Re: JSH: Math journals do not just die

tim.peters@xxxxxxxxx wrote:
...

[jstevh@msn]
Last I checked you were making statistical arguments.

In part, yes; in part, no.

We'll see as I've read down and it looks like you try to elaborate more
below, so I'll answer there.

Readers should note how long this discussion has continued.

However, with prime numbers an excellent example of an area where
things are not completely random is the prime distribution itself,

More accurate to say they're "completely non-random".


That would seem to indicate completely predictable.

If so then, is 2^2147483647 - 1 prime or not?


where 1/(ln x) rules, and that is an example of a guiding equation.

1/ln(x) doesn't "rule" anything. A non-trivial theorem /relates/ the
distribution of primes to the curve 1/ln(x), which is a derived result,
not a guiding principle (or an /a priori/ "rule").

It is guiding in that it tells you approximately what is the
probability that x is prime.

So it has predictive value.

Otherwise there is no REASON for the behavior mathematically.

Gibberish.


Cheating. I say much of what you are touting as proof is just
chattering and hoping to win points by disagreement, and you call
things I say gibberish.

Part of the problem here is that mathematicians have routinely gotten
away with mathematical gibberish as an argument style, where by
babbling enough of what I call math-ese you can b.s. your way through
and convince people.

True or false, that's none of the problem /here/. The problem here is
that you don't know anything about the topic at hand, and steadfastly
refuse to learn.


Sounds like an attack on the messenger, otherwise known as ad hominem.

You want to convince people by asserting that I know nothing.

So I'm bottom-lining it for people who know that in mathematics you
have equations.

LOL. Yes, you do.


And they do. Readers should note that further down the poster does
finally try to answer the call for equations.

If you are right, give the equations.

"The equations" for /what/, specifically? If you want to know "why"
the residue pairs

<1, 1>
<1, 2>
<2, 1>
<2, 2>

distribute as they do up to a given x, I've explained that several
times already. It's entirely about the distribution of prime gaps, and
you can use Brent's formulas in:


So NOW after all of that the poster finally tries to give some
equations.

"The Distribution of Small Gaps Between Successive Primes"
http://wwwmaths.anu.edu.au/~brent/pd/rpb021.pdf

to get good predictions of how those pairs distribute up to a given x.
Computationally they work very well, although they build on conjectures
due to Hardy & Littlewood from the 1920's that still haven't been
proved. It's a consequence of the formulas that the pairs <1, 1> and
<2, 2> appear through "small" x far less often than they would if the
sequence were truly random. That wholly matches what everyone who got
off their ass (leaves you out) long enough to check observed.

It's also a consequence that "small" here extends at least through
primes with a few hundred bits. Also that the sequence can never act
truly randomly through any finite x, no matter how large. I would bet
that asymptotic ("at infinity") equidistribution also follows from the
formulas, but haven't been able to show that rigorously.


But the ideas that Hardy & Littlewood use are probabilistic.

I've already noted the appearance of (p-2)/(p-1) in what's called the
twin primes constant, which shows up repeatedly in this area.

So the poster has gone completely to math-ese, where a complicated
sounding paragraph is about work that actually SUPPORTS my points.

But how many of you figured that out?


None of this is new: I've explained it several times already, and as I
said last time, you ignore substantive replies. You still have no
explanation whatsoever for the behavior people observed, while Brent's
formulas can be used to make testable quantitative predictions. You're
at least a week behind here, still spinning your wheels at the starting
line. Catch up or give it up.


Explain the appearance of (p-2)/(p-1) in the twin primes constant when
that is about probability.

...
I emphasize this as it's crucial to make the point that something is
wrong here,

Have a mirror?


Have an ability to argue objectively versus turning to tricks?

so that people do NOT simply decide that if you keep
disagreeing with me, I must be wrong, and you right, which is an
unfortunate default that often takes place.

I want them to notice you are not really answering the question.

As above, you don't ask specific questions, just deliever rants and
make unfounded accusations. How many times do you need a reference to
Brent's paper before its supreme relevance sinks in? Try reading it
(no, not skimming it with a brain clouded by anger, desperate to "get
even", but /reading/ it dispassionately, as the piece of mathematics it
is).


Mathematics that relies on probabilistic ideas.

...
I say, if you are not just trying to convince people of your position,

No need for that -- the argument based on Brent's formulas is clear.
People are free to check the math themselves, several have, and there's
no disagreement about it among those who have.

Now I suspect you /did/ look at Brent's paper, but weren't able to
understand it. That would be fine if you said you needed help with it,
but you'll never do that. Instead you'll continue bluffing. /That/
earns contempt, not that you simply don't understand the references
given to you -- you don't care spit about learning or truth.


