HDTenEightyP/NetNews huggingface dataset:
From: pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt)
Subject: Re: Report on Philosophies of Physicists
Organization: Computer Science Department,  Stanford University.
Date: Mon, 14 Sep 1992 07:32:24 GMT

In article <TORKEL.92Sep14074902@bast.sics.se> torkel@sics.se (Torkel Franzen) writes:
>   >Meanwhile, now my answer is much much easier than with #.  I have no
>   >reason to suppose that the satisfiability of a random Diophantine
>   >equation is independent of ZFC, so I'm certainly not going to waste my
>   >time doing mathematics under the assumption that it is satisfiable.
>
>  I was insufficiently explicit. I was presupposing the fact that by the
>theorem of Matiyasevic et al, "ZFC is inconsistent" is equivalent in ZFC
>to a statement (not too horribly complex, I believe) of the form "the
>Diophantine equation ... has a solution".

Unfortunately it's now harder than the # we had before.  To do this you
still have to Goedel code "ZFC is inconsistent", except now with one
hand tied behind your back since you've now required # to be a single
existentially quantified polynomial.  Your previous challenge was
identical to this, only minus that restriction.  With the restriction
things don't get any shorter, although mercifully they only get larger
by some constant, maybe 100, I don't know, I'm not too experienced at
coding proof generators as polynomial equations.

So with or without the Diophantine restriction, which is a purely
syntactic restriction with no semantic significance, your question
remains the same: what does it mean for ZFC+# to be a foundation for
mathematics?  I've already done the best I could to answer this to your
satisfaction, sorry we didn't make more progress.

-- 
======================================================| God found the positive
Vaughan Pratt   pratt@cs.Stanford.EDU   415-494-2545  | integers, zero was
======================================================| there when He arrived.
From: jac@ds8.scri.fsu.edu (Jim Carr)
Newsgroups: sci.physics
Subject: Re: Lebesgue integral (was: Couple of questions
Date: 14 Sep 92 15:17:25 GMT
Reply-To: jac@ds8.scri.fsu.edu (Jim Carr)
Organization: SCRI, Florida State University

In article <92257.165003MRG3@psuvm.psu.edu> MRG3@psuvm.psu.edu writes:
>Jim Carr writes

 [ regarding the value of Lebesgue measure theory to physics students ]

>>Theoretical students should definitely have a grounding in more than the
>>usual advanced calc and complex variables courses.  Or is the problem
>>that Lebesgue measure theory is not taught in the advanced calc courses
>>taken by many undergrad physics majors?
>
>As an undergrad, my real analysis course seemed basic nuts and bolts epsilon
>delta approach to calculus.  (i.e. BORING)  I don't remember any there being
>any significant reference to topology or measure theory.  I get the impression

I was fortunate to be a math major as an undergrad and took a special 
honors course in real analysis that started right in with topological 
methods (we sophomores felt like we had just jumped off a cliff!) and 
went on from there.  Never took the standard advanced calc class, but it 
must surely be as you describe and thus does not meet the needs of a 
future theory Ph.D.  The problem is that there is little room in the 
curriculum for any electives, let alone another course in math, so 
unless the existing courses change one is left with dropping in on a 
grad course later on in your career. 

>that most undergrad complex variables courses are straight out
>of Churchill, with emphasis on evaluating nasty integrals with
>elegant selection of contours.  As a grad student, however, I sat in on
>the math grad sequence in analysis (real+complex, functional). I found the
>material fascinating and relevant.  So why limit the young physicist to only
>Legese measure theory?  After all, are the only spaces of interest in Physics
> R:n?

I would encourage any theory grad student to do the same.  The trouble is, 
you would like someone to do this before advanced quantum, but usually one 
does not have the free time until after comps in the 2nd year -- which is 
a bit too late.  Along the same lines, a good grounding in finite groups 
would not hurt either, although the courses in a math department leave 
something to be desired from a physicist's viewpoint. 

