(4:04:42 PM)
FluxDrip:
lo
(4:04:53 PM)
PrincetonGuy:
sup matt
(4:04:57 PM)
FluxDrip:
not much
(4:05:07 PM)
FluxDrip:
how's life at
Princeton?
(4:05:14 PM)
PrincetonGuy:
good
(4:05:19 PM)
PrincetonGuy:
lots and lots and lots of work
(4:05:24 PM)
PrincetonGuy:
all of it challenging
(4:05:25 PM)
PrincetonGuy:
nah
(4:05:26 PM)
PrincetonGuy:
i lie
(4:05:26 PM)
FluxDrip:
yeah. I think that's pretty much
universal
(4:05:34 PM)
PrincetonGuy:
about 2/3 challenging
(4:05:35 PM)
PrincetonGuy:
1/3 bs
(4:05:40 PM)
PrincetonGuy:
same at harvard?
(4:05:49 PM)
FluxDrip:
I don't have much bs,
unfortunately
(4:05:59 PM)
PrincetonGuy:
it's all bs really
(4:06:00 PM)
FluxDrip:
but that's probably mostly a
function of classes
(4:06:01 PM)
PrincetonGuy:
esp math
(4:06:07 PM)
PrincetonGuy:
and physics
(4:06:07 PM)
FluxDrip:
heh - what math class are you
taking?
(4:06:14 PM)
PrincetonGuy:
like analysis
(4:06:16 PM)
FluxDrip:
I don't find my physics class to
be bs
(4:06:17 PM)
PrincetonGuy:
and linear algebra
(4:06:24 PM)
PrincetonGuy:
all proofs
(4:06:26 PM)
FluxDrip:
right
(4:06:30 PM)
PrincetonGuy:
physics is mostly proofs too though
(4:06:34 PM)
PrincetonGuy:
astrophysics is PURE ps
(4:06:35 PM)
PrincetonGuy:
bs
(4:06:35 PM)
FluxDrip:
metric topology? or mostly
euclidean topology?
(4:06:47 PM)
PrincetonGuy:
math is half half
(4:06:50 PM)
PrincetonGuy:
physics is euclid
(4:06:53 PM)
PrincetonGuy:
astro is all metric
(4:06:54 PM)
FluxDrip:
well right
(4:06:58 PM)
FluxDrip:
and again
(4:06:59 PM)
FluxDrip:
right
(4:07:06 PM)
FluxDrip:
because you don't use the
euclidean metric in spacetime
(4:07:18 PM)
PrincetonGuy:
i should hope not
(4:07:21 PM)
FluxDrip:
but I doubt in astrophysics
you're doing work in arbitrary
metric spaces...
(4:07:31 PM)
PrincetonGuy:
thats' not entirely true
(4:07:44 PM)
FluxDrip:
hmm
(4:07:46 PM)
PrincetonGuy:
we spent maybe 2 weeks playing with
metrics
(4:07:54 PM)
PrincetonGuy:
from then on harder stuff assumign
metrics
(4:08:49 PM)
PrincetonGuy:
what's; ure major man?
(4:09:37 PM)
FluxDrip:
probably cs and
physics
(4:10:17 PM)
PrincetonGuy:
nice
(4:10:20 PM)
PrincetonGuy:
what about math?
(4:11:14 PM)
FluxDrip:
I took linear algebra and basic
topology last semester
(4:11:25 PM)
FluxDrip:
what kind of harder stuff did
you do in your math class?
(4:11:40 PM)
PrincetonGuy:
algebra
(4:11:50 PM)
FluxDrip:
what sorts of
algebra?
(4:12:28 PM)
PrincetonGuy:
groups
(4:12:29 PM)
PrincetonGuy:
rnigs
(4:12:36 PM)
PrincetonGuy:
sylow theorem
(4:12:42 PM)
PrincetonGuy:
euclidian rings
(4:12:52 PM)
PrincetonGuy:
just bs like that
(4:12:59 PM)
FluxDrip:
that is in fact
algebra
(4:13:06 PM)
PrincetonGuy:
yeh i think so
(4:13:27 PM)
PrincetonGuy:
doesnt' apply too much to physics
though
(4:13:32 PM)
PrincetonGuy:
though maybe later with string
theory
(4:13:42 PM)
FluxDrip:
mm
(4:13:44 PM)
FluxDrip:
Ed whitten and all
(4:13:46 PM)
PrincetonGuy:
it's more of hte approach of how to
prove i am lookin for
(4:13:48 PM)
FluxDrip:
err
(4:13:51 PM)
FluxDrip:
witten
(4:14:15 PM)
PrincetonGuy:
yeh
(4:14:20 PM)
PrincetonGuy:
analysis is good too
(4:14:53 PM)
FluxDrip:
hmm... I have a stupid math
problem I can't figure out... feel
like giving a crack at it?
