming at me, then in me, almost knocking me over. My eyes had closed, overwhelmed by nausea and dizziness. Finally, I stabilized. Opening my eyes, we three were standing in an energy veil. Before us was the outer world where we experience our life stories, made possible by unique perceptions. Behind us was an exalted inner world where life stories are created. Here, in the veil, we could experience both simultaneously.
Staring out at mundane reality, I heard rather whimsical music about us, and had a sudden urge to be a bit playful.
As an insight struck me, I thrust my foot out from the veil into the mundane "The push to survive launches us into experiences. Survival basically is about clinging to a certain reality with the impending feeling that if we don't, all will be lost."
I was surprised and almost laughed when my dad popped out a foot next to mine. "This urgency extends beyond putting food in our stomachs, shelter over our heads, and escaping the predator's hungry jaws, even if those jaws are germs."
And I was just loving it when My Fool followed suit, His foot popping out next my dad's. "This sense that we must believe what we believe in order to be mentally and emotionally alright, can feel tantamount to fighting death itself."
Feeling in a hokey pokey mood, I popped an arm out to the mundane side and said, "To feel safe, we must have a sense of control."
My dad's arm popped out next to mine. "Some people do this by trying to control their environment or the people in their lives."
My Fool's arm popped out next to my dad's. "Some feel better relinquishing control to those they feel are more capable, and become something akin to 'back seat drivers'.
In rhythm with our jig, I snapped my foot back into the energy veil. "Then there are those who just try to control their own thoughts, emotions, and actions, which is my choice if I can help it."
My dad's foot came back through the veil, aligning with mine. "All these methods create experiences that propel our storylines."
My Fool's foot came back through the veil next to my dad's. "The strategy against death or psychological demise offers infinite possibility for interaction with each other, propelling us into the journey toward the enlightenment we already have, but forgot."
I pulled my arm back in. "The journey itself enlightens we humans, and without it, we all remain in the dark."
My dad pulled his arm back in. "Enlightenment can't be handed over or it would not be enlightenment; it comes from having experiences."
My Fool pulled His arm back in. "In that, beyond the level of social and individual judgment, there is no right or wrong, good or bad, just experiences."
Without thinking, my head popped out of the energy veil into the mundane. "However believing in good, bad, wrong and right is necessary to have said experiences!"
My dad's head popped into the mundane next to mine, "All these life stories are but a single page of a greater story that beholds all of us as characters in the global plot."
My Fool's head popped out next to my dad's. "We are all One with countless angles of the same experiences. This is the greater plurality, which is the culmination of the pluralities of all people places and things."
We continued on this way for a while until we all laughed.
I suddenly ran out of energy, and with that, we were back in the meadow by our golden mats. My dad looked tired too, and without My Fool's suggestion, we both retired.
I about melted into my mat, looking up at sunset colors in the meadow sky, when closer to my face I noticed a tiny object.
My Fool knelt to my ear. "The Gem of Experience."
Focusing my eyes on the object, I could see it was a wagon wheel hovering over me."
He said softly, "We roll along covering all imaginable territory, often many times in different ways, gathering experiences that change us. What would earth life be without experiences?"
I smiled, as the wagon wheel began to shrink and found its way to the seventh charm on my gold bracelet. I drew my hand up to view the charms that represented my journey so far. All these experiences, and many more to come, were transforming me into who I am meant to be.
Fatigued, my arm dropped to my side. As my eyes slipped shut, I, for the first time, embraced all my life experiences without judgment. I had been long repelling certain memories I'd deemed not okay, even though they'd already been had. But now I felt a congealing inside me of every single experience I ever had, that like puzzle pieces, once missing, now were in place, putting me together inside myself. Without accepting all those pieces, I was incomplete, and I needed them to become a whole, fully evolved person. At this moment, everything was all right. Everything. I sank into slumber.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
Rolling along, pioneering this and that, we each cover grand territory in the realm of experience. Our experiences are as an endowment, giving us the green light to explore the vast playground of life. The experiences we gather along the way change the very fabric of our existence into something more grand than we could ever imagine.
The harshest experiences yield the greatest gifts. So take heart when life seems to dole you impossible challenges, and know somehow, some way, they are transforming you into an enlightened being who can begin to understand life's greatest mysteries.
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# In the Land of Crazy
# GEM #8 TRAGEDY
In tragedy we fall and break;
broken, we heal and rise.
##
SOMETHING FELT DIFFERENT when I awoke on my mat in the inner world. I mean really different, redolent of that quite eerie feeling before the onset of a monster storm.
I sat up warily, curious, wondering.
Looking about, I startled to see my dad and Fool mounted on the edge of yet another whirring vortex.
My heart thundered as I scampered to them, but not so near the vortex as they. Peering into it from behind their backs, the force and speed of the spinning almost hypnotized me. Black with thin white lines whirled, creating a residual wind that pounded our faces.
My forehead dipped to my dad's back. "Please don't tell me we are going in there. It feels like . . . too much."
My Fool looked over His shoulder at me. "We all touch this force at the onset of a tragic pivotal event."
I grimaced. "Is my dad going to die? Is it time?"
My dad scooped me closer between the two of them, so near the vortex, I cringed. My long hair blew back over my shoulders and my body felt electrified.
My dad's voice sounded softly in my ear, "My end is my beginning, Sue. But this is not that time. Remember how I told you there was an event brewing that I didn't want to go through?"
"Yesss," I eked tensely.
My dad and Fool said together, "This is it."
My Fool added, "It will set the stage for your father's next life so that he, along with many others, can help create the new Rome." His eyes penetrated mine. "This pivotal event will involve you."
I whined, "More drama?"
My Fool said, "Some dramas cannot be avoided, and are in fact . . . imperative."
My dad sounded shaky, "I don't know what this event will be, but I do know it will test me to my core." He let out a huff of air, "You think you dread this. Think how I feel."
Looking to My Fool, my eyes widened with hope. "Is it an inner world adventure?"
He answered, "It is more an outer world adventure."
I frowned, then peered into the vortex. A vision arose. My dad was sitting on the top of a very steep acute triangle. He fell off it, and was sucked into the vortex.
I snapped my head to my dad next to me, but he was flat on his face.
I knelt to him and cried out, "Dad, dad!" He faded away.
I whipped my head up to My Fool, "What's happening!"
He said gravely, "It is time for you to return your focus to the physical world for awhile. He's had an accident, and will need you in this trying time, perhaps the most difficult of his life, yours too. But this must be experienced, lest his next life be a repeat of many old lives."
"Will we be meeting here at all during this time?"
"No. You will, however, be visiting now and again, an inner world. I call it, The Land of Crazy. Go on now, you'll see what I mean."
My brow creased with worry.
"Take with you the wisdoms that have helped you be calm." His eyes deepened. "You will reap invaluable reward from this hardship."
I nodded, feeling an urgent need to go to my dad, knowing he needed me, maybe more than ever. I focused on my body, on really being there. Instantly, I was back.
I ran through the house in a fruitless search for my dad. I scampered up the loft stairs, focusing on my blue jean clad knees pumping toward the top. He was not there. I flew down the stairs, and shot through the door into the driveway, scanning the area, tinted in sunrise. I saw a body in a white tee shirt and shorts on the road in front of our house.
My heart about stopped. Clutching my black tee shirt, I willed my feet to move, but for a few moments, they were frozen as if my jogging shoes were stuck on the doorstep.
Then I bolted into action down the long driveway. My dad was lying face down in the street. He looked dead.
Reaching him, I crouched, then stroked his head gently. "Dad," I said softly.
He groaned in pain. His whole body trembled. Trapped words sounded between his lips and the pavement, "I thought I was going to die here. I went to get yesterday's mail. My legs . . . gave out," he panted."
A male voice sounded behind me. "At least he's conscious."
My eyes slanted toward the voice, viewing brown boots, blue jeans, and looking up past the tucked in white button down shirt, I saw it was our neighbor Karl. I was so relieved to see him, tall and strong, just what I needed to help me with my dad. Synchronicity. It was meant to be.
Karl squatted to my dad. "Where does it hurt, Robert?"
My dad answered, "It's my . . . shoulder, my . . . right shoulder."
I blurted, "Let's get you to the emergency room."
Karl and I helped my dad to his feet. I was surprised to see a gash on his chin, blood dripping down his knee, and his hand sporting a bloody scrape.
I exclaimed," I'll pull the car up out here."
Karl nodded.
I ran into the house and grabbed my purse and car keys, barely breathing. Calm down, Susan. Calm down. I took a few deep breaths, hurried into my dad's green Honda Civic, and backed it up to the street. I hopped out to help Karl maneuver my dad in the front seat. Not an easy task, given his balance was gone, and he was quite adrift in a foggy reality.
As I raced back into the car, I shouted to Karl, "Thanks!" I drove off in shock the twenty-minute drive to the hospital emergency entrance. Parking in the cul-de-sac, I raced inside and anxiously spit words out to the lady at the front desk, "I need help getting my dad inside. I think he broke his arm. He's eighty six, badly shaken, and has no balance."
Once inside, after the usual long wait, and x-rays, it was determined that his shoulder was fractured. While they tended him on a gurney in a public area, I called my brother and sister and let them know the score. The ER doctor had a sling put on him, and wrote a prescription for oxycontin. Once we left, I had to leave him in the car at the pharmacy to get his medicine. I feared he might try and leave the car, and having no balance, fall again.
I had to breathe deep and slow as I waited twenty minutes for the prescription to be filled. Every minute felt like a million years.
I told myself, "This was all the way it was supposed to be, and there would be good in it if I was patient and looked through the eyes of synchronicity. There were gifts in this tragedy. One I could see right off. This event might reinstate the family unity we had before my mom died. She was the glue that held us together. With her gone, the job fell to me, but I was in Oregon, and my family in Arizona, so that wasn't working too well. Coming home helped, reconnecting me with them, but still not each other.
Somehow, during my wait at the pharmacy, my wallet got pick pocketed, or pick pursed. Yippee. The old saying, When it rains, it pours, I think is partially made true because when we are discombobulated, we attract discombobulation.
Finally, the prescription was ready. I raced to my dad in the parking lot. Although he was still in the car, everything went downhill from there.
Over the next week, in addition to my dad having zero balance (meaning everywhere he went I had to steady him), the sling they gave him, and the two others I tried, were about worthless as his arm kept slipping out. Topping that was the pain medication, all three we tried, made him delusional, even psychotic.
It was worse than senility. He had become the power monger he'd been in other times and places, only he had no power to even take care of himself. But it wasn't like, Sue, can you help me? It was, Sue! Do this, do that, all day long and all night long, and he hardly ever slept. He was basically a grumpy tortured invalid.
I had to help him in the bathroom almost every hour. And showering, gees, modest me, seeing my dad naked was a trial in itself, but I pushed on through because I loved him, because I had to be strong. His acute anxiety propelled him up and about almost constantly forcing me to stand behind him, hands on his hips to keep him steady.
And that wasn't the worst of it. He was obsessive about completing invisible life and death missions, and enlisted my help. I tried to play act fulfilling his orders, but since I wasn't in his world, I didn't know what the hell he was talking about. Consequently, he blew up at me often, accusing me of not caring. This was all so shocking to me, as my dad never ever treated me with anything other than the utmost respect.
This also was triggering my recent Northwest hell when I was consistently persecuted for all my loving intentions. The current of defeat sucked hard at me, but I had to move toward triumph, for my dad. He'd always been my hero. Now I must be his.
After a week, by hospital rules, we had to see an orthopedist. My sister, who for a number of reasons, had severe difficulty getting over to my dad's house, pushed through her obstacles, and came to help me that day. This grueling endeavor was a true labor of love for her, yet she needed to do it. As she seldom saw my dad, and I knew once he died, she would regret those scant reunions and be plagued with guilt. So, it had to be something like this to push her out of her comfort zone.
Upon her arrival, I was greatly relieved to have her aid. It was almost joyful having just the three of us together. It had been so long. At the orthopedists, another x-ray was taken, and it was determined that the fracture had turned into a break (likely due to the shoddy slings). Unbelievably, the orthopedist's advice was to keep wearing the worthless sling for a few more months and see if the break heals. If not, then surgery would be required.
I just couldn't see how I could care for him for months this way, with no balance, no mind, and slings that did not keep his arm stable.
My sister and I agreed we needed a second opinion. I made an appointment with his primary care physician, but it took another week to get him in. My sister had gone back home on reserve for emergencies. And yes, you'd think that this was an ongoing emergency, but she needed her home base for a bit, and martyr that I am, I soldiered on in that way I do.
The week left me sleep deprived, barked at, and nearly joining my dad in the land of crazy. I wanted my dad back, my dad. I would cry myself to sleep with that great wish, my hour of sleep before my dad's voice would cry out, Sue! Sue!" And every hour after.
My siblings offered to help, but as it was grueling for my sister to get here, and my brother had a full time job, a family, and some stressful drama going on, I decided to try and get through this on my own.
Interestingly, during this time, my son and his wife in New Mexico were on the verge of having a way overdue baby, which tapped upon fears of their own. My dad was trying to die, and his great granddaughter was trying to be born. Death and life. They always go hand in hand.
Finally, it was time for my dad's appointment. The primary care physician had another x-ray taken, and comparing x-rays announced the break was getting worse. He was appalled at the orthopedist's handling of this case. He urged us to see a different orthopedist and had one in mind.
I just loved that man for getting us an appointment from his office then and there, for the very next day! I didn't even care that we had to drive two hours to get there.
The next morning, we headed down the highway to the new and better doctor. My dad was on morphine at that time, and threw up in the car. I had to pull over to clean him up. Feeling his anguish every mile of the way, I topped off the unlovely trek with getting lost. By the time I found the place, we were quite late, but they took us anyway, probably because I was hysterically crying.
That orthopedist took another x-ray, reporting it was three quarters broken, and was so bad, and had gone untreated so long, surgery needed to be immediate, and a new shoulder might be warranted if the old shoulder was dead. We set up surgery for a week later, the time needed to get insurance clearance, and prep his body for the operation.
During that week, I was even more distraught, exhausted from not sleeping, enduring my dad's extreme reaction to constant pain, frequent hallucinations, and very bad temper. The dad I knew was nowhere in sight. I could imagine though how he may have been in his past lives as a power monger, the one he became in the Ancient Rome so very long ago.
I had him sleeping in a chair because it lessened the pain, but he kept sliding out of it, or somehow winding up on the floor, and having no balance, couldn't get up. I tried and tried to lift him, but five foot two, not so muscular me, failed. I had to call the fire department numerous times to do it for me.
It was suggested we put him in a convalescent home until surgery, but I really didn't trust any convalescent home to care for him especially with his mind all messed up. He needed me. I understood his metaphysical ways and how to work with him. I would never fail him. He had saved me so many times in my life. Now it was my turn to save him. Time for the whole family to save him. I realized then, not only did I need my siblings, but doing it all myself was robbing them of their own needed resolutions with him before he died.
The night before my dad's surgery, my sister came and helped me prep him, then the next morning drive him to the hospital two hours away. Family members were there for the surgery, and it did bring us together. My dear aunt from Washington and her companion happened to arrive in Arizona just the day before to escape the northwest winter. She had not seen my siblings for ages, and their reunion was wonderful, albeit in a hospital. My brother's daughter came too, and so did my sister's daughter. We actually had a very warm and pleasant time all the many hours we waited. This tragedy united the family more than I ever expected.
Though the surgery went well, and a new shoulder was not needed, the anesthesia made my dad lose his mind so completely, they put him in the Intensive Care Unit. It was after visiting hours by then, so the family went home without seeing him. I spent the night with him in ICU on a lounge chair not far from his bed. All my experience with him the last three weeks paled to what happened that night.
He was in a tyrannical rampage. He didn't know who I was. He kept trying to get out of bed and leave the hospital. He wasn't even Robert anymore. It was like he'd already died. He was a dictator through and through. He yelled, ordering the nurses and I to pay attention to him (he acted as if we were all his employees), and follow his instructions. The more meds they gave him for pain and sedation, the more his mind went haywire, but he never seemed sedated or free of pain. He moaned almost constantly, and he cried out often. He didn't sleep at all, so, neither did I.
If not for a male nurse, Josh, wonderful Josh, who excelled with impossible patients, I am not sure what my dad's fate, or mine for that matter, would have been. His whole energy had a calming affect on us both, and he accomplished what needed to be done with great compassion and a positive outlook.
The next morning, as the anesthesia wore off, my dad knew who I was, but he was still very lost, agitated, sighing constantly, and crying out often. All I wanted to do was get him home, but the medical staff wanted him to stay another day to give him I.V pain meds, as they were stronger than pills. They also wanted to wait until his mind cleared more. Since the meds were making him crazy, I didn't see that happening. I just couldn't stay another night. I just couldn't survive it. My brain was fried, and I couldn't think straight, and sheer exhaustion bade me collapse, but then I'd never get home.
My sister's daughter, my niece, who worked not too far away from the hospital, appeared out of the blue, to see how her grandpa was doing. Again, synchronicity.
Assessing my tortured state, she took off work, and basically assumed my role and conversed with doctors and me with calm rationale. She deduced that if the main reason to keep him another night was to give him I.V meds, but if meds administered that way weren't really easing his pain significantly more than pills, then why keep him here? We spent several hours testing that out.
During this time, she worked with my dad, her grandpa to calm him down. She even set her phone to classical music, then engaged him in some positive conversation. In this, his mind state improved. Whatever we needed to do to get out of there, she helped navigate it. She was my angel that day. She even drove my dad's car around to the front of the hospital so we could more quickly move along.
Nice too, that she had an opportunity to bond with her grandpa in ways that she couldn't before. When we are vulnerable, our walls are down, and beautiful connections can be made.
I finally got him home, but for the next six weeks, the pain pills continued to make him crazy. However, two weeks in, his balance returned, which was really something, but in a way not so good as he now roamed the house all night long with only brief bouts of sleep. The house would often have objects moved all about in strange places. I spent hours one day looking for a pile of bills ready to be put in the mailbox, only to find them outside on the back porch steps.
The ongoing use of pain pills kept him truly nuts, not the good kind of crazy our family has been called when out of the box, powerful insights and meaningful acts ensue, but the destructive, completely out of touch with the physical reality, kind of crazy.
I was cracking up too, operating on hours of broken sleep as my dad continued calling for me all night along for this or that. Ignoring him didn't help. He could call for hours. I was so tired, feeling hurled away from the comfort my dad usually gave me. I watched him in his confusion, the agony of feeling helpless, vulnerable, and lost, no longer the warrior at the gate, a man of the world, a rock for his family, or hero to anyone.
Music had always calmed my dad, taking him into a trance of wisdom and inner balance. He couldn't get upstairs, so we moved his stereo downstairs to his bedroom by the chair he slept in. One particularly bad day, I pressed the button to play his favorite, hopeful it would help, but it didn't. He remained agitated.
I asked, "Dad, can't you feel the music like you always do?"
His eyes were real big and his mouth hung open as he cried out in anguish with slurred, barely audible words, "I used to, but I can't feel it anymore!" This broke my heart so badly I had to slip off into the bathroom to sob, and I mean SOB.
I called my brother, told him about it, and then sobbed some more.
In a subsequent attempt to listen to music, he cried out in a rapid chant, "Bring me back. Bring me back. Bring me back," forty or fifty times. He was fighting to become uncrazy. It was so heartbreaking, I wanted to die.
One night, I found him outside knocking on my sliding glass door trying to get inside. I let him in and he explained, he'd been trapped in the attic. I went into his room and everything was torn down, all the clothes from the closet, everything on his desk was on the floor, and the covers off his bed. It looked like a war zone. In his mind, it was the attic.
Another time, I straightened out his desk as he seemed disturbed that it was messy, but then he yelled at me, ranting for hours that I had touched his desk without his permission. Again, this triggered that old wound of being loving and caring, but persecuted for it.
I finally broke down and found myself yelling and screaming my woe at him for his maltreatment of me. I know he couldn't help it, but neither could I. I could almost hear My Fool say, It's okay, you don't have to be the good little girl.
Many a time, I begged him dramatically to please, please, please let me sleep!
He would just look at me blankly as if he didn't understand what I was saying.
Then, like the Calvary, my daughter and her mate came all the way from New Mexico to take the graveyard shift. My daughter worked with him beautifully, having great intuition on how to guide him into doing what he needed to do. Helping one's eighty six year old, out of his mind, temperamental grandpa in the bathroom nine or ten times a night, takes something. She was calm, yet balanced in herself, not taking anything personally, even though he kept accusing her of trying to steal his house.
I just felt like I would have melted away and died if she and her kindly mate (who was also quite helpful) had not come when they did. They repeated this kindness twice more.
My brother came for a few sleepovers too. I was falling apart, on the inside anyway. What everyone else saw for the most part was a cool cookie with occasional shrieks of hysteria. But this cool cookie was crumbling.
My sister stayed one night to spell me. He thought she was a mean nurse, and made her cry. My other niece, my brother's daughter, drove a very long way to spell me for many afternoons interspersed with my aunt and her mate so I could run errands, clean the house, or take a nap.
The whole family experienced my dad completely lost, vulnerable, and in hell, suffering from the wrath of his dictatorial demeanor, that if inhibited, triggered rage. He was completely contrary to the dad we all knew, and yet, the whole family continued to unite.
Even though I could see the beauty of the family coming together, and my dad stripped of his personal power and even dignity, to prepare for the South Pacific life, I too was being stripped bare to the bone. Post-traumatic stress became the present, casting me into survival mode once more. In many ways, this was worse than my last Northwest years, because my dad, my protector, my mentor, and my hero, was the cause of my hell.
My brain was on fire. I desperately needed a break from all this trauma. I needed My Fool. I cried to my brother to come for a few days. He came and said he'd stay as long as I needed.
I went to my room, closed the door, and fell into bed, sinking fast into the deepest sleep. I appeared in the inner world meadow, but everything was blurry. I scanned the area for any shape that might be My Fool, but didn't see Him.
I sank to my knees on the meadow floor. Close up, I could see that the grasses were brown, everything was brown, drained and dying just like me. I leaned forward with my hands on the stiff, dead grass and sobbed.
I had tried to be the martyr, but couldn't. Yet, because I needed my family, it worked out better for us all, and all because my dad was in the worst hell of his life. His very identity and anchor of strength and wisdom that made him who he was, had been cut loose and he was adrift with no direction, save the one the family kept trying to give him. I had never felt so alone in all my life. My mental shield was gone, and so was my dad's.
I sank to my elbows crying harder, feeling crushed by the events of the last two months. I heard a voice in front of me, "Susan."
I lifted my head with open eyes. My Fool was there crouched down facing me. I sat back on my knees.
I said tearily, "It is all so hard, so sad, so sad. He can't even feel the symphonic music anymore. He is crying out, in utter hell, tortured beyond measure, and there is nothing I can do about it."
He reached out his hand. "Come," He said, "I want to show you something."
I took his hand and rose. He guided me forward. The scene changed and we were back at the cliffside where we'd seen the spirit of my dad's old Roman identity who had tried to create a wise and just Rome.
"Look," My Fool pointed.
Looking at a panoramic view of the city, it was changing. Colors seemed more vibrant, the people looked brighter and in more peaceful harmony with each other.
I said, I thought the New Rome wasn't really about the Old Rome."
"All just perceptions," My Fool said, "It is easier for you to see the change this way."
I nodded. That was true. Since I knew nothing about South Pacific life, how could I measure any change?
My Fool elaborated, "Your father's tragedy has catalyzed a great transformation within him making his next life possible. The New Rome will be a safe haven for those nearing the finish of their earth journey. It will be a place where those of like mind, though perhaps scattered all over the globe, can on a deep level, connect, love and support each other in a metaphysical conglomeration of Creative Energy. This assembly serves as a shining beacon for all the lost who are ready to be found. This does not mean they will necessarily physically unite, but on a psycho-spiritual level, they will comfort and empower each other."
I let out a comforting sigh, "So my dad will be part of that."
My Fool confirmed, "Yes, but first he needed to be vulnerable, even broken, to ensure he would not repeat the old pattern. He had to know what it is to feel helpless, so when he is reborn in the South Pacific, his rudder to create, what we shall call the New Rome, will be stronger than ever before. This too is why he must be discarded as a baby in that life, to have a beginning that humbles him."
I nodded. "It also seems that his hell of feeling helpless is creating an imprint on him to free others from that feeling."
My Fool added, "Yes, his current hell is creating a heaven for you both. His, for what we just discussed. Yours, for forcing you off the martyr pedestal and letting your family help. This created a caliber of unity, that over many lives, your family has been trying to achieve, as well as boosting your dad to contribute to what is now needed on earth—an influx of Pure Creative Energy. In this, instruments of wisdom will appear to channel what is needed into earth currents."
I said with a half smile, "Like you."
He said, "My focus is simply beyond separation. I am merely a symbol now of the Pure Creative Energy of everything. I am my own light in the seeming sky that reminds the billions of me's on earth, who are all of you, where home is."
