is Penrose a crackpot?
Nathan Urban
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
Seriously enough that people still invite him to talk about it. But I'd
have to say that most people I've talked to are rather skeptical.
However, that doesn't make him a crackpot. It does put him on the
fringe, though.
> Is it even worth considering?
That depends on your definition of "worth". Might he be right? Sure,
no one has proven him wrong. As far as I'm concerned, that's enough to
make it worth thinking about, assuming you find it interesting. If you
don't find it interesting, then you'll probably find little point in
considering it.
> Just look at how much effort is going into
> building a quantum computer, with success extremely remote if even
> possible.
Constructing a quantum computer is quite a different thing from
determining whether quantum mechanics influences the workings of the
mind or showing that quantum mechanics requires modification.
Anyway, I know a number of people who would contest your claim that
success in building a quantum computer is "extremely remote". Within the
next few years? Probably. Within a longer time span? I don't see
what's stopping us. Sure, maybe the NP-complete stuff in polynomial
time might not be practical, but that's not the only reason to build a
quantum computer.
> And even if the dream comes true the final product would have to be some
> pretty exotic gadgetry. Are we really to believe our good old brain
> cells are just the thing required for a quantum computer?? Now, *that*
> is a leap of the imagination!
Don't confuse quantum computing with what Penrose is proposing. It's not
at all clear whether there is a relationship. (Especially because Penrose
has never really nailed down any specific details of his proposal.)
Furthermore, arguments from incredulity aren't themselves very credible.
It's better to admit that we don't yet know enough about how the brain
works.
Chris Hillman
On Tue, 1 Feb 2000, Rajarshi Ray wrote:
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
Do you mean, any -physicist-? Obviously, lots of nonscientists spend a
lot of time "discussing" these ideas in various newsgroups.
I know several mathematicians who know Penrose and various aspects of his
work, as I am myself to some extent: mostly his work on tilings and on
general relativity; I know much less about his work on twistors, although
I've attended several talks he's given on that subject, and have attended
talks by some of his coworkers, so I know something about that too.
Hmm... actually, strangely enough, I might just be the only person besides
Penrose who knows -both- his work on tilings (which directly inspired my
thesis) -and- his fundamental work in general relativity :-/ (a subject
which has been my chief obession for over a year).
Let one thing be clear at the outset: Penrose is a mathematical genius (a
much overused term--- but Penrose is the real McCoy) who played a pivotal
role in revolutionizing our understanding of one of the most important
scientific theories ever created (general relativity). His ideas on
twistor theory may or may not turn out to be useful in physics, but which
have certainly led to a mathematical theory which is very interesting and
worthwhile in its own right.
So it would be a mistake to dismiss Penrose's arguments simply because you
(we) can't understand them. There are two very obvious possible reasons
why person A can't understand an argument made by person B:
1. B cannot express himself very clearly because he is confused in his
own mind (and possibly wrong in his conviction, but due to some mental
block unable to realize that)
2. B is so much smarter than A that A couldn't possibly understand what B
is trying to say.
Because Penrose is very obviously (to my mind) much smarter than everyone
else who has commented on his claims, I think the second possibility has
to be taken seriously. On the other hand, it is by no means without
precedent for a genius to become obsessed with an idea which is basically
incorrect. Hamilton, for example, seriously misunderstood the
mathematical nature of quaternions (ironically, Penrose was one of the
first to undrestand how quaternions are relevant to understanding the
Lorentz group in a simple and beautiful way) and spent much of his life
trying to develop a "quaternion calculus" founded upon a crucial
mathematical misunderstanding. So, both possibilities need to be taken
seriously. I'm not sure there's much middle ground: either everyone will
suddenly "get it" and realize that Penrose was right all along, or else
this stuff is completely wrong and will die when he does.
Coming back to the reaction of Penrose's professional colleagues: well, he
is both a mathematician and a physicist, who has made great contributions
to both subjects. I'll let one of the physicists address the question of
what physicists tend to think about Penroses ideas about quantum and mind;
for the mathematical side, I think it is fair to say that we find his
ideas completely baffling. I've heard him, while speaking at the NATO
conference on Aperiodic Order in Waterloo several years ago (speaking to
an audience of specialists in aperiodic tilings) make what sounded like an
argument using hierarchichal tilings to draw a conclusion about human
reasoning which sounded to me like utter nonsense (the argument, not the
conclusion, although that sounded very weird too). But that might be only
because Penrose is obviously much smarter than me or the people I later
asked about that particular remark.
I don't know any mathematician who has bothered to try very hard to
understand what Penrose is saying, however-- mainly because there are so
many other interesting ideas out there which are much more accessible and
which appear much less likely to prove disappointing, so we choose to
learn about some other things which interest us more.
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
Chris Hillman
On Tue, 1 Feb 2000, Uncle Al wrote:
> Penrose is clever and heterodox, but not a crackpot.
Just so.
> It's a good argument if you cannot marshall orthodox counterargument.
> That is what experimentation is all about - theory can be wrong.
Unfortunately, as far as I know, Penrose has been unable to suggest a
plausible experiment, or at least, to persuade any biophysicists to try to
perform an experiment. But -if- someone ever come up with a reasonable
experiment, I certainly hope it will be performed! Penrose just might be
right. I think the concensus is that despite his other achievements,
which are -very- impressive, this is a rather long shot, but his ideas if
correct would be so important that it would certainly be worth performing
any experiment which could decide the issue. If, as I say, anyone can
ever concieve of such an experiment. As far as I know, no one has done
that yet.
Rajarshi Ray
Penrose's arguments about mind and quantum physics seriously?
Is it even worth considering? Just look at how much effort is going into
building a quantum computer, with success extremely remote if even
possible.
And even if the dream comes true the final product would have to be some
Bryan Reed
>Penrose's arguments about mind and quantum physics seriously?
>
I tend to have the same reaction, though for somewhat different reasons
than what you listed. I would have cited results from neurobiology, for
instance.
Not only does Penrose's assumption seem a rather bizarre and unsupported
one, but I don't even see how it does what he seems to want it to do
(i.e. explain our sense of "free will").
Then again, I haven't read Penrose's book myself--I've only seen synopses
of the basic argument. Maybe it makes more sense upon reading the book, I
can't say I know for sure . . .
Have fun,
Bryan
Uncle Al
Rajarshi Ray wrote:
>
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
>
> Is it even worth considering? Just look at how much effort is going into
> building a quantum computer, with success extremely remote if even
> possible.
>
> And even if the dream comes true the final product would have to be some
> pretty exotic gadgetry. Are we really to believe our good old brain
> cells are just the thing required for a quantum computer?? Now, *that*
> is a leap of the imagination!
Penrose is clever and heterodox, but not a crackpot. It's a good
argument if you cannot marshall orthodox counterargument. That is
what experimentation is all about - theory can be wrong.
--
Uncle Al
http://www.mazepath.com/uncleal/
http://www.ultra.net.au/~wisby/uncleal/
http://www.guyy.demon.co.uk/uncleal/
(Toxic URLs! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Pertti Lounesto
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
>
> Is it even worth considering? Just look at how much effort is going into
> building a quantum computer, with success extremely remote if even
> possible.
>
> And even if the dream comes true the final product would have to be some
> pretty exotic gadgetry. Are we really to believe our good old brain
> cells are just the thing required for a quantum computer?? Now, *that*
> is a leap of the imagination!
Penrose has introduced
1. Penrose tribar (impossible figure),
2. Penrose tile (non-periodic filling of the plane by polygons),
3. Penrose transform (by integrals),
4. Penrose twistor (conformal spinors),
or labelled these concpets by his name. At least
the last concept, twistor, is a hoax. See the book
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164,
in particular the chapter on the conformal groups
"Moebius transformations and Vahlen matrices",
pages 244-254.
nospam
the possibility that the State Vectors which describe quantum phenomena may
indeed have an actual orientation that the density matrix smears over in its
computation.
Consider the fact that both Bell's Inequality and explanations of the EPR
Paradox involve a measurement process that disturbs a quantum state. However,
Null measurements have shown to be "Real' phenomena. But Null measurements
require a state vector to have a particular orientation so that their
undetection in THAT PARTICULAR STATE, results in another, macroscopically
determinable event to NOT OCCUR.
The converse is also shown to be true, in that a state vector NOT in that
pre-configured state causes a macroscopic phenomena to occur.
But where does this leave both experimentalists and theoreticians alike? It
requires us to measure that a particular orientation is such a reality that it
causes a recording device to measure it in that particular state without the
occurence of the NULL event. I am not so sure we can do this.
Rich
Psanjay
Rajarshi Ray wrote in message <38963EE2...@home.com>...
>It's not my intention to flame anyone but does anybody *really* take
>Penrose's arguments about mind and quantum physics seriously?
>
>Is it even worth considering? Just look at how much effort is going into
>building a quantum computer, with success extremely remote if even
>possible.
>
>And even if the dream comes true the final product would have to be some
>pretty exotic gadgetry. Are we really to believe our good old brain
>cells are just the thing required for a quantum computer?? Now, *that*
>is a leap of the imagination!
Some people like www.andcorporation.com are using equations similar to QM
for constructing ANN's with great success .
Robert Low
>Penrose has introduced
> 1. Penrose tribar (impossible figure),
> 2. Penrose tile (non-periodic filling of the plane by polygons),
> 3. Penrose transform (by integrals),
> 4. Penrose twistor (conformal spinors),
> or labelled these concpets by his name.
Play nice, Pertti; he didn't label them with his name himself.
He wrote about them and other people labelled them with his name.
> At least
> the last concept, twistor, is a hoax.
In what sense is it a 'hoax'? The geometry of twistor space
as the space of null geodesics in complexified Minkowksi
space is classical algebraic geometry, and has been pretty
fruitful in the study of wave-equations in space-time (though
some of it turns out to have been known in the 19th century
in different language); the group representation approach
has spawned considerable pure maths; and various generalizations
have been of interest in GR.
(And if twistors are a hoax, then the Penrose transform
must be a hoax too, since the Penrose transform
takes fields on Minkoswki space to objects involving
twistor space.)
Gerry Quinn
>
>On Tue, 1 Feb 2000, Rajarshi Ray wrote:
>
>> It's not my intention to flame anyone but does anybody *really* take
>> Penrose's arguments about mind and quantum physics seriously?
>
>So it would be a mistake to dismiss Penrose's arguments simply because you
>(we) can't understand them. There are two very obvious possible reasons
>why person A can't understand an argument made by person B:
>
The problem with Penrose's arguments in (say) Shadows of the Mind, is
that we _can_ understand them, and they are wrong.
The first half is a "proof" that is no proof, and the second half is a
"theory" that is no theory.
- Gerry Quinn
jddescr...@my-deja.com
Pertti Lounesto <Pertti....@hit.fi> wrote:
> Rajarshi Ray wrote:
>
> > It's not my intention to flame anyone but does anybody *really* take
> > Penrose's arguments about mind and quantum physics seriously?
> >
into
> > building a quantum computer, with success extremely remote if even
> > possible.
> >
> > And even if the dream comes true the final product would have to be
some
> > pretty exotic gadgetry. Are we really to believe our good old brain
> > cells are just the thing required for a quantum computer?? Now,
*that*
> > is a leap of the imagination!
>
>
> 1. Penrose tribar (impossible figure),
> 2. Penrose tile (non-periodic filling of the plane by polygons),
> 3. Penrose transform (by integrals),
> 4. Penrose twistor (conformal spinors),
>
> the last concept, twistor, is a hoax. See the book
> http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164,
> in particular the chapter on the conformal groups
> "Moebius transformations and Vahlen matrices",
> pages 244-254.
>
>
----------------------------------------------------------------------
Are you giving us a preview of your next book? I can't find
twistors mentioned explicitly in this chapter of your book.
I know there is an extensive literature on twistors apparently
mainly by Penrose students. Have you found some defects in this
approach similar to your previous comments about the Atiyah
period 8 works and triality? Is it possible to compare
conformal spinors and Dirac double spinors and your flag pole
spinors all as biquaternion objects or operators? Could you
give more details?