Ad hominem.

then you can give some freaking equations

Already done, multiple times.

or something versus denial of randomness

Still relevant: your sequence remains non-random, and /obviously/ so,
by any accepted meaning of the word. No "freaking equations" are
needed to demonstrate that beyond the one you started with: mod(p, 3).

or going to statistical arguments.

Beyond moronic. Talking about prediction and correlation /necessarily/
invokes statistical arguments -- they're statistical concepts.


Gratuitous insult.

Attempt to sneak in a wrong position.

Prediction is not necessarily about statistics, as a flawed coin, to
emphasize that example can be CHECKED and flaws noted that might make
it tend to give heads over tails.

So statistics can point in a direction, but proof is about the REASON.

Readers should note the tactic here of grouping an insult with an
unsupportable statement.

I'll give yet another example:

Say you flip a coin 10 times and it comes up head 10 times.

By statistical tests the coin is probably flawed, right?

Definitely not, and this has been explained multiple times too. I'm
not going to repeat it again.


Yes it is.

And the coin MAY be flawed. But it'd have to be checked.

Why deny that statistical tests would state the obvious?

You don't even need them.

10 heads in a row has a lower probability than any other sequence of 10
flips, except 10 tails in a row.

But how can you be sure?

Well, check the damn coin!

Statistics can point in a direction, but it cannot prove.

When probabilities are smaller than 1 in 10^60000, as they /have/ been
in some computational experiments here, a sane person draws the obvious
conclusion.


Appeal to "common-sense" against logic.


Is that absolute proof? Of course not. The absolute proof was that
your sequence is defined by a computable formula, and nothing beyond
that was truly needed. That's "checking the coin" here, and it was
absolutely known to be non-random before trying /any/ computational
tests. The latter were just interesting to perform, to see how the
non-randomness might manifest via one of the simplest standard
statistical tests for randomness. That brought up some interesting
math, in fact. Unfortunately, you don't know what it was; fortunately,
if you care to find out, I don't delete my posts from archives, so it's
still there waiting for you to notice.

Appeal to authority followed by ad hominem.

You actually have to go in and prove something one way or the other.

Already done.


Nope. You've given statistical arguments and when pushed to give
equations gone to research that relies on probabilistic ideas.

If p mod 3 is not random then there is a RULE or there are RULES which
would be embodied in MATHEMATICIAL EQUATIONS that would show that it's
not.

Already done.


Just obstinate denial of the truth.

You have statistical arguments, no proof.

As an example, the prime distribution--the count of primes--shows
non-randomness in its close relation to 1/(ln x).

If the Hardy-Littlewood conjectures are true, the distribution of prime
gaps follows very similar formulas. See Brent for details. In general
the conjectures give that the number of primes <= x with gap g
asymptotically equals the sum of

x * C_g_k * integral of dt/ln(t)^(k+1) from 2 to x

where k ranges from 1 to g/2, and C_g_k are constants depending on g
and k. That in turn is asymptotically equal to the sum of

x * C_g_k/ln(x)^(k+1)

That explains the distribution of residue pairs actually seen, and
/quantitatively/ explains how <1, 1> and <2, 2> are doomed to appear
"far less often than their fair share" through primes with at least a
few hundred bits.

But none of that was necessary to show non-randomness. Non-randomness
was immediate.

... [more old stuff; don't care about it myself] ...

Readers should note that the poster deleted out a second section where
I noted he put himself above Mathematical Reviews in disdaining the
journal--now dead--that published and retracted a paper of mine under
pressure.

Posters attempt to attack the journal to push the position that the
death of a math journal is this minor thing, and that publication of my
paper can be explained away without people considering the
obvious--that it was right.

Readers should see

http://mathworld.wolfram.com/k-TupleConjecture.html

where you will see a key expression that has (q-2)/(q-1) where in this
case they are using q for primes.

Note that the probability given a prime p_1 that p_1 + 2 does NOT have
another prime p_2 as a factor is

1 - 1/(p_2 - 1)

which is (p_2 - 2)/(p_2 - 1) and you'll see something like that or its
inverse

(p_2 - 1)/(p_2 - 1)

showing up in the research in this area repeatedly.

One the link I gave you'll also see Brent listed as a reference.

The poster goes to research that supports my position claiming it does
not, and how many of you can't tell one way or the other?

Consider that if intelligent people wish to lie to you about subjects
you are not expert on, then what can you do?

Why would they argue?

Because for mathematicians primes are big business.

By claiming that rules can be found in areas where things are random
they can operate indefinitely, getting government grants, writing
papers and selling books, in an area where just about any pattern can
be found if you look long enough because no pattern actually dominates.

So a "mathematician" can have an entire career doing nothing of value
at all.

That's lot of incentive for certain types of people to fight the truth.


James Harris

.

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