Subject: Re: Hermeneutics and the difficulty to count to three...
From: meron@cars3.uchicago.edu
Date: Wed, 30 Oct 1996 20:34:23 GMT
]In article <557tlm$2hm@panix2.panix.com>, +@+.+ (G*rd*n) writes:
>patrick@gryphon.psych.ox.ac.uk (Patrick Juola) writes:
>| >Faith in Science is not necessary.
>| >Science works whether you believe it or not.
>
>pieterh@sci.kun.nl (Peter den Haan):
>| This statement is already based on an article of faith: the validity of
>| induction. Of course, in science, we call it an 'axiom' because we don't
>| like to borrow religious idiom.
>
>This really isn't the same as religious faith; it could be
>tentative and operational. The only faith science needs is
>the belief that phenomena can be modeled, usually as some
>kind of text, and this is the kind of faith that can be
>checked out regularly.
Yep, definitely.
> The religious stuff comes in when
>people become excited because someone talks about Newton in
>the wrong way,
I think that I've mentioned more then once (or twice, or thrice) that
we're not talking about Newton but about classical mechanics, using
"Newton" just to refer to it. Classical mechanics, as any other
physical theory, stands on its merits regardless to any personalities
involved. You can take a text of classical mechanics, delete all the
names from it and you didn't change the meaning a single bit. Same as
Euclidean geometry won't change if you delete the word "Euclid".
Perxonally I consider the realization that in science theories are
completely separated from theis originators, to be essential for any
meaningful discussion of the subject.
>or says that improper rhetoric will "KILL."
I agree, maintaining cicility is important. Lets not forget, though,
that irrational attitudes may at time be dangerous. Still, one should
combat them by becoming irrational.
>As I've pointed out before, too, the violent, obscene
>language used against supposed infidels is reminiscent of
>religious passion.
Sometimes. And sometimes it is just the result of being annoyed.
Important to recognize it, elase you may read religious passion into
the situation of two taxi drivers arguing over right of way (believe
me, the language can get quite violent and obscene in such case).
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Subject: Re: Do gravitational waves carry momentum? was: Does gravitational waves carry momentum
From: abostick@netcom.com (Alan Bostick)
Date: Wed, 30 Oct 1996 20:21:12 GMT
kfischer@iglou.com (Ken Fischer) writes:
>magnus.lidgren (magnus.lidgren@swipnet.se) wrote:
>: ( I should attend a course i grammar)
>: I wonder.....
>:
>: 1. Do gravity waves carry momentum?
> The gravity waves that LIGO and other experiments are
>trying to detect are not the carriers of gravity (they are not
>the mechanism by which gravity works).
BZZZZT! Thank you for playing.
The gravitational radiation that LIGO and other experiments are trying
to detect are freely propagating waves in the gravitational field, i.e.
the curvature of spacetime.
No theory of gravity has been successfully quantized. But it is exceedingly
likely that in a successful quantum theory of gravity, the fundamental
quantum of the gravitational field (i.e. the curvature of spacetime)
would be a quantized gravitational wave -- a graviton -- just as the
fundamental quantum of the electromagnetic field is a quantized
electromagnetic wave, aka a photon.
So if quantum gravity ever lives up to our current expectations,
gravitational radiation *is* the mechanism by which gravity works in
just the same way that photons are the mechanism that electromagnetism
works, even in electrostatic systems.
> No repeatable experiments have detected gravity waves.
>The gravity waves they are trying to detect are secondary
>vibrations in spacetime from massive collisions of distant
>galaxies or stars, or any lopsided explosion that would
>cause a lot of mass to move violently.
> The laboratory experiment that would cause these
>"waves" (which some people feel general relativity presicts)
>is a heavy bar spinning perpendicular to it's axis.
> But the amplitude of these "waves" would be so small
>that it is a very difficult experiment to make, that is why
>the distant catastrophic events are the focus of the current
>experiments.
> Hopefully in the near future there will be news
>releases of the progress.
>
>: 2. Do gravity waves slow down when prapagating mass? If so, it is
>: according to something similar to index of refraction.
> Since no gravity waves have been detected, study
>is needed to determine any facts.
The gravitational index of refraction of a matter field (e.g. a dust cloud)
ought to be calculable, in the same way that the index of refraction
of a dielectric material can be calculated. Here is a handwaving sketch
of how to carry out the calculation:
Start with a plane gravitational wave incident on a layer of dust. The
wave propagates in the z-axis direction and has +-polarization (i.e.
aligned with the x- and y-axes and has intensity h.
First step: calculate the tidal motion of an area element of this dust
layer under the influence of the wave. This is (or ought to be) trivial
Second step: calculate the gravitational radiation emitted by this
oscillating bit of dust.
Third step: Integrate over the entire layer to find its contribution
to the radiation field. You ought to be able to use symmetry to make
this into a reasonable expression.
Fourth step: just as in the electromagnetic calculation, use this result
to compute the resultant overall wave and from this the gravitational
index of refraction of the dust cloud.