In the referenced chapter you use some very suggestive
visualization terminology like stretch and translate and
inversion and transversion which all relate to compounding
reflections in Hamilton biquaternion terminology. What about
the various visual invariants like cross ratio and the relation
to the Mobious transforms you describe? Will these topics be in
your next book? Thanks. JD
----------------------------------------------------------------------
-----------------------------------------------------------------------
Sent via Deja.com http://www.deja.com/
Before you buy.
Andy Resnick
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
>
> Is it even worth considering? Just look at how much effort is going into
> building a quantum computer, with success extremely remote if even
> possible.
>
> And even if the dream comes true the final product would have to be some
> pretty exotic gadgetry. Are we really to believe our good old brain
> cells are just the thing required for a quantum computer?? Now, *that*
> is a leap of the imagination!
This situation seems similar to that of Linus Pauling, especially when he
started toting the benefits of vitamin-C megadoses late in life.
I'll never forget, I was in high school, and Pauling was on the local radio
station some night (this was mid-80's) going on about the benefits of taking
100k+ mg of vitamin-C daily, how it can cure this and that, when a lowly med
student from Case Western Reserve called in and cut Pauling to shreds. At
one point the student said:
"I have much respect for the two Nobel Prozes you have earned, professor
Pauling, but it is absolutely unconsionable (sp?) that you are saying these
things. If someone were not to seek professional medical help and instead
rely on these megadoses of vitamins you are pushing and die as a result,
their death is directly your fault."
bullshit is bullshit, regardless of who says it. Some people have merely
earned a careful listening.
--
Andy Resnick, Ph.D.
Optical Physicist
Dynacs Engineering Corporation
Pertti Lounesto
> Pertti Lounesto wrote:
> >Penrose has introduced
> > 1. Penrose tribar (impossible figure),
> > 2. Penrose tile (non-periodic filling of the plane by polygons),
> > 3. Penrose transform (by integrals),
> > 4. Penrose twistor (conformal spinors),
> > or labelled these concpets by his name.
>
> Play nice, Pertti; he didn't label them with his name himself.
> He wrote about them and other people labelled them with his name.
You are right: people try to take advantage by naming
concepts after those they perceive worth lip-service.
> > At least
> > the last concept, twistor, is a hoax.
>
> In what sense is it a 'hoax'? The geometry of twistor space
> as the space of null geodesics in complexified Minkowksi
> space is classical algebraic geometry, and has been pretty
> fruitful in the study of wave-equations in space-time (though
> some of it turns out to have been known in the 19th century
> in different language); the group representation approach
> has spawned considerable pure maths; and various generalizations
> have been of interest in GR.
Maybe I was exaggerating. Twistors are spinors of the
conformal group, but they do have some extra structure
(= dependence on the place).
jddescr...@my-deja.com wrote:
> Are you giving us a preview of your next book?
No.
>> See the book
>> http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164,
>> in particular the chapter on the conformal groups
>> "Moebius transformations and Vahlen matrices", pages 244-254.
>
> I can't find twistors mentioned explicitly in this chapter of your
book.
That is right, twistors are not mentioned in my book, although
spinors are mentioned in Penrose's book: it is 1-0 for me in
my competition with Penrose.
> Is it possible to compare
> conformal spinors and Dirac double spinors and your flag pole
> spinors all as biquaternion objects or operators?
Yes and yes. In fact Feza G"ursey invented bi-biquaternion
representation of the Dirac equation, as a forerunner of
David Hestenes geometric form of Dirac theory.
> What about
> the various visual invariants like cross ratio and the relation
> to the Moebius transforms you describe?
Lars Ahlfors, Fields Medalists from 1936, has done something
on this in higher dimensions. The cross ration turns out to be
the trace of some product of matrices.
james d. hunter
>
> On Tue, 1 Feb 2000, Rajarshi Ray wrote:
>
> > It's not my intention to flame anyone but does anybody *really*
take
> > Penrose's arguments about mind and quantum physics seriously?
>
because you
> (we) can't understand them. There are two very obvious possible
reasons
> why person A can't understand an argument made by person B:
>
his
> own mind (and possibly wrong in his conviction, but due to some
mental
> block unable to realize that)
>
> 2. B is so much smarter than A that A couldn't possibly understand
what B
> is trying to say.
>
> Because Penrose is very obviously (to my mind) much smarter than
everyone
> else who has commented on his claims, I think the second possibility
has
> to be taken seriously.
I think where Penrose ceases to be smart is that non-mathematicians
put up with mathematicians real number crap as long as it appears to
be
useful. Beyond that the math goobers are on their own.
Chris Hillman
On Tue, 1 Feb 2000, Gerry Quinn wrote:
> The problem with Penrose's arguments in (say) Shadows of the Mind, is
> that we _can_ understand them, and they are wrong.
They might well be wrong, but I doubt that you or anyone else (including
Penrose) really knows why.
Things are developing very rapidly in physics and a real revolution in
physics is almost upon us--- or so I and many much more knowledgeable and
experienced observers believe.
I think the smart reaction would be to sit tight and see what happens in
the next five years, which might well be as revolutionary as the years
1920-25 in the last century.
james d. hunter
>
> On Tue, 1 Feb 2000, Gerry Quinn wrote:
>
> > The problem with Penrose's arguments in (say) Shadows of the Mind, is
> > that we _can_ understand them, and they are wrong.
>
> They might well be wrong, but I doubt that you or anyone else (including
> Penrose) really knows why.
>
> Things are developing very rapidly in physics and a real revolution in
> physics is almost upon us--- or so I and many much more knowledgeable and
> experienced observers believe.
What are you supposedly "knowledgable" about?
Penrose's "math" education?
Chris Hillman
In article <38966B59...@hit.fi>,
Pertti Lounesto <Pertti....@hit.fi> wrote:
> Penrose has introduced
>
> 1. Penrose tribar (impossible figure),
> 2. Penrose tile (non-periodic filling of the plane by polygons),
> 3. Penrose transform (by integrals),
> 4. Penrose twistor (conformal spinors),
>
> or labelled these concpets by his name. At least the last concept,
> twistor, is a hoax.
I'll have to chime in with those saying this is grossly unfair and even
misleading. As Robert Low says, everyone knows that Penrose did not name
anything after himself; others did. Also, the tribar was a collaboration
between Roger Penrose and his father.
Also, as I said in my previous post, the twistor transform has lead to a
purely mathematical theory which is certainly no "hoax". I know some very
smart mathematicians who have worked hard on developing this in directions
motivated by purely mathematical considerations.
Also, some might try to claim that I am biased, but I don't think I am in
the slightest biased in saying that Penrose's work on tiling theory turned
out to be far more than a mathematical game. Several Field's Medalists
have worked in tiling theory, directly inspired by Penrose's contributions
in this area. I don't have time to try to explain this, but one of the
major transformations underway in mathematics is a unification of number
theory and dynamical systems theory, and generalized Penrose tilings
provide one of the simplest examples where it is clear that the dynamics
and certain rational approximation phenomena are different aspects of the
same thing. There are also surprising connections between aperiodic
tilings and physics besides the most obvious one: some (not all) physical
quasicrystals are very well modeled by generalized Penrose tilings in the
strongest sense: their atoms are located at the vertices of a particular
such tiling. The connection with quasicrystals alone is enough to make
Penrose's contributions to tiling theory of considerable importance in
physics.
And last but not least, Pertti omitted any mention of Penrose's greatest
contributions to science (in my view), namely his introduction of
conformal compactification (global analysis of solutions to the EFE) and
his proof of several of the singularity theorems which played such a
crucial role in fostering the development of gtr.
(Ironically, this development has now come back full circle, to the point
were several key leaders in gtr now agree that quantum phenomena can have
measureable effects at scales where the classical approximation is valid
(e.g., scalar fields, particularly conformally invariant scalar fields),
and the energy conditions which underlie the singularity theorems are now
all in doubt, thus implying the possible physical reality of warp bubbles,
traverseable wormholes, and time machines--- without, I hasten to add,
calling into question the standard hot Big Bang theory, the inflationary
scenario (quite the contrary) or black holes (event horizons). The
reality of time machines may seem less repugnant if one remembers that in
quantum gravity it is almost certain that "time" will turn out to be
merely an illusion, even though "spacetime" will emerge in the classical
limit. At any rate, what this means is that gtr is even -more- important
than we thought, and we are learning how to combine it with brane theory
and the like to draw some truly amazing conclusions! It's a very exciting
time to be studying gtr! Coming back to the point, even though one of the
key assumptions underlying each of the various the singularity theorems,
positive mass theorem, topological censorship--- namely, the various
energy conditions--- no longer appear plausible in the light of recent
developments, this does not in any way change the tremendous importance
and influence of Penrose's early work in gtr.)
Chris Hillman
On Tue, 1 Feb 2000, Pertti Lounesto wrote:
> Robert Low wrote:
>
> > Pertti Lounesto wrote:
> > >Penrose has introduced
> > > 1. Penrose tribar (impossible figure),
> > > 2. Penrose tile (non-periodic filling of the plane by polygons),
> > > 3. Penrose transform (by integrals),
> > > 4. Penrose twistor (conformal spinors),
> > > or labelled these concpets by his name.
> >
> > Play nice, Pertti; he didn't label them with his name himself.
> > He wrote about them and other people labelled them with his name.
>
> You are right: people try to take advantage by naming
> concepts after those they perceive worth lip-service.
This is very unfair. People named those things after Penrose because he
was the sole author of 2-4, and two people named Penrose were the authors
of 1.
> Maybe I was exaggerating.
All right, let's let it rest there.
> Lars Ahlfors, Fields Medalists from 1936, has done something on this
> in higher dimensions. The cross ration turns out to be the trace of
> some product of matrices.
Gosh, and I thought I was the only person who read that obscure little
book! :-) But I'd have to say that it didn't help me do whatever it was
I was interested in at the time--- something having to do with Sturmian
tilings. Probably what I really wanted was closer to a quite different
generalization of Moebius transformations of the UHP, namely the Siegel
UHP, although that doesn't work for me either :-( Anyway, for those who
know about moduli spaces in modern physics, some of these references may
lend credence to what I just said about the unification of number theory
and dynamical systems theory.
Chris Hillman
On Tue, 1 Feb 2000, james d. hunter wrote:
> I think where Penrose ceases to be smart is that non-mathematicians
> put up with mathematicians real number crap as long as it appears to
> be useful.
(LOL)
Gems like this are the reason why so many of us read these newsgroups (and
post the best on the department bulletin board for all to have a good
laugh at).
Chris Hillman :-)
Home Page: http://www.math.washington.edu/~hillman/personal.html
james d. hunter
>
> On Tue, 1 Feb 2000, james d. hunter wrote:
>
> > I think where Penrose ceases to be smart is that non-mathematicians
> > put up with mathematicians real number crap as long as it appears to
> > be useful.
>
> (LOL)
>
> Gems like this are the reason why so many of us read these newsgroups (and
> post the best on the department bulletin board for all to have a good
> laugh at).
Yes, I can tell. Your education department for "relativity"
is a self-reflective, transitive "scholars" gem.
james d. hunter
Number theory and dynamic systems have already been unified by
-engineers-.
This happened about -3000- years ago for the mathemagicians who have
not been keeping with the National Enquirer. That is where the
observant
inquiring minds learn about what's -new- in physics.
Rajarshi Ray
"consciousness". This seems to me equivalent to the notion that we seem
to have an "identity" about our thought process; we may think about lots
of different things at different times but throughout we preserve a
sense of "identity".
Perhaps this sense of "identity" (which seems to confer our
"consciousness") is simply the basic instinct wired in through
evolution, once vital for our survival but now not so vital. No matter
what we may turn our mind to, the basic animal instincts we are born
with never leave our mind; perhaps they give us the sense of "identity"
or "consciousness" we so strongly feel.
