Random Magic Paths - is it truly random?

[BigDaddy]

That equation looks very familiar, but I've misplace my book... (not my advance statistics books with all their distributions and tests, just the basic one).

Anyway, for anyone who stumble across this with some arcane pattern and thinks it might not be random, remember that radomness is elusive even to statisticians. Understanding randomness could be likened to understanding the actual magnitude of infinite. We can use it and test it, just like infinite, but our perception of it will never be quite accurate. So, consider a random number off of an infinitely long number line. . .

[alexti]

Ivan Pedroso said:
Yeah - your initial formula is correct. But I must admit that it could do with some explanations.

Thanks for the explanation why my formula is obvious Indeed, that's where it comes from. It reminds me of my teacher in the university who was used to say "and obviously *something* follows". After it would take me couple of hours to figure out why it was obvious

Ivan Pedroso said:
I looked at it (briefly, I'll admit) and could not see what it all meant, or what the idea behind the factors and numbers were. And when I saw that p(i)=0 for i=8 I just disregarded the whole thing and wrote up my (wrong) ideas. (now I get it, and that p(8)=0 is perfectly fine. It's the probability of getting 20 sages in a row with eight(!) paths missing - zero of cause.)

In general case, formula is
Code:

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p=sum[i=1..m]((-1)^(i+1)*C(i,m)*p(i)), where p(i)= ((M-i)/M)^N

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where M is a number of picks and m <= M is number of picks in a subset, so the formula gives the probability of missing one (or more) of the paths out of subset of m paths.
I've just substitued 8 for m and M for our case, which produced curious p(8)=0

[bone_daddy]

So, does this have to do with true randomness not being possible within a system containing a limited number of variables?

[BigDaddy]

A computer can never make really random numbers, a computer scientist has ensured me that that is the case as I believed it was. Instead it uses the clock to produce seemingly random numbers. The numbers themselve seem very much random, in fact, you could call them "virtually random".

True randomness is a rather complicated term, but according to my text randomness is part of anything who's probability of occurence or omission is <100%. So, I'd say that the probability of failure of a device, or the probability of throwing heads on a coin are still random, regardless of their distribution. Distributions just describe some specific random systems. So, I'd have to say no. It's just easier to feel you've grasped random with a coin flip.

Considering a random point on an infinitely long numberline is just a good way to illustrate a humans inability to truly understand certain concepts. Cosider a point on a numberline, if you take an infinitely small movement from that number to any other position on that numberline, there are an infinite number of uniques points between the first and the second, until the movement = 0.

Similarly, we make do with random models and distribution that resemble the things we can test. So, consider this, the probability of flipping heads or tails on a coin 1000 times is 9.3326E-302. IF the coin is flipped an infinite number of times, the probability of this occuring is 1.

In this example we have a demonstration of true randomness, with only two choices (heads or tails).

[Saber Cherry]

Via's CPU's produce random numbers, using special hardware. A Turing Machine cannot make random numbers, but modern computers don't have all the limitations of Turing machines (as shown by Via).

[Ivan Pedroso]

alexti said:
It reminds me of my teacher in the university who was used to say "and obviously *something* follows". After it would take me couple of hours to figure out why it was obvious

Hehehe. I can relate to that , I've heard and read it many times too. What about: "The proof of [bla bla] is left to the reader as an exercise" - that occured alot in my text books.

(It's a typical situation in math, until you get the point you are more or less in the dark, but when you get it, it really feels obvious afterwards. All teachers really could do with remembering their fumblings in the dark in their early days.)

[bone_daddy]

Ok, so although the occurence of any given number within the set of variables will be random, there will be an emergent pattern (the distribution) which is not. Is my comprehension of what you are saying correct?

Please forgive my ignorance concerning stats and probs, but I've never taken any math courses beyond basic algebra and trig. Never really needed them. I have a tendency to only learn things as I need them, unless it's something I find interesting. :-/

[BigDaddy]

It is true that a computer can give numbers that have a nearly random distribution, BUT because they use a distribution (my brother called it an MT, for I think Marsenne Twist) and a seed (from the clock) there is an element of forecasting available that is completely impossible with true random systems. I think ANSI, which regulate random numbers I guess, has determined the the MT is the new method of choice! Still sophisticated software CAN match/nearly match random distributions, but it can't come up with random numbers. Nearly matching distributions is all you have to prove, and I don't believe that it was ever speculated that computers couldn't come close to random. In a logical system such as the computer, its impossible for the PC to pull a number out of it's B***, it's programmed how to follow a distribution.

Bone_daddy, yes, random systems have their own "patterns". Such as the normal distribution, where outliers of very high numbers are explained, but most number fall close to the average.

[Verjigorm]

Interesting... is this device a miniature Geiger-Muller tube with some sort of radioactive isotope in a sealed chamber (similar to the technology used to make smoke detectors)? Is there a website where I can see a press release for it--I couldn't seem to find one in my own search (although I didn't look very long).

[BigDaddy]

That IS interesting. Basically, its like programming a robot to roll a die and then read the number, but it doesn't remove the theoretical limitation (that being that a computer is unable to come up with its own random numbers, in any case because you can forecast them knowing the time/function).

A very good use of it would be to make a pregenerated table or random numbers to seed your RNG.