Friday, May 22, 2015


In my personal life and professional life I have always worked best alone, and second best as a supporter. I do not join many clubs.  When I am in a community group, if I choose to volunteer for office, I get elected as secretary or vice president.  I never let myself be made president. 

Lifelong experience taught me that no one accepts my suggestions.   I know what to do. I see a solution. No one likes it.  What everyone else does is common sense: it gets the job done, but is suboptimal. 
Connect all five dots with four straight lines.
It is not so much that I figure them out -
though that does happen -
but that I learn the answers.
Informal leadership is chemical, like love.  I question everything, even my own ideas.  My solutions are heuristics, not algorithms; theories, not formulas.  By “theory” I mean the formal, scientific definition: a conceptual explanation of facts that allows prediction and falsification.  New facts may require new a new theory. Not many people are comfortable with that.  

The military is all about leadership at a depth of commitment that the corporate world cannot understand.  Everyone from corporal to general is in charge of other people.  You do not go into leadership in a quantum leap.  Three grades separate the trainee, private, and specialist from the corporal who has earned responsibility for a group of four.   The army corporal is an E-4, Enlisted grade 4.  A command sergeant major is an E-9.  Above the 2nd and 1st lieutenants and the captain, is Officer grade 4, the major. The four-star general is an O-9.  It is all very granular. 

Customs and courtesies get complicated. Basically, enlisteds do not salute each other. We do salute officers.  Officers salute each other.  (Enlisted E-4 and above are “non-commissioned officers”; real officers are “commissioned officers.”)  Even though America was founded specifically and purposely as a democratic republic, the military follows the British tradition of a class-based society.  You address an officer as “Sir” or “Ma’am”, but they call you only by your rank.  Invitations to social events go out to “officers and their ladies, sailors and their wives.”  Just as in Animal Farm, our revolution left some of us more equal than others. 
Texas State Guard
Regional Basic Orientation Training
RBOT Class 009 graduation.
May 17, 2015

Customs and courtesies can get complicated. I am a petty officer third class in the Texas maritime regiment (TMAR), within the Texas State Guard, which is a component of the Texas Military Department, a state agency.  As an E-4, I am equivalent to a corporal. Teaching a class in computer operations earlier this month, I stood before a class of 14 people, from sergeants to captains.  I called attention, “Class… Ten…. Hut!” And they came to their feet.  I was in charge of the class.  It is common in the military for non-coms to train officers.  Unlike the corporate world and informal society, compliance does not depend on approval.


Sunday, May 10, 2015

The Man Who Loved Only Numbers

Paul Erdős was easily the most influential mathematician of the 20th century, and arguably so for all time.  He published 1475 papers almost all in collaboration.  Mathematicians have Erdős Numbers.  Your number is 1 if you co-authored with him, 2 if you co-authored with a co-author, and so on.  Movie star Natalie Portman has an Erdős number of 7.  Danika McKellar’s 4 is lower than her Kevin Bacon number. 
Sketch portrait of mathematician Paul Erdős pronounced like Air-dash created with numerals.

Erdős’s work was beyond prolific. He knew how to offer motivating challenges to people working at all levels of mathematics from his academic peers to children.  In that, Paul Erdős was responsible for hundreds of proven insights that extended the frontiers of number theory. 

The fact that Erdős’s life (1913-1996) intersected so many others allowed Paul Hoffman’s biography  to explore the domain and range of the history of mathematics.  The Greeks, Fibonacci, and pi are here along with Hardy, Ramanujan, and  transfinite numbers, as well a bit of graph theory, and “what’s behind door number two?”

The Man Who Loved Only Numbers by Paul Hoffman (Hyperion, 1998) explains most of the mathematics with integers.  After all, God created the integers and we built the rest – or so it was claimed by Leopold Kronecker (1821-1893) and echoed by Stephen Hawking.  As a result, many of these puzzles could be explained to a child in third through ninth grade.  The fact is, though, that few would be.  The stampede for standardized testing in K-12 education forces teachers to focus on the examinations to the detriment of the true understanding that comes from the artful competence of leisure and play.