Rajarshi Ray wrote:
>
> It's not my intention to flame anyone but does anybody *really* take
> Penrose's arguments about mind and quantum physics seriously?
>
Pertti Lounesto
>
> On Tue, 1 Feb 2000, Pertti Lounesto wrote:
>
> > Robert Low wrote:
> >
> > > Pertti Lounesto wrote:
> > > >Penrose has introduced
> > > > 1. Penrose tribar (impossible figure),
> > > > 2. Penrose tile (non-periodic filling of the plane by polygons),
> > > > 3. Penrose transform (by integrals),
> > > > 4. Penrose twistor (conformal spinors),
> > > > or labelled these concpets by his name.
> > >
> > > Play nice, Pertti; he didn't label them with his name himself.
> > > He wrote about them and other people labelled them with his name.
> >
> > You are right: people try to take advantage by naming
> > concepts after those they perceive worth lip-service.
>
> This is very unfair. People named those things after Penrose because he
> was the sole author of 2-4, and two people named Penrose were the authors
> of 1.
That is right; in science we have to try to be objective.
But, Penrose is my competitor, because he pushes forward
his twistor theory as an alternative to my spinor theory
and my theory of representing the conformal group by the
Clifford algebra matrices. My overshoot was due to my
wish to eliminate my competitors, and as such it is only
human.
Gerry Quinn
>
>On Tue, 1 Feb 2000, Gerry Quinn wrote:
>
>> The problem with Penrose's arguments in (say) Shadows of the Mind, is
>> that we _can_ understand them, and they are wrong.
>
>They might well be wrong, but I doubt that you or anyone else (including
>Penrose) really knows why.
>
I tried hard with _Shadows of the Mind_. But I still think Penrose made
a fairly banal error in his proof that intelligent thought is
non-algorithmic.
His argument depends on the statement that mathematicians can recognise
truth by an intuitive process. But let us (in the most standard of
moves used in this type of discussion) apply his own argument - which is
surely a mathematical one - to itself. Can we recognise the truth of
falsity of his argument? The intuition of the vast majority of
mathematicians says that Penrose is wrong. Either their intuition is
wrong (and Penrose is wrong) or it is right (and Penrose is wrong).
Q.E.D.
I don't have the book to hand, but I found other arguments highly
dubious too. And his physical theories are as dubious as his proofs...
- Gerry Quinn
Gerry Quinn
>(Ironically, this development has now come back full circle, to the point
>were several key leaders in gtr now agree that quantum phenomena can have
>measureable effects at scales where the classical approximation is valid
>(e.g., scalar fields, particularly conformally invariant scalar fields),
>and the energy conditions which underlie the singularity theorems are now
>all in doubt, thus implying the possible physical reality of warp bubbles,
>traverseable wormholes, and time machines--- without, I hasten to add,
>calling into question the standard hot Big Bang theory, the inflationary
>scenario (quite the contrary) or black holes (event horizons). The
>reality of time machines may seem less repugnant if one remembers that in
>quantum gravity it is almost certain that "time" will turn out to be
>merely an illusion, even though "spacetime" will emerge in the classical
>limit. At any rate, what this means is that gtr is even -more- important
>than we thought, and we are learning how to combine it with brane theory
>and the like to draw some truly amazing conclusions! It's a very exciting
>time to be studying gtr! Coming back to the point, even though one of the
>key assumptions underlying each of the various the singularity theorems,
>positive mass theorem, topological censorship--- namely, the various
>energy conditions--- no longer appear plausible in the light of recent
>developments, this does not in any way change the tremendous importance
>and influence of Penrose's early work in gtr.)
>
>Chris Hillman
In my opinion, those theorems are only needed to rule out the Star Trek
fantasies that emerge from reifying the curved spactime of gtr. Quantum
phenomena are not going to give you your space warps and wormholes -
their whole nature is inimical to such things. (I would quite like to
be proved wrong, incidentally.)
Still, if those theorems have failed, it makes my own alternative ideas
more interesting, not to say testable!
- Gerry Quinn
Daryl McCullough
>
>
>On Tue, 1 Feb 2000, Gerry Quinn wrote:
>
>> The problem with Penrose's arguments in (say) Shadows of the Mind, is
>> that we _can_ understand them, and they are wrong.
>
>They might well be wrong, but I doubt that you or anyone else (including
>Penrose) really knows why.
In the _Shadows of the Mind_, there are two separate arguments
advanced: (1) An argument, starting with Godel's theorem, that
is supposed to show that human mathematical reasoning cannot
be reproduced by any computer program. (2) A suggestion that
the noncomputability in the brain is due to quantum effects.
The second part is Penrose' speculation about future directions
of physics and brain research, and I agree that none of us know
enough to say that he is wrong. However, the first part is
pretty straight-forward, and I think it is straight-forward
to say that it is wrong. The *conclusion* may be right---maybe
human brains really *are* noncomputable---but his *argument*
isn't. Penrose simply does not present a valid argument, and
there is no obvious way to patch it up to make it valid.
That's not to say that a valid argument along the lines
Penrose attempts may not be possible, but Penrose doesn't
give it.
>Things are developing very rapidly in physics and a real revolution in
>physics is almost upon us--- or so I and many much more knowledgeable and
>experienced observers believe.
>
>I think the smart reaction would be to sit tight and see what happens in
>the next five years, which might well be as revolutionary as the years
>1920-25 in the last century.
I agree with you about Penrose' speculations about the future
directions of physics and/or brain research. He could very well
be prescient in this regard. But his Godelian arguments don't
hold water. Future developments can't retroactively make his
current argument any more sound (although they may prove his
conclusion to be true).
Daryl McCullough
CoGenTex, Inc.
Ithaca, NY
james d. hunter
>
> In article <Pine.OSF.4.21.000201...@goedel2.math.washington.edu>, Chris Hillman <hil...@math.washington.edu> wrote:
> >
> >
> >> The problem with Penrose's arguments in (say) Shadows of the Mind, is
> >> that we _can_ understand them, and they are wrong.
> >
> >They might well be wrong, but I doubt that you or anyone else (including
> >Penrose) really knows why.
> >
>
> a fairly banal error in his proof that intelligent thought is
> non-algorithmic.
>
> His argument depends on the statement that mathematicians can recognise
> truth by an intuitive process.
His a priori major mistake is "mathematicians can recognise truth".
That is known to be possible on occasion, but so unlikely that we
should
estimate the odds of Penrose landing in -this- universe as less than
zero,
or effectively zero.
Paul Arendt
Daryl McCullough <da...@cogentex.com> wrote:
>
>In the _Shadows of the Mind_, there are two separate arguments
>advanced: (1) An argument, starting with Godel's theorem, that
>is supposed to show that human mathematical reasoning cannot
>be reproduced by any computer program.
Folks may enjoy reading an article in the latest Smithsonian
magazine (of all places), about a guy at Los Alamos who is
taking a non-traditional approach to artificial "intelligence."
(I don't know the issue number, but there's a picture of a
gargoyle on the front.)
He's made a bunch of "bug" robots whose brains aren't the usual
computer programs, but just a *few* transistors wired together
to provide for interesting nonlinear behaviors. These
transistors are coupled directly to sensors on the bug's body,
so that feedback between its surroundings and its "thinking"
becomes possible.
The results are astonishing: the bugs have an uncanny ability
to deal with new situations, overcoming obstacles and such. Plus,
they have a distinctive "memory" of recently-overcome obstacles
(so that they're easier to overcome the second time around),
basically tracable to currents still resonating in the particular
pattern which was amplified when it overcame the obstacle before.
People are reported to be astonished that the bugs contain no
sophisticated computer program inside, since they seem to exhibit
fairly advanced-looking thinking.
(Of course, quantum mechanics IS involved, but only in the
operation of the transistors -- it'd be perfectly possible to
use vacuum tubes instead, for instance. But given the way
these devices operate, I'm comfortable in not considering
Penrose's premise further.)
Daryl McCullough
>Folks may enjoy reading an article in the latest Smithsonian
>magazine (of all places), about a guy at Los Alamos who is
>taking a non-traditional approach to artificial "intelligence."
>(I don't know the issue number, but there's a picture of a
>gargoyle on the front.)
I haven't seen the article, but it sounds a lot like
the approach taken by Rodney Brooks, whose insect-like
robots were featured in the documentary "Fast, Cheap,
and Out of Control".
Chris Hillman
On Tue, 1 Feb 2000, james d. hunter wrote:
> Number theory and dynamic systems have already been unified by
> -engineers-.
(LOL)
For those interested in a more knowledgeable assessment of the situation,
let me point out that the concept of a dynamical system did not exist
until about 1920, and a really powerful and general theory did not come
together until the early eighties. Beyond that, anyone curious about what
I was talking about wrt the coming unification of some of the oldest and
most important branches of number theory (Diophantine problems,
extremalizing quadratic forms in integers) and dynamical systems should
see recent preprints by Margulis, Kleinbock, Eskin and others on the LANL
server. The conference proceedings from last summer in Seattle will
contain an excellent introduction by Kleinbock to his work with Margulis
(a Field's medalist) and Eskin.
Chris Hillman
On Tue, 1 Feb 2000, james d. hunter wrote:
> > > I think where Penrose ceases to be smart is that non-mathematicians
> > > put up with mathematicians real number crap as long as it appears to
> > > be useful.
> >
> > (LOL)
> >
> > Gems like this are the reason why so many of us read these newsgroups (and
> > post the best on the department bulletin board for all to have a good
> > laugh at).
>
> Yes, I can tell. Your education department for "relativity"
> is a self-reflective, transitive "scholars" gem.
"Self-reflexive" is an oxymoron, but I guess "transitivity" in scholarship
can be explained by this example:
1. Roger Penrose is 10^m times smarter and more knowledgeable
than Chris Hillman, m >> 1.
2. Chris Hillman is 10^n times smarter and more knowledgeable
than james d. hunter, n >> 1.
3. Therefore, Roger Penrose is 10^(mn) times smarter and more
knowledgeable than james d. hunter.
Works for me! :-)
Chris Hillman
Home Page: http://www.math.washington.edu/~hillman/personal.html
^
|
CHECK IT OUT! My very own "Education Department" :-)
jddescr...@my-deja.com
100...@goedel2.math.washington.edu>,
>
> > Penrose has introduced
> >
> > 1. Penrose tribar (impossible figure),
> > 2. Penrose tile (non-periodic filling of the plane by polygons),
> > 3. Penrose transform (by integrals),
> > 4. Penrose twistor (conformal spinors),
> >
number
> theory and dynamical systems theory, and generalized Penrose tilings
> provide one of the simplest examples where it is clear that the
dynamics
> and certain rational approximation phenomena are different aspects of
the
> same thing. There are also surprising connections between aperiodic
> tilings and physics besides the most obvious one: some (not all)
physical
> quasicrystals are very well modeled by generalized Penrose tilings in
the
> strongest sense: their atoms are located at the vertices of a
particular
> such tiling. The connection with quasicrystals alone is enough to
make
> Penrose's contributions to tiling theory of considerable importance in
> physics.
>
> And last but not least, Pertti omitted any mention of Penrose's
greatest
> contributions to science (in my view), namely his introduction of
> conformal compactification (global analysis of solutions to the EFE)
and
> his proof of several of the singularity theorems which played such a
> crucial role in fostering the development of gtr.
>
----------------------------------------------------------------------
Is it possible to say anything in a General Theory of
Relativity (GTR) sense about how the Penrose twistors
are compounded spinors and how they characterize the
space time curvature of particular massive objects?
Thanks. JD
Robert Low
> Is it possible to say anything in a General Theory of
> Relativity (GTR) sense about how the Penrose twistors
> are compounded spinors and how they characterize the
> space time curvature of particular massive objects?
Yes. There have been attempts to use twistor methods
to study momentum and angular momentum in GR; see
chapter 13 of Huggett & Tod's 'An Introduction to Twistor
Theory' for more.
