Ji bai zi

Where did “360 degrees” come from?

Jibaizi returned from a very long trip recently, to find a copy of Jon Bosak's The Old Measure sitting on the night-stand. The book is a erudite inquiry into the history and development of the traditional weights and measures: the pound, the gallon, the foot.

I was interested by the ancient emphasis on 12 as a divisor. It's not an obvious choice, mathematically; why 2 times 2 times 3? Why not 2 times 3? Why did the Babylonians choose 60 as a number base --60 is 3 times 4 times 5. Why not 30, which is 2 times 3 times 5, and the product of the first three primes? Why skip two? Of course, 12 and 60 are still deeply embedded in daily life – they are the basic units of time. Why? It begs the question to say "the ancients measured the heavens, and our concept of time comes from their measurements of the universe as a clock", or to claim that 12 is a rough analogy to the number of full moons in a year.

I have a speculation to offer.

Consider that division and fractions were messy. The Old Measure points out that Egyptians generally calculated with reciprocals rather than true fractions. So any fraction such as 2/5 would have to be written instead as (1/3 + 1/15). Evidently reciprocals were more intuitive.

Most reciprocals can be represented (and visualized) as regular polygons inscribed within a circle. Here are the first five regular (convex) polygons.

Note that there is no two-sided polygon – so we have to start with the triangle, representing division into thirds, followed by the square, representing division of the circle into quarters. Multiplying these two "reciprocals" together give you the dodecagon, with 12 sides:

times

equals 12:

 

In addition to being the Egyptian division of day and night into hours, twelve spokes was a ancient division for the wheel -- for example:

Twelve spokes, one wheel, navels three.
Who can comprehend this?
On it are placed together
three hundred and sixty like pegs.
They shake not in the least.

– Dirghatamas , Rigveda 1.164.48 (cited here)

Of course, 12 is deeply embedded in English counting –one through twelve are primitive numbers, twelve inches make a foot, twelve jurors make a jury, and so forth.

Twelve as a division of the whole is a natural geometric outcome of taking the two smallest polygons and combining them (by multiplication) to get a finer fractional division of the circle. This is a much more satisfying explanation than claiming that it represents the number of months in the year – the lunar length of the year has been known since deep antiquity to be closer to 13 months.

I'm sure you already see where this is going. Let's multiply from triangle through pentagon:

times

times

equals 60:

 

Triangle times Square times Pentagon yields the sixty-fold division of the circle beloved of the Babylonians. There aren't as many just-so stories about why 60 was chosen as a significant number, compared to the stories about 12; people say it's because it has lots of factors, but so does 30 (2 times 3 times 5), and 30 is close to the number of days per month – certainly as close as 12 is to the number of months per year.

Next, let's add the hexagon:

times

times

times

equals 360

 

Of course, 360 is the number of degrees in a circle. Apparently this was a Hellenic invention; it's alleged to have been chosen because it's close to 365. It's more satisfying to think of 360 as the extension of a series, than to think of it as a not-very-accurate approximation to the number of days in a year.

So a simple geometric progression based on the regular polygons gives us all of the common units seen in traditional measure: 12 (inches, Troy ounces, hours); 60 (minutes, seconds, Babylonian sexagesimal counting.

(Adding a heptagon gives 2520 as the next circular division in sequence. This is curiously similar to the tun that Bosak reports (p 44) as being composed of 252.0 wine gallons, but otherwise seems to have no special meaning. However, such fine division of the circle had little application for the ancients.)

Current Reading

Reading Simon Sebag Monetfiore's Young Stalin; came across it in the MSP bookstore.  Portrait of the tyrant as a young man.  The prose is a bit breathless at times, but it's clear that Stalin was never the mediocrity Trotsky called him.  Very interesting (and apposite) reading after reading Dipak Gupta's Understanding Terrorism and Political Violence (discovered by sitting next to the author on an airplane).  Gupta is an economist by training; I was reading Minsky; a conversation ensued.

Of course, am still working on Minsky' Stabilizing an Unstable Economy (previous post).  Nice quote from p 252:

Money, banking and finance cannot be understood unless allowance is made for fincancial evolution and innovation:  money, in truth, is an endogenously determined variable -- the supply is responsive to deman and not something mechanically controlled bythe Federal Reserve.

 

Books of Interest

A quick list of books that are helpful for understanding what's going on right now.

Keynes' General Theory as Punishment?

