From: Mark Murray on
JSH wrote:
> I have heard of him.

Really? There is no evidence to suggest that you have compared
yourself favourably with Descartes. That I could Google (must be
Google) for in the short time I have before I am blinded by your
brilliance. Care to enlighten?

> My definition does not contradict prior ones.

Missing the point, utterly. Read, James, read.

OK, OK, I'll help out. ANY idiot can do this. History is full of
credible efforts; we don't need yours.

> What is the definition of "deductively"? What is the definition of
> "truth of a proposition"? What is the definition of "previously
> proved"?

What is the definition of "what"?
What is the definition of "is"?
What is the definition of "the"?

What is your bloody point?

> It's well established that mathematical proof is about using some
> argument and prior truths or axioms as they're usually called by math
> people in order to prove some conclusion.

Correct!!

> It's not the overall picture that's important here.
>
> It's the skill in boiling things down to only what matters.

Like Leibniz did?

> I would argue that "deductively" is at best redundant, at worse, at
> times is wrong--are all mathematical proofs deductive? And "truth of
> a proposition" seems vague. While "previously proved" seems to be
> circular.
>
> Not to knock Descartes but he died a long time ago.
>
> Humanity has learned a few things since his body turned to dust.

Humanity, Yes. JSH, No.

But I'm getting a clue how JSH can't "deduce" much.

M
From: sanboz on

"JSH" <jstevh(a)gmail.com> wrote in message
news:23f3f9ec-ab26-4064-a30c-5dfe8dcb958e(a)u36g2000prn.googlegroups.com...
On Nov 29, 12:40 pm, Jym <Jean-Yves.Moyen+n...(a)ens-lyon.org> wrote:
> On Sun, 29 Nov 2009 04:18:01 +0100, JSH <jst...(a)gmail.com> wrote:
>> > In my case I have defined mathematical proof.
>>
>> As a matter of fact, before reading
>> "A mathematical proof is a mathematical argument that begins with a truth
>> and proceeds by logical steps to a conclusion which then must be true."
>> I must say I kinda expected something more... revealing ?
>>
>> By the way, maybe you'd like to read "some guy named Descartes" and

>I have heard of him.

>> especially his "Discours de la m�thode" (http://descartes.free.fr/in
>> french, you'll probably find english translations in a couple of minutes)
>> �2.7 to 2.10 seems pretty similar to your definition. You should probably

>My definition does not contradict prior ones.

your definition is horseshit.

>> sue him for plagiarism.
>>
>> Or the "Tr�sor Informatis� de la Langue fran�aise" (numerised treasure of
>> the french language" which defines "d�mosntration" (proof), for the
>> logical meaning of the word, by :
>> "Raisonnement qui �tablit la v�rit� d'une proposition d�ductivement,
>> c'est-�-dire en la rattachant par un lien n�cessaire � d'autres
>> propositions admises comme vraies ou ant�rieurement d�montr�es"
>> (reasonning which deductively establishes the truth of a proposition,
>> that
>> is proceeding by necessarily steps to other propositions admitted as true
>> or previously prooved).

>What is the definition of "deductively"? What is the definition of
>"truth of a proposition"? What is the definition of "previously
>proved"?

You always have an extremly hard time with pure math.


>> Again, I find that one suspiciously close to your definition (excuse my
>> poor translations skills).

>It's well established that mathematical proof is about using some
>argument and prior truths or axioms as they're usually called by math
>people in order to prove some conclusion.

Which you *hate* so you rolled your own definition. (and smoked it)

>It's not the overall picture that's important here.

Yes it is. and you missed it, cant even comprehend it.

>It's the skill in boiling things down to only what matters.

Which you are unable to do, without incurring HUGE amount of errors.

>I would argue that "deductively" is at best redundant, at worse, at
>times is wrong--are all mathematical proofs deductive? And "truth of
>a proposition" seems vague. While "previously proved" seems to be
>circular.

Always in the passive, as you should be.
Let the big boys do their work, and go count ants at the park, JSH.

>Not to knock Descartes but he died a long time ago.

You did too. didn't you get the memo?

>Humanity has learned a few things since his body turned to dust.

your mind turned to dust, it is obvious when you try algebraic math, quit
snorting dust my boy and your head may clear.


>James Harris


From: Ray on
JSH wrote:

> One of the more fascinating things that I've faced recently is the
> question of why some of my own amateur research like on my math blog
> comes up highly in certain Google search results. But one thing is
> clear, when *newsgroups* are presented with the information, posters
> immediately make efforts to discount such results, which is actually
> kind of interesting in and of itself.
>

Google doesn't have any magical instrument that can measure what's
true. There is no such thing as an atheliometer. They don't even
have a staff of the world's leading experts in all disciplines
feverishly reviewing every page on the net in realtime. Nobody
can afford that, and their users couldn't pay them enough to do
afford it.