Gerry Quinn
>
>
>On Wed, 2 Feb 2000, Gerry Quinn wrote, referring (I think) to my mention
>of the fact that the energy conditions of gtr are now in doubt:
>
>> In my opinion, those theorems are only needed to rule out the Star
>> Trek fantasies that emerge from reifying the curved spactime of gtr.
>> Quantum phenomena are not going to give you your space warps and
>> wormholes - their whole nature is inimical to such things. (I would
>> quite like to be proved wrong, incidentally.)
>
>
>This is another one of those priceless gems.
>
>> Still, if those theorems have failed, it makes my own alternative ideas
>> more interesting, not to say testable!
>
>
> 1. no knowledgeable physicists doubt the "reality" of spacetime curvature
> at the level of classical approximation,
>
Nor do I dispute that spacetime, as defined in gtr, is curved. I note,
however, that there is no compelling reason to describe space and time
in this manner.
Describing space and time in a more sensible manner (with gravity
as a field in a Euclidean 'absolute' space) allows us to see at once
that wormholes etc. are fantasy.
(By absolute space I mean a space as described by a metric that is not
affected by graviton interactions, though it may be created by more
fundamental interactions.)
> 2. far from "ruling out" wormholes, time machines, and warp bubbles, the
> fact that the energy conditions are now in doubt suggests that they
> are possible,
>
Exactly as I said, these theorems seemed to rule out nonsense of this
sort, but they turned out to be nonsense themselves, meaning that
general relativity again predicts nonsense.
> 3. these arguments rest upon the discovery that gtr and quantum fields
> can be combined in classical approximations which show that "quantum
> phenomena" can have profound effects at large scales, even
> cosmological scales, in addition to the "inflationary scenario" which
> has been known for some time,
>
And quantum phenomena are not going to give you wormholes etc.
> 4. this arguments do not affect the reality of the Hubble expansion or
> black holes (event horizons) or other things so many ignorant people
> argue are fictitious (their "arguments" really come down to "I don't
> know anything about the relevant physics, but these ideas are so
> abhorrent that they must be wrong!").
Black holes exist. The 'Hubble expansion' exists. Space - as described
by general relativity - expands. But you don't _have_ to describe space
this way. Taking the gtr description too seriously has led many
physicists to create a palimpsest of nonsense (warp-drives, wormholes,
extra universes inside black holes etc., and non-proofs of their
non-existence).
- Gerry Quinn
Richard Herring
> Chris Hillman wrote:
> >
> > On Tue, 1 Feb 2000, james d. hunter wrote:
> >
> > > -engineers-.
> > (LOL)
> >
> > For those interested in a more knowledgeable assessment of the situation,
> > let me point out that the concept of a dynamical system did not exist
> > until about 1920, and a really powerful and general theory did not come
> > together until the early eighties.
> For those interested in a TRUE assessment of the situation, let me
> point out that because mathemos are 3000 years late with their
> CONCEPTS of X, doesn't affect the EXISTENCE of X.
Right. They are entirely different things. Actual dynamical systems
of moving objects, and the abstract theory which describes them.
So an engineer who claimed to have unified number theory and dynamical
systems would be making an elementary category error.
Or has someone invented a machine whose existence proves the
Goldbach conjecture?
--
Richard Herring | <richard...@gecm.com>
JMFBAH
Date: Thu, Feb 3, 2000 00:30 EST
Message-id: <mark-468BBB.0...@news1.on.sympatico.ca>
>In article <3898BB3F...@jhuapl.edu>,
>jim.h...@spam.free.jhuapl.edu. wrote:
>> "Scientists" have a habit of using any oddball "math" that "works"!!!.
>>
>> Engineers don't!!!! That's why we're SUPER intelligent beings.
>you don't use math that works?
Right. And he thinks he's an engineer. :-)
/BAH
Trevor Jackson, III
> the fact that the energy conditions are now in doubt suggests that they
> [wormholes - ed] are possible,
Can you clarify this statement? I am unsure of the intended meaning of the
phrase "the energy conditions are now in doubt".
Trevor Jackson, III
> Rajarshi Ray <raja...@home.com> wrote in message
> news:38991B7C...@home.com...
> > any thoughts? anyone?? (eager anticipation...)
> I've always thought, the best way to think about consciousness is as a
> feedback loop. A process which requires some appropriate substrate to run,
> like the brain. I don't think there is anything about consciousness or
> intelligence, that cannot be explained in terms of large scale, read - way
> above quantum, changes occurring in the brain.
>
> Ability to communicate, is a prerequisite. When you can hear what you're
> saying, and what you hear affects what you say, a feedback loop develops. It
> is basically an ability to hold a conversation internally - at some point,
> sooner or later, the feedback loop must be able to refer somehow to it's own
> mechanism, and we develop an identity - I.
>
> I ;-) don't think that there is any mystery to consciousness, I'm sure it
> can be reproduced artificially, the process I mean, not some actual person's
> consciousness - that would be very difficult.
What is the rationale for this conclusion? If we can create systems that are
indistinguishable from consciousness why can we not create systems that are
indistinguishable from a particular consciousness?
(I'm using perceptual terminology because the equality and identity operators
may not apply to Identities :-)
Robert Low
The energy conditions are usually imposed by hand on the grounds that
any reasonable matter should satisfy them. It is not entirely clear
that physical fields (as we now often model them, i.e. as quantum fields
on a fixed space-time background) do in fact necessarily satisfy them.
In fact, it's clear that they don't, at small length-scales. The
issue has become whether the energy conditions must be satisfied
in some suitable averaged sense over macroscopic regions of
space-time. I think Chris's point is that although the energy
conditions seem very plausible from a classical (i.e. non-quantum)
point of view, quantum considerations suggest that it might actually
be a mistake to assume them.
Chris Hillman
On Thu, 3 Feb 2000 jddescr...@my-deja.com wrote:
> Is it possible to say anything in a General Theory of
> Relativity (GTR) sense about how the Penrose twistors
> are compounded spinors
^^^^^^^^^^^^^^^^^^
Urk...
> and how they characterize the space time curvature of particular
> massive objects?
Suggestion: don't try to learn about this unless you already have a strong
background in graduate math and physics, including real analysis,
integration theory, integral transforms, representation theory, complex
analysis, algebra and geometry of the Moebius group, Lie groups, and
semi-Riemannian geometry and curvature of connections a la Cartan on the
mathematical side, and a mastery of str, gtr, spinors and the spinor
formalism for gtr (cf. the Petrov classification) and Yang-Mills theories
on the physical side.
If you have a strong background, you can start by reading
Huggett and Tod
An Introduction to Twistor Theory
Cambridge University Press, 1994
If you have a strong mastery of gtr and the other stuff I mentioned, but
don't know the spinorial formalism, the classic reference is
Penrose and Rindler
Spinors and Space-time / Roger Penrose,
Cambridge University Press, 1984-1986 (two volumes).
For the twistor transform and field theories, try:
Ward and Wells,
Twistor Geometry and Field Theory
:Cambridge University Press, 1990
For twistor transforms and Yang-Mills fields, try:
Mason and Woodhouse
Integrability, Self-Duality, and Twistor Theory / L.J. Mason and
Oxford University Press, 1996
For twistor theory and gtr, here is an interesting new approach:
Schlesinger
Generalized Manifolds : a Generalized Manifold Theory with
Applications to Dynamical Systems, General Relativity
and Twistor Theory.
Harlow : Longman, 1997
There are a whole bunch of books out there; this is just a small
selection. If you look to see what is there, you will find that there are
more math books on the twistor transform than physics books--- as I said,
so far twistor theory has generated more interest among mathematicians who
can use the ideas and techniques introduced by Penrose in a purely
mathematical context, than it has among physicists.
Chris Hillman
On Thu, 3 Feb 2000, Gerry Quinn wrote:
> Nor do I dispute that spacetime, as defined in gtr, is curved.
Well, we -are- making progress!
> I note, however, that there is no compelling reason to describe space
> and time in this manner.
Have you read the articles I suggested on the compelling astrophysical
evidence for curved spacetime outside black holes?
> Describing space and time in a more sensible manner (with gravity
> as a field in a Euclidean 'absolute' space)
If you had read the articles I suggested on astrophysical evidence
strongly supporting the prediction of gtr that the Kerr geometry should be
an excellent approximation to the exterior field of any massive rotating
astrophysical object, and if you had thought about why there cannot be any
spacelike slices conformal to E^3, you would see that this is inconsistent
with observational evidence. IOW, you are wrong. Not because what you
say is incompatible with the mathematics of gtr (although it is) but
because observations agree with the Kerr geometry, which does not permit
the kind of foliation you are proposing.
> allows us to see at once that wormholes etc. are fantasy.
You still don't get it. The facts are as I stated them: gtr now appears
even -more- important and useful in physics than before, the existence of
specific astrophysical objects which are black holes, and the Hubble
expansion are -facts-; the surprise is that it now appears that
traversable wormholes, warp bubbles, and even time machines are most like
physically possible, and therefore they probably exist or can be
constructed. To say the least, this is development with far reaching
ramifications for all of physics.
> (By absolute space I mean a space as described by a metric that is not
> affected by graviton interactions, though it may be created by more
> fundamental interactions.)
That's still too vague to mean anything, so I have taken the liberty of
interpreting this in the context of gtr as a claim that any "physically
realistic solution" in gtr must contain a foliation by spacelike
hyperslices all of which are at least conformally equivalent to E^3.
This is a pretty weak requirement but it is still violated by many
important exact solutions in gtr, most notably the Kerr vacuum.
> > 2. far from "ruling out" wormholes, time machines, and warp bubbles, the
> > fact that the energy conditions are now in doubt suggests that they
> > are possible,
>
> Exactly as I said, these theorems seemed to rule out nonsense of this
> sort, but they turned out to be nonsense themselves, meaning that
> general relativity again predicts nonsense.
Well, you seem to find event horizons and all sorts of things "abhorrent",
but the trouble is, these phenemona have been -observed-. The evidence in
favor of gtr is overwhelming, so one has to take seriously these new
predictions, although I am sure there will be much debate about that the
exact traversable wormhole solutions found by Visser, Wald, and others
mean.
> > 3. these arguments rest upon the discovery that gtr and quantum fields
> > can be combined in classical approximations which show that "quantum
> > phenomena" can have profound effects at large scales, even
> > cosmological scales, in addition to the "inflationary scenario" which
> > has been known for some time,
>
> And quantum phenomena are not going to give you wormholes etc.
Well, duh! That's -known- to be wrong. The whole point is that in fact
"well understood" quantum fields (the kind underlying the Standard Model
in particle physics, which again is for all intents and purposes -fact-;
this model has been confirmed by zillions of experiments) -do- lead to the
prediction of traversable wormholes. This is precisely what Visser and
others have shown.
> Black holes exist. The 'Hubble expansion' exists. Space - as
> described by general relativity - expands. But you don't _have_ to
> describe space this way. Taking the gtr description too seriously has
> led many physicists to create a palimpsest of nonsense (warp-drives,
> wormholes, extra universes inside black holes etc., and non-proofs of
> their non-existence).
Heaping abuse upon these predictions hardly constitutes a scientific
argument. If you want to carry on a scientific discussion, you'll need to
master the background, read the papers (and understand them correctly!),
and give a mathematically reasoned argument to the effect that the
conclusions drawn by Visser et al. are wrong.
The only way to shoot down high quality theoretical physics is by even
higher quality theoretical physics. If you think you are up to the task,
by all means go for it, since as I say, the conclusions drawn by Visser
and others are indeed startling.
But you should prepare yourself for the possibility that someone will
create a small warp bubble (for instance) in a physics laboratory sometime
in the next five or ten years, or that astrophysical evidence of natural
warp bubbles formed during gravitational collapse will be found. Right
now, in my judgement, engineering traversable wormholes is a somewhat more
remote possibility, but if one can make even a small warp bubble in the
lab, one doesn't have to do that much more to make a small time machine.
