The fourth book of rationality
This is part 4 of 6 in my series of summaries. See this post for an introduction.
Part IV
Mere Reality
Interlude: A Technical Explanation of Technical
Explanation
Next: The fifth (and penultimate) book of rationality
Part IV
Mere Reality
M
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oving on from evolutionary and cognitive
models, this part explores the nature of mind and the character of physical
law. What kind of world do we live in, and what is our place in that world? We
will look at past scientific mysteries, parsimony, and the role of science in
individual rationality.
Previous sections have
explained patterns in human reasoning and behavior through the lenses of
mathematics, physics and biology, but haven’t said much about humanity’s place
in nature or the natural world in its own right. Humans are not only
goal-oriented systems, but also physical systems. We are built out of inhuman
parts, like atoms. We can relate the human world to the world revealed by
physics through reductionism: in
particular, by applying it to present-day controversies in science and
philosophy, like the debates on consciousness and quantum physics.
The philosopher Thomas Nagel
famously asked whether anyone can ever know what it’s like to be a bat – what
it would subjectively feel like. Even if we could perfectly model bat neurology
and predict bat behavior, how could we be certain that the bat isn’t just an
unconscious automaton? David Chalmers argues that third-person cognitive models
can never fully capture first-person consciousness, and that consciousness is a
“further fact” not fully explainable by the physical facts. But can this
argument stand up to a technical
understanding of how explanation and belief work?
The other topic, quantum
mechanics, is our best mathematical model of the universe to date. The
Schrödinger equation deterministically captures everything there is to know
about the dynamics of physical systems, including “superpositions”… as long as
we aren’t looking. Whenever we make observations, the superpositions seem to
vanish without a trace, and we need to use Born’s probabilistic rule to make
predictions. What all of this even means
has produced many views on the nature of quantum mechanics. Yudkowsky uses this
scientific controversy as a proving ground.
15
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Lawful Truth
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This
chapter introduces the basic links between physics and human cognition.
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In the late 18th century,
Antoine-Laurent de Lavoisier discovered that people, like fire, consume fuel
and oxygen and produce heat and carbon dioxide. Today, phosphorous (part of ATP,
crucial for metabolism) is found in matches. We may use different surface-level
rules for different phenomena, but the underlying laws that govern nature are
not so divided. Due to this, you can’t change just one thing in the world and
expect the rest to continue working as before. For example, if matches didn’t
light, we couldn’t breathe. Reality is laced together a lot more tightly than
we might like to believe.
Newton’s unification of falling apples with the
course of planets gave rise to the idea of universal laws with no exceptions.
Even though our models of fundamental
laws may not last, reality itself is (and was) always constant and rigid. To
think the universe itself is whimsical is to mix up the map and the territory. In
our everyday lives we are accustomed to rules with exceptions, but apparent
violations of the basic laws of the universe exist only in our models, not in
reality. Remember: since the beginning, not one unusual thing has ever
happened.
Just as physics came before the physicist,
mathematics came before the mathematician in a structured universe. The beauty
of math is discovering new
properties that you never built into the mathematical objects you created (like
building a toaster and realizing that your invention also, for some unexplained
reason, acts as a rocket jetpack and MP3 player). Don’t prematurely end the search
for mathematical beauty by trying to impose order; sometimes you have to dig a
little deeper. Finding hidden beauty isn’t certain, but it has happened frequently enough
throughout history to be better than unfounded faith. Consider the sequence {1,
4, 9, 16, 25, …}. Can you predict the next item in the sequence? You could take
the first differences to get {4-1, 9-4, 16-9, …} = {3, 5, 7, 9,…} and then
second differences to get {5-3, 7-5, 9-7, …} = {2, 2, 2, …}.
If you predict the next second
difference is also 2, then the next first difference must be 11, hence the next
item in the original sequence must be 36. But perhaps the “messy real world”
lacks the order of these abstract mathematical objects? It may seem messy for
three reasons: first, we may not actually know the rules due to empirical uncertainty; second, even if
we do know all of the math, we may not have enough computing power to do the
full calculation due to logical
uncertainty; and third, even if we could compute it, we still don’t know
where in the mathematical universe we are living due to indexical uncertainty. We are not omniscient. However, uncertainty
exists in the map, not in the territory. Our best guess is that the “real”
world is perfectly regular math. In many cases we’ve already found the
underlying simple and stable level – which we name “physics”.
Bayesian probability theory is attractive
because it comprises unique and coherent laws,
as opposed to the ad-hoc tools of frequentist statisticians. Bayesians expect
probability theory and rationality to be self-consistent, neat, and even
beautiful, which is why they think Cox’s
theorems are so important. Rationality is fundamentally math, and using a
useful approximation to a law (in the map) doesn’t change the law (in the
territory). Any approximation to the optimal answer will be explainable in
terms of Bayesian probability theory, and just because you may not know the
explanation does not mean no explanation exists. Instead of thinking in terms
of tricks to throw at particular problems, we should think in terms of the
extent to which we approximate the optimal Bayesian theorems.
There is a proverb that “outside the
laboratory, scientists are no wiser than anyone else”. If there’s any truth to
this, we should be alarmed. Rationality should apply in everyday life, not just
in the laboratory. We should be disturbed when scientists believe wacky ideas
(e.g. religion), because it means they probably don’t truly understand why the
scientific rules work on a gut level, but blindly practice scientific rituals
like a social convention. Those who understand the map-territory distinction
and see that reality is a single unified process will integrate their knowledge.
The Second Law of Thermodynamics says that the
phase space volume of a closed system is conserved over time. The link between
heat and probability makes this Bayesian. Any rational mind does “work” in the
thermodynamic sense, not just the sense of mental effort. Like a car engine or
refrigerator, your brain (an engine of
cognition) must interact thermodynamically with the physical world to form
accurate beliefs about something. In other words, you really do have to observe
it. True knowledge of the unseen would violate the laws of physics.
People tend to think that teachers tell them
things that are certain and that this is like an authoritative order that must
be obeyed, whereas a probabilistic belief is like a mere suggestion. Probabilities
are not logical certainties, but the governing laws of probability are harder
than steel. It is still mandatory to expect a smashed egg not to spontaneously
reform. It is still mandatory to expect a glass of boiling-hot water to burn
your hand rather than cool it, even if you don’t know that with certainty. So
beware believing without evidence and saying “no one can prove me wrong!”
Otherwise you’ll end up building a vast edifice of justification and confuse
yourself just enough to conceal the magical step, similar to people designing
“perpetual motion machines”.
Philosophers have spilled ink over the nature
of words and various cognitive phenomena. But it was Bayes all along! Mutual
information between a mind and its environment is physical negentropy, which is
Bayesian evidence, implying that any useful cognitive process must to some
extent be in harmony with Bayes-structure. For a mind that arrives at true
beliefs or better-than-random beliefs, there must be at least one process with
a sort-of Bayesian structure somewhere, or it couldn’t possibly work. The quest
for the hidden Bayes can be exciting, because Bayes-structure can be buried
under all kinds of disguises.
