Roll the Dice
3 Mar 2002
I'm listening to "The Infinite Mind" on public radio right now --
they're talking about gambling. If you've read any of my entries on
poker - whether bluffing, wild cards, or optimal draw poker strategy -
or have played poker or backgammon against me, you will know that I
enjoy games of chance and strategy.
Most of us have been forced to take certain courses in school, and one
notices patterns of preferences amongst people. For example, I noticed
that there was complementarity with algebra and geometry. Most people
really liked one or the other; I liked algebra and hated geometry. I
love geometry now -- it's just that the two subjects were taught so
differently then, and though both had a particularly soulless
presentation, geometry proofs seemed even more tedious. I think I know
the difference -- you didn't know what answer you were headed for when
you did algebra -- you might end up with an imaginary answer! However,
you were =told= what you were going to prove, and it was just a matter
of lining up the dominoes.
Likewise, when I was in college, I noticed that people either preferred
the surity of Newtonian physics (with Einsteinian adjustments, which
weren't that difficult) or quantum mechanics. Truth be told, almost
everybody recoiled from quantum mech. When we had our eensty-sophomore
preview, we could just pretend in our minds that what was going on was
simply something like statistical mechanics; at bottom, the systems were
inherently deterministic, we just didn't know enough initial conditions
to be able to predict the trajectory of each individual electron. The
reason for the Heisenberg Uncertainty Principle was that observation
involved sending in photons or other test particle to be able to measure
the state of the system, and that would inject measuring error. I
shouldn't say "we" because a few of us had taken Doc Kolena's Modern
Physics class at NCSSM, my favorite physics class and probably my
favorite NCSSM class, come to think of it.
(I think my three favorite classes were: Modern Physics, Math Modeling,
and Fractals).
In any case, when we got into the senior-level quantum course, and we
started right in with matrix mechanics, most first were confused as to
what it all meant (because many hadn't taken linear algebra -- which
should be a =prerequisite= for doing this). Even though the math
involved in the quantum mech we were doing -- either 2-state
possibilities (spin up/down) or 1-D distributions (particle in a 1-D
potential box) -- was much more simple than the stuff we had to do for
our Electromagnetism class or advanced Mechanics class, most students
simply did not believe that electrons would actually behave that way.
Ooh, you hussy, you =tease= -- spin up or spin down? Make up your mind,
you vacillating point mass! How can a 0-dimensional object have
handedness? What fresh hell is this?
Still, I found quantum mech aesthetically pleasing. To a certain
extent, I suppose there's comfort in the "God as Watchmaker" view -- a
totally deterministic universe. Someone once said that he could
calculate the trajectory of the universe if he were given all the
initial conditions. Some noted the practical difficulties of this
approach - "chaos theory" is just a convenient way to remark that with
limited precision math, one =can't= compute exact deterministic
trajectories. However, chaos theory is founded on determinism -- what a
poorly named field. Some of the neater observations of chaos theory,
though, were that though the exact trajectory couldn't be computed
numerically, one could characterize the overall behavior, because there
were "general" trajectories that would attract everything (yes, the
"strange attractors".) In any case, people for quite a while were
pleased with the thought that there was an overarching order to life,
that all motion and behavior was directed, that theoretically the future
was predictable.
However, this view of life allows for no free will.
Perhaps free will doesn't actually exist -- there's no way we could
tell; obviously, not all human behavior is governed by free will,
because we do have a great deal of instinct. I've read in an article in
=Natural History= magazine that we may be the animal with the largest
number of instincts (if one could count them), because to learn the
complex behaviors we use - speech, 3-d color vision, abstract thought -
we need to have some structure predetermined. The way we learn our
native language is certainly not contingent on free will; I remember
learning all sorts of neat reflexes babies have that we lose over time
(though some can be brought back if we're drugged enough). There's a
sucking reflex, a swimming reflex, a grabbing reflex, and a foot-curling
reflex. For all we know, we're highly complex automatons on programs
that are highly contingent on outside influences, and part of the
program is to create the illusion that we are making choices. This is
the same principle as the possibility that every moment the universe is
destroyed and then immediately replaced by identical matter; this is
the same principle as creationists use to rationalize a 4000-year-old
universe: an earth created with fossils deceptively planted in the
crust, a universe with light "already on the way".
I see no reason that we have to give in so easily, though. Most people
prefer to think of themselves as free agents; dammit, we should be able
to conceive of a universe consistent with our science that allows us to
have free will.
I think a probabilistic universe allows us this. I also think that it
allows God more free choice, but my theology is not terribly developed,
so I will think on that a little more. Some think that a dice-throwing
God is seedy compared to the watchmaker God, but I don't say God throws
the dice. God =is= the dice.
Sorry to get sidetracked in philosophy, when I meant to talk about games
of chance in particular.
So back to the mundane -- I do like logic and abstract thinking, but I
hate completely deterministic games like chess. I think it requires
=too much= thinking, and the possibilities are constrained. Thus my
love of backgammon -- one still must consider possibilities, and each
move involves considering which path of possibilities one wants to open
for one's self. There is a great deal of skill in backgammon,
particularly in multi-game, multi-point matches (otherwise, I wouldn't
lose so consistently.) However, I still have a chance of winning a
single game simply due to the luck of the roll.
I enjoy poker even more, because the reasoning over the probable
possibilities also includes lying. There is no bluffing in chess or
checkers. If you make a mistake at go, if the other player is good
enough, you have no chance to recover -- in poker or backgammon, if you
make a bad choice, chance can get you out.
But more to the point, chance is not uniform in these games. There is a
great deal of skill involved, and those who think the law of large
numbers means that they will win eventually are the suckers from whom
those in the know make a great deal of money. This is why I play
nickel-ante poker and backgammon for points, not money. I'm simply not
skillful. I win often enough that I'm happy, but I lose so often that
if I were playing for "real" money, I wouldn't have enough money to buy
more probability books.
I think the next math topic I will speak on will be random walks, and
excursions from zero (yes, the arcsin law -- or was it arctan? No, I
think arcsin). Once I have enough money to waste, i.e. I have a job
that pays me a decent amount of money and I've paid off my debts, I
think I'll play the stock market with my own choices. That's a gambling
game where the odds can be on one's side. What I can do right now is
play "ghost" portfolios, and see how well my choices do. Perhaps, if it
turns out I'm a loser (I pick worse than the market as a whole is
doing), I'll gamble on the market the same way I do poker and backgammon
- no real money at all.
=Sigh=