It looks like a straightforward problem to me -- I would hope that
someone who had taken an undergraduate-level course in relativity
could work it through. There would be no excuse for not being able
to do this in a graduate-level course.
Expectation: the index of refraction for a plausible dust cloud is
going to be very, very, very close to 1.
Question for thought: When plane gravitational waves interact, they
produce singularities. Imagine a plane gravitational wave incident
on the edge of an infinite dust cloud. Even though the index of the
cloud is going to be close to unity, *some* of that wave is going
to be reflected. Will a singularity result? Why would you expect
(or not expect) this to happen with real gravitational waves incident
on real dust clouds?
>: 3. I know it is believed to create curvature in time-space wich means
>: incredible and amazing thing, but from another point of view, can gravity
>: waves as building momentum while propagating a mass unit, then, in order
>: to conserve momentum, force the mass unit backwards while passing throug.
> The mechanism that causes gravity in General Relativity
>is inertia, but instead of space being a three dimensional
>checkerboard coordinate system, spacetime has the coordinate
>system flowing toward the center of massive bodies.
Coordinate systems are arbitrary. Go back and read MTW
> It would be nice if someone close to one of the
>experiment teams would post something here.
Worked on the Caltech LIGO from 1984 to 1988.
--
Alan Bostick | "Dole is so unpopular, he couldn't sell beer on
mailto:abostick@netcom.com | a troop ship." (Ohio Republican Senator William
news:alt.grelb | Saxbe on Bob Dole's early career in the Senate)
http://www.alumni.caltech.edu/~abostick
http://www.theangle.com/ The first site with a brain. Yours.
Subject: Re: Magnetic symmetry supports new ocean ridge model
From: john@mail.petcom.com. (John S.)
Date: 30 Oct 1996 20:10:35 GMT
In article <32767EF4.130A@cardiff.ac.uk>, irvingd1@cf.ac.uk says...
>
>John S. wrote:
>>
>> In article , skrueger@arco.com says...
>> >
>>
>> >
>> >Jupiter is an enormous gaseous planet with a nuclear furnace in it's core
>> >(hence the radiation). What's this got to do with the Earth?
>> >
>> If Jupiter has a nuclear furnace at its core, then maybe Earth does too!
>
>I think it would have been detected by now if there were. If this was the
>case then we would expect to pick it up using seismic methods. As shear
>waves can pass through the core, it must be a solid as a fluid cannot
>support shear forces. We find the properties of the shear waves to be
>those expected in a solid iron-nickel mix with the odd bit of cobalt too.
>
>
>> After all, we're not seeing any neutrinos from the Sun's 'nuclear
furnace'-
>> so why would we see any from Jupiter's- or Earth's?
>> Hey, my watch is powered by the same kind of non-neutrino producing
nuclear
>> reaction. (That was neat how that 'gas' splashed when the comet hit it,
eh?
>> When we were proving what's happening at Jupiter's core, did we also prove
>> what kind of gas forms long-lasting craters?)
>
>You can make a hole in a gas by dropping an object through it (e.g. a
>comet)
But does the gas exhibit a long-lasting (several rotations) SPLASH pattern?
>
>> Actually, the extinctions happened at intervals over a long period of
time,
>> corresponding with the ice ages. The Saber-toothed Tiger didn't go as
early
>> as T. Rex did he? The mammoths were around until just before the last Ice
>> Age, not?
>
>The sabre-toothed tiger was never around at the same time as the
>dinosaurs, in fact it evolved many millions of years later and, as far as
>we know, large glaciations or ice-ages have only been occurring during
>the Quaternary and late Tertiary (about the last 20Ma). How does this
>correspond to dinosaur extinctions, the last of which was approx 60Ma
>ago?
The way it corresponds is that I would think it is a shift in the axis that
would throw ice out in these spirals- because the polar ice cap would become
off-center. Previous to the Quaternary perhaps there were no polar ice caps
for some reason. Maybe there was higher land in those locales than there is
now. But these axis shifts may have been happening since before dinosaurs
were here. I know that the equator used to run close to where I live, which
is in the center of a (rapidly-cooling-off, damn it) Canada.
But an axial shift would still cause large-scale upheaval in the short range.
And it is my theory that a gradual increase in mass is not gravitationally
recognized for some reason until the axis, and therefore the magnetic poles,
are finally pressured into shifting. So it is this sudden incrementation in
gravity that causes the punctuated evolution we see, happening at intervals
like a snake shedding its skin.
>Go to your local library and find some geology books, take them out and
>read them.
Thanks, I will. Are there any you recommend? Have you read "Theories of the
Earth and Universe (A History of Dogma of the Earth Sciences)" by S. Warren
Carey? He's professor Emeritus or some such at some University in Australia.
Read my page, if you like http://www.petcom.com/~john
John (I was kidding about the nuclear reactions at the Earth's center. I
don't even think nuclear reactions happen at the Sun's center.)
