All the ways—

What scares you more: that I will talk of death, and injustice, and spiritual annihilation?  Or that I will explain how the equation

Pfi  = ∑ Γ(S)

affects your life?

Admit it.  You want death.  You want injustice.

You want spiritual annihilation.

I get it, I get it.  Math is an annoyance; math is anathema.  As it did for the learn’d astronomer, math makes you unaccountable tired and sick.

Maybe math scares you.  Or worse—maybe math bores you.  Fear you can take, and anxiety in equal measure; but boredom, never.  It wasn’t time but boredom that sunk Ozymandias into the lone and level sands.  Because—

Because (you say) math is about numbers.  That’s it.  It’s just numbers.  By enumerating, you take away a spark.  That which can be counted, can be dismissed.  A mathematician is a bean counter with a pocket protector, somewhere on the spectrum, digitizing nature, walling off the soul with a wall of 1’s and 0’s.

But it isn’t true.

I could plead that mathematicians don’t usually think of numbers.  They think about patterns, symmetries, interconnectedness.  They see math in the petals of a daisy, and in the predator/prey cycle of lynx and snowshoe hares.  Math is in the strength of nanowires, and the delicacy of hoar frost, and the oomph of an engine, and the whorls of a Spirograph.

I could plead that math is about connections, structures.  Math is the study of logical systems.  Numbers are beside the point.

Beside the point.

I’m looking right now at the white-board in my office.  Ignore the calendar with a picture of Crater Lake, and ignore the poster of Han in Carbonite, and ignore the Albert Einstein action figure, and the pamphlet which says “Welcome Aboard Marine One.”  Focus on the white-board itself: it’s covered with equations, in red and green and blue, with doodles, starts and stops, arrows and spirals, letters both Roman and Greek.  There are graphs of velocity vs. time.  There’s a derivative, and an integral.  There’s Newton’s 2nd Law, half-erased.

There are no numbers on the board.

I could plead still, but here is what I know: that math is beauty, and that the whole world is math.  Here in my ivory tower, I adhere to the Mathematical Universe Hypothesis, which posits that the multiverse is itself is “just” a mathematical structure.  It’s not infinite turtles, but math, all the way down.

Jump if you like: you’ll never hit the bottom.

And what of the equation I gave?  What does it say?  To whom does it speak?

It comes from a paper I wrote, across a gulf of years and disciplines.  It says, in English, that the probability of going from quantum state A to quantum state B is the sum of all the products of closed-loop amplitudes that include A and B.

I am A.

You are B.

To get from me to you, we have to count all the ways we can interact, including ways that go backwards from you to me.

We add up all the ways.

And in the end you don’t have a number, but possibilities.



I’ve talked in the past about the RGB color scheme, and about extra spectral colors.  Here I want to ask a specific question: why do some RGB color combinations have names, while others do not?

First, a review.  Most (but not all!) colors that humans can perceive can be represented (approximately) by a set of three numbers (R,G,B) where each variable runs from 0 to 255.  Roughly speaking, a 0 is “none” of that color and 255 is “maximum” of that color.  Thus (0,0,0) is black, (255,0,0) is red, etc.  What’s interesting is which combinations get names in English, and which do not.

Suppose two colors are maxed out.  (255,255,0) is equally red and green; if you’re familiar with color addition, you know this is yellow.  Similarly, (255,0,255) is magenta, and (0,255,255) is cyan.  So far, so good.

Now suppose one color is maxed, and another is at half value.  Here’s where things get interesting.  Consider (255,128,0), which is (in a sense) halfway between red (255,0,0) and yellow (255,255,0).  Not surprisingly, (255,128,0) is called orange.  But what about halfway between yellow and green, i.e. the color (128,255,0)?  Mathematically, this should be as unique a color as orange, but (sorry) it just looks like a different shade of green to me.  Why is that?  What’s special about (255,128,0), but not about (128,255,0)?

It turns out that (128,255,0) has a name: chartreuse.  But probably only one person out of twenty could identify chartreuse out of a line-up.

If you want to experiment, try the other “halfsies” using this RGB applet.  The combinations you should test are

(255,128,0) = ORANGE

(128,255,0) = CHARTREUSE

(0,255,128) = ?

(0,128,255) = ?

(128,0,255) = ?

(255,0,128) = ?