Columbia Professor Ray Horton says (in this post):

I don't ask my students to read the whole of [Keynes' The General Theory of Employment, Interest and Money], which would indeed be cruel and unusual punishment, but I do require them to read chapters 10, 12 and 24.

Jibaizi is somewhat dismayed to hear that reading The General Theory is punishment of any kind.  Professor Horton is teaching MBA students, who are (one assumes) university graduates.

More on The Men Who Stare at Goats

I know, I know, it's a strange mix: Adam Smith and the tinfoil-hat brigade from Ronson's The Men Who Stare at Goats.  Apologies to those who seek coherence.  But I digress....

Ronson's book cries out for a conclusion.  It almost seems that he's afraid to utter it, because it requires that a large statement be made without enough evidence, based only on anecdotes, inferences and hunches. 

Fortunately, journalism on weblogs consists mostly in overly general statements made without enough evidence.  ("In what household activity commonly involving sticks and bundles of rush are statements found?  Sweeping.")

America is not, these days, a rational society: we indulge in too much magical thinking.  "Use the force, Luke," moves us because the quack Zen Buddhism resonates with our native optimisim, Transcendentalism (yes, I have been reading Emerson in my spare time -- luckily I'm really more interested in Adam Smith), sentimentality, and love of happy endings. 

I take magical thinking to be "wishing will make it so".  Of course, all change in the world, all creativity, is in a way an expression of this magical thought -- I desire it to be, I make it so.  The desire is necessary. 

But desire is not sufficient.  Labor (aha, here's our road back to Smith) is required -- whether it be the physical labor of moving bricks or the physical labor of writing things down.  Discipline (a less tangible tendency to defer immediate pleasure in favor of future outcomes, which one may not even be alive to enjoy) is also required for most things, because the making itself is normally less pleasurable in the event than in the anticipation (or recollection).

Furthermore, desire, no matter how earnest and disciplined, sometimes cannot avail.  Death is final.  Aging is inexorable.  The past cannot be changed. I can climb Everest more easily (though it's not a realistic possibility) than I can undo something (cruel, stupid or enlightened) I did a second ago.  If I emulate the master and kill a kitten to educate my students, I cannot unkill it after the lesson is done.

("The past", of course, can be changed; and I don't mean Orwell's George Winston changing physical evidence.  I'm talking about what happens all the time.  Politicians notoriously change the past, by redefining events and actions post-hoc.  We all do it, and not just in the public space -- we redefine how we think about things so that we can live with them; or we simply forget them.  This is not changing anything that happened, however; it just changes how we think about the past -- in the present and for some time in the future.) 

To return to Goats:  this magical thinking is dangerous.  If you think that willpower can take you through walls like a disembodied spirit, and you act on that thought, you will probably get a bruised nose.  If you think you can fly as an act of will, and you jump off a building, you're likely to get a nasty fall. 

Magical thinking is controllable; we control it in most cases in due course.  It is avoidable.  As a lack of discipline, it is a form of sloth, a deadly sin, and therefore prima facia wicked.  But it's not just wicked in this scholastic sense: it causes people to do evil. 

People can do evil from many reasons.  Evil may come from acts consciously committed.  Even though Hollywood's overuse of this tends to make one suspicious, from time to time some people plan and execute plans that are consciously intended to cause harm, simply for the pleasure of it.

In common life, however, I think that evil is more likely to arise from magical thinking. 

The contractor in China who sells lead-tainted paint to a manufacturer is probably not thinking, "Aha, I can get more profit by poisoning small children".  He or she's probably thinking, "I need to save some money, and a little lead won't hurt": magical thinking.  The contractor has a family and a business to support. 

Similarly, the person infected with HIV who engages in unprotected sex is probably not thinking, "Now you've got it too," (though unquestionably some people have done so), but rather, "I don't really have HIV".

Less dramatically, the person (Rush Limbaugh or Happy Homeowner) who denies the reality of greenhouse gases and the likely consequences thereof, who denies the limited availability of oil and the eventual consequences, is not thinking, "Forget about the future, I'll live for today;" he or she is instead likely thinking, "It's not really that way -- I can't perceive it myself so it's not really happening."

These are not mistakes of "rationalization".  Rationalization means, at its root, taking an irrational action and making it rational, by constructing a logical framework.  This framework may be specious -- but it doesn't involve madness ("white is black", "if I walk towards this wall with the right attitude, I can pass right through it").

These are not mistakes of calculation -- they are mis-takes of reality.  They come from a lack of intellectual self-discipline (or equivalently, from intellectual self-indulgence). 

