Re: Peano's space-filling curve

From: Jesse F. Hughes (jesse_at_phiwumbda.org)
Date: 06/10/04 

Date: Thu, 10 Jun 2004 20:50:07 +0200

"John Morgan" <john.morgan@REMOVECAPSataraxie.fr> writes:

> Jesse F. Hughes <jesse@phiwumbda.org> wrote in message
> news:87fz94iyyl.fsf@phiwumbda.org...
>> "John Morgan" <john.morgan@REMOVECAPSataraxie.fr> writes:
>>
>> > Jesse F. Hughes <jesse@phiwumbda.org> wrote in message
>> > news:87aczf2vq1.fsf@phiwumbda.org...
>> >
>> >> Evidently, you work in a scientific field so simple
>> >> that every theory of the field can be explained
>> >> and justified to a layman using just the standard
>> >> tool of Usenet. In only a few posts.
>> >
>> > Yes, yes, yes. And maybe. How very perceptive of you.
>> > But maybe you read my post where I said what I did
>> > (oops - used to do).
>
>> I don't believe any of your answers,
>
> Do I detect the beginning of a scientific argument
> approaching. This P-K4 is a good solid start.
>
>> however. I don't believe that you can succinctly
>> state and justify every ecological theory to the
>> layperson.
>
> I am, of course, over-generalising. But even some of the
> more obscure stuff, like applying Shannon-Weiner measure to
> diversity can be described, thanks to the existence of
> simpler methods of measure viz. species richness. This
> technique could work even in mathematics, I believe. If
> someone understands a wooden ruler, and knows how to smash
> it into bits, you should have no difficulty giving them at
> least a feeling for the meaning of Lebesgue measure.

This explains, I think, some of your misconceptions about
mathematics. Mathematics is about precision and deduction.
Sometimes, valid arguments from plausible axioms yield surprising and
counterintuitive results, results which may even be undesirable. In
these cases, your simplification involving wooden rulers will fail
utterly to capture the counterintuitive result.

Maybe the Peano curve is one such result.

>> just as simple to explain at the drop of a hat to the
>> interested listener.
>
> I didn't propose anything that quick, and you know it.

Well, drop of a hat is loose talk, to be sure, but you expressed
disappointment that you weren't well tutored on the Peano curve when
you raised the question here.

>
>> [...]
>>
>> > I apprehend some things, though, including simple set
>> > theory, Cantor's middle third and his diagonal proof of
>> > the alephs. When I first saw it, Peano's curve didn't
>> > seem to me to be a whole lot more involved. What I
>> > was unprepared for was the
>> > welter of jargon embedded in unfamiliar semantic
>> > surroundings.
>>
>>As far as I can tell, it is not the jargon that has caused
>>your problems so much as the logic. When someone
>>wrote that (1) there are bijections between [0,1] and
>>[0,1]^2 and (2) the Peano curve is a continuous
>>surjection, you guessed that (2) was "because
>>of" (1). This isn't a problem with technical terms.
>>This is simply going beyond the explicit statements
>>and making guesses without reason.
>
> And the scientific method worked perfectly. It always does
> and always will.

You have a naive view of the scientific method and a gross willingness
to apply it outside of reasonable domain. Asking questions on Usenet
is not an application of the scientific method, unless you're engaged
in deviant psychology and/or the sociology of dysfunctional groups.

> The data (read sci.math subscribers) failed
> to support this hypothesis (which I think is a slight
> mis-quote, but I'm not going to back track to see, so we'll
> let it go) and I rejected it. N.b.Due to the power of any
> test of the data never being 100% I could have rejected a
> true hypothesis :-) Cue next hypothesis.

Either support your claim that I mis-quoted you or don't mention it at
all. Hint. Try <2ij6g2Fmc61aU2@uni-berlin.de>.

[...]

>
>> I am a fan of sorts. I regard Dylan as a touch more
>> perceptive than Harris, but I don't use Dylan in my
>>.sigs (though I do use some other musicians).
>
> Name names. I like good poetry. Oh, and good irony,too.

Bad Livers. Lyle Lovett. The Waterboys. Charlie Patton (a blues
musician whose music I don't really know, but who wrote a song I know
from some other musician. But I can't recall *who* I know that did
Banty Rooster Blues).

These are just songwriters whose lyrics happened to catch my attention
when I was near my computer keyboard. I'm not suggesting that they're
better poets than those not in my collection or even that they're my
favorite songwriters or writers of my favorite lyrics. Except for Bad
Livers. They're geniuses.

"My kinfolk killed a rat in their yard.
  Life is good when it ain't too hard." 

-- 
Jesse Hughes
"She testified they had sex near the Oval Office, not in the famous
room itself, because that `wouldn't be appropriate, you know.'"
                                         -AP article

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