Only one of these is obvious to me, i.e. the color (0,128,255) which is halfway between cyan and blue.  That’s the color of a clear sky, and is known in English as azure.

Do any of these combinations have unique names in other languages?

Here’s a modern-day color wheel (thanks, Wikipedia!), which puts all of this into perspective:


[Note that “violet” here isn’t really true violet (as in a rainbow), which cannot be represented on an RGB computer monitor.]

Are these the names you came up with?  Personally, I called (0,255,128) “dark mint green” instead of Spring Green, but what do I know.

And here we get to the psychology of color, which is the main point of this post.  Look at the trifecta of red/orange/yellow: most people would classify those as three really distinct colors.  Now look at the trifecta chartreuse green/green/spring green.  Those all just look like green, to me.  They aren’t as distinct.  And I think the reason is completely in my mind.

Think back to when you studied color in kindergarten.  The “primary” subtractive colors were red/yellow/blue.  [That’s now known to be bullshit, of course; there are no three canonical primary subtractive colors; we instead make a choice of three primaries based on what colors those three could possibly make upon mixing (this is called the gamut) and  cyan/yellow/magenta gives a better gamut than red/yellow/blue.  Put another way, if you only had three crayons, then choose cyan/yellow/magenta instead of red/yellow/blue because more mixed colors will be available to you.]  Anyway, now look at the RGB wheel and find red/yellow/blue.  They aren’t equidistant.  Something is wrong.

Here’s my thesis: I think that the red/yellow/blue bullshit we lived through at the age of 6 has biased us towards thinking that red and yellow are more different than they really are.  Look at the wheel again.  In terms of RGB numbers, red and yellow are as similar as blue and cyan.  Hard to believe, I know, but that’s the way the cookie crumbles.

One final thought: in English, in kindergarten, when you mix white with red, you get pink.  What about mixing white with green?  Or white with blue?  How come there aren’t unique names for those colors?

(255,200,200) = PINK

(200,255,200) = ?

(200,200,255) = ?

There once lived a man who had strange dreams.

One of the dreams regularly involved a tennis tournament played on a mountaintop in Peru.  Another had an origami master who was the operator of an armored personnel carrier.  Yet another consisted of an Australian women’s rugby coach who moved to Serbia, opened a brewery, and wrote a novel based on the life of Python of Byzantium (Πύθων ὁ Βυζάντιος).

The worst of these dreams, however, was a nightmare which tormented the man periodically.  In this nightmare, there was a xylophone made from human bones: finger bones for the high notes on the right, down to an enormous femur for the lowest note on the left.   In this nightmare, the man was invariably tied to the xylophone with shigawire, while a demonic musician played something execrable (such as Vivaldi’s Four Seasons).  At the climax of the music, just when the man was on the point of being driven entirely insane, the ghost of Warren G. Harding poured grape juice onto the xylophone from an amphora made of jade.

At this point the man always awoke with a start, in a cold sweat, sometimes screaming, sometimes crying.

It goes without saying that the man developed a lifetime phobia of grape juice being poured onto xylophones.  And worse: he developed a fear of almost any juice product being dumped onto any percussive mallet-based instrument.

He avoided Kindergarten classrooms, for who could say that little Timmy might not pour his juicebox onto that glockenspiel?  He avoided performances of Danse Macabre by Saint-Saëns, for might not the percussionist have a flask of wine which could spill forth?  And forget ever going to see the Rolling Stones in concert: might not a band member spill a screwdriver onto the marimbas during “Under My Thumb”?  All told, the man’s phobia represented a very minor, but non-zero, inconvenience.

Our story would be of little interest were it not for the fact that the man became Emperor of the World.  How this was achieved is of no consequence to this parable; suffice to say that the man lied, preened, stole, and schmoozed his way to the top.  But once he was in power, the now-Emperor decided that he could now rid himself of fear, by passing a law.  The law was presented thus:

As Emperor of the World I hereby ban the pouring of grape juice onto xylophones.  Anyone caught committing such a traitorous, cowardly act, will face the full wrath of our justice system, and be imprisoned for not more than 33 years.

The Emperor released this edict and went to bed content, confident that his nightmares were over.

But there were unintended consequences.

