Re: Pls help with sister becoming crackpot

Thanks everybody! I really didn't think to receive so many answers to a
problem that is, after all, just a personal one. Thanks everybody but,
of course, Tonio: not to worry, though, you will soon get the visit of
a few "amici" of mine, and I'm sure they will set you straight once and
for all. I'm just sorry for the horse they'll have to decapitate
(anybody seen "The Godfather"?).

As I said, thanks everybody, but you all seem to think that there might
be some mathematical worthiness or at least knowledge behind what she
says, which is not the case, so I will try to to explain in short her
theory (and no, dl, it's really a "she" and not an "I"; and, Ioannis,
while your answer is deeply wise and I agree with you, she is
threatening not to talk with me anymore because I don't want to start
calling up mathematicians and spreading the good news, and I wouldn't
like to lose a sister because of a cranky theory; I suppose all of this
should be better posted on a psychology group, but if you can help me
in giving a foolproof demostration of crankiness, maybe this will
help).

So. Bear with me, it will take time. First thing she did was building
up a table of numbers. I can't replicate a number table in a text only
post (as I said, I have a nice excel spread*** to send you, if you
want it) but it goes like this:

1) first line is the natural number sequence (1, 2, 3, 4, 5...)
2) second line is generated by [ n ( n + 1 ) ] / 2 (1, 3, 6, 10,
15...)
3) third line is the same as the second one minus one (0, 2, 5, 9,
14...)
4) fourth line is the same as the third one minus two (-2, 0, 3, 7,
12...)
5) fiffth line is the same as the fourth minus three (-5, -3, 0, 4,
9...)

and so on, ad lib. This is worrying enough (sort of an
obsessive-compulsive behaviour) but it's just the beginning. Now, if
you build this table, you will notice that the top-left, bottom right
center diagonal is the sequence of the odd number. She discovered that
in the whole of the table, prime numbers are only on this diagonal; and
since she found out other regularities in the table, she became
convinced that there must be a way to build only the portion of the
table that should contain the prime candidate; if it's not there,
presto!, we find out it's a prime with no long calculation. I don't
really see how this might be connected with the Riemann Hypothesis; you
should ask _her_ (by the way, just today she called me to tell me that,
based on some line of reasoning I didn't really feel like following,
with this same table she could probably prove the Goldbach Conjecture).

My explanation to her: skipping the first line (the natural number
sequence) her table can be generated by

{ [ n ( n + 1 ) ] / 2 } - { [ m ( m + 1 ] / 2 }

where n increases according to the natural number sequence in each
horizontal line; and m = 0 in the second line, m = 1 in the third line,
and so on. Now simple algebra tells me that the preceding formula is
equal to

[ ( n - m ) (n + m + 1 ) ] / 2

Now, ( n - m ) and ( n + m + 1 ) have opposite parity (their difference
is always 2m + 1 , so one is odd and one is even); the even one will
simplify with the 2 at the denominator but you will always have two
factors. So with this formula you can't generate prime numbers, except
on the odd number diagonal where the difference between n and m is
exactly 2, ( n - m ) will simplify exactly with the 2 at the
denominator and you will be left with ( n + m + 1 ) as the only factor,
wich could be a prime number. My answer to her: you have simply found a
formula that will never generate prime numbers, there must be a billion
of them (more exactly, an infinity).

Her reply: she doesn't understand formulas and she doesn't care about
them, anyway formulas have no relevance here because what she found is
an algorhythm and algorhythms have nothing to do with formulas; so my
reasoning is useless and her table/algorhythm/whatever works, period.
And, of course, if I don't want to deny the light of truth, I must help
her to spread the good news.

And, Narcoleptic: I tried to tell her "If your formula works, take your
time and - let's forget RSA numbers - just tell me if 337.537.117 is a
prime number" (it is); but she said that she cannot do it by hand and
anyway she still doesn't know how to generate only the relevant part of
the table (I doubt there's a way), and that's why she need the
mathematics community help. And your arxiv.org link is very
interesting, but way over her head (mostly, it's way over _my_ head,
too).

She even sent all of this to Piergiorgio Odifreddi, Mathematical Logic
professor at Columbia University, who very kindly answered her that
this is not his field of competence.

I want to stress this: she knows almost nothing about math; she added
up numbers, put them up in column, saw some regularities and decided
that this regolarities were an epochal discovery; probably her problem
is that, as so many people ignorant of math, she thinks doing math is
the fruit of a creative flash, not different from writing poetry (but a
real poet would have something to say about this, too); and she is
convinced she just had one of those flashes.

I hesitate to believe that anybody followed me through up to here; but
if you did, you could:

1) Find out a very simple explanation (simpler than the one I gave,
which she did not understand) to explain her why all of this is a pile
of rubbish;
2) Address me to a psycology page with proper explanations on how to
treat crackpot cases (I looked for it but did not find it).

Anyway, you will make me very happy.

Of course, it could always be the case that this _is_ an epochal
discovery and I'm a moron; in that case, you will make _her_ very
happy: just ask me her email, get in touch and go happily down the
slope together. Anyway, you will make somebody very happy: you cannot
lose.

Well, I hope you will let me know what you think. Hope to hear from you
all soon (but not from Tonio).

.

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