I smiled faintly. "I wish I was there now, in that state, instead of this one." My tears began dripping. "I know I have more plight to endure in my physical reality, but I'm so tired."
"Then close your eyes. Where do you need to be?"
I said, "The ocean. I need the ocean."
"Then be there. You know you don't need to be physically somewhere to tap the energy of that environment."
I nodded. "Yes, I know that." With that, I let myself go into a deep trance, and I was on my favorite Oregon beach out past Tillamook. I looked out at the mighty rolling waves and reveled in the sound of the surf, and seagulls cawing overhead. I drank in the energy. The crown of my head buzzed, and I felt relief as if the expansive ocean all over the earth was me.
I began chanting, "I am the river running free into the sea." I stepped farther and farther back from my conscious identity of Susan, to the greater me beyond.
I noticed then I was in the water up to my chest, my legs tangled in seaweed, caught by the old things of religion, martyrdom, suffering, and worthlessness. I am always a sinner no matter what. This idea always held me back from being fully me. When I am caught like this, as I currently was with my dad's ordeal, I can't breathe and begin suffocating from this old pattern. If I can't fully break free, the pattern will claim me once again in my current consciousness. I will break free. I must!
Then I was further back on the beach, only ankle deep in water. Four crabs came upon a wave with legs flailing.
I stepped back, as it came to me that the four crabs represented four directions: east, west, north, south, and four elements; air, water, fire, and earth, all in collision, creating confusion and strife, the trauma jumbling my mind. I knew I needed to balance myself in the center of directions and elements.
I focused harder on this.
I chanted, "Power of the sea, set me free, to be me."
Then the words came, "I call to the sea to untangle me.
I call to the trees that I know
to free me from this ancient woe.
I call to the sky to raise me high.
I call to the earth for rebirth."
I felt myself rearranging inside, changing consistency and vibration. It was working. It was working! I walked further into the ocean, to my waist, free of entanglement, and splashed water up in my face, scooping it all over my body, baptizing myself with seawater. I cried with joy and felt whole again.
Then I was back at the meadow with My Fool.
"Better?"
I nodded, "Much."
He produced a wand and pointed to the triangle top. The acute point is a tragic pivotal event that teeters us between one reality and another. We labor to keep our balance, but sometimes we fall into tragedy into the land of crazy. But instability has its gifts, for in the struggle to become stable, we must dig deep and harness every ounce of strength and courage within us. This results in profound personal growth, like a shedding of a skin and an unexpected renewal that feels quite good. Obstacles have been overcome, and we can consciously touch our 'soul', and see our path as never before."
He swung back his hand like he was going to throw a baseball, and hurled into me an acute triangle that simultaneously appeared as the eighth charm on my bracelet, perhaps the most important one of all.
I held up my hand and jiggled the charms.
He said, "Return to your body now. Continue the adventure. Learn from it. You will soon reap the rewards."
I woke up in my body after a ten hour sleep, feeling pretty good. In the weeks that followed, my dad got off painkillers and the much better sling the more competent doctor gave him. I researched like crazy supplements that would help his brain and his pain. I made supplement cocktails four times a day, and amazingly, along with getting off pain medication, and with the discovery of one of natures medicines, a fungus type mushroom that grows in China and Tibet, his brain cleared, I mean cleared as if he never gone crazy or had any semblance of dementia. What a gift! His mind was far better than it had been since my arrival. Not sure what that meant in terms of the inner world, but he was the old dad I knew, and I was going to enjoy every minute of it.
He had come through the tunnel of the dreaded event he had long sensed was before him, and out the other side. I never ever thought I'd see him mentally healthy again, and I knew now, we could finish our final adventure together with My Fool. We went to bed that night ready to reconvene.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
Calamity happens to us all. Though often seeming like a monster, unexpected tragedies, such as being diagnosed with a severe disease, death of a loved one, a nervous breakdown, accidentally killing someone, life changing injuries, or even a woman's enduring excruciating or dangerous labor in birthing a child, are gifts. We take the journey, we win the prize, a prize so dear that without that event, we would remain unaware and held back in a world we have outgrown.
Tragic times are as a trebuchet that hurls us into what we need to finish growing into what we are meant to be. Once the smoke has cleared, we can see the shining path before us, showing us the way 'home'.
So, if a tragic pivotal event should knock you off balance into the land of crazy, keep your eye on the prize. This trauma is your gift, that when unwrapped and beheld as such, will lift you into your higher purpose for living. Your true self is out there beyond the clouds, and in there behind your identity. It is I. It is I. It is I. Don't you know who I am?
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# The Long Road Home
# GEM #9 SPIN
From our source, we spray into time;
then spiral from time, back to our source.
##
I awoke on my mat in the meadow to the sound of chirping birds. Their seeming joy matched mine. I sat up, so very glad to be back on track with my dad and Fool to continue our inner world journey. Gazing up, the sky was pure blue. Gazing about, I noticed more trees, mostly aspen, leaves flickering in the gentle breeze. The whole meadow seemed luscious and bright, as things do in the aftermath of surviving something intense.
Vaughn Williams, The Lark Ascending was playing rather cheerfully in the background. Suddenly, I noticed My Fool was skipping a rope made of vines with little purple flowers, headphones clamped on ears.
He looked so funny, this very old looking, grey bearded man, jumping in the air as the rope whipped under His feet over and over again. I giggled a bit, and He looked to me with twinkling eyes. He jumped His rope closer to me, and I laughed some more. He stopped jumping, then handed me the rope. "Even in repetition, nothing is the same. That is, not exactly the same."
Taking the beautiful rope, I wondered what experience He had in mind for me today.
He pointed to my dad.
My dad, not quite conscious, was flat on his back, with half-closed eyes, in a seeming trance. Words slipped through his lips. "As the years cycle round, our bodies grow old."
My Fool smiled softly at me, then walked toward him, signaling me to follow. Jump rope in hand, I did. We knelt by my dad to listen.
"If, instead of gripping our past, we slowly loosen our hold to experience what comes next, we grow into age."
I murmured softly to My Fool. "He sounds like you."
My Fool murmured back. "The closer we come to oneness, the more we all sound alike."
I cocked my head digesting His comment. That did make sense.
My dad went on, "Those who grow into age instead of just growing old can find pleasure in their plurality, increasingly aware of their many magnificent selves in innumerable configurations of personalized energy, as I have been doing."
I whispered to My Fool, "By personalized energies, does he mean all his identities under the banner of his Great Self?"
My Fool nodded.
My dad's voice plumped up with warm emotion, "All identities are growing and experiencing their life stories the best they can. In feeling the teamwork of one's plurality, there is endless togetherness overriding any possible feeling of alienation."
Every once in a while I had a flash of my other selves. I could feel their struggle, and sense their yet unrealized potential as they journeyed on the long road home. I loved them so.
My dad went on, "I zero in on the moment that like a whirlpool takes me into the vibration of my life story. I am experiencing what it is all about and beholding my primary purpose, which is to give credence to the gentler aspects of myself reminiscent of women, children, and animals. In this, I bring to balance the strongest aspect in me, the conquering warrior."
Tears wet his eyes. "As the whirlpool takes me deeper, it is as a tunnel leading to a new identity and life as this old one plays out. When that shift is made, I believe there will be little sense of what I leave behind as I shall be more focused on what I am coming into."
My first thought was that my dad would forget me when he dies, but quickly I remembered that who we really are is beyond identity. Identities are like clothes we wear until we have worn them out, and then put on a new set. Our deceased loved ones can always be tapped from the Wall of Remembrance, and we can communicate with them in their old identity as if they are in front of us and nowhere else. But as we all have great multiplicity, we are actually many places simultaneously.
My dad's voice intensified, "My current self is an old man releasing harbored memories of a colorful life. My mind wanes and my body seldom follows my commands. I will soon take a bow and exit this stage, welcoming my new identity. This will be my last round for all the selves in my plurality in the earth story. After that, my plurality, like a molecule with all its particles, will dissipate from the impression of separation into oneness.
"But even as my identity fades, I believe I will have a moment experiencing that reconciliation before moving on to my next adventure, as many do upon death or in near death experiences."
His head rolled side to side, his lashes wet with tears. "This is often experienced as moving through a long tunnel, Highway Eleven, I presume, that opens up to a brilliant white light which, I suppose, is Pure Creative Energy. "
My eyes and throat welled a bit. I wanted that for my dad. I did.
My dad's eyes snapped open. He sat up with a big grin and a deep sigh. "It is over, the hardest part is over."
My Fool rose and offered my father a hand. "Yes Robert, your journey into madness has paid off."
Grasping My Fool's hand, my dad rose. "I think so."
"You have successfully set the stage for your next life experience to help create the New Rome."
As I rose, my dad shrugged his shoulders. "What now?"
My Fool stepped back, then glanced at the jump rope in my hand. "You jump rope for awhile and enjoy a bit of solitude. I need to do something with your father."
"I am fine with that." I looked to my dad. "I'm just so glad to have you back better than ever."
"Happy jumping," my dad said whimsically, then turned with My Fool, walking toward the green hill.
I began jumping rope, watching their backs grow smaller as they ascended the grassy mound. After a while, huffing a bit, I plopped down in a cluster of wildflowers, and set the vine rope aside. Spying a clump of grass, I picked a blade and sucked on the tiny stem. I used to do that as a girl. Oh, how the years have evolved me since then!
I glanced at the green hill now vacant of personage. My Fool was likely preparing my dad for his upcoming journey into the little black girl. After what we'd been through with his broken shoulder, I somehow found it easier to let them go off without feeling left out. I mean, if what we'd experienced was a snapshot of my dad's future, well, the opportunity to duck out before that happened would, in a way, be a blessing for all. Still, I didn't want to think about him dying.
To escape the thought, I drank in the bustling meadow around me: short green grasses sprinkled with bluebells, clover and buttercups, butterflies and bees flitting about the delicious blossoms. The brimming meadow was likely a reflection of my mind state, as I was feeling pretty good. The spring-like feel, I think, was about me regenerating, not only from my Northwest peril, but from the hell I'd just endured with my dad.
Suddenly I noticed vast amounts of black-eyed Susans growing thicker about me as seconds passed. These bright orange daisy-like flowers with protruding black centers were quite striking, and oh yeah . . . black eyed SUSANS.
No need, I guess, to wait for my dad and Fool to return to continue the adventure. I was having one now.
The air turned greyer, the flowers sparser, and the grasses yellow and overgrown to my shoulders. A chill air encased me as I peered about with nary a bee or butterfly in sight. It felt like winter. Oh no. What did this mean? Was this happening because my dad and Fool had left?
Or, perhaps given my Northwest experience felt like a three-year winter in Siberia; this change of scene might be symbolic of a slip back, or maybe a sign of what is to come. As much as I generally like winter, I really was done with it for a long while, or at least I wanted to be.
Perhaps things turned cold because I still have a ways to go to finish my regeneration. I have found my way back to myself, but there was still a lot of me that needed to thaw out. Plus, I was kind of thwarted with my dad's accident, which created that cold survival feeling again, even though interestingly, it also warmed me up with all the help I received. I couldn't be a martyr even if I wanted to; I just couldn't do it all alone without cracking up.
Then it came to me why it turned winter-like. Today is about cycles, the jump rope, My Fool's comment about repetition. Everything is a cycle I guess. Or maybe the better word is a circle. Spring, summer, autumn, winter, around and around everything goes. Morning, noon, and night, around and around and around. We like to sleep on a certain side of the bed, sit in certain chairs at the table, and develop rituals to comfort us in this uncertain world, as we go around and around in our days and years.
I felt energy inside me, changing, shifting, as if creating something. I was gone from the meadow and had become the inner workings of an old-fashioned clock. I experienced myself as circulating gears. I wasn't afraid. In fact, it was fun and freeing. I didn't have to worry about anything because I knew what would be happening next.
Words came to me. Cycles. Peace leads to war and war leads to peace. Birth leads to death and death leads to birth. Conflict leads to resolution and as things change, resolution leads to conflict. Electrons fly around the atoms nucleus, moons fly around planets, planets spin, and stars orbit in accordance to various gravitational forces.
We all orbit, seconds into minutes, into hours, into days. Cycling also, our blood and breath. Everything seems to cycle. We humans tend to see life in a linear fashion, but things just feel different because we are always transforming, even if our cycles stay the same. There is never really anywhere to go, it is about experiencing things differently each time we go around, just like every year feels different because when the same events occur repeatedly, we find different ways to deal with them, creating a feeling of change or newness. This seems like linear progression, but is it? As we experience things, we change, just as molecules change when they interact. What is time anyway?
Like chemicals coming together, we are always being altered. Humans call it evolution, whether within ourselves, or earth life, or the universe. Even as we grow older and enough time passes between us and the distant past, we can, as if circling around but on a different level, finally see other perspectives we had once proclaimed faulty.
Perhaps our points of view are like all things that revolve. When we are in a winter cycle, we can't see what is going on at the summer time of the globe, and draw conclusions about life based on the winter scene we view. Eventually though, the more we grow, the more we see. Like a mighty Redwood, the taller we get, the more we can behold.
Or sometimes we stay in the loop repeating the cycle with a stagnate frame of mind, such as I am always the victim; and that's all there is to it. When stuck in one point of view, we spin on a merry go round with scant change unable to get on with our journey. In this, our journey then is to experience sameness, although we may not view it that way. It's akin to being in a parked vehicle near other cars that are moving. We might, for a moment, think the cars around us are still, and our car is moving. Everything around us is changing, but we can't touch it.
Eventually, however, the sameness wears us to the bone and we come to our wits end, unbearably damaged, or maybe just excruciatingly bored. We long for something new.
As thoughts kept rolling through my mind, I was enjoying the safety of going around and around. It was comforting. And as gears hooked in with others, feeling connections that helped us work together was invigorating.
Though the mechanics are the same with every cycle, to we humans, the time projected with each revolution meant something different. Today means something different than tomorrow. This winter is different from last winter. So we can traverse the same cycle, but different things can happen along the way. I drive to work every day, but one day, my car breaks down. Even when we do things the same, change is still in motion.
I heard My Fool's jovial voice as if calling into a cavern, "Are you in there?" Even though I was temporarily clock gears, I managed a smile.
I followed the voice and reappeared before My Fool.
"Where is my dad?" I asked a bit concerned.
"I left him where we were. Come," He said, "I'll show you."
"I suppose as I wasn't invited on the mission, you can't fill me in on what happened?"
"Sure I can, but I'd rather show you."
"Why couldn't I come to begin with?"
"You had your own work to do."
"Speaking of that, I had some insights about time," I said, as He touched my hand and we seemed to rise up and fly along like something out of Peter Pan, the surface far below us. "Ahh," I said unsteadily, then let out a sigh marveling at how so very small the surface world seemed even though we were in a metaphysical realm.
"You were saying about time?"
"Yes, I actually meant clocks, the circular patterns of the gears and how everything goes around, and that we, without realizing it, tend to think in circles. We have the impression we are thinking linearly, but every time we think, we usually repeat the thought multiple times with only a minor change, unless we have an epiphany."
My Fool confirmed, "Yes, we think in circles until we are open for a change. The epiphany seeps in from a broader reality, like a hole poked in a wall letting in the light. Then, with that wisdom, we can move into a new cycle."
I blurted, "And then around we go again for awhile."
My Fool glanced at me just before we went through a sort of tunnel. I was feeling a bit of turbulence.
"Relax," He said, "Your dis ease is causing the turbulence."
I took in another deep breath with a long cool exhalation.
He urged, "Go on with what you were saying."
Swept into the experience of what was currently happening, I uttered, "It can wait."
"It doesn't have to," He said, "Go on."
"Okay." I gathered my thoughts. "For instance at mealtime, most prefer to sit in the same spot. We feel safe in our habits. It seems to calm us down. But if we were to actually break all our circular patterns, I almost think we would zoom across time into some foreign reality, kind of like going through a wormhole."
My Fool chortled, "Like we are about to do now?"
My eyes grew wide as we approached blue green, what looked like a thick of trees. We flew into them and suddenly dropped so fast, the trees blurred into streaks.
Though alarmed, I was with My Fool, so I managed to keep quiet and go with the experience. We came to an abrupt halt, as if an elevator had stopped on the destined floor.
My Fool led me off, and we witnessed a scene.
My dad was with a black woman. Naked, they stood facing each other seeming more like spirit forms than solid. They did a weird blending thing, blurring into one, just as the trees looked when we fell through time, then they seemed to blink back into their individual forms.
I asked, "So are we on a different earth now?"
"Indeed," My Fool answered.
Suddenly, like a camera zooming in on a close up, I saw a panoramic view of a baby in a womb, its beating heart, and its brain collecting references that would determine the course of its life, and all the characteristics the infant would possess.
I asked, "That's her, isn't it? The person my dad will be?"
My Fool nodded. "In reference to your dialogue about cycles, circles contain spirals. To simplify a complex understanding, basically we circle around, repeating a kind of experience until achieving saturation. For instance, subjecting ourselves to constant abuse and dreaming of being well-treated, or being too long on the road without a home base, craving roots. When we have milked the experience dry, we embark upon the next cycle, analogous to the next ring of the spiral."
"Hmm," I grunted. "I had never thought of circles that way, I mean containing spirals. To me there are circles and there are spirals and they are not the same, and while they aren't, they apparently also are. Like fingers are fingers, but they are also part of a hand.
He nodded. "As your father alluded to earlier, he is soon to spiral out of the earth experience, all the earths, for as we have already discussed, they are connected, just different versions of the same story. The upcoming incarnation will serve as a conclusion to a very long story for all the many selves that make up his Great Self."
I envisioned a molecule breaking off from a great mass and floating away, and then a chunk of glacier breaking off and melting into the sea.
My Fool waved a hand across my face, and I saw a detailed scene of my dad's next incarnation in this parallel earth.
On a small boat in the South Pacific Ocean, a black man placed his baby on a plank of floating wood very near an island and abandoned it, apparently because it was female, and to him at that time, a bad omen. The plank floated away and amazingly washed up on the island shore whereupon the child was discovered by a black man that seemed of high rank. He picked her up and held her as if she were a gift from divinity. He brought her home to his wife who could not bear children.
My Fool's hand waved over my eyes again. Time passed, and the baby, named Sallee, had grown into a woman. That she was black was important, for in the more powerful lands, that race was somewhat demeaned. Her existence would help break that injustice. She had a natural way of bringing people together for the better, in fairness and unconditional love. She came to be known near and far as a beacon of true womanhood, different from woman trying to emulate man. And yet, she also represented the feminine side of man, just as there is a masculine aspect in women.
It actually did seem to me that we earthlings were a little top heavy on male energy, at least in our earth version, and needed to inject more of the feminine: nurturing, emotional connection, and more peaceable solutions to conflict. Then the scene disappeared.
I smiled faintly. "It helps me to see how much my dad is already shifting into his next adventure."
My Fool looked at me, into me, so deeply, that for a split second, I blinked into oneness and had no identity. He spoke as if billions of voices came out as one. "All earths in the reality of time, are going through their paces in numerous cycles, milking every possible interaction, in various orders, until the experience of the Eleven plays out."
I murmured what he'd long ago taught me, "Eleven. Earth's vibration. Earth's Story."
"Yes, the earth symphony is magnificent, and though fully created, it is ever evolving into what it is meant to be. Yet, within that evolvement, personal revolutions are constantly in tow, and integral to the symphony being what it is. Circles open to spirals, maybe in, maybe out, maybe up, maybe down into another ring. In the center of it all is an altered state that is timeless. Move into that altered state now, Susan."
I inhaled a deep breath, and began feeling a spinning sensation. Either everything around me was spinning, or I was. I felt like a fast whirling gyroscope, blurring to the naked eye. I focused on staying in the center of the spinning so I would not be sucked into the outer whirling. Then I felt myself as a cyclone moving over the land, affecting everything I touched. I heard Rachmaninoff's Symphony #5 accompanying the experience.
My Fool's voice slipped into my ears, "The cyclone is made of specific energies cemented into the creation of a reality that becomes a force of nature in the world. Each human has a profound affect on all around him or her throughout their lives."
I had never quite thought of it like that, how powerful each human is and what a profound affect we have on each other. We are, every one of us, cyclones, gaining momentum and power in our current drama, then dissipating as that drama ends, only to brew another cyclone as a new drama begins.
I became aware of my own cyclone and all the lives I've touched for better or worse, as well as feeling the insanity of whirling fast but getting nowhere. It is easy to get lost in our own commotion.
The times I loved best were when I could sink into the stillness within the cyclone's center. In my last Northwest years I was getting lost in my own spin, but not going anywhere.
That spinning stopped once I fell into my safety net, my dad's home. And here I was, hibernating mostly in the depth of my being, recovering. It is hard though, so hard to stay centered in tornado energy. But I was doing that now. Suddenly, the tornado seemed to fade and I saw only pink sky.
My Fool said, "This is what blackness becomes when we stop fearing the unknown. This unknown, feared by many, was once known before we narrowed our consciousness to manifest into separate beings, or seemingly separate beings."
"Yes." I confirmed, remembering My Fool's old lessons. "Our fear of moving ahead often keeps us focused on where we are at. Imagined futures are often fraught with fear and gruesome feelings, so we perseverate on our current reality to keep it in place. The only way to move on is to let go of where we are at, and throw our whole being into the unknown known. Or more simply put, throwing our small individual self into our greater being."
My Fool smiled. "Then do that," He paused, "now."
I gave a light nod. "Yes, I need to do that."
Rachmaninoff's Symphony's last movement sounded louder in my ears, sweeping me into pure beauty. I gave myself completely to the pink sky which seemed invisibly filled with all existence homogenized.
I felt myself shedding something. It is quite traumatic in its own way to release the familiar. But the seeming unfamiliar actually is more familiar to our spirits than the old world in which our human selves have grown accustomed.
I felt myself matriculating into the pink sky, blending into it, and it felt so good, like a thousand pound weight had risen from my shoulders. Opening, opening, tingles of electromagnetic energy stimulated me.
My Fool narrated as I absorbed my experience. "We are reborn by breathing, opening, trusting ourselves and life to take us to next cycle, the next ring of the spiral, the next reality. There is nothing to fear, as all realities are really one great reality, just as at our core, we are all one person, and all that exists is but one energy. By allowing old barriers to break down, we give a day in the sun to our deepest self.
"Shifting reality usually does not mean physical death, although it can, but it is a death and rebirth within one's body such as meant by the phrase, He is a different person now. Or I hardly recognize her.
"These happenings are the manifestations of these jumps within ourselves, dismantling the old cyclone that loses power when we don't feed it with repetitive thoughts and feelings. When the cyclone loses steam and becomes no more, we are in a different world, even though to others we may appear the same. Or we might see familiar surroundings, but experience them differently. Now, as you prepare for the next adventure, become the rainbow, which is also a circle. Focus on that. Start at the end of your old cycle and move forward."
Suddenly, as corny as it sounds, I felt like I slid down the curve of the rainbow. I landed back in the meadow as the rest of the rainbow went into the earth.
My dad was there too, apparently done with what he was doing. I was glad he was back as I sensed our adventure was nearing its end. I threw my arms around him. "I love you dad. I know we'll never really part. It only seems that way."
For a moment I felt like we blended into one and I forgot myself as Susan. Behind me, My Fool touched my shoulder. "That's enough for now. It is far too easy for you to float away from your human endeavors in the life of Susan."
He was right, enough adventure for now. Time to rest. I stepped back from my dad and Fool, and we wordlessly retired to our mats.
My dad lay down and seemed to slip into instant sleep. Soon . . . soon, he would fly away. Instead of feeling sad, I said to myself, Happy journey, dad.
Before I could lie down, My Fool threw something into me, which actually made me fall back on my mat. What came to mind was a miniature black hole. I felt a powerful whirling from a circular shape and my whole body was this force, but in a small way, like feeling the spin of a washing machine inside me.
"The gem of spin," My Fool said, as I began to fall asleep, "is the power of everything, Creative Energy creating, making itself known everywhere with a bounty of incidents. Each incident, no matter how trivial, contributes to the earth story. The tiniest brush stroke adds so much to the painting of life's masterpiece. Nothing is ever menial. In that, everything in mundane reality is as important as the deeper more spiritual worlds. It has its spin and is an integral part of all life versions, realities, and realms."
I felt the small weight of the ninth charm appear on my gold bracelet. I imagined it was a little gold black hole, as I couldn't seem to open my eyes to view it.
Just like a spinning wheel, we weave the fabric of life, I thought, as I spiraled into sleep.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
As you fly around your days, your habits, your obligations, take moments now and then to sink deeper into the cyclone, into the eye of the chaos, to that centered quiet place deep within. Here, regeneration and enlightenment can be had to prepare us for the next leg of our journey. It is a long road home, these circles and spirals take us, the spin that in its own way slows everything down into time. Each step of the way, each ring of the spiral is captured in a circle. These circles keep us focused into a particular reality that presents us with a gift of such magnitude, it supersedes our consciousness. But there it is, this gift, this gift from the greatest I of all—Creative Energy. Us.
