Actually, humans are excellent at generating random numbers! What we're hopeless at is generating random sequences with a uniform transition distribution p(x[ k+1 ]|x[ k ]), where x is a number and k an index in the sequence. Please folks, if you're going to have this discussion, at least use the correct terminology so that there are no misunderstandings and miscommunications.

One clarification should be made as well. A random number is not necessarily one drawn according to a uniform distribution over a given set. I.e., numbers don't have to be equally likely to be drawn randomly. They only need to be drawn in proportion to their probability according to the governing distribution. So, a human asked to pick a number between 1 and 10 will still pick one "at random" (and I qualify that by saying that the mental process isn't likely to be random, but the outcome has the properties of randomness), but if you asked many humans to do it, you would notice that the preponderance of certain numbers suggested a non-uniform generative distribution. If human mental processes are indeed independent (i.e., no telepathy) then this non-uniform distribution will be present in each human (with some qualifications not really needed here).

Here's a good test of whether people can generate random sequences or not... ask as many people as you know to order the digits 0,1,2,...,9 in any order they like. Don't let them know what other people wrote. Take all of the answers and count the frequency with which digits appeared in each place in the sequence and compute the conditional distribution. A particularly interesting result is to look at the trend line for the sequence (did they tend to place them in increasing order, decreasing order, or flat (totally mixed)).

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








How many of you said 6?

Cheers,

Timkin

Quote: Original post by Anonymous Poster
random numbers is stupid but your concept is good look i am not a programmer but i am trying to learn and i think that a random AI would make games different and better more real life ??? something like randomized paths for AI gaurds and random ways an AI can ask you to acomplish a task or quest is this possible

Err, are you saying random numbers are good for AI or bad? You say "random numbers is [sic] stupid" in the beginning, but later you seem to say that you think it's more lifelike. Also, an AI which uses random numbers does not necessarily act completely randomly.

Quote: 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.

Quote: 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? :)

Quote: 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]

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.)

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]