Chris Hillman
On Thu, 3 Feb 2000, Trevor Jackson, III wrote:
> Chris Hillman wrote:
>
> > the fact that the energy conditions are now in doubt suggests that they
> > [wormholes - ed] are possible,
>
> Can you clarify this statement? I am unsure of the intended meaning of the
> phrase "the energy conditions are now in doubt".
See an archived post on my relativity pages for some of the energy
conditions, which include the null energy condition, the dominant energy
condition, the strong energy condition, and the weak energy condition,
plus "on average" versions of these. All of these conditions involve
inequalIties expressed in terms of the stress-energy tensor. But when you
take the classical field theory approximation to quantum fields of types
for which we have very strong observational and theoretical evidence, and
try to verify the inequalities, straightforward computation shows that
they all fail. Thus, whereas these conditions looked plausible for a long
time, they now look much less plausible; indeed, it appears that they are
all incorrect. Since the statements of the only general theorems
characterizing solutions to the EFE, namely the singularity theorems, the
positive mass theorem, and the topological censorship theorems, all
include as a hypothesis one of these energy conditions, all of these
theorems are now in doubt: they are mathematically correct, but they are
in doubt because the hypotheses they assumed, which once looked very
plausible, now appear to be incorrect.
Let me stress once again two points: first, the reality of event horizons
(black holes), the Hubble expansion and the standard hot Big Bang theory,
etc., are not in doubt. Second, it is very possible that new and improved
versions of the theorems I mentioned can be proven without appealing to
any of the energy conditions.
To sum up: the energy conditions are probably all wrong (violated in real
physical situations), the theorems I mentioned in their current form all
assume one of these conditions, but their conclusions may nonetheless be
correct (this will require further theoretical work to decide), and the
"usual fun stuff" like black holes and the Big Bang theory are not in
doubt. The overall effect of the new work is the gtr appears to be even
more powerful and important than we previously thought, because it can be
combined with quantum theory to yield powerful classical field theory
treatments which have (apparently) several far-reaching implications for
astrophysics and cosmology.
Chris Hillman
On Thu, 3 Feb 2000, Robert Low wrote:
> "Trevor Jackson, III" wrote:
> >
> > Can you clarify this statement? I am unsure of the intended meaning of the
> > phrase "the energy conditions are now in doubt".
>
> The energy conditions are usually imposed by hand on the grounds that
> any reasonable matter should satisfy them. It is not entirely clear
> that physical fields (as we now often model them, i.e. as quantum fields
> on a fixed space-time background) do in fact necessarily satisfy them.
>
> In fact, it's clear that they don't, at small length-scales. The
> issue has become whether the energy conditions must be satisfied
> in some suitable averaged sense over macroscopic regions of
> space-time. I think Chris's point is that although the energy
> conditions seem very plausible from a classical (i.e. non-quantum)
> point of view, quantum considerations suggest that it might actually
> be a mistake to assume them.
Just so, but even more--- it has long been appreciated that the energy
conditions can all be violated for a short time in a small region. The
new work suggests very strongly that they can in fact be violated on
length and time scales which permit a classical approximation, e.g.
treating a quantum field and a classical conformally invariant scalar
field with minimal coupling to gravitation as in the recent preprints by
Visser and Barcelo.
james d. hunter
>
> In article <3898BB3F...@jhuapl.edu>,
> jim.h...@spam.free.jhuapl.edu. wrote:
>
> > "Scientists" have a habit of using any oddball "math" that "works"!!!.
> >
> > Engineers don't!!!! That's why we're SUPER intelligent beings.
>
> you don't use math that works?
Well yes. I did say that scientists use math that "works".
When you got the Mojo working, the mother-in-law's
REALLY REAL NUMBER STREAM OF UNCONSCIOUSNESS is unnecessary.
james d. hunter
>
> In article <3898BC8E...@jhuapl.edu>, james d. hunter (jim.h...@jhuapl.edu) wrote:
> > Chris Hillman wrote:
> > >
> > > On Tue, 1 Feb 2000, james d. hunter wrote:
> > >
> > > > Number theory and dynamic systems have already been unified by
> > > > -engineers-.
> > > (LOL)
> > >
> > > For those interested in a more knowledgeable assessment of the situation,
> > > let me point out that the concept of a dynamical system did not exist
> > > until about 1920, and a really powerful and general theory did not come
> > > together until the early eighties.
>
> > For those interested in a TRUE assessment of the situation, let me
> > point out that because mathemos are 3000 years late with their
> > CONCEPTS of X, doesn't affect the EXISTENCE of X.
>
> Right. They are entirely different things. Actual dynamical systems
> of moving objects, and the abstract theory which describes them.
>
> So an engineer who claimed to have unified number theory and dynamical
> systems would be making an elementary category error.
Since "categories" and "category errors" are simply more of the
mathemos CONCEPTS, you have made the -most- fundamental of thinking
errors.
>
> Or has someone invented a machine whose existence proves the
> Goldbach conjecture?
>
Since I'm certain I don't care what Goldbach conjectured, I don't
know.
Gerry Quinn
>
>
>On Thu, 3 Feb 2000, Gerry Quinn wrote:
>
>> Nor do I dispute that spacetime, as defined in gtr, is curved.
>
>Well, we -are- making progress!
>
No, I've always said this.
>> I note, however, that there is no compelling reason to describe space
>> and time in this manner.
>
>Have you read the articles I suggested on the compelling astrophysical
>evidence for curved spacetime outside black holes?
>
>> Describing space and time in a more sensible manner (with gravity
>> as a field in a Euclidean 'absolute' space)
>
>If you had read the articles I suggested on astrophysical evidence
>strongly supporting the prediction of gtr that the Kerr geometry should be
>an excellent approximation to the exterior field of any massive rotating
>astrophysical object, and if you had thought about why there cannot be any
>spacelike slices conformal to E^3, you would see that this is inconsistent
>with observational evidence. IOW, you are wrong. Not because what you
>say is incompatible with the mathematics of gtr (although it is) but
>because observations agree with the Kerr geometry, which does not permit
>the kind of foliation you are proposing.
>
Now this is progress. Suppose we have an observer some distance from a
massive rotating object. He creates a naive Newtonian coordinate
system, using distant fixed stars as markers. Then he plots the
trajectories of photons passing close to the massive rotating object.
(Assume he can send satellites to it or plant markers on its surface and
carry out experiments with light beams, clouds of dust, etc. He does
not assume anything about the speed of light, and he remains
relentlessly determined to use his Newtonian coordinates. He notes that
his satellite clocks slow down near the object, and he does his best to
correlate the calculations in a reasonable manner. Anyway, he
eventually comes up with a formula for photon speed in every direction
at every point.)
Are you saying that in every such formula (even in the limiting case of
an infinitely distant observer) some speeds, at particular points and
directions, must be greater than the speed of light as measured locally
by the observer? That would certainly be inconsistent with my
hypothesis, and I would have to have a major rethink. Otherwise, I fail
to see the problem. That observers near the object will see apparently
superluminal speeds does not affect my hypothesis, because their clocks
are slow.
- Gerry Quinn
Chris Hillman
On Thu, 3 Feb 2000, Gerry Quinn wrote:
> Suppose we have an observer some distance from a massive rotating
^^^^^^^^^^^^^
> object. He creates a naive Newtonian coordinate system,
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> using distant
> fixed stars as markers. Then he plots the trajectories of photons
^^^^^ ^^^^^^^^^^^^ ^^^^^^^
> passing close to the massive rotating object.
^^^^^
You just cannot think very carefully, can you?
People who know a bit about gtr will know what is wrong with the
underlined phrases; people who don't, won't.
I suggest you continue this "discussion" with someone with a higher
tolerance for idiocy than I have, or with no knowledge of gtr.
Adrian Kuciak
Trevor Jackson, III <full...@aspi.net> wrote in message
news:38999618...@aspi.net...
Boy, what a can of worms.
Defining consciousness as a process the way I did, would make it relatively
easy to create under lab conditions. That does not say anything about its
ability to feel, be afraid, hungry, what have you, and in general talk about
philosophy or some other meaningful thing with the researchers. We could
observe and learn from it, by giving it problems and obstacles, but never
fully relate to it - as we do to each other.
Human consciousness is about in the same relationship to that idealized form
of consciousness, as a car is to motion. Human consciousness is an ability
we evolved, many of the different parts of the brain contribute to the
feedback loop, and are influenced by it. Some are influenced but do not
contribute themselves, some contribute but are not influenced... Human brain
is so complex it's scary. Just to reproduce all those complexities - wow,
not to even mention any ethical considerations. You won't see me
volunteering for such an experiment.
Adrian
Gerry Quinn
>
>
>
> ^^^^^^^^^^^^^
>
>> object. He creates a naive Newtonian coordinate system,
> ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
already have created such a monstrosity.
>
>> using distant
>> fixed stars as markers. Then he plots the trajectories of photons
> ^^^^^ ^^^^^^^^^^^^ ^^^^^^^
everything from every angle and distance, recording their local
timechecks on every image. Everything is transmitted back to base, and
our observer - at his leisure - reconciles the data according to his
Newtonian prejudices.
>
>> passing close to the massive rotating object.
> ^^^^^
the satellites can pick up images of them waving, that sort of thing.
There might well be difficulties in evaluating distances exactly, due to
anomalies in clock rate, light bending, and photon speed. Our observer
toils ceaselessly to produce a formula for such anomalies. He insists
that no speed will ever exceed c, but otherwise he is willing to adjust
measurements in any consistent manner to allow for such anomalies. Can
he possibly succeed? If the answer is no, my hypothesis is wrong. You
were going to prove it wrong, remember?
>
>You just cannot think very carefully, can you?
This is an argument?
>
>People who know a bit about gtr will know what is wrong with the
>underlined phrases; people who don't, won't.
I do know a bit about gtr. Not much, but certainly a bit. And I don't
see anything wrong with them at all. Indeed, they are really nothing to
do with gtr, just simple observations of light beams in a simple
coordinate system that was used by astronomers for centuries. You
cannot demonstrate the falsity of my argument that curved spacetime is
an unnecessary concept by an argument that starts with the unsupported
assertion of the necessity of treating spacetime as curved. No wonder
you can't see what's wrong with Penrose's proofs!
>
>I suggest you continue this "discussion" with someone with a higher
>tolerance for idiocy than I have, or with no knowledge of gtr.
>
Too bad Chris, your crapology has here been exposed for all to see.
If the Sun were replaced by a rapidly rotating neutron star, the
situation would be much as I describe. The Newtonian observer would see
anomalies in light speed and clock rates near the star, just as
observers at the turn of the century (using _exactly_ such a coordinate
system as I specify; _they_ didn't seem to find it impossible) saw
anomalies in the precession of Mercury. They didn't even have
satellites, and their clocks ran on clockwork.
But if you can't show that he would be forced to see some beams moving
superluminally in his terms, then you have not after all demonstrated
the unfeasibility of a field theory of gravitation.
That is not something of which you should be ashamed, but your
dishonesty in falsely claiming to be able to do so is. In someone of
such evident talent, it is - quite frankly - a disgrace.
- Gerry Quinn
Richard Herring
> Richard Herring wrote:
> >
> > In article <3898BC8E...@jhuapl.edu>, james d. hunter (jim.h...@jhuapl.edu) wrote:
> > > For those interested in a TRUE assessment of the situation, let me
> > > point out that because mathemos are 3000 years late with their
> > > CONCEPTS of X, doesn't affect the EXISTENCE of X.
> >
> > Right. They are entirely different things. Actual dynamical systems
> > of moving objects, and the abstract theory which describes them.
> >
> > So an engineer who claimed to have unified number theory and dynamical
> > systems would be making an elementary category error.
> Since "categories" and "category errors" are simply more of the
> mathemos CONCEPTS, you have made the -most- fundamental of thinking
> errors.
Sure. If you say so. Is the following statement true or false?
"Force equals rate of change of momentum"
Good. Now, how far can you throw it?