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# The Invisible Crowd
# GEM #10 PLURALITY
Everyone is an "I"; and "I" is everyone.
##
A PATTERN HAD DEVELOPED. Every inner world morning for the last two weeks, I had awakened alone and remained that way until the end of our inner world day. My Fool was off with my dad, preparing him for his next incarnation. I sighed and rose from my mat, gazing about my beautiful meadow hazed in grey.
I was lonely. Sometimes we all feel alone, experiencing a heart breaking sadness that permeates our state of mind. It was such a time for me. I knew I was making a deal of it, my dad and Fool excluding me, for good reason, I'm sure. My loneliness was all in my head, or my heart.
I decided to walk away my woe. I was barefoot, but my feet were not assaulted by the meadow floor. My long white dress looked a bit tattered at the hem, and had smudges of dirt about the fabric. My hair suddenly stretched long down my back, just like the imagery I had as a girl when needing to feel better. Long hair feels like freedom to me, like the stallion galloping along the ocean shore, long mane and tail flying. However, right now, I was more like the plodding stallion, head drooping.
We all feel alienated sometimes. How can we not? Here we are, housed in a body that seems to be a singular entity staring out at the rest of the world. As My Fool would say, It is the way it is supposed to be.
Suddenly, I seemed to be walking along inside a dark tube awash with colors, reminding me of colored chalks on wet pavement blurring into something indefinable.
Sometimes we just feel what we feel. The thrum of life's vibrant dance can be felt from miles away, but we are insulated in our tube of sadness.
What is this sadness? This feeling of being plucked from a crowd to endure solitary confinement. It comes sometimes, I think, when we feel the dastardly slap of others repelling us from their personal space. On the other end, when we bask in the glow of other people's approval of us, it feels like home. We have reached out and received acceptance. This warm embrace is redolent of the oneness we knew before experiencing identity, and touch upon in altered states of consciousness.
Though we are all one, the experience of aloneness is painfully real. I kept walking and walking, hoping the long tube would lead me somewhere nice, but I feared it would go on forever unless I changed my mind state.
I stopped walking, closed my eyes, and inhaled a deep breath, allowing my mind to deepen into whatever was true, and not what my mind was telling me. I felt a shift then, and opened my eyes. Before me were numerous passages that led to various lifetimes. I don't how I knew that. I just did. It reminded me of all the little shoots in a fuzzy dandelion, making up a bushy ball. The tube I'd been walking was as the dandelion stalk, but now, upon reaching the fuzzy ball, there was much to see.
I peered down one shoot, then another, and another, noticing identities in various scenes. Deciding to explore, I walked down a shoot, and came upon a shirtless man with a shovel, vigorously digging a trench. It seemed to be his job. His determined face left no room for sloughing.
I gasped as I was suddenly in the man. I have to keep going or my family will go hungry. I am the man, and I have to take care of my wife and four children. I must do this. There is no other option. I could feel his aching back and arms growing weaker, but his appendages moved as if they had all the power in the world.
I realized then that what actually powered him was love, and a feeling of responsibility, even importance, that without him his family was in peril. His thoughts barreled over mine. No one knows how hard this is for me, how hard it is to give myself up for the ones I love. I am alone, killing myself to keep my loved ones afloat.
I felt his "I" as my own. The pain in his heart overwhelmed me, bumping up against my own sadness about being excluded from my dad and Fool's many treks away from me.
Disliking the feeling, and having had enough of it in my own identity, I left the man and headed back up the shoot, whereupon I peered down numerous other shoots. I chose one with a female toddler on the beach, happily digging in the sand with a blue plastic bucket and shovel.
Walking toward her, I began to feel her reality, and then suddenly I was in it. I love wet sand. Feels good on my legs. It sticks to me. Her joy brightened my heart. Suddenly a pang of fear stabbed her. Feeling it, I gasped. My little head looked around for my mom amongst the various bodies posed along the beach: sitting, standing, lying, in clusters, some walking along the shore. Not seeing mom, terror rose, and I started to cry really loud, fearing I was all alone now and forever, and how would I be protected or even eat? My cry became shrieking screams.
Warm arms wrapped around me from behind. My mother's voice. "It's okay, I am here, I was standing right behind you. I was just talking to someone. I love you sweetheart."
My mommy. Oh, my mommy. I am safe now.
I felt her "I" as my own.
Again, the little girl's experience of feeling abandoned bumped against me. I left her reality, and headed back up the shoot, feeling mine. Every time my dad and Fool left me, I feared they would not return. What would I do without them? Without their wisdom and deep understanding of me? I was so alone without them, or at least I felt that way. But just like the little girl had learned, I knew deep down they were always there, there in the ways that none of us are really ever apart. It just feels that way because we are so steeped into our identity, which gives us the impression of separation.
It kind of hit me then that the more we identify with our specific human reality, the more prone we are to feeling alienated and cut off from the whole of creation.
This is one reason, I think, people go to church. In focusing on an idea of god, we feel connected somehow to what is beyond our identity. This is true too when we yearn for the natural world where we feel connected to something that seems pure and bigger than us. Those fighting to preserve nature are really, in a way, fighting to save that feeling of oneness that we so desperately seek.
I reached the base of the stem, not sure I needed to go down any more shoots as every "I" seemed to have the same underlying fear, hope, and struggle, highlighting the sadness of alienation, so very common for us all. This sadness comes through when our grown children don't seem to need us and have flown the coop to make their own way, or when our mate shuns us. Or when we can't seem to find that soul mate who will love us forever, totally and completely.
I cocked my head. Interesting that once we've scattered out into the physical world as identities to have adventures, all we are ever trying to do is get back 'home' where we feel whole. Or maybe that is the prize that lures us through the maze of earth life to have adventures and become more than we are.
Identity, after all, is an impression of feeling single, a very real impression that looms high and mighty with a solitary idea of who and what it is. That too, is a lonely feat. No one can take us to the finish line. That, we must do on our own.
Curious, I peeked down more shoots to view other scenes. I saw an interesting one, a cat running along a wall ledge in the night. Loving cats, I was drawn down the shoot toward the feline. Then I was her, my paws padding along a narrow brick ledge, heading toward an open garbage can. My stomach rumbled with hunger. I reached the can, but in pawing through it, it only smelled like food. I always found food here, but not now. I jumped to the dirt, and looked around in the dark for something else to eat.
I hear a high-pitched voice, "Here kitty kitty." A woman squats on the ground with a dish of food. I am so hungry. I go to her and she touches my back, stroking it. It feels so fine. She comes to me sometimes like this. I only remember that she does this when it is happening. She picks me up this time. I am held close to her. I feel her beating heart as she floods me with a warm something, and it feels good.
I felt the cat's "I" and its loneliness, even though it didn't know it was lonely.
This made me yearn for my dad and Fool's return. Then suddenly, I felt them peering into my cat reality. I quickly left the cat and made my way back along the shoot to greet them.
When I arrived, My Fool said with a cherry-cheeked smile, "Had a bit of adventure into loneliness, did you?"
I nodded. "I felt like those identities were me. I could feel them as 'I'. I mean all I's were the same I."
My Fool said, "All I's are you, and me, and all of us, the greater plurality. However, as you have discovered, the 'I'— dentities you just experienced are not only in your specific plurality, but they coincide with your current feeling of alienation."
"Yes," I confirmed. I have had enough of that."
My Fool pointed to a batch of shoots. "Look down some more avenues Susan, keeping in mind what you see are your various selves playing out themes that you experience in your current identity. Just observe. You don't have to go into those realities. There is more than loneliness going on."
I took a deep breath. "Okay."
I peered down another shoot, viewing a chamber with an innocent girl sitting in a corner with a piece of twine, lacing it through her fingers, while in some sort of shock. She had lovingly trusted someone and her innocence had been marred somehow.
I looked down another shoot and saw a dark-skinned boy being lashed for simply standing up for his friend who was being treated unkindly. The look in his eyes cried out to me as I stared hard at his anguished face.
My Fool said, "Just like dreams, the lives you glimpse, will ever reflect your state of mind."
Curious to get a better grasp on exactly the state my mind was in, I peered down shoot after shoot, viewing myself in various situations of being hurt for shining love. This was such a big issue for me; always has been as far as I can remember, even back into other lives (simultaneously occurring, even though they seem linear). Even my fiction books feature a woman who struggles to accept the more primitive nature of earth in a 'must survive, dog eat dog' reality, her loving heart unappreciated.
Even after all my work on accepting the nature of everything, I falter when I get too near those in that survival level of reality, and wind up hurt or sad. I confront my sadness with the wisdom that we all are as we should be. Earth would not be earth without a setup to explore vast realities of opposites. Giving and taking are integral to life. My current personal task is to take as much as I give without apology. This is hard for me. I never want to inconvenience anyone, even though I freely inconvenience myself for others. This must stop.
My Fool, having read my thoughts, consoled me. "It is a process, Susan. It is just that the closer you get to the finish, the more you can see, and the harder it is to play out the last part. He looked to my dad, "This is what you now endure, Robert. You are but a breath away from finishing the warrior experience. He looked at me, "Just as you are the martyr."
My dad and I looked at each other.
"That's it, Susan and Robert, now gaze more deeply into each other's eyes, for in there, if you go deep enough, you will discover yourselves in relationship to one another."
I slanted my eyes to Him. "Do you mean how we behave with each other?"
"Deeper than that," He replied. "You and your father are closely intertwined, playing out opposite energies, but helping each other to do it. Moving into your father to find yourself is to see and understand your symbiotic relationship."
"We have a strong one," my dad said warmly.
I smiled, looking back at him. I had always felt that with my dad.
Heeding My Fool's instructions, I faced my father and gazed deeply into his eyes, as he did mine. I was surprised and happy when he took my hands in his. His eyes felt like warm portals as I journeyed inside him, while feeling him enter me.
I witnessed various warrior scenes, from raw to noble. The raw ones were in dull colors, almost faded away to a wash of blurred black and white. The warriors with the noblest personalities were clearer, but even they were fading. It was the warrior of him that had ever saved my day. This was probably the most important reason his impending death scared me. Yet, he had been training me my whole life how to be a warrior, and really, I had become one.
I went further into him, finding my reality in numerous split screens of all the lives that I gave myself away, only to feel used, betrayed, or unappreciated. At the same time, I felt him in me, seeing versions of his downfalls.
Just beyond the split screens of my lives, I could see my dad's warrior persona encased in an energy field. And inside me, beyond viewing his various lives, I could feel him viewing my martyr persona being bombarded with assaulting energy. My love flowed toward him like waves, penetrating his shield of mightiness. And I felt his love inside me creating a shield to protect my innocence. I was transforming into a fighter, and he a lover, as evidenced in his apparent next life.
My Fool's voice broke into me, "Open up Susan, release the pent up feelings."
It was weird, but I somehow felt He was simultaneously giving directions to my dad.
I inhaled cool air slowly, deeply, through my nose, filling my head with sweet breath. Exhaling slowly, air slipped through my lips. As my lungs deflated, much like an untied knot on an air-filled balloon, so too did my pent up anguish of being punished for giving love.
I could see how I had kindly set myself up for those experiences to motivate me to jump to the next level of my evolution. But I had done that, and I didn't need to have those experiences anymore. The fact that I was becoming so aware of it is a sign of enlightenment, which as previously said, usually signals the ending of a particular story before moving on to the next adventure.
My Fool said softly, "Now reclaim the energy that has left you depleted, and let it build up inside you."
I nodded, loving that idea. I inhaled slow deep breaths, reclaiming myself from all those to whom I gave myself away. Inhale. I sucked back my energy from those who used my love against me. Exhale. Store the energy in myself. Inhale. I sucked back my energy from those who did not want it. Exhale. Store the energy in myself. Inhale. I sucked back my energy from those who ignored it. Exhale. Store the energy in myself. I felt my reclaimed energy growing stronger inside me, and it felt so good. I was taking my power back.
I saw it clearly then, how my energy could be too intense, like a laser beam boring into people, even if it is all loving and well intentioned. I imagine to those who don't want it, it maybe felt as an invasion, like a blaring sun that hurts their eyes. People can only grow in their own time. They can't speed up their story, for then they would miss it.
Yet, when they force my retreat, I am hurt and shocked, whereupon I retract my loving energy all together, and recuperate in the lonely cavern of myself. It was becoming apparent that I tended to ping pong from opening and shining too much, or closing off and not shining at all. But the balance, I had not yet achieved.
A first step would be to better conserve my energy, rather than give it away at every opportunity. The world will be fine with less of my energy input. It isn't my energy anyway. It is the creative life force that we all have. And when we are full within ourselves, we naturally shine out into the world, not too much, and not too little.
Feeling better, my focus returned to my dad's inner being.
I heard Sibelius, Symphony #2 playing all around us, even in us, culminating in beauteous power. I saw a flood of Pure Creative Energy wash over my dad, breaking up crystallized energy clogs, which were certain perceptions, thoughts, and experiences.
As he became freer within, his energy flow heightened, enriching his being. Hearing him speak, I came out of him and opened my eyes.
His voice sounded trance-like. "Our quietest, uneventful lives are vitally important for they counterbalance the dynamic ones, like the night sky that makes it possible to see the stars. Each life is a unique formation. Each formation, each life is essential to our being's whole story."
His voice strengthened, "I gather now all the identities of my many lives, the quiet and adventurous alike. I give importance to each one, and every experience I have ever had. I unite them by consolidating my power to pull each life, like a living chapter, into one long book."
His words seem to catalyze me to do the same. Suddenly, I was transported to somewhere in the far reaches of the ether lands. I was in a sea of an expansive variety of incorporeal bodies. Though it was crowded, perhaps due to far less density than the human third dimension, I did not feel scrunched in any manner, as I normally would.
Not seeing my dad or Fool, I moved about, walking on air with copious space beneath me. Like bubbles, ethereal bodies fell around me and parted as I moved along, as if giving me passage and incapable of obstruction. These same ethereal bodies also floated about unimpeded by any who came upon them. It felt as if a million bubbles had been blown all at once, and in flurries, eddies, and currents in the air, we almost seemed to dance.
I began to recognize some of the bubbly spirits appearing as those I had known in my life. Some were friends, and others who in my human thinking, did me wrong, but here it was as if we existed beyond our human identities, still attached but also detached. I mean everyone felt like me.
I think, in this realm, we were the personification of our core depth, or maybe spirit is the word. I am not sure. More than ever, it felt like our earth identities were costumes we wore, and the dramas we experienced together were just plays we performed. And here in this realm, we all acknowledged it. There were no swords to parry, or tears to shed. We were one great family, all the same, just playing different roles.
It was strange to see people I disliked and those who disliked me, yet to feel nothing but realization that behind the costumes and the plays, here, we were all the same; just reflections of one vast being.
Wondering where my dad and Fool were, I gazed about for them once more, when a giant hand scooped me up from the ethereal crowd. My dad was already in the hand, still bare, save his purple boxer shorts, looking light and bright as a peacock feather. Compared to the hand, we seemed about an inch long.
He rubbed his chin. "This is fun, isn't it?"
"Hmm," I grunted, as we sat side by side. My dad was always fearless in these types of adventures, not so me, but I did them anyway.
I looked to my dad. "Where is My Fool?"
His eyes rolled up.
Gazing upward, I couldn't really see anything, but My Fool's words seemed to rain down on us from above. "Observe the ethereal crowd below as you rise."
Higher and higher we went, like an elevator going up. The crowd was more expansive than I had imagined, for no matter how high we were lifted, making the ethereal bodies appear smaller, there seemed to be an infinite sea of them. From here, they appeared as a honeycomb comprised of countless units.
"Okay," I said, "Let me guess. Each unit is a Great Self harboring its many selves, and all the units together are the global plurality?"
"Indeed," assured My Fool from far above. "Everything seeming singular is connected to everything else, and hence not really singular at all. We are all, always unified."
I said, "Like the sea of humanity?"
"Humanity, but greater than that; it is an infinite sea of the collective singular. Not only do all selves in a plurality feel each other, even if they don't know what that feeling is about or where it is coming from, but everything in existence affects us, as we are all made of the same things."
My dad declared, "Basically then, what one experiences, so do we all."
I chimed in, "I have known that to be true with trees, and there have been scientific experiments that show one group of animals in one location learning something from humans, and then the same species in other locations concurrently exhibiting the same knowledge, as if all experiences are shared."
My dad interjected, "These seepages of unified experience, I think, can be had with humans as well, usually in between sleep and waking periods, dreams, or in altered states of consciousness. This is when I usually have them. Many, however, seem to tune out these psychic impressions as imagination, craziness, fatigue, or maybe even intoxication."
I said, "I think that's because when we can't make sense of what we see, such as the flash of an unfamiliar face or scene, or an experience, such as déjà vu, we feel safer writing it off as not real."
My Fool's voice fell upon us. "These flashes can be bits of glimmering memory in our own life, other lives, or the lives of our ancestors as far back as the beginning of humankind."
"Yes," I concurred. "I always felt that sometimes we get flashes of what our ancestors experienced, but assume it is a past life."
My dad and I started growing bigger in My Fool's hand as He elaborated, "No matter where these flashes originate, all these small memory fragments are stew in the pot of plurality—the global plurality experiencing identity in the vastness of one being."
Feeling myself grow, I tried not to get distracted. "That concept helps me better accept that even the villains are us, for at some time or another, I guess we play all parts. And all parts are needed to actualize the story. Villains, as we have said, tend to bring out the hero in us to save the day."
My dad and I had now grown big enough to fill My Fool's hand, or maybe His hand was shrinking. Either way, His voice seemed nearer. "It doesn't diminish the horror victims may experience, nor should it, but when all is said and done, even the perpetrators are all a part of our greater gene pool that is us as a human race. Yet, in this, all these combined experiences and journeys are creating energy by fulfilling the curiosity of what if? Every character in our plurality is exploring slightly different angles of the same theme, eventually giving a 360-degree view and thorough exploration of that story line. And every unit of plurality is doing the same with various themes."
I giggled a bit at a vision of human ant colonies working together for a common cause. Finally, we stopped rising. I glanced up and saw My Fool's giant face. I gasped. Though I knew we were in His hand, seeing His humongous face, well . . . I eked, "It seems like you are—"
"Don't say god. I am only perceived in the way you need. If you were able to keep broadening your perception, you would see no difference between anything, and grow as large as me. The more finite your vision, the further away Pure Creative Energy seems, and is then to the human mind definable as an omnipotent being. The closer you are to Pure Creative Energy, the more 'one' everything seems."
My dad clarified, "Basically then, when in our identity, we don't feel like 'god', but at the core of our greater beingness, we are."
The topic propelled me into a more exalted state. Even though mini me was in My Fool's giant hand, I also suddenly felt myself as a giant next to My Fool. I looked down at the ethereal crowd again. The entities now appeared as a sea of flowers. Each flower was as a Great Self encompassing their many selves, who were the layered flower petals.
My Fool's voice echoed in my giant ears, "Now, in this exalted state, release the last fear of your father's nearing departure."
As I did what He bade, before me were living flashes of my dad's many lives. I saw him in various battles, crucifixions, and victories. I saw him in many bodies of man and woman, and even a few animals, in so many circumstances, I could not count. The flashing went quicker and quicker until I got dizzy.
In My Fool's hand, my miniature dad, gulped back tears, emotional, I think because he viewed the same flashes as I. Yet, he also seemed a giant next to me.
My Fool continued speaking in my both mammoth ears simultaneously, and apparently in my dad's too. "These are your memories, Robert. Your soulic journey nears completion as you have been working toward the finale for quite more time than you might realize. This final chapter as a black female, in a different time and earth, will do its part to bring into fruition all that you have become on your earth journey, contributing to balancing the scales for women of all ethnicities, women in general, the feminine side of man, and feminine energy itself. The other selves in your plurality will have similar experiences."
As the small person in My Fool's hand, I heard my dad weep with a kind of relief, even as he was also a giant beholding it all.
My Fool continued, "Just as it is said that before we die, our lives flash before our eyes, you Robert, in the multiplicity of your plurality, see all those memories flash before yours."
I heard Richard Strauss' symphony, A Heroes Life, playing. So appropriate for my dad. I saw dancing vibrations of the music as various squiggly lines creating sound. I saw each line as an identity, quite special, yet not feeling so special when unable to hear all the other lines vibrating in synchronicity to it. But when we can hear the other lines of the universal symphony, we behold our worth and can experience tear-dripping beauty, as I have so many times before.
My Fool said in my giant ears, "The experience of "I" really means all. Every time one of us says 'I', we are emanating from the source of our existence. Behind all I's, or identity's, is one Pure Creative Energy. We, Pure Creative Energy, are the product of those creations, as well as the creator."
I felt a strange shift as my dad, Fool, and I became the same giant being for one brilliant moment. Then we snapped into a quiet, dark space as three. It took me a minute to adjust. My dad was next to me with closed eyes. He seemed kind of steamy like in a space deeper than mine, though I could see him here.
My Fool said, "Move into your father's being once more. He has always served as an anchor for you, so it would be well to anchor yourself before what is about to happen."
I nodded faintly.
I projected my being into his, and he let me. I fell into his world. There were door-sized mirrors everywhere. Each mirror seemed to reflect one of his various selves in a reality. All the mirrors touched upon each other at assorted angles.
The crown of my head sizzled with a sensation of opening. It came to me that while in the outer world we all seem sealed into an identity, when we interrelate, we are actually touching what is inside of each other, like stepping into each other's mirrors. The closer we feel to another, the more we are in that person's world. This extends to animals, plants, and all of nature.
I touched the mirror closest to me, and to my surprise, my hand went through the silvery mass. So I stepped inside, observing many more connecting mirrors, much like the inner workings of crystal facets. Though each mirror appeared separate and impenetrable, none were.
I continued walking into mirror after mirror, not really sure where I was in the scope of his vast inner being, but once inside a mirror, it felt like flavored energy. One energy might feel war-like mixed with creativity. Another might feel fairy tale-like mixed with spontaneity.
Walking through my dad's mirror worlds, I discovered that if I lingered long enough, story lines appeared, complete with characters, and scenes began to play. All the players were of my dad's Great Self, and each felt themselves the center of their own play, and they were.
Then I shook my head as a visage of my incorporeal father glided through the many mirrors, glowing a little brighter with each passing. The mirrors he left, interestingly, became blank.
And though I had long explored and experienced multiple realities; my heart was warmed profoundly by exploring those of the man who raised me: my hero, my rock, my dad.
I jumped, hearing My Fool's voice, "Susan."
I opened my eyes, beholding my dad still in trance. And from what I'd just witnessed, he was doing important inner world work.
I looked to My Fool.
His eyes twinkled. "Your turn."
I raised my brows, wondering what was about to happen.
"Buckle down and buckle up." My Fool pointed at what seemed to be a star field of holograms. These holograms I recognized as the perceived obstacles in my life.
One had an image of me before a closed door, hunched over, crying, face in hands. This visage reflected my constant struggle to participate in the mundane world as an authentic person. How can I be me in a world that demands conformity?
Another image was me standing sadly with tears dripping down my cheeks as masks are thrown at me. This reflected my shock from accusations of being fake when I shine unconditional love. How can I make it in a world that doesn't believe I am real?
Another image was me crying in a corner as my family walked away with their backs to me. This reflected my fear that all my effort to unite the family, would fail. An old adage came to mind. You can lead a horse to water, but you can't make them drink.
I saw a plethora of Susans stanced in discord. I hadn't realized how many perceived obstacles were floating around in my head.
Beyond the images, far far away, and seemingly over a curve of dimension and into it, then through something else, was a ball of brilliant rainbow light, like a burning sun, but with curvy rainbow beams.
My Fool pointed to it. "There . . . focus there."
"What is that?" I asked.
"That . . . is yourself, the sum of all the you's you have ever been, are, or will be. By focusing there, you are no longer inhibited or upset by perceived obstacles. See that ball of light as a manifestation of all your living. This living that slowly brings your being into full fruition. The light shines brighter as experiences upon experiences nourish it. In that, you (your plurality) become more than you were, just as tree becomes more than the seed from which it sprung."
I shook my head, mostly at myself. "How small we humans so often think, assuming the worst, imposing restrictions, quashing possibilities, and inflicting unnecessary pain on ourselves and others. I can't, so easily sits on, I can."
He said, "It is the way it is supposed to be. However, our roadblocks are often bigger than meets the conscious eye. The collective experiences from other times and places can serve to keep the 'I can't' in place to protect us from what has hurt us in the past. It is a defense mechanism that goes beyond the experiences of our current identity."
I nodded. "Yes, I can see that. For instance, the child who can't seem to leave home because panic attacks arise. Or the drug addicted person who can't break the curse. Or the person who can't stop cheating on their mate."
He elaborated, "All these behaviors are linked to resolutions born from massive activity of our other identities in our plurality, which includes, in the concept of linear time, our many incarnations. While these behaviors are often safeguards, they can also be the product of conclusions drawn over the course of centuries, such as If I go out into the world, I will be punished. Or, Self-sacrifice is the only way to redeem my worth. Or, Accumulating power is the only way to feel alive.