America is an extremely self-indulgent society -- what is the inalienable right to "the pursuit of happiness" other than a license to self-indulgence?  But nobody in Philadelphia in 1776 thought that happiness could be pursued irrationally.  Magical thinking is the invidious enemy of rational thought.  We need to indulge ourselves in what we do, in how we shape our lives, but not in how we think.  "Pursuit of happiness" is not the "accomplishment of happiness" -- the phrase itself implies that discipline is needed, along with rational consideration of means.

We especially need to guard against magical thinking in politics, as it's something that the adversarial system in the US is not set up to contain.  Our system was set up on the assumption of rationality in the elite, and designed to contain the enthusiasms of the masses. Checks and balances were set up to constrain people who try to grab power, not to constrain people who are functionally irrational.  Calling someone crazy in a political debate is simply not done -- and if that someone is not literally barking, it would not be an effective ploy in our system.  Let's face it, Cheney's behavior and demeanor are quite bizarre, and yet nobody dares call him mad.  It's easier to call someone stupid or evil.

Magical thinking can affect anyone, no matter their intelligence.  It is fundamental human nature.  The self-esteem movement -- haven't heard too much about that recently, have we? -- in some ways encouraged it.  Thinking you can't do something is always negative, but is not always wrong!  Therefore thinking you can do something may be magical thinking, and so needs to be tempered by reflection. 

It is frightening, therefore, not amusing, to read a book that seems to show that a big part of the US defense establishment is not only infected by, but is practicing, magical thinking. 

It is one thing for people like Bush, Cheney and Rumsfeld to be mad.  It is another thing for whole echelons of the Army and of the CIA to be mad.  What is it other than madness to seriously consider The First Earth Battalion Operations Manual as a basis for reorganizing the US Army?  It's hard to dismiss the evidence from Goats that it was seriously considered. 

Once magical thinking is admitted into an organization, the organization loses its ability to function rationally (and in accordance with its goals).  This cause organizations, while attempting to do good, to do what they ordinarily would recognize as reprehensible.  The Catholic church is an organization that tends towards good, but the Inquisition was evil done in evil ways.  The American Army consists of men and women who are generally good, but our treatment of "enemy combatants" is reprehensible.  On the evidence of Abu Ghraib and Guantanamo, and the connections between the interrogation techniques used there, and psycho-babble of the most irrational kind, the tendency to madness has spread through the organization.  Given how far it's already gone at times of rather mild stress, it's unclear how far this might go. 

An aside on Uri Geller

Some of the evidence in The Men Who Stare at Goats is, in retrospect, unconvincing.

I was originally going to say that it would be madness to recruit psychics such as Uri Geller or Prudence Calabrese to alert the authorities should they have visions of future terror attacks.  It were madness to ask Guy Savelli to help train Special Forces to do thought projection.  Ronson quotes them as saying that they were, and by embedding in much stonger evidence, one might think it's so. 

But here Ronson is on thin ice.  His cited evidence comes from people who are themselves clearly maddened by magical thinking.  This makes the evidence suspect (falsus in unum, and so forth).  Embedded in a book with more concrete evidence of delusion, the stories are suggestive -- but nothing more.

Read the book and judge for yourself.

Magical thinking and the war

Somone recently wrote that war between nation-states may have become obsolete, as a way of achieving national goals?  (Perhaps it was in Harpers.  I'll check and post the reference if I can find it.)  The essay started by quoting Oliver Wendell Holmes rhapsodizing to students at Harvard about the glory of the experience of war [surprising on two levels: Holmes is somewhat of an icon to me, and I think of him as saddened by his experience; and I knew about the speech, and didn't place it as glorification of war, though it unquestionably is].

Certainly magical thinking applies to the choice to go to war.  What rational decision maker would choose war if they really considered the costs and the risks, especially if they knew they were weaker and bound to lose?  People in government in Japan knew that they couldn't win a sustained war against the US, but out of "magical thinking" -- a belief that spiritual superiority could compensate for lack of material -- the government went to war anyway.

More trivially, people in the US government had sufficient evidence to know that there was no reason to go to war with Iraq in 2003, that there were no weapons of mass destruction and that there was no good exit plan.  In this case, it seems that the madness was more pervasive -- there's no evidence of any rational thought at the highest levels, except possibly for Colin Powell, and the generals, quickly fired, who wanted a much higher commitment of troops.  During the occupation, Brennan wasn't mad, merely incompetent, so we can also exclude him from this indictment. 