(4:15:09 PM)
PrincetonGuy:
waht subject?
(4:16:45 PM)
FluxDrip:
We have to show that:
GIVEN ANY ISOTROPIC POLYTOPE IN C^N , THERE EXISTS AN ISOTROPIC SUBSET OF THE P-adics OF MEASURE 0 WITH RESPECT TO THAT POLYTOPE
GIVEN ANY ISOTROPIC POLYTOPE IN C^N , THERE EXISTS AN ISOTROPIC SUBSET OF THE P-adics OF MEASURE 0 WITH RESPECT TO THAT POLYTOPE
(4:17:36 PM)
PrincetonGuy:
never heard the word polytope
(4:17:38 PM)
PrincetonGuy:
what does it mean?
(4:18:42 PM)
FluxDrip:
A regular polytope is a
generalization of the Platonic solids to
an arbitrary dimension.
(4:19:59 PM)
PrincetonGuy:
i can't think of any easy way to
prove it
(4:20:30 PM)
PrincetonGuy:
but prolly induction
(4:20:31 PM)
FluxDrip:
they give a hint
(4:21:12 PM)
FluxDrip:
they suggest starting with some
complex manifold locally
resembling C^2
(4:23:34 PM)
PrincetonGuy:
i would stil use induction though
(4:25:21 PM)
FluxDrip:
I dunno. I think the professor
may have messed up
somewhere. It doesn't seem logical
(4:25:37 PM)
FluxDrip:
How can something be of measure
0 with respect to a
polytope?
(4:25:54 PM)
PrincetonGuy:
because it's a subset of that field?
(4:26:09 PM)
FluxDrip:
I'm not exactly sure what is
meant by measure 0 then...
(4:26:30 PM)
PrincetonGuy:
yeh neither am i
(4:26:39 PM)
PrincetonGuy:
i think onceu that is defiend it should
be easy to show induction
(4:26:47 PM)
FluxDrip:
some analysis class you're
in...
(4:27:07 PM)
PrincetonGuy:
yah
(4:28:26 PM)
PrincetonGuy:
we never used these measures in
describing riemann
(4:28:33 PM)
FluxDrip:
the mathematician?
(4:29:17 PM)
PrincetonGuy:
anh the sums
(4:29:38 PM)
FluxDrip:
hmm...I think the concept of
measure is fairly essential to
topology on an arbitrary metric
(4:30:00 PM)
PrincetonGuy:
true
(4:30:37 PM)
PrincetonGuy:
a finite # of points has 0 measure
(4:30:47 PM)
PrincetonGuy:
i mean a set of suck
(4:30:48 PM)
PrincetonGuy:
such
(4:31:11 PM)
PrincetonGuy:
and prolly also if u can arrange them
in a sequence the measure will be 0
(4:31:11 PM)
FluxDrip:
right but a polytope is not
finite
(4:31:16 PM)
PrincetonGuy:
even if it's finite
(4:31:18 PM)
PrincetonGuy:
infintie
(4:31:24 PM)
PrincetonGuy:
yeh i think that's true
(4:31:26 PM)
FluxDrip:
hmm
(4:31:27 PM)
FluxDrip:
damn
(4:31:39 PM)
FluxDrip:
induction is bound to fail on
measure 0 subsets of the P-adics
though
(4:31:47 PM)
FluxDrip:
by the continuum
hypothesis
(4:32:30 PM)
PrincetonGuy:
but all the parts which make up the
subset are of measure of 0
(4:33:14 PM)
FluxDrip:
what do you mean?
(4:33:37 PM)
FluxDrip:
(then there wouldn't be a
polytope...)
(4:33:40 PM)
PrincetonGuy:
if u can show one of the lower
subsets has a measure 0
(4:33:51 PM)
PrincetonGuy:
then all the subsets should have the
same measure
(4:34:02 PM)
FluxDrip:
but...we need to show there's a
polytope
(4:34:04 PM)
PrincetonGuy:
as u can't make up something of
measure 0 from anyting else
(4:34:06 PM)
FluxDrip:
and not that they have measure
0
(4:34:09 PM)
FluxDrip:
what paving are you
using?