I smiled, reiterating an old lesson He had taught me. "These conclusions keep the storyline in place until it has played out. Reaping what we gained from the experience, we then begin anew as if for the first time."
"Yes," He affirmed, "Your old story, Susan, is fading, and like a chick hatching from a shell, your shell has been cracking for a long time. So prepare to experience merging Susan and all the identities before her that led to who she is, into the sum of yourself, which is your plurality, your totality. Not 'the' totality, but yours."
I sucked in a quick breath to prepare myself.
He looked straight through me. "Ready?"
I nodded, scared, but ready. "What do I do?"
My Fool's hands drifted over my head, which seemed to steady me. The crown of my head, though remaining intact, felt opened, like the cap removed from a bottle.
My Fool directed, "Focus on your rainbow sun shining through the haze of dimension and time, nothing else. There are no longer any obstacles; they are just illusions. They are no longer needed, just remnants of habit."
I looked into the distance and focused on my rainbow sun, quite surprised that it began to move toward me, as if attracted. Nearer and nearer it came. My heart pounded.
My Fool said, "Stay calm, breathe deep and slow, inhaling Creative Energy."
I did as he bade. As my breathing steadied, my consciousness deepened, opening to possibility. I felt unwrapped, receptive to what was, beyond what I believed what was. Then touch down, the rainbow sun entered my head, pouring into me. It did not burn, but rather engulfed the solid perceptions I had about life, making them transparent, blending them in with the purity of what is beyond all perception.
Our perceptions are a reflection of our reality, not reality itself. What is reality? Given we can only assess it from our individual human brain, can anyone ever know collective reality as it truly is?
My perceptions continued to fade in the light. I had been bound in the house of my current perceptions, unable to open the doors and windows until I was ready to move on. Sometimes we are ready to move on, but get stuck in a holding pattern, and can't seem to take off. This is partly because we decide that taking off is an outer world effort, and though it partially is, the real inertia is in making that esoteric connection to Creative Energy itself, staying open to it, keeping one's focus on that charge filling the body, mind, and spirit, sparking growth into our full capacity. And I was beginning to feel that now.
I went deeper still, opening to the energy of creation, focusing on the source, and the source alone. I felt somehow that this could power me, or anyone, to move about in the world, in a sense, as a living sun filtered through one's personality and body.
Strange, in all this, I did not close my eyes, yet saw only inward. I felt an energy tingle on my forehead and my focus was drawn to My Fool standing before me. Just above the bridge of our noses, a beam formed, joining our third eyes, uniting us as one. It was the most soothing, yet powerful energy I'd ever known. My whole body felt renewed.
My Fool then superimposed over me as if He were a rocket ship that I sat in, and keeping my focus on the rainbow sun inside me, I also felt it outside me in a deeper realm, as if waiting for my arrival. Something about it coming into me and me going into it.
We shot through seeming hyperspace. I had to work not to succumb to fear of the unknown. Every time I did, we slowed down. I intensified my concentration, and soon after we zapped into my rainbow sun. Instantly, I felt so invigorated, strong and alive, with an intensity I had never known as a human. We seemed also to spray outward. I felt vast beyond identity, my rainbow sunrays stretching into star-studded space.
My Fool had said it was not the totality but my totality. I have before, I think, touched for a second the totality, or neared its presence and felt it, but this was different and beautiful in its own way. It was as if all my earth explorations and even otherworldly explorations, not of earth, all had incredibly beauteous rhyme and reason.
I became aware that all around me were many other rainbow suns, millions of them, many other totalities. Each had a sea of identities exploring and experiencing, but in this state, there was only, for lack of better words to explain it, and it does fall short, pure love. It was like the planter of seeds watching how its seedling grew under a variety of circumstances without judgment or even emotion as we know it, just the purest unconditional adoration.
My heart was full. My cup runneth over. My Fool then seemed to fly apart from me while I remained in my rainbow sun. His wise face, like a god in the sky, smiled faintly with warm eyes.
His words echoed into me, "Beyond this level of being, my dear, all the rainbow suns of plurality are suns blended into one unfathomable energy, an energy you have not yet fully experienced, nor should you, not yet, lest your identity disappear."
I knew He was right. My identity is as a tool I use to have earth adventures, and I was not done.
"Your current mandate, like so many others, is to be an expanded being in the world, while continuing to develop your individuality, flowing in the present, not pushing ahead, nor falling behind. Do not concern yourself with how you imagine this will manifest. There are no obstacles now to your own becoming. So . . . become!"
With that, my reality shifted, and I was in a field of wild flowers.
I sat up looking at a giant yellow aster with My Fool's face in the center. "Hello," He said.
I laughed and laughed.
"Hello," I retorted whimsically. Then I was in a flower too. Then I noticed my dad's face in a flower, happy he had joined us.
Then we each became a mountain. Then a drop of rain falling side by side through the sky, turning to snowflakes that fell on the ocean, and then we were the ocean.
Then I was back in the meadow, sitting on my golden mat, holding an old-fashioned clock next to my heart. Tick tock. Tick tock. Tick tock. So comforting the countless beats that help us feel steady. We, like the clock's hands, move around its edges, experiencing every point in time. Each point is real from where it stands. One o'clock is the center of reality to that position on the clock. We are each in the center of our own reality, but reality is the whole clock.
It is easy to get lost in the story of our lives and the concept of "I". Yet, if we could but concurrently behold our plurality spanning a googolplex (largest imaginable number) of all life forms, our reality would pleasantly broaden.
In this moment, when we consciously experience our singular selves as a plurality, our own face looks back at us and says, "It is I. It is I. Don't you know who I am?"
The ticks on the clock grew louder, then transformed into a heartbeat. Baboom-baboom-baboom. The clock had disappeared from my hands. Then the beating turned to a pulsation. On-off-on-off. Start-end, start-end. Inhale-exhale, inhale-exhale. Give-take, give-take. You-me, you-me. Then it sped up so fast that I couldn't tell the difference. This and that were the same. Here and there were the same. The last words I heard from My Fool were, "The gem of the plurality brightens the one." In my mind, I saw a symbol of four intersecting circles, and knew this would be the tenth charm on my bracelet.
I passed out, and spiraled into a deep sleep.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
As you go about your days and nights, take comfort in the plurality of all that you are, and endeared to the identity in which you are currently focused. Never alone, never inferior, never inconsequential, your every move is a meaningful stroke on the painting of life. We are all in this together, this living, this adventure, all each other in a forgotten beginning, and will be together as one through the course of many endings.
Rest in the calm now, knowing that everything that happens to you is meant to be, that each of us are doing our part for the plurality to become more that it was. We are each important, so important that without every single one us, there would be no plurality. Without one, there is none. Your "I" is the most important "I" in the world.
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# Jumping the Grid
# GEM #11 INTERMUNDIAM
Our identity jumps over the in-between from here to there; in oneness we are the in-between, and there is no here or there.
##
I AWOKE THE NEXT MORNING to a crisp clarity in the air. I sat up, looking about at a yellowish orange glow illuminating the meadow floor.
My Fool's voice whispered like a soothing breeze in my brain. "This is the hundredth day of your becoming."
Only a hundred days? I thought, as I rose. But then it came to me that time is different in the inner world. Maybe a hundred days was more like a hundred visits to a certain level of my consciousness.
A bird began chirping in song from a nearby aspen tree. I allowed myself to go with the flow. Words swept across my mind. "The lark sings praises on the hundredth day of my becoming."
I began meandering about the enriched amber lit meadow as if seen through yellow sunglasses. My long white dress seemed whiter and cleaner than usual, and my hair had grown longer, cascading to my waist. Surging up in my heart was a feeling of embracing my individuality so deeply, I felt connected to everything, freer to be me, somehow. Gazing upward, the blue sky shown wispy cloud layers that softened my brain. About me, tall sunflowers cradled their seeds with bright yellow petals that bespoke pride.
For a hundred days, I had crossed over from the land of separation into the realm of plurality. I had been so lonely in that other place, in that dramatic world where people make up what they want to believe and behave as if it is true.
Here, on the hundredth day of my becoming, I shed all beliefs, exposing what is without having to understand. Turned inside out, I felt empowered, not as an identity, but by experiencing plurality through my identity.
In the land of persona, fooling everyone is often the way to survive. In this deeper world, it is about fooling no one, for as I make my way about the meadow at this level of being, all I encounter feels like me. Shame is nonexistent. Time is just the beating of hearts. Storylines fall to the creative mind.
I came upon a patch of peas. I picked a pea pod from the vine and peeled back the sheath, revealing perfectly spaced peas. I dislodged a pea and slipped it in my mouth, tasting the sweetness life has to offer. Does anything else even exist?
As if shaking myself awake, I turned around, beholding My Fool. "Where is my dad?
My Fool glanced at the hill behind us.
Looking that way, my dad stood at the hilltop in the same white flowing robe worn when we had given our speech to the crowd about folly. So interesting how this archetypal symbol for holiness seemed to be the choice of perception when encountering wise or spiritual beings. The hill's base was packed with a multitude of ethereal people.
"What's this about?" I asked My Fool.
"Those gathered are the elderly who are preparing to die. They have been drawn here in their dreams to gain the comfort they seek."
Though my dad was far from me, his voice rang clear in my ears. "In youth we are told to pay attention to our conscious activities, and not unseen realities. We are conditioned that rewards come from achievement. In this, our boundaries become strong, as they should.
"In age, as we near dissolution, for most, our boundaries begin to fade between each other and other worlds, and our roots loosen from our once cemented storyline. Then it becomes normal to hear and perhaps see what we are told is not there.
"If we share our experiences with those around us, we are often viewed as lesser than, out of our minds, and our opinions and feelings rendered invalid. We might even be put away somewhere for own protection.
"Yet, in this, we can halt our effort to be as we were in youth, and instead look toward our next adventure. We are all vast, always valid, always worthy.
"We each have a plurality of identities which manifests as many sides to our current identity. Each identity in our plurality has a life of its own. There are countless overlays of realities our plurality experiences, all embedded in our subconscious. We each are a breath away from other realms that exist beyond the one our identity has come to know. If fear of moving on is removed, then communing with these other overlays becomes common place.
"The general public will perceive our one identity as the top of the iceberg, and not the iceberg beneath the surface that is layered with multiple identities in our plurality. This visible identity is often seen as the totality of who we are, assuming there is nothing more.
"But there is. Communing with our whole being requires us to further loosen our construction, open our minds, and experience the energy configurations of the identities that make up our Great Self."
"We need not perceive ourselves in the singular, but as many, each just a little different, who together form a workable community of many selves as one. This is an energized approach to understanding our lives and our master purpose.
"Although it is the way of the social world to program us to march to their song, we near the time now, where we needn't. The time is now upon us to be free of the ties that bind.
"It is a great time, though not viewed that way by most. We must sidestep the view that we are being put out to pasture and are no longer useful or needed.
"For me, I struggle to maintain my self-respect, knowing that I am no longer able to take care of the family or myself, the way I once did. Such a thing it is to step forward and find there is no next step to be taken. I want to die with honor, but honor is a trap for me, even though it once put the wind into my sails, propelling my adventure. But now the wind dies down, and it is time for the story of honor to dissolve.
"That is the wisdom of growing into age for us all, to release the memory of past accomplishments and the need to cling to what we have known. Before us is a new adventure! We here, each face death, but birthing and dying is just a shift of focus. With each blink, we die and are reborn."
He threw his hands in the air, and cried out, "Happy journey!"
The crowd seemed to burst into a cloud of gold, then disappeared. My eyes widened with surprise when my dad flew down the hill to us like a ghost.
I felt a shift then. My eyes burst open as I sat up on my mat. I had been dreaming. Weird to have such a dream when already in an altered state. I snapped my eyes to my dad's mat, and he too was sitting up in his purple boxer shorts, rubbing his sleepy eyes awake.
My dad and I rose slowly from our mats, looking about us with awe and wonder at the same golden orange glow I had seen in my dream.
My Fool appeared as if manifesting from the glow in his usual garb with Walkman on waist and headphones on ears. Mahler's Symphony #2 sounded all around us. My Fool gently swept His open palm up in front of us. "This day, we walk the worlds."
My dad and I raised our eyebrows at each other and smiled gently. It was fitting somehow to visit other worlds, as soon, very soon, maybe this day, my dad would leave his body for good. In the physical world, he had slipped back into that foggy abyss of dementia, that came and went, and his faculties were waning.
My Fool began walking. I stepped up beside him, as my dad did me. Our walk felt like a glide as white misty clouds wafted through the yellow golden air, sometimes moving right through us.
"Humans are rainbow beings," My Fool declared, almost affectionately, "of many vibrations: colors, shapes, and sizes with mixtures and hues thereof."
The golden air turned yellower and sunnier as we moved along. I suddenly felt compelled to refute all close-minded solutions that feed unsavory manifestations.
"Can you feel it?" asked My Fool.
My dad and I answered in tandem, "Yes."
My Fool elucidated, "The energy of warm sunny yellow is unabashed and strong in thought, effortlessly communicating without performing. Yellow is shining true self without care of what others think. It burns through judgment."
I interjected, "Yes, that it what it feels like to me, a kind of joyful, honest openness without defining."
His eyes slanted my way. "That is but one thing the yellow vibration can facilitate."
I began to see forms, shapes of white light bursts and what felt like waves of thought. Some of them came shooting at me. I jumped, a bit startled.
My Fool said, "What comes at you is an attraction of like mindedness. Like minded thoughts join just as molecules might merge."
Other waves repelled off me. "So the waves that repel from me, I suppose, are ideas that conflict with mine?"
He nodded. "And there others that never come near us at all because—"
My dad finished, "—those thoughts are not on our mind."
My Fool smiled. "Precisely. If you don't want something to come at you, don't think it."
As we walked on, the yellow slowly became green. My Fool said, "Everyone grows in different ways and paces. Let all grow to their own shade of green."
An old dream I once had came to mind. It was of the Redwoods. My brother was standing over my bed looking at me strangely. I woke up and screamed because I saw him as an alien that on earth took the form of a Redwood tree. Not aliens like scary malintented dudes, just otherworldly beings that take form in accordance to the vibration of the world they are in. In the same way, everything on earth has a form that if placed in a different world would eventually appear in accordance to the energy there. In other words, we evolve according to our environment. I mean, apparently the seeds of life came from outer space, so this isn't really that far out. So, just as we are manifestations of alien energy, well, isn't everything?
As we walked through leaf green energy, my dad spoke as if he'd read my mind. "It does seem that life forms feed off the make up of any particular environment, and that is why they look different from each other. I mean, our form would likely evolve into the vibration of any world we visit."
I grinned, not just at his statement, but that because his boundaries were dissolving, in a way, he was kind of becoming more one with me, reading my mind and all.
I added, "Also I think we attribute to alien forms at least in science fiction, something similar to us, not just a similar appearance with a twist, but for instance, since we have a strong warrior side, we generally assume most aliens would likely be out to get us. Just as in religion, we seem to attribute to deities what a regular mother or father would be, just personified."
Entering a forest green energy, my dad interjected, "And who's to say how other life forms on earth, such as a bug, see what we see?"
My Fool confirmed, "Each species has unique vision."
Really, that seemed so true, even humans see a little differently from each other depending on the makeup of their eyeballs.
We walked into colored worlds, one by one learning a bit about them on the way. To simplify, blue was calming, indigo was intuition, violet was higher mindedness, red was action, and orange was energized creativity.
Then My Fool stopped, looking first to me, then my dad. "That was just a warm up. Are you ready to traverse dimensions?"
We nodded, both a bit wide eyed, me more than my dad. I let out a deep sigh of apprehension when a pool like energy appeared before us, like a gateway.
My Fool said, "Robert, you have dreamed of the upside down, and orange world. We can go there. They are real worlds. All worlds are real."
"I have long believed that," my dad concurred.
I was surprised when My Fool dove into the center as if it were a pool of water. My dad and I looked at each other. My dad held out his hand, gesturing, 'you first'. I nodded and dove in after My Fool. I could feel my father's energy behind me. I was waiting to pop up somewhere, but instead, it seemed we were swimming through something like energy water that went through a series of barriers, marking new dimensions. I wasn't sure why we were swimming, but it felt something like we had to go faster and the process just took us off our feet.
My Fool's breaststroke was impeccable. My dad caught up with Him doing a sidestroke. I was lagging a bit behind in a dog paddle. I just couldn't seem to go any faster. They both slowed a bit, and soon we swam side by side, My Fool in the middle. Strangely, He seemed to expand and deepen at the same time, encompassing me and my dad, powering us as a butterfly does its wings but in a kind of breaststroke.
We moved through a world where people were orange. I looked at dad. "Dad, your orange world! This is so exciting."
My dad seemed so involved, he didn't comment.
Then we moved through an upside down world.
I cried out, "Your upside down world, dad!"
He muttered in awe, "Just as I remember it."
My Fool powered us onwards through various strange worlds of colored beings and dimensions in a variety of angles. Some worlds had beings like us, only with variations. One had double vision type beings, others had a variety of forms too numerous to mention. Some worlds had unrecognizable life forms, yet there they were.
As we swam, I could see how everything vibrated to the world we were in, manifesting uniquely, and resonating with that energy.
My Fool's voice echoed into us, "All around us, all the time, a variety of beings exist in various realms and dimensions. Even humans have realities in these worlds. They are not necessarily 'out there' but in realms indefinable to the human mind."
I always knew we were vast, but just how vast, I never could have imagined.
Then we walked into future worlds that seemed to slow down.
I said, "This is really just like human experiences. As we all know, when we want something to happen and are waiting impatiently, whether for the pot to boil or our ship to come in, the more we want time to speed up, the more it seems to slow down. Sometimes we speed up as if that will make things happen faster, but we usually wear ourselves out by expending such a long burst of energy. Even if we manage to accomplish other things in our wait, what we are waiting for still does not come any faster."
My dad sighed, "Sometimes a moment can feel like forever, like the moment I can finally leave my current body."
"It will come dad," I assured him, "it will come."
Then we moved into past worlds, mostly of human scenes. Though we were flying straight, it seemed we kept circling around to the same sights over and over again. There I visited things I had done but regretted, and things I loved and did not want to let go.
My Fool's voice vibrated into us, "In past worlds we can get stuck in a time loop, replaying old memories that stir painful emotions from a scene long gone. Those involved may have currently changed significantly, or might even be dead, but we keep replaying the scene as if we can change it and make it better, even if in the present, it already is."
My dad added, "Or, as we previously discussed, sometimes we replay it because we are trying to fuel our current mode of thought. Such as, I am a victim, and replaying our version of past events repeatedly fuels the reality we currently want to cement. Usually, because we have found it gets us attention, or an excuse to continue our unproductive behavior."
I said, "The time loop of the past is like being in a hamster wheel, it never ends until we decide to let it go and focus our thoughts in the moment or future. But sometimes past time loops are pleasant and we enjoy taking the trip down memory lane, bringing to life what was into the moment."
My Fool's voice turned lofty as we flew into a world that matched his tone. "The old joys are present then as we bring them into our future."
This lofty world seemed comprised of changing cloud like energies with various tones and scenes. I was stunned. Glancing at my dad, his jaw was agape. I guess he was stunned too.
My Fool's voice echoed through us, "This is the land of hopes and dreams. This is where the energy congregates. If enough energy in a hope or dream can build, it will then manifest into that being's reality."
Then we swam into a world that felt horrible to me. It was like the hopes and dreams world, but darker.
My Fool said, "This is the world where our fears build, and can manifest the same if given enough energy."
We quickly passed through it, and I was grateful.
Then with a sudden inward, yet upward, or maybe an all direction trajectory, we seemed in a space, quiet, yet full of everything. It felt like a suspended animation, except that we were conscious. I was me, but also larger and smaller than my identity. It was different from when we were tiny in My Fool's hand, yet a giant too, for then, as a giant we seemed like an expanded identity. This feeling here seemed more like my identity was a glove that fits over a hand, and my reality was on either side of the glove.
"Dad?" I said, "Do you feel that?"
He answered, "What, experiencing the other sides of myself as both the universe and a quark concurrently?"
"Exactly!"
We both sighed in awe.
My Fool still seemed to encompass us, but not in a persona. It was like He (as the butterfly) had paused to give us (his wings), a moment to rest.
My breath trembled in my ears, even though at the moment, I couldn't feel them.
Even my dad's breath was a bit shaky.
I relaxed into the quiet dark, growing comfortable. My words flowed. "This adventure into other worlds further confirms my ideas that at least some of the crazy experiences people have, such as alien abduction or seeing fairy tale like creatures, really are just other realms of existence. It seems the majority poo poo this because they are looking for third dimensional proof, and so much exists in other realms."
My dad jumped in, "I have noticed that nay sayers are often highly cemented in the physical world and mundane reality. And the more open minded, metaphysically oriented, or even mentally unstable commonly have other worldly experiences."
"Yes," I went on, "I think though the mentally unstable generally see that which is a reflection of their inner turmoil, and in turn subjectively interpret it in an unhealthy manner. Those more stable people who have metaphysical experiences can still discern the difference between the generally agreed upon collective definition of reality from the experience they are having. They know the difference between the worlds without mixing them up."
"Yes, my dad concurred. "This is why grounding is important for existential explorers."
"I know it is for me. I am glad I had children for they are the best anchors of all!"
Then I realized that we were in an anchoring spot. I murmured aloud, "I think we are in the moment here. I mean not the surface moment. The surface moment can be unpleasant, like the flu, but going deeper into the moment, we go deeper into ourselves, like going into a cave away from outer world clamor. I find great solace in this mind state, and almost omnipotent beyond identity."
My dad said, "Me too. From here, in the deep moment, it seems that our dramatic realities are just slivers of perception, puffs of imagery that briefly come alive. Even as our memories slip into our present, they are filtered through our current and ever changing perceptions. New meaning is assigned to everything. This then changes the shape of our past and future, and on we go to new dramas. From here, in the deep moment, however, it is so easy to see how subjective reality is."
Struck by an epiphany, I gasped. "There are two sides to a moment. One quiet, like this, and the other active. The active side is when we feel truly alive, when we laugh, or cry, are fighting for our lives, or feel our hearts spill over with love."
"Very good, Sue," my dad said. "No matter what side of the moment we are on, there is no time. We are not thinking of tomorrow or yesterday. In the purity of a single moment that has captivated our complete focus, we touch the source of creation."
I just couldn't believe how much my dad was sounding like My Fool. Then again, those so near Pure Creative Energy probably would sound a lot alike, as their connection with their identity is extremely loosened.
We remained in this quiet state for some time as if attuning ourselves, or catching up to ourselves.
Then suddenly My Fool powered us into what seemed to be a crystalline world that went into a deeper crystalline world, on and on. Or maybe outside a crystalline world into a larger crystalline world, on and on. When one gets this far into inner space, directions seem the same. Maybe they are.
It seemed then that our butterfly formation broke apart, and the three of us were floating along, side by side, through crystalline worlds going into, or out of, world after world.
I asked My Fool, "Does it ever end, this trek through the crystalline portals?"
"Not like this, for they are infinite. The real treasure lies not in the journey, but what powers the journey."
"What do you mean?"
My dad chimed in. "He means the Creative Energy that makes the journey possible."
We slowed our flight, slower, slower, and the crystalline world we were in shone thousands of doors on either side of us. Some opened as we passed and other remained closed.
I asked, "Why are some opening and others not?"
My Fool answered, "If we were more spread out, you'd see that doors open only in if the vibration of who are matches what is on the other side."
"Oh," my brows furrowed, "so a door that opens for you, might not open for me?"
He nodded.
"Well, what lurks behind the doors?"
"Passageways."
"Where do they lead?"
"Everywhere, and no where."
"What do you mean?"
"Well," My Fool looked toward a door. "Let us each enter a door that opens for us and follow the passageway as far as we can, and see what happens."
"Are there any dead ends? What if I get trapped? Can I come back this way and find you here?"
My Fool shook His head. "You're getting ahead of yourself, hummingbird girl. Settle into the moment and just stay there."
I scowled, "Okay." I said hesitantly."
My Fool walked ahead of us for awhile, then I started moving. A few moments later, I felt my dad following. A door opened for me almost instantly. Following instructions, I entered. Behind my door was a corridor. I could hear voices and sensed a heaviness about me, and noticed that this corridor also had many other doors on either side, some open, some shut. I really didn't want to get lost or distracted in here, so I kept to the corridor and proceeded.
The corridor seemed to broaden as I walked, until the actual walls seemed to fall away, and I was suddenly in an expansive sphere of light. I felt expanded, exalted, and energized, free of all concern and void of fear. I sensed then, that my dad and Fool were here too. Then I could see them. We all seemed rather porous but also had image.
"Well?" My Fool looked at me.
I answered, "All paths lead here. I am guessing even if I went into doors after door into the maze, eventually they would all lead here."
"Where is here?"
"Where time and place are conceived, and dissolved?"
My Fool nodded. "In the simplest sense, yes."