Most people had never, in their wildest fantasies, entertained the notion of pouring grape juice onto xylophones.  The whole concept never crossed their minds.  But now, with the Emperor explicitly banning the practice, the pouring of grape juice onto xylophones (PGJOX) became A THING.  Suppose you wanted to irk the Emperor, get under his skin, be a gadfly, protest his policies.  What better way, than PGJOX?  Whereas before the Emperor clawed his way to power, there was not a single case of PGJOX, after the edict there were thousands of such cases.

The Emperor was too dense to realize that his law had caused all that grape juice to be poured.  Indeed, the ballooning of PGJOX cases reaffirmed his pre-conceived notion that PGJOX was A THING, and had always been A THING, and so his law was justified.  There was a vicious cycle: the more he railed against PGJOX, the more people performed the act he hated; this in turn caused him to rail against PGJOX all the more.

What became of the Emperor?  And what became of the law?  And what became of pouring grape juice on xylophones?  In the first case, his nightmares returned, his dreams became indistinguishable from reality, and we are still to this day (centuries later) recovering from the 30-year rule of the Mad Emperor.  Of course, the law banning PGJOX was repealed eventually, but (interestingly) pear juice is still poured onto vibraphones every Nov. 30 in parts of Alberta and Saskatchewan (on Banff Day).

Moral: if you’re a lawmaker, and there’s some strange act that makes you uncomfortable, then shhhhhhh…don’t do anything.  Don’t bring attention to it.  Passing a law against your pet peeve is just lighting a match and handing it to your opponents.

But don’t trust me.  Trust the ghost of Warren G. Harding.


There’s a lot of talk these last few days of how horrible it would be if, for example, Penn State wins the Big Ten championship but doesn’t make the college football Final Four playoff.  This would happen if, say, Washington (the current #4) loses to Colorado in the Pac-12 championship.  Presumably, then, Michigan (now currently #5) would move up into the #4 slot, leaving the Nittany Lions crying into their Wheaties.

Why would this (ostensibly) be horrible?  Well (the argument goes) you’d then have two Big Ten teams (Ohio State and Michigan) in the playoffs who didn’t even win their conference.  Some people think this would be a travesty.

I disagree.  Winning (or not winning) a conference is essentially meaningless.  That’s because it’s entirely possible to win the conference with a shitty record.

Image result for big 10 trophy

First, we have to discuss how the Big Ten champ is chosen.  There are 14 teams in the Big Ten, not 10. (We’re already in Twilight Zone territory here).  7 of the teams are in the West division, and 7 are in the East.  Each year, each team plays 4 non-conference games, and 8 conference games; of those 8, 6 are in the same division, and 2 in the other division.  The winner of the West will play the winner of the East to determine the Big Ten conference champ.

Suppose, in the East, Michigan, Ohio State, and Maryland all post 11-1 records; each losing only one division game to one of the other two.  Based on arcane tie-breaks, one of these (presumably) good teams will be invited to the Big Ten championship.  Let’s say it’s Maryland.

In the West, however, imagine that all 7 teams have identical 3-9 records.  They achieve this by losing all non-divisional games, and splitting their West division games 3-3.  One of these (crappy) teams will go to the Big Ten championship game by tie-break.  Let’s say it’s Iowa.

So it’s Maryland (11-1) vs. Iowa (3-9).  Maybe Iowa wins on a fluke (Maryland’s QB gets the flu, or a ref gives the game to Iowa by awarding a 5th down…these things happen).   Despite this head-to-head result, is anyone really going to rank the now 4-9 Iowa Hawkeyes over the 11-2 Maryland Terrapins?  Of course not.

Here’s the mathematical reason that conference championships are meaningless: all they tell you is that you’re the best team out of a subset of teams.  And that doesn’t really tell you much at all.

Suppose we had a tournament for BIG COUNTRIES.  Who would you rank among the top BIG COUNTRIES?  My top four would be Russia, Canada, USA, and China.  “But wait!” says Algeria.  “I won the Africa division!  And the USA is smaller than Canada and so didn’t even win its division!”

If we want to pick the BIG COUNTRIES, then being the biggest country in your continent is meaningless.  Similarly, if we want to find the best teams, finding the best teams in conference divisions is meaningless.

One way to mitigate this problem is to eliminate conference divisions entirely.  In the hypothetical scenario mentioned above, if the Big Ten just had one 14-team division, then Iowa would stay home and Maryland would play Michigan (say) for the conference title.  Still not perfect, but we’d definitely know then that a good team had won the conference.

