Re: JSH: Math journals do not just die


jstevh@xxxxxxx wrote:
gjedwards@xxxxxxxxx wrote:
With primes that can only give 1 or 2. And without a reason to pick,
the values just flop around like coin flips.

I still can't quite work out whether you *do* understand but are just
trying to cling on to some pride (bad move, since you look even more
foolish with every post), or whether you genuinely don't understand
people's arguments here.


Readers should note that now just about everything I put forward has
now been deleted out and more than one person has come in to help out
Tim Peters who was floundering.

Yes they are regular posters on the sci.math newsgroup.

I'll go through the exercise of refuting them yet again, so you can see
how math people do this in the real world, and also understand how hard
it is to beat people who are willfully misleading others and working as
a group.

I'll be generous and assume the latter...so, hurumph, here it goes
again.....

Being 'like coin flips' means BOTH:

A) equal likelihood of heads or tails, AND
B) no correlation between flips (the next flip shouldn't be affected by
what the previous result was - or indeed *any* of the previous results
or patterns in them).


Yup.

Let's, for the sake of your argument, ignore the fact that mod(p,3) is
actually entirely deterministic - it being generated

Random is about prediction. If you go back in the discussion, you'll
notice I've said that before.

The issue is the predictablity of p mod 3, not what it actually is
after you've checked, or that sitting out there in infinity there is an
answer for every value.

Prediction goes to knowing the reason. That is, why the sequence is
one way versus another.

by...er....mod(p,3). Let's say we just discovered this sequence of 1s
and 2s in some scientific experiment. You glance at the sequence and
think: hmm, looks like coin flips - I wonder if it's generated by
something which shows the properties of a random process? You check the
number of 1s and 2s and find a split extremely close to 50/50. OK, that
looks good, exactly what I'd expect from a random process.

THEN, *IF YOU HAVE A BRAIN* you check (B). The first thing you might
check is whether there's a relationship between adjacent pairs. And
guess what? You find (as numerous posters have found and demonstrated)
that a 2 is more likely to follow a 1 and a 1 more likely to follow a
2. Not *definitely* - that would be 1,2,1,2,1,2, etc.., but *more
likely*. In fact, the chances of it being 'like coin flips' is AT LEAST
1/10^60000.


Statistical argument.

Why would that happen? Why would subtracting 3 from a prime greater
than 3, as many times as you can without getting a negative number tend
to leave 1 for the next prime after one that gave 2, or 2 after one
that gave 1?

Why?

In the absence of a reason, you can test various patterns and see what
you think is a pattern with a very high probability that it is in fact
a pattern, when it's not, because it's random.

Can you get the logic?

What if you were talking to a person who flipped a coin 10 times, and
thought it meant it wasn't a fair coin, and you say, well that doesn't
prove it, check the coin.

So that person flips the coin a thousand times, and keeps getting more
heads than tails, and they tell you, NOW do you believe me?

So you say, sorry, that doesn't prove anything, check the coin.

So this obstinate person flips the coin 100,000 times!!!

And gets more heads than tails, and jumps up and down asking, NOW DOES
THAT PROVE IT'S NOT FAIR??!!!

What's the answer?

So, unless he or she believes a practical approach to science is to
pursue hypotheses that have a likelihood of truth of 1/10^60000, a
scientist rejects the hyphothesis that it's 'like coin flips'.


You're like that person above, who keeps flipping the coin, and coming
back claiming proof.

Do you understand what random means?

Can a random sequence have what appear to be patterns of very low
probability?

Do you understand that or not?

Guess what? If the chance of stock-market collapse and me being chased
with flaming torches is less than 1/10^60000, I'll take that chance.


So? Human beings are known to get probability wrong, and very wrong,
with a high degree of confidence.

But they're still wrong, even if they take that chance.

Now, remembering we're pretending that we just stumbled on the sequence
in some field of research ( i.e. we don't know it's mod(p,3) ), I still
don't have a formula for exactly predicting whether I'll get 1 or 2.


I never asked for one. Are you implying I did?

Your posts indicate that you believe not having such a formula is the
definition of randomness. If so, then that is *your* definition of
randomness. In mathematics it has a much more precise definition.


Yet I talked about 1/(ln x) being a guiding formula for the prime
distribution--the count of primes--and gave 100/(ln 100) equals
approximately 21.7, which is close to the EXACT answer of 25, as an
example.

Part of my point here for skeptical readers is that math people do this
deliberately where a group of them will just lie.

And what can you do?

Notice that as I refute, they keep at it, and THEY WILL work
cooperatively as a group, as you can see in this thread.

It's perfectly reasonable position to assert that a sequence is
non-random, even if you don't know 'why?' . Of course, getting back to
the concrete example - in this case we do know why - mod(p,3).

So, do you get it?

So why? Answer the question. Why would subtracting 3 from some prime
as many times as you can without getting a negative number, tend to
give 2 or 1, if the prime before it gave 1 or 2?

Oh yeah, for people wondering what that mod thing is, consider 7 mod 3
= 1, because you can subtract 6 from 7. And 15 mod 3 = 0 as another
example, while 29 mod 3 = 2.

There isn't any real point to whether or not with a prime number you
get 1 or 2, so without a reason you just get this flopping around.

Trouble is, mathematicians build careers claiming to look for patterns
with what I say is a random process.

I've been arguing in this thread to point out that these people avoid
simple checks, dance around explaining, and play to people's emotions
and foibles, like emphasizing statistics when they should know that
with a random sequence you can get all kinds of stuff that looks like a
pattern.

My full goal here is to show you dedicated and willful behavior from a
group of people you may think can be trusted.

And this is big business, prime numbers are worth millions to
mathematicians in various ways, from grant money to prizes for research
to books on the subject, to their salaries as experts in random areas.

It's a racket with a big pay-off for certain people.


James Harris

My argument doesn't claim 'proof' (though others' might) that the
sequence generates something that mimics a random process. (As for
truly 'non-random' the proof that it isn't is self-evident - it's
mod(p,3), end of story).

If the sequence was a sequence of 10^9 coinflips I would be
overwhelmingly convinced that this coin (or the flipper) had some
'memory' of earlier flips which had an influence on future flips. I
might be wrong - there's a 1/10^60000 chance of that. I'll take the
(1-1/10^60000) side of the deal, you keep working on the 1/10^60000.

Let me know if you get anywhere.

.

Relevant Pages

  • Re: No Unique Initial Segment And No Characteristic Expansion.
    ... H> Infinite people each flip coins infinite times. ... R>the number of people and the number of coin flips per person? ... H> Can you always find a different sequence of heads and tails? ...
    (sci.math)
  • Re: JSH: Math journals do not just die
    ... Being 'like coin flips' means BOTH: ... In the absence of a reason, you can test various patterns and see what ... Can a random sequence have what appear to be patterns of very low ...
    (sci.skeptic)
  • Re: Universes...ad infinitum
    ... But we do need to keep in mind that there are ways of doing coin flips that aren't at all fair, ... This doesn't take away from the fact that existence is full of extremely unlikely events. ... Flip a coin 100 times and the sequence of heads and tails that you get is will be extremely unlikely, ...
    (uk.philosophy.atheism)
  • Re: Prove that Randomness Exists?
    ... Trows with a coin that comes up heads 51% of the time ... are still perfectly random. ... (as a handy rule of the thumb the scatter will go as sqrt(n)) ... disbelieve you based on 10 flips. ...
    (talk.origins)
  • Re: Entropy in crystalization: up or down?
    ... coin flip is fair (50% chance of landing heads or tails), ... show the coin turning up heads 14 times out of 20 total flips. ...
    (talk.origins)