Subject: Re: New Relativity - Autodynamics
From: Mountain Man
Date: Thu, 31 Oct 1996 05:37:09 -0800
Gordon D. Pusch wrote:
> In article <846101428.28688@dejanews.com> amnon.meyers@trw.com writes:
>
> > A new theory of relativity is quickly gaining world-wide attention
> > http://www.autodynamics.org
>
> Hits on a web-site do not even translate to ``world-wide attention,''
> let alone proof of validity. Furthermore, even if a =BILLION= netizens
> happen to believe in a stupid idea, it is =STILL= a _STUPID IDEA_.
Argumentative little soul aren't we?
How =NON-STUPID= thou art !!!!
> The Univerves is =NOT= a democracy, and does not give a frozen fig
> in Finland what the ``Usenet consensus'' on =ANY= subject is...
The universe =DOES= however display distinct eco-systemic relationships.
>
> > * decay phenomena explained without the "undetectable" neutrino
>
> You're beating a dead horse --- Neutrinos have been reliably produced
> and detected for =DECADES=.
So had the rising of the sun in its geocentric orbit.
Or had you forgotten this remnant theory?
> > * a feasible mechanism for gravity is postulated.
>
> In what way is General Relativity ``infeasible'' ???
It fails to explain the observed planetary precessions.
Why is this so?????
> > * many experiments that Einstein's relativity (and the "Standard
> > Model") cannot account for are now explainable.
>
> Name two.
(1) As above (planetary precession)
(2) Decay phenomena
(3) Certain binary star phenomena.
> Describe in detail the experiment, what Einstein's Special Relativity
> predicts, and what ``autodynamics'' predicts.
See the website.
> Given that the ``equations of autodynamics'' haven't even appeared the
> same way twice in any of Carrenzi's (very limited!) publications on the
> subject, it's not clear that =ANYONE= can make =ANY= clear statement of
> what ``autodynamics'' predicts, since no definitive statement of the
> ``theory'' of ``autodynamics'' even =EXISTS= !!!
>
> -- Gordon D. Pusch
Typical government response.
Pete Brown
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Subject: Re: [Fwd: Re: The hard problem and culture.]
From: gclind01@starbase.spd.louisville.edu (George C. Lindauer)
Date: 30 Oct 1996 20:54:45 GMT
Jack Sarfatti, Ph.D. (sarfatti@well.com) wrote:
: Message-ID: <327684B5.2D51@well.com>
: Date: Tue, 29 Oct 1996 14:27:01 -0800
: From: "Jack Sarfatti, Ph.D."
: Reply-To: sarfatti@well.com
: Organization: Internet Science Education Project
: X-Mailer: Mozilla 3.0 (Win95; U)
: MIME-Version: 1.0
: To: "Lawrence B.Crowell"
: CC: Barron Burrow , nixon@geneseo.edu,
: tmoody@sju.edu, hubey@amiga.montclair.edu, jeff@aiai.ed.ac.uk,
: norwoodr@etsuarts.east-tenn-st.edu,
: acampbell@cix.compulink.co.uk, srh@ccit.arizona.edu,
: jcs@richmond.infi.net, md2738@mclink.it, P.Bains@uws.edu.au,
: HRSG57A@prodigy.com, rhett@teleport.com, trehub@psych.umass.edu,
: mikebarker@delphi.com, heuvel@muc.de, matpitka@rock.helsinki.fi,
: mgm@santafe.edu, GGLake@aol.com, rwolf@usfca.edu,
: Lyle_Fuller@mindlink.bc.ca, NEONLEO@aol.com, Puthoff@aol.com,
: LeonMaurer@aol.com, creon@nas.nasa.gov, physics@intuition.org,
: kelvin@fourmilab.ch, rfelder@flagstaff.az.us, stiger@cnet.gr,
: rwarner@kentlaw.edu, wordenr@logica.com, hswift@swcp.com,
: chalmers@paradox.ucsc.edu, onesong@ix.netcom.com,
: hilken@maths.ox.ac.uk, pdavies@physics.adelaide.edu.au,
: JPL.Verhey@inter.nl.net, jeanbur@netcom.com,
: anthony@imprint.co.uk, com@dircon.co.uk, bdj10@cam.ac.uk,
: MaitEdey@aol.com, hensm@essex.ac.uk
: Subject: Re: The hard problem and culture.
: References:
: Content-Type: text/plain; charset=us-ascii
: Content-Transfer-Encoding: 7bit
:
: Lawrence B.Crowell wrote:
: >
: > > Jack Sarfatti notes (10/26/96):
:
: >
: > >It is postulated that the quantum pilot wave is Chalmer's fundamental
: > >"felt" information field in sense of his Dec 1995 Sci Am article. Stapp
: > >makes an equivalent postulate in his Heisenberg ontology approach which
: > >he says goes beyond the "orthodox" Bohr pragmatic interpretation.