I’m not lobbying for any sort of change in the NCAA playoff selection rules.  I have every expectation that the committee will do the right thing, regardless of whether Washington wins or not.  Their ranking Ohio State #2 despite not even going to the Big Ten title game is indicative of that.  What I am advocating for is for people to shut up about conference champions.

Hey, Algeria: just because you’re the biggest country in Africa doesn’t make you a top-4 country.

Image result for algeria flag










Huang Gongwang: Dwelling in the Fuchun Mountains (Part)

If you listen to one piece of music today, let it be this:

When I need comfort, this is the best piece of music I can imagine. It’s one long movement. It’s one continuous narrative. There is no suspension of disbelief required, by which I mean you don’t really hear individual instruments as instruments, or hear the whole orchestra and think “that’s an orchestra”. You forget you’re listening to a performance at all. You forget you’re listening to something man-made called “music”. It’s almost as if you’re listening to perfection, translated into the medium of music. The notes swell and ebb, and you wander through a beautiful yet haunting landscape. When every climax is reached, when every section finds its conclusion, the music evolves gradually, and a new summit is attempted, a new path is taken. But the previous sections don’t end; they become (in turn) the backgrounds for what lie before you. Listening to the 7th is like hiking a ridge line in the mountains, cresting apex after apex, but your previous climbs are always behind you, receding only gradually into the past. At many points in the journey, you think you’ve reached the top of the mountain, only to see the sun glint off a snowy peak in the distance, and realize you can yet climb higher. The ending is abrupt and resigned, like freezing to death on the mountaintop. If you cry, it’s just the cold wind in your eyes.

Here’s something that will never happen, but it would be awesome:

The NCAA should go to a Swiss-system for college football.  And I don’t mean for the playoffs; I mean for the entire season.

First of all, here’s a brief primer on what the Swiss-system is.  I don’t think I can explain it better than the hive mind on Wikipedia, so here’s a quote:

“A Swiss-system tournament is a non-eliminating tournament format which features a predetermined number of rounds of competition… In a Swiss tournament, each competitor (team or individual) does not play every other. Competitors meet one-to-one in each round and are paired using a predetermined set of rules designed to ensure that each competitor plays opponents with a similar running score, but not the same opponent more than once. The winner is the competitor with the highest aggregate points earned in all rounds.”

Such systems are very common in chess tournaments, and also used in backgammon, squash, and eight-ball tournaments.  I’ve never heard of them being used in team sports, which is a pity.

Image result for bern

If I were Emperor of the World, here’s how I would implement the Swiss-system for college football.  At the beginning of the season, I’d rank the 128 FBS teams (teams that normally are bowl eligible) from #1 to #128.  (Well, I probably wouldn’t rank the teams personally, but I’d have a computer and/or a committee rank the teams much as the BCS does now.)  The great thing is that a ranking of #1 vs. a ranking of #5 (say) at the beginning of the season wouldn’t matter much at all.

The first week of the season, #1 would play #65, #2 would play #66, and so on.  For illustrative purposes, if we based seeding on the current NCAA rankings (as of Nov. 7, 2016), we’d have Alabama (#1) playing Southern Mississippi (#65), Michigan (#2)  vs. Texas Tech (#66), Clemson (#3) vs. Georgia (#67), Washington (#4) vs. NC State (#68), and so on, down to California (#64) vs. Florida Atlantic (#128).  Every higher-ranked teamed would be favored of course, but you’re going to get plenty of upsets: every one of the matchups I just (arbitrarily) presented would be a decent game.  Gone would be the days when an Alabama would play a non-FBS Western Carolina for their first game and win 49-0 to pad their resume.

Starting with week #2, things are already interesting.  Every week after the first, each team plays another team with the exact same record (if possible).  Continuing with my example, and assuming that all the higher ranked teams won in week 1, you’d already have on the table Alabama (#1) vs. Troy (#33), Michigan (#2) vs. Tulsa (#34), Clemson (#3) vs. Minnesota (#35), etc.  None of these games are cake-walks by any means (for perspective, the current records of Alabama, Michigan, and Clemson are all 9-0, but the current records of Troy, Tulsa, and Minnesota are 7-1, 7-2, and 7-2, respectively.)

