The Parable of Alien Chess
A parable on the Logical Positivist “interpretation” of scientific models.
The Parable
Suppose an alien race comes to Earth and wants to observe our games. They are
very interested in chess, despite the fact that they have eyes with properties
that make it impossible to make out what actually happens on a chess board. (The
whites and blacks of the squares and pieces all blur together.)
They can still learn about chess experimentally, they know they can sit two
players (a so-called “white” and “black” player) down to play it, and they can
tell behaviorally who at the end wins.
After extensive experimentation, they realize this: 50% of the time, the white
player wins and 50% of the time, the black player wins (we’ll ignore draws and
any first-move advantage for the example).
The best model
A logical positivist alien thus creates the ultimate, long-term model of chess
as an iterated game: half of the time white wins and half of the time black
wins, therefore we can model chess with a simple simple coin flip.
Obvious any coin flip doesn’t not necessarily necessarily predict an individual
chess game, but over time and iteration, the coin-flip model of chess matches
the data perfectly. While this statistical technique might not be useful for
predicting a single game, over the long run and over iterated games, it is the
most efficient and parsimonious possible model.
The model is so parsimonious it has no place or need for concepts like chess
pieces or opening strategies (or strategies generally). It is as effective and
simple as a model can be.
Inferior models
Suppose, however that a “crank” scientist of the alien race posits that “God
doesn’t play dice” and that chess is a more complicated game, despite the fact
that the aliens cannot observe it. Suppose even he asks around and determines
from humans that there are actually pieces on the board with functions, and he
even devises a machine that allows his alien eyes to see the first move of the
game of chess.
Seeing this move allows him to create a new theory and model of the game, one
that takes into account the first move made and he tries to generate a new set
of probabilities of victory based on that move. The model he makes, is of course
highly arbitrary, stipulated and ad hoc. In fact, this model is inferior on
many inevitable accounts. For example:
1. It is less predictive over iterated games than the coin flip model.
2. It is not as parsimonious/minimal as the coin flip model.
3. It adds new variables to the theory (chess pieces) that are suspect.
4. There is no known causality behind how the moving of a piece has anything to
do with victory in chess. Supposing that moving a piece somehow relates to
the victory of a player is a novel kind of metaphysics, one that seems
constantly disproven considering a certain first move does not always
guarantee a loss or victory.
Which model is right?
Which model is closer to truth?
Unlike the aliens, we are not prevented by congenital defect from observing
chess. We know that the second, “inferior” theory of chess is truer in the sense
that it is aware of piece and understands that how a player moves a piece
contributes to victory. We also know that the “better” model of iterated chess
games: the coin-toss is only accidentally accurate and the statistics of a
coin-toss has nothing whatsoever with how the victor of chess is determined.
The new model’s theoretical categories, such as the concept of chess pieces and
moves, if apparently arbitrary in the eyes of the aliens, are getting at the
actual underlying mechanics of chess. Even if the model is less effective, it is
certainly righter.
Which will cause fruitful scientific inquiry?
The coin-flip model is a scientific dead-end. Firstly, the coin flip model is
constructed statistically, which presents the underlying mechanism to be
randomness, and thus unworthy of inquiry. This isn’t statistics hoisted above
random variation we know to exist, instead, it’s utterly blind statistics that
covers over whatever principles underlie it.
Secondly and more importantly, in order to actually improve that model, it has
to lose or at least jeopardize empirical solvency and/or parsimony:
embracing the abstractions of chess pieces means introducing mess and deviating
in some way from the empirical generalization that half of all chess games are
won by white and half by black.
This is not an abnormal circumstance.
The parable here, really an example, is not abnormal. In most affairs in
science, whether that be physics or neuroscience or economics or chemistry, we
are exactly like the partially-blind aliens.
This presents a very clear contrast between a simple and parsimonious theory
that works and a radical theory that adds new and questionable content at the
price of both effectiveness and simplicity, but is nonetheless closer to the
truth.
But science isnt about truth!
Yeah, it is dude.
Even if you are pretending that science is about “models” or just fitting
equations and the like, again, the well-fit 50-50 statistical model of chess
made by the aliens is impossible to perfect, while the flawed, yet more true to
reality model does have a potential over the long-term to be a superior one as
an alien researcher learns more.
After exhaustive inquiry, an alien race might not only discover the chess pieces
and the full set of rules behind chess, they might be able to predict what
moves are good or bad and predict individual chess games. Even on the standards
of mere instrumentalism, the mindless positivistic theory is still actually
inferior.
In this case, can the positivistic alien scientists bear to tolerate an
alternate “metaphysical” theory until it gradually acquires the descriptive
adequacy that the preexisting theory have?
Local maxima
The plot
One way helpful to think of scientific truth and model accuracy is to visualize
an optimization plot—a three-dimensional surface peppered with various mountains
and valleys of various heights and depths. “Truth,” is upwards and the goal of
science is to get further that way—or if you deny truth as being “metaphysics,.”
how about “accuracy in data” or “well-fit equations.”
At the point you’re at, you can tell which direction is “up,” you can tell which
incremental changes to your theory or equations move you upward, or, which
little changes you can make to improve your model. That is what incremental
science is, after all: don’t change assumptions and just fine-tune your
equations. The continued fine-tuning is sometimes thought of as “progress.” Of
course I don't think that this is bad, but it is a very minor and
scientifically less important part of science as a whole.
But the reality of incremental science is that once you’re at a local maximum, a
peak on the plot—once you’ve fine-tuned your equations about as perfectly as
possible, it’s over! Science is completed, but you might not actually be at the
absolute maximum of truth, but you might be languishing on the peak of a local
maximum, thinking nonetheless that you are the smartest guy in the universe.
Everything next to you looks like a disimprovement. It looks just like
those inferior theories of alien chess that posit the existence of chess pieces.
From that, you might erroneously conclude that you have found the
global/absolute maximum, which due to the nature of the complexity of
the universe and the multiplicity of possible answers and theories, you flatly
haven't.
Logical positivism is kind of theoretical lobotomy that implicitly tells
scientists that they should never, ever, ever change foundational assumptions:
tweaking equations like an oblivious autist is Science® and everything else is
“philosophy” or “metaphysics” or “pseudoscience.” This amounts to keeping each
scientific field on whatever local maximum is closest, utterly unable to
extricate themselves from it even when they see on the horizon abberant data.
If you want to understand the stagnation of science or any other specific
field, this is where it comes from.
Purposefully bad science
In Against Method, Paul Feyerabend, in what
an unreflective mind might misinterpret as a “troll,” says that it is important
for science that people have biases, financial interests, interfering religious
and political doctrines and the like in science. Looking at the plot, you might
now see why. When we are stuck on a local maximum, every new data keeps our
already-optimized model where it is no matter how low that maximum actually is.
What you need to shake it up is an external shock that totally moves our
theoretical position somewhere new on the plot where we can try to optimize at
another point, and then compare.
Basic assumptions
A prudent person should be able to question, “Am I even on the right track or am
I playing with some model that has a fundamental flaw?” I can guarantee you,
optimizing for data and fitting math and equations is easy.All theoretical
programs are wrong because they make incorrect core assumptions. This is very
hard for the ego of scientists because it means:
1. Possibly illiterate dilettantes on the internet might see and bring to
attention legitimate theoretical flaws.
2. All the years you spend in graduate school counting angels on pinheads in
your respective theoretical framework is mostly a waste of time.
3. The borders of science are borders more of a sociological club than being the
border of raw rigor.
4. Most of the scientific work is not meaningful outside of the theoretical
framework that gave rise to it.