: >
: > ------------------------------------------------------------------
: >
: > It is best to say that the pilot wave, or quantum hydrodynamic fluid,
: > contains the implicate information that is ascribable to the nonlocality
: > of the mind. Whether this IS the mind is a little tough to say.
:
: Right, that's why I call it "mind-stuff" or, perhaps "subconscious" mind
: since, IMHO, it takes back-action from beable to pilot wave to awaken
: consciousness.
:
: > However,
: > the pilot wave is associated with the quantum force that influences the
: > motion of the particle (beable) and is thus physical.
:
: This is how thought influences the brain IMHO. Back-action is how the
: brain changes its subconscious thought. The change in thought is the
: conscious experience. This corresponds to Stapp's Heisenberg
: "actualization" and Penrose's "orch OR".
:
: > One of the
: > objectives of a study of consciousnesss is to exorcise the ghost from the
: > machine. The pilot wave is not simply a physicist ghost that plays the
: > role of more mystical or poetic notions of a ghost. Maybe for a holloween
: > costume I should go as a pilot wave that has lost it beable, even though
: > that is physically impossible.
: >
: > L. Crowell
:
I? often wonder that noone realizes the difference between a mountain and a
molehill.
David
Subject: Re: Constancy of the Speed of Light--Purely Mathematical?
From: Christopher R Volpe
Date: Wed, 30 Oct 1996 16:04:21 -0500
Brian D. Jones wrote:
In the following line, bjon admits that absolute motion has not been
detected.:
> >> all I am saying is that it has not been done,
I'll come back to this later. Now on to facts versus theories:
> >> leaving open the possibility, however slight, that it may be done in
> >> the future. In fact, this "open-end" view is necessary if SRT is to
> >> be a testable (i.e., scientific) theory.
>
> >BS. Is the "open end" of possibly discovering the world's flatness
> >someday necesssary if the round-earth theory is to be a testable
> >scientific theory?
>
> There's a very small but critical distinction between a fact and a
> theory.
> >>
What bjon fails to understand is that facts are observations and
theories are explanations for them. Theories do not become facts.
"Theory" is not a stepping-stone to fact-hood.
> >> And the main point I was trying to make was about absolute motion
> >> itself having existence. To say that absolute motion does exist is not
> >> the same as saying we have not detected it yet.
>
> >True, but it IS the same thing as saying that it can never be detected,
> >even in principle.
>
> Essentially, it's detected everyday.
Bjon just got through saying that absolute motion has not been detected,
and now he says it is detected every day. Since this is apparently all
SR says can't be done, one wonders why bjon has not yet received the
nobel prize for his disproof of SR.
> It's the only thing that
> distinguishes one observer from another.
No, that would be called "relative motion".
> But, of course it's not the detection that is important, it's the
> determination of one's absolute velocity.
When one speaks of "detecting absolute velocity", what one usually means
is the determining of one's absolute velocity in general, or
distinguishing it from zero in particular. Demonstrating that
alpha-centauri is receding from is *not* a detection of absolute motion,
but rather of the relative motion between it and us.
> >There is no difference between existence and the ability to be detected.
> >The ability to be detected, in principle (even if technologically it is
> >not currently possible), is the very essence of "existence".
>
> See above.
Gee, I did, but there's nothing bjon has said that addresses this point.
All he did was point to relative motion, and mis-label it absolute
motion.
> >> And of course one can say that this is
> >> "good enough" for physicists to "deny its very existence," but by so
> >> doing they deny the very testability of SRT itself.
>
> >Does denying the existence of "absolute up" deny the testability of the
> >round earth theory?
>
> Facts don't need testing, only theories.
I could grant bjon that the roundness of the earth is a fact, but that
would be beside the point. Getting back to his erroneous claim: Bjon has
stated time and time again that SR must be *FALSE* in order to be
*FALSIFIABLE*. That is, SR's mere assertion that there is no way to
detect absolute motion makes itself unscientific. Completely bogus. SR
provides for many ways in which it can be disproven. In fact, its
assertion that there is no way to detect absolute motion provides for
its falsifiability. All you have to do is detect it. Go ahead and detect
absolute motion, and you've disproven SR. SR is very falsifiable. It
just hasn't been falsified. Given the number of ways and number of times
it has been tried, a reasonable person might conclude that the reason
for the failure to falsify it is that it is an accurate description of
reality in the realm it was designed to describe.
A good analogy is Thermodynamics's claim that it is impossible to build
a perpetuual motion machine. I suppose bjon thinks that the laws of
thermodynamics are unfalsifiable, and hence unscientific, because of the
inability to find a perpetuual motion machine. Most, if not all,
scientifically literate people would agree that the claim of the
impossibility to build a PMM itself demonstrates falsifiability. In
order to demonstrate falsifiability of a claim, one must merely be able
to anwser the following question in the affirmative: "Is there anything
I can do or observe that will demonstrate the falseness of the claim
under consideration?" With thermodynamics, the answer is obviously yes:
Build a device that outputs as much or more energy than it consumes.