Here’s the thing: starting with week 2, every single game in college football is a competitive game.  And starting around week 4, every single game is almost evenly-matched.  We’ve eliminated the all-too-common problem with the current system: that the top teams really only play 2 or 3 meaningful games a year.

Suppose we were using the Swiss-system, and we were making the matchups for the coming week’s games (Nov. 12).  What games would be on tap?  Well, there are currently 5 undefeated teams, which in a Swiss-system would be very unlikely after 9 weeks.  Just for fun let’s assume that it’s possible, but let’s ignore Western Michigan (no way they’d go 9-0 if they faced a few good teams).  With Alabama, Michigan, Clemson, and Washington all 9-0, this week’s marquee matchups would be Alabama vs. Washington, and Michigan vs. Clemson.  It’s likely that next week you’d have Alabama facing Michigan.  This, in early November!

The good matchups continue all the way down the line.  One-loss teams would all face each other, and you’d perhaps have games like Louisville vs. Ohio State.  Even at the bottom of the barrel, with a Rice playing a Florida Atlantic, the games would be evenly-matched.  This would be great for fans, because as it stands, when a Rice fan attends a game, they fully expect a loss; but with a Swiss-system, that same fan can be hopeful for at least a 50-50 shot at winning.

At the end of the season, an undefeated team would be almost impossible.  It’s likely you’d have 3 or 4 teams that were 10-2, and they’d all have already played each other.  That’s when a playoff would kick in.

For the playoff, we’d have the 4 (or better yet, 8) teams with the best records play each other in a standard elimination format.  At this point, it wouldn’t matter if they’d already faced each other in the regular season; rematches at this point would be desirable.  The great thing is that these teams would all be excellent teams.  In a Swiss-system, if you go 10-2, facing tougher opponents every single week, no one can argue you aren’t one of the best teams in the country.  Built into the Swiss-system is an important feature, which is that basically, every team at the end with a similar record faced a similar strength of schedule.

This is important, for in the current system, teams which are 12-0 can be left out of the playoff discussion if they’d didn’t play any good teams.  That’s never struck me as particularly fair.  If my team goes 12-0 and doesn’t get to the playoffs, then that means the team never even had a theoretical shot at making the playoffs to begin with.  What’s the point, then?  It’s a sordid fact that in the current system, there are only 30 or so teams that can ever even theoretically make it to the playoffs in a given year.  I’m sorry, Florida Atlantic, but if you go 12-0 next year you ain’t playing in a major bowl game.

There are obviously a few objections one could raise to my brilliant scheme.  Let’s address them.

  1. What about logistics? How in the world could you have teams flying around the country, facing each other, planning trips on only a week’s notice?  Well, as Emperor, it wouldn’t be my problem.  But in any case, it’s the 21st century for Xenu’s sake, so I think with some 747’s and the internet, it could be done.
  2. What about revenue? If Western Carolina doesn’t get to play and get crushed by Alabama, then Western Carolina loses out on some big time TV money!  OK, sure, but the games will in general be much, much more competitive, and many more fans will go to see WCU home games since they finally have a chance to win.  I really believe TV revenue would be up across the board.  We could even implement a TV revenue-sharing scheme, but that’s a topic for another day.
  3. What about rivalries? Well, what about them?  The current system doesn’t give a fuck about them in any case.  I can’t even keep track of who’s in what conference these days.  (Syracuse is in the ACC?  When did that happen?  They’ll always be a Big East team to me.)  With a Swiss-system, conferences become meaningless, and I say good riddance.

Image result for army navy game 1963

As for the handful of actual rivalries that still exist, and haven’t become jokes, such as Army vs. Navy (come to think of it, that has become a joke) or Alabama vs. Auburn, you could have the teams play an extra game in mid-December that doesn’t really count for anything.  If you think it’s unfair that a team has to play an extra game compared to other teams, well then, why not have every team pick a greatest rival that they have to play every year?  Hell, these games might even be the first games of the year, a sort of pre-season-type game, and the results don’t affect the Swiss-system per se, but the results might inform the seedings.  So Navy plays Army (a joke game, usually) but if Navy loses, we might initially rank them a little lower than otherwise.

Would any of this ever happen?  Not one chance in a million.  But it’s fun to speculate about.  And mark my words, in the universe(s) where I actually do become Emperor, initiating an NCAA football Swiss-system is one of my first magnanimous acts.