I think it's well known that you can't argue with madness.  If all parties are rational, as for example in most trials in the US (referring to the lawyers and the judges, not to the plaintiffs, defendants or juries), rational arguments can be made.  Opposition is expected, and must be dealt with in a more or less principled and rational way.  But when dealing with madness, rational argument just slides off, as it were.  Opposition is personalized, or demonized.

Opposition to magical thoughts is very threatening to the magical thinker.  Because they're irrational, the mind organizes itself around them to insulate the mind from data that contradicts them, and uses emotion to this purpose.  This is not conscious or cynical -- it's just a consequence of magical thought.  It's why mental self-discipline is so important -- discipline lies in doing unpleasant things for future benefit, and taming magical thought is extremely unpleasant.  If you're not used it -- and it requires constant practice -- it's not easy.

Given magical thinking, it's no wonder that no amount of argument could prevent the war that basically everyone who thought clearly about it could immediately see was stupid, wrong and unwinnable.

Most of the press was not thinking magically about the war -- it was just incompetent. The NY Times was incompetently edited during the run-up to the war; Judith Miller's infamous articles should never have been printed,  It is easy to see in retrospect, and therefore it was the editors' responsibility at the time to see, that they were based on magical thinking.  Perhaps the only magical thinking in the press was this:  "Bush, Cheney, Rumsfeld, Wolfowitz, et al: they're not stupid people, surely they can't be mad?"

But they were, functionally.  Cheney, by all evidence, still is.  It's interesting that the madness became obvious to the country during and after Hurricane Katrina; it took obvious dysfunctional behavior to convince the press that something was seriously wrong in government.  They decided that the government was stupid, but that's either the wrong conclusion or it's sugar-coated.  The horrible truth is that a large number of the people running the current government are simply functionally mad.  Our political system cannot deal with this problem. 

The Men Who Stare at Goats -- a precis

Enough about bookstores.

The Men Who Stare at Goats is a book about odd people doing strange things verging on wickedness.  It describes the same kind of delusional behavior that drove Bush's entry into Iraq.  It connects a number of people, groups and events that I had not known were connected, including:  US military intelligence, the New Age lunatic fringe, Uri Geller, Art Bell (of midnight radio fame), remote viewing, Branch Davidians, the Heavens Gate cult, Manuel Noriega, Abu Ghraib, Guantanamo, MK-ULTRA, the suicide of Army scientist Frank Olson in 1953 after the CIA slipped him LSD, and Barney the Purple Dinosaur. 

The book reports compounded irrational behavior in a commonplace way.  This matter-of-factness makes it rather hard to get a grip on the book itself, or to respond to it in any straightforward way.  The author, Jon Ronson, maintains a wry detachment, and leaves the conclusions to the reader. 

In the second chapter, he explains that he got interested in the story when he heard that Uri Geller had been working for the US government in the 1980s.  He figured there were four possibilities:

• "It just never happened.
  
• "A couple of crazy renegades ... had brought in Uri Geller.
  
• "US intelligence is the repository of incredible secrets, which are kept from us for our own good; one of them is that Uri Geller has psychic powers....
  
• "The US intelligence community was, back then, essentially nuts through and through."
  

The book presents evidence tending to prove the last point, and moreover indicates that there is a deep strain of delusional behavior and magical thinking traceable from the mid-70s to 2003 Iraq.

Ronson makes these connections in a picaresque way.  In some ways, the book is really the story of how he got people to tell him their stories.  He's pretty sympathetic to his sources, who include:

• General Albert Stubblebine (who apparently believed and believes that it's possible for people, including himself, to walk ghost-like through walls),
  
• Jim Channon (who, as a Lieutenant Colonel in 1979, apparently wrote a presentation for the US Army called The First Earth Battalion Operations Manual)
  
• Prudence Calabrese (who, as a psychic and remote viewer, participated in the Art-Bell-driven mania that culminated in the mass suicide of the Heaven's Gate group)
  
• Guy Savelli (a martial arts teacher who believed he could kill hamsters with mental energy)
  

A lot of this material is so nutty that it's hard to believe that it's not all made up.  But... as it happens, I have heard people on Art Bell's show going on about "remote viewing".  (Don't ask my why I was listening.  Ithaca is a long way from anywhere and so I sometimes end up coming back from, or going to, a distant airport late at night.)  So Ronson hasn't made it all up.