With SR the answer is also obviously yes: Conduct an actual experiment
whose outcome depends on the inertial frame in which it is carried out,
without any "outside" information coming in from other identifiable
frames. No one but bjon claims that SR is not falsifiable.
At this point I would like to point out that so far bjon has held three
mutually inconsistent positions regarding SR:
1) The conditions of SR's disproof (detection of absolute motion) have
not been met. (See the very top of this post).
2) The conditions of SR's disproof are met every day. (Roughly 35 lines
down from top of post.)
3) The conditions of SR's disproof do not exist because SR is not
falsifiable and not scientific. (Preceding discussion)
> >Does denying the existence of perpetuual motion machines also deny the
> >testability of the laws of thermodynamics?
>
> Yes.
I'm glad Bjon admits it. At least he is consistent, even if consistently
wrong.
Again, in order for Claim X to be falsifiable, there must merely be a
set of identifiable circumstances that would constitute disproof of
Claim X. When Claim X is something like "it is impossible to build a
perpetuual motion machine", or "there is no way to distinguish any
inertial frame from being at absolute rest", the identifiable
circumstances of falsifiability are self evident. When Claim X is of the
form "there exists an inertial frame which is absolutely at rest, and in
this frame only are E-synched clocks 'truly synched', even if there is
no way to distinguish this frame", the circumstances which would
disprove the claim are much more difficult, if not impossible, to
identify.
>
> >Why? I claim that there is a "real" up direction, and that a plane
> >perpendicular to this direction is "really horizontal". It's as
> >meaningful a claim as your claim regarding absolutely-synched clocks
> >being able to identify the absolute rest frame.
>
> Because an "up" has no possible existence, being a mere concept.
Says who? I could just as easily claim that "absolute rest" has no
possible existence, being a mere concept.
> CLocks are real instruments, and can actually be truly set, if only by
> sheer accident.
Arrows are real pointy things, and can actually be truly pointing up, if
only by sheer accident.
> >> And even though true clock synch is equivalent to
> >> the concept of absolute motion,
>
> >I'm holding you to this admission. When I quote you in the future, don't
> >deny you said this.
>
> Of course it is, as I have said all along. But this is no fantastic
> secret as you seem to think.
Fair enough. Then you admit that it is of no consequence to claim that
you can detect absolute motion by using a pair of truly synched clocks,
just as it is of no consequence to claim that you could detect unicorns
if you had a unicorn-detector.
>
> >>it does make for a clear example to
> >> help get across the point that absolute motion has an existence
> >> because one can see that it is physically possible for two clocks to
> >> be truly synch'd,
>
> >Non-sequitur. Absolute up has an existence because one can see that it
> >is physically possible for a plane to be truly horizontal.
>
> It is not possible because truly horizontal itself has no existence.
Proof by blatant assertion. Of course, I really do in fact agree that
"truly horizontal" has no existance, but the point is that "truly
horizontal" has as much existance as "truly synched" or "truly at rest".
They are all the same thing: "Up", "At rest", and "In synch" are all
relative concepts. "Up" depends on where you are on earth, and the other
two depend on what inertial frame you are in. It's that simple. But if
you want to claim that it is possible for two clocks to be truly
synched, I will continue to make the equivalent claim that it is
possible for a plane to be truly horizontal.
>
> >> >Detectableness is equivalent to existence, as far as physics is
> >> >concerned. Einstein was pretty clear about that.
> >>
> >> They'd better not be precisely equivalent, or his own theory becomes
> >> untestable.
>
> >Non-sequitur. In no way does the use of the word "existence" to mean
> >"detectability in principle" make the specific quantitative claims of SR
> >untestable.
No response to the above claim?
>
> SRT makes only one (1) claim, and this single claim must be testable
> if SRT is to be an acceptable theory,
SRT makes two claims, each one expressed in the form of a postulate.
The first claim is the principle of relativity (PR). It says that all
inertial frames are completely equivalent for purposes of expressing
the laws of physics in a quantitative way. It is another way of saying
that it is impossible to distinguish one frame from another based on the
way in which physical processes transpire. This implies the
impossibility of distinguishing "absolute rest" from "absolute motion".
It is falsifiable merely by doing what is claimed can't be done: Conduct
an experiment entirely within an inertial frame, without using any
information regarding that frame's motion relative to some other
identifiable frame, that demonstrates that physical processes behave
differently in different inertial frames.
The second postulate is called the law of propagation of light (LPL). It
says that, given an observer at rest in some arbitrary inertial frame,
and two light sources moving with different, and arbitrary, velocities
in that inertial frame, light emitted by each of the two sources at the
same place and time will be emitted with the same speed, and that the
observer will therefore note that the two light waves are
"co-travelling" with each other in all directions, with arrivals at any
given target coinciding.