(4:34:19 PM)
PrincetonGuy:
i am making it up
(4:34:28 PM)
FluxDrip:
huh?
(4:34:35 PM)
PrincetonGuy:
we dind't see polytopes in analysis
(4:34:44 PM)
FluxDrip:
it's a shape
(4:34:44 PM)
PrincetonGuy:
but ure right we did see measure
(4:34:49 PM)
FluxDrip:
a square? a
rectangle?
(4:34:55 PM)
FluxDrip:
how about a rectangular
prism.
(4:34:58 PM)
FluxDrip:
cept
(4:35:00 PM)
PrincetonGuy:
in what space?
(4:35:04 PM)
FluxDrip:
generalized into the set of the
complex numbers...
(4:35:11 PM)
FluxDrip:
here
(4:35:14 PM)
FluxDrip:
try this
(4:35:25 PM)
FluxDrip:
given a square of non-zero area
in R^2, how can we pave it
with subsets of measure 0?
(4:35:31 PM)
FluxDrip:
i think if I can do that I can
get the rest of the waay
(4:35:33 PM)
FluxDrip:
way, even
(4:37:46 PM)
PrincetonGuy:
i remeber some thm like
(4:38:02 PM)
PrincetonGuy:
if A is compact and has 0 measure ->
A has content 0
(4:38:15 PM)
FluxDrip:
which imples?
(4:38:16 PM)
FluxDrip:
err
(4:38:18 PM)
FluxDrip:
implies?
(4:38:58 PM)
PrincetonGuy:
nothign really cuz it doesn't go
backwards
(4:39:25 PM)
PrincetonGuy:
the subsets of this square must 0
measure?
(4:39:35 PM)
PrincetonGuy:
and the square must have non-zero
measure?
(4:39:39 PM)
FluxDrip:
no, the paving must be made up
off subsets of measure 0
(4:39:45 PM)
FluxDrip:
and the square has non-zero
area
(4:40:35 PM)
PrincetonGuy:
could it be a question of countability
and how many subunits u need?
(4:42:21 PM)
FluxDrip:
hmm...not really. if you needed
uncountably many subunits
then it would be a somewhat trivial paving, no?
(4:42:36 PM)
PrincetonGuy:
0 measure is pretty trivial
(4:42:56 PM)
PrincetonGuy:
or at least can easily be so if u wish
(4:43:31 PM)
FluxDrip:
hmm...it seems like if it's
trivial the answer should be
self-evident
(4:44:24 PM)
PrincetonGuy:
and it easily could be so with this kidn
of definitin
(4:44:39 PM)
FluxDrip:
sorry what?
(4:44:54 PM)
FluxDrip:
so...what is it?
(4:46:06 PM)
PrincetonGuy:
with uncountable 0 measures it would
be possible to construct an area
(4:46:43 PM)
FluxDrip:
by definition, a set is not of
measure 0 if it can only be paved
with uncountably many subsets...
(4:46:57 PM)
PrincetonGuy:
aiite
(4:47:08 PM)
PrincetonGuy:
then i dun see an easy way to do this
(4:47:50 PM)
PrincetonGuy:
aiite
(4:47:56 PM)
PrincetonGuy:
i am gonna go do some nuymber
thoery
(4:47:58 PM)
FluxDrip:
oh!
(4:48:03 PM)
FluxDrip:
I just got it!
(4:48:05 PM)
PrincetonGuy:
good man
(4:48:07 PM)
PrincetonGuy:
good job
(4:48:46 PM)
FluxDrip:
it's almost trivial - construct
it directly from a basis of the
P-adics
(4:49:03 PM)
PrincetonGuy:
ah true
(4:49:18 PM)
FluxDrip:
how silly we were...
(4:49:34 PM)
PrincetonGuy:
haah
(4:49:35 PM)
PrincetonGuy:
sure
(4:49:43 PM)
PrincetonGuy:
u have break yet?
(4:49:56 PM)
FluxDrip:
not next week but the week
after
(4:50:21 PM)
PrincetonGuy:
nice
(4:50:23 PM)
PrincetonGuy:
mine starts tomororw
note: this is a real IM conversation, and an excellent illustration of a possible application of the Theorem of the Day. "PrincetonGuy" is a replacement screenname, put in place to reduce someone's risk of burning ears.