Re: JSH: Math journals do not just die

marcus_b wrote:

jstevh@xxxxxxx wrote:

tim.peters@xxxxxxxxx wrote:

I missed a bit before that deserves a reply:

[jstevh@xxxxxxx]

I think others would think you were claiming proof as well.

Yes.


I may be wrong, but you keep posting as if I am just wrong.

Yes.


If these are conjecture then why not say maybe p mod 3 is random?

Because the Hardy-Littlewood conjectures have nothing to do with
whether the sequence is random. The sequence isn't random because it's
given by a computable rule. That's absolute proof, end of story, no
appeal -- and if you don't like that, you /first/ need to sell the
world a different idea of what "random" means.


Random is about lack of predictability.

If the sequence is not random then predictions can be made and the
numbers seen to behave as predicted.

But this sequence:

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

is just flopping around. Yeah, it looks kind of like 1 is followed by
2 or 2 by 1, but why?



Two answers on this. One, the likely reason for the probabilistic
alternation is that the gaps between the primes have certain
preferences, especially for "small" primes. For example, a frequent
gap between small primes is 4. If the ith prime equals 1 mod 3, and
the gap to the next prime is 4, then the (i + 1)st prime equals 2 mod
3.

Two, even if there were no obvious answer, that does not prove
that the preference is not there. Things can be very clearly nonrandom
without your knowing why. That would be true, for example, for
sunspot cycles. Not random at all, no one doubts the patterns are
real, but no one has the slightest idea why they happen.



Readers wondering where that comes from need know that p mod 3 just
means subtract 3 from p as many times as you can without getting a
negative number.



Ho hum. Playing to the kiddies in the audience? Why not a
a little remedial lesson on clock arithmetic?


Here's more detail on the sequence above:

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

Without a reason to be 1 or 2, the numbers just flop in an
unpredictable way--random.



See above. It is completely obvious that the sequence of
primes is not random - you yourself have noted that it is totally
predictable. And as noted above, the alternation mod 3 is
directly related to gaps between successive primes. As the
primes get larger, the gaps tend to get larger - gaps of size 2
and 4 will be rare for very large primes, and there will be less
of a preference for 1-2 and 2-1 pairs mod 3. But for "small"
primes, that preference is still there.



But mathematicians study these areas, and they can't study something
random, can they?



Of course they can, and do. Probability theory and the mathematical
theory of statistics are entirely about random processes.



Not if people know its random and that studying something random
looking for patterns is useless they can't, not and get paid for it.



Whatever the sequence of primes is, it's not random. It would
be very bad, for example, to base cryptography on the
sequence of primes. Your enemies would be able to decode
things instantly.


So mathematicians have to maintain the process is not random, or that
it's not completely random.



The evidence is overwhelming and there are obvious explanations.


Easy trick is to use statistical arguments on various ways of grouping
numbers, like 1,2, or 2, 1, which is the approach the poster keeps
talking about, but statistics do not prove.



Sure. Just like flipping a coin a million times and getting heads
every time would not prove that it was a 2-headed coin. You can
believe whatever you want, but believing the sequence of primes
mod 3 is random makes considerably less sense than believing
in the tooth fairy. There is more statistical evidence for the latter.



They CAN point in a direction.

Proof is about working out mathematical reasons. Here with a random
thing, none can be found, so math people turn to what I call math-ese,
where they babble, but in a highly technical way that's hard to follow.



Hard for whom? You and your imaginary grandstand full of idiots?



It IS incomprehensible because it doesn't actually make sense, but many
people today are programmed to believe that mathematics is just so hard
and beyond them, that it not making sense means they just don't get it.

Sometimes, it means what's being said just does not make sense.



For sure ... and sometimes what's being said makes so much sense
that only a fool would deny it.



I've stayed with p mod 3 because it's so simple. Why in the hell
SHOULD it matter whether you get 1 or 2 with this mod thing and 3?

Easy for people to grasp, and harder for math people to lie.



No one's lying. People have cited numbers. Cold, hard numbers.
They indicate preferences. There is rationale behind those
preferences. The rationale makes sense and the data are consistent.
It's not absolute proof. But people have been convicted and
executed (or acquitted!) on the basis of statistical DNA data with
MUCH weaker evidence than the data regarding patterns of the
primes mod 3.


Not that they won't try though, as you can see reading through this
thread.

Some of you who actually believed in these people may cry if you read
through the entire thread, and see how obvious it is how they mislead.



I'm sure many morons in your imaginary grandstand are just sobbing
their heads off right now.



But I can assure you that the posters I'm replying to have no shame,
and no conscience in this area. It's like they can't FEEL at all why
anyone would care about them lying to them, so they keep at it.

They are completely without shame or conscience, like both are foreign
concepts to their psyches.

Don't believe me? Read the thread for yourself.



Excellent suggestion. Nothing like data to convince people.

Marcus.


James Harris


It is not intuitively obvious that the difference bwteen two primes is an even number if the sequence is mod 2 the result of p mod 3 will be 2 and it it is 4 p mod 3 will be 1. so we could have 0 , 1, or 2. some prime difference is a multilple of two? maybe so we can have (3 p 2) events pair wise. this implies the function is a binomial function.
that in turn makes it non-random.
josephus
.

Relevant Pages

  • Re: JSH: Math fakes and blind belief
    ... But even readers who don't know a lot about primes can understand how ... gaps don't act randomly, but you fail to take the utterly obvious next ... then your sequence can't possibly act randomly either ... It's not "shifting the issue" to talk about prime gaps here, ...
    (sci.skeptic)
  • Re: JSH: Math journals do not just die
    ... The sequence isn't random because it's ... preferences, especially for "small" primes. ... directly related to gaps between successive primes. ... They indicate preferences. ...
    (sci.skeptic)
  • Re: Switching to Linux, now what to buy?
    ... > notice that the peaks in the phi function WERE the sequence given. ... of intelligence tests and quizes, ... Toward the end I began critizicing my work, feeling that the sets ... suggested inclusion of knowledge about primes as something ...
    (comp.os.linux.setup)
  • Re: About random, primes and statistics
    ... randomness of the sequence ... Let x be an EID sequence. ... same relative frequency. ... Then the sequence of primes ...
    (sci.math)
  • Re: About random, primes and statistics
    ... composites and composites ... Therefore, I strongly suggest to you, primes split ... A sequence is random if there is ... Yes, however assuming JSH meant pseudorandomness or randomness as in the digits of a number like pior any other normal number, he still has an interesting idea. ...
    (sci.math)