12 views

### Mike Jacobs

Nov 5, 1998, 3:00:00 AM11/5/98
to
This says simply put that an object can be decomposed into pieces the
pieces are put together to form an object of larger volume; a marble can
be broken into pieces to form a sphere the size the sun. Is this a
correct statement of the paradox ?If so is there an intuitive expanation?

### Tangent60

Nov 5, 1998, 3:00:00 AM11/5/98
to

Well, yes, sort of. The Banach-Tarski theorem doesn't work in real life,
though, because there are only finitely many indivisible elements of matter
(definitely not uncountably many), namely atoms, leptons, or whatever. In the
mysterious, abstract world of analysis, there are uncountably many points,
which makes the Banach-Tarski theorem possible. Now, here's an inuitive (in my
opinion!) explanation:

Say a sphere is cut up into a finite number of pieces to form another, larger
sphere upon reunion of the pieces. Now, the pieces DON'T ALL HAVE TO BE
PATH-CONNECTED CHUNKS. They can be incomprehensibly weird and "discontinuous"
sets of points that, upon reunion, use the property of infinity to make the
sphere larger. (I hope that didn't confuse anyone.) In fact, I am currently in
the belief that the reason everyone believes this is a paradox because of their
misinterpretation of infinity (which is annoying to all of us and is found in
every single human. Sigh...).

### Mike Oliver

Nov 5, 1998, 3:00:00 AM11/5/98
to

Tangent60 wrote:
> Now, the pieces DON'T ALL HAVE TO BE
> PATH-CONNECTED CHUNKS.

I have a memory of seeing written somewhere that the pieces can be
chosen to be both connected and locally path-connected. Does anyone
know whether this is true?

> In fact, I am currently in the belief that the reason everyone
> believes this is a paradox because of their misinterpretation of

> infinity [....]

Oh, there's no question that it's a paradox. It's a paradox you
can get used to, so that it no longer seems paradoxical ... but
that's true of all paradoxes, intuition being the highly trainable
thing that it is.

--
Disclaimer: I could be wrong -- but I'm not. (Eagles, "Victim of
Love")

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### Mike Jacobs

Nov 6, 1998, 3:00:00 AM11/6/98
to
If the theorem assumes that there are an infinite number of individual
elements of matter and we know this is not the case for real matter then
it is not a paradox. It is just a waste of time.
I read in the book by Gibbons "Shrodingers Kittens etc etc" where he
spends a few pages spouting out that there are profound physical
consequencesof the BTT in quantum theory .That is too incredible to be
true. Thank you Mr Tangent for your response.

### Mike McCarty

Nov 6, 1998, 3:00:00 AM11/6/98
to
You are confusing Math with Physics. Math does not assume anything
about matter, and in fact has nothing to do with matter.

Doesn't mean it's a waste of time, though.

Mike

In article <71uij6\$1gma\$1...@newssvr03-int.news.prodigy.com>,
Mike Jacobs <CBR...@prodigy.com> wrote:
)If the theorem assumes that there are an infinite number of individual
)elements of matter and we know this is not the case for real matter then
)it is not a paradox. It is just a waste of time.
) I read in the book by Gibbons "Shrodingers Kittens etc etc" where he
)spends a few pages spouting out that there are profound physical
)consequencesof the BTT in quantum theory .That is too incredible to be
)true. Thank you Mr Tangent for your response.
)

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### Mike Jacobs

Nov 6, 1998, 3:00:00 AM11/6/98
to
It is possible to prove anything if you assume false statements. Life
is to short to worry about hypothetical mathematical constructs.

### Tangent60

Nov 7, 1998, 3:00:00 AM11/7/98
to
>It is possible to prove anything if you assume false statements.

For a minute, I'd say you were a mathematician.

>Life is to short to worry about hypothetical mathematical constructs.

But...

### Mike Jacobs

Nov 7, 1998, 3:00:00 AM11/7/98
to
I was a math person until I saw the light. Physics is so much more fun.
Try it youll like it.