--
J. A. Carr                                    |  "The New Frontier of which I  
jac@gw.scri.fsu.edu                           |  speak is not a set of promises
Florida State University  B-186               |  -- it is a set of challenges."
Supercomputer Computations Research Institute |   John F. Kennedy (15 July 60)
Newsgroups: sci.physics
Subject: Re: It's Down to the Last Blank Check
From: mcirvin@husc8.harvard.edu (Mcirvin)
Date: 10 Sep 92 15:36:18 GMT
Distribution: na

jbaez@riesz.mit.edu (John C. Baez) writes:


> I sort of agree, sort
>of disagree, etc. etc. etc..  I just wanted to pass this one
>on without endorsing this fellow's opinions.  Since he's in power his
>opinions matter.

Some parts of the letter seemed odd to me.  It seems like between the lines 
what he's proposing is essentially the cessation of most scientific
research, and the establishment of some means of requiring that proposed
research explicitly work toward his stated goals for humanity.  If
this is the "new contract" he advocates (it's hard to tell), it would be
utterly stifling.  Physics, for one, would be essentially over.  It's
absoutely true, as he says, that science as currently practiced doesn't
happen in a moral or political vacuum; that doesn't mean that it would
continue to thrive if the ability to do research for the sake of acquiring
knowledge were taken away.

I also found interesting the statement about scientists' desire to
maintain their elevated status in society.  I'm not sure what that means.
Do scientists have an "elevated place" as opposed to anyone else?  They 
certainly aren't the richest or most adored class of people, and they're
far from the most powerful.  People sometimes hold them in a kind of
superstitious awe for knowing secret things, but I don't think many
scientists find that particularly desirable.  It may just be that I
wasn't around in the period during World War II and shortly thereafter,
when physicists were seen as the miracle workers who helped win the war and
opened Pandora's box. 

-- 
Matt McIrvin, Cambridge, Massachusetts, USA
From: terry@aslws01.asl.dl.nec.com (Terry Bollinger)
Newsgroups: sci.physics
Subject: Re: Did electric/magnetic symmetry "break"?
Date: 9 Sep 92 21:28:56 GMT
Organization: NEC America, Inc. Irving, Texas

Oopsy time:

In article <1992Sep9.204019.17182@asl.dl.nec.com>
terry@aslws01.asl.dl.nec.com (Terry Bollinger) writes:

> The monopole equivalent of a hydrogen atom (it cannot exist, of course)
> would need to be 68.5 times smaller than a regular hydrogen atom ... 
> (If you do not understand why, please think on it a bit before responding.)

Hmm, maybe *MOI* had better think on such things better before RESPONDING!
It's not a factor of 68.5 shrinking, probably more like 68.5^2.  Anyone?

And by the way, I keep quoting this 68.5 figure, but still haven't looked
it up -- this IS the same as the proposed charge of a monopole in particle
physics, isn't it?  I seem to recall that one or two supposed monopole
findings turned out to be ordinary nuclei with charges roughly in that
charge range.  (The effects of either electric or magnetic charge passing
though an emulsion is supposed to be quite similar, as best I can recall.)


				Cheers,
				Terry Bollinger
Newsgroups: sci.physics
From: jbaez@riesz.mit.edu (John C. Baez)
Subject: Re: Mass renormalization.
Organization: MIT Department of Mathematics, Cambridge, MA
Date: Mon, 14 Sep 92 20:08:22 GMT

johan@blade.stack.urc.tue.nl (Johan Wevers) writes:
>>jbaez@riesz.mit.edu (John C. Baez) writes:

>>>m(r)=m_0 + e^2/r - Gm^2(r)/r

>>>Because in the third term on the right-hand side we have m(r) instead
>>>of m_0 , we receive in the limit r->0: m(r)= e/\sqrt{G}. Finite.

>>Typical renormalization theory arguments ignore general relativity (and
>>indeed, gravity altogether)...

>Maybe the equation above is an indication that quantum gravity will solve
>the problem of renormalization.

Yes, that is the best way of putting it: not that QG has solved the
problem of renormalization, but that it might.

>(though all QG theories offered yet are not renormalizable........).

Not quite true.  All traditional attempts to quantize gravity
perturbatively like other field suffered from nonrenormalizability. 
However, string theory, which claims to treat quantum gravity and all
other forces and particles (including lots that probably don't exist
:-)), is supposed to be renormalizable and perhaps even finite.  Here
I am talking about it's usual perturbative formulation... people are
seeking a nonperturbative formulation.  Also, the loop variables
approach to quantum gravity is nonperturbative and so the problem of
renormalization doesn't even come up!  (That's one reason why I like
it.)  Of course, the loop variables approach is still in its infancy
and there are lots of other things that might go wrong.