These are the two claims of special relativity. The second one is
confirmed over and over again by experiment. Bjon likes to call this
second postulate "fact". In actuality, it is a claim that is consistent
with a finite number of experiments, just like the first postulate, and
is subject to later disproof, just like the first postulate.
Bjon likes to claim that the first postulate is all that SR claims. This
is of course false, since Newton also claimed the PR was true, but
Newtonian relativity is quantitatively different, i.e. makes different
predictions, from Einsteinian relativity.
--
Chris Volpe Phone: (518) 387-7766
GE Corporate R&D; Fax: (518) 387-6560
PO Box 8 Email: volpecr@crd.ge.com
Schenectady, NY 12301 Web: http://www.crd.ge.com/~volpecr
Subject: Re: Hermeneutics and the difficulty to count to three...
From: meron@cars3.uchicago.edu
Date: Wed, 30 Oct 1996 21:45:48 GMT
In article <557uqf$om4@netnews.upenn.edu>, weinecks@mail1.sas.upenn.edu (Silke-Maria Weineck) writes:
> <54rrks$39k@netnews.upenn.edu> <5566cl$jir@dwst13.wst.edvz.sbg.ac.at>
>Distribution:
>
>meron@cars3.uchicago.edu wrote:
>: In article <5569qp$n6j@netnews.upenn.edu>, weinecks@mail1.sas.upenn.edu (Silke-Maria Weineck) writes:
>: >
>: >That's precisely how I use it as well. In the case of Newton, however,
>: >if I can trust the here=present scientists, a theory that was held
>: >universally applicable became not-universally applicable. So its field
>: >of applicability got restricted.
>: >
>: Right. So in comes relativity which reduces to Newtonian Mechanics
>: within a restricted area, but which is also valid over a way broader
>: area. So is it a generalization of Newtonian Mechanics or no. I'll
>: put it simpler yet. We find that Newtonian mechanics is working over
>: area A while relativity works over B which includes A as proper
>: subset. Generalization or no?
>
>In the field of common usage, I'm still happier with modification, or
>perhaps simply "improvement," if you must know. What I'm pointing out
>here, however, is that this matter isn't half as clear-cut as was
>suggested by you and others earlier on. And I don't think you would jump
>at someone who'd say, Einstein modified Newton, or Einstein improved on
>Newton -- would you?
No, definitely not. The last thing I would like to see is some
"orthodoxy of language", some strict definitions of what terms can be
used, when and by whom. That's for religion, not science (Gordon's
claims nonwithstanding). There many ways same or similar content may
be conveyed and I'm certainly not going to react each time somebody's
description doesn't exactly match the way I would say it, as long as
there is some overlap. Mind you, the words "generalize", "improve"
and "modify" do overlap to some extent, they're not mutually
exclusive. At most I could comment that saying "modified" or
"improved" without additional details may leave one with the feeling
that it was but a small change, which is inaccurate.
So, anyway, there may be many different descriptions whaich doesn't
mean that any imaginable description is correct. And if I see a
statement which, as it stands, bears no resemblance to reality, then
yes, I would react. Not "jump at" its author, mind you, just state
why I think the statement is incorrect. You may want to look back at
my first post on the issue and see whether it constitutes an attack on
anybody. Of course, we may get back into the "you've to realize that
different groups of people have different standards of what is and
what isn't offensive". That I may believe. I'll find it rather
difficult to believe, though, that any group of people may sincerely
believe in "anything I say, even if worded as personal attack, is just
a legitimate expression of opinion but anything you say, unless it is
a total acceptance of my position, is an expression of hostility."
Mati Meron | "When you argue with a fool,
meron@cars.uchicago.edu | chances are he is doing just the same"
Subject: Re: When will the U.S. finally go metric?
From: Markus Kuhn
Date: Wed, 30 Oct 1996 17:54:21 -0500
Lawrence Crowl wrote:
> The advantages of converting to a duodecimal number system are clear.
> Are you willing to convert?
What is so exciting about 12 = 3*3*2*2?
If I ever would advocate to change our common representation of numbers
(I don't, as they are already really globally standardized today), then
my only choice would of course be the sedecimal system (base 16=2^(2^2),
in computer technology commonly called for unknown reasons the
hexadecimal system).
Rationale: Base two is the most natural number system as it uses the
minimal number of digits. Hexadecimal numbers are the most compact
representation of binary numbers that can still be handeled easily by
human brains. Written multiplication can be done very easily in a binary
number representation. And those with a computing background will find
hexadecimal numbers anyway the only obvious choice.
If I really had to reinvent a common number representation without
looking at what is well established today in all countries, I would
probably use something like the Martin digits for a base 16 system
instead of for instance the digits 1-F that are used in computing today.
[Reference for those interested in what Martin digits are:
Communications of the ACM, Vol 11, No. 10, October 1968, p. 658.]
But before we talk about optimal representation of natural numbers,
let's first fully introduce the set of natural numbers in the U.S. I
have so far seen here mostly, what I call the "set of supernatural
numbers" (aka the set of superstitious numbers):
S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, ...}
Where is the number 13 in hotel floors, plane seats, apartment numbers?
