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Original post by Timkin Anyway... it's all good fun... now, think of a number between 345 and 789! How many of you said 6? Cheers, Timkin

I read the first bit (think of a number..) and immediately came up with 621 and thought nothing of it and then I read the next thing you said and realised I've just filled in the blanks without "knowing" it.

I still don't think people are capable of generating random numbers. After this little experiment though I think one of the big factors in people choosing "random" numbers is the way the mind has been trained. For example my brain just subconsciously filled in the blanks in the pattern (you said between 345 and 789 and I picked 621). Also people may have favorite numbers or numbers that are special or stand out to them for whatever reasons therefore weighting their "random number generation" (e.g. age, date of birth, phone numbers, house number).

As said before, I think humans are very good at pulling "random" numbers out of the air. However, I don't think that poeple are good at giving a sequence of numbers, because they base the number they are choosing on the number previously chosen and some pattern.

Very interesting conversation though.

I ask myself, what's really a random event? Something that's unpredictable?

Given enough lack of information/intelligence, the most obvious outcome from something can look random.

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Original post by Timkin Anyway... it's all good fun... now, think of a number between 345 and 789!

452! Did I win? :)

Did anyone notice that the middle between 345 and 789 is 567? Isn't that curious? :)

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Original post by owl I ask myself, what's really a random event? Something that's unpredictable?

Do you want a mathematical answer, a physical answer or a phenomenological answer?

The problem is that the word 'random' has different meaning to different people. Some people think of it as 'unpredictable' while others think that it means all possibilities have equal likelihood, while others think of it as meaning that prior knowledge plays no bearing on the outcome of the event, while still others think of it as an event with outcome likelihood equal to the probability of the event given all knowledge of the domain! ;)

That's why I prefer the term stochastic... it has definitive mathematical meaning and most people don't know what it means, so there's little chance of them misunderstanding it! ;)

in probability saying "all possibilities have equal likelihood" means when the possibilities num is infinite all possibilities are Zero likelihood.


So for example, asking someone (or an algorithm) to give a random integer number so that all the numbers have equal likelihood has a paradox built in,
there is zero probability for any result.

so.... the definition of random cant be "all possibilities have equal likelihood" because its like defining something to be a triangular circle.


Iftah.

Maybe Quantom's Probabilistic can be implemented or used (as in hardware generating random from waves example) to generate random numbers.

Just an Innocent Thought.. Don't Kill me because I know nothing about Quantom physics................... YET

[Edited by - arithma on January 18, 2006 3:42:22 PM]

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Original post by Iftah in probability saying "all possibilities have equal likelihood" means when the possibilities num is infinite all possibilities are Zero likelihood.

That's not true. One divided by infinity is not zero. (At least, as far as matters for summation.)

But we haven't even begun to get into the Determinism of the Universe question yet.

[wink]

Even in quantum mechanics where it is a world of probabilities, we don't have the ability to PROVE that the results are random, since it would require states outside the Universe. (See Godel's and other people's work for that.)


It gets really interesting when you start throwing around Judeo-Christian beliefs, Determinism, and the Chance/Freedom models around.

Deterministic model = All things that happen, including thought, follow from the previous state and all things were determined from the instant of creation.
Chance model = some things happen by chance, everything else follows from the previous state.
Freedom model = people (or at least a subset thereof) are able to freely manipulate the Universe through their thought independant of the previous state.


When you start citing biblical prophecy, and statements like "I know the end from the beginning", you can make a case that the religions propose determinism, but then you have the freedom to make choices and choose right and wrong, so you get the Freedom model.


You can also argue that any nondeterminism in the universe means that all of physics can be completely ignored in any place where nondeterminism is allowed.

Existential debates about random numbers can be so much fun. [smile]

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Original post by frob When you start citing biblical prophecy, and statements like "I know the end from the beginning", you can make a case that the religions propose determinism, but then you have the freedom to make choices and choose right and wrong, so you get the Freedom model. Existential debates about random numbers can be so much fun. [smile]

In Judeo-Christian religions, the human freedom doesn't surpass God's ability to know/plan our entire existance beforehand. So, at least Catolicism is deterministc. Prophecy and predestination defends that.

But lets NOT turn this thread into a religious debate. I agree with you it's fun tough :)

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Original post by Sneftel Quote: Original post by Iftah in probability saying "all possibilities have equal likelihood" means when the possibilities num is infinite all possibilities are Zero likelihood. That's not true. One divided by infinity is not zero. (At least, as far as matters for summation.)

I havent learnt advanced probability (which requires measure theory) so maybe I got some things confused, but here is what I think:

First, you are wrong: 1 divided by inifinity is zero.
proof: it is obviously not negative and it must be smaller than any (non zero) positive number. Give me a counter example to prove me wrong.

I over-simplified: yes, I know you can give equal probability to continious numbers (i.e. between zero and one) and ask about the probability of a subset, but I was talking about a discrete infinite set. In the continuous world you need to enter the problem of measure ("size" of infinte sets), but the same problem exists with sets of infinite measure.

If you say I am wrong then please tell me this:
suppose there is a way to make an algorithm output a (real) number with each number having the exact same probability.

what is the probability of output "1" ? *zero* (because it must be less then every epsilon)
what is the probability of output which is an even number? *zero*
what is the probability of output between 0 and 1? *zero*
what is the probability of output which is a positive number? I am not sure about this one... zero? half? I think its zero because you can make a series of growing segments each with zero possibility so the limit is zero.

So even for a continious set of numbers if the set is of inifinte measure then you cant give equal possibility for each or you get zero for each.
(and whatever the algorithm will return it will be an error)

PS. a real computer algorithm will never work on an inifinite set because it has only finite memory (and for example a number with 10^10^10^10^10^10 digits is still a possibility, but it too much to hold in memory even for a computer the size of the universe). But even with inifinte memory I argue that you cant make an algorithm to give all numbers an equal possibility.

Iftah.