How is this not about Francis Galton?!
The Man Who Invented Modern Probability
41–50 of 73 posts
Re: The Man Who Invented Modern Probability
#42Earlier quoted context omitted.
>And this is what "big data" and NLP were like before computers :) aside, I recently interviewed a candidate for a "Big Data" position. He got quite chatty about Kolmogorov & Measure Theory, so I quickly cooked up an interesting problem to relax his nerves. I opened the interview with "If the side of a cube comes from a uniform distribution between 1 and 5 inches, what's the expected volume of the cube ?" I thought h…
27?
27 would be correct if each side were independent random variables rather than the cube of a random variable. The way the problem is set up you are suppose to solve for E[a^3] (the third moment of the random variable) rather than (E[a])^3.
Re: The Man Who Invented Modern Probability
#43How is this not about Francis Galton?!
For those not in the know, Galton invented the simplest way of understanding normal distribution. Here's a copy you ca ceck on your phone.
www.intromath.ca/aakkozzll
A quote from Galton: http://www.aakkozzll.com/docs/order/galton.htm
Re: The Man Who Invented Modern Probability
#44> Kolmogorov armed a group of researchers with electromechanical calculators and charged them with the task of calculating the rhythmical structures of Russian poetry And this is what "big data" and NLP were like before computers :). One can only imagine what he could have done with a modern computer. (Which is particular hard to imagine because he's responsible for advances which ultimately led to these same modern…
>One can only imagine what he could have done with a modern computer.
The historical anecdote my thesis advisor was telling about origins of his (i mean founded by him) branch of the science was along the lines "Americans had computers and could get good numerical solutions, while we didn't have computers and thus were forced to work on analytical solution". Well, that analytical solution he produced happened to be a great insight into the problem space and still continues to be the key tool for the research in that area almost 60 years later.
Re: The Man Who Invented Modern Probability
#45I am not a statistician, but if I found myself in an infinite forest, I would probably get drunk, too.
Re: The Man Who Invented Modern Probability
#46I have no reason to particularly disbelieve the research that went into this article. But I'm just naturally skeptical when he reels off a list of puns that depend on the english language used by a group of Russian researchers. This seems unlikely to me. It seems like unnecessary color of dubious provenance.
Re: The Man Who Invented Modern Probability
#47> Kolmogorov armed a group of researchers with electromechanical calculators and charged them with the task of calculating the rhythmical structures of Russian poetry And this is what "big data" and NLP were like before computers :). One can only imagine what he could have done with a modern computer. (Which is particular hard to imagine because he's responsible for advances which ultimately led to these same modern…
>And this is what "big data" and NLP were like before computers :) aside, I recently interviewed a candidate for a "Big Data" position. He got quite chatty about Kolmogorov & Measure Theory, so I quickly cooked up an interesting problem to relax his nerves. I opened the interview with "If the side of a cube comes from a uniform distribution between 1 and 5 inches, what's the expected volume of the cube ?" I thought h…
He was staring at it because he was looking for a shortcut that must make the problem obvious enough to be done in 10 secs. If you don't provide context on such tasks, that's expected.
Re: The Man Who Invented Modern Probability
#48Earlier quoted context omitted.
Your proof seems to only prove that a finite number of programs (described by you) which can produce a finite number of irrational numbers, while there are infinite number of irrational numbers. But we're surely not talking about a finite number of programs. I'm not even sure what the Kolmogorov complexity of a "complex irrational number" means. If you need the sequence of digits and you cannot use an algorithm to pr…
For each fixed length there are a finite number of programs of that length. If we use 8-bit bytes for the alphabet, there are 256^N programs of length N. The set of ALL programs is infinite (we don't limit the length of programs), but it is countable. The "countable" part means we can put the set into one-to-one correspondence with the natural numbers. The correspondence starts with 0 mapping to the empty program, th…
In some sense, the existence of irrational numbers with no pattern in their digits is an illusory artifact of the number system. We can talk about them collectively because decimals are not required to have an end, and we have to postulate them to fill in the gaps in the number line, but such numbers lack any description or means of being separated as individuals.
But then, is any mathematical abstraction real? I guess it's all beside the point.
Re: The Man Who Invented Modern Probability
#49I thought this was going to be about Pierre Simon Marquis de Laplace who wrote A Philosophical Essay on Probabilities in 1814.
http://neuroself.com/2012/01/21/pierre-simon-laplace-1814-a-...
Re: The Man Who Invented Modern Probability
#50Earlier quoted context omitted.
39
from random import random sum([(random()*4+1)**3 for x in xrange(1000000)])/1000000 => ~39 Weird.
sum(random.uniform(1, 5)**3 for i in range(10000)) / 10000