>Sorry, my physics skills are much beter than my language skills. And I'm
>not a native speaker (as you all might have observed from my postings and
>my email adress).

Actually I hadn't noticed, for some silly reason.  If you want to fit in as an 
American native speaker, don't bother improving your spelling and
grammar.  I have been mistaken for a European, in fact.


.

Xref: sparky sci.physics:14653 sci.math:11442
From: gjm11@cus.cam.ac.uk (G.J. McCaughan)
Newsgroups: sci.physics,sci.math
Subject: Re: Probability Question
Date: 14 Sep 92 23:23:48 GMT
Organization: U of Cambridge, England

In article <1992Sep14.212528.29098@uwm.edu>, gunter@csd4.csd.uwm.edu (David O Gunter) writes:
> A particle is equally likely to be found anywhere on the circumference of a
> circle.  Choose some line which passes through the center of the circle to be
> a reference axis.  Then the line joining the center of the circle to the 
> particle will make some angle, theta, with respect to this axis.
> 
> Question:  What is the probability that the angle will lie between theta
> and theta + dtheta (dtheta is some increment amount.)
> 
> Here are two ways I've tried to tackle the problem:
> 
>   First, the total range of theta is 2*Pi, so that the probability should be
> proportional to dtheta/(2*pi).  But there are 4 positions around the circle
> at which the particle will be at some angle theta w/respect to the axis.  So
> it appears that the probability should be
> 
>                             2 dtheta
>                        P =  ---------
>                                Pi
> 
>   However, if I think of the problem in another way, I get a different
> answer:
>   Imagine that we are dealing with only one quarter of the circle.  Now
> there is a range of Pi/2 for the theta values, and there is only one
> position at which the particle makes an angle theta w/respect to the axis
> (one of the sides of the 'pie slice'.)  So the prob. for this piece is
> 2*theta/Pi.  But since there are 4-quarters, the total prob. is
> 
>                                 8 dtheta
>                           P =  -----------
>                                   Pi
> 
> Which, if any, of these two methods gives the correct answer?  Or what is
> the correct answer?

The first.

There are 4 quarters, as you say; and the probability that the point is in
each of them is 1/4. So you multiply 2.dtheta/pi by 4x1/4 = 1.

>                         |"How arrives it joy lies slain, and why unbloomed the
> david gunter            | the greatest hope ever sown . . ." 
> gunter@csd4.csd.uwm.edu |           -Thomas Hardy
> gunter@mcs.anl.gov      |               "Hap"                            

Are there meant to be two "the"s there? I'm sure Hardy didn't write them both
(though I've never read that particular poem).

-- 
Gareth McCaughan     Dept. of Pure Mathematics & Mathematical Statistics,
gjm11@cus.cam.ac.uk  Cambridge University, England.    [Research student]
From: mcirvin@husc8.harvard.edu (Mcirvin)
Newsgroups: sci.physics
Subject: Re: Quantitized Length
Date: 7 Sep 92 03:19:37 GMT

cannon@scs.unt.edu (Dustin Cannon (Lab 3460)) writes:

>	I have a question.  I was thinking about the problem of the man 
>walking across a bridge, but he first walks half the distance and then can 
>only walk half the remaining distance and so on.  He never gets to the end, 
>right?

This is one of Zeno's paradoxes of motion.  As another poster correctly
pointed out, it evaporates when you think correctly about summing series.
But Zeno was concerned with exactly the sorts of issues you are describing.
 
>	Well, I was thinking that if length was quantitized just like 
>charge.  Then the man would get to a point were he simply could no longer 
>walk half the distance because he would be halving a quanta of length.

In other words, put the universe on a lattice. 

>	I liked this because it also solves a rather disturbing idea one of 
>my professors once said, which was that as two point charges come in contact 
>with each other they have infinte potential energy due to 1/r. 

This is closely related to problems involving infinities in quantum
field theory, and one rather brute-force way to get rid of the infinities
when deriving results is exactly what you have proposed: make spacetime
into a discrete lattice.  It is quite possible that spacetime is something
other than a continuum on very short scales; it probably (IMHO) isn't
a lattice, but when doing calculations you often need some kind of short-
distance cutoff for physics to get rid of these infinities, and many
theories are insensitive to what kind of cutoff you use.  Therefore
some calculations in quantum field theory, especially computer
studies of quarks and gluons, put the universe on a fictitious lattice. 
 
