Re: JSH: Math journals do not just die

tim.peters@xxxxxxxxx wrote:
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.


Then demonstrate with them.

...

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.


I do. I have noted the tell-tale sign of (p-2)/(p-1) before.

I've looked down through your post, and noted you simply CLAIM it is
not what it must be.

...
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.


But there's one problem with that claim:

If you DO go by the probabilistic approach then the probability if x is
prime that x+2 has a prime greater than x as a factor is

1/(p-1)

or do you deny?

So the probability that x+2 does NOT have p as a factor is

1 - 1/(p-1) = (p-2)/(p-1)

which shows up repeatedly.

Yet now you just state that it's not about probability.

Ok, so do you claim it's a coincidence?

Explain then why that particular expression keeps popping up in this
area.

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.


Really? Then it should be easy to explain here for the sci.skeptic
readership.


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.


Then give some predictions for p mod 3.

How about the sequence of 100 primes after x = 192?

What do the formulas say should be the occurrence of 1 versus 2?

And what is the reality?

For those who wonder what p mod 3 is, it's what you get if you subtract
3 from p as many times as you can without getting a negative numbers.

So 17 mod 3 = 2, while 15 mod 3 = 0 because it's not prime.

And 19 mod 3 = 1. Notice no prime greater than 3 can equal 0 mod 3.

I've noted that there is no reason for primes greater than 3 like 17 to
show a preference for 1 or 2, so without a reason to pick one or the
other, either shows with equal probability in a random manner.

But mathematicians build CAREERS ignoring this point, and now I'm
challenging a poster defending the mathematicians position to put up an
example, where I want him to use formulas he claims have predictive
value on the first 100 primes after x = 192.

Why x=192?

I was just randomly typing--as randomly as I could--and those are the
first three digits of what I typed, as I had something longer, but
shortened it to make the test easier--and easier for me to check
claims.

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.


Now you say conjecture, but repeatedly you've claimed proof.

And I do have one prediction: 1 or 2 will show up with roughly equal
probability because the sequence is random.

An example 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

Anyone see a pattern there?

The poster I'm replying to claims one, and that's the point of my
request for a test of his claims.

Reality testing is basic.

I am asking for a demonstration of predictive power with that sequence.

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 ;-)


Well, I don't think they do show what you claim.

I think people like you lie.

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

Have already; won't repeat.


I will. That is the probability if x is prime and p is a prime greater
than x that x+2 does NOT have p as a factor.

If it were just a coincidence that it appears for arguments that do not
depend on probability then it would be a remarkable coincidence--well
worth noting.

Skeptical readers can simply look over research on "twin primes
constant" to see that no one has noted it!!!

It's a tell-tale sign. Mathematicians quite simply are either
deliberately ignoring the truth here or lying.

Otherwise you have to believe they never realized that they had this
remarkable coincidence in this area, when research in this area goes
back over a hundred years.

So then, are mathematicians brilliant but remarkably stupid with
something simple in just one area or are they ignoring a simple truth?

...

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.


Ad hominem, again.

My guess is that you think you're convincing above, but you have just
stated I am wrong.

In response I've challenged you to actually explain how (p-2)/(p-1)
comes into the equations, and I've asked for you to use what you claim
are equations with predictive value on the sequence of the first 100
primes after x=192, where I picked that in what I hope is a random way.

Also I've noted that if it does not have to do with probability
(p-2)/(p-1) showing up in an area where it would show up if random
process dominated is a remarkable coincidence.

So readers can google to see if it's remarked upon.

See what I'm doing? I'm asking you to explain facts versus relying on
people trusting you.

...

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.


Yet another gratuitous insult.

I note that you repeat here like you did above.

Oh yeah, for sci.skeptic readers, my main point for a while has been
that math people routinely lie.

So they do NOT want the truth here but instead work to convince people.

So tactics are important to them, as well as ignoring when they are
caught using them.

Some of you may have read his reply before I came back to reply and
been convinced.

That's why they use those tactics. They work.

Math people do this, I am certain, deliberately.

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?


I give examples. If you are making bets on a tossed coin, and it shows
up heads repeatedly, you might think it flawed by statistical tests.

But to be sure you have to CHECK the coin!!!

How can you miss that point when I make it over and over again.

Statistics do not prove. They simply point in a direction.

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.


I think the truth is the opposite of what you claim. And readers
should note that the poster had my example already.

So then, an important point I'm trying to make is that math people are
working against the truth being learned, and not working to find out
what is the truth.

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?


Well, at least he didn't just repeat here like he did twice above.

You may think what I'm showing here is extraordinary, but remember I
had a paper published in a peer reviewed mathematical journal, yet
posters claim to have refuted the paper in Usenet posts, but when I
explain how their objections don't matter or are incorrect--they just
keep claiming they refuted my paper.

So I should go off Usenet, right? I have. That's how I had a paper
published in the first place.

Math society gets away with behavior like this because it has been
categorized by many people as brilliant, so they rationalize away
behavior that contradicts their strongly held beliefs.

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.


So by convention 10 is too small a sample size?

How many coin flips would be a large enough one then?

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.


Point taken. I was incorrect. I should have said that 10 heads in a
row is a lower probability than any smaller grouping like 7 heads in a
row, except 10 tails in a row.

Of course any particular sequence of 10 is just 1 out of 1024 as you
noted.

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.


I simply made a mistake.


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.


Appeal to "common-sense" against logic.

Here is the third time you've repeated when a flaw in your reasoning is
shown.

I also remind that statistics point in a direction, so sure that seems
highly improbable, but still--you have to check the coin.

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"


But I don't think there is a computable formula that actually works.

I think it's a random process where patterns can seem to appear.

By claiming there is one, you appeal to authority--the primary one that
math people have with most people--the belief that there are
mathematical equations that prove one position or another.

Readers should note that above I've asked for a demonstration on this
very point: reality testing.

Where I've tried to randomly pick a number, x = 192, and asked for a
prediction.

followed by ad hominem.

If the shoe fits ... does it?


Fourth time the poster has simply repeated when a logical fallacy is
pointed out.

...

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.


But readers can do a web search on the subject and find no mention of
(p-2)/(p-1) as coincidentally appearing when it should appear by
probabilistic argument.

... [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.

...

I'll check out the pdf, but will go ahead with this reply. Hey, if I'm
wrong, I have no problem noting it.

You have a prediction to make on x=192 with the first 100 primes that
follow it.

If that is too many I can drop it to say, first 50 primes? Or even the
first 25.


James Harris

.

Relevant Pages

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  • Re: JSH: Math journals do not just die
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