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16
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Reductionism 101
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This
chapter deals with the project of scientifically explaining phenomena.
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A philosophical argument that free will does or
does not exist is different from the question, “what cognitive algorithm, as
felt from the inside, drives the intuitions about the debate?” Dissolve the
question by explaining how the
confusion arises. Good philosophy should not respond to a question like “if a
tree falls in a forest but no one hears it, does it make a sound?” by picking
and defending a position (“Yes!” or “No!”), but by deconstructing the human
algorithm to the point where there is no feeling of a question left. What goes
on inside the head of a human who thinks they have free will?
Confusion exists in the map, not in the
territory. Questions that seem unanswerable, where you cannot imagine what an
answer would look like, mark places where your mind runs skew to reality. Where
the mind cuts against reality’s grain, it generates questions like “do we have
free will?” or “why does anything exist at all?” Bad things happen when people
try to answer them: they inevitably generate a Mysterious Answer. These wrong questions must be dissolved by
understanding the cognitive algorithms causing the feeling of a question.
When facing a wrong question, don’t ask “why is
X the case?” but instead ask “why do I
think X is the case?” and trace back the causal history of your belief. You
should be able to explain the steps in terms of smaller, non-confusing
elements. For example, rather than asking “why do I have free will?” try asking
“why do I think I have free will?” This latter question is guaranteed to have a
real answer whether or not there is any such thing as free will, because you
can explain it in terms of psychological events.
Science fiction artists seem to think that
sexiness is an inherent property of a woman, such that an alien invader would
find her attractive despite having a different mind and different evolutionary
history. Ancient magazine covers depicted “bug-eyed monsters” carrying off girls
in torn dresses.
This is a case of the Mind Projection Fallacy, coined by E.T.
Jaynes. It is a general error to project your own mind’s properties into the
external world. Other examples include Kant’s declaration that space by its
very nature is flat, and Hume’s definition of a priori ideas as those “discoverable by the mere operation of
thought, without dependence on what is anywhere existent in the universe”.
Probabilities express states of partial
information; they are not inherent
properties of things. It is only agents who can be uncertain. Ignorance is in
the mind, and a blank map does not correspond to a blank territory. And via
Bayes’s Theorem, learning different items of evidence can lead you to different
states of partial knowledge (unsurprisingly). There is no “real probability”
that a flipped coin will come up heads; the outcome-weighting you assign to it
depends on the information that you have about the coin. The coin itself has no
mind and doesn’t assign a probability to anything.
The morning star and evening star are both
Venus, but the quotation “the morning star” is not substitutable for “the evening star”. You have to distinguish
beliefs/concepts from things, and remember that truth compares beliefs to
reality, but reality is real regardless. (Reality itself does not need to be
compared to any beliefs in order to be real.) If you don’t make a clear enough
distinction between your beliefs about the world, and the world itself, it is
very easy to derive wrong conclusions. As Alfred Tarski said: “snow is white”
is true if and only if snow is white.
Confusing belief with reality is easier when
using qualitative reasoning, which leads to mistakes like thinking “different
societies have different truths” (no, they have different beliefs). Instead of a qualitative binary belief or disbelief, you
should use quantitative probability distributions and degrees of accuracy
(measured in log base 2 bits). For example, if you assign a 70% probability to
the sentence “snow is white” being true, and if snow is white, then your
probability assignment is more accurate than it would have been if you had
assigned a 60% chance; in fact, it will score log2(0.7) = -0.51
bits. For meta-beliefs (i.e. beliefs about what you believe), you may assign
credence close to 1, since you may be less uncertain about your uncertainty
than you are about the territory. This way you can avoid mixing up beliefs,
accuracy, and reality – which are all different things.
Reality itself is not “weird” or “surprising”.
If your intuitions are shocked by the facts, then those are poor intuitions
(i.e. models) and they should be updated or discarded. People think that
quantum physics is weird, yet they have the bizarre idea that reality ought to
consist of little billiard balls bopping around, when in fact reality is a
perfectly normal cloud of complex amplitude in configuration space. If you find
this “weird”, that’s your problem,
not reality’s problem, and you’re the
weird one who needs to change. Reality has been around since long before you
showed up. There are no surprising facts, only models that are surprised by
facts.
Yudkowsky gives the example of how he used to
browse random websites when he couldn’t work, and he thought that he couldn’t
predict when he would become able to work again. But if you see your
hour-by-hour work cycle as chaotic or unpredictable, your productivity may not
actually be unpredictable; you may just be committing the Mind Projection
Fallacy – i.e. the problem being your own stupidity with respect to predicting
it. Inverted stupidity looks like chaos, and we often fail to think of
ourselves; we just see a chaotic feature of the environment. Hence we miss
opportunities to improve.
Reductionism is disbelief in the mind projection fallacy
that the higher levels of simplified multilevel models exist in the territory.
Only the fundamental laws of physics
are “real”, but for convenience we use different representations at different
levels or scales of reality. For example, we use different computer models for
the aerodynamics of a 747 and collisions in the Relativistic Heavy Ion Collider
(RHIC), but they obey the same fundamental Special Relativity, quantum
mechanics and chromodynamics. We build models
of the universe that have many different levels of description, but so far
as anyone has been able to determine, the universe
itself has only the single level of fundamental physics (reality doesn’t
explicitly compute protons, only quarks). The scale of a map is not a fact
about the territory; it’s a fact about the map.
Poets like John Keats have lamented that “the
mere touch of cold philosophy” has destroyed haunts in the air, gnomes in the
mine, and rainbows. But one of these things is not like the others. There is a
difference between explaining
something (e.g. rainbows) and explaining
it away (e.g. gnomes and haunts). The former, the rainbow, is still there.
The latter has been shown to be an error in the map, since there never were
gnomes in the mine! When you don’t distinguish between the multi-level map and
the mono-level territory, then when someone tries to explain to you that the
rainbow is not a fundamental thing in physics, acceptance of this will feel
like erasing rainbows from your multi-level map, which feels like erasing
rainbows from the world. But when physicists say “there are no fundamental rainbows”, it does not mean
“there are no rainbows”.
It is fake
reductionism to profess that something has been explained by Science,
without seeing how it is reducible. Imagine a dour-faced philosopher, who isn’t
able to see where the rainbow comes
from, telling you that “there’s nothing special about the rainbow, scientists
have explained it away, just something to do with raindrops or whatever,
nothing to be excited about.” The anti-reductionists experience “reduction” in
terms of being told that the password is “Science”, with the effect of moving
rainbows to a different literary genre (one
they’ve been taught to regard as boring). Genuine knowledge and understanding
lets you do things like play around with prisms and make your own rainbows with
water sprays. Scientific reductionism does not have to lead to existential
emptiness.