Consider Ramsey theory.  Among the pursuits of Frank Plumpton Ramsey (1903-1930) was the question of the smallest possible "universe" that contains some element.  How many ordinary people would you have to fetch at random in order to be guaranteed one of each sex (not gender)?  Three, right?  If you want to plan a party, what is the smallest number of guests that guarantees that three of them must know each other?  Six; no proof is offered, so it must be hard.  (The opposite problem that no three of them will know each other is the same problem, again stated without proof.)  If you wrote out the first so-many integers in any order you wanted, how many would you need to guarantee a run of eleven in a row ascending (or descending)? 101, but 100 might work for special cases. To find a string of length n+1, you must have a universe of n^2 + 1.  Anyone in a first-term computer programming class could write a "Ramsey generator." 

Reading the book while commuting to work on the city busses, I misread one of the problems and worked a different one entirely.  It so happens that any odd positive integer raised to any integer power can always be expressed as the sum of two consecutive integers:  9^2 = 81; 81= 40+41.  7^5 = 16807 = 8403+8404. 

Suggestive as isolated cases may be, in mathematics, we need proof, and the more general the proof, better.  Best of all is a simple proof.  And a proof must reveal not merely that something is true, but why it must be true.  As abstract as mathematics is, when you work with integers these necessary truths became necessary factual truths because party guests and anything else we count are sensible evidentiary empirical objects.

So, one morning, I started with 2n+1, the common form of an odd number.  (2n+1)^2 = 4n^2 + 4n + 1.  That can be written as (2n^2 + 2n) + (2n^2 + 2n + 1), clearly some number and the next higher.  The next night, I did the same for cubes.  The following day, I had to open up a math book to see how to write out the expansion for any power n, an algebraic statement for Pascal’s Triangle.  I was pretty sure that I could complete the proof.  Then I realized that if an odd number can be expressed as 2n+1, that 2n is always some integer that admits to the existence of n and the next number would be one more than that.  More to the point, no matter what power (2n+1) is raised to, the last term of the polynomial will be 1.  You always will be able to find half the number and the integer next to it.  (I called it "Proving Gershon's Theorem" after the Sidney Harris cartoon: "You can't call it Gershon's Equation if everyone has known it for centuries.")

Then I tried it with negative integers.  They only work with odd powers.  And I can prove why.  It is child’s play, really.  But few people ever approach mathematics that way. Paul Erdős did.  In fact, he exhibited neoteny, never having any intimate relationships, being cared for by his mother into his sixties, being unwilling to cook for himself or otherwise look after the simplest daily tasks.  Instead, he was in constant motion, traveling to visit colleagues, imposing on their hospitality, in return for which, he gave them the impetus to publish over 1400 significant new ideas in mathematics.


Monday, May 4, 2015

Casa Brasil Coffee

Austin runs on cerebral energy.  Dell, Inc., is headquartered here, of course, but even South by Southwest gives top billing to mathematician and cybernetic futurist Stephen Wolfram. So, as freely as technology start-ups bring beer to user group meetings, we love coffee more. 

"Tuca left the Vale da Grama at a young age for Sao Paulo, pursuing a career in architecture and never imaging that farming would be in her future. After her grandfather passed away, the family considered renting out the farm, exiting the business they had been in since 1907. However, in 2010 Tuca returned to the Vale da Grama and, along with family business partner Rodrigo Fernandes, took over the management of Santa Alina. Their mission was two-fold, to increase the production of high quality micro-lots and to increase the living standard of those living and working on the farm."

The Casa Brasil website explains safra zero, or zero harvest.  “In the zero harvest system a producer prunes the branches of a coffee tree completely back to the trunk. After a year of regeneration with no yield, the tree will then produce larger amounts of coffee the following year. The process can then be repeated.”