Other people's delusions can be very funny.  Ronson's approach reminds me very much of Michael Moore's early documentaries:  deadpan sympathy for the characters, combined with just enough irony to let the reader know that Ronson thinks it's all crazy.  (It's probably no accident that I'm reminded of this -- the inside blurb notes that Ronson is a documentary maker. That probably set me up to make the connection of style, but while reading the book, I was also trying to place the approach -- something was happening but I knew not what it was.)

So it's a documentary in prose, not a report, nor a polemic. 

The title, by the way, refers to a group of people at Fort Bragg who, it seems, sincerely believed that they could kill goats by pure thought, or at least believed enough in the possibility to set up a secret research facility.  (I suppose it would be easier if they were "fainting goats".)  Evidently after perfecting the trick on goats, they planned to move on to people.  It appears that they never perfected the trick, but that they moved on anyway.

A man after my own heart

What a wonderful sentence at the end of Smith's chapter on the Origin and Use of Money:

I am always willing to run some hazard of being tedious in order to be sure that I am perspicuous; (p42)

I just want to pause in admiration of his modesty and honesty.  The sentence continues:

and after taking the utmost pains that I can to be perspicuous, some obscurity may still appear to remain upon a subject in its own nature extremely abstracted.

Money is indeed an abstract subject.  The possible tedium that Smith refers to is his extremely patient, step-by-step consideration of the topic.  Possibly only a programmer (a systems programmer at that) would be interested in anything considered in such detail.  But that's me, or the part of me who found the careful presentation wonderfully precise and intelligible exactly because of the minute consideration of the details.

Mourning the death of bookstores

Bookstores are dying.  This cannot be denied.  In Tokyo (apologies for name-, or perhaps, city-, dropping), my favorite bookstore (Maruzen in Nihombashi) was recently upgraded and dumbed down to meet the current market situation.  No art books, many racks of foreign books reduced to four, no Blyth on the shelf.  Too sad.

This change is understandable -- we're a world of people who know what they like, and like to get it from Amazon.  It's less and less practical to use retail space to store books sorted by the essentially accidental attributes of topic and author.  There just are not enough eccentrics who like to browse, especially to browse foreign books.  As a result, we lose the quirky and wonderful juxtapositions that naturally arise when a foreign buyer stocks a large store with English books.

Still, we're not quite at the last hurrah.  Recently at the Maruzen in Ochanomizu (only one rack of foreign books: even the new Nihombashi store is better) I chanced upon The Men Who Stare At Goats (ISBN 0-33043646-5).

I have no idea what prompted me to pull it out.  I don't remember exactly why I opened it -- the title doesn't particularly move me, it seems.  It may have been the back-jacket blurb:

"Why are Iraqi prisoners of war forced to listen to Barney the Purple Dinosaur's theme tune repeatedly, at top volume?"  [Perhaps it was the anglicism, "top volume".] 

"Why have 100 de-bleated goats been secretly placed inside the Special Forces command centre at Fort Bragg, North Carolina?"  [Maybe it was the Lee Childs book I recently read, with Reacher based at Fort Bragg, and bad things happening all around.] 

"Has the US Army really enlisted the help of Uri Geller?" [That must have been it -- Uri Geller is a great hook, especially in conjunction with the US Army and Iraq.]

Alas for me, there are no book-jacket blurbs on Amazon, and there's no browsing of a quirky selection.  (Don't tell me about reader posted lists -- bad lists drive out good.]  The serendipity of browsing on Amazon (be there any) is programmed.... if you like X, statistics say you'll like Y. 

Doesn't seem to work for me.  I like Bob Dylan an awful lot and I've bought many CDs from Amazon.  The conclusion Amazon draws is that I'll like Dave Matthews; so I immediately become suspicious of Amazon's recommendations.

But I digress.

Or maybe not. My point is that there is no substitute for the serendipity of a bookstore, an encyclopedia, a dictionary, where the editors have [anonymously] put things in array, and the reader cannot help but find unrelated things through searching.

Contemporary search is, by contrast, too bloody precise.  You enter the words you're looking for, and whether they be embedded in Edward Gibbon or Marquis de Sade, you get results.  Narrow it down, and you nail it -- but you lose the serendipity.

I love nailing a search request.  Saves me time on the job.  But for my life (as opposed to my job) I want serendipity.  I want to see the quirky books that happen to be close by, chosen by some unknown buyer.  I know it can be done -- I can see the interface in my minds eye.  Someone else will do the interface (independently) -- but then who make the selections, and how will they be paid?  Google ads are just repulsive....  like the personals at the back of Harpers....