It seems, some folks in the U.S. are so excited about the 12 that they
even killed the successor of 12, in order to enhance the full glory of
this holly number. BTW: Where can I find an algebra textbook about
calculation in S?
Markus ;-)
(living in a 1995 apartment complex in Indiana, USA, with no
apartment with a number between apartment 12 and 14 ...)
--
Markus Kuhn, Computer Science grad student, Purdue
University, Indiana, US, email: kuhn@cs.purdue.edu
Subject: Re: Design in nature
From: jhvh-1@geocities.com (Mike Turk)
Date: Wed, 30 Oct 1996 22:29:49 GMT
/On the date of Fri, 18 Oct 1996 09:48:54 -0600, "Mr. Smith"
did inscribe into the group alt.atheism and
unto the ether thereof:\
>If I murder someone, God must,
>> > : : if he were all-knowing, know that I was going to do it. This
>> > : : implies that I must do it, or God would be wrong (if the outcome
>> > : : is not determined, it cannot be known). This negates the idea of
>> > : : free choice.
>"And just as they did no approve of holding God in accurate knowledge,
>God gave them up to a disapproved mental state, to do the things not
>fitting, filled as they were with all unrighteousness, wickedness,
>covetousness, badness, being full of envy, murder..." Romans 1:28,29
In this, we see that at the time that Romans was written, someone had
already figured out that little omniscience/free choice paradox and
was rebutted (as usual) by biblical quotations.
Mike Turk
--
/=== e-mail: jhvh-1@geocities.com
/ 111 homepage: http://www.geocities.com/SiliconValley/6966/
111
J H V H Energetic is the goblin that fears the
111 turquoise wallpaper.
111
-=====-
SLACK FIRST
Subject: Re: Hermeneutics and the difficulty to count to three...
From: candy@mildred.ph.utexas.edu (Jeff Candy)
Date: 30 Oct 1996 23:03:48 GMT
|> moggin:
|> > Newt offered a theory of cats (TOC) which described all cats as
|> > black. Given Stein's findings, Newt's description was inaccurate,
|> > and his theory was false. His observations were fine, as far as
|> > they went, but the conclusions he drew from them were invalid.
Jeff:
|> (i) MR-cat theory = valid TOC (false)
|> (ii) MR-cat theory = valid theory of MR-cats (true)
Jeff:
|> (i) and (ii) summarize quantitatively the logical content of our
|> present discussion; that is, the restricted discussion of idealized
|> cats.
moggin:
|> They may summarize some discussion that you would prefer to have,
|> perhaps even one you believe you are having -- but they don't pertain
|> to any discussion I'm participating in. In relation to the discussion
|> I'm having with you, they were and are irrelevancies, for the reasons I
|> mentioned above.
Your words in quotes:
LHS of (i),(ii): "Newt offered a theory of cats (TOC) which described
all cats as black."
(i) => "Given Stein's findings, Newt's description was inaccurate"
(i) => "and his theory was false."
(ii) => "His observations were fine, as far as they went"
(i) => "but the conclusions he drew from them were invalid"
To wit,
As a TOE, Newtonian mechanics is indeed invalid. (i)
As a nonrelativistic theory, it is quite nice. (ii)
QED (again).
-------------------------------------------------------------------
Jeff Candy The University of Texas at Austin
Institute for Fusion Studies Austin, Texas
-------------------------------------------------------------------
Subject: Fermat's Last Theorem: Proof re-edited on the basis of good suggestions
From: James Harris
Date: Wed, 30 Oct 1996 00:59:09 -0800
I received email with cogent criticisms of my previous posts concerning
the difficulties in reading it. This post is a first attempt to put it
all in more readable format. I've included a definitions section to
explain more of what I simply stated before.
Despite the fact that this is still a rough draft it should be possible
now to follow it to its conclusion, and see that the method proves
Fermat's Last Theorem.
Further, constructive criticism will be appreciated.
James Harris
------------------------------------------------------------------
Introduction.
Fermat's Last Theorem has long been a magnet to the amateur and
professional mathematician alike because of its seeming simplicity; yet,
extraordinary difficulty. Although there is a proof by Andrew Wiles, I
think it is understandable that the problem still would incite
curiosity. I would also assume that a simpler solution would also be of
interest.
1. Statement of the Problem: Fermat's Last Theorem
Given x,y,z, relatively prime, n odd prime
no solution exists for the equation x^n + y^n = z^n
2. Definitions.
f=(z-y), g=(z-x), h=(x+y);
Now using the substitution for y with n=3 gives
x^3 = 3fy^2 + 3f^2 y + f^3 from which it is obvious by inspection
that x^3 is divisible by
f only once, except for possibly one other factor of 3. In general,
that also requires that those factors of f be raised to the nth power
except for the n factor. So now, using a,b,c for the other factors
x=af or naf, y=bg or nbg, z=ch or nch
x+y=h^n or n^{n-1}h^n, z-x=g^n or
n^{n-1}g^n, and z-y=f^n or n^{n-1}f^n.