> This, he 
>said, was in his mind a proof of God's exsistence.

That's bizarre.  Renormalization theology?  I much prefer your approach.  

>	I have asked several of my professors about quantitized length, but 
>they seem to dodge the question.  One however did tell me that quantum 
>mechanics is couched in the idea of a countinous space-time and that this 
>seems to be a good approximation, so why make the problem harder by throwing 
>in quantitization of length.

Because, sometimes, it makes the problem easier-- and for pretty much
the reason you've given.  Making spacetime discrete is one way of
getting rid of the infinities that plague theories with point particles.
 
-- 
Matt McIrvin, Cambridge, Massachusetts, USA 
Newsgroups: sci.physics
From: owens@hilbert.wharton.upenn.edu (Susan Owens)
Newsgroups: sci.physics
Subject: Question about falling elevator...
Date: 11 Sep 92 03:25:06 GMT
Organization: University of Pennsylvania

Hi,

  I have a question that I thought maybe someone here could answer.  It
concerns a falling elevator.  If I was in an elevator that was falling
say 20 stories what would happen if I jumped right before I hit the
ground.  I say that I wouldn't be able to jump because of the force
being exerted against me, some collegues here say that I  would be able
to jump but that I would not affect the force with which I hit the ground with
to any degree to be worth mentioning.  I agree with that but I still say
that I would not be able to jump. 

 And if I am right I am sure that there is a less distance that I  
could fall that I would be able to jump right before I hit the ground
(I would say roughly around 4 stories).  Does anyone know the aprox.
height at which an avarage person would be able to jump before hitting
the ground. Or maybe I am totally wrong (wouldn't be the first time) 

thanks for any responses,

susan
owens@hilbert.wharton.upenn.edu



Newsgroups: sci.physics
From: palmer@sfu.ca (Leigh Palmer)
Subject: Re: How old is the universe?
Organization: Simon Fraser University
Date: Tue, 15 Sep 1992 21:49:47 GMT

In article <Sep.15.15.57.43.1992.13699@ruhets.rutgers.edu>
bweiner@ruhets.rutgers.edu (Benjamin Weiner) writes:

>...
>the "open vs. closed" issue which used to dominate popular accounts
>of cosmology is, for the moment, a non-issue.

I'm afraid that statement misrepresents the responsible scientific
view that there is still a missing mass problem in observational
astronomy. The view that the problem is not there assumes that the
currently popular theoretical construct (which is principally 
supported by the observation that there is a question, since omega 
is so nearly unity by observation!) is true. In using the word
"true" I intend to entrain all the philosophical baggage which is
implicit in the word. A belief on the part of some theorists that
the missing mass problem was solved by a theory cannot be be held
by all.

Leigh
Newsgroups: sci.physics
From: jfreter@triton.unm.edu (The Myth)
Subject: Re: Quantitized Length
Date: Mon, 07 Sep 92 03:26:57 GMT
Organization: University of New Mexico, Albuquerque

In article <cannon.7.715829635@scs.unt.edu> cannon@scs.unt.edu (Dustin Cannon (Lab 3460)) writes:
>	I liked this because it also solves a rather disturbing idea one of 
>my professors once said, which was that as two point charges come in contact 
>with each other they have infinte potential energy due to 1/r.  This, he 
>said, was in his mind a proof of God's exsistence.

This would be true if the only force acting on any charge were the Coulombic
repulsoion (or attraction) between the charges.  But, there are other phenoma
at work.  For two electrons approaching each other, there is a certain dist-
ance at which the Pauli exclusion principle will keep the electrons from
getting closer.  This is the same "force" at work inside of White dwarf stars.
The exclusion principle states that no two electrons can share the exact same
quantum state (which includes position).  So it is impossible to get the 
'trons closer to each other without other effects.

Fora proton and a nucleus, the strong nucleart force will attract the proton
when it gets within about one nuclear radii.  Between two protons, the
situation is the same as for two electrons, and rarely one proton will either
beta + decay or electron capture into a neutron (I'mm too tired to do the
calculations).

