The Man Who Invented Modern Probability • Hacker News Board

Re: The Man Who Invented Modern Probability

#51

Post by bachback » Fri, Aug 23, 2013, 8:36 AM UTC

lutusp wrote: post #36

tlarkworthy wrote: post #35

Discovered, not invented.

> Discovered, not invented. This refers to a philosophical debate that asks whether mathematics is part of nature or an artificial invention of man. I think the debate has begun to lean toward mathematics being part of nature, in which case yes, the proper term is discovered.

Interestingly enough this notion, that there is only this one type of probability was debated before Kolmogorov by people like Ramsey and Keynes. Now the subjective interpretation of probability is called Bayesian statistics, which is not a helpful term.

http://plato.stanford.edu/entries/probability-interpret/

Re: The Man Who Invented Modern Probability

#52

Post by James_Duval » Fri, Aug 23, 2013, 9:01 AM UTC

tikhonj wrote: post #4

> 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…

I only know NLP as an abbreviation of the pseudoscience of neuro-linguistic programming.

What does it mean in this context? Non-linear probability?

Re: The Man Who Invented Modern Probability

#53

Post by stiff » Fri, Aug 23, 2013, 9:05 AM UTC

James_Duval wrote: post #52

tikhonj wrote: post #4

> 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…

I only know NLP as an abbreviation of the pseudoscience of neuro-linguistic programming. What does it mean in this context? Non-linear probability?

Natural Language Processing.

Re: The Man Who Invented Modern Probability

#54

Post by phaemon » Fri, Aug 23, 2013, 9:57 AM UTC

mtdewcmu wrote: post #48

nwhitehead wrote: post #34

Earlier quoted context omitted.

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 gue…

This is wrong. The square root of two was identified as irrational by the ancient Greeks, when considering the length of the diagonal of the unit square. The proof has nothing to do with decimal fractions (they didn't use decimal fractions at all).

Re: The Man Who Invented Modern Probability

#55

Post by lutusp » Fri, Aug 23, 2013, 10:12 AM UTC

mtdewcmu wrote: post #48

nwhitehead wrote: post #34

Earlier quoted context omitted.

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 gue…

> In some sense, the existence of irrational numbers with no pattern in their digits is an illusory artifact of the number system.

But irrational numbers remain irrational in any integer number base. Therefore no, they aren't illusory at all, nor are they an artifact of the "number system".

> ... such numbers lack any description or means of being separated as individuals.

Also false. Many irrational numbers are easy to identify unambiguously. For example, the square roots of numbers that are not perfect squares are irrational, but they can be easily identified by squaring them.

While we're on the topic, the terms in the running sum of odd numbers are all perfect squares:

    0 + 1 =  1
    1 + 3 +  4
    4 + 5 =  9
    9 + 7 = 16
   16 + 9 = 25

As is often true in mathematics, this is easier to explain with a picture:

http://arachnoid.com/example/#Math_Example

> But then, is any mathematical abstraction real?

Certainly. Consider general relativity. It's a mathematical abstraction, and it's also real.

Re: The Man Who Invented Modern Probability

#56

Post by hollerith » Fri, Aug 23, 2013, 10:39 AM UTC

bluetech wrote: post #50

solve wrote: post #23

Earlier quoted context omitted.

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 Many people don't know that the random module allows to sample from many distributions directly without having to construct your own.

I like the first version better because everyone knows what infix * and + do.

Re: The Man Who Invented Modern Probability

#57

Post by dev1n » Fri, Aug 23, 2013, 12:19 PM UTC

consz wrote: post #3

My father was the grand-grad student of Kolmogorov. He (Kolmogorov) is a very impressive mathematician. My father's advisor, Yakov Sinai, is equally impressive and arguably one of the founders of Dynamical Systems, a very interesting subfield of mathematics (and, in some ways, probability theory) in its own right.

Do you mean Kolmogorov-Sinai entropy? I just read about this in Chaos Theory Tamed by Garnett P. Williams. Really interesting stuff with respect to information theory in dynamical systems.

Re: The Man Who Invented Modern Probability

#58

Post by vasilipupkin » Fri, Aug 23, 2013, 12:30 PM UTC

dxbydt wrote: post #9

tikhonj wrote: post #4

> 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…

It's stories like this why I keep coming back to Hacker News

Re: The Man Who Invented Modern Probability

#59

Post by saucetenuto » Fri, Aug 23, 2013, 12:58 PM UTC

hollerith wrote: post #56

bluetech wrote: post #50

Earlier quoted context omitted.

sum(random.uniform(1, 5)**3 for i in range(10000)) / 10000 Many people don't know that the random module allows to sample from many distributions directly without having to construct your own.

I like the first version better because everyone knows what infix * and + do.

I like the second version better because it taught me something I didn't know.

Re: The Man Who Invented Modern Probability

#60

Post by pseut » Fri, Aug 23, 2013, 2:03 PM UTC

vladimirralev wrote: post #47

dxbydt wrote: post #9

Earlier 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…

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.

The shortcut's E h(X) = ∫ h(x) f(x) dx. So, math.