

Einstein's Arrogance - Neoryder
http://www.overcomingbias.com/2007/09/einsteins-arrog.html
inspired by the corroborating evidence discussion in the comments for Paul B's post
======
aston
I don't really like this view of hypothesis. Or maybe I just don't understand
it.

Take this hypothesis: 2+2 = 4. There are an infinite number of things 2+2
could equal, but I, like Einstein, without any empirical testing of my
mathematical hypothesis, believe it to be 4. If you believed the sum to be 5,
again without any testing, I don't see how you or I have any different number
of bits dedicated to our answers. Your bits, however, are wrong.

~~~
jey
There's plenty of empirical evidence for 2 + 2 = 4, it's just so pervasive
that we fail to recognize it as such. Take two apples, place them on a table.
Now take two more apples, and place them on the table. How many apples are on
the table? 3? 4? 5? I have an astronomically high probability assigned to
"2+2=4", but if I kept doing this experiment and suddenly ended up with 3
apples every time, I'd have to decrease the probability I assign to 2+2=4, and
increase the probability assigned to 2+2=3.

The apples example is from "How to Convince me that 2 + 2 = 3":
<http://www.overcomingbias.com/2007/09/how-to-convince.html>

Interesting essay on Bayesian reasoning:
<http://yudkowsky.net/bayes/technical.html>

~~~
Tichy
From the article:

"But from a Bayesian perspective, you need an amount of evidence roughly
equivalent to the complexity of the hypothesis"

But what is the "complexity of the hypothesis"? Without a proper definition,
there is not much left to the article, or is there?

~~~
Eliezer
Fixed with linky.

------
kirse
"I myself often slip into this phrasing, whenever I say something like, 'To
justify believing in this proposition, at more than 99% probability, requires
34 bits of evidence.'"

Error: Social robot could not compute. Please input valid parameters into
auditory interface again.

------
maths
i just want to point out that einstein wasn't 'arrogant' here. he said what he
did because he 'knew' GR had to be right -- it was just the generalization of
special relativity, which was already known to be right.

of course, it turns out that GR is wrong, at least at small-scales. while
special relativity is compatible with quantum field theory (indeed, SR was the
motivation for moving from quantum mechanics to QFT, as quantum mechanics does
not respect SR), general relativity is not.

------
DanielBMarkham
I'm going to go out and swim in the deep water with this comment, but I didn't
care for the article that much.

All science is provisional, this much is true. Math, however, is a formal
symbolic system for representing things in reality. 2 + 2 = 4 not because of
some inner truth in math but because when we observe nature and combine 2
things and 2 things we have what we call 4 things. We could change the symbols
around all day and they would still work. So math is just a generic way of
talking about that which we can observe.

The interesting thing happens when our symbolic system escapes that which can
be observed, or when it is incomplete, say in the case of negative numbers
(then rational, the imaginary, then irrational, etc.) At this point the
exercise becomes one of either bringing the system of symbols to some
application that has observable impact (applied physics) or changing the
symbolic tools. There's nothing Bayesain about 2+2=4 -- that's the way the
symbols are supposed to work.

Now whenever we get "stuck" we have to go back and check out symbolic systems.
Just like geeks build O/S as a hobby or college experiment, I imagine physics
and mathematicians build calculi, or systems of symbols and rules for working
with them. Wolfram came up with a great question in NKS -- what if the
universe is really discrete and not continuous? In other words, when Newton
created the integral he might have taken math down a path that ends up
breaking when you try to put a GUT together. I think that's a helluva
question, but it's above my pay grade.

There was a book George Gamov wrote: 1-2-3-Infinity about the way various
counting systems and numbers play together. Go read it -- it's better than
this blog article.

~~~
jey
" _There's nothing Bayesain about 2+2=4 -- that's the way the symbols are
supposed to work._ "

How did you come to this decision that "that's the way the symbols are
supposed to work"? I bet it's some sort of process of taking in information
and updating your beliefs. And the idealized optimal version of _that_ is
Bayesian inference.

" _Wolfram came up with a great question in NKS -- what if the universe is
really discrete and not continuous?_ "

Sorry for the anal-retentive nitpicking, but this question isn't due to
Wolfram. I'm not qualified either, but it's definitely a fascinating thing to
think about. Maybe our universe is just a small computer program.
<http://en.wikipedia.org/wiki/Digital_physics>

~~~
DanielBMarkham
I did not come to any decision about that's the way the symbols are supposed
to work -- that's my whole point. The symbols represent the way it works. They
are a self-referencing representation. There's no decision involved here at
all. You can call it an axiom, but that misses the point. An "axiom" only has
meaning inside certain formal symbolic systems. It. Just. Is. It exists.
Different people with different numbers and operators? They'd be asking why %^
$% $#^ #$$%, for instance. But it's the same thing. The answer is in the
question. It's like asking "Why is red a color?"

I didn't mean to imply Wolfram came up with computational reality, I simply
mentioned that he brought it up in his book. It may turn out the integral was
just a nifty little shortcut that took a lot of impossible-to-calculate math
off the table for physicists. Thanks for letting me clarify that.

~~~
jey
" _I did not come to any decision about that's the way the symbols are
supposed to work -- that's my whole point. The symbols represent the way it
works. They are a self-referencing representation. There's no decision
involved here at all._ "

There's a difference here between _what you believe_ and _what is true in
external reality_. (Yes, I know you can spend lots of time debating whether
the latter is even a coherent idea, blah blah blah, but all that stuff isn't
relevant.) You had to come to a belief about what "+", "=", "2", and "4" mean.
You were not born with this information embedded inside your head! :) This is
true regardless of whether the symbols by themselves unambiguously and
uniquely pin down the meaning of the expression. Even if a certain symbol
sequence has a "unique unambiguous" interpretation, you still had to read
those symbols and interpret them, and you learned something in the process --
which means you updated your beliefs about the symbols. I agree that the
"real" interpretation in external reality of these symbols didn't change (if
such a thing even exists), but your understanding of the symbols changed.

In general, probabilities are subjective and a property of the observer. They
describe degrees of belief that the observer has in various propositions, and
don't directly have anything to do with external reality. The only way they're
connected to external reality is that you make observations in reality and use
the gathered information to update the probabilities you assign. This means
the claim that the symbols "2", "4", "=", and "+" are unambiguous is
irrelevant even if it's true.

BTW - Thanks for the link on your blog to the NYT graph of the price of gas in
constant dollars.