All Google measures is all that it really can -- what's popular,
what gets linked, and what answers particular search criteria.
Frankly, they've even become rather vague about matching search
criteria lately, to the point where some searches drive me to
despair of ever finding things with Google or their imitators
and wanting to set up an alternative search engine that does
*NOTHING* with popularity, page rank, link counts, or anything
else and just returns random unordered links to pages actually
matching the search terms.

If you want to validate an idea, but you don't have the math chops
to prove that it's true (or untrue) looking to Google (or any search
engine) is unproductive. A more appropriate method would be to

A) code your algorithm.
B) code the dominant alternative (in this case Dijkstra).
C) code a random problem generator that produces problems in
the space you think you've found a solution for.
D) Run the dominant alternative side by side with yours on a
long series of randomly generated problems and keep score.
E) If the scores are interesting (better than the dominant
alternative in any consistent way) then publish the code,
along with an article explaining it and documentation of
the scores.
F) If people don't believe you, they can run the code themselves
and see the scores develop for themselves (you produce
repeatable results) and you don't have to argue about it.
G) If other people are interested in the scores, they will do
the serious mathematical analysis of your algorithm and may
discover interesting things about it that you didn't think
of, or figure out why (or when) it works better than existing
alternatives. Even if it doesn't turn out to be a solution
for the general TSP, it could turn out to be a complete
solution for some useful subset of it.


If the dominant alternative finds a better solution to *any*
problem, then you *know* you don't have an algorithm that always
finds the best solution. You could have eliminated that possibility
(and avoided making the claim that got people to ridicule you so
much) on your own before ever posting here. The method outlined
above would not require any ability to do hardcore proofs.

And even if your algorithm *doesn't* always produce the best
solution, it can still be a very interesting algorithm. If, for
example, someone finds a heuristic for the TSP that produces
better solutions on average than Dijkstra's algorithm, or runs
an average of 10% faster, or both, and never runs slower or
produces a worse solution by more than, say, a factor of 10, then
that would be revolutionary and worth rewriting every introductory
computer textbook now in use.

The headline over it wouldn't say "TSP solution", it would say
"TSP heuristic - possibly better than Dijkstra's Algorithm." The
article would contain the code you used. And the results would
be repeatable, and possibly extensible, anywhere, by anybody,
because you included the code.

Bear





From: Ray on
Mark Murray wrote:

> Just because someone else /may/ be wrong, doesn't mean you aren't.


<snarf> Quote file!

Bear

From: JSH on
On Dec 2, 7:35 pm, Ray <b...(a)sonic.net> wrote:
> JSH wrote:
> > One of the more fascinating things that I've faced recently is the
> > question of why some of my own amateur research like on my math blog
> > comes up highly in certain Google search results.  But one thing is
> > clear, when *newsgroups* are presented with the information, posters
> > immediately make efforts to discount such results, which is actually
> > kind of interesting in and of itself.
>
> Google doesn't have any magical instrument that can measure what's
> true.  There is no such thing as an atheliometer.  They don't even

I never said they did. However, "authority" is a reality of the
modern world where academics DO claim it in their own fields based on
things like publication in formally peer reviewed journals.

They would probably cite such publication in a highly respected
journal as important!

Web search results offer "citation" as well by showing interest in a
particular topic.

The question is, to what authority level?

> have a staff of the world's leading experts in all disciplines
> feverishly reviewing every page on the net in realtime.  Nobody
> can afford that, and their users couldn't pay them enough to do
> afford it.

Editors at journals around the world--who may not be paid--currently
represent something of an authority as they determine what papers to
publish, while people who bother to read journals--I don't--offer
additional by what they cite, or talk about with others.

It is a lot of communication.

The web is a lot of communication as well.

> All Google measures is all that it really can -- what's popular,

Spoken like a person with a lot of confidence who is also massively
uninformed.

Even I hesitate to define Google, but when I do, I say they are a
multi-media company.

I don't dare say they are just people who measure what is "popular".

If research shows up highly in Google, like say, solving quadratic
Diophantine equations, so that people searching on that subject get
it, while it is NOT in a journal, while journal research does not, and
provably MOST people were to start using Google and ignoring journals,
would there be a shift in authority?

If that trend were to happen, what impact might it have on the journal
system?

Or, if I can just put up a webpage and have traffic from people all
over the world coming to my research, why in the hell should I bother
with editors and some freaking journal?

Can't I just jump around them completely? Forget they even exist?

Get authority based on usage *in spite* of them?


James Harris