A rather strange conversation about Albert Einstein
2008-07-02
Recently, Scott Aaronson posted
part
15 of his Democritus
lecture which includes
"a swipe at Bayesian fundamentalism". Naturally, several Bayesians
posted comments
and this is how the
following conversation started:
zf: I’m never
sure what ‘Bayesianism’ is, but Bayes decision rules — like
another
poster pointed out — are optimal, meaning given whatever data
the world throws at you
in that context, it’s the best you could do. [..]
wolfgang: So, when
A.E. discovered the theory of relativity, all he did was
update probabilities
according to the (surprisingly little) data he
had, following Bayes’ rule?
komponisto: Yes.
wolfgang: the page you
linked to is really cute. I liked especially this sentence
“It’s just the prior was over the possible characters of physical law,
and observing other physical
laws let Einstein update his model of the
character of physical law, which he then used to predict
a particular
law of gravitation.”
Perhaps you can explain to me what it means that “the prior was over
the possible characters of
physical law”, because to my slow mind that
is just meaningless nonsense.
komponisto: Perhaps
you can explain to me what it means that “the prior was
over the
possible characters of physical law”, because to my slow mind
that is just meaningless nonsense
Look a couple of paragraphs before that: “Rather than observe the
planets, and infer what laws might
cover their gravitation, Einstein was observing the other laws of
physics,
and inferring what new law
might follow the same pattern. Einstein
wasn’t finding an equation that covered the motion of gravitational
bodies. Einstein was finding a character-of-physical-law that covered
previously observed equations, and
that he could crank to predict the
next equation that would be observed”
wolfgang: I am able to
read - that is not the problem. My problem is that I
cannot make any sense of this.
(An additional problem is that I cannot
match this description with other descriptions of what A.E. was
actually doing - see e.g. the biography of Abraham Pais.)
Does the author suggest some sort of probability distribution over the
“space” of all possible laws of physics?
How would one construct such a “space” without the benefit of hindsight?
Perhaps I could make progress by parsing the sentence you quote?
“Einstein was finding a character-of-physical-law” What is a
‘character-of-physical-law’ ?
“that covered previously observed equations” How does one “observe
equations"?
“that he could crank to predict the next equation” Does the author
suggest that careful observation of
non-relativistic
equations (which was the ‘character of physics’ prior to A.E.) allows
us to predict relativistic
physics? I think that “crank” is perhaps the key word in this
text. I am sorry to be frank…
komponisto: Does
the author suggest some sort of probability distribution over the
“space” of all possible
laws of physics?How would one construct such a “space” without the
benefit of hindsight
See here and here (and pages linked therein).
“Einstein was finding a character-of-physical-law” What is a
‘character-of-physical-law’ ?
A physical law might be simple, it might be complex, it might have a
Kolmogorov complexity of 102, it might be
in three variables, it might
involve second-order differential equations, or Riemannian manifolds,
or Hilbert spaces…
all these are “character(istic)s” that a physical law
may or may not have.
“that covered previously observed equations” How does one “observe
equations"?
By opening a history book or a physics text, which is how Einstein
would have observed such equations as
F=Gm_1m_2/r^2, K= (1/2)mv^2,
V=IR,…
At this point I decided to
end this conversation. After all I don't know how to calculate the
Kolmogorov
complexity of the theory of relativity...
And I have no clue how one could discover relativity from 'observing'
the character of physical law in text books.
(By the way, what equation is V=IR, Ohm's law?)
And I was afraid the conversation would go in this
direction:
komponisto:
[..] I suppose the best I can do (besides referring you to the
totality of
Yudkowsky’s posts on Overcoming Bias), is quote a paragraph from here: "In the extreme case, a Bayesian
superintelligence could use enormously
less sensory information than a human scientist to come to correct
conclusions. First time you ever
see an apple fall down, you observe
the position goes as the square of time, invent calculus, generalize
Newton’s Laws… and see that Newton’s Laws involve action at a distance,
look for alternative explanations with increased locality, invent
relativistic covariance around a hypothetical speed limit, and consider
that General Relativity might be worth testing. Humans do not process
evidence efficiently - our minds are so noisy
that it requires orders of magnitude more extra evidence to set us back
on track after we derail. Our collective, academia, is even slower.”
Beware of the Bayesian superintelligence!
I'm glad at least one
commenter agreed...
main page