Before anyone could say another word, we seemed to be absorbed into the energy ball, going deeper into the brilliant white, condensing into each other as the ball itself seemed to collapse within. Suddenly, we sprayed outward, but it was different from when I had sprayed outward into my totality. This time it seemed we sprayed outward into 'the' totality. Every particle was I, or all of us, or Pure Creative Energy. My identity must have been anchored somewhere as I could still feel it, and was conscious of having this experience.
I startled a bit to hear My Fool speak, as we all seemed beyond persona and expanded. "This moment is our focus, therefore, it is the only moment there is. When we experience both sides of the moment, quiet and active, as you have discovered, Susan, then the moment becomes the entire world as we know it, boundaries dissolve, and we begin to feel 'all there is' beyond conscious understanding." He paused, then said, "And Robert, your moment is now. We have one last stop to make."
We drifted downward, falling through space, at first feeling like billions of particles, but then coming back into form. We landed in the South Pacific, watching a black woman on a golden sand beach in labor, another woman at her feet aiding her.
My mouth fell open. "It is time, isn't' it?"
My Fool nodded.
My dad said, "I am in there, in her womb, aren't I?"
My Fool looked to my dad and nodded.
I glanced at my dad, and noticed a faint energy cord between his heart and mine. It felt restrictive, as if my dad was having a hard time moving on because a part of me held on so tight. I swallowed hard, staring at my dad's profile. "I love you dad," I murmured, "good bye." I sucked in a trembling breath. "I know we are one. Focus on your next adventure." I gulped back tears as I consciously released him and concentrated on our oneness beyond identity. I felt a popping of sorts and the cord disappeared.
My dad looked at me. Returning his gaze, I smiled faintly and nodded with teary breath. "Let the music play."
His head tilted with a faint smile. "I won't be far, just getting a fresh set of clothes, a new job, a new location. I will just be moving across the street, as my old body barely works any more."
I had a quick flash of where we were at in our physical bodies. Then suddenly I was back in my dad's house helping him up the stairs to his loft. I had moved his music back up there so he could do as he had so loved. I helped him sit in his purple chair where he adored looking out the big picture window at the desert wildlife.
As he looked out the window at the setting sun, I pressed the cd player button as if setting the stage for his death. Mahler's second symphony that had been playing in the inner world, played here.
I sat in the chair next to him. I felt his energy dip down and in, as if consciously connecting to Sallee
"I have fulfilled my intent as Robert. The curtain now closes. One last kick of the can in the life of Sallee, as the others in my plurality experience theirs. This last life marks the end of my soulic journey on all earths."
How strange it was to think of my dad nearing the finish of experiencing earth, or earths, save one more go around. He had been gathering his plurality, readying to jump the grid to another earth, so like ours, only with variations. I found it so interesting that the earths affected each other, just as the many selves in our plurality do. And I suppose all the Great Selves affect each other as well. Of course, why not, if indeed we are all one energy.
Words emerged from my dad's lips, "You have released me, now I must release me. I am now tasked with experiencing what all the cells already know and feeling the last of the smoking cinders of he whom I have known—as Robert." He sighed a shaky breath, "I am between here and nowhere turning inside out milking the last of my emotions as Robert, the emotions that hold me to him. In this, I hoist up that anchor and prepare to sail away. The final release is upon me."
My face was full of liquid pain, a good and sad sweet pain of goodbye coupled with knowing my dad would soon be free.
He paused, then said. "I need to rest now, Sue."
I nodded, not wanting to leave him, but felt he needed that time alone to do this last bit of inner work.
An hour later, I returned to check on him. Night had descended, so I flipped on the light that led up the stairs, and went to my dad.
"Sue," he said in a bit of anguish. "Take me outside."
I helped him downstairs and outside. We stretched out on two lounge chairs under a starry sky, gazing upward. And there it was again, Mahler's second symphony finding our ears without a cd player.
He said, "I cannot tell if I am home anymore. My identity is fading. Before I came out here, I felt momentarily lost. But gazing at this night sky, I am found. A brief moment on the wind before I am reborn into Sallee. She will remember the oneness, for as I am so near to ending my human experience, there is no need to forget." Tears of seeming joy streamed down his cheeks, glistening in the subtle glow of moonlight.
Something warm filled me, and strangely, it felt like My Fool. My dad's head lifted slightly and I surmised he felt this too. I heard My Fool speak, and I have no doubt so did my dad. "This day of days, after a night of nights, it begins for the first time."
My breath trembled, my dad's too, as our eyes lifted upward to behold a meteor shower, I almost choked on my own breath for the beauty of it all. Was I really seeing this? The shower, like the spray of our pluralities, beautified everything.
The sweeping notes of Mahler's second symphony mounted. My Fool's voice whispered and seemed to echo in the night sky, "It . . . is I. It is I. It is I. Don't you know who I am?"
I looked to my dad. His eyes were closed, lashes wet, and a small smile on his face. He seemed to be feeling a quiet beauty as if looking through the window to his soul.
Christopher mewed at the foot of my lounge chair. I was momentarily paralyzed to acknowledge him as the music and chorus of voices exploded into unfathomable magnificence in the middle of the last movement. After a moment, I reached down and pulled his little body up onto my lap, and held him near my heart, hugging him tight for I needed to hug something. "The journey of one is the journey of all!" I cried out in a whisper so that I could let my dad go.
Suddenly, my consciousness zoomed inward, deeper and deeper into what felt like a dream. In the dream, I was in the dark. I saw my father, but he was incorporeal. I knew he was dying. I knew it, but I'd rather be here to say goodbye than consciously watch his body slip away.
He started running. I chased after him, not to hold him back but to see him off. I noticed then we were running through a dark corridor. On the sides of the corridor were open doors with entities standing there. As he ran by them, one by one they jumped into his running form, making him glow brighter and brighter.
He was running, running, running, inhumanely fast, as if on a mission. Ahead, way ahead, I glimpsed rays of light shining through an opening, cliché as it sounds, it was the light at the end of the tunnel, his tunnel, the life of Robert. And there at the end, I thought I saw a face, a dark skinned face, a child and yet a woman. She was not an old life, but a new life.
My dad ran faster as if the music was drawing him out. I found that I was slowing down even though I didn't feel breathless. It was as if gravity was holding me back. He got further and further ahead of me, picking up speed against my stifled pace.
I heard the music grow louder, even though I was far away. I kept pushing on, although it was getting harder and harder to do so.
My dad reached the opening just as the last symphony notes played out in a chorus of voices at peak intensity. Then I saw an amazing thing. My Fool was at the exit where the light shined in.
An object came sailing toward me. As it neared, it appeared to be a hyphen, comma, and period connected. Splashing into me, I felt it to be the between worlds, the pause between breaths; it was the blink.
My Fool's voice sounded in my brain. The gem of Intermundium, the space between worlds. I heard My Fool in my head. "A moment into everything, between the worlds of time. The blink takes us here and there, yet in the blink, we are neither here, nor there, but everywhere."
I glanced at my wrist, and saw the eleventh charm of Intermundium on my bracelet. Focusing back on my dad, My Fool jumped into him as he shot outside the tunnel into the stars. Then, just like the scene in science fiction movies, he split into two Roberts, each going a different direction, one into Sallee, and the other into Pure Creative Energy.
I abruptly came to conscious awareness, and whipped my head to my dad in the lounge chair next to me. All was silent. My dad's moonlit face was in repose, eyes closed, that slight smile yet upon his face. Christopher was sitting on his stilled chest.
I pressed my ear to dad's mouth. I felt no breath. I pressed on his neck. I felt no pulse.
He was free. At long last, he was free. My dad had grown into age and beyond, into Sallee and yet also, into the infinite music of being.
I sat there for a long while absorbing that reality before calling the coroner, my brother, and my sister. We all came together in bittersweet pain hinted with joy for our dad and his new lease on life, as the coroner wheeled my dad's body away.
Later that night I spent a long while under the stars, lying in a lounge chair with Christopher curled on my chest. I was in such a deep pure state that the pain was kind of beautiful. Words came to my head, but I did not speak them. However, I did write them down.
##
THE CONFINES OF THESE wild days of human living have left me bereft at moments, sometimes minutes, hours or days, and rarely years, but and all in all not for terribly long. Diving into my ethereal world beneath the waves of the great long play on the earthly stage, I can always feel my pure essence, a vibrant force, like that of the sun and all the natural world.
A new life. An old life. And all the stages in between, melding into a continuous circle. The old are young and the young are old, endless, eternal, this life force that is everywhere and in all things. And yet in the grand illusion, the reflection epitomized by mundane living is beauteous in its own right. It is the manifestation of Creative Energy creating beyond what it is.
There is no here here or there there, or you or me or this or that in wholeness. Wholeness holds the power of earth and heavens of every drop in the ocean and molecule in existence. And in the experience of totality, of wholeness, of oneness, we are all of it. We are our enemies and friends and strangers. We are seeming cruelty and great compassion.
There is nothing to save and everything to save, and only we can save our selves. We are the mirror and the reflection, experimenting, experiencing, dancing, playing across the dimensions of seeming time and space.
What is—is. The vibration of what is shines outward and no person or group of people can stifle the beauty of a thing no matter how hard the effort. While things seemingly feel unfair, in the greater scope, everything is as it should be in synchronicity with all existence.
##
LATER THAT WEEK ON a very blustery day, my brother, sister, and I, took my dad's ashes, and my mother's too (which none of us could previously bear to scatter) to the top of a mountain near their home where they spent so many years together. When a big wind came, we simultaneously let the ashes fly out of the respective boxes. The ashes mingled together in flurries, with big winds carrying them outward. We watch them ride the winds together, far and away, into realms that skeptics call make-believe.
But it didn't matter what I thought or anyone thought about what happens when we die, skeptics and dreamers alike, for it is what it is. And as I exhaled, I felt my breath matriculate with the wind as a kiss goodbye. My brother, sister, and I held hands, looking at each other tearfully. And then we smiled lightly, all was as it should be, all was well, and we felt each other as peas in a pod, born of our parents and lovingly joined until the end of our current journey. Our family fully united, at last.
Life . . . in all its mystery, of turmoil and sweet joy, was . . . Well it just was, and that was good enough for me.
∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞∞
We are always and forever one. Remember this when loneliness bids you cry, or anger spurs you to lash. Remember this when life seems too hard, or people too cruel. Oh, to play the play, to have the guts and fortitude to see it through. Like fireflies gathering light, or drops making an ocean, we are singular, yet whole, working together, even though it may feel like we are working apart.
Then this great adventure we all share far transcends our personal drama, and yet our personal drama adds so much to our shared adventure. Behold your "I" in reverence, as sacred and holy beyond surface judgment. And in that moment, so too shall you touch plurality bequeathing love to all.
| |
---|---|---
# Note from the Author
Thank you for reading, and please remember to leave a review! For Updates on sales and new releases, please sign up for my mailing list by following the link below:
<http://eepurl.com/b2Ymo5>
| |
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# About the Author
Susan was born in Seattle, WA. Her first profession was a psychotherapist treating those suffering from depression, anxiety, post-traumatic stress, substance abuse, sexual abuse, family violence, and severe mental illness. She employed therapies such as communication skill building, relaxation training, systematic desensitization, bioenergetics, and psychodrama. She has facilitated stress management, parenting, and self-discovery workshops that have aided in the psycho-spiritual healing of many. She has lectured on metaphysical and psychological topics, and been involved in various social activist pursuits.
Her education includes an M.A. in Ed. in Counseling/Human Relations and Behavior (NAU), a B.S. in Sociology (ASU), and ten months of psychological and metaphysical training in a Tibetan community.
Susan writes entertaining books steeped in psychology, sociology, and metaphysics in genres such as visionary fiction, dark fantasy, horror, and romance. All her books are designed to facilitate personal growth and transformation.
In her words: I love to sing, meditate, and play in nature. I love fairy tales, going outside the box, and reading between the lines. I strive to see what is often missed, and to not miss what can't be seen. There is such a life out there, and in there—beyond all perception! So I close my eyes, feel my inner rhythm, and jump off the cliff of convention. And when I land, though I might be quaking in my boots, I gather my courage and go exploring.
Through travel, study, and work, I've gained a rich awareness of cultural differences among people and their psychosocial struggles. I have discovered that oppression often results from the unexamined adoption of outside perceptions. The healing always has been in the individual's stamina to expel outside perceptions of self and constructively exert one's unique core being into the world. I am driven to facilitate expanded awareness that people may separate who they are from who they are told to be. Embracing personal power by loving our unique selves in our strengths and weaknesses . . . forever—is a key to joyous living. My motto is: Trust your story. Live the Mystery.
| {
"redpajama_set_name": "RedPajamaBook"
} | 4,382 |
Most FAU students aren't voting in Student Government elections
Less than 10 percent of FAU's 28,000 students voted for student body president this year despite Student Government's efforts to promote the election.
Political science professor denies ties to white supremacy
Marshall DeRosa is denying any accusations of racism and white supremacy after receiving generous grants from the Koch Foundation caught the eye of a non-profit campaign.
Opinion: Writing about Owlsley shouldn't be this difficult
The school's spirit department takes itself too seriously. Instead of a feature on the life of a university mascot, I was given half truths and tall tales
FAU Relay for Life raises thousands for cancer research
The annual event hosted 33 teams of FAU students, faculty, and members of the community to take laps around the Boca campus track and field.
Comparing campus sustainability programs at Florida universities
A look at the eco-friendly initiatives at six public Florida universities and their recycling and environmental efforts.
Washington Post columnist talks Trump presidency, social media's influence
Eugene Robinson spoke as part of an annual lecture series.
A look at the Boca campus' history as a former U.S. air base
The Boca Raton Army Air Field eventually aided the Allies to win the second world war.
Police Chief Sean Brammer talks why he became an officer, his goals for the department
Brammer was in his 20s studying civil engineering before he found his calling for law enforcement. Today, he works to ensure the safety of more than 30,000 college students
FAU to host Black History Month events
The events will appear on the Boca, Davie, and Jupiter campuses.
FAU provost to step down
Dr. Perry was appointed as FAU provost and Vice President for Academic Affairs in 2014.
Students respond to completed Breezeway
Students were asked if the Breezeway construction was worth the wait.
FAU senior starts Adaptive Tennis program
Oscar Fonseca is bringing one of the most popular sports in Florida to local children with disabilities. | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,601 |
Q: Repositioning pagenumber field in the pager of a jqgrid I am using jqgrid in my cshtml page. The problem is that the area for grid is narrow, and so I want the page number field in the pager of grid to appear somewhere else in the page near the grid. I need relocating the page number field only, not the pager itself.
A: The page number field is a part of the pager itself and so cannot be separated from the same. But there is a workaround for this. You can set the variable pginput to false as given on the link . It determines if the input box, where the user can change the number of the requested page, should be available. So on setting false it will not appear to the user. Using the code given below, you can get the current page number of the grid and set into any text box defined by you on the page.
$('#your_grid').getGridParam('page'); // get current page
When user changes the page number, all you need to do is set the page number using code below.
$('#your_grid').setGridParam({page:value}).trigger('reloadGrid'); // set page to grid and reload. value is the page number to be set
This code should be handled within keydown function of the text box defined by you to hold the page number.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,748 |
Промислова революція ПросвітництвоРосійська імперіяВелика французька революція
Геополітична ситуація
В Османській імперії султан Селім III (до 1807). Під владою османів перебувають Близький Схід та Єгипет, Середземноморське узбережжя Північної Африки, частина Закавказзя, значні території в Європі: Греція, Болгарія і Сербія. Васалами османів є Волощина та Молдова.
Священна Римська імперія охоплює крім німецьких земель Угорщину з Хорватією, Трансильванію, Богемію, Північ Італії, Австрійські Нідерланди. Імперію очолює Франц II (до 1835). У Пруссії править Фрідріх-Вільгельм II (до 1797).
У Французькій республіці завершилася Епоху терору. Франція має колонії в Північній Америці та Індії. Король Іспанії — Карл IV (до 1808). Королівству Іспанія належать південь Італії, Нова Іспанія, Нова Гранада, Віце-королівство Перу, Внутрішні провінції та Віцекоролівство Ріо-де-ла-Плата в Америці, Філіппіни. У Португалії королює Марія I (до 1816). Португалія має володіння в Бразилії, в Африці, в Індії, в Індійському океані й Індонезії. На троні Великої Британії сидить Георг III (до 1820). Британія має колонії в Північній Америці, на Карибах та в Індії.
Сполучені Штати Америки займають територію частини колишніх британських колоній. Президент США — Джордж Вашингтон. Територія на півночі північноамериканського континенту, що належить Великій Британії, розділена на Нижню Канаду та Верхню Канаду, територія на півдні та заході континенту належить Іспанії й Франції.
Північ Нідерландів займає Республіка Об'єднаних провінцій. Вона має колонії в Америці, Індонезії, на Формозі та на Цейлоні. Король Данії та Норвегії — Кристіан VII (до 1808), на шведському троні сидить Густав IV Адольф (до 1837). На Апеннінському півострові незалежні Венеціанська республіка та Папська область. Король Речі Посполитої — Станіслав Август Понятовський (до 1795). У Російській імперії править Катерина II (до 1796).
Україну розділено між трьома державами. Королівство Галичини та Володимирії належить Австрії. Правобережжя розділене між Річчю Посполитою та Російською імперією. Лівобережя та Крим належать Російській імперії. Задунайська Січ існує під протекторатом Османської імперії.
В Ірані закінчилося правління династії Зандів, до влади прийшли Каджари. Імперія Маратха контролює значну частину Індостану. Зростає могутність Британської Ост-Індійської компанії. У Бірмі править династія Конбаун. У Китаї володарює Династія Цін. В Японії триває період Едо.
Події
В Україні
2 вересня указом Катерини II порту Хаджибей були виділені гроші на реконструкцію. У 1795 році Хаджибей перейменували в Одесу
У світі
4 березня Національний конвент скасував рабство у Франції.
12 березня польський генерал Антоній Мадалінський відмовився розпустити свої підрозділи й повів їх на Краків.
23 березня Британія захопила Мартиніку.
24 березня Тадеуш Костюшко виголосив прокламацію й розпочав повстання проти окупації Речі Посполитої військами Російської імперії й Пруссії.
4 квітня війська Речі Посполитої під проводом Костюшка здобули перемогу над росіянами в битві під Рацлавицями.
5 квітня у Франції страчено Жоржа Дантона.
17-19 квітня у Варшаві відбувся напад на російський гарнізон. Жителі міста приєдналися до повстання Костюшка.
19 квітня Росія, Велика Британія та Пруссія утворили союз проти революційної Франції.
7 травня Робесп'єр проголосив у Франції культ Верховної Істоти державною релігією.
8 травня в Парижі страчено 28 членів генерального відкупу, зокрема відомого хіміка Антуана Лавуазьє.
18 травня французька революційна армія здобула перемогу над британцями у битві під Туркуеном.
4 червня британці захопили Порт-о-Пренс на Гаїті.
17 червня виникло Англо-корсиканське королівство.
26 червня французи виграли битву при Флерюсі, що призвело до остаточної втрати Австрійських Нідерландів та падіння Республіки об'єднаних провінцій.
13 липня почалася облога Варшави російсько-прусськими військами.
17 липня у Парижі страчено 16 комп'єнських мучениць.
27 липня (9 термідора ІІ року за революційним календарем) термідоріанський переворот повалив у Франції якобінську диктатуру.
23 вересня французи захопили Аахен.
28 вересня Австрія, Росія та Британія уклали союз проти Франції.
2 жовтня французька революційна армія виграла битву при Альденговені й повністю окупувала Австрійські Нідерланди.
4 жовтня президент США востаннє вів війська в бій при придушенні повстання через віскі.
10 жовтня російські війська перемогли прихильників повстання Костюшка у битві при Мацейовицях. Поранений Тадеуш Костюшко потрапив у полон.
4 листопада російські війська Олександра Суворова взяли штурмом передмістя Варшави Прагу.
18 листопада США та Велика Британія підписали Договір Джея, врегулюввавши взаємні відносини.
В Ірані до влади прийшли Каджари, полонивши й стративши останнього шаха із Зандів.
Наука і культура
Ернст Флоренс Фрідріх Хладні висловив припущення, що метеорити виникли в космосі.
Ладзаро Спалланцані звобив висновок, що кажани послуговуються іншим засобом, відмінним від зору, для орієнтації в темряві.
Еразм Дарвін опублікував перший том «Зоономії».
Медаль Коплі отримав Алессандро Вольта.
Засновано Університет Теннессі.
Засновано Політехнічну та Нормальну школи.
У Парижі відкрито Музей мистецтв і ремесел.
Томас Пейн опублікував трактат «Століття розуму».
Засновані
Республіка Буйон
Корсиканське королівство
Литовське генерал-губернаторство
Зникли
Занди
Брієнн (графство)
Буйон (герцогство)
Юліх-Берг
Прусський Гелдерланд
Народились
див. також :Категорія:Народились 1794
27 травня — Корнелій Вандербільт, американський індустріаліст, залізничний магнат
Померли див. також :Категорія:Померли 1794''
27 жовтня — Григорій Сковорода, найвидатніший український просвітитель-гуманіст, філософ, поет, педагог.
1790-ті | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 5,202 |
A Star Trek Spin-Off Series Starring Michelle Yeoh? Yes Please.
The Crazy Rich Asians star is in talks to lead her own CBS All Access series.
By Chelsea SteinerNov 10th, 2018, 3:29 pm
SPOILER ALERT: This post will discuss plot points from Star Trek: Discovery.
CBS All Access is in talks with Michelle Yeoh to star in her own spin-off Star Trek series for the streaming channel. Yeoh, who was the first actor cast in Star Trek: Discovery, played a recurring role in the series as Captain Philippa Georgiou of the USS Shenzhou, as well as the mirror universe's Emperor Georgiou.
It is still unknown which version of Georgiou will lead the series, with many speculating that her story will take place in Starfleet's Section 31 division. This is great news, as Yeoh is a captivating and always welcome presence on screen. She most recently co-starred in Crazy Rich Asians, but is perhaps best known for her role as Yu Shu Lien in Crouching Tiger, Hidden Dragon.
Section 31 🖖🏻🖖🏻🖖🏻 @startrekcbs
A post shared by Michelle Yeoh 楊紫瓊 (@michelleyeoh_official) on Oct 6, 2018 at 7:23pm PDT
As the first (and most well known) actor cast in Discovery, viewers were excited to see a woman of color helming her own ship alongside another woman of color, Sonequa Martin-Green's First Officer Michael Burnham. It was disappointing then, when Georgiou was killed off at the end of the second episode. Many fans had tuned in to see Michelle Yeoh in the captain's seat, so the plot twist felt like a bait and switch.
The Georgiou spin-off joins several other Star Trek projects currently in development at CBS All Access, including Patrick Stewart's Picard spin-off and an upcoming animated comedy series Star Trek: Lower Decks, which already has a two season order. Lower Decks comes from Mike McMahan (Rick and Morty), and will be a workplace comedy about the grunts at the bottom of the food chain.
Yeoh is already confirmed to reappear in season two of Discovery, which will likely launch her spin-off series. The actress has a busy year ahead of her: in addition to a potential Crazy Rich Asians sequel, Yeoh has signed an overall deal with SK Global Entertainment, with a first look deal for her to produce, direct and act in select projects.
Yeoh said of the deal, "I'm truly excited to continue my relationship with Ivanhoe and SK Global to develop stories that bridge cultures. The success of Crazy Rich Asians has shown us that there are many more wonderful stories to tell from around the globe and I am delighted to partner with this very creative and wonderful team."
Are you excited for a Captain Georgiou spin-off, or just psyched to see Michelle Yeoh get cast in all the things?
(via Hollywood Reporter, image: CBS All Access)
CBS All AccessMichelle YeohStar Trek (franchise)
Chelsea Steiner
Chelsea was born and raised in New Orleans, which explains her affinity for cheesy grits and Britney Spears. She currently lives in sunny Los Angeles, with her husband and two poorly behaved rescue dogs. She is a former roller derby girl and a black belt in Judo, so she is not to be trifled with. She loves the word "Jewess" and wishes more people used it to describe her.
More Stories by Chelsea Steiner
A Primer on All You Need to Remember Ahead of Picard
Star Trek 4 Director Says the Movie Will Be a Return to the Essence of Trek
Quentin Tarantino Might Drop out of Star Trek and … Yes Please?
6 Women of Star Trek and What We Can Learn From Them
Things We Saw Today: Rest in Peace, René Auberjonois
Unpacking How We Feel About Noah Hawley Directing the Next Star Trek Movie | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 6,435 |
===============================
django-openstack-auth-websso
===============================
Federated Single Sign On for OpenStack Dashboard"
* Free software: Apache license
* Documentation: http://docs.openstack.org/developer/django-openstack-auth-websso
* Source: http://git.openstack.org/cgit/openstack/django-openstack-auth-websso
* Bugs: http://bugs.launchpad.net/django-openstack-auth-websso
Features
--------
* TODO
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,906 |
Q: Derive DC motor formula with drum driving a conveyor belt The setup is a DC motor directly connected via its shaft to a drum which drives a horizontal conveyor belt. There is a load of mass, M, on the conveyor belt.