Now in general, (x+y-z)^n = n(z-x)(z-y)(x+y)Q + x^n + y^n - z^n
where Q represents all those other terms that are hard to write out for
the general case. For
n=3 it is one. And for n=5
Q = z^2 - (x+y)z + x^2 + xy + y^2
I also use q where Q = q^n or n^{n-1}q^n
Finally, I use a term p, where nfgp = (f+g)^n - (f^n + g^n)
From which it is obvious that p is divisible by (f+g)
-------------------------------------------------------------------------
Now by Fermat's Little Theorem, since x^n + y^n = z^n,
x^n - (z-y) = 0(mod n), therefore x^n - f^n = 0(mod n), x - f = 0(mod n)
and also y - g = 0(mod n) and z - h = 0(mod n)
And therefore that (a - 1) = 0(mod n) with similar relations for b and
c
-------------------------------------------------------------------------
2. General Proof
Now from before remembering that x^n + y^n = z^n
(x+y-z)^n = n(z-x)(z-y)(x+y)Q which gives
(x+y-z) = nfghq
To use the above it is easier to consider individual cases where one of
x,y or z is divisible by n or none of them are. Note that if z is
divisible by n, then (x+y) and therefore (f+g) must be divisible by n,
as explained in the definitions section.
a. Case where z is divisible by n
x + y-z = x-f^n ; y + x-z = y - g^n; x+ y -z = n^{n-1}h^n-z = nfghq
Adding them gives
x+ y -z - f^n - g^n + n^{n-1}h^n = 3nfghq
Which is just
-f^n - g^n + n^{n-1}h^n = 2nfghq
From which I get
f^n + 2nfghq + g^n = n^{n-1}h^n and subtracting f^n + nfgp +
g^n=(f+g^)n
nfg(p-2hq) = (f+g)^n - n^{n-1}h^n
neither f or g or q can be divisible by n, because that would mean that
x or y would have to share a factor of n with z which violates the
condition of relative primeness. Therefore, the above requires that h
be further divisible by n.
-----------------------------------------------------------------------
The same comes up with x or y divisible by n since you get
g^n + 2nfghq - h^n = n^{n-1}f^n subtracting
g^n + nghp - h^n = (g-h)^n
gives
ngh(p-2fq) = (g-h)^n - n^{n-1}f^n
which requires that f,g,h or q be divisible by n because (g-h) is
divisible by n which again requires that f be further divisible by n for
the reasons stated before.
3. Proof for Case x,y,z not divisible by n
-------------------------------------------------------------------------
lemma(1): Extension of Fermat's Little Theorem:
Given a-b divisible by n, a^n - b^n must be divisible by n^2
Proof: a-b divisible by n implies that a equals some jn+r and b
equals some kn + r
Then, a^n - b^n = (jn)^n +...+n(jn)r^{n-1} + r^n -
[ (kn)^n +...+n(kn)r^{n-1} + r^n]
by inspection r^n can be subtracted off and the other terms are
multipled by n^2
-------------------------------------------------------------------------
So by lemma(1) if neither x,y nor z are divisible by n and q is
then
(x+y)^n - (x^n + y^n) must be divisible by n^2.
But since f has the same modulus with respect to n as x and g has the
same as y, it also requires that (f+g)^n - (f^n +g^n) be divisible by
n^2.
and from before
(f+g)^n - (f^n + g^n) = nfgp and p is seen to be required to be
divisible by n
But like before I can write
f^n + 2nfghq + g^n = h^n and again subtract f^n + nfgp + g^n =(f+g)^n
which gives
nfg(p-2hq) = (f+g)^n - h^n
and since both sides are divisible by n^2, q is then forced to be
further divisible by n.
4. Case for (x+y-z) divisible by n^2 or higher powers of n
Now then, these cases force me to rewrite my expression for (x+y-z).
Considering the situation with divisibility by n^2, I have
(x+y-z)=(n^2)fghq
-------------------------------------------------------------------------
But still for my other relations at least two aren't divisible by n.
Considering the possibility x,y not divisible by n
x+y-z = af - f^n = (n^2)fghq
This requires that af - f^n be divisible by n^2. But if I rewrite
using moduli
f=kn+r a=mn+1 giving (kn+r)(mn+1) - (kn+r)^n
Expanding (kn+r)^n all terms are divisible by n^2 except the last r^n
term
Now (kn+r)(mn+1) = km(n^2) + (rm + k)n + r , r
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Subject: Satellite--Geosynchrous Orbit Question
From: kimbrel@pld.com (Ryan K.)
Date: Thu, 31 Oct 1996 00:53:53 GMT
How fast and at what height above the earth must a satellite travel to
stay stationary relative to the earth?
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Byron Palmer