Re: JSH: Math journals do not just die

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[Tim Peters]
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.

[jstevh@xxxxxxx]
Now you say conjecture, but repeatedly you've claimed proof.

This is why I cut most of the reply -- it's so typical. I've mentioned
the Hardy-Littlewood conjectures at least 20 times in replies to you on
this topic so far, and just about /every time/ noted that they're
conjectures. Suddenly this is news to you?

A problem here appears to be that since you don't know anything about
the topic, and refuse to learn anything, all technical discussion may
as well be "briosleilek asouled toiblap" to you. That is, nothing
registers -- it all looks like gibberish to you. If a piece of
knowledge is repeated often by enough people, you'll finally recognize
one of the phrases, and reply with a mechanical idiocy like

Oh, /now/ you say briosleilek asouled toiblap. I say you lie.

Why respond?

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

Are you truly incapable of understanding that equidistribution of 1 and
2 in isolation implies /nothing/ about equidistribution of adjacent
pairs 11, 12, 21, 22, or of longer subsequences? The sun comes up
about as often as it goes down, but that doesn't mean it's just as
likely to come up twice in a row. Do you truly not understand that
everyone agrees 1 and 2 in isolation /are/ asymptotically
equidistributed here, and that the error term on the generalized prime
number theorem assures that they're going to occur about equally often
over relatively small finite ranges too? That nothing there implies
"random"?

...
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.

How stupid are you? I mean, really. People /have/ tested that
sequence, through millions (& millions, & ...) of primes. /You/
haven't tested it (despite your hypocritical claim that testing is
basic), but you've been given detailed results from about a dozen
large-scale computer tests. I suppose that because the results were
disastrous to your claim, you're ignoring them, or decided they were
"lies".

There's an easy cure for that: /you/ test it. Then you can call
yourself a liar, because the results don't depend on who does the
testing.

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

And I posted a computer program that demonstrated predictive power in
this specific case, and moving to p=541 demonstrated a
correct-prediction rate 100x better than chance level. I even
explained why that's so, in considerable detail -- there are
subtleties.

...
I think people like you lie.

Be honest, then: you believe /all/ mathematicians lie about your work,
except for some "top mathematicians", who secretly agree with you but
deviously pretend to ignore you completely.

At some level I suspect you know how crazy your beliefs really are,
because, as above, you hold back when you're arguing for "points".

.... [foolish rants, mixed with endless "challenges" to do things that
have
already been done] ...

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

Closer, but you're still holding back: don't the sci.skeptic readers
deserve to know the full sordid truth here?

...
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.

Doh. How can you miss that I haven't missed it even once? This will
in fact be the first time I /don't/ repeat what "checking the coin"
consists of in the mod(p, 3) case.

....

...
You may think what I'm showing here is extraordinary,

Nope.

but remember I had a paper published in a peer reviewed
mathematical journal,

Yup, before the editor yanked it.

yet posters claim to have refuted the paper in Usenet posts,

Yup.

but when I explain how their objections don't matter or are incorrect--they
just keep claiming they refuted my paper.

Yup -- and they also explained back to you why and how your
explanations were in error.

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.

Warming up, but still holding back. Go into /full/ rant mode -- that
should convince people you /must/ be telling the truth ;-)

....

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?

What do you think? You've probably forgotten that the /first/ time you
gave this example, on sci.math, you yourself said that the correct
conclusion was "not enough information". Standard statistical tests
aren't stupider than you here ;-)

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

You first need to state a specific hypothesis to be tested, and name
the specific test you intend to use. For example, if the hypothesis is
that all possible 1024 outcomes of flipping a coin 10 times occur
uniformly at random, and you want to use a 1024-bin chi-square test,
then a minimum of 1024*6 10-toss trials is good practice, to ensure
that the expected count in each bin is at least 6. The chi-square test
is then equally sensitive to whether 10 heads in row occurs more than 6
times, or /less/ than 6 times. This has all been explained before,
although previously in more detail.

...

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

mod(p, 3) is obviously computable, and obviously "works".

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

As was stated in the very first reply to you, equidistribution of 1 and
2 is a necessary consequence of randomness here, but is not sufficient
to establish randomness. You can /think/ "it's random" all you want,
but the only evidence you have for that position is mechanical
repetition of the claim, along with a basic error in mistaking
necessary conditions for sufficient conditions, and world-class ability
to clamp your eyes shut when overwhelming opposing evidence is
presented.

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

Then they should also note that extensive testing has already been
done, although none of it by you. Your only substantive response to
early testing reports was "try larger primes". Which people did, and
got even worse results.

As I've explained, I believe the residue pairs here probably are
/asymptotically/ equidistributed, and Brent's formulas (despite
building on the H-L conjectures) /quantitatively/ do a good job of
explaining why any test performed on "small" primes must conclude
they're not equally common. I expect you need to try 200-bit primes
(about 90 decimal digits) before imbalance isn't dead obvious. But
there's no finite prime you can start with such that imbalance won't
still be detectable by a sufficiently sensitive statistical test. This
becomes purely a matter of arguing from the H-L conjectures then,
because it's intractable to do large-scale tests on, e.g., primes with
millions of digits.

...
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.

Do it yourself. I've pointed you to the formulas, and there's no
mystery about how to proceed. If you need help understanding how to
apply Brent's formulas, just ask. Do note that, like /all/ asymptotic
formulas (including the beloved pi(x) ~ x/ln(x)), they work better the
larger the input. x=192 is rather small compared to infinity ;-)

.