A "Random" problem

Following on from our discussions of "Random" I have a problem I would like people to see if they can answer.

Is there a "pattern" to the following set of numbers that are listed in a specific sequence as follows :

97,01,09,17,25,29,37,41,41,45,49,50,53,57,61,65,69,77,81,81,
85,89,93,97,01,09,13,21,23,29,33,45,53,61,63,69,74,77,81,89,
93

Sam said he had a program or something that cuold tell if these numbers are "random" or not.

If anyone can tell me :

1. If the numbers are truely "random"?
(And no I didn't just pluck them out of my head)
2. If these numbers will ALWAYS be random?
(ie there will NEVER be a pattern to these numbers)
3. What these numbers mean if they are NOT random?
(ie explain the pattern)

What I belive is that random numbers follow billions of diffrent formulas everytime so its almost imposibble to tell if its random or not. I mean stuff that people come up with in real life, not like 2, 4, 6, 8, 10, 12, 14, etc.

Guv

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I am not absolutely certain, but I really doubt that Sam or anyone else could determine whether or not a given set of numbers is random, without knowing how they were derived

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HAHAHAHAHA!!!!!

So you are saying that unless they know what the source is they can't tell if its random?

Doesn't that defeat the point? If you already assume the process is random then of course you will say the answer is random... if a pattern is found you will claim it is coincidence.

What a wonderful "speel" to completely and totally avoid the fact that you could NOT prove if this set (is that a better word... don't be pedantic) of numbers is random or not.

Gen-X, what is your background? some of your concepts are incredibly naive.

First, as suggested by my previous post, I disagree with Sam. I do not think he could correctly judge that a given set of numbers is random. I do not think the question itself makes any sense.

The questions/statements in this and other threads indicate that you have very little knowledge pertinent to a discussion of probability, random sequences, random processes, et cetera.

For example, in one of your recent posts (not to this thread), you mention the following as coming from some dictionary definition of random.

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Of or relating to the same or equal chances or probability of occurrence for each member of a group

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You do not seem to realize that the above definition relates to certain specific situations or processes. For example: When tossing a single cubical die, each face has the same probablity (1/6) of being face up. If you make a non-cubical die, this definition does not apply. This definition does not apply to all sorts of random processes. A person knowledgable about probability would not make this error.

I think that the most you could do with any set of numbers is apply various statistical tests and provide the resulting data.

As mentioned elsewhere, there are processes considered to be random. A set of numbers associated with such a process is called a "random sequence." Sometimes "random number" (singular) is defined as a concatenation of all the digits from all the numbers in a "random sequence."

A given random process produces numbers which conform to some statistical test or tests. If you take any set of 40-50 numbers derived from the random process, they will not closely match the test criteria. If you take a set of 50,000 numbers generated from the process, they will match the test criteria well. This is like rolling dice 36 times and counting how many snake eyes, how many box cars, how many sevens, et cetera. The 36 tosses will not match the expected probabilites very well. You expect 1 instance of snake eyes every 36 tosses. You are quite likely to get none or two. Now if you toss the dice 36,000 times the resulting counts will match the expected results pretty good. If you had the time to make 3.6E50 tosses, the match would be incredible.

If you gave a statistician the results of your dice throws and asked him if they were dice throw statistics, you would get answers like: There is a 10% probabililty that this set came from throwing dice (a small set of values); There is a 90% probabilty that this set are dice toss statistics (a large set); For a really big sample, he might say 99.9%.

If you asked him to similarly analyse the same data for conformance to poisson statistics, you would get similar answers.

If you asked him if he thought your numbers were random, he would probably say "Do not bother me with silly questions!" He might say "meaningless" instead of "silly." He might just stare at you for a few seconds and ignore you. At any rate, I would be surprised if he would make any attempt to give you a yes or no answer.

I have no idea where you got your 41 or so numbers. I would have a very small chance of making a correct guess after a lot of analysis. It just is not worth the effort, especially since the result is likely to be "Ha Ha Ha, Guv, you are a jerk, because you are wrong."

Without a lot of effort (perhaps an hour or so of paperwork), I could provide you with the coefficients of a polynomial which had all your numbers & only your numbers as roots. It would just require the application of some well known algebraic procedures. The definition of those numbers as roots of the polynomial is every bit as valid as whatever definition you have for them. There is no way you could claim that the numbers were not the roots of my polynomial. If I provided you with the polynomial as the "pattern" or algorithm behind the numbers and you said "no, they came from ...", I could present a good argument claiming that you are lying and made up another "pattern" when I got the right answer. After all, my polynomial has your numbers as roots. If you said, "but I specified the numbers in a particular sequence." I could reply "Gee, that is just the order in which you happened to obtain the roots" or "Your mention of a particular sequence was just a ploy to make the problem harder."

I am not certain, but I think there are techniques for generating other types of functions which can produce a given set of 40-50 numbers.

In a later post to this thread, you said

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Doesn't that defeat the point? If you already assume the process is random then of course you will say the answer is random... if a pattern is found you will claim it is coincidence.

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In the light of my above comments, you should now realize that I personally would not expect to get any answer to the question: "Are these random numbers?"

You say some of my views are naive?