--
Richard Herring | <richard...@gecm.com>
Pertti Lounesto
> On the other hand, it is by no means without
> precedent for a genius to become obsessed with an idea which is basically
> incorrect. Hamilton, for example, seriously misunderstood the
> mathematical nature of quaternions (ironically, Penrose was one of the
> first to undrestand how quaternions are relevant to understanding the
> Lorentz group in a simple and beautiful way) and spent much of his life
> trying to develop a "quaternion calculus" founded upon a crucial
> mathematical misunderstanding.
Hamilton did found the quaternion representation of
rotations in 3D, as r -> qr/q, where
q = cos(alpha/2) + u sin(alpha/2)
where alpha is the angle of rotation and u is a unit
vector parallel to the axis of rotation. But, he
did not appreciate his finding, and let Cayley publish
it, in 1845. Instead, Hamilton considered rotations
in the special case, when r is orthogonal to u, and
wrote r -> pr, where p = q^2. This misinterpretation
was first corrected by Marcel Riesz, in 1958, see page
21 of his book "Clifford numbers and spinors", Kluwer
1993 (reprint of 1958), see publisher's URL:
http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-2299-1
Thus, Penrose was not the first one to correct Hamilton.
Penrose was not the first one to formulate the Lorentz
transformation by quaternions. This was done by
L. Silberstein, in 1912/1914, see his book: "The theory
of relativity", Macmillan, London, 1914.
jimh...@my-deja.com
If you are so into logic and categories, you should know
that you need a theory of TRUTH before you can ask
questions like that.
jddde...@my-deja.com
Robert Low <rob...@coventry.ac.uk> wrote:
> jddescr...@my-deja.com wrote:
>
> > Is it possible to say anything in a General Theory of
> > Relativity (GTR) sense about how the Penrose twistors
> > space time curvature of particular massive objects?
>
> to study momentum and angular momentum in GR; see
Thanks for the reference.I had it in my library and after
looking at it I think the example I'm lookings for [to
understand how Twistors are expressed as Quaternions]
occurs on page 31 in expressing the Maxwell equation
GRAD_A,^A * PHI_ABCD = O.
Obviously my problems with the poor index uses and the fact
that everyone does it differently [nonspecificity of the
symbols ] are apparent. Why couldn't Dirac, Penrose, Berry,
Atiyah and Lounesto, as important examples, all have used
Hamilton's original terminology that he invested so much
effort into developing [ he called the whole quaternion
calculus = symbolical geometry ] instead of converting his
biquaternion methods into Dirac spinors, modules, twistors,
flag pole spinors,... and all the rest.
At least these scientists have made real science
description advances and aren't just the worthless French
grammarians we see so often in "modern" mathematics as
king's men followers of the bourbakians. I've now
identified the Cambridge Conspiracy as an intellectual
conspiracy far beyond the Cambridge Five scandals. What
they did to Heaviside and his methods for 50 years is still
going on with the Hamilton methods [ HV = Hamilton
Visualization ].
Thanks again. JD
-----------------------------------------------------------------------
Chris Hillman
On Sat, 5 Feb 2000 jddde...@my-deja.com wrote:
> Why couldn't Dirac, Penrose, Berry, Atiyah and Lounesto, as important
> examples, all have used Hamilton's original terminology that he
> invested so much effort into developing [ he called the whole
> quaternion calculus = symbolical geometry ] instead of converting his
> biquaternion methods into Dirac spinors, modules, twistors, flag pole
> spinors,... and all the rest.
Because Hamilton completely misunderstood the way in which quaternions
represent rotations in three-dimensional space. Once this is understood
correctly, the simplest notation which is faithful to the mathematical
facts is best. As it turns out, several notations seemed preferable to
different people in the early days, and these have become entrenched in
the literature. However, one thing you should realize is that some of the
ideas you mentioned above (e.g. modules) are connected to far more general
and extremely powerful theories in mathematics.
> At least these scientists have made real science description advances
> and aren't just the worthless French grammarians we see so often in
> "modern" mathematics as king's men followers of the bourbakians. I've
> now identified the Cambridge Conspiracy as an intellectual conspiracy
> far beyond the Cambridge Five scandals. What they did to Heaviside and
> his methods for 50 years is still going on with the Hamilton methods [
> HV = Hamilton Visualization ].
(LOL)
This is one of those priceless gems which makes reading these newsgroups
so amusing :-)
Chris Hillman
On Sun, 6 Feb 2000 jddde...@my-deja.com wrote:
> Thanks for the Twistor and General Theory of Relativity [GTR]
> references. I'm not trying to learn GTR since I'm still struggling on
> a complete understanding of SR and it seems too remote and
> speculative[black hole horizons with virtual photon leakage and such]
> from my interests.
Well, you obviously have little idea why astrophysicists have such
confidence in the reality of event horizons or how Hawking radiation
works, but I'd agree that if you are struggling with str you'd better not
try to think about gtr.
> I'm applying the Hamilton methods of biquaternions [the Hamilton
> Visualization = HV ]
Did you listen to word any of us were saying? Hamilton made a serious
conceptual error in the use of quaternions in representing rotations in
E^3 and then proceeded to go further and further wrong from there.
There is no such thing as "Hamilton visualization", btw, except in your
dreams.
> to human science description based on the happiness theories
> (philosophy) of Ayn Rand.
(LOL)
This newsgroup never ceases to amaze :-)
> Thus I was asking about a clear example of twistor symbol use in GTR
> rather than hoping to learn GTR.
Suggestion: if you are struggling with str, there is no way you are going
to be able to grasp what a spinor is, much less learn twistor theory.
The simplest nontrivial example of a spinors involves the representation
of the rotation group SO(3), the very thing which Hamilton got wrong!
> In another message you made a comment about Hamilton which makes me
> think that you may have been infected with an anti Hamilton pov by
> some of those who devalue the giant accomplishments he made. We would
> have to go into the reasons this happens but Pertti Lounesto once
> commented that it is often jealousy of child protegy accomplishments.
Actually, my comments were based upon knowledge of exactly what
quaternions (and spinor representations) are really all about, and
knowledge of the precise conceptual errors made by Hamilton. I know you
won't benefit from this reference, but for the benefit of others who will,
I'll mention the very clear article
Simon L. Altmann,
Hamilton, Rodrigues, and the Quaternion Scandal.
Math. Mag. 62 (1989), no. 5, 291--308.
> Hamilton is a fascinating case of real science genius because; 1)
> he was a child protegy and accomplished amazingly spectacular things
> before the age of 30.
Absolutely correct. Hamilton's reformulation of classical optics and then
classical mechanics is if anything -even more- important today than it was
in his own time, since it provides one of the very few mathematical
formalisms which applies to both classical and quantum physics.
> These were real objective physical science description advances and
> not phony balony language games like we see with memorizing
> mathematicians
Right, mathematicians other than Hamilton never think of anything
original, we just memorize what we read in textbooks :-)
> and 2) he recognized that there was a Cambridge Conspiracy designed by
> the king's men at Cambridge University [actually the BS = British
> Socialists in general like keynes ]
(ROFL)
Jd, you are a one creature -international resource-. When it comes to
unintentional comedy, you are a Citizen of the World!
William Rowan Hamilton (1805-1865)
John Maynard Keynes (1883-1946)
I guess Hamilton had available for his use either a time machine or a
crystal ball, eh?
> to monopolize the intellectual powers of science visualization. He
> realized they were exploiting his fantastic products and intent on
> keeping them out of the hands of average people like himself
Right, someone who has mastered reading and basic arithmetic by age four,
Latin, Greek, and Hebrew by age five, had written a Syrian grammar at age
twelve, had mastered Persian by fourteen, had mastered the mathematical
methods of Newton, Lagrange and Laplace by age sixteen, and wrote his
great paper on optics age seventeen--- yup, he sounds like an "average
person" to me too.
> particularly out on the fringes of the king's men rule like Ireland.
> Thus he withdrew his most important last 25 years of work from the
> Cambridge Conspiracy. He published and spoke mainly at Trinity
> College, Dublin from then on.
And John Maynard Keynes and the Cambridge Conspiracy are responsible for
The Great Depression, The Troubles, the Ascent of Winston Churchill,
Linear Algebra, Vector and Tensor Calculus, and Big Science, the Decline
of the Monarchy and the Readership of The Socialist Worker, two World
Wars, the downfall of Alger Hiss and the Evil Empire, the cancellation of
the Superconducting Supercollider, and the Assassination of Presidents
Lincoln and Kennedy, right? Did I leave anything out?
Oh, right, the fact that Ronald Reagan came down with the Disease That
Cannot Speak It's Name, yeah, they were responsible for that too.
> I'm guessing that you read one of the alibis by the Cambridge
> Conspiracy (CC) for what they did to suppress Hamilton's giant
> accomplishments. It's even worse than what they did for 50 years to
> the Heaviside methods. [Eventually they gave up that part of the
> conspiracy, changed the names to Laplace Transform and pretended that
> it never happened.]
No, we conspirators say that Laurent Schwartz is the man who turned
Heaviside's informal ideas concerning "generalized functions" into an
elegant mathematical theory, part of what is generally called functional
analysis.
The method of Laplace Transforms is indeed due to Laplace, but that's not
the same thing.
> An example that you might have seen is "Rotations, Quaternions and
> Double Groups" by S. L. Altmann.
As a matter of fact, I -have- read that book, yes.
Hmm... I guess this means you won't read the paper I cited, will you?
:-/
Too bad, since it's not hard to understand Hamilton's first fundamental
mistake. (He made others, but Altmann doesn't discuss those.)
> They have so covered up Hamilton's giant accomplishments in
> visualization that I recommend this book to people even though warning
> them that it is an alibi for the CC.
Would that be the Communist Cartel? Or the Cheerio Confederation?
> By carefully screening the material you can still learn some of
> Hamilton's breakthroughs.
Screening--- is that a pun? The optical plane and all that?
> Your comment that Hamilton was wrong and fixated on false methods is a
> mistake.
Oh dear me, I must be wrong, because I know so much mathematics I just
cannot understand how simple the world really is, right?
> As I study the relations of biquaternions to modern methods related to
> vectors, matricies, tensors, spinors, twistors, modules, flag spinors,
> octonions.....I find that all the powers of these methids were
> developed by Hamilton and every space, every object in a space, and
> every operator on the objects has an explicit visualization picture
> which is understandable at the level of grade school geometry by me
> and my kids and their kids. {It turns out to be mainly circle pictures
> in complex projective planes as stereo projections from the Hamilton
> Sphere (HS)!}
Well, duh! That's exactly what I explained in my own postings years ago
to this newsgroup. And it's the -Riemann- sphere. Aka the complex
-line-, CP^1, not the complex projective -plane-, CP^2.
"Grade school geometry" (is there such a thing?) is overstating the case,
though. But certainly a correct modern understanding of quaternions,
spinors, and the rest is well within reach of a good undergraduate
student.
> Incidentally, Hamilton invested the last 25 years of his works to
> documenting Symbolical Geometry [his term] in very simple terms so you
> don't need to take my word for any of these claims. See "Elements of
> Quaternions", William Rowan Hamilton two volume set completed at his
> death in 1865. He starts with the careful meaning of negative numbers.
And I guess that's about as far as you got, eh? And mathematics hasn't
made one iota of progress since 1865, correct?
Hamilton unfortunately based his book upon several -fundamental-
conceptual errors which he never overcame. (Exhibit two: how do you
differentiate a function of one quaternion variable? This is not so easy
to answer, and even today most nonmathematicians don't understand the
importance of even -asking- this question.) Despite Hamilton's brilliant
mathematical insights in other areas, when it comes to quaternions the
simple truth is that Gauss, who discovered quaternions a decade -before-
Hamilton, understood them far better than he did.
Hamilton is a very curious case--- he really did make unparalleled
contributions to mathematical physics as a very young man, and eventually
produced his greatest work (Hamiltonian mechanics) in 1835.
Unfortunately, after his discovery of quaternions and their law of
multiplication in 1843, he then slowly and steadily declined in his
intellectual powers until 1850 or so, he was basically a crank---
something which was clear to many of his contemporaries, such as Josiah
Willard Gibbs. This decline may have been due to his losing battle with
alcoholism, or perhaps that was merely another symptom of his general
mental and physical decline.