### Tangent60

Nov 8, 1998, 3:00:00 AM11/8/98
to
>I was a math person until I saw the light. Physics is so much more fun.
> Try it youll like it.

The same thing happened to me, just in the opposite direction. I was very
interested in physics at one point, but then I _gradually_ slipped into
mathematics. I liked it much more. But then again, I didn't _really_ do
physics, like the majors do. Perhaps when I get all the right math knowledge
(on the side of infinitesimals and tensor calculus, which I may learn only for
the purpose of this or that theory..) I could dabble for a while in physics,
and see how it is. :)

Nov 9, 1998, 3:00:00 AM11/9/98
to
Mike Jacobs wrote:
>
> I was a math person until I saw the light. Physics is so much more fun.
> Try it youll like it.

I wanted to study physics until I met this four-letter word named "lab"
:)

--
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### Mike Jacobs

Nov 9, 1998, 3:00:00 AM11/9/98
to
After I found out how to generate the real numbers from set theory and
learned some pre 20th century math I went over to to Physics. The
rest of the stuff gives me a headache. Post 20th century physics on the
other hand is intensely interesting. Read Feynman if you want more
philosopy on this subject. But in any case have fun.

### Tangent60

Nov 9, 1998, 3:00:00 AM11/9/98
to
>four-letter word named "lab"

Oh, yeah. I remember that now...one less reason for me to study physics - the
boring part. :(

### Michael Wodzak

Nov 9, 1998, 3:00:00 AM11/9/98
to
Mike Jacobs wrote:
>
> After I found out how to generate the real numbers from set theory and
> learned some pre 20th century math I went over to to Physics. The
> rest of the stuff gives me a headache. Post 20th century physics on the
> other hand is intensely interesting.

Ah ah! so the true turn of the Millenium came in or before 1998. I'm
glad we can lay that controversy to rest! ;o)

Michal

### Ron Rood

Nov 11, 1998, 3:00:00 AM11/11/98
to

> I wanted to study physics until I met this four-letter word named "lab"

What is this four-letter word named "lab"?

Ron

### Mike McCarty

Nov 11, 1998, 3:00:00 AM11/11/98
to
In article <3649482A...@th.vu.nl>,
Ron Rood <"P.T.M. Rood"@th.vu.nl> wrote:
)
)
)
)> I wanted to study physics until I met this four-letter word named "lab"
)
)What is this four-letter word named "lab"?

It is "lab". Actually, he left off a layer of quotes. He should have
written

I wanted to study physics until I met this four-letter word

named "'lab'".

Mike

### Michael Wodzak

Nov 11, 1998, 3:00:00 AM11/11/98
to
Mike McCarty wrote:
>
> It is "lab". Actually, he left off a layer of quotes. He should have
> written
>
> I wanted to study physics until I met this four-letter word
> named "'lab'".

Isn't it a six letter word??? ;o)

### Ronald Bruck

Nov 11, 1998, 3:00:00 AM11/11/98
to
In
Mike McCarty <jmcc...@sun1307.spd.dsccc.com> wrote:
:In article <3649482A...@th.vu.nl>,

:Ron Rood <"P.T.M. Rood"@th.vu.nl> wrote:
:)
:)
:)
:)> I wanted to study physics until I met this four-letter word named "lab"
:)
:)What is this four-letter word named "lab"?
:
:It is "lab". Actually, he left off a layer of quotes. He should have

:written
:
: I wanted to study physics until I met this four-letter word
: named "'lab'".

I wasn't sure whether this question wasn't a subtle joke, a la Alice,
talking to the White Rabbit? not sure which, distinguishing between a
thing, a thing's NAME, and what the thing is CALLED.

So the four-letter word could be NAMED "lab" yet be some other word ;-)

More likely, I think it was in the genre of the old saw, "There are three
kinds of mathematicians; those that can count, and those that can't." A
joke.

