Re: Chord connection


"Abstract Dissonance" <Abstract.Dissonance@xxxxxxxxxxx> wrote in message
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"Bob Pease" <Popester@xxxxxxxx> wrote in message
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"Steve Latham" <llatham@xxxxxxxxxxx> wrote in message
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RJ P asked

Just for Fun.. What would you think if someone asked you to prove
that
2
+
2
= 4 ?


lol. I'm not sure. I don't know how to prove it but I suppose my
response
is that its provable and I would tell them were they could find the
proof.

I would definately say that its not always the case that 2 + 2 = 4 and
give
them a counter example. On a practical side I might say that it
doesn't
matter if its true or not because its still useful. I'd then probably
go
off
on some long explaination about grammars, groups, operations, and
representation theory and probably try to include some history of man
type
of crap ;) (i.e., 1 + 1 = 2 hence 2 + 2 = 1 + 1 + 1 + 1 = 4 = 1 + 1 + 1
+
1).

It would all depend on if I thought they really wanted to know or was
just
trying to waste my time.


I, ofcourse, don't really know the proof but I have read that Hardy and
Whitehead have proved it and its very complicated. Actually, at this
point
in my life I don't care to much about it. I don't think being a great
mathematician is going to save my soul or make me life for ever(which I
guess is what I truely want... well, that or knowing everything).

caution ... not a simple question

It's one of those things where the reaction to the question is more
important than the question itself.

To me an analysis of why it would NEED to be proved is the candy here.

It's a thing where the journey is much more interesting than what's at
the
destination.

Try Peano's axioms and the field axiomms. It's not complicated if you
don't
get too picky about existential quantifiers.


I agree. Life would be boring if it was easy. If you knew everything then
what would be the point? I think part of the goal is the struggle. The
problem is that we only have a finite amount of time and so one has to
choose what is more important. Theres also a lot of other problems that
interact together to make it more difficult than it needs me(such as
survival(pretty much equal money), pride, ego, etc...)).

I do think that its human nature to want to understand the world around
us... else I think one would have a hard time explaining our
accomplishments. I'm glad that someone had the need to prove 1 + 1 = 2 as
I
feel it is necessary. Fortunately I have realized that there is much more
to life than mathematics and it is only part of the equation if I want to
really understand life. (and in my adventure I feel that everything seems
to be connected in one way or another)

Jon


My point is that for some reason a whole buncha guys were interested in
abstract number theory. there was a feeling that the state of mathematics
was simply a lot of tricks, which sometimes did not work
My entire undergraduate education in Math was stuff that was cool in 1790,
but there was almost a Starburst rennaissance about that ime in Math.

It was the swimmers against the tide of complacency that made Math into the
foundations of modern analysis.

To understand even Applied math, it is universally believed that the
intellectual basics need too be known at least by the first year of Graduate
level.


It doesn't really bother me that almost anyone would feel that Provng 2 + 2
= 4 is omphalism or solipsy, But it's not

What DOES bother me is that the folks who teach High School Math in general
don't have the intellectual curiousity to have though about much except what
page we aare on in the text.

Yes 2 + 2 = 4 needs to be proven, but the main reason is not "Why not just
accept it as a Fact, and not be late for Footall Practice ", if you get my
drift .

The "Moving rocks " proof is valid, and hopefully would trigger the
principles of abstraction in the connection of grouping rocks and the
Assoociative Principle
My fear is that it generally doesn't and "I weep for the youth of America"
( said by By the snobbish waiter about Ferris Bueller"

This is gettng way off topic, but the SYMBOL for 1 + 1 IS "2" ..
It need not be proven.

If you're interested, the "Completion of the Number System" is a pretty
standard exercise for any Ph.D Candidates in abstract Math.

Bob Pease


.

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