Re: JSH: Math journals do not just die

Shotgun mode (this isn't worth real effort):

...
[Tim Peters]
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").

[jstevh@xxxxxxx]
It is guiding in that it tells you approximately what is the
probability that x is prime.

So it has predictive value.

And Brent's formulas have predictive value in exactly the same sense.

....

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

As I said, you're at least a week behind. All of this was explained
several times last week -- there was nothing new here. Your "finally"
above is just confirmation of how far behind you are. Spend less time
ranting and creating endless new threads? Oh, right -- you don't
actually care about the math here.

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

They were given repeatedly last week.

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

But the ideas that Hardy & Littlewood use are probabilistic.

Not true, and that's also been explained multiple times. H&L
explicitly refused to take a probabilistic approach, although it's
common to /view/ their work probabilistically today, and there's no
problem with talking about probabilities over finite sets.

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.

What of it? That's already been explained multiple times too.

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?

Sorry, but you haven't "figured out" /any/ of it yet. Those "math-ese"
formulas allow computing specific predictions for the distribution of
residue pairs in your sequence, and those predictions match well with
computational experiments.

In contrast, you have no quantitative predictions, and have no
explanation for why computational observations contradicted your
qualitative "it's perfectly random" assertion. Established theory
explains all of it already, although the H-L portion of it is still
just conjecture.

So how exactly do those formulas support your points again? Let's see.
You claim "it's perfectly random" but can't account for any of the
computational evidence overwhelmingly opposing that hypothesis. OTOH,
the formulas not only qualitatively account for the computational
evidence, but do a good job of predicting just how far off from "it
looks perfectly random" experiments showed. So they do a good job on
all of it, and you do a good job on none of it, and /that's/ why they
support your points? Got it now -- it was a little subtle ;-)

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

Have already; won't repeat.

....

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.

Who do you think you're fooling here? You /could/ learn something
here, you know.

....

or going to statistical arguments.

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

Gratuitous insult.

Nope, not gratuitous: you earned that one.

Attempt to sneak in a wrong position.

Huh?

Prediction is not necessarily about statistics,

And you propose to measure the success or failure of prediction exactly
how then?

as a flawed coin, to emphasize that example can be CHECKED and flaws noted
that might make it tend to give heads over tails.

Yes -- and a computable formula delivers a non-random sequence by all
accepted meanings of the word "random". There's no need to /test/ your
"coin" at all.

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.

Huh?

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?

Because it's the plain truth: /any/ standard statistical test would
say that a sample size of 10 is too small to draw a conclusion. If the
sample size were substantially increased, then that wouldn't apply, and
I've already explained multiple times how "10 heads in a row" /would/
be treated then. "Probably flawed" is incorrect.

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.

Beyond moronic again, James. There are 2^10 = 1024 possible outcomes
after flipping a coin 10 times, and if the coin is fair /each/ of those
outcomes occurs with probability 1/1024. HHHHHHHHHH is exactly as
likely as, e.g., HTHTHTHTHT or HHHHHTTTTT or any of the other 1021
possible outcomes.

If you knew anything about what you were talking about, I'd be more
charitable and assume you had a Bernoulli distribution in mind, but
screwed up stating how that works. But since you've always given me
cause to regret being charitable in the past, I'm not going to cut you
that kind of slack anymore. What you actually said was plain idiotic.

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.

Probability is entirely logical, although I can understand why you'd
doubt that (your understanding of probability is purely "intuitive" and
careless). Odds of 1 in 10^60000 is roughly the chance of flipping a
fair coin and have it come up heads 200000 times in a row, BTW.
Seriously: would a sane person who saw that happen hold a belief that
the coin is fair, and they were just unlucky 200000 times in a row? I
don't think so.

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

Explaining the consequences of standard definitions isn't "appeal to
authority", any more than is pointing out that 25 is odd by all
standard definitions of "odd"

followed by ad hominem.

If the shoe fits ... does it?

....

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

As above, you still don't understand this, and I give up. Read Brent's
paper. Show a sign that you understand any part of it and maybe I'll
respond.

... [repetitive ranting about his old paper] ...

...

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.

If readers are curious to see /successful/ heuristic arguments about
primes, and want to know where /sub/expressions like (q-2)/(q-1) really
come from, see Chris Caldwell's wonderful intro to the subject:

http://www.utm.edu/staff/caldwell/preprints/Heuristics.pdf

Of course that's been explained to James before too (on other
newsgroups). /Parts/ of successful arguments do intersect with James's
attempts to think along "similar" lines. This isn't surprising,
because it truly is trivial, e.g., to note that there are q-1 positive
integers smaller than prime q. It's what people do with the
non-trivial parts following that account for the difference between
success and failure.

...

.

Relevant Pages

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