Poets write about Jupiter the god, but not
Jupiter the spinning sphere of ammonia and methane. Equations of physics aren’t
about strong raw emotions. Classic great stories (like those told about Jupiter
the god) touch our emotions, but why should Jupiter be human when we are humans? It’s not necessary for
Jupiter to think and feel in order for us to tell stories, because we can
always write stories with humans as their protagonists. We don’t have to keep
telling stories about Jupiter. That being said, we could do with more diverse
poetry and original stories. The Great Stories are old!
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17
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Joy in the Merely Real
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This
chapter touches on the emotional, personal significance of the scientific
world-view.
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Keats wrote in his poem Lamia that rainbows go in “the dull catalogue of common things”. Anything
real is, in principle, scientifically explicable. Nothing that actually exists
is inherently mysterious. But being unmagical and knowable doesn’t make
something not worth caring about! We have to take joy in the “merely” real and
mundane, or else our lives will always be empty. Don’t worry if quantum physics
turns out to be normal; if you can’t take joy in things that turn out to be
explicable, you’re going to set yourself up for eternal disappointment – a life
of irresolvable existential ennui.
Solving a mystery can feel euphoric –
especially if you discover the answer to a problem that nobody else has
answered. But if you personally don’t know, why should it matter if someone
else has the answer? If you don’t understand a puzzle, there’s a mystery, and
you should still take joy in discovering the solution. We shouldn’t base our
joy on the fact that nobody else has done it before. Stop worrying about what
other people know, and think of how many things you don’t know! Rationalists shouldn’t have less fun.
Why talk about joy in the merely real when
discussing reductionism? One reason is to leave a line of retreat; another is
to improve your own abilities as a rationalist by learning to accomplish things
in the real world rather than in a fantasy. Getting close to the truth requires
binding yourself to reality. Don’t invest your emotional energy in magic (or
lotteries), but redirect it into the universe. This should not create
existential anguish, because that which the truth nourishes should thrive. Emotions
that cannot be destroyed by the truth are not irrational. Understanding the
rainbow does not subtract its beauty; it adds
the beauty of physics.
If people don’t have a scientific attitude in
this universe, why would they become powerful sorcerers in a fantasy world if
magic were “merely real”? Magic, like UFOs, gets much of its charm from the
fact that it doesn’t actually exist. If dragons were real, they wouldn’t be
exciting, because people don’t take joy in the merely real. If we ever create
dragons or find aliens, people would treat them like zebras – most people
wouldn’t bother to pay attention, while some scientists would get oddly excited
about them. If you’re going to achieve greatness anywhere, you may as well do
it in reality.
Rationalists should bind themselves emotionally
to a lawful reductionistic universe, and direct their hopes and care into
merely real possibilities. So why not make a fun list of abilities that would
be amazingly cool if they were magic, or if only a few chosen people had them?
Imagine if, instead of the ordinary one eye, you possessed a magical second eye
which enabled you to see into the third dimension and use legendary
distance-weapons – an ability we’d call Mystic Eyes of Depth Perception. Speech
could be “vibratory telepathy”. Writing could be “psychometric tracery”. Etc.
We shouldn’t think less of them for commonality.
Science doesn’t have to be recent or
controversial to be interesting, beautiful, or worth learning. Indeed,
cutting-edge news is often wrong or misleading, because it’s based on the
thinnest of evidence (and often conveys fake explanations). By the time anything
is solid science, it is no longer a “newsworthy” headline. Scientific
controversies are topics of such incredible difficulty that even people in the
field aren’t sure what’s true. So it is better to read well-written elementary
textbooks rather than press releases. Textbooks will offer you careful
explanations, examples, test problems, and likely true information. Study the
settled science before trying to understand the outer fringes.
Breaking news in science is often controversial
and hard to understand (and have a high chance of not replicating), so why
don’t newspapers report more often on understandable explanations of old science?
Sites like Reddit and Digg do this sometimes already. Perhaps journalists
should make April 1st a new holiday called “Amazing Breakthrough
Day”, in which journalists report on great scientific discoveries of the past
as if they had just happened and were still shocking (under the protective
cover of April Fool’s Day). For example, “BOATS EXPLAINED: Centuries-Old
Problem Solved By Bathtub Nudist” (Archimedes).
Trying to replace religion with atheism,
humanism or transhumanism doesn’t work, because it would just be trying to
imitate something that we don’t really need to imitate. Atheistic hymns that
try to imitate religion usually suck. But in a world in which religion never
existed, people would still seek the feeling of transcendence; and this isn’t
something we should always avoid. A sense of awe is not exclusive to religion. Unlike
theism, space travel is a lawful dream; and humanism is not a substitute for
religion because it directs one’s emotional energies into the real universe.
It’s not just a choice of drugs: humanity actually
exists.
We value the same objects more if we believe
they are in short supply. Scarcity makes the unobtainable more desirable, and
“forbidden” information seems more important or trustworthy. This is shown by
experimental evidence (see Robert Cialdini’s ‘Influence: The Psychology of Persuasion’). Psychologically, we seek
to preserve our options (and leaping on disappearing options may have been
adaptive in a hunter-gatherer society). However, desiring the unattainable is
likely to cause frustration. And as soon as you actually get it, it stops being
unattainable. Tim Ferriss recommends that, instead of asking yourself which
possessions or status-changes would make you happy, ask which ongoing experiences would make you
happy.
Watching the birth of a child or a space
shuttle launch can inspire feelings of “sacredness”, but religion corrupts
this; religion makes the experience mysterious, faith-based, private, and
separated from the merely real – but it doesn’t have to be! Religion twists the
experience of sacredness to shield itself from criticism. Some folks try to
salvage “spirituality” from religion. But the many bad habits of thought that
have developed to defend religious and spiritual experience aren’t worth
saving. Let’s just admit we were entirely wrong, and enjoy the universe that’s
actually here.
Too few people study science, because they
think it’s freely accessible, so it doesn’t fit their need for deep secret
esoteric hidden truth. (In fact, you have to study a lot before you actually
understand science, so it’s not public knowledge.) Because it is perceived that
way, people ignore science in favor of cults that conceal their secrets, even
if those secrets are wrong. So if we want to spread science, perhaps we should
hide it in vaults guarded by mystic gurus wearing robes, and require fearsome
initiation rituals.
This parody sketch about “the Bayesian
Conspiracy” depicts how Brennan, a character in the Beisutsukai series, is inducted into the Conspiracy. After climbing
sixteen times sixteen steps, Brennan passes through a glass gate into a room
lined with figures robed and hooded in light-absorbing cloth. They chant the
names of Jakob Bernoulli, Abraham de Moivre, Pierre-Simon Laplace, and Edwin
Thompson Jaynes, who are dead but not forgotten. Brennan is asked to perform a
Bayesian calculation, and is given a ring when he finally gives the correct
answer.
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18
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Physicalism 201
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This
chapter is on the hard problem of consciousness.