I am stuck on trying to figure out what 'D' in the equation below means.
Title: Pulley, Conveyor Belt & Load system
Description: Load-Inertia to the motor consists of pulley (of radius r) and mass of load (M) on conveyor belt. The load-torque, to be delivered by the motor is given as:
where,
M is the mass of load on the conveyor belt.
r is the drum radius
ω = angular velocity
But i don't know what D means and i cannot figure out how that equation was derived in the first place. Any help would be much appreciated.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 1,190 |
Q: Has anyone done a Javascript front end to a commercial rules engine? If so, did you use a JS templating framework (like Moustache or Jade) and CSS preprocessor (like LESS or Stylus) or let the BRE handle it all?
A: If I understood correctly you want to use the rules engine to control the client side.
One example that does something like this is TOHU.
Tohu is an engine built on Drools to create dynamic UIs. It is an alternative to the traditional MVC approach which instead uses a generic UI layer to render arbitrary UIs defined using simple business rules.
A: I am working on a product that uses a quite sophisticated rule engine, so that you can "drop in" a set of rules to radically change the behavior of the system without having to change the system code.
Initially our rule engine was .NET based, but we are now considering migrating to a JS rule engine so that we can execute both client and server side. Then we can use handlebars to keep the view in sync with the js model and bind the rules to model events.
Of course you'll want to double check server side that the rules executed on the client have been adhered to, so you can execute the same code server side to verify.
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 7,642 |
/*
* linux/fs/fat/inode.c
*
* Written 1992,1993 by Werner Almesberger
* VFAT extensions by Gordon Chaffee, merged with msdos fs by Henrik Storner
* Rewritten for the constant inumbers support by Al Viro
*
* Fixes:
*
* Max Cohan: Fixed invalid FSINFO offset when info_sector is 0
*/
#include <linux/module.h>
#include <linux/pagemap.h>
#include <linux/mpage.h>
#include <linux/vfs.h>
#include <linux/seq_file.h>
#include <linux/parser.h>
#include <linux/uio.h>
#include <linux/blkdev.h>
#include <linux/backing-dev.h>
#include <asm/unaligned.h>
#include "fat.h"
#ifndef CONFIG_FAT_DEFAULT_IOCHARSET
/* if user don't select VFAT, this is undefined. */
#define CONFIG_FAT_DEFAULT_IOCHARSET ""
#endif
#define KB_IN_SECTORS 2
/*
* A deserialized copy of the on-disk structure laid out in struct
* fat_boot_sector.
*/
struct fat_bios_param_block {
u16 fat_sector_size;
u8 fat_sec_per_clus;
u16 fat_reserved;
u8 fat_fats;
u16 fat_dir_entries;
u16 fat_sectors;
u16 fat_fat_length;
u32 fat_total_sect;
u8 fat16_state;
u32 fat16_vol_id;
u32 fat32_length;
u32 fat32_root_cluster;
u16 fat32_info_sector;
u8 fat32_state;
u32 fat32_vol_id;
};
static int fat_default_codepage = CONFIG_FAT_DEFAULT_CODEPAGE;
static char fat_default_iocharset[] = CONFIG_FAT_DEFAULT_IOCHARSET;
static struct fat_floppy_defaults {
unsigned nr_sectors;
unsigned sec_per_clus;
unsigned dir_entries;
unsigned media;
unsigned fat_length;
} floppy_defaults[] = {
{
.nr_sectors = 160 * KB_IN_SECTORS,
.sec_per_clus = 1,
.dir_entries = 64,
.media = 0xFE,
.fat_length = 1,
},
{
.nr_sectors = 180 * KB_IN_SECTORS,
.sec_per_clus = 1,
.dir_entries = 64,
.media = 0xFC,
.fat_length = 2,
},
{
.nr_sectors = 320 * KB_IN_SECTORS,
.sec_per_clus = 2,
.dir_entries = 112,
.media = 0xFF,
.fat_length = 1,
},
{
.nr_sectors = 360 * KB_IN_SECTORS,
.sec_per_clus = 2,
.dir_entries = 112,
.media = 0xFD,
.fat_length = 2,
},
};
int fat_add_cluster(struct inode *inode)
{
int err, cluster;
err = fat_alloc_clusters(inode, &cluster, 1);
if (err)
return err;
/* FIXME: this cluster should be added after data of this
* cluster is writed */
err = fat_chain_add(inode, cluster, 1);
if (err)
fat_free_clusters(inode, cluster);
return err;
}
static inline int __fat_get_block(struct inode *inode, sector_t iblock,
unsigned long *max_blocks,
struct buffer_head *bh_result, int create)
{
struct super_block *sb = inode->i_sb;
struct msdos_sb_info *sbi = MSDOS_SB(sb);
unsigned long mapped_blocks;
sector_t phys, last_block;
int err, offset;
err = fat_bmap(inode, iblock, &phys, &mapped_blocks, create, false);
if (err)
return err;
if (phys) {
map_bh(bh_result, sb, phys);
*max_blocks = min(mapped_blocks, *max_blocks);
return 0;
}
if (!create)
return 0;
if (iblock != MSDOS_I(inode)->mmu_private >> sb->s_blocksize_bits) {
fat_fs_error(sb, "corrupted file size (i_pos %lld, %lld)",
MSDOS_I(inode)->i_pos, MSDOS_I(inode)->mmu_private);
return -EIO;
}
last_block = inode->i_blocks >> (sb->s_blocksize_bits - 9);
offset = (unsigned long)iblock & (sbi->sec_per_clus - 1);
/*
* allocate a cluster according to the following.
* 1) no more available blocks
* 2) not part of fallocate region
*/
if (!offset && !(iblock < last_block)) {
/* TODO: multiple cluster allocation would be desirable. */
err = fat_add_cluster(inode);
if (err)
return err;
}
/* available blocks on this cluster */
mapped_blocks = sbi->sec_per_clus - offset;
*max_blocks = min(mapped_blocks, *max_blocks);
MSDOS_I(inode)->mmu_private += *max_blocks << sb->s_blocksize_bits;
err = fat_bmap(inode, iblock, &phys, &mapped_blocks, create, false);
if (err)
return err;
BUG_ON(!phys);
BUG_ON(*max_blocks != mapped_blocks);
set_buffer_new(bh_result);
map_bh(bh_result, sb, phys);
return 0;
}
static int fat_get_block(struct inode *inode, sector_t iblock,
struct buffer_head *bh_result, int create)
{
struct super_block *sb = inode->i_sb;
unsigned long max_blocks = bh_result->b_size >> inode->i_blkbits;
int err;
err = __fat_get_block(inode, iblock, &max_blocks, bh_result, create);
if (err)
return err;
bh_result->b_size = max_blocks << sb->s_blocksize_bits;
return 0;
}
static int fat_writepage(struct page *page, struct writeback_control *wbc)
{
return block_write_full_page(page, fat_get_block, wbc);
}
static int fat_writepages(struct address_space *mapping,
struct writeback_control *wbc)
{
return mpage_writepages(mapping, wbc, fat_get_block);
}
static int fat_readpage(struct file *file, struct page *page)
{
return mpage_readpage(page, fat_get_block);
}
static int fat_readpages(struct file *file, struct address_space *mapping,
struct list_head *pages, unsigned nr_pages)
{
return mpage_readpages(mapping, pages, nr_pages, fat_get_block);
}
static void fat_write_failed(struct address_space *mapping, loff_t to)
{
struct inode *inode = mapping->host;
if (to > inode->i_size) {
truncate_pagecache(inode, inode->i_size);
fat_truncate_blocks(inode, inode->i_size);
}
}
static int fat_write_begin(struct file *file, struct address_space *mapping,
loff_t pos, unsigned len, unsigned flags,
struct page **pagep, void **fsdata)
{
int err;
*pagep = NULL;
err = cont_write_begin(file, mapping, pos, len, flags,
pagep, fsdata, fat_get_block,
&MSDOS_I(mapping->host)->mmu_private);
if (err < 0)
fat_write_failed(mapping, pos + len);
return err;
}
static int fat_write_end(struct file *file, struct address_space *mapping,
loff_t pos, unsigned len, unsigned copied,
struct page *pagep, void *fsdata)
{
struct inode *inode = mapping->host;
int err;
err = generic_write_end(file, mapping, pos, len, copied, pagep, fsdata);
if (err < len)
fat_write_failed(mapping, pos + len);
if (!(err < 0) && !(MSDOS_I(inode)->i_attrs & ATTR_ARCH)) {
inode->i_mtime = inode->i_ctime = CURRENT_TIME_SEC;
MSDOS_I(inode)->i_attrs |= ATTR_ARCH;
mark_inode_dirty(inode);
}
return err;
}
static ssize_t fat_direct_IO(struct kiocb *iocb, struct iov_iter *iter,
loff_t offset)
{
struct file *file = iocb->ki_filp;
struct address_space *mapping = file->f_mapping;
struct inode *inode = mapping->host;
size_t count = iov_iter_count(iter);
ssize_t ret;
if (iov_iter_rw(iter) == WRITE) {
/*
* FIXME: blockdev_direct_IO() doesn't use ->write_begin(),
* so we need to update the ->mmu_private to block boundary.
*
* But we must fill the remaining area or hole by nul for
* updating ->mmu_private.
*
* Return 0, and fallback to normal buffered write.
*/
loff_t size = offset + count;
if (MSDOS_I(inode)->mmu_private < size)
return 0;
}
/*
* FAT need to use the DIO_LOCKING for avoiding the race
* condition of fat_get_block() and ->truncate().
*/
ret = blockdev_direct_IO(iocb, inode, iter, offset, fat_get_block);
if (ret < 0 && iov_iter_rw(iter) == WRITE)
fat_write_failed(mapping, offset + count);
return ret;
}
static int fat_get_block_bmap(struct inode *inode, sector_t iblock,
struct buffer_head *bh_result, int create)
{
struct super_block *sb = inode->i_sb;
unsigned long max_blocks = bh_result->b_size >> inode->i_blkbits;
int err;
sector_t bmap;
unsigned long mapped_blocks;
BUG_ON(create != 0);
err = fat_bmap(inode, iblock, &bmap, &mapped_blocks, create, true);
if (err)
return err;
if (bmap) {
map_bh(bh_result, sb, bmap);
max_blocks = min(mapped_blocks, max_blocks);
}
bh_result->b_size = max_blocks << sb->s_blocksize_bits;
return 0;
}
static sector_t _fat_bmap(struct address_space *mapping, sector_t block)
{
sector_t blocknr;
/* fat_get_cluster() assumes the requested blocknr isn't truncated. */
down_read(&MSDOS_I(mapping->host)->truncate_lock);
blocknr = generic_block_bmap(mapping, block, fat_get_block_bmap);
up_read(&MSDOS_I(mapping->host)->truncate_lock);
return blocknr;
}
/*
* fat_block_truncate_page() zeroes out a mapping from file offset `from'
* up to the end of the block which corresponds to `from'.
* This is required during truncate to physically zeroout the tail end
* of that block so it doesn't yield old data if the file is later grown.
* Also, avoid causing failure from fsx for cases of "data past EOF"
*/
int fat_block_truncate_page(struct inode *inode, loff_t from)
{
return block_truncate_page(inode->i_mapping, from, fat_get_block);
}
static const struct address_space_operations fat_aops = {
.readpage = fat_readpage,
.readpages = fat_readpages,
.writepage = fat_writepage,
.writepages = fat_writepages,
.write_begin = fat_write_begin,
.write_end = fat_write_end,
.direct_IO = fat_direct_IO,
.bmap = _fat_bmap
};
/*
* New FAT inode stuff. We do the following:
* a) i_ino is constant and has nothing with on-disk location.
* b) FAT manages its own cache of directory entries.
* c) *This* cache is indexed by on-disk location.
* d) inode has an associated directory entry, all right, but
* it may be unhashed.
* e) currently entries are stored within struct inode. That should
* change.
* f) we deal with races in the following way:
* 1. readdir() and lookup() do FAT-dir-cache lookup.
* 2. rename() unhashes the F-d-c entry and rehashes it in
* a new place.
* 3. unlink() and rmdir() unhash F-d-c entry.
* 4. fat_write_inode() checks whether the thing is unhashed.
* If it is we silently return. If it isn't we do bread(),
* check if the location is still valid and retry if it
* isn't. Otherwise we do changes.
* 5. Spinlock is used to protect hash/unhash/location check/lookup
* 6. fat_evict_inode() unhashes the F-d-c entry.
* 7. lookup() and readdir() do igrab() if they find a F-d-c entry
* and consider negative result as cache miss.
*/
static void fat_hash_init(struct super_block *sb)
{
struct msdos_sb_info *sbi = MSDOS_SB(sb);
int i;
spin_lock_init(&sbi->inode_hash_lock);
for (i = 0; i < FAT_HASH_SIZE; i++)
INIT_HLIST_HEAD(&sbi->inode_hashtable[i]);
}
static inline unsigned long fat_hash(loff_t i_pos)
{
return hash_32(i_pos, FAT_HASH_BITS);
}
static void dir_hash_init(struct super_block *sb)
{
struct msdos_sb_info *sbi = MSDOS_SB(sb);
int i;
spin_lock_init(&sbi->dir_hash_lock);
for (i = 0; i < FAT_HASH_SIZE; i++)
INIT_HLIST_HEAD(&sbi->dir_hashtable[i]);
}
void fat_attach(struct inode *inode, loff_t i_pos)
{
struct msdos_sb_info *sbi = MSDOS_SB(inode->i_sb);
if (inode->i_ino != MSDOS_ROOT_INO) {
struct hlist_head *head = sbi->inode_hashtable
+ fat_hash(i_pos);
spin_lock(&sbi->inode_hash_lock);
MSDOS_I(inode)->i_pos = i_pos;
hlist_add_head(&MSDOS_I(inode)->i_fat_hash, head);
spin_unlock(&sbi->inode_hash_lock);
}
/* If NFS support is enabled, cache the mapping of start cluster
* to directory inode. This is used during reconnection of
* dentries to the filesystem root.
*/
if (S_ISDIR(inode->i_mode) && sbi->options.nfs) {
struct hlist_head *d_head = sbi->dir_hashtable;
d_head += fat_dir_hash(MSDOS_I(inode)->i_logstart);
spin_lock(&sbi->dir_hash_lock);
hlist_add_head(&MSDOS_I(inode)->i_dir_hash, d_head);
spin_unlock(&sbi->dir_hash_lock);
}
}
EXPORT_SYMBOL_GPL(fat_attach);
void fat_detach(struct inode *inode)
{
struct msdos_sb_info *sbi = MSDOS_SB(inode->i_sb);
spin_lock(&sbi->inode_hash_lock);
MSDOS_I(inode)->i_pos = 0;
hlist_del_init(&MSDOS_I(inode)->i_fat_hash);
spin_unlock(&sbi->inode_hash_lock);
if (S_ISDIR(inode->i_mode) && sbi->options.nfs) {
spin_lock(&sbi->dir_hash_lock);
hlist_del_init(&MSDOS_I(inode)->i_dir_hash);
spin_unlock(&sbi->dir_hash_lock);
}
}
EXPORT_SYMBOL_GPL(fat_detach);
struct inode *fat_iget(struct super_block *sb, loff_t i_pos)
{
struct msdos_sb_info *sbi = MSDOS_SB(sb);
struct hlist_head *head = sbi->inode_hashtable + fat_hash(i_pos);
struct msdos_inode_info *i;
struct inode *inode = NULL;
spin_lock(&sbi->inode_hash_lock);
hlist_for_each_entry(i, head, i_fat_hash) {
BUG_ON(i->vfs_inode.i_sb != sb);
if (i->i_pos != i_pos)
continue;
inode = igrab(&i->vfs_inode);
if (inode)
break;
}
spin_unlock(&sbi->inode_hash_lock);
return inode;
}
static int is_exec(unsigned char *extension)
{
unsigned char exe_extensions[] = "EXECOMBAT", *walk;
for (walk = exe_extensions; *walk; walk += 3)
if (!strncmp(extension, walk, 3))
return 1;
return 0;
}
static int fat_calc_dir_size(struct inode *inode)
{
struct msdos_sb_info *sbi = MSDOS_SB(inode->i_sb);
int ret, fclus, dclus;
inode->i_size = 0;
if (MSDOS_I(inode)->i_start == 0)
return 0;
ret = fat_get_cluster(inode, FAT_ENT_EOF, &fclus, &dclus);
if (ret < 0)
return ret;
inode->i_size = (fclus + 1) << sbi->cluster_bits;
return 0;
}
static int fat_validate_dir(struct inode *dir)
{
struct super_block *sb = dir->i_sb;
if (dir->i_nlink < 2) {
/* Directory should have "."/".." entries at least. */
fat_fs_error(sb, "corrupted directory (invalid entries)");
return -EIO;
}
if (MSDOS_I(dir)->i_start == 0 ||
MSDOS_I(dir)->i_start == MSDOS_SB(sb)->root_cluster) {
/* Directory should point valid cluster. */
fat_fs_error(sb, "corrupted directory (invalid i_start)");
return -EIO;
}
return 0;
}
/* doesn't deal with root inode */
int fat_fill_inode(struct inode *inode, struct msdos_dir_entry *de)
{
struct msdos_sb_info *sbi = MSDOS_SB(inode->i_sb);
int error;
MSDOS_I(inode)->i_pos = 0;
inode->i_uid = sbi->options.fs_uid;
inode->i_gid = sbi->options.fs_gid;
inode->i_version++;
inode->i_generation = get_seconds();
if ((de->attr & ATTR_DIR) && !IS_FREE(de->name)) {
inode->i_generation &= ~1;
inode->i_mode = fat_make_mode(sbi, de->attr, S_IRWXUGO);
inode->i_op = sbi->dir_ops;
inode->i_fop = &fat_dir_operations;
MSDOS_I(inode)->i_start = fat_get_start(sbi, de);
MSDOS_I(inode)->i_logstart = MSDOS_I(inode)->i_start;
error = fat_calc_dir_size(inode);
if (error < 0)
return error;
MSDOS_I(inode)->mmu_private = inode->i_size;
set_nlink(inode, fat_subdirs(inode));
error = fat_validate_dir(inode);
if (error < 0)
return error;
} else { /* not a directory */
inode->i_generation |= 1;
inode->i_mode = fat_make_mode(sbi, de->attr,
((sbi->options.showexec && !is_exec(de->name + 8))
? S_IRUGO|S_IWUGO : S_IRWXUGO));
MSDOS_I(inode)->i_start = fat_get_start(sbi, de);
MSDOS_I(inode)->i_logstart = MSDOS_I(inode)->i_start;
inode->i_size = le32_to_cpu(de->size);
inode->i_op = &fat_file_inode_operations;
inode->i_fop = &fat_file_operations;
inode->i_mapping->a_ops = &fat_aops;
MSDOS_I(inode)->mmu_private = inode->i_size;
}
if (de->attr & ATTR_SYS) {
if (sbi->options.sys_immutable)
inode->i_flags |= S_IMMUTABLE;
}
fat_save_attrs(inode, de->attr);
inode->i_blocks = ((inode->i_size + (sbi->cluster_size - 1))
& ~((loff_t)sbi->cluster_size - 1)) >> 9;
fat_time_fat2unix(sbi, &inode->i_mtime, de->time, de->date, 0);
if (sbi->options.isvfat) {
fat_time_fat2unix(sbi, &inode->i_ctime, de->ctime,
de->cdate, de->ctime_cs);
fat_time_fat2unix(sbi, &inode->i_atime, 0, de->adate, 0);
} else
inode->i_ctime = inode->i_atime = inode->i_mtime;
return 0;
}
static inline void fat_lock_build_inode(struct msdos_sb_info *sbi)
{
if (sbi->options.nfs == FAT_NFS_NOSTALE_RO)
mutex_lock(&sbi->nfs_build_inode_lock);
}
static inline void fat_unlock_build_inode(struct msdos_sb_info *sbi)
{
if (sbi->options.nfs == FAT_NFS_NOSTALE_RO)
mutex_unlock(&sbi->nfs_build_inode_lock);
}
struct inode *fat_build_inode(struct super_block *sb,
struct msdos_dir_entry *de, loff_t i_pos)
{
struct inode *inode;
int err;
fat_lock_build_inode(MSDOS_SB(sb));
inode = fat_iget(sb, i_pos);
if (inode)
goto out;
inode = new_inode(sb);
if (!inode) {
inode = ERR_PTR(-ENOMEM);
goto out;
}
inode->i_ino = iunique(sb, MSDOS_ROOT_INO);
inode->i_version = 1;
err = fat_fill_inode(inode, de);
if (err) {
iput(inode);
inode = ERR_PTR(err);
goto out;
}
fat_attach(inode, i_pos);
insert_inode_hash(inode);
out:
fat_unlock_build_inode(MSDOS_SB(sb));
return inode;
}
EXPORT_SYMBOL_GPL(fat_build_inode);
static int __fat_write_inode(struct inode *inode, int wait);
static void fat_free_eofblocks(struct inode *inode)
{
/* Release unwritten fallocated blocks on inode eviction. */
if ((inode->i_blocks << 9) >
round_up(MSDOS_I(inode)->mmu_private,
MSDOS_SB(inode->i_sb)->cluster_size)) {
int err;
fat_truncate_blocks(inode, MSDOS_I(inode)->mmu_private);
/* Fallocate results in updating the i_start/iogstart
* for the zero byte file. So, make it return to
* original state during evict and commit it to avoid
* any corruption on the next access to the cluster
* chain for the file.
*/
err = __fat_write_inode(inode, inode_needs_sync(inode));
if (err) {
fat_msg(inode->i_sb, KERN_WARNING, "Failed to "
"update on disk inode for unused "
"fallocated blocks, inode could be "
"corrupted. Please run fsck");
}
}
}
static void fat_evict_inode(struct inode *inode)
{
truncate_inode_pages_final(&inode->i_data);
if (!inode->i_nlink) {
inode->i_size = 0;
fat_truncate_blocks(inode, 0);
} else
fat_free_eofblocks(inode);
invalidate_inode_buffers(inode);
clear_inode(inode);
fat_cache_inval_inode(inode);
fat_detach(inode);
}
static void fat_set_state(struct super_block *sb,
unsigned int set, unsigned int force)
{
struct buffer_head *bh;
struct fat_boot_sector *b;
struct msdos_sb_info *sbi = MSDOS_SB(sb);
/* do not change any thing if mounted read only */
if ((sb->s_flags & MS_RDONLY) && !force)
return;
/* do not change state if fs was dirty */
if (sbi->dirty) {
/* warn only on set (mount). */
if (set)
fat_msg(sb, KERN_WARNING, "Volume was not properly "
"unmounted. Some data may be corrupt. "
"Please run fsck.");
return;
}
bh = sb_bread(sb, 0);
if (bh == NULL) {
fat_msg(sb, KERN_ERR, "unable to read boot sector "
"to mark fs as dirty");
return;
}
b = (struct fat_boot_sector *) bh->b_data;
if (sbi->fat_bits == 32) {
if (set)
b->fat32.state |= FAT_STATE_DIRTY;
else
b->fat32.state &= ~FAT_STATE_DIRTY;
} else /* fat 16 and 12 */ {
if (set)
b->fat16.state |= FAT_STATE_DIRTY;
else
b->fat16.state &= ~FAT_STATE_DIRTY;
}
mark_buffer_dirty(bh);
sync_dirty_buffer(bh);
brelse(bh);
}
static void delayed_free(struct rcu_head *p)
{
struct msdos_sb_info *sbi = container_of(p, struct msdos_sb_info, rcu);
unload_nls(sbi->nls_disk);
unload_nls(sbi->nls_io);
if (sbi->options.iocharset != fat_default_iocharset)
kfree(sbi->options.iocharset);
kfree(sbi);
}
static void fat_put_super(struct super_block *sb)
{
struct msdos_sb_info *sbi = MSDOS_SB(sb);
fat_set_state(sb, 0, 0);
iput(sbi->fsinfo_inode);
iput(sbi->fat_inode);
call_rcu(&sbi->rcu, delayed_free);
}
static struct kmem_cache *fat_inode_cachep;
static struct inode *fat_alloc_inode(struct super_block *sb)
{
struct msdos_inode_info *ei;
ei = kmem_cache_alloc(fat_inode_cachep, GFP_NOFS);
if (!ei)
return NULL;
init_rwsem(&ei->truncate_lock);
return &ei->vfs_inode;
}
static void fat_i_callback(struct rcu_head *head)
{
struct inode *inode = container_of(head, struct inode, i_rcu);
kmem_cache_free(fat_inode_cachep, MSDOS_I(inode));
}
static void fat_destroy_inode(struct inode *inode)
{
call_rcu(&inode->i_rcu, fat_i_callback);
}
static void init_once(void *foo)
{
struct msdos_inode_info *ei = (struct msdos_inode_info *)foo;
spin_lock_init(&ei->cache_lru_lock);
ei->nr_caches = 0;
ei->cache_valid_id = FAT_CACHE_VALID + 1;
INIT_LIST_HEAD(&ei->cache_lru);
INIT_HLIST_NODE(&ei->i_fat_hash);
INIT_HLIST_NODE(&ei->i_dir_hash);
inode_init_once(&ei->vfs_inode);
}
static int __init fat_init_inodecache(void)
{
fat_inode_cachep = kmem_cache_create("fat_inode_cache",
sizeof(struct msdos_inode_info),
0, (SLAB_RECLAIM_ACCOUNT|
SLAB_MEM_SPREAD|SLAB_ACCOUNT),
init_once);
if (fat_inode_cachep == NULL)
return -ENOMEM;
return 0;
}
static void __exit fat_destroy_inodecache(void)
{
/*
* Make sure all delayed rcu free inodes are flushed before we
* destroy cache.
