inspired by the corroborating evidence discussion in the comments for Paul B's post
Einstein's Arrogance
overcomingbias.com
Einstein's Arrogance
1–10 of 19 posts
Re: Einstein's Arrogance
#2I 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.
Re: Einstein's Arrogance
#3I 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. You…
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
Re: Einstein's Arrogance
#4I 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. You…
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 t…
I don't disagree, but my hypothetical assumes that no one has done the experiment before making their belief known.
Re: Einstein's Arrogance
#5"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.'"
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Re: Einstein's Arrogance
#6Earlier quoted context omitted.
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 t…
I don't disagree, but my hypothetical assumes that no one has done the experiment before making their belief known.
Sounds like an unreasonable assumption. Either way, it's not about "wrong" or "right", it's only about what can be derived from evidence. Without evidence you have no justification to assign a higher probability to "2 + 2 = 4" than "2 + 2 = 3".
Caveat: It's true that some knowledge does have to be put into the prior distribution. Apparently you can't just bootstrap from a zero-information ("maximum entropy") prior. So it's possible that 2 + 2 = 4 is burned into our brains at birth.
Re: Einstein's Arrogance
#7Earlier quoted context omitted.
I don't disagree, but my hypothetical assumes that no one has done the experiment before making their belief known.
Sounds like an unreasonable assumption. Either way, it's not about "wrong" or "right", it's only about what can be derived from evidence. Without evidence you have no justification to assign a higher probability to "2 + 2 = 4" than "2 + 2 = 3". Caveat: It's true that some knowledge does have to be put into the prior distribution. Apparently you can't just bootstrap from a zero-information ("maximum entropy") prior. S…
> So it's possible that 2 + 2 = 4 is burned into our brains at birth.
Yup, there is plentiful evidence... not specifically the addition, but 2 and 4 are innately perceptible quantities.
Re: Einstein's Arrogance
#8I 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. You…
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 t…
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?
Re: Einstein's Arrogance
#9I 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. You…
I don't even think it is a good idea to think about theoretical physics as the blogger does. Math doesn't require any probabilistic validation whatsoever. Biology needs lots of it because there are too many unknowns. Physics is much closer to math than to biology, and evaluating it like one does a biological experiment, to me, is perplexing. For 2 + 2 = 4, there doesn't seem to be any need for "bits of information." And even though the author is probably talking about hunches and intuition, the probability that a theoretical physics can go about his field thinking in hunches seems small enough... ok, maybe this statement required 27 bits of information?
Maybe I am missing something.
Re: Einstein's Arrogance
#10I'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.