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As we’ve seen, the reductionist thesis is that
we use multi-level models for computational reasons, but physical reality has
only a single level. You can see how your hand (the higher level) reduces to
your fingers and palm (the lower level). These are the same, but from different
points of view. While it is conceptually
possible to separate them, that doesn’t make it logically or physically
possible. It is silly to think that your fingers could be in one place and your
hands somewhere else. And just because something can be reduced to smaller
parts doesn’t mean the original thing doesn’t exist.
How can you reduce anger to atoms, when atoms
themselves are emotionless? Instead of professing passwords, try to understand
how causal chains in your mind compute the consequences of options, and how
this echoes the environment. But this is challenging, and the ideas of neurons,
information processing, computing etc. give us the benefit of hindsight.
Without them it is hard to understand how little bouncing billiard balls could
combine in such a way as to make something angry. But yes, even something like
anger can be reduced to atoms.
For a very long time, people had a detailed
understanding of kinetics (with concepts like momentum and elastic rebounds)
and an understanding of heat (with concepts like temperature and pressure). In
hindsight it is obvious that heat is motion, but in 1824 it was conceivable
that the two were separate. It took an extraordinary amount of work to
understand things deeply enough to make us realize that heat and motion were
really the same thing. To cross the gap, you’d have to conceive it possible for
heat and motion to be the same, and then see how the former reduces, which is hard.
As an example of “Amazing Breakthrough Day”,
one could write an article talking about how the brain has recently been
discovered by a multinational team of scientists to be made from a complicated
network of cells called neurons, which use electrochemical activities to
perform thought. This discovery indicates that mind and body are of one
substance, contrary to Descartes. The brain, as the seat of reason, could
according to Darwin be the product of a history of non-intelligent processes,
and therefore mental entities are probably not ontologically fundamental.
In the hunter-gatherer era, animism (i.e. the
belief that things like rocks and streams had spirits or minds) wasn’t
obviously stupid; if the idea were obviously stupid, no one would have believed
it. But now we know, thanks to microscopes, neuroscience, cognition as
computation, and Darwinian natural selection, that trees and rivers don’t think
or have intentions. Anthropomorphism only became obviously wrong when we
realized that the tangled neurons inside the brain were performing complex
information processing, and that this complexity arose as a result of
evolution.
Your brain is an engine that works by processing entangled evidence; this includes
thoughts themselves, because thoughts are existent in the universe (in the form
of neural patterns, i.e. the operation of brains). The facts that philosophers
call “a priori” arrived in your brain by a physical process. You might even
observe them within some outside brain. There is no “a priori truth factory”
that works without a reason. The reason why simple algorithms are more
efficient, and Occam’s Razor works, is because our simple low-entropy universe
has short explanations to be found.
The map is multi-level but reality is
single-level, and truth involves a
comparison between belief and reality. The higher levels of your map have
referents in the single level of physics. Concepts note only that a cluster
exists, and do not define it exactly. We can’t practically specify everything
in terms of quarks, so our beliefs are “promissory notes” that refer to (and implicitly exist in) empirical clusters
in what we think is the single, fundamental level of physics. Implicit
existence is not the same as nonexistence. Virtually every belief you have is
not about elementary particle fields, but this doesn’t mean that those beliefs
aren’t true. For example, “snow is white” does not mention quarks anywhere, and
yet snow nevertheless is white – it may be a computational shortcut, but it’s
still true. This view of how we can form accurate beliefs way above the
underlying reality is not circular, but self-consistent upon reflection.
Your philosophical zombie is putatively a being that is exactly identical to you,
except that it’s not conscious. Some argue that if zombies are “possible” then
we can deduce a priori that
consciousness is extra-physical. Epiphenomenal property dualists (who think zombies are possible) like David
Chalmers believe in consciousness, but also that is has no real-world effects. (They
are not the same as substance dualists like
Descartes who believe that mind-substance is causally active.) But you can be
aware of your awareness and write about it, which requires physical causality.
Whatever makes you say “I think therefore I am” causes your lips to move, and is thus within the chains of cause-and-effect
that produce our observed universe. Philosophers writing papers about
consciousness would seem to be at least one effect of consciousness upon the
world. Zombie-ists would need an entirely separate reason within physics of why people would talk about subjective
sensations. So epiphenomenalism is pointlessly complicated! It postulates a
mysterious, separate, extra-physical, inherently mental property of
consciousness, and then further postulates that it doesn’t do anything. That is
deranged. Don’t try to put your consciousness or your personal identity outside
physics.
A few more points on p-zombies: Your internal
narrative can cause your lips to say things, and consciousness is probably that which causes you to be aware of your
awareness. The reductionist position is that that-which-we-name “consciousness”
happens within physics, even if we
don’t fully understand it yet. It should be logically impossible to eliminate
consciousness without moving any atoms. It seems deranged to say that something
other than consciousness causes my internal narrative to say “I think therefore
I am” but that consciousness does exist epiphenomenally.
The argument against zombies can be extended
into a more general principle, albeit with some difficulty. The Generalized Anti-Zombie Principle (GAZP)
says that something that can’t change your internal narrative (which is caused
by the true referent of “consciousness”) can’t stop you being conscious. Any
force smaller than thermal noise won’t “switch off” your consciousness, because
it doesn’t significantly affect the true cause of your talking about being
conscious. This implies that you could, in principle, transfer your
consciousness to artificial silicon neurons.
A Giant
Lookup Table (GLUT) could in principle replace a human brain and thus seem
conscious, but a randomly generated GLUT is extremely unlikely to have the same
input-output relations as the human brain. The GAZP says that the source of a
GLUT that mirrors the brain is probably a conscious designer. When you follow
back discourse about “consciousness”, you generally find consciousness, because
it is responsible for the improbability of
the conversation you’re having. This kind of GLUT would have to be precomputed by
a human using a computational specification of a human brain.
That it is impossible to observe something is
not enough to conclude that it doesn’t exist. If a spaceship goes over the
cosmological horizon relative to us, so that it can no longer communicate with
us, should we believe that the spaceship instantly ceases to exist? We cannot
interact with a photon outside our light cone, but it continues to exist as a
logical implication of the general laws of physics, which themselves are
testable. Believing this doesn’t violate Occam’s Razor, because Solomonoff
induction applies to laws or models, not individual quarks. The photon is an
implied invisible, not an additional invisible.
Under the Minimum Message Length formalism
of Occam’s Razor (which is nearly equivalent to Solomonoff Induction), if you
have to tell someone how your model of the universe works, you just have to
write down some equations to simulate your model – not specify individually the
location of each quark in each star in each galaxy – and the amount of time it
takes to write down the equation doesn’t depend on the amount of “stuff” that
obeys it.
This is a satirical script for a short scene in
a zombie movie –but not about the folkloric lurching and drooling kind of
zombie; the philosophical kind. Imagine a world where normal people are
infected with an “epiphenomenal virus”, which cannot be experimentally
detected. Things would go on just as before. Or would they? The victims sure look conscious… but don’t let the fact
that they look like humans, talk like humans, claim to have qualia, and are
identical to humans on the atomic level, fool you. These clever scumbags are
zombies!
