Einstein's Arrogance

I don't really like this view of hypothesis. Or maybe I just don't understand it. <p>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.

"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.'"<p> Error: Social robot could not compute. Please input valid parameters into auditory interface again.

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. <p>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.

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.<p> 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.<p> 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.<p> 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.<p> 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.