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...


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