Is science only about “natural” things? People
say this when invoking the supernatural,
which appeals to ontologically basic mental entities like souls. But firstly,
this is a case of non-reductionism, which is a confusion because it is
incoherent. It is not clear what an irreducibly mental and fundamentally
complicated universe is even supposed to look like. Secondly, if you test
supernatural explanations the way you would test any other hypothesis (by
converting them into a reducible and natural formulation), you will probably still
find out that they aren’t true.
There is a prediction of supernatural models:
that information can be transferred “telepathically” between brains in the
absence of any known material connection between them. If psychic powers were
discovered they would be strong Bayesian evidence that non-reductionism is
correct and that beliefs are ontologically fundamental entities. But more
likely, this will not be discovered, and the reason we are tempted by
non-reductionist worldviews is that we just lack self-knowledge of our own brains’
quirky internal architecture. If naturalism is correct, then the attempt to
count “belief” or the “relation between belief and reality” as a single basic
entity is simply misguided anthropomorphism.
›
19
|
Quantum Physics and Many Worlds
|
This
chapter is on the measurement problem in physics. Yudkowsky discusses
many-worlds interpretations as a response to the Copenhagen interpretations.
Since he is not a physicist, you are free to consult outside sources to vet
his arguments or learn more about the physics examples. Note that the
Many-Worlds Interpretation is still controversial.
|
Quantum mechanics doesn’t deserve its fearsome
reputation. Quantum mechanics is considered by many to be weird, confusing or
difficult; yet it is perfectly normal reality. There are no surprising facts,
only models that are surprised by facts: the issue lies with your intuitions, not with quantum
mechanics. A major source of confusion is that people are told that quantum
physics is supposed to be mysterious, and they are presented with historical
erroneous concepts like “particles” or “waves” rather than a realist
perspective on quantum equations from the start.
What
is the stuff reality is made of? The universe isn’t made of little billiard
balls, nor waves in a pool of aether, but mathematical entities called configurations that describe the
position of particles, and amplitude
flows between these configurations (measured as square moduli of complex
numbers). A configuration can store a single value in the form of a complex
number (a + bi) where i is defined as √(-1).
These complex numbers are what we call amplitudes, and they are out there in
the territory. We cannot measure amplitudes directly, only the ratio of
absolute squares of some configurations. To find the amplitude of a
configuration, you sum up all the amplitude flows into that configuration.
The figures above depict the
classic split-photon experiment with half-silvered mirrors. On the left, a
photon is sent from the source toward the half-silvered mirror A; this is a
configuration. We can give the configuration “a photon heading toward A” a
value of (-1 + 0i). From there, the
photon can take alternative pathways – B and C are full mirrors and D is
another half-mirror. The half-mirrors multiply by 1 when the photon goes
straight and multiply by i when the
photon turns at a right angle. The full-mirrors always multiply by i. Note that all these amplitude flows happen,
and that they can cancel each other out, which is why no photon is detected at
E. In the diagram on the right, the configuration of “a photon going from B to
D” has an amplitude value of zero (because it’s blocked), so Detector 1 now goes
off half the time.
While the previous experiment deals with one
moving particle, real configurations are about multiple particles (in fact, all
the particles in the universe). Configurations specify where particles are (e.g. “a photon here, a photon there…”), but
they don’t keep track of individual particles!
In the figure above, two
photons head toward D at the same time. But whether both photons are deflected
or both go straight through, the resulting configuration is the same. Amplitude
flows that put the same types of particle in the same places flow into the same
configuration, even if the particles came from different places. Unlike
probabilities, amplitudes can have opposite signs (positive or negative) and
thus cancel each other out (giving a squared modulus of zero for the sum),
which is how we can detect which configurations are distinct. So it is an
experimentally testable fact that “photon B here, photon C there” is the same
configuration as “photon C here, photon B there”. This is why we may see Detector
1 go off twice or Detector 2 go off
twice, but not both Detectors go off at the same time.
A configuration is defined by all particles. What
makes a configuration distinct is at least one particle in a different state –
including particles constituting the experimental equipment! Adding a sensor
that tries to “measure” things introduces a new element into the system and
thus makes it a distinct configuration. If amplitude flows alter a particle’s
state, then they cannot flow into the same configuration as amplitude flows
which do not alter it.
In the above experiment, sensitive thingy S is in a different
state between “a photon from D to E and S in state no” and “a photon from D to E and S in state yes”. By measuring the
amplitude flows, we have stopped them from flowing to the same configurations. In
this case the amplitudes don’t cancel out, leading to a different experimental
result. We find that the photon has an equal chance of striking Detector 1 and
Detector 2. (Remember, in the first diagram in “Configurations and Amplitude”,
the photon always struck Detector 2.) This phenomenon confused the living
daylights out of early quantum experimenters. But the distinctness of
configurations is a physical fact, not a fact about our knowledge, and there’s
no need to suppose that the universe cares what we think.
Macroscopic
decoherence, also known as
“many-worlds”, is the view that the known quantum laws that govern microscopic
events simply govern at all levels without alteration. Collapse postulates assume that wavefunction superposition
“collapses” at some point before reaching the macroscopic level (some say due
to conscious awareness!), leaving only one configuration with non-zero
amplitude and discarding other amplitude flows. Many Worlds proposes that configurations where we observe and don’t
observe a measurement both exist with non-zero amplitude, but are decoherent
since they are too different from each other for their amplitude flows to flow
into common configurations. But early physicists used to assume that
measurements had single outcomes. They simply didn’t think of the possibility
of more than one world, even though it’s the straightforward result of applying
the quantum laws at all levels. So they invented an unnecessary part of quantum
theory which says that parts of the wavefunction spontaneously and mysteriously
disappear when decoherence prevents us from seeing them anymore. Yet collapse
theories are still supported by physicists today.
The idea that decoherence fails the test of
Occam’s Razor is wrong as probability theory. Occam’s Razor penalizes theories
for explicit entities that cannot be summed over; but the Many-Worlds
interpretation of quantum mechanics does not
violate Occam’s Razor because decoherent worlds follow from the compact laws of
quantum mechanics. Measurements obey the same quantum-mechanical rules as all
other physical processes. Some physicists just use probability theory in a way
that is outright mathematically wrong, on the level of 2+2=3. This is one
of the reasons why Yudkowsky, as a non-physicist, dares to talk about physics.
To probability theorists, words like “simple”, “testable”
and “falsifiable” have exact mathematical meanings; e.g. we can use Bayes’s Theorem
to concentrate the probability mass of a hypothesis into narrow outcomes (falsifiability) and look for evidence
that would favor one hypothesis over another (testability). Macroscopic decoherence is falsifiable for the same
reasons quantum mechanics is, and compared to the collapse postulate, it is
strictly simpler – because decoherence is a deductive consequence of the
wavefunction’s evolution. Within the internal logic of decoherence, the many
superposed worlds are simply a logical consequence of the general laws that
govern the wavefunction, and as such, do not cost us extra probability. Adding
collapse is a useless complication.