Chris Hillman
On Sun, 6 Feb 2000 jddde...@my-deja.com wrote:
> In article <Pine.OSF.4.21.0002051454160.30469-
> 100...@goedel1.math.washington.edu>,
> Chris Hillman <hil...@math.washington.edu> wrote:
>
> > On Sat, 5 Feb 2000 jddde...@my-deja.com wrote:
> >
> > > Why couldn't Dirac, Penrose, Berry, Atiyah and Lounesto, as
> > > important
> > > examples, all have used Hamilton's original terminology that he
> > > invested so much effort into developing [ he called the whole
> > > quaternion calculus = symbolical geometry ] instead of converting
> > > his
> > > biquaternion methods into Dirac spinors, modules, twistors, flag
> > > pole
> > > spinors,... and all the rest.
>
> > Because Hamilton completely misunderstood the way in which
> > quaternions represent rotations in three-dimensional space.
>
> ---------------------------------------------------------------------
>
> Please! You actually believe this is possible?
>
> ---------------------------------------------------------------------
No, of course not. I just sometimes get these weird urges to DENEGRATE
THE DIGINITY OF THE OFFICE OF THE PRESIDENCY!
> > > At least these scientists have made real science description
> > > advances
> > > and aren't just the worthless French grammarians we see so often in
> > > "modern" mathematics as king's men followers of the bourbakians.
> > > I've
> > > now identified the Cambridge Conspiracy as an intellectual
> > > conspiracy
> > > far beyond the Cambridge Five scandals. What they did to Heaviside
> > > and
> > > his methods for 50 years is still going on with the Hamilton
> > > methods [
> > > HV = Hamilton Visualization ].
>
> > (LOL)
> >
> > This is one of those priceless gems which makes reading
> > these newsgroups > so amusing :-)
>
> ---------------------------------------------------------------------
>
> If LOL means Love Of Life thanks for the inspiration
> since it makes me think of the DECLARATION!
The Declaration of Independence? You mean the Cambridge Five were
responsible for -that too-?!!
> I'm afraid I must tell you that it is you and those who share your
> opinion, who don't understand the rotations in 3D space that Hamilton
> used as the basis for his calculus.
Oh, pardon me. You are RIGHT. jd, I AGREE WITH YOU! Clearly, we
mathematicians need to go back to 1865 and START ALL OVER AGAIN. We need
to STOP JOHN WILKES BOOTH. If we can do that, FDR WILL NEVER BECOME
PRESIDENT!!! It'll be LINCOLNS ALL THE WAY DOWN!
> I mentioned Heaviside above and although he was a great scientist and
> made foundational advances in physical description , particularly in
> extending the Maxwell description of electromagnetics, he made a
> similar mistake to you. This was followed by Gibbs to some extent when
> he translated the Hamilton methods into Vector Analysis.
Yarr, I can't seem to do anything right, ever since I lent J.W.B. my
derringer. And forgot to take out the bullets first.
> Heaviside couldn't figure out why the repeating product or A^2 is
> negative thus showing the same mistake that you make only expressed
> differently. It's why Heaviside also didn't continue the Maxwell
> derivations in quaternions where everything is very physically simple.
> I wonder how widespread your error is?
Its the FREAKIN CAMBRIDGE CONSPIRACY, for Chrissake! And you're asking
how WIDESPREAD it is?! If I told you THAT, we wouldn't have a CONSPIRACY
anymore, would we, now?!
> When Tait saw what Vector Analysis had done to the HV [Hamilton
> Visualization] he called it an "hermorphadite monster" [maybe this was
> the first use of the French grammar in math!?]. Where does that put
> you I wonder?
You mean I didn't make the Cambridge Five?
> The Hamilton rotation in 3 D space is not a planar
> rotation except in singular cases. Rather, it is a
> conical rotation. Hamilton is not, fundamentally,
> rotating a displacment "vector" in a plane. He is
> rotating a conical operator(cone operator) in three
> dimensions. This is why each of his base "vectors"
> [he is the one who defined the term originally] is
> the square root of a reflection (minus one stretcher).
> Are you familiar with his discoveries of conical
> refraction in biaxial crystals following his
> development of the HAMILTONIAN characterisic
> function, before the age of 30? He discovered it
> mentally(visually), predicted the experimental
> validation of the theory and then his colleague at
> Trinity demonstrated it experimentally.
>
> Does your present discovery, which you experience
> as you read this, give you some idea of the size
> of the CC [Cambridge Conspiracy] cover up?
Oh, wow, gosh, yeah, I can see that WE HAVE BEEN VERY, VERY BAD.
We are so ASHAMED of us.
> Incidentally, these facts about the visual meaning of quaternions is
> why the HV is so powerful relative to the Berry Phase rediscoveries of
> the ways Hamilton compounds physical operations in a quantum mechanics
> context. Of course, your meaning of planar rotation can be done with
> quaternions but it is a contorted, double process. See some of Pertti
> Lounesto's recent expressions for rotating a planar "vector" expressed
> in Clifford symbology.
We have been very, very, very bad. And we are SO ASHAMED.
> The method that Hamilton used is not just some chance discovery. He
> spent many long years setting up the calculus so that most of the
> geometric properties of the Euler use of C#s applies directly with
> care in sequencing and associating. Visually it loses no meaning
> simplicity compared to the Euler relations.
>
> Good seeing.
First you have to take your head out of the place where you have jammed
it.
Hmm... you've got it pretty far up in there...
Hey, anybody remember where we left the Head Extractor?!
jddde...@my-deja.com
>
> > Is it possible to say anything in a General Theory of
> > Relativity (GTR) sense about how the Penrose twistors
> > are compounded spinors
>
> Urk...
>
> > and how they characterize the space time curvature of particular
> > massive objects?
>
strong
> background in graduate math and physics, including real analysis,
> integration theory, integral transforms, representation theory,
complex
> analysis, algebra and geometry of the Moebius group, Lie groups, and
> semi-Riemannian geometry and curvature of connections a la Cartan on
the
> mathematical side, and a mastery of str, gtr, spinors and the spinor
> formalism for gtr (cf. the Petrov classification) and Yang-Mills
theories
> on the physical side.
>
> If you have a strong background, you can start by reading
>
> Huggett and Tod
Thanks for the Twistor and General Theory of Relativity
[GTR] references. I'm not trying to learn GTR since I'm
still struggling on a complete understanding of SR and
it seems too remote and speculative[black hole horizons
with virtual photon leakage and such] from my interests.
I'm applying the Hamilton methods of biquaternions
[the Hamilton Visualization = HV ] to human science
description based on the happiness theories (philosophy)
of Ayn Rand. Thus I was asking about a clear example of
twistor symbol use in GTR rather than hoping to learn GTR.
In another message you made a comment about Hamilton
which makes me think that you may have been infected
with an anti Hamilton pov by some of those who devalue
the giant accomplishments he made. We would have to go
into the reasons this happens but Pertti Lounesto once
commented that it is often jealousy of child protegy
accomplishments. I call such actions king's greed [ if
i'm so smart why aren't i king? ]. Hamilton is a
fascinating case of real science genius because; 1) he
was a child protegy and accomplished amazingly
spectacular things before the age of 30. These were real
objective physical science description advances and not
phony balony language games like we see with memorizing
mathematicians and 2) he recognized that there was a
Cambridge Conspiracy designed by the king's men at
Cambridge University [actually the BS = British Socialists
in general like keynes ] to monopolize the intellectual
powers of science visualization. He realized they were
exploiting his fantastic products and intent on keeping
them out of the hands of average people like himself
particularly out on the fringes of the king's men rule
like Ireland. Thus he withdrew his most important last
25 years of work from the Cambridge Conspiracy. He published
and spoke mainly at Trinity College, Dublin from then on.
I'm guessing that you read one of the alibis by the
Cambridge Conspiracy (CC) for what they did to suppress
Hamilton's giant accomplishments. It's even worse than
what they did for 50 years to the Heaviside methods.
[Eventually they gave up that part of the conspiracy,
changed the names to Laplace Transform and pretended
that it never happened.] An example that you might have
seen is "Rotations, Quaternions and Double Groups" by
S. L. Altmann. They have so covered up Hamilton's giant
accomplishments in visualization that I recommend this
book to people even though warning them that it is an
alibi for the CC. By carefully screening the material
you can still learn some of Hamilton's breakthroughs.
Your comment that Hamilton was wrong and fixated on
false methods is a mistake. As I study the relations
of biquaternions to modern methods related to vectors,
matricies, tensors, spinors, twistors, modules, flag
spinors, octonions.....I find that all the powers of
these methids were developed by Hamilton and every space,
every object in a space, and every operator on the
objects has an explicit visualization picture which is
understandable at the level of grade school geometry by
me and my kids and their kids. {It turns out to be mainly
circle pictures in complex projective planes as stereo
projections from the Hamilton Sphere (HS)!}
Incidentally, Hamilton invested the last 25 years of
his works to documenting Symbolical Geometry [his term]
in very simple terms so you don't need to take my word
for any of these claims. See "Elements of Quaternions",
William Rowan Hamilton two volume set completed at his
death in 1865. He starts with the careful meaning of
negative numbers.
Thanks again.
Good seeing. JD
jddde...@my-deja.com
>
> On Sat, 5 Feb 2000 jddde...@my-deja.com wrote:
>
> > Why couldn't Dirac, Penrose, Berry, Atiyah and Lounesto, as
important
> > examples, all have used Hamilton's original terminology that he
> > invested so much effort into developing [ he called the whole
> > quaternion calculus = symbolical geometry ] instead of converting
his
> > biquaternion methods into Dirac spinors, modules, twistors, flag
pole
> > spinors,... and all the rest.
>
> Because Hamilton completely misunderstood the way in which quaternions
> represent rotations in three-dimensional space.
---------------------------------------------------------------------
Please! You actually believe this is possible?
---------------------------------------------------------------------
Once this is understood
> correctly, the simplest notation which is faithful to the mathematical
> facts is best. As it turns out, several notations seemed preferable
to
> different people in the early days, and these have become entrenched
in
> the literature. However, one thing you should realize is that some
of the
> ideas you mentioned above (e.g. modules) are connected to far more
general
> and extremely powerful theories in mathematics.
>
> > At least these scientists have made real science description
advances
> > and aren't just the worthless French grammarians we see so often in
> > "modern" mathematics as king's men followers of the bourbakians.
I've
> > now identified the Cambridge Conspiracy as an intellectual
conspiracy
> > far beyond the Cambridge Five scandals. What they did to Heaviside
and
> > his methods for 50 years is still going on with the Hamilton
methods [
> > HV = Hamilton Visualization ].
>
> (LOL)
>
> This is one of those priceless gems which makes reading these
newsgroups
> so amusing :-)
>
> Chris Hillman
>
> Home Page: http://www.math.washington.edu/~hillman/personal.html
>
>
---------------------------------------------------------------------
If LOL means Love Of Life thanks for the inspiration
since it makes me think of the DECLARATION!
I'm afraid I must tell you that it is you and those
who share your opinion, who don't understand the
rotations in 3D space that Hamilton used as the basis
for his calculus. I mentioned Heaviside above and
although he was a great scientist and made foundational
advances in physical description , particularly in
extending the Maxwell description of electromagnetics,
he made a similar mistake to you. This was followed by
Gibbs to some extent when he translated the Hamilton
methods into Vector Analysis. Heaviside couldn't figure
out why the repeating product or A^2 is negative thus
showing the same mistake that you make only expressed
differently. It's why Heaviside also didn't continue
the Maxwell derivations in quaternions where everything
is very physically simple. I wonder how widespread your
error is? When Tait saw what Vector Analysis had done
to the HV [Hamilton Visualization] he called it an
"hermorphadite monster" [maybe this was the first use of
the French grammar in math!?]. Where does that put
you I wonder?