*/
rcu_barrier();
kmem_cache_destroy(fat_inode_cachep);
}
static int fat_remount(struct super_block *sb, int *flags, char *data)
{
int new_rdonly;
struct msdos_sb_info *sbi = MSDOS_SB(sb);
*flags |= MS_NODIRATIME | (sbi->options.isvfat ? 0 : MS_NOATIME);
sync_filesystem(sb);
/* make sure we update state on remount. */
new_rdonly = *flags & MS_RDONLY;
if (new_rdonly != (sb->s_flags & MS_RDONLY)) {
if (new_rdonly)
fat_set_state(sb, 0, 0);
else
fat_set_state(sb, 1, 1);
}
return 0;
}
static int fat_statfs(struct dentry *dentry, struct kstatfs *buf)
{
struct super_block *sb = dentry->d_sb;
struct msdos_sb_info *sbi = MSDOS_SB(sb);
u64 id = huge_encode_dev(sb->s_bdev->bd_dev);
/* If the count of free cluster is still unknown, counts it here. */
if (sbi->free_clusters == -1 || !sbi->free_clus_valid) {
int err = fat_count_free_clusters(dentry->d_sb);
if (err)
return err;
}
buf->f_type = dentry->d_sb->s_magic;
buf->f_bsize = sbi->cluster_size;
buf->f_blocks = sbi->max_cluster - FAT_START_ENT;
buf->f_bfree = sbi->free_clusters;
buf->f_bavail = sbi->free_clusters;
buf->f_fsid.val[0] = (u32)id;
buf->f_fsid.val[1] = (u32)(id >> 32);
buf->f_namelen =
(sbi->options.isvfat ? FAT_LFN_LEN : 12) * NLS_MAX_CHARSET_SIZE;
return 0;
}
static int __fat_write_inode(struct inode *inode, int wait)
{
struct super_block *sb = inode->i_sb;
struct msdos_sb_info *sbi = MSDOS_SB(sb);
struct buffer_head *bh;
struct msdos_dir_entry *raw_entry;
loff_t i_pos;
sector_t blocknr;
int err, offset;
if (inode->i_ino == MSDOS_ROOT_INO)
return 0;
retry:
i_pos = fat_i_pos_read(sbi, inode);
if (!i_pos)
return 0;
fat_get_blknr_offset(sbi, i_pos, &blocknr, &offset);
bh = sb_bread(sb, blocknr);
if (!bh) {
fat_msg(sb, KERN_ERR, "unable to read inode block "
"for updating (i_pos %lld)", i_pos);
return -EIO;
}
spin_lock(&sbi->inode_hash_lock);
if (i_pos != MSDOS_I(inode)->i_pos) {
spin_unlock(&sbi->inode_hash_lock);
brelse(bh);
goto retry;
}
raw_entry = &((struct msdos_dir_entry *) (bh->b_data))[offset];
if (S_ISDIR(inode->i_mode))
raw_entry->size = 0;
else
raw_entry->size = cpu_to_le32(inode->i_size);
raw_entry->attr = fat_make_attrs(inode);
fat_set_start(raw_entry, MSDOS_I(inode)->i_logstart);
fat_time_unix2fat(sbi, &inode->i_mtime, &raw_entry->time,
&raw_entry->date, NULL);
if (sbi->options.isvfat) {
__le16 atime;
fat_time_unix2fat(sbi, &inode->i_ctime, &raw_entry->ctime,
&raw_entry->cdate, &raw_entry->ctime_cs);
fat_time_unix2fat(sbi, &inode->i_atime, &atime,
&raw_entry->adate, NULL);
}
spin_unlock(&sbi->inode_hash_lock);
mark_buffer_dirty(bh);
err = 0;
if (wait)
err = sync_dirty_buffer(bh);
brelse(bh);
return err;
}
static int fat_write_inode(struct inode *inode, struct writeback_control *wbc)
{
int err;
if (inode->i_ino == MSDOS_FSINFO_INO) {
struct super_block *sb = inode->i_sb;
mutex_lock(&MSDOS_SB(sb)->s_lock);
err = fat_clusters_flush(sb);
mutex_unlock(&MSDOS_SB(sb)->s_lock);
} else
err = __fat_write_inode(inode, wbc->sync_mode == WB_SYNC_ALL);
return err;
}
int fat_sync_inode(struct inode *inode)
{
return __fat_write_inode(inode, 1);
}
EXPORT_SYMBOL_GPL(fat_sync_inode);
static int fat_show_options(struct seq_file *m, struct dentry *root);
static const struct super_operations fat_sops = {
.alloc_inode = fat_alloc_inode,
.destroy_inode = fat_destroy_inode,
.write_inode = fat_write_inode,
.evict_inode = fat_evict_inode,
.put_super = fat_put_super,
.statfs = fat_statfs,
.remount_fs = fat_remount,
.show_options = fat_show_options,
};
static int fat_show_options(struct seq_file *m, struct dentry *root)
{
struct msdos_sb_info *sbi = MSDOS_SB(root->d_sb);
struct fat_mount_options *opts = &sbi->options;
int isvfat = opts->isvfat;
if (!uid_eq(opts->fs_uid, GLOBAL_ROOT_UID))
seq_printf(m, ",uid=%u",
from_kuid_munged(&init_user_ns, opts->fs_uid));
if (!gid_eq(opts->fs_gid, GLOBAL_ROOT_GID))
seq_printf(m, ",gid=%u",
from_kgid_munged(&init_user_ns, opts->fs_gid));
seq_printf(m, ",fmask=%04o", opts->fs_fmask);
seq_printf(m, ",dmask=%04o", opts->fs_dmask);
if (opts->allow_utime)
seq_printf(m, ",allow_utime=%04o", opts->allow_utime);
if (sbi->nls_disk)
/* strip "cp" prefix from displayed option */
seq_printf(m, ",codepage=%s", &sbi->nls_disk->charset[2]);
if (isvfat) {
if (sbi->nls_io)
seq_printf(m, ",iocharset=%s", sbi->nls_io->charset);
switch (opts->shortname) {
case VFAT_SFN_DISPLAY_WIN95 | VFAT_SFN_CREATE_WIN95:
seq_puts(m, ",shortname=win95");
break;
case VFAT_SFN_DISPLAY_WINNT | VFAT_SFN_CREATE_WINNT:
seq_puts(m, ",shortname=winnt");
break;
case VFAT_SFN_DISPLAY_WINNT | VFAT_SFN_CREATE_WIN95:
seq_puts(m, ",shortname=mixed");
break;
case VFAT_SFN_DISPLAY_LOWER | VFAT_SFN_CREATE_WIN95:
seq_puts(m, ",shortname=lower");
break;
default:
seq_puts(m, ",shortname=unknown");
break;
}
}
if (opts->name_check != 'n')
seq_printf(m, ",check=%c", opts->name_check);
if (opts->usefree)
seq_puts(m, ",usefree");
if (opts->quiet)
seq_puts(m, ",quiet");
if (opts->showexec)
seq_puts(m, ",showexec");
if (opts->sys_immutable)
seq_puts(m, ",sys_immutable");
if (!isvfat) {
if (opts->dotsOK)
seq_puts(m, ",dotsOK=yes");
if (opts->nocase)
seq_puts(m, ",nocase");
} else {
if (opts->utf8)
seq_puts(m, ",utf8");
if (opts->unicode_xlate)
seq_puts(m, ",uni_xlate");
if (!opts->numtail)
seq_puts(m, ",nonumtail");
if (opts->rodir)
seq_puts(m, ",rodir");
}
if (opts->flush)
seq_puts(m, ",flush");
if (opts->tz_set) {
if (opts->time_offset)
seq_printf(m, ",time_offset=%d", opts->time_offset);
else
seq_puts(m, ",tz=UTC");
}
if (opts->errors == FAT_ERRORS_CONT)
seq_puts(m, ",errors=continue");
else if (opts->errors == FAT_ERRORS_PANIC)
seq_puts(m, ",errors=panic");
else
seq_puts(m, ",errors=remount-ro");
if (opts->nfs == FAT_NFS_NOSTALE_RO)
seq_puts(m, ",nfs=nostale_ro");
else if (opts->nfs)
seq_puts(m, ",nfs=stale_rw");
if (opts->discard)
seq_puts(m, ",discard");
if (opts->dos1xfloppy)
seq_puts(m, ",dos1xfloppy");
return 0;
}
enum {
Opt_check_n, Opt_check_r, Opt_check_s, Opt_uid, Opt_gid,
Opt_umask, Opt_dmask, Opt_fmask, Opt_allow_utime, Opt_codepage,
Opt_usefree, Opt_nocase, Opt_quiet, Opt_showexec, Opt_debug,
Opt_immutable, Opt_dots, Opt_nodots,
Opt_charset, Opt_shortname_lower, Opt_shortname_win95,
Opt_shortname_winnt, Opt_shortname_mixed, Opt_utf8_no, Opt_utf8_yes,
Opt_uni_xl_no, Opt_uni_xl_yes, Opt_nonumtail_no, Opt_nonumtail_yes,
Opt_obsolete, Opt_flush, Opt_tz_utc, Opt_rodir, Opt_err_cont,
Opt_err_panic, Opt_err_ro, Opt_discard, Opt_nfs, Opt_time_offset,
Opt_nfs_stale_rw, Opt_nfs_nostale_ro, Opt_err, Opt_dos1xfloppy,
};
static const match_table_t fat_tokens = {
{Opt_check_r, "check=relaxed"},
{Opt_check_s, "check=strict"},
{Opt_check_n, "check=normal"},
{Opt_check_r, "check=r"},
{Opt_check_s, "check=s"},
{Opt_check_n, "check=n"},
{Opt_uid, "uid=%u"},
{Opt_gid, "gid=%u"},
{Opt_umask, "umask=%o"},
{Opt_dmask, "dmask=%o"},
{Opt_fmask, "fmask=%o"},
{Opt_allow_utime, "allow_utime=%o"},
{Opt_codepage, "codepage=%u"},
{Opt_usefree, "usefree"},
{Opt_nocase, "nocase"},
{Opt_quiet, "quiet"},
{Opt_showexec, "showexec"},
{Opt_debug, "debug"},
{Opt_immutable, "sys_immutable"},
{Opt_flush, "flush"},
{Opt_tz_utc, "tz=UTC"},
{Opt_time_offset, "time_offset=%d"},
{Opt_err_cont, "errors=continue"},
{Opt_err_panic, "errors=panic"},
{Opt_err_ro, "errors=remount-ro"},
{Opt_discard, "discard"},
{Opt_nfs_stale_rw, "nfs"},
{Opt_nfs_stale_rw, "nfs=stale_rw"},
{Opt_nfs_nostale_ro, "nfs=nostale_ro"},
{Opt_dos1xfloppy, "dos1xfloppy"},
{Opt_obsolete, "conv=binary"},
{Opt_obsolete, "conv=text"},
{Opt_obsolete, "conv=auto"},
{Opt_obsolete, "conv=b"},
{Opt_obsolete, "conv=t"},
{Opt_obsolete, "conv=a"},
{Opt_obsolete, "fat=%u"},
{Opt_obsolete, "blocksize=%u"},
{Opt_obsolete, "cvf_format=%20s"},
{Opt_obsolete, "cvf_options=%100s"},
{Opt_obsolete, "posix"},
{Opt_err, NULL},
};
static const match_table_t msdos_tokens = {
{Opt_nodots, "nodots"},
{Opt_nodots, "dotsOK=no"},
{Opt_dots, "dots"},
{Opt_dots, "dotsOK=yes"},
{Opt_err, NULL}
};
static const match_table_t vfat_tokens = {
{Opt_charset, "iocharset=%s"},
{Opt_shortname_lower, "shortname=lower"},
{Opt_shortname_win95, "shortname=win95"},
{Opt_shortname_winnt, "shortname=winnt"},
{Opt_shortname_mixed, "shortname=mixed"},
{Opt_utf8_no, "utf8=0"}, /* 0 or no or false */
{Opt_utf8_no, "utf8=no"},
{Opt_utf8_no, "utf8=false"},
{Opt_utf8_yes, "utf8=1"}, /* empty or 1 or yes or true */
{Opt_utf8_yes, "utf8=yes"},
{Opt_utf8_yes, "utf8=true"},
{Opt_utf8_yes, "utf8"},
{Opt_uni_xl_no, "uni_xlate=0"}, /* 0 or no or false */
{Opt_uni_xl_no, "uni_xlate=no"},
{Opt_uni_xl_no, "uni_xlate=false"},
{Opt_uni_xl_yes, "uni_xlate=1"}, /* empty or 1 or yes or true */
{Opt_uni_xl_yes, "uni_xlate=yes"},
{Opt_uni_xl_yes, "uni_xlate=true"},
{Opt_uni_xl_yes, "uni_xlate"},
{Opt_nonumtail_no, "nonumtail=0"}, /* 0 or no or false */
{Opt_nonumtail_no, "nonumtail=no"},
{Opt_nonumtail_no, "nonumtail=false"},
{Opt_nonumtail_yes, "nonumtail=1"}, /* empty or 1 or yes or true */
{Opt_nonumtail_yes, "nonumtail=yes"},
{Opt_nonumtail_yes, "nonumtail=true"},
{Opt_nonumtail_yes, "nonumtail"},
{Opt_rodir, "rodir"},
{Opt_err, NULL}
};
static int parse_options(struct super_block *sb, char *options, int is_vfat,
int silent, int *debug, struct fat_mount_options *opts)
{
char *p;
substring_t args[MAX_OPT_ARGS];
int option;
char *iocharset;
opts->isvfat = is_vfat;
opts->fs_uid = current_uid();
opts->fs_gid = current_gid();
opts->fs_fmask = opts->fs_dmask = current_umask();
opts->allow_utime = -1;
opts->codepage = fat_default_codepage;
opts->iocharset = fat_default_iocharset;
if (is_vfat) {
opts->shortname = VFAT_SFN_DISPLAY_WINNT|VFAT_SFN_CREATE_WIN95;
opts->rodir = 0;
} else {
opts->shortname = 0;
opts->rodir = 1;
}
opts->name_check = 'n';
opts->quiet = opts->showexec = opts->sys_immutable = opts->dotsOK = 0;
opts->utf8 = opts->unicode_xlate = 0;
opts->numtail = 1;
opts->usefree = opts->nocase = 0;
opts->tz_set = 0;
opts->nfs = 0;
opts->errors = FAT_ERRORS_RO;
*debug = 0;
if (!options)
goto out;
while ((p = strsep(&options, ",")) != NULL) {
int token;
if (!*p)
continue;
token = match_token(p, fat_tokens, args);
if (token == Opt_err) {
if (is_vfat)
token = match_token(p, vfat_tokens, args);
else
token = match_token(p, msdos_tokens, args);
}
switch (token) {
case Opt_check_s:
opts->name_check = 's';
break;
case Opt_check_r:
opts->name_check = 'r';
break;
case Opt_check_n:
opts->name_check = 'n';
break;
case Opt_usefree:
opts->usefree = 1;
break;
case Opt_nocase:
if (!is_vfat)
opts->nocase = 1;
else {
/* for backward compatibility */
opts->shortname = VFAT_SFN_DISPLAY_WIN95
| VFAT_SFN_CREATE_WIN95;
}
break;
case Opt_quiet:
opts->quiet = 1;
break;
case Opt_showexec:
opts->showexec = 1;
break;
case Opt_debug:
*debug = 1;
break;
case Opt_immutable:
opts->sys_immutable = 1;
break;
case Opt_uid:
if (match_int(&args[0], &option))
return -EINVAL;
opts->fs_uid = make_kuid(current_user_ns(), option);
if (!uid_valid(opts->fs_uid))
return -EINVAL;
break;
case Opt_gid:
if (match_int(&args[0], &option))
return -EINVAL;
opts->fs_gid = make_kgid(current_user_ns(), option);
if (!gid_valid(opts->fs_gid))
return -EINVAL;
break;
case Opt_umask:
if (match_octal(&args[0], &option))
return -EINVAL;
opts->fs_fmask = opts->fs_dmask = option;
break;
case Opt_dmask:
if (match_octal(&args[0], &option))
return -EINVAL;
opts->fs_dmask = option;
break;
case Opt_fmask:
if (match_octal(&args[0], &option))
return -EINVAL;
opts->fs_fmask = option;
break;
case Opt_allow_utime:
if (match_octal(&args[0], &option))
return -EINVAL;
opts->allow_utime = option & (S_IWGRP | S_IWOTH);
break;
case Opt_codepage:
if (match_int(&args[0], &option))
return -EINVAL;
opts->codepage = option;
break;
case Opt_flush:
opts->flush = 1;
break;
case Opt_time_offset:
if (match_int(&args[0], &option))
return -EINVAL;
/*
* GMT+-12 zones may have DST corrections so at least
* 13 hours difference is needed. Make the limit 24
* just in case someone invents something unusual.
*/
if (option < -24 * 60 || option > 24 * 60)
return -EINVAL;
opts->tz_set = 1;
opts->time_offset = option;
break;
case Opt_tz_utc:
opts->tz_set = 1;
opts->time_offset = 0;
break;
case Opt_err_cont:
opts->errors = FAT_ERRORS_CONT;
break;
case Opt_err_panic:
opts->errors = FAT_ERRORS_PANIC;
break;
case Opt_err_ro:
opts->errors = FAT_ERRORS_RO;
break;
case Opt_nfs_stale_rw:
opts->nfs = FAT_NFS_STALE_RW;
break;
case Opt_nfs_nostale_ro:
opts->nfs = FAT_NFS_NOSTALE_RO;
break;
case Opt_dos1xfloppy:
opts->dos1xfloppy = 1;
break;
/* msdos specific */
case Opt_dots:
opts->dotsOK = 1;
break;
case Opt_nodots:
opts->dotsOK = 0;
break;
/* vfat specific */
case Opt_charset:
if (opts->iocharset != fat_default_iocharset)
kfree(opts->iocharset);
iocharset = match_strdup(&args[0]);
if (!iocharset)
return -ENOMEM;
opts->iocharset = iocharset;
break;
case Opt_shortname_lower:
opts->shortname = VFAT_SFN_DISPLAY_LOWER
| VFAT_SFN_CREATE_WIN95;
break;
case Opt_shortname_win95:
opts->shortname = VFAT_SFN_DISPLAY_WIN95
| VFAT_SFN_CREATE_WIN95;
break;
case Opt_shortname_winnt:
opts->shortname = VFAT_SFN_DISPLAY_WINNT
| VFAT_SFN_CREATE_WINNT;
break;
case Opt_shortname_mixed:
opts->shortname = VFAT_SFN_DISPLAY_WINNT
| VFAT_SFN_CREATE_WIN95;
break;
case Opt_utf8_no: /* 0 or no or false */
opts->utf8 = 0;
break;
case Opt_utf8_yes: /* empty or 1 or yes or true */
opts->utf8 = 1;
break;
case Opt_uni_xl_no: /* 0 or no or false */
opts->unicode_xlate = 0;
break;
case Opt_uni_xl_yes: /* empty or 1 or yes or true */
opts->unicode_xlate = 1;
break;
case Opt_nonumtail_no: /* 0 or no or false */
opts->numtail = 1; /* negated option */
break;
case Opt_nonumtail_yes: /* empty or 1 or yes or true */
opts->numtail = 0; /* negated option */
break;
case Opt_rodir:
opts->rodir = 1;
break;
case Opt_discard:
opts->discard = 1;
break;
/* obsolete mount options */
case Opt_obsolete:
fat_msg(sb, KERN_INFO, "\"%s\" option is obsolete, "
"not supported now", p);
break;
/* unknown option */
default:
if (!silent) {
fat_msg(sb, KERN_ERR,
"Unrecognized mount option \"%s\" "
"or missing value", p);
}
return -EINVAL;
}
}
out:
/* UTF-8 doesn't provide FAT semantics */
if (!strcmp(opts->iocharset, "utf8")) {
fat_msg(sb, KERN_WARNING, "utf8 is not a recommended IO charset"
" for FAT filesystems, filesystem will be "
"case sensitive!");
}
/* If user doesn't specify allow_utime, it's initialized from dmask. */
if (opts->allow_utime == (unsigned short)-1)
opts->allow_utime = ~opts->fs_dmask & (S_IWGRP | S_IWOTH);
if (opts->unicode_xlate)
opts->utf8 = 0;
if (opts->nfs == FAT_NFS_NOSTALE_RO) {
sb->s_flags |= MS_RDONLY;
sb->s_export_op = &fat_export_ops_nostale;
}
return 0;
}
static int fat_read_root(struct inode *inode)
{
struct msdos_sb_info *sbi = MSDOS_SB(inode->i_sb);
int error;
MSDOS_I(inode)->i_pos = MSDOS_ROOT_INO;
inode->i_uid = sbi->options.fs_uid;
inode->i_gid = sbi->options.fs_gid;
inode->i_version++;
inode->i_generation = 0;
inode->i_mode = fat_make_mode(sbi, ATTR_DIR, S_IRWXUGO);
inode->i_op = sbi->dir_ops;
inode->i_fop = &fat_dir_operations;
if (sbi->fat_bits == 32) {
MSDOS_I(inode)->i_start = sbi->root_cluster;
error = fat_calc_dir_size(inode);
if (error < 0)
return error;
} else {
MSDOS_I(inode)->i_start = 0;
inode->i_size = sbi->dir_entries * sizeof(struct msdos_dir_entry);
}
inode->i_blocks = ((inode->i_size + (sbi->cluster_size - 1))
& ~((loff_t)sbi->cluster_size - 1)) >> 9;
MSDOS_I(inode)->i_logstart = 0;
MSDOS_I(inode)->mmu_private = inode->i_size;
fat_save_attrs(inode, ATTR_DIR);
inode->i_mtime.tv_sec = inode->i_atime.tv_sec = inode->i_ctime.tv_sec = 0;
inode->i_mtime.tv_nsec = inode->i_atime.tv_nsec = inode->i_ctime.tv_nsec = 0;
set_nlink(inode, fat_subdirs(inode)+2);
return 0;
}
static unsigned long calc_fat_clusters(struct super_block *sb)
{
struct msdos_sb_info *sbi = MSDOS_SB(sb);
/* Divide first to avoid overflow */
if (sbi->fat_bits != 12) {
unsigned long ent_per_sec = sb->s_blocksize * 8 / sbi->fat_bits;
return ent_per_sec * sbi->fat_length;
}
return sbi->fat_length * sb->s_blocksize * 8 / sbi->fat_bits;
}
static bool fat_bpb_is_zero(struct fat_boot_sector *b)
{
if (get_unaligned_le16(&b->sector_size))
return false;
if (b->sec_per_clus)
return false;
if (b->reserved)
return false;
if (b->fats)
return false;
if (get_unaligned_le16(&b->dir_entries))
return false;
if (get_unaligned_le16(&b->sectors))
return false;
if (b->media)
return false;
if (b->fat_length)
return false;
if (b->secs_track)
return false;
if (b->heads)
return false;
return true;
}
static int fat_read_bpb(struct super_block *sb, struct fat_boot_sector *b,
int silent, struct fat_bios_param_block *bpb)
{
int error = -EINVAL;
/* Read in BPB ... */
memset(bpb, 0, sizeof(*bpb));
bpb->fat_sector_size = get_unaligned_le16(&b->sector_size);
bpb->fat_sec_per_clus = b->sec_per_clus;
bpb->fat_reserved = le16_to_cpu(b->reserved);
bpb->fat_fats = b->fats;
bpb->fat_dir_entries = get_unaligned_le16(&b->dir_entries);
bpb->fat_sectors = get_unaligned_le16(&b->sectors);
bpb->fat_fat_length = le16_to_cpu(b->fat_length);
bpb->fat_total_sect = le32_to_cpu(b->total_sect);
bpb->fat16_state = b->fat16.state;
bpb->fat16_vol_id = get_unaligned_le32(b->fat16.vol_id);
bpb->fat32_length = le32_to_cpu(b->fat32.length);
bpb->fat32_root_cluster = le32_to_cpu(b->fat32.root_cluster);
bpb->fat32_info_sector = le16_to_cpu(b->fat32.info_sector);
bpb->fat32_state = b->fat32.state;
bpb->fat32_vol_id = get_unaligned_le32(b->fat32.vol_id);
/* Validate this looks like a FAT filesystem BPB */
if (!bpb->fat_reserved) {
if (!silent)
fat_msg(sb, KERN_ERR,
"bogus number of reserved sectors");
goto out;
}
if (!bpb->fat_fats) {
if (!silent)
fat_msg(sb, KERN_ERR, "bogus number of FAT structure");
goto out;
}
/*
* Earlier we checked here that b->secs_track and b->head are nonzero,
* but it turns out valid FAT filesystems can have zero there.