Suppose a murder case in a big city leaves no
evidence, yet one of the police detectives says, “Well, we have no idea who did
it, but let’s consider the hypothesis
that it was Mortimer Q. Snodgrass.” This can be called the fallacy of privileging the hypothesis. Before promoting a specific
hypothesis to your attention, you need to have some rational evidence already
at hand, because it takes more evidence to narrow down the space of all
possibilities, than to figure out which
of the handful of candidate hypotheses is true. The anti-epistemology is to
talk endlessly about how you “can’t disprove” an idea, how the negative
evidence is “not conclusive”, how future evidence could confirm it but hasn’t happened yet, and so on. Single-world
quantum mechanics (i.e. collapse postulates) has no evidence in favor of it,
and there are a billion other possibilities that are no more complicated, so
it’s not worth even thinking about it. But due to historical accident, collapse
postulates are indeed spoken about.
Some people may be disturbed by the
straightforward prediction of quantum mechanics that they are constantly
splitting into zillions of other people. Egan’s
Law says: “It all adds up to normality”. The many worlds of quantum
mechanics have always been there, and they are where you have always lived –
not some strange, alien universe into which you have been thrust. But you
cannot causally affect other worlds, and decoherence has nothing to do with the
act of making decisions. Living in multiple worlds is the same as living in
one. Worrying about an extremely pleasant or awful world in your future is like
the lottery. So live in your own world. Quantum physics is not for building
strange philosophies around many-worlds, but for answering the question of what adds up to normality. If there were
something else there instead of
quantum mechanics, then the world
would look strange and unusual.
Before Hugh Everett III proposed his relative
state formulation (aka many-worlds) in 1957, none of the theories were very
good and the best quantum physicists could do was to “shut up and calculate”.
But that is not the same as claiming that “Shut up!” actually is a theory of physics, and that the
equations definitely don’t mean anything. Nevertheless, some jumped to the
conclusion that the wavefunction is only a probability.
This contributed to quantum non-realism, which is a semantic stopsign. If you
can’t say exactly what you mean by calling the quantum-mechanical equations
“not real”, then you’re just telling others to stop asking questions. The
equations do describe something – the
quantum world is really out there in the territory and the classical world
exists only implicitly within the quantum one (at least from the realist
perspective).
If wavefunction collapse actually happened, it
would be the only informally specified (qualitative), non-linear, non-unitary,
non-differentiable, discontinuous, non-local in the configuration space,
acausal (non-deterministic), and superluminal (faster than light) law in
quantum mechanics, and the only fundamental phenomenon to violate CPT symmetry,
Special Relativity and Liouville’s Theorem, and be inherently mental. It would
be the only fundamental law adopted without precise evidence to nail it down.
If early physicists like Niels Bohr had never made the mistake, and thought
immediately to apply the quantum laws at all levels to produce macroscopic
decoherence, then “collapse postulates” would today seem like a completely
crackpot theory. There would be many better hypotheses proposed to explain the
mysterious Born probabilities.
Early quantum physicists made the error of
forgetting that they themselves were made of atoms, so they concluded that conscious observation had a fundamental
effect. They didn’t notice that a quantum theory of distinct configurations
already explained the experimental result, without any need to invoke
consciousness. In retrospect, could philosophers have told the physicists that
this was a big mistake? Philosophical insight would not have helped them,
because it’s usually science that
settles a confusion. That’s why we don’t usually see philosophers sponsoring
major advances in physics. At the frontier of science, it takes intimate
involvement with the scientific domain in order to do the effective
philosophical thinking.
Some people think that free will and
determinism are incompatible. If the laws of physics control everything we do,
then how can our choices be meaningful? But “you” and physics are not competing
causal nodes; you are within physics!
Your desires, plans, decisions and actions cannot determine the future unless we live in a lawful, orderly
universe.
Things should not seem like
the causal network on the left, but the one on the right. If the future were
not determined by reality, it could not be determined by you. Yudkowsky calls
this view “Requiredism”: that planning, agency, choice etc. require some lawful determinism.
Anything you control is necessarily controlled by physics.
If collapse theories (or any theory of a
globally single world) were true, they would violate Special Relativity; and
although Special Relativity seems counterintuitive to us humans, what it really
says is that human intuitions about space and time are simply wrong. Given the
current state of evidence, the “many-worlds interpretation” (i.e. macroscopic
decoherence) wins outright. There is no reason to suppose that quantum laws are
different on the macroscopic level, so it seems obvious that there are other
decoherent Earths. You shouldn’t even ask,
“Might there only be one world?” The argument should have been over fifty years
ago. New physical evidence could reopen it, but we have no particular reason to
expect this. The main problem for Many Worlds is to explain the Born
probabilities.
›
20
|
Science and Rationality
|
This
chapter relates the ideas of previous ones to scientific practice. So if it
was many-worlds all along, and collapse theories are silly, did physicists in
the first half of the 20th century really screw up that badly? How
did they go wrong, and what lessons can we learn from this whole debacle?
|
This is another short story set in the same
universe as “The Ritual” and “Initiation Ceremony”. Future physics students
look back on the cautionary tale of quantum physics. Einstein, Schrödinger, and
Von Neumann failed to see Many Worlds, perhaps because of administrative
burdens imposed by a system of science that thought it acceptable to take 30+
years to solve a problem, rather than resolving a major confusion faster. Eld Science was based on getting
to the truth eventually… but people
can think important thoughts in far less than thirty years if they expect speed
of themselves.
The failure of physics in the first half of the
20th century was not due to straying from the scientific method,
because the physicists who refuse to adopt many-worlds are obeying the rules of Science. Science and rationality (i.e.
Bayesianism) aren’t the same thing. The explanation of quantum mechanics was
meant to illustrate (among other things) the difference between the scientific method,
which demands new testable predictions, and Bayesian probability theory, which
suggests that macroscopic decoherence is simpler than collapse. Science says
that many-worlds doesn’t make new testable predictions because we can’t see all
the other worlds; Bayes says that the simplest quantum equations that cover all
known evidence don’t have a special exception for human-sized masses. This is a
clear example of when it comes time to break your allegiance to Science.
The social process of Science doesn’t trust the
rationality of individual scientists, which is why we give them the motive to
make falsifiable experimental predictions. But the rational answer comes from Bayes’s Theorem and Solomonoff
Induction. Science doesn’t always agree with the exact, Bayesian, rational
answer, and Science wants you to go out and gather overwhelming experimental
evidence, because it doesn’t trust you
to be rational. It assumes that you’re too stupid and self-deceiving to just
use Solomonoff induction.