--Ron Bruck

### Bill Taylor

Nov 12, 1998, 3:00:00 AM11/12/98
to
|> > I wanted to study physics until I met this four-letter word named "lab"
|>
|> What is this four-letter word named "lab"?

Thank you Lewis.

I think he meant that it is called "lab".

But we still don't know what its name is called!

Anyway, he's right, physics labs are a ####!

-------------------------------------------------------------------------------
Bill Taylor W.Ta...@math.canterbury.ac.nz
-------------------------------------------------------------------------------
We should all try to avoid the "c" word and the "f" word. (chaos & fractals)
-------------------------------------------------------------------------------

### bo...@rsa.com

Nov 12, 1998, 3:00:00 AM11/12/98
to
In article <72dtrb\$r2e\$1...@math.usc.edu>,

Nope. Your response seems to indicate you missed the joke.

"four letter word" = "dirty word"

The jokes says that "lab" is a dirty word.

-----------== Posted via Deja News, The Discussion Network ==----------

### Mike McCarty

Nov 12, 1998, 3:00:00 AM11/12/98
to
In article <72dtrb\$r2e\$1...@math.usc.edu>,
Ronald Bruck <br...@math.usc.edu> wrote:
)In
)Mike McCarty <jmcc...@sun1307.spd.dsccc.com> wrote:
):In article <3649482A...@th.vu.nl>,

):Ron Rood <"P.T.M. Rood"@th.vu.nl> wrote:
):)
):)

):)
):)> I wanted to study physics until I met this four-letter word named "lab"
):)
):)What is this four-letter word named "lab"?
):
):It is "lab". Actually, he left off a layer of quotes. He should have
):written

):
): I wanted to study physics until I met this four-letter word
): named "'lab'".
)
)I wasn't sure whether this question wasn't a subtle joke, a la Alice,
)talking to the White Rabbit? not sure which, distinguishing between a
)thing, a thing's NAME, and what the thing is CALLED.
)
)So the four-letter word could be NAMED "lab" yet be some other word ;-)

Um, that's possible, in which case he didn't need the second layer of
inverted commas.

)More likely, I think it was in the genre of the old saw, "There are three
)kinds of mathematicians; those that can count, and those that can't." A
)joke.

That's the way I took it, in which case he missed a layer of quotation.
IOW, he needed to put the name in quotes. The name is then "lab", and to
put the name itself in for reference, another layer is needed "'lab'".

### Mike McCarty

Nov 12, 1998, 3:00:00 AM11/12/98
to
In article <72evqj\$14k\$1...@nnrp1.dejanews.com>, <bo...@rsa.com> wrote:
)In article <72dtrb\$r2e\$1...@math.usc.edu>,
) br...@math.usc.edu (Ronald Bruck) wrote:
)> In

)> Mike McCarty <jmcc...@sun1307.spd.dsccc.com> wrote:
)> :In article <3649482A...@th.vu.nl>,
)> :Ron Rood <"P.T.M. Rood"@th.vu.nl> wrote:
)> :)
)> :)
)> :)
)> :)> I wanted to study physics until I met this four-letter word named "lab"
)> :)
)> :)What is this four-letter word named "lab"?
)> :
)> :It is "lab". Actually, he left off a layer of quotes. He should have
)> :written
)> :
)> : I wanted to study physics until I met this four-letter word
)> : named "'lab'".
)>
)> I wasn't sure whether this question wasn't a subtle joke, a la Alice,
)> talking to the White Rabbit? not sure which, distinguishing between a
)> thing, a thing's NAME, and what the thing is CALLED.
)>
)> So the four-letter word could be NAMED "lab" yet be some other word ;-)
)>
)> More likely, I think it was in the genre of the old saw, "There are three
)> kinds of mathematicians; those that can count, and those that can't." A
)> joke.
)
)
)Nope. Your response seems to indicate you missed the joke.
)
)"four letter word" = "dirty word"
)
)The jokes says that "lab" is a dirty word.

That is the way I took it, and that is why he needed another layer of quotes.