mm-194
Or you could tell us what causes v to rotate in the 'rst
place.>>There's nothing that >causes> v to rotate. v is a
vector - a >mathematical>>entity that has direction and
magnitude. That's all. It's not a 
material>>thing, so the
notion of causation is utterly irrelevant.>>This is such an
appalling expression of pre scienti'c ignorance 
and>mysticism,
it leaves me completely speechless. If it were only true.
 > Kind of related, but I wonder if anybody has ever
attempted to *model* > the universe through time by:> > 1) let
U = {(x,y,z,t,p)}, where x,y,z,t,p are reals, and (x,y,z) are
> points in 3-dimension Euclidean space for a given t,> and p
is just the >property> of the corresponding (x,y,z,t)> 2)
axiomatize x,y,z,t,p in a >meaningful> way, if not close to a
> famliliar physics model, say Newton physics.> > ?Ever heard
of >General Relativity>? Einstein used certain symmetries in
nature as axioms for hisaxiomatization. You know, like the
invariance of the speed of light,symmetry of acceleration and
gravitation, etc. He then proceeded topredict physical laws on
the basis of his axioms. (To be historicallyaccurate, he
formulated the Special Theory 'rst. But even then,
heapproached the problem axiomatically. For instance, he
deduced thatthe speed of light must be constant in every frame
of reference, aprediction which was later veri'ed
experimentally.)The tricky part was coming up with a function
(which you call p) whichcaptures the meaning of the
symmetries. It turns out to be, roughly,the curvature at the
point (x, y, z, t)Alex SollaJuniorReed College
=I want to
sum following in'nite series to obtain a closed form
expression. sum { ( x ^ ( 2 ^ 2n ) ) * 2^n } , n=-in'nity to
,Sanjeevsanjeev_bgp@yahoo.com
=Anyone know latent variable
willing to take on a data analysis assignment
>(paid)?
=> >> >I'm using the fact that H(n) is
noncomputable ...>> That *fact* is wrong. H(n) *is* computable
(for every n). H(n) is >simply> an integer; in fact, quite
restricted: a member of {0, 1}. But H (the> function) is NOT
computable.>> Daryl said it well:he certainly did, that is a
direct quote of his you just rebuked :DHerc
=> >I'm using
the fact that H(n) is noncomputable to prove that H(555)
>cannot> >be equal to 1 *and* that H(555) cannot be equal to
0.>> Well, that doesn't make any sense. The fact that H is a
noncomputable> function doesn't imply that H(555) is
noncomputable.But H(555) can be noncomputable, the analysis is
perfectly valid usingthat assumption, and there certainly exist
n where H(n) is non computable.Which makes pi/4 a contender for
r since you used the same proof technique.Interesting related
thread on using modus ponens deduction with non
>decidablepropositions, in the subject >how to prove a true
but meaningless >theorem>.> The same proof goes through for
every computable real.> No computable real can be equal to
r.Nice work, but I suggest its a convention that well de'ned
programs >terminate,and applying that to map to reals suggests
this is oversimpli'ed, obviously >forsome reals the TM could 
be
considered valid and would necessarily not >terminate,so unless
conventional de'nitions are modi'ed TMs are 
stuck in a cyclic
>de'nitionsince terminating programs will fall short trying 
to
generate non >terminating results.Herc
=>>... more
interesting by requiring distinct values? >> Even that harder
version may be tractable, by using >> some appropriate
perturbation of {1,2,...,n}.>>Do you have examples already?
Sure do:2: 1 23: 1 2 44: 1 2 4 65: 1 2 3 6 76: 1 2 3 4 6 77: 1
2 3 4 6 7 88: 1 2 3 4 6 7 8 109: 1 2 3 4 5 6 7 9 1010: 1 2 3 4
6 7 8 9 10 1111: 1 2 3 4 5 6 7 8 9 10 1212: 1 2 3 4 5 6 7 8 9
10 11 1313: 1 3 4 5 6 7 8 9 10 11 12 13 1414: 1 2 3 4 5 6 7 8
9 10 11 12 14 1515: 2 3 4 5 6 7 8 9 10 11 12 13 14 16 1716: 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 1717: 1 2 3 4 5 6 7 8 9 10
11 12 13 15 16 17 1818: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
18 1919: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 2020: 1 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 2121: 1 2 3 4 5 6 7
8 9 10 11 12 13 14 15 16 17 18 19 21 2222: 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 20 21 22 2323: 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 2424: 1 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 19 20 21 22 23 24 25My program starts to get
slow after this point, but hey at least we havea 24 now :).
Notice that every one of these cases is just a subset
of{1,...,n+2}, but I think to prove this is always true would
requiresomething as strong as Riemann Hypothesis since it
implies a prime gapof order sqrt(p).Here are the results
(again minimum largest element) allowing multisets:2: 1 13: 1
1 14: 1 2 2 25: 1 1 1 2 26: 1 1 2 2 3 47: 1 1 1 2 2 3 38: 1 1
1 2 2 2 2 29: 1 1 1 1 1 2 2 2 210: 1 1 1 2 2 2 2 2 3 311: 1 1
1 2 2 2 2 2 2 2 212: 1 1 1 1 1 2 2 2 2 2 2 213: 1 1 1 1 1 1 1
2 2 2 2 2 214: 1 1 1 1 1 1 1 1 1 2 2 2 2 215: 1 1 1 1 1 1 1 1
1 1 1 2 2 2 216: 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 317: 1 1 1 1 1
1 2 2 2 2 2 2 2 2 3 3 318: 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3
319: 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 320: 1 1 1 1 1 1 1 1
1 1 1 1 2 2 2 2 2 3 3 321: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2
3 3 322: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 3 3 323: 1 1 1 1
1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3This is just from a few
minutes' worth of computation. I can leave itrunning
overnight, and see how far it gets, but my algorithm scales
verypoorly, since it blindly looks at all 2^n subsets.>It is
an interesting question too, I agree.>But the original
question ist still funny enough,>because I don't see a
generating rule in these>multimultimulti-sets, which you found
and which>Robert's posting shows.You're right, 
my idea of only
using 1's and 2's isn't 
workable since itrelies on having
arbitrarily large twin primes. So I agree the originalone is
still quite interesting. -- Erick
=>>Have you got any
paradoxes to share? Write them here!>(1) How many kinds of
in'nity are there? An in'nite number? If so, 
>whatkind of
in'nity? (2) In the town of Placerville (CA) the barber 
shaves
everyone who doesn'tshave himself. Who shaves the 
barber?Rich
Burge