Science doesn’t care if you waste ten years on testing
a stupid theory, as long as you recant and admit your error. But some things (e.g.
cryonics) cannot be experimentally tested right now despite huge future
consequences; so you have to think rationally to figure out the answer. You
should not automatically dismiss such theories. You have to try to do the thing
that Science doesn’t trust you to do, and figure out the right answer before you get clubbed over the head
with it. Evolutionary psychology is another example of a case where rationality
has to take over from science.
Your private epistemic standard should not be
as lax as the ideal of Science, which asks only that you do the experiment and
accept the results. Science lets you believe any stupid idea that hasn’t been
refuted by experiment, and it lets people test whatever hypotheses they like,
as a social freedom. Science accepts slow, generational progress. But you need
Bayes (and Tversky & Kahneman) to tell you which hypotheses to test and precisely how much probability to
assign to them. Bayesianism says that there is always an exactly rational
degree of belief given your current evidence, and this does not shift a
nanometer depending on your whims.
It seems that scientists are not trained in
precise rational reasoning on sparse evidence (e.g. the formal definition of
Occam’s Razor, the conjunction fallacy, or the concepts of “mysterious answers”
and “fake explanations”). These are not standard. Hence why modern world-class
scientists, like Sir Roger Penrose, still make mistakes like thinking that
consciousness is caused by quantum gravity. They were not warned to be stricter
with themselves. Maybe one day it will be part of standard scientific training,
but for now it’s not, and the absence is visible.
You can’t think and trust at the same time. To
grow as a rationalist, you must lose your emotional trust in the sanity of
normal folks. You must lose your trust that following any prescribed pattern
will keep you safe. Not even Science or Eliezer can save you from making
mistakes. There is no known procedure you can follow that makes your reasoning
defensible. Since the social rules of Science are verbal rather than
quantitative, it is possible to believe you are following them; but with
Bayesianism, it is never possible to do an exact calculation and get the exact
rational answer that you know exists. You are visibly less than perfect. So
learn to live with uncertainty while still having something to protect and
striving to do better.
Yudkowsky is less of a lonely iconoclast than
he seems, as many of these ideas are surprisingly conventional and are being
floated around by other thinkers (e.g. Max Tegmark and Colin Howson). Perhaps
Popper’s falsificationism should be replaced with Bayesianism. But this is not
as simple as redefining science. It would require not just teaching probability
theory, but also things like cognitive biases and social psychology. We need to
form a new coherent Art of Bayescraft
before we are actually going to do any better in the real world than modern
science.
Whether scientists accept an idea depends not
just on epistemic justification, but also a social pack and extra evidence to
overcome cognitive noise – hence why Science is inefficient at reaching
conclusions. And Science doesn’t say which
ideas to test. Yet the bulk of work in progressing knowledge is in
elevating the right hypothesis to attention. Hence Bayesianism is faster than
science. Ironically, science would be stuck if there weren’t some people who could get it right in
the absence of overwhelming experimental proof, because in many answer spaces
it’s not possible to find the true hypothesis by accident.
Albert Einstein is an example of an individual
scientist who, in the presence of only a small amount of experimental evidence,
was unusually good at arriving at the truth faster than the social process of
Science (and even more unusually, he admitted it). Deciding which ideas to test
can entail high-minded thoughts like noticing a regularity in the data, or
inferring a new law from characteristics of known laws (as Einstein did with relativity).
Einstein used the data he already had more efficiently – in his armchair. It’s
possible to arrive at the right theory this way, but it’s a lot harder.
Einstein used evidence much more efficiently
than other physicists, but he was still extremely inefficient in an absolute sense. Imagine a world where
the average IQ is 140 and a huge team of physicists and cryptographers was
examining an interstellar transmission; going over it bit by bit for thirty
years, they could deduce principles on the order of Galilean gravity just from
seeing two or three frames of a picture. But a Bayesian superintelligence would make much more efficient use of sensory
data, such that it could invent Newtonian mechanics the instant it sees an
apple fall.
On the scale of intelligence, the distance
between Einstein and “village idiot” is tiny compared to the distance between
Einstein and a Bayesian superintelligence. In other words, it looks not like
this:
But more like this:
Yudkowsky was disappointed
when his childhood hero, Douglas Hofstadter, disagreed. Perhaps this is a “cultural
gap” explained by Yudkowsky reading a lot of science fiction from a young age. This
was helpful for thinking beyond the human world. That is why he looked up to
the ideal of a Bayesian superintelligence, not Einstein. The ideal role model
you should aim for should come from within your dreams, because by letting your
ideals be composed only of dead humans, you limit yourself to what has already
been accomplished, and you will ask too little of yourself.
People talk as if Einstein had magical
superpowers or an aura of destiny. There’s an unfortunate tendency to talk as
if Einstein, even before he was famous, had a rare inherent disposition to be
Einstein. But Einstein chose an important problem, had a new angle of attack,
and persisted for years. An intelligent person under the right circumstances can do better than Einstein. (Not
everyone, but many have potential.) The way you acquire superpowers is not by
being born with them, but by seeing with a sudden shock that they are perfectly
normal. What Einstein did isn’t magic; just look at how he actually did it!
In another story from the Beisutsukai series, Brennan and the other students are faced with
their midterm exams, and are given one month to develop a theory of quantum
gravity. Einstein was too slow to formulate General Relativity (taking ten years),
and his era lacked knowledge of cognitive biases and Bayesian methods. It
should be possible to do better, if you expect it. An open challenge in science
is quantum gravity, which is the question of how to unify General Relativity
and quantum mechanics.
›
Interlude: A Technical Explanation of Technical
Explanation
YOU’VE SEEN THE Intuitive Explanation of Bayesian reasoning, but when do the
mathematical theorems apply and how do we use the theorems in real-world
problems? Is there a controversy? We begin by asking: What is the difference
between a technical
understanding and
a verbal understanding?
One visual metaphor for
“probability density” or “probability mass” is a lump of clay that you must
distribute over possible outcomes. This lets you visualize how probability is a
conserved resource – to assign higher probability to one hypothesis requires
stealing some clay from another hypothesis. This matters when you have to bet
money, because by not being careful with your bets, you will not maximize your
expected payoff.
Imagine there is a little
light that flashes red, green, or blue each time you press a button. You have
to predict the color of the next flash and you can bet up to one dollar. If the
game uses a proper scoring rule, then
if the actual frequencies of the lights are 30% blue, 20% green and 50% red,
you maximize your average payoff by betting 30 cents on blue, 20 cents on green
and 50 cents on red. If you press the button twice in a row, you get the same
score regardless of whether you are scored once for your prediction P(green1
and blue2) or twice for
P(green1) and P(blue2|green1).
In Bayesian terms this is
known as an invariance. Note that
P(green1) x P(blue2|green1) = P(green1
and blue2). So it doesn’t
matter whether we consider it two predictions or one prediction; we get the
same result. Mathematically, the scoring rule would be: Score(P) = log(P);
meaning that your score is the logarithm of the probability you assigned to the
winner. And your expected score would be:
This is different from the colloquial way
of talking about degrees of belief.