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As mentioned elsewhere, there are processes considered to be random. A set of numbers associated with such a process is called a "random sequence

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"considered" random?

So if you believe a process is random then the list of numbers it produces is therefor a "random sequence".

If you are not going to talk reasonably... even after my behaving myself out of respect for your other post then don't bother responding at all... The fact you consider "anything" I say as a quibble without looking at its merrit only proves your unwillingness to think anything other than what you do.

Had you taken the time to honestly and genuinely show the flaws in the things I said in the other post I would have happily agreed with you.... yet you chose to flame instead.


You bore me little man

Gen-X, what is the problem with the quote you gave?

Perhaps the reason that Guv says you are quibbling is because you are. If you aren't then what are you doing?

It looks a lot like you feel out of your depth on the subject and are backing out. If you don't understand then I'm sure someone will explain if you ask. If you disagree with what Guv said then say why - his post contained some very rational comments on the nature of your numbers and the possibility of deciding whether they're random.

Thats very rich Harry.....


Guv posts something you agree with and his post "contains some very rational comments on the nature of numbers..."

*I* post something you DONT agree with and immediately my post "is quibbling because I am".

Is that how you rate all information Harry? Decide first if you agree with it then promote it to well thought out and consise, or that you disagree with it and say its "quibbling"?

There isn't any backing out coming from me... the only backing out is on your behalf in deciding not to answer the questions and instead just place a label of "quibbling" on it.


Do I have to say something that you personally DEEM to be of value before you consider something I say as worth reading? If that is the case then there is absolutely no information whatsoever I could say on any subject to you that you wouldn't deem quibbling.

What I put in response to Guv's post was honest and genuine rebuttal to what he said, it pointed out a few basic flaws (which he also corrected because he just "assumed" everyone knew certain completely unobvious things like using "Las Vegas" rules, or using a die NOT a coin), yet you think I am quibbling.


I genuinely thought we might have started to get somewhere with that post, it was very well written but when the only response I got (and I was being so nice too) was "Your quibbling" it proved that for yourself and Guv you don't care about truth or honest debate... only that you are right.


I just love the way you give him credit for "the nature of numbers" like he created the damn things but if I write a plausible, rational and reasonable logical argument that refutes something he said I am "out of my depth, backing out, have no idea"...

You deserve every last scrap of sarcastic venom I throw at you if that is going to be your attitude.

You would have to be the most hypocritical person I have met in a long time.... Now I know who the ****** is.

You can't read, and you only take quotes out of context.


You think I said: "contains some very rational comments on the nature of numbers..."

I actually said: "contained some very rational comments on the nature of your numbers and the possibility of deciding whether they're random."


You think I said: "is quibbling because I am"

I actually said: "Perhaps the reason that Guv says you are quibbling is because you are. If you aren't then what are you doing?"


How you ever read all those journals you talk about is beyond me. I'm surprised you're not still on Roger Red Hat and the Village With Three Corners.

I didn't say you were quibbling, I asked you to clarify what the purpose of your statements were.

You have not even attempted to answer the very simple question at the beginning of my message which asked what the problem with the quote you gave was.


Given that you failed to read your own first language properly (and you complain about Kedaman's English!) the rest of your post is just nonsense. Come back when you have some reading/logic/social skills.

Don't you understand what paraphrasing is??!?!?!

What do you think the "..." were???? They were just quoting the portion back to you... Now who is "quibbling" and being pedantic???

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I didn't say you were quibbling, I asked you to clarify what the purpose of your statements were.

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To quote EXACTLY for his highness :

"Perhaps the reason that Guv says you are quibbling is because you are"

Now tell me again that you didn't say I was quibbling???

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You have not even attempted to answer the very simple question

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Granted it was not obvious... though I would have expected someone with a shred of intelligence to have worked it out.

He said "considered". That means he subjectively decided it was "random" thus allowing the results to be considered a "random sequence". If that is not "Random assuming Random" which you accused me of doing I don't know what is.

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Come back when you have some reading/logic/social skills.

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My reading skills are fine... your ability to extract information seems to be misfiring.

My logic skills are also fine, it is only your subjective filter that suggests otherwise.

As for my social skills... yeah you have me there, I just haven't learned that level of restraint when people are in my perception either being hypocritial, plain stupid or blind.

Come back when you have learned the ability to admit your own mistakes and have the GUTS to acknowledge when you do so.

You weren't paraphrasing, you were misquoting. If you were paraphrasing the extract would convey the same information. Your quotes were out of context. Not only that, one of them was just wrong, and if you can't see that then your reading skills are lacking as stated.

Okay, I'll tall you again: I wasn't saying you weer quibbling, I was asking you to justify your statement inferring that you weren't. Was that too big a word for you? here let me help I N F E R R I N G.


I still don't see your point with Guv's quote. It didn't look like a statement of proof that the sequence was random, just a definition of a random sequence. Perhaps I've missed the point or perhaps I just don't think it's very relevant. To be honest I no longer place any value in what you say on this thread so it doesn't much matter either way. Carry on with the sarcastic venom, maybe it'll give me a laugh.

Thats nice dear

Seems I was wrong, I was hoping for a laugh, but instead I just pity you.