For an electron and a proton (or nucleus), the electron will become captured
and form an atom (or less positively ioninzed ion) or will get captured into
the nucleus to form a neutron from a proton.

So, in any of these cases, there is no need to invoke the devine.  Simple
nuclear theory will suffice.  I might not be 100% correct on this post,
but I would get partial credit for this answer on a test (as opposed to the 
person who invoked a god and would get zero points).



Newsgroups: sci.physics
From: prim!dave@germany.eu.net (Dave Griffiths)
Subject: Re: Is Spacetime Absolute?
Organization: Primitive Software Ltd.
Date: Mon, 7 Sep 1992 16:45:32 GMT

In article <mcirvin.715799578@husc8> mcirvin@husc8.harvard.edu (Mcirvin) writes:
>prim!dave@germany.eu.net (Dave Griffiths) writes:
>
>>Just to muddy the waters, here is a quote from Einstein's Relativity:
>
>>"There is no such thing as an empty space, i.e. a space without field.
>>Space-time does not claim existence on its own, but only as a structural
>>quality of the [gravitional] field."
>
>Hmmm... that's an interesting way of thinking about it. 
>If you define "gravitational field" in the right way, I suppose it
>can be thought of as true; if you call the metric the gravitational 
>field (in which case it exists even in situations where we'd normally 
>say there's "no gravity,") it exists everywhere that there is spacetime,
>and (with the exception of statements about boundary conditions) the
>only way the properties of spacetime enter into physics is through the
>metric, at least in torsion-free general relativity. 
>
>In *quantum* field theory, it's absolutely true that there's no space
>without a field, but I don't think that's what Einstein was talking about.
>
>I prefer a point of view in which "space-time" and "field" are 
>interchanged in the second sentence, personally. 
>

Perhaps the expansion of the Universe demonstrates that there is no such
thing as empty space. To take an analogy with the big-bang, if you imagine
a man holding a football as being the entire universe, then presumably
there is _no_ space outside them. If the man now decides to kick the
football away, then whoosh! space is automatically created and exists only
as the gap between them (ie the galaxies aren't rushing apart because
space is expanding, but vice-versa). Now presumably there is a gravitational
field between the man and the football - how does the field travelling
from the man to the football "know" it has to stop when it reaches the
end of space? Why shouldn't the gravitational field, travelling at the speed
of light, _create_ space as it goes along?

Another way of phrasing this question: if after the big-bang, particles
_hadn't_ been rushing away from each other but had been stationary, would
the universe/space still have expanded due to the gravitational field being
transmitted?

Dave Griffiths
Newsgroups: sci.physics
From: aduncan@rhea.trl.OZ.AU (Allan Duncan)
Subject: Re: Question about falling elevator...
Organization: Telecom Research Labs, Melbourne, Australia
Date: Mon, 14 Sep 1992 00:57:18 GMT

From article <12SEP199208273790@rover.uchicago.edu>, by frank@rover.uchicago.edu (Frank - Hardware Hacker - Borger):
> In article <1992Sep11.212549.645@CSD-NewsHost.Stanford.EDU>, pratt@Sunburn.Stanford.EDU (Vaughan R. Pratt) writes...

>>This leaves the question of how to press your head against the floor
>>while in free fall.  With luck the fall won't be completely free.
> 
> 	Actually, elevator mechanisms have braking mechanisms that do just
> 	this, limit falling speed, independant of any cable, etc.
> 
> 	So, in the event that the very unlikely does occur, and you end up
> 	in an elevator dropping at HIGH SPEED, but not in FREE FALL, the
> 	best thing to do would be to lay down flat on your back.

In this country the lift will stop dead.  There are brakes that grip the
side rails that are held off by gravity.  If the lift drops suddenly,
these active and jamb the slides _before_ the link has gained so much
kinetic energy that it is unstoppable.

I suspect that this is universal.

Allan Duncan	ACSnet	 a.duncan@trl.oz
(+613) 253 6708	Internet a.duncan@trl.oz.au
		UUCP	 {uunet,hplabs,ukc}!munnari!trl.oz.au!a.duncan
Telecom Research Labs, PO Box 249, Clayton, Victoria, 3168, Australia.
Newsgroups: sci.physics