When people
say “I am 98%” certain…” what they usually mean is “I’m almost but not entirely
certain”, which reflects the strength of their emotion rather than the expected
payoff of betting 98% of their money on that outcome. But technically, your
confidence would be poorly calibrated if
you said that you were “98% sure” but you get more than two questions wrong out
of a hundred independent questions of equal difficulty. The Bayesian scoring
rule rewards accurate calibration.
But calibration is just one component; the other component is discrimination. This refers to
discriminating between right and wrong answers: the more probability you assign
to the right answer, the higher your score. You can be perfectly calibrated by
saying “50% probability” for all yes/no questions, but this is merely
confessing ignorance, and you can do better.
Now imagine
an experiment which produces an integer result between zero and 99. You could
predict “a 90% probability of seeing a number in the fifties”, which is a vague
theory compared to “a 90% probability of seeing 51”. The precise theory has an
advantage because it concentrates its probability mass into a sharper point. So
if we actually see the result 51, this is evidence in favor of the precise
theory. If the prior odds were 10:1 in favor of the vague theory, seeing a 51
would make the odds go to 1:1 and seeing a 51 again would then bring it to 1:10 in favor of the precise theory.
However, the vague theory
would still score better than a hypothesis of zero knowledge (or maximum-entropy, which makes any result
equally probable). Even worse than
the ignorant theory would be a stupid theory which predicts “a 90% probability
of seeing a result between zero and nine”, and thus assigns 0.1% to the actual
outcome, 51. By making confident predictions of a wrong answer, it is thus
possible to have a model so bad that it is worse than nothing. Ignorance is
better than anti-knowledge.
Under the laws of probability theory, it is not possible for both A and not-A to be evidence
in favor of B, so a true Bayesian can only test
ideas of which they are genuinely uncertain; they cannot try to prove a
preferred outcome or to prevent disproof. Unfortunately, human beings are not
Bayesians. People don’t distribute conserved probability mass over advance
predictions, but try to argue that whatever event did happen “fits” the
hypothesis they had in mind beforehand. The consequence of this is that people
miss their chance to realize that their models did not predict the phenomenon.
So when a class’s physics students observe a square plate of metal next to a hot radiator, and
feel that the side next to the radiator is cool and the distant side is warm,
the students may guess that “heat conduction” is responsible. This is a vague
and verbal prediction. If they had measured the heat of the plate at different
points at different times and applied equations of diffusion and equilibrium,
they would soon see a pattern in the numbers, and their sharp predictions might
lead them to guess that the teacher turned the plate around before they entered
the room.
You now have a technical
explanation of the difference between a verbal explanation and a technical
explanation, because you can calculate exactly how technical an explanation is.
Bayesian probability theory gives you a referent for what it means to “explain”
something. Other technical subjects (like physics, computer science, or
evolutionary biology) permit this too – which is why it is so important that
people study them in school. And as long as you can apply the math, and
distinguish truth from falsehood, you are allowed to have fun and be silly.
A useful
model is knowledge you can compute in reasonable time to predict real-world
events you know how to observe. This is why physicists use different models to
predict airplanes and collisions in a particle accelerator, even though the two
events take place in the same universe with the same laws of physics. A Boeing
747 obeys Conservation of Momentum in real life, even if some aerodynamic
models, which are cheap approximations, violate Conservation of Momentum a
little. As long as the underlying fundamental
physics supports the aerodynamic model, it can be a good approximation. Even a
“vague” theory can be better than nothing, and given enough experiments, vague
predictions can build up a huge advantage over alternate hypotheses. Such
theories, if they produce not-precisely-detailed but still correct predictions,
may be called “semitechnical” theories.
But aren’t precise, quantitative theories still better than vague, semitechnical theories? Well,
in the nineteenth century, Darwinian evolutionism was a semitechnical theory
(they did not yet have quantitative models) but physics was already precise and
mathematical. The physicists said that the Sun could not have been burning for
that long, so people like Lord Kelvin challenged natural selection. Of course,
evolution turned out to be correct. Nineteenth century physics was a technical
discipline, but it was incomplete – they didn’t know about nuclear reactions.
The lesson is that every correct
theory about reality must be compatible with every other correct theory, and if
there seems to be a conflict between two well-confirmed theories, then you are
applying one of the two theories incorrectly or applying it outside the domain
it predicts well.
The social process of Science requires you to make advance predictions. This custom exists to
prevent human beings from making human mistakes. But the math of probability
theory does not distinguish between advance predictions and post facto ones,
which is why nineteenth century evolutionism still worked. Today, evolutionary
theory can make quantitative predictions about DNA and genetics, and as a technical theory it is far better than a
semitechnical theory. But
controversial theories at the cutting-edge of science are often semitechnical,
or even nonsense.
The discipline of rationality is very important for distinguishing a good semitechnical
theory (truth) from nonsense (falsehood). But scientific controversies should
matter only if you are an expert in the field, or if it affects your life right
now. For the rest of us, elementary textbook
science shows the comprehensible beauty of settled science. If you do have a
reason for following a scientific controversy, then you should pay attention to
the warning signs that historically distinguished vague hypotheses that turned
out to be gibberish, from those that later became confirmed theories.
A sign of a poor hypothesis
is that it expends great effort in avoiding falsification. In terms of Bayesian
likelihood ratios, falsification is stronger than confirmation. As Popper
emphasized, the virtue of a scientific theory lies not in the outcomes it
permits, but the outcomes it prohibits. The same Bayesian scoring rule we saw
earlier can be used to accumulate scores across experiments, which we should
strive to maximize. The only mortal sin of Bayesianity
is to assign probability 1 or zero to an outcome, because this is like
accepting a bet with a payoff of negative infinity.
By making
predictions in advance, it is easier to notice when someone is using too much
probability mass to try to claim every possible outcome as an advance
prediction. Imagine waking up one morning to find that your left arm has been
replaced by a blue tentacle. How would you explain this? Well, you wouldn’t
because it’s not going to happen. There are verbal explanations (like divine
intervention, or hallucination) that could “fit” the scenario, but such
explanations can “fit” anything. If aliens did it, why would they do that
particular thing to you as opposed to the other billion things they might do?
What will the aliens do tomorrow? If you guess a model with no internal detail
or a model that makes no further predictions, why would you even care? People
play games with plausibility, explaining events they expect to never actually
encounter.
If you
had a “good explanation” for the hypothetical experience, then you would go to
sleep worrying that your arm really would
transform into a tentacle. Under Bayesian probability theory, probabilities are
anticipations: if you assign probability mass to waking up with a blue
tentacle, then you are nervous about waking up with a blue tentacle. To explain
is to anticipate, and vice versa. If you don’t anticipate waking up with a
tentacle, you need not bother crafting excuses you won’t use. Remember: since the beginning, not one unusual thing
has ever happened.
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Next: The fifth (and penultimate) book of rationality
Loved it, compelling and throughlly enjoyable
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