Re: Suggesting a Poll

On Sun, 22 Feb 2009 02:23:14 +0000, Angus Rodgers
<twirlip@xxxxxxxxxxx> wrote:


Although I'm still shaking with shock and anger, I think I might
even find it an amusing exercise to see my own words (in the post
to which quasi was just responding so viciously and fanatically)
through his malicious eyes, so as to "see myself as others see me".

On Sat, 21 Feb 2009 18:48:35 +0000, I wrote:

On Sat, 21 Feb 2009 08:16:08 -0500, David Bernier
<david250@xxxxxxxxxxxx> wrote:

Angus Rodgers wrote:
On Thu, 19 Feb 2009 14:13:46 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

[...]

Ah! OK. I agree. However, there must be some common culture of
rational debate, not a sterile Babel of mutually uncomprehending
monologues. (Thinks: I must read David Bohm's book /On Dialogue/.)

Translation (into quasi-speak):

The crank AHR sees all of mathematics as an irrational dogma, and
deludedly imagines that he can expose it to rational criticism,
and be lauded to the skies by the common people for doing so on
their behalf, exposing the scandalous fraud that is mathematics.

I think you greatly overestimate the extent to which human
beings are already free and rational, and underestimate the
gravity and responsibility of the task of educating human
beings to make the most of that potential for freedom and
rationality which we all undoubtedly possess.

Ditto.

Good, but note that it is quite possible (and it often seems to
happen in practice) that a healthy culture of rational debate
becomes mistaken (in some presumably Freudian way - although
there are also sound political reasons for being sceptical of
all claims of scientific neutrality and rationality) for some
evil dominant bully.

I can't quite see how even quasi could misinterpret this as an
attack on mathematics! Quasi, you're going to have to help me
out on this one ... Ah, I see, I've got it now. You took the
bit about "sound political reasons" completely out of context,
and interpreted me as saying that I, the crank AHR, disbelieve
"all claims of scientific neutrality and rationality". Is that
it?

I won't accuse you of lacking reading comprehension, because I
am not a good writer (except occasionally), and I am probably
at fault for not having made myself clear here. You're just
at fault for assuming the worst. Try reading more charitably
sometimes.

You mentioned "a healthy culture of rational debate", and I've
been thinking about how to conduct a rational debate.

So have I, and I've been undergoing something of a medieval
religious crisis over the question of what constitutes proof
in mathematics

Well, this one is easy: obviously, AHR = JSH! The crank AHR
has his own definition of "mathematical proof", which will no
doubt shortly be making its way up the Google search rankings.

The only interesting question is, will these two deluded cranky
superbrains compete, or will we be treated to an amusing parody
of collaboration between them, rather like Zippy the Pinhead
being psychoanalysed in emacs?

Stay tuned to the Crankbusters channel for further developments!

, and whether I have any moral right to consider
myself even a student of mathematics, let alone a mathematician.

OK, it really is rather hard to see this as anything other than
self-criticism or self-doubt on my part. But let's not give up
too easily - quasi wouldn't! I think he could quite easily see
it as an unguarded confession of my true wicked intentions: to
invade the territory of mathematics, as a crank fifth columnist,
and subvert it from within! How evil I am! Even in my "medieval
religious crisis", I didn't suspect this of myself! Well spotted,
Crankfinder General Quasi!

(Yesterday, either wisely or out of cowardice, I held back
a 258-line post on the subject of my own eccentric ideas
over the last three decades or so.)

Ah, you see, the witch confesses! Burn him!

However ...

(I'm off on a ramble of my own right now, but feel free to give
us some of those thoughts on how to conduct a rational debate!)

After reading the MacTutor biography of Kronecker,
http://www-history.mcs.st-andrews.ac.uk/Biographies/Kronecker.html
I realized just how different Kronecker's views were, and
if one trusts MacTutor, this was not limited to criticism
of Cantor's set theory:

" [...] in a lecture given in 1886 Kronecker complimented Lindemann
on a beautiful proof but, he claimed, one that proved
nothing since transcendental numbers did not exist. "

(Even more, from the same article: "It appears that, from the early
1870s, Kronecker was opposed to the use of irrational numbers".)

OK, so the crank AHR is presumably appealing to the authority of
the redoubtable Kronecker, here, in order to back up his own
miserably inferior, cranky ideas.

That's straightforward enough. No challenge for anyone of quasi's
interpretive genius.

This was after Lindemann's proof that pi is transcendental,
arrived at in 1882.

... in spite of my doubts as to both the meaningfulness of math-
ematics, and my own (in)capacity to appreciate whatever meaning
it might have,

OK, another clear confession of the crank AHR's evil cranky nature.