The Hamilton rotation in 3 D space is not a planar
rotation except in singular cases. Rather, it is a
conical rotation. Hamilton is not, fundamentally,
rotating a displacment "vector" in a plane. He is
rotating a conical operator(cone operator) in three
dimensions. This is why each of his base "vectors"
[he is the one who defined the term originally] is
the square root of a reflection (minus one stretcher).
Are you familiar with his discoveries of conical
refraction in biaxial crystals following his
development of the HAMILTONIAN characterisic
function, before the age of 30? He discovered it
mentally(visually), predicted the experimental
validation of the theory and then his colleague at
Trinity demonstrated it experimentally.
Does your present discovery, which you experience
as you read this, give you some idea of the size
of the CC [Cambridge Conspiracy] cover up?
Incidentally, these facts about the visual meaning
of quaternions is why the HV is so powerful relative
to the Berry Phase rediscoveries of the ways
Hamilton compounds physical operations in a quantum
mechanics context. Of course, your meaning of planar
rotation can be done with quaternions but it is a
contorted, double process. See some of Pertti
Lounesto's recent expressions for rotating a planar
"vector" expressed in Clifford symbology.
The method that Hamilton used is not just some chance
discovery. He spent many long years setting up the
calculus so that most of the geometric properties of
the Euler use of C#s applies directly with care in
sequencing and associating. Visually it loses no
meaning simplicity compared to the Euler relations.
Good seeing. JD
Pertti Lounesto
> Actually, my comments were based upon knowledge of exactly what
> quaternions (and spinor representations) are really all about, and
> knowledge of the precise conceptual errors made by Hamilton. I know you
> won't benefit from this reference, but for the benefit of others who will,
> I'll mention the very clear article
>
> Simon L. Altmann,
> Hamilton, Rodrigues, and the Quaternion Scandal.
> Math. Mag. 62 (1989), no. 5, 291--308.
The author brings brings his point of view better forth in the book
S.L. Altmann: Rotations, Quaternions, and Double Groups,
Oxford University Press, Oxford, 1986.
It should be emphasized though that Hamilton's misinterpretation
was first discussed by Marcel Riesz, in 1958, see page 21 of his
book "Clifford numbers and spinors", Kluwer 1993 (reprint of
1958), see publisher's URL:
http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-2299-1
Hamilton's misinterpretation indeed occurred, but it is rather a
matter of emphasize, probably a simplification he made in order
to conform to intellectual limitations of his students (Hamilton
lectured quaternions several years for classes of 50 students).
Hamilton considered rotations of R^3 in the special case, when
the vector r, in R^3, to be rotated is orthogonal to the axis of
rotation, say u in R^3; Hamilton wrote r -> pr, where
p = cos(alpha) + u sin(alpha)
and alpha is the angle of rotation. Hamilton did found the
so-called conical representation of rotations, as r -> qr/q, where
q = cos(alpha/2) + u sin(alpha/2)
(p = q^2) as Cayley admitted in his paper of 1845, when the
result was first published.
> But certainly a correct modern understanding of quaternions,
> spinors, and the rest is well within reach of a good undergraduate
> student.
I agree. The main obstacle is the doctrine of traditional syllabus.
However, an openminded teacher might well be able to teach
quaternions, in a modern approach, using my book, and the
relevant chapter on quaternions, as a textbook, see the URL
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
> > Incidentally, Hamilton invested the last 25 years of his works to
> > documenting Symbolical Geometry [his term] in very simple terms so you
> > don't need to take my word for any of these claims. See "Elements of
> > Quaternions", William Rowan Hamilton two volume set completed at his
> > death in 1865. He starts with the careful meaning of negative numbers.
>
> And I guess that's about as far as you got, eh? And mathematics hasn't
> made one iota of progress since 1865, correct?
>
> Hamilton unfortunately based his book upon several -fundamental-
> conceptual errors which he never overcame. (Exhibit two: how do you
> differentiate a function of one quaternion variable?
No. Hamilton did not make errors about differentiating a
quaternion valued function of a quaternion variable. Instead,
Hamilton invented Hamilton's operator, called today nabla,
nabla = id/dx + jd/dy +kd/dz.
> This is not so easy
> to answer, and even today most nonmathematicians don't understand the
> importance of even -asking- this question.)
Right, that is not an easy question. In fact, differentiation of
complex analytic functions has five different generalization to
quaternion functions; for a complete discussion, see the Section
5.8 "Function theory of quaternion variables", pages 74-76, of
my book "Clifford algebras and spinors", CUP, 1997/98, URL
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
> Despite Hamilton's brilliant
> mathematical insights in other areas, when it comes to quaternions the
> simple truth is that Gauss, who discovered quaternions a decade -before-
> Hamilton, understood them far better than he did.
No. Among Gauss' posthumous papers there was a five-line
note about linear factorization of a product of two quadratic
sums, similar to the corresponding complex number formula
(x^2+y^2)(u^2+v^2) = (xu-yv)^2+(xv+yu)^2. Nothing else.
That hardly amounts to 'understanding quaternions'.
> Hamilton is a very curious case--- he really did make unparalleled
> contributions to mathematical physics as a very young man, and eventually
> produced his greatest work (Hamiltonian mechanics) in 1835.
> Unfortunately, after his discovery of quaternions and their law of
> multiplication in 1843, he then slowly and steadily declined in his
> intellectual powers until 1850 or so, he was basically a crank---
> something which was clear to many of his contemporaries, such as Josiah
> Willard Gibbs.
Evidently, you have not read Hamilton's posthumous "Elements of
Quaternions", but only express a sevond-hand opinion. Your
remark about Gibbs shows that you have not read Gibbs' book
of 1901 or his student's lecture notes of 1881-84.
Chris Hillman
On Sun, 6 Feb 2000, Pertti Lounesto wrote:
> Chris Hillman wrote:
>
> > Actually, my comments were based upon knowledge of exactly what
> > quaternions (and spinor representations) are really all about, and
> > knowledge of the precise conceptual errors made by Hamilton. I know you
> > won't benefit from this reference, but for the benefit of others who will,
> > I'll mention the very clear article
> >
> > Simon L. Altmann,
> > Hamilton, Rodrigues, and the Quaternion Scandal.
> > Math. Mag. 62 (1989), no. 5, 291--308.
>
> The author brings brings his point of view better forth in the book
>
> S.L. Altmann: Rotations, Quaternions, and Double Groups,
> Oxford University Press, Oxford, 1986.
The article is a lot shorter than the book :-)
> It should be emphasized though that Hamilton's misinterpretation
> was first discussed by Marcel Riesz, in 1958, see page 21 of his
> book "Clifford numbers and spinors", Kluwer 1993 (reprint of
> 1958), see publisher's URL:
>
> http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-2299-1
>
> Hamilton's misinterpretation indeed occurred, but it is rather a
> matter of emphasize, probably a simplification he made in order
> to conform to intellectual limitations of his students (Hamilton
> lectured quaternions several years for classes of 50 students).
Hmm...
> Hamilton considered rotations of R^3 in the special case, when
> the vector r, in R^3, to be rotated is orthogonal to the axis of
> rotation, say u in R^3; Hamilton wrote r -> pr, where
>
> p = cos(alpha) + u sin(alpha)
>
> and alpha is the angle of rotation.
Which is not the "right way" to think about it.
> Hamilton did found the so-called conical representation of rotations,
> as r -> qr/q, where
>
> q = cos(alpha/2) + u sin(alpha/2)
>
> (p = q^2) as Cayley admitted in his paper of 1845, when the
> result was first published.
OK, I stand corrected on this. For readers who followed the "night sky
thread" some years back, this is equivalent to what I wrote as
X -> Q X Q^(-1)
where X is a Hermitian matrix and Q is an element of SU(2).
> > Hamilton unfortunately based his book upon several -fundamental-
> > conceptual errors which he never overcame. (Exhibit two: how do you
> > differentiate a function of one quaternion variable?
>
> No. Hamilton did not make errors about differentiating a
> quaternion valued function of a quaternion variable. Instead,
> Hamilton invented Hamilton's operator, called today nabla,
>
> nabla = id/dx + jd/dy +kd/dz.
Hmm... maybe my memory failed me, but I thought I read somewhere (maybe in
Ahlfors' book?) that Hamilton had been confused about differentiation wrt
a quaternionic variable. If I recall incorrectly and Hamilton -realized-
he was confused, well, that makes him look a lot better, I agree.
> > This is not so easy
> > to answer, and even today most nonmathematicians don't understand the
> > importance of even -asking- this question.)
>
> Right, that is not an easy question. In fact, differentiation of
> complex analytic functions has five different generalization to
> quaternion functions; for a complete discussion, see the Section
> 5.8 "Function theory of quaternion variables", pages 74-76, of
> my book "Clifford algebras and spinors", CUP, 1997/98, URL
> http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
>
> > Despite Hamilton's brilliant
> > mathematical insights in other areas, when it comes to quaternions the
> > simple truth is that Gauss, who discovered quaternions a decade -before-
> > Hamilton, understood them far better than he did.
>
> No. Among Gauss' posthumous papers there was a five-line
> note about linear factorization of a product of two quadratic
> sums, similar to the corresponding complex number formula
> (x^2+y^2)(u^2+v^2) = (xu-yv)^2+(xv+yu)^2. Nothing else.
> That hardly amounts to 'understanding quaternions'.
If I find time I'll try to look up the reason by people think Gauss knew
about quaternions. I believe this might be in one of Van Der Waerden's
books on algebra or the book by Weyl on the history of number theory. My
recollection is that Gauss -explicitly- wrote down the formulae found by
Olinde Rodrigues for the composition of rotations (in Euler angle
notation) and also wrote down a more complicated quadratic factorization
than the one you quoted. My recollection is also that Gauss definitely
wrote down the (x,y) notation for complex numbers before Hamilton did.
But until I can give explicit references, I'll have to let your statement
stand unchallenged. The above paragraph is a summary of my recollection
of various things I've read.
> Evidently, you have not read Hamilton's posthumous "Elements of
> Quaternions", but only express a sevond-hand opinion.
I looked at it last year.
> Your remark about Gibbs shows that you have not read Gibbs' book of
> 1901 or his student's lecture notes of 1881-84.
I read that too -last year-! My memory is not perfect but I don't
think its all -that- bad!
Someone has taken the trouble to LaTeX all of Hamilton's papers on
quaternions AND Gibbs lecture notes on linear algebra and vector
calculus--- poke around on the web; I've lost the url. Anyone interested
can find these things and read them for himself. It makes very
interesting reading!
I found Hamilton to be very confused writer and Gibbs to be a very clear
writer. Whenever I find A to be a very confused writer about subject X
and B to be a very clear writer about the same subject, I generally
conclude that B understands subject X and A does not. I admit that this
rule of thumb is not infallible (cf. Grassmann's writings), and obviously
I came to a completely different conclusion than Pertti about the relative
merits of their work on what we'd now call vector calculus. Since Pertti
obviously knows more about this stuff than I do (although I think I know
alot more than most people), I guess I'll have to let his statements stand
unless I can find the time to try to make a detailed argument to the
contrary, quoting from the original monographs (which as I say I have back
home in a box somewhere).
Peter Willard
This is just to say that these posts work better if you replace
"Hamilton" with "Hillman". HTH!
--
Peter Willard
www.drizzle.com/~petew
"Rarely is the question asked - is our children learning?"
George W. Bush (London Telegraph,2/4/2000)
jdescript
<Pertti....@hit.fi> wrote: the comments with one(1) mark(>)
--------------------------------------------------------------
>>Chris Hillman wrote: the comments with two(2) marks (>>)
>> Actually, my comments were based upon knowledge of exactly
what
>> quaternions (and spinor representations) are really all
about, and
>> knowledge of the precise conceptual errors made by Hamilton.
I know you
>> won't benefit from this reference, but for the benefit of
others who will,
>> I'll mention the very clear article
>>
>> Simon L. Altmann,
>> Hamilton, Rodrigues, and the Quaternion Scandal.
>> Math. Mag. 62 (