*/
if (!fat_valid_media(b->media)) {
if (!silent)
fat_msg(sb, KERN_ERR, "invalid media value (0x%02x)",
(unsigned)b->media);
goto out;
}
if (!is_power_of_2(bpb->fat_sector_size)
|| (bpb->fat_sector_size < 512)
|| (bpb->fat_sector_size > 4096)) {
if (!silent)
fat_msg(sb, KERN_ERR, "bogus logical sector size %u",
(unsigned)bpb->fat_sector_size);
goto out;
}
if (!is_power_of_2(bpb->fat_sec_per_clus)) {
if (!silent)
fat_msg(sb, KERN_ERR, "bogus sectors per cluster %u",
(unsigned)bpb->fat_sec_per_clus);
goto out;
}
error = 0;
out:
return error;
}
static int fat_read_static_bpb(struct super_block *sb,
struct fat_boot_sector *b, int silent,
struct fat_bios_param_block *bpb)
{
static const char *notdos1x = "This doesn't look like a DOS 1.x volume";
struct fat_floppy_defaults *fdefaults = NULL;
int error = -EINVAL;
sector_t bd_sects;
unsigned i;
bd_sects = i_size_read(sb->s_bdev->bd_inode) / SECTOR_SIZE;
/* 16-bit DOS 1.x reliably wrote bootstrap short-jmp code */
if (b->ignored[0] != 0xeb || b->ignored[2] != 0x90) {
if (!silent)
fat_msg(sb, KERN_ERR,
"%s; no bootstrapping code", notdos1x);
goto out;
}
/*
* If any value in this region is non-zero, it isn't archaic
* DOS.
*/
if (!fat_bpb_is_zero(b)) {
if (!silent)
fat_msg(sb, KERN_ERR,
"%s; DOS 2.x BPB is non-zero", notdos1x);
goto out;
}
for (i = 0; i < ARRAY_SIZE(floppy_defaults); i++) {
if (floppy_defaults[i].nr_sectors == bd_sects) {
fdefaults = &floppy_defaults[i];
break;
}
}
if (fdefaults == NULL) {
if (!silent)
fat_msg(sb, KERN_WARNING,
"This looks like a DOS 1.x volume, but isn't a recognized floppy size (%llu sectors)",
(u64)bd_sects);
goto out;
}
if (!silent)
fat_msg(sb, KERN_INFO,
"This looks like a DOS 1.x volume; assuming default BPB values");
memset(bpb, 0, sizeof(*bpb));
bpb->fat_sector_size = SECTOR_SIZE;
bpb->fat_sec_per_clus = fdefaults->sec_per_clus;
bpb->fat_reserved = 1;
bpb->fat_fats = 2;
bpb->fat_dir_entries = fdefaults->dir_entries;
bpb->fat_sectors = fdefaults->nr_sectors;
bpb->fat_fat_length = fdefaults->fat_length;
error = 0;
out:
return error;
}
/*
* Read the super block of an MS-DOS FS.
*/
int fat_fill_super(struct super_block *sb, void *data, int silent, int isvfat,
void (*setup)(struct super_block *))
{
struct inode *root_inode = NULL, *fat_inode = NULL;
struct inode *fsinfo_inode = NULL;
struct buffer_head *bh;
struct fat_bios_param_block bpb;
struct msdos_sb_info *sbi;
u16 logical_sector_size;
u32 total_sectors, total_clusters, fat_clusters, rootdir_sectors;
int debug;
long error;
char buf[50];
/*
* GFP_KERNEL is ok here, because while we do hold the
* supeblock lock, memory pressure can't call back into
* the filesystem, since we're only just about to mount
* it and have no inodes etc active!
*/
sbi = kzalloc(sizeof(struct msdos_sb_info), GFP_KERNEL);
if (!sbi)
return -ENOMEM;
sb->s_fs_info = sbi;
sb->s_flags |= MS_NODIRATIME;
sb->s_magic = MSDOS_SUPER_MAGIC;
sb->s_op = &fat_sops;
sb->s_export_op = &fat_export_ops;
mutex_init(&sbi->nfs_build_inode_lock);
ratelimit_state_init(&sbi->ratelimit, DEFAULT_RATELIMIT_INTERVAL,
DEFAULT_RATELIMIT_BURST);
error = parse_options(sb, data, isvfat, silent, &debug, &sbi->options);
if (error)
goto out_fail;
setup(sb); /* flavour-specific stuff that needs options */
error = -EIO;
sb_min_blocksize(sb, 512);
bh = sb_bread(sb, 0);
if (bh == NULL) {
fat_msg(sb, KERN_ERR, "unable to read boot sector");
goto out_fail;
}
error = fat_read_bpb(sb, (struct fat_boot_sector *)bh->b_data, silent,
&bpb);
if (error == -EINVAL && sbi->options.dos1xfloppy)
error = fat_read_static_bpb(sb,
(struct fat_boot_sector *)bh->b_data, silent, &bpb);
brelse(bh);
if (error == -EINVAL)
goto out_invalid;
else if (error)
goto out_fail;
logical_sector_size = bpb.fat_sector_size;
sbi->sec_per_clus = bpb.fat_sec_per_clus;
error = -EIO;
if (logical_sector_size < sb->s_blocksize) {
fat_msg(sb, KERN_ERR, "logical sector size too small for device"
" (logical sector size = %u)", logical_sector_size);
goto out_fail;
}
if (logical_sector_size > sb->s_blocksize) {
struct buffer_head *bh_resize;
if (!sb_set_blocksize(sb, logical_sector_size)) {
fat_msg(sb, KERN_ERR, "unable to set blocksize %u",
logical_sector_size);
goto out_fail;
}
/* Verify that the larger boot sector is fully readable */
bh_resize = sb_bread(sb, 0);
if (bh_resize == NULL) {
fat_msg(sb, KERN_ERR, "unable to read boot sector"
" (logical sector size = %lu)",
sb->s_blocksize);
goto out_fail;
}
brelse(bh_resize);
}
mutex_init(&sbi->s_lock);
sbi->cluster_size = sb->s_blocksize * sbi->sec_per_clus;
sbi->cluster_bits = ffs(sbi->cluster_size) - 1;
sbi->fats = bpb.fat_fats;
sbi->fat_bits = 0; /* Don't know yet */
sbi->fat_start = bpb.fat_reserved;
sbi->fat_length = bpb.fat_fat_length;
sbi->root_cluster = 0;
sbi->free_clusters = -1; /* Don't know yet */
sbi->free_clus_valid = 0;
sbi->prev_free = FAT_START_ENT;
sb->s_maxbytes = 0xffffffff;
if (!sbi->fat_length && bpb.fat32_length) {
struct fat_boot_fsinfo *fsinfo;
struct buffer_head *fsinfo_bh;
/* Must be FAT32 */
sbi->fat_bits = 32;
sbi->fat_length = bpb.fat32_length;
sbi->root_cluster = bpb.fat32_root_cluster;
/* MC - if info_sector is 0, don't multiply by 0 */
sbi->fsinfo_sector = bpb.fat32_info_sector;
if (sbi->fsinfo_sector == 0)
sbi->fsinfo_sector = 1;
fsinfo_bh = sb_bread(sb, sbi->fsinfo_sector);
if (fsinfo_bh == NULL) {
fat_msg(sb, KERN_ERR, "bread failed, FSINFO block"
" (sector = %lu)", sbi->fsinfo_sector);
goto out_fail;
}
fsinfo = (struct fat_boot_fsinfo *)fsinfo_bh->b_data;
if (!IS_FSINFO(fsinfo)) {
fat_msg(sb, KERN_WARNING, "Invalid FSINFO signature: "
"0x%08x, 0x%08x (sector = %lu)",
le32_to_cpu(fsinfo->signature1),
le32_to_cpu(fsinfo->signature2),
sbi->fsinfo_sector);
} else {
if (sbi->options.usefree)
sbi->free_clus_valid = 1;
sbi->free_clusters = le32_to_cpu(fsinfo->free_clusters);
sbi->prev_free = le32_to_cpu(fsinfo->next_cluster);
}
brelse(fsinfo_bh);
}
/* interpret volume ID as a little endian 32 bit integer */
if (sbi->fat_bits == 32)
sbi->vol_id = bpb.fat32_vol_id;
else /* fat 16 or 12 */
sbi->vol_id = bpb.fat16_vol_id;
sbi->dir_per_block = sb->s_blocksize / sizeof(struct msdos_dir_entry);
sbi->dir_per_block_bits = ffs(sbi->dir_per_block) - 1;
sbi->dir_start = sbi->fat_start + sbi->fats * sbi->fat_length;
sbi->dir_entries = bpb.fat_dir_entries;
if (sbi->dir_entries & (sbi->dir_per_block - 1)) {
if (!silent)
fat_msg(sb, KERN_ERR, "bogus directory-entries per block"
" (%u)", sbi->dir_entries);
goto out_invalid;
}
rootdir_sectors = sbi->dir_entries
* sizeof(struct msdos_dir_entry) / sb->s_blocksize;
sbi->data_start = sbi->dir_start + rootdir_sectors;
total_sectors = bpb.fat_sectors;
if (total_sectors == 0)
total_sectors = bpb.fat_total_sect;
total_clusters = (total_sectors - sbi->data_start) / sbi->sec_per_clus;
if (sbi->fat_bits != 32)
sbi->fat_bits = (total_clusters > MAX_FAT12) ? 16 : 12;
/* some OSes set FAT_STATE_DIRTY and clean it on unmount. */
if (sbi->fat_bits == 32)
sbi->dirty = bpb.fat32_state & FAT_STATE_DIRTY;
else /* fat 16 or 12 */
sbi->dirty = bpb.fat16_state & FAT_STATE_DIRTY;
/* check that FAT table does not overflow */
fat_clusters = calc_fat_clusters(sb);
total_clusters = min(total_clusters, fat_clusters - FAT_START_ENT);
if (total_clusters > MAX_FAT(sb)) {
if (!silent)
fat_msg(sb, KERN_ERR, "count of clusters too big (%u)",
total_clusters);
goto out_invalid;
}
sbi->max_cluster = total_clusters + FAT_START_ENT;
/* check the free_clusters, it's not necessarily correct */
if (sbi->free_clusters != -1 && sbi->free_clusters > total_clusters)
sbi->free_clusters = -1;
/* check the prev_free, it's not necessarily correct */
sbi->prev_free %= sbi->max_cluster;
if (sbi->prev_free < FAT_START_ENT)
sbi->prev_free = FAT_START_ENT;
/* set up enough so that it can read an inode */
fat_hash_init(sb);
dir_hash_init(sb);
fat_ent_access_init(sb);
/*
* The low byte of FAT's first entry must have same value with
* media-field. But in real world, too many devices is
* writing wrong value. So, removed that validity check.
*
* if (FAT_FIRST_ENT(sb, media) != first)
*/
error = -EINVAL;
sprintf(buf, "cp%d", sbi->options.codepage);
sbi->nls_disk = load_nls(buf);
if (!sbi->nls_disk) {
fat_msg(sb, KERN_ERR, "codepage %s not found", buf);
goto out_fail;
}
/* FIXME: utf8 is using iocharset for upper/lower conversion */
if (sbi->options.isvfat) {
sbi->nls_io = load_nls(sbi->options.iocharset);
if (!sbi->nls_io) {
fat_msg(sb, KERN_ERR, "IO charset %s not found",
sbi->options.iocharset);
goto out_fail;
}
}
error = -ENOMEM;
fat_inode = new_inode(sb);
if (!fat_inode)
goto out_fail;
MSDOS_I(fat_inode)->i_pos = 0;
sbi->fat_inode = fat_inode;
fsinfo_inode = new_inode(sb);
if (!fsinfo_inode)
goto out_fail;
fsinfo_inode->i_ino = MSDOS_FSINFO_INO;
sbi->fsinfo_inode = fsinfo_inode;
insert_inode_hash(fsinfo_inode);
root_inode = new_inode(sb);
if (!root_inode)
goto out_fail;
root_inode->i_ino = MSDOS_ROOT_INO;
root_inode->i_version = 1;
error = fat_read_root(root_inode);
if (error < 0) {
iput(root_inode);
goto out_fail;
}
error = -ENOMEM;
insert_inode_hash(root_inode);
fat_attach(root_inode, 0);
sb->s_root = d_make_root(root_inode);
if (!sb->s_root) {
fat_msg(sb, KERN_ERR, "get root inode failed");
goto out_fail;
}
if (sbi->options.discard) {
struct request_queue *q = bdev_get_queue(sb->s_bdev);
if (!blk_queue_discard(q))
fat_msg(sb, KERN_WARNING,
"mounting with \"discard\" option, but "
"the device does not support discard");
}
fat_set_state(sb, 1, 0);
return 0;
out_invalid:
error = -EINVAL;
if (!silent)
fat_msg(sb, KERN_INFO, "Can't find a valid FAT filesystem");
out_fail:
if (fsinfo_inode)
iput(fsinfo_inode);
if (fat_inode)
iput(fat_inode);
unload_nls(sbi->nls_io);
unload_nls(sbi->nls_disk);
if (sbi->options.iocharset != fat_default_iocharset)
kfree(sbi->options.iocharset);
sb->s_fs_info = NULL;
kfree(sbi);
return error;
}
EXPORT_SYMBOL_GPL(fat_fill_super);
/*
* helper function for fat_flush_inodes. This writes both the inode
* and the file data blocks, waiting for in flight data blocks before
* the start of the call. It does not wait for any io started
* during the call
*/
static int writeback_inode(struct inode *inode)
{
int ret;
/* if we used wait=1, sync_inode_metadata waits for the io for the
* inode to finish. So wait=0 is sent down to sync_inode_metadata
* and filemap_fdatawrite is used for the data blocks
*/
ret = sync_inode_metadata(inode, 0);
if (!ret)
ret = filemap_fdatawrite(inode->i_mapping);
return ret;
}
/*
* write data and metadata corresponding to i1 and i2. The io is
* started but we do not wait for any of it to finish.
*
* filemap_flush is used for the block device, so if there is a dirty
* page for a block already in flight, we will not wait and start the
* io over again
*/
int fat_flush_inodes(struct super_block *sb, struct inode *i1, struct inode *i2)
{
int ret = 0;
if (!MSDOS_SB(sb)->options.flush)
return 0;
if (i1)
ret = writeback_inode(i1);
if (!ret && i2)
ret = writeback_inode(i2);
if (!ret) {
struct address_space *mapping = sb->s_bdev->bd_inode->i_mapping;
ret = filemap_flush(mapping);
}
return ret;
}
EXPORT_SYMBOL_GPL(fat_flush_inodes);
static int __init init_fat_fs(void)
{
int err;
err = fat_cache_init();
if (err)
return err;
err = fat_init_inodecache();
if (err)
goto failed;
return 0;
failed:
fat_cache_destroy();
return err;
}
static void __exit exit_fat_fs(void)
{
fat_cache_destroy();
fat_destroy_inodecache();
}
module_init(init_fat_fs)
module_exit(exit_fat_fs)
MODULE_LICENSE("GPL");
| {
"redpajama_set_name": "RedPajamaGithub"
} | 6,072 |
Reports: Fulham signs goalkeeper Sergio Rico from Sevilla
By Kyle BonnAug 8, 2018, 3:45 PM EDT
Craven Cottage continues to be a hub of activity this summer as the wheeling and dealing from the Khan family continues.
Already with seven signings this transfer window, Fulham has gone out and reportedly grabbed another. According to reports in both Spain and England, the Whites have grabbed Sevilla goalkeeper Sergio Rico on loan. Upon completion, Rico would be Fulham's eighth signing of the summer and second goalkeeper inked this window. The signing is being reported by both AS in Spain and Sky Sports in England, among others.
The move is a slightly odd one. Fulham shelled out $5 million to sign Besiktas netminder Fabri, but the 30-year-old Spaniard has been shaky in his preseason appearances.
[ MORE: Chelsea announces Courtois move to Real Madrid ]
Considering Fabri's weak start in White, this move seems to suggest that the club was pushed by one of two possible factors: either Fabri's poor start was so alarming to the club that they felt obligated to make immediate amends, or incumbent starter Marcus Bettinelli is either injured or on his way out. 26-year-old Bettinelli, a former England U-21 international, was spectacular last season for Fulham in the Championship, snatching the starting job from David Button midway through the season and lost just two games of the 26 he started.
Fulham have agreed a deal to sign Sevilla goalkeeper Sergio Rico on loan. #FFC #Sevilla
— Pete O'Rourke (@SportsPeteO) August 8, 2018
One would think, based on resumes, that Rico would come in and immediately become the starter. While Bettinelli is a local hero and a fan favorite, he doesn't have the track record that Rico does despite his young age. The Spaniard has made 170 total appearances for Sevilla since joining the senior team from the youth squad as a 20-year-old in 2014. In addition, it's possible Bettinelli is hurt, which may have triggered the transfer in the first place.
No matter the circumstances, the signing is a quality one for the Whites. Goalkeeper was one position that still felt shaky heading into the season, in part due to Fabri's unconvincing preseason. Now, it becomes yet another squad strength. The Whites have had a busy summer, signing the likes of midfielder Jean-Michael Seri, winger Andre Schurrle, and defenders Alfie Mawson and Calum Chambers.
On the other side of things, the departure of Rico is an odd one for Sevilla. Rico lost his starting spot late last season to 25-year-old David Soria, but he has since left for Getafe. If Rico does indeed head out as well, it would leave just 29-year-old Thomas Vaclik as the only goalkeeper left on the senior team.
Follow @the_bonnfire | {
"redpajama_set_name": "RedPajamaCommonCrawl"
} | 7,145 |
set -e
mongoimport --host localhost --db test --collection ratings --drop --file /app/data/ratings_data.json
| {
"redpajama_set_name": "RedPajamaGithub"
} | 252 |
MURFREESBORO – Middle Tennessee started off strong, but was not able to withstand the scoring onslaught from Tennessee Tech at Reese Smith Jr. Field on Tuesday as it suffered another midweek loss.
In the third inning, the Blue Raiders were able to get the game's first run as second baseman Dustin Delgado was able to drive in catcher Will Schnure on a double.
In the bottom of the sixth inning, Schnure came around to score on a Brad Jarreau single to right field, putting MTSU up, 2-0. It appeared as if the Blue Raiders were cruising to a victory.
However, Tennessee Tech (13-18) was able to take advantage of the MTSU bullpen in the top of the seventh, which saw the Blue Raiders use three relievers in the inning, for six runs.
After recording an out in the seventh, Troutt was replaced by the struggling Heath Slatton (1-6). Slatton failed to record an out, allowing four runs on three hits. His earned run average is now a whopping 9.11 this season.
Kooper Kessler then came in and gave up one run on one hit in 0.1 innings. Will Small replaced Kessler, and finished off the inning. He threw the next 2.1 innings, allowing no runs on two hits.
The Blue Raiders were not going to go down without a fight as they fought back to be one run down going into the ninth inning.
The fireworks really went off when Jared Allen, who went 3-for-4 at the plate Tuesday, hit a two-run homer – his eighth of the season – to get the Blue Raiders to within one run, 6-5. This was still not enough as they were shut down in the bottom of the ninth inning.
Jeb Scoggins (1-0) picked up the win for TTU in relief. Cain Sloan recorded his second save of the season, shutting down MTSU in the last 1.1 innings of the game.
MTSU is now 0-7 in midweek games this season.
The Blue Raiders will hit the field again Wednesday when they travel to Clarksville to face Austin Peay. The game will begin at 6 p.m. CST. | {
"redpajama_set_name": "RedPajamaC4"
} | 2,769 |
Sacred Heart Pioneers (español: los Pioneros del Sagrado Corazón) es el nombre de los equipos deportivos de la Universidad del Sagrado Corazón, situada en Fairfield, Connecticut. Los equipos de los Pioneers participan en las competiciones universitarias organizadas por la NCAA, y forman parte de la Northeast Conference, excepto en hockey sobre hielo masculino, que pertenecen a la Atlantic Hockey, el voleibol masculino a la Eastern Intercollegiate Volleyball Association y la lucha libre a la EIWA.
Programa deportivo
Los Pioneers compiten en 13 deportes masculinos y en 17 femeninos:
Instalaciones deportivas
William H. Pitt Center es el pabellón donde disputan sus partidos los equipos de baloncesto, voleibol, lucha libre y esgrima. Fue inaugurado en 1997 y tiene una capacidad para 2.062 espectadores.
Campus Field, es el estadio donde disputan sus encuentros los equipos de fútbol americano, fútbol, lacrosse y atletismo. Fue inaugurado en 1993 y tiene una capacidad para 3.334 espectadores.
Referencias
Enlaces externos
Web oficial de los Pioneers
Clubes y equipos deportivos del estado de Connecticut
Equipos de la National Collegiate Athletic Association
Northeast Conference
Universidad del Sagrado Corazón (Connecticut) | {
"redpajama_set_name": "RedPajamaWikipedia"
} | 4,067 |
Q: do i need seperate files and database for each subdomain i have made a web application in php and mysql. It is actually an online test software. I have hosted it on www.vstudy.in. Now anyone signing up on the page can give test. But i also provide coaching institutes online test software. Like for a coaching name xyz i create a subdomain xyz.vstudy.in and host files there with their seperate database. i am providing the test portal to 4 institutes. Now if i change a file i have to change it on all the subdomains.It isn't a big deal initially but as my clients will grow it can become hectic also. Do i need to continue it in the way i am doing or there is any easy way out to manage things so that i don't need to manage files on all the subdomains. Please help ??
| {
"redpajama_set_name": "RedPajamaStackExchange"
} | 5,170 |
Claim Listing! Off the Track is located at 106 Westminster Street, St Albans, Christchurch 8014, New Zealand. You can contact Off the Track with telephone number +64 3-355 8398 .
Be the first to write a review for Off the Track! Click Here!
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Find local listings for "Off the Track" in Christchurch Click Here!
User Notice: This is a free business listing provided for Off the Track. We do not guarantee the accuracy of this listing and recommend that you verify the information by calling the business or by visiting their website link, if available. User-generated content like reviews or Off the Track are opinions expressed solely by our users. Any article submission for Off the Track should only be made by or with permission from the author. Media content such as photos and videos for Off the Track are sourced from the public domain and social media websites submitted and tagged by users who have access or owned by them. | {
"redpajama_set_name": "RedPajamaC4"
} | 3,889 |
/* RUN: %clang_cc1 %s -Eonly -std=c89 -pedantic -verify
*/
/* PR3937 */
#define zero() 0
#define one(x) 0
#define two(x, y) 0
#define zero_dot(...) 0 /* expected-warning {{variadic macros were introduced in C99}} */
#define one_dot(x, ...) 0 /* expected-warning {{variadic macros were introduced in C99}} */
zero()
zero(1); /* expected-error {{too many arguments provided to function-like macro invocation}} */
zero(1, 2, 3); /* expected-error {{too many arguments provided to function-like macro invocation}} */
one() /* ok */
one(a)
one(a,) /* expected-error {{too many arguments provided to function-like macro invocation}} */
one(a, b) /* expected-error {{too many arguments provided to function-like macro invocation}} */
two() /* expected-error {{too few arguments provided to function-like macro invocation}} */
two(a) /* expected-error {{too few arguments provided to function-like macro invocation}} */
two(a,b)
two(a, ) /* expected-warning {{empty macro arguments were standardized in C99}} */
two(a,b,c) /* expected-error {{too many arguments provided to function-like macro invocation}} */
two(
, /* expected-warning {{empty macro arguments were standardized in C99}} */
, /* expected-warning {{empty macro arguments were standardized in C99}} \
expected-error {{too many arguments provided to function-like macro invocation}} */
)
two(,) /* expected-warning 2 {{empty macro arguments were standardized in C99}} */
/* PR4006 & rdar://6807000 */
#define e(...) __VA_ARGS__ /* expected-warning {{variadic macros were introduced in C99}} */
e(x)
e()
zero_dot()
one_dot(x) /* empty ... argument: expected-warning {{varargs argument missing, but tolerated as an extension}} */
one_dot() /* empty first argument, elided ...: expected-warning {{varargs argument missing, but tolerated as an extension}} */
/* rdar://6816766 - Crash with function-like macro test at end of directive. */
#define E() (i == 0)
#if E
#endif
| {
"redpajama_set_name": "RedPajamaGithub"
} | 4,147 |
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