I have never entertained any serious doubts as to
the existence - in /some/ sense (to be defined, of course!) [*1]
- of transcendental numbers,

Hmmm ... wait a minute, what's this? Could this be the Devil
quoting Scripture? Probably. How evil! Still, it's a bit
hard to prove. (Try the ducking stool? Torture?) Let's read
on. I'm sure we'll find some more evidence, if we look hard
enough.

since (I think this was in 1979) I
noticed that if you consider positive integers as "magnitudes"
which are "added" by multiplying them (so that 1 is the "zero"
on the scale - which has no natural unit, although an extension
of the same idea does lead to a definition of e),

Oh, CLEAR evidence of crankiness here! Hallelujah! Obviously
this deluded freak AHR is still living in the early nineteenth
century, if not even earlier, and wants to turn the clock back
on the arithmetisation of analysis! He denies Dedekind, Cantor
and Weierstrass! Heretic!

then, in the
sense of Eudoxus, the "proportion" 3:2 is the number log_2(3),
which is (evidently, by unique factorisation) irrational, and
(less evidently, but provably) transcendental.

Abomination! He wants to go even further back into primitive
times! He actually imagines that the theory of proportion as
expounded in Euclid - whose logical flaws have been patiently
unravelled over more than two millennia, by the finest minds
humanity has produced - he actually thinks it can still be
used, uncritically! What an idiot! What a buffoon!

I don't think
I have ever mentioned this to anybody, so I have no idea if it
would carry any intuitive conviction to anybody but myself, but
it has always worked for me:

Typical crank self-delusion, of course. Comment hardly needed.

in a sense, an indisputably real [*2]
"object" can have an infinitely precise, irrational, and even
transcendental "measurement", in terms of another such "object"
(a natural number > 1) as "unit".

Meaningless. He just hasn't grasped the idea of pure mathematics,
and imagines that all of mathematics is something to do with
measurement and physics. What a dolt!

Oh boy, just wait until my fellow crankbusters see this!
We'll have a party! I must get some beer in.

The idea is even quite useful
from a number-theoretic perspective,

Here we go ... this AHR gets more like JSH by the minute ...
he actually thinks he can prove something in number theory,
using his silly, cranky, centuries-out-of-date ideas! He's
really giving the game away now! I almost feel sorry for him.

because it leads naturally
to something called (if I remember right) the Four Exponentials
Conjecture (still unproved) - or rather, a special case of it.
It is quite natural to wonder exactly when Eudoxus's definition
of "equal ratios" applies to this "dimension of measurement", and
the conjecture in question (implied by the Four Exponentials [*3]
Conjecture) is that essentially the only such case is the trivial
proportionality relation: a^m:a^n::b^m:b^n, i.e. a^m:b^m::a^n:b^n
(a, b, m, n in N; a > 1, b > 1).

More meaningless gibberish! Still, he hasn't actually said
he's /proved/ anything, yet. Not sure what's going on here.
Need more evidence, to really clinch this case.

(Or something very like that,
anyway - I may not have got the details quite right, because
I haven't thought about this for years, and I prefer not to! -
also, please excuse me if I have rambled on too much, as my
judgement is a bit suspect at the moment.)

Heh. Yeah, right. You got one thing right, crank!

[*1] Of the well-established methods, that of Dedekind seems
to be the most, er, natural here. Also, I have never been able
to entertain any serious doubts as to the existence of the
infinite sets involved in Dedekind's construction -

Huh? Wait a minute ... I feel confused ... damn, I really
need more sleep ...

although
(perversely, perhaps) I could quibble as much as Kronecker as
to the sense in which the rational numbers belonging to those
sets exist!

Ah! That's more like it! He IS trying to use Kronecker to
back up his nonsense! I knew it! I don't feel so tired now.
I think I'm really going to get this damned crank, gonna nail
him good, maybe tonight.

[*2] One doesn't have to take a particularly abstract view of
natural numbers here: tally numerals will do. As I mentioned
in the thread "Wittgenstein and the philosophy of mathematics",
I have a bunch of eccentric ideas (dating from about 1988) as
to the sense in which character strings (and mathematical and
logical) formulae exist, and what the adjective "finite" means.

Yeah. Right. Crank!

[*3] I heard of the Four Exponentials conjecture in sci.math:
<http://groups.google.co.uk/group/sci.math/browse_frm/thread/fb1ca767d5f21e45/>
= <http://snipurl.com/cdehg> (12 Jun 1993)
<http://groups.google.co.uk/group/sci.math/browse_frm/thread/20959105aacae97b/>
= <http://snipurl.com/cdeet> (14 Jun 1993)
<http://groups.google.co.uk/group/sci.math/browse_frm/thread/9327860b091bea05/>
= <http://snipurl.com/cdemy> (15 Jul 2008)

Hmmm ... well, nothing actually wrong with those references,
even if they are only to sci.math ... and he even seems to have
read them ... no doubt in some superficial way, to support his
grandiose fantasies. And he obviously hasn't /proved/ anything
... even though he didn't actually say he had ... annoying, that!
... he's a bit of a slippery customer, not as easy to pin anything
on as JSH. But I'll get him tomorrow! I'll /prove/ he's a crank!

So you see, kids, that's how it's done! Crankbusting is easy.

I said I was leaving the thread, but your inspired parody forces me to
make at least some minimal response.

All I can say is -- it's really funny!

Well done!

(But now I'm really leaving.)

quasi
.

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