Is randomness = indeterminsim?

[BillHoyt]

I have to agree, Central Limit Theorems usually imply convergence to a normal distribution. In some rare cases, Cauchy, it depends on the set up. My probability theory is rusty.

Oops, my error. I should have written "normal" distribution.

 

[BillHoyt]

I shall investigate these 4 terms!
"non-uniformly distributed." Central Limit Theorem. binomial distribution. uniform distributions

Note the binomial -> normal correction.

My proposition; a fair die has no bias or no tendency whatever regarding its numbers, statistically in the long run every number is equal frequent, the die have no significant tendencies to show any particular number more than any other number, that die is truly random!

The tendency of a fair die is to converge upon a uniform distribution. That is a "tendency."

That sequence of digits is not possible to describe in any shorter terms than the sequence it self, therefore that sequence is random! In what sense invalidate the Central Limit Theorem that?

If you think about what you just wrote you should realize you've contradicted yourself. The sequence from an unfair die also cannot be described except by the sequence itself.

there is no quotes arund true there, but the word not is there!
Please read the word not in this context!

Don't be an ass.

we both agree that mutation is random, I have not alleged otherwise!
But you have said that "tend to is a statement of randomness" which is not consistently compatible with nonrandom natural selection's tendency to favor survival of the fittest!

Selection is the force operating on a population that culls from that population the least fit (or adds to the population the most fit) in the current context. That context isn't static, though, is it? Perhaps this has some essential meaning...

 

[Peter Soderqvist]

Bill Hoyt what do you say about my post 11-17-2004 12:50 PM about random number, the third post above?

 

[BillHoyt]

Soderqvist1: In the unfair die set, all numbers is not equally probable as outcomes, therefore; every number which this die output is nonrandom, when some number is statistically determined as more frequent than other numbers, then this frequency give us information that the die is biased in that way! Conversely a fair die doesn't give us any information about its further state!

This is pure bunk, Peter. You cannot predict either die's next face based on the past face. If you believe otherwise, then please give me the equation that shows what the next face will be based on the previous face

 

[Peter Soderqvist]

Is it also pure bunk that the unfair die generates nonrandom numbers, because all elements of that set are not equally probable as outcomes?

Random number From Wikipedia
A number itself cannot be random except in the sense of how it was generated. Informally, to generate a random number means that before it was generated, all elements of some set were equally probable as outcomes. In particular, this means that knowledge of earlier numbers generated by this process, or some other process, do not yield any extra information about the next number. http://en.wikipedia.org/wiki/Random_number

 

[69dodge]

Originally posted by BillHoyt
The sequence from an unfair die also cannot be described except by the sequence itself.

A program like PKZIP could compress it into a shorter sequence that nevertheless completely describes it.

to Peter: Even a fair die is somewhat predictable: after all, even before you toss it, you know for sure it won't end up showing 7 spots, right? So maybe that isn't random either?

There's no real argument here, I think. It's just a matter of terminology.

 

[BillHoyt]

Is it also pure bunk that the unfair die generates nonrandom numbers, because all elements of that set are not equally probable as outcomes?

Peter,

1. I thought you had written earlier that you would look up some key terms I gave you. Have you yet done so?

2. I think JREF posters should be fully aware of exactly what "Wikipedia" is. This disclaimer surely should make its unreliability abundantly clear:

"Wikipedia is an online open-content encyclopedia, that is, a voluntary association of individuals and groups who are developing a common resource of human knowledge. Its structure allows anyone with an Internet connection and World Wide Web browser to alter the content found here.Therefore, please be advised that nothing found here has necessarily been reviewed by professionals with the expertise necessary to provide you with complete, accurate or reliable information.

That's not to say that you won't find valuable and accurate information at Wikipedia, however please be advised that Wikipedia cannot guarantee, in any way whatsoever, the validity of the information found here.It may recently have been changed, vandalized or altered by someone whose opinion does not correspond with the state of knowledge in the particular area you are interested in learning about. "

 

[BillHoyt]

A program like PKZIP could compress it into a shorter sequence that nevertheless completely describes it.

True, but it perforce starts with the original sequence, doesn't it? It is, simply, a transformational engine

There's no real argument here, I think. It's just a matter of terminology.

I disagree. Read Peter's posts closely. He has many fundamental misconceptions about probability.

 

[Walter Wayne]

The Wikipedia definition is incorrect. Its definition applies to a random process with a uniform probability distribution.

A fair die (numbered 1,2,3,4,5,6) is a random process with uniform probability distribution.
An unfair die (say 1,1,2,3,4,5) is a random process with non-uniform probability distribution.
A die with all 1's is a non-random process.

Walt

 

[Jorghnassen]

The Wikipedia definition is incorrect. Its definition applies to a random process with a uniform probability distribution.

A fair die (numbered 1,2,3,4,5,6) is a random process with uniform probability distribution.
An unfair die (say 1,1,2,3,4,5) is a random process with non-uniform probability distribution.
A die with all 1's is a non-random process.

Walt

You could say a die with all ones is a random process, it's just that there's only 1 event which has probability 1 .