Wednesday, August 30, 2006

 

Randomness debate, some ground rules

So now I'm in a debate about whether or not p mod 3, with p an odd prime greater than 3, is random or not, when I say the result of marching up the primes is random, like coin flips.

That is crucial for my more political claim that mathematicians wrongly ignore randomness that can be found with primes.

But hey, maybe I'm wrong, but what does that mean exactly?

Well, I say primes show no preference for a particular residue modulo a lesser prime, so the behavior is random because no rules are around to make it not be random.

If I am wrong, then that statement is what is wrong, and primes DO show some preference modulo a lesser prime.

To understand what that means consider yet again what I showed with the first 23 primes after 3:

5 mod 3 = 2, 7 mod 3 = 1, 11 mod 3 = 2, 13 mod 3 = 1, 17 mod 3 = 2, 19 mod 3 = 1, 23 mod 3 = 2, 29 mod 3 = 2, 31 mod 3 = 1, 37 mod 3 = 1, 41 mod 3 = 2, 43 mod 3 = 1, 47 mod 3 = 2, 53 mod 3 = 2, 59 mod 3 = 2, 61 mod 3 = 1, 67 mod 3 = 1, 71 mod 3 = 2, 73 mod 3 = 1, 79 mod 3 = 1, 83 mod 3 = 2, 89 mod 3 = 2, 97 mod 3 = 1

So the sequence is

2, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1

and if the sequence is random, you can only say that 1 or 2 is next in the sequence.

In case that doesn't make sense, randomness is about NOT knowing what is coming next beyond the 50% probability, like with a coin, can you predict whether it will be heads or tails?

(If you can you can make a lot of money betting people against your ability.)

If there are no rules so that either possibility is equally likely, then either possibility can occur.

That is crucial, if I am wrong, then there are rules that slant whether you get 1 or 2, one way or the other and rules mean PREDICTION is possible.

So someone might be able to say that after the 321st prime, you are actually more likely to get 1 than 2, considering p_321 mod 3.

PREDICTION is key here.

If p mod 3 is NOT random, then knowing rules governing the behavior could allow you to predict, that say, 2 is more likely to be next.

So remember, and this is crucial in this debate, that if I am wrong, then there are some rules that could help you figure out which number—1 or 2—would come next in that sequence.

There can be no other way, logically.

My fear, which is why I'm making yet another post, is that too many of you have been beaten down by the easy tactic that mathematicians and math people have of simply being abstruse.

If things get complicated, people zone out or fear that they're just too stupid to get it.

Well let me be the one who looks stupid here. I'll ask the questions no matter how stupid I look, and notice that people from math circles have no problems with the put-downs.

And neither do I.

The politics here are HUGE. If I can convince some of you that math people routinely lie in this area it could be an immense swing.

If I am wrong, then, oh well, I'll learn something myself about primes. My credibility is not an issue.

Math people have already marked me as a crackpot across the web.

So now you know the stakes. I say math people are vicious and ruthless, quite capable of lying on a huge scale, and of course, they would be mad as hornets and ornery as cornered rattlesnakes for that to come out, so I expect it to get very brutal.

But make no mistake, if p mod 3 is NOT random, then damn it, somebody better start talking about how you predict the next number in the sequence beyond saying there is a 50% chance it is 1, or 2.

Concrete tests are CRUCIAL when dealing with intelligent people who have a lot to lose, and a history of successfully lying to a lot of people all over the world.





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