If you shop directly with Casa Brasil, you can get blends or single-source (currently from the Fazenda Ambiental Fortaleza and Fazenda Recreio estates).  In all, they offer seven different roasts, including a Swiss water process decaf.


Sunday, May 3, 2015

Evolution vs. God

The premise is that Darwinian evolution is unproved and unprovable. It is accepted on faith, passed to students on the authority of professors.   Darwinian evolution has its problems, but this video does not address any of them.  It is a religious tract.

I got the video on the UT campus where they were being handed out.  Packaged as a bait and switch,  Evolution vs. God is a one-sided argument with an assortment of college students and professors. They are neatly boxed in by their own ignorance of Darwinian evolution and their personal failings as moral philosophers.  And, of course, we never see the ones who were not defeated.

Scientists have bombarded fruit flies with radiation for over 100 years, and never created a new species.  However the monsters turn out, they remain fruit flies, apparently still able to breed with others of their kind.  (Institute for Creation Research.)  On the other hand, the Archaeopteryx of the late Jurassic remains factually among several transitional animals between reptiles and birds. Gratefully, we can go swimming without meeting any of the creatures of Devonian.  What survived is fearsome enough. 

William Smith’s geological map of England was possible only because he relied on the facts of evolution. Simpler forms of the same kind never appear in rock strata higher than more complex forms.  Smith died 20 years before Charles Darwin published The Origin of Species.  

None of that is discussed in this video.  Nor did anyone ask the interviewer what happened to the dinosaurs.  And why do we not find fossil dogs and cats in rocks 150 million years old?

In the nineteenth century, geologists debated catastrophism versus uniformitarianism, and volcanism versus neptunism.  In other words, did the world we know now come about by sudden changes or gradual processes?  Were the primary forces violent explosions or accreting deposits?  Today, we regard those as false dichotomies. 

The debate between Darwinian evolution and Lamarckism may be another false dichotomy.  Epigenetics is the relatively new study of how the environment affects heredity.  The evidence seems compelling – and it seems unlikely that the environment would have no affect, leaving all evolutionary processes at the level of quantum physics.  The easy answer is: “I don’t know.” 

In science we live with our limits.  Science is self-correcting as we work to discover more about the world around us, and put that knowledge into an order that allows predictions.  Religion has no such limits.  They all claim absolute knowledge and – obviously and tragically – disagree about what that absolute truth may be.  Several times near the end, the interviewer (Ray Comfort, the producer) quoted an English translation of the Bible.  Which translation is right?  What happens when they disagree?  And, for that matter, the Qu’ran mentions Jesus about 25 times calling him Messiah and the Son of God.  And the Qu’ran acknowledges Mary as the Virgin and Mother of God.  Yet, somehow Muslims and Christians seem not to get along well. 

Evolution vs. God offers a second thesis: Darwinian evolution allows (even encourages and advocates) immorality.  According to this video, survival of the fittest excuses the harms, crimes, and horrors we perpetrate.  People embrace evolution to avoid following God’s Commandments.  “Are you a good person?” the interviewer asks.  Of course the subjects think well of themselves.  “Have you ever told a lie?”  “Have you ever stolen anything?” "Have you ever had lust in  your heart?" “Have you ever taken God’s name in vain?”  If you stop and think about it, the interviewer is also a sinner, but having accepted Christ’s sacrifice, he does not need to worry about that – or even mention it.  That being as it may, it is not a divine revelation that a selected handful of university undergraduates and professors have no idea what morality is.

All in all, the presentation was no better or worse than Reason TV productions where university students who say they voted for President Obama are happy to sign a petition based on the 1931 Nazi Party election platform. 


Friday, May 1, 2015

Happy May Day, Comrades

"Defending Capitalism Against Ayn Rand" by Steven Farron on Liberty Unbound, the website successor to R. William Bradford's print magazine, challenges mainstream Objectivism on what it means to be a capitalist.  Farron's thesis is that Ayn Rand was deeply influenced by the grand ideas of the Bolshevik Revolution while capitalism is really concerned with the seeming trivialities of life such as soap and lipstick. 

The essay resonated with me because from my first reading of The Fountainhead in 1966, it was obvious that Howard Roark was some kind of beatnik.  "He pulled his clothes on: old denim trousers, sandals, a shirt with short sleeves and most of its buttons missing."  At one of several crossroads in the story, we meet his antithesis, Hopton Stoddard, a mushy man, terrified by religion, and successful in several lines of business including real estate and contraceptives.  

The heroes of Atlas Shrugged could have continued living materially very well from page one if they just put up with some inconvenient government regulations.  But as The Internationale tells us: "You have nothing if you have no rights."

The Internationale
modern English lyrics

Stand up, all victims of oppression,
For the tyrants fear your might.
Don't cling so hard to your possessions
For you have nothing, if you have no rights.

Let racist ignorance be ended
For respect makes the empires fall.
Freedom is merely privilege extended
Unless enjoyed by one and all.

So come brothers and sisters
For the struggle carries on!
The Internationale
Unites the world in song.
So comrades come rally
For this is the time and place!
The international ideal
Unites the human race!

Let no one build walls to divide us,
Walls of hatred nor walls of stone.
Come greet the dawn and stand beside us;
We'll live together or we'll die alone.
In our world poisoned by exploitation,
Those who have taken, now they must give.
And end the vanity of nations;
We've but one Earth on which to live.

And so begins the final drama
In the streets and in the fields.
We stand unbowed before their armor.
We defy their guns and shields.
When we fight, provoked by their aggression,
Let us be inspired by like and love.
For though they offer us concessions,
Change will not come from above.

You can find many montages on YouTube.  
This is my favorite so far.

Also on NecessaryFacts

Tuesday, April 28, 2015

Sunday at the Co-op

A co-operative recognizes the reinforcing roles of consumer and producer.  I discovered something of truism that at any marketplace with high cultural context, such as a hardware store or fabric store, you could take the people on one side of the counter and switch them with the people on the other side and get the same result.  Co-ops are like that.  A co-operative is a community of providers and users, buyers and sellers, all of whom share a common interest in mutual profit.  Here are the vendors whom I met last Sunday at the Wheatsville Co-operative store on South Lamar  in Austin.

In Austin, Central Texas Bee Rescue (CTBR) sells wild honey and rescued honey.  Wild honey is collected from feral bees.  
They also sell crayons.
 "CTBR has led classes in beekeeping and other agricultural sciences in two Austin Charter schools (grades 1-9) and the Austin Montessori School.  They have also led workshops with Master Gardener Associations, libraries, and other institutions dedicated to education about the environment. They have noticed that beekeeping and caring for other animals has a positive effect on kids who grew up in the city and previously had no experience nurturing and caring. It melts your heart to watch."

Karen (right) suffered several small but significant bone injury accidents
over a few years.  Having tried many products,
she became a supporter of SunWarrior

"I can't say enough good things about them," she said. 
SunWarrior mineral-rich plant proteins sells a broad and deep range of “super green”  products.  Most are glutine-free.  All are vegan.  Typical ingredients include nrown rice, quinoa, and fermented bio-barley. 
Ismar and Daniel came to Wheatsville to
run taste tests and give out drinking cups.
I first drank Topo Chico about a year after I moved to Austin.  I was guarding a residential high-rise downtown and one of the residents – a serial entrepreneur – treated me to a bottle.  As mineral waters go, I found it to be high quality, richer, more satisfying than the other brands I usually buy, Crystal Geyer, and Whole Foods’ (Italian) Mineral Water. In this product, the sodium, potassium, magnesium, calcium, and manganese come directly from the geology of the spring.  They are not blasted in at a factory.

The legend of Topo Chico tells of an Aztec princess, a daughter of Moctezuma I who was cured of a mysterious ailment by bathing in the mineral spring.  Apparently, the entire royal troup all came home invigorated and refreshed.  
Topo Chico is great in cocktails (no surprise there) and, according to the AustinAmerican-Statesman, Topo Chico makes a heck of a coffee.  The company has its fan base, that's for sure.

"There are a plethera of records of co-operatives started out as small grassroots organisations in Western Europe, North America and Japan in the middle of the nineteenth century, however, it is the Rochdale Pioneers that are generally regarded as the prototype of the modern co-operative society and the founders of the Co-operative Movement in 1844. The Rochdale Pioneers are regarded as the prototype of the modern co-operative society and the founders of the Co-operative Movement." (International Co-operative Association.)


Monday, April 27, 2015


This year’s vernal equinox brought a solar eclipse that was visible across northern Eurasia. To view totality, you had to be on the Faroe Islands, 62° north between Scotland and Iceland, or the Svalbard group between Norway and the North Pole at 74° to 81° north.  I missed it entirely, and only saw the news the next day.  But I kept my head, unlike the drunken astronomers of ancient China.

(This is expanded and revised from an article published by The Sidereal Times (April 2015) of the Austin Astronomical Society.)

The story of Hsi and Ho came to my colleague Bradford S. Wade and me while we met often at The Tower Inn Cafe in Ypsilanti, across the street from Eastern Michigan University.  We had a class together, Ethics in Physics with Dr. Patrick Koehn.  After a few meetings or maybe only after a few beers, we took up a joint publication, a review of Astronomical Symbols on Ancient and Medieval Coins by Marshall Faintich.  We placed that in the Bulletin of the Society for the History of Astronomy, Issue 21, Spring 2011. 

As for the drunken astronomers, the stories vary and are often retold, especially by sky gazers, but the teaching point is easy.  Hsi  (also given as Hi or He) and Ho were the court astronomers.  Among their duties, they were responsible for predicting eclipses so that people could beat gongs, shoot arrows, and otherwise scare off the dragon that was eating the sun.  However, they spent most of their time drinking rice wine, so they not only failed to predict an eclipse, but they also slept through it.  Fortunately for all of us, the common people rallied and chased the demon away.  Hsi and Ho were executed. 

The story comes from an ancient manuscript known as The Book of Documents, which has been variously rendered as Shu-king, Shu Ching, Shujing, and Shangshu. (Wikipedia has an entry, of course: Book of Documents.)  The story of Hsi and Ho comes from the fourth part, fifth book, thirteenth chapter.  There, the chancellor, prime minister, or “prince” Yi Ying exhorts government officials not to be derelict in their duties as were Hsi and Ho. All of that happened in legendary times.  (The earliest attested date in Chinese history is equivalent to 831 BCE.)  The most likely date for the eclipse in question is October 22, 2137 BCE.

You can find some reliable modern detail at the Astronomy Today website.  Put “ancient eclipses” in the search box and it should come up first after the Google Ads.  The story of Hsi and Ho is in Part I. The story is embellished in Totality: Eclipses of the Sun, by Mark Littmann, Fred Espenak, and Ken Willcox (Oxford 1991; also on Google Books).  A brief note about the drunken Chinese astronomers, ending with an original poem, appeared in The Journal of the Astronomical Society of India, vol. 4. No. 3, Jan. 1914.  It was cited as coming from The Observatory for December 1913.  Indeed, it did appear in Volume XXXVI, Number 468, page 478. The author was C. Thomas Edgar

The pages below are from The Chinese Classics, Volume 3: The Shoo King or Book of Historical Documents by James Legge, first published by the author at Hong Kong in 1865, then reprinted with errata and corrigenda by Clarendon Press, Oxford 1893-1895.   Below these lines are lengthy glosses on the nuances of the grammar and syntax  of the ideograms.  A modern version (with only a few notes) was edited by Clae Waltham and published by Gateway Editions from Henry Regnery, Chicago, 1971.  You will see that at first Hsi and Ho are the family names of two sets of brothers.  Then, they became individuals.  Also, Legge's translation was before even the Wade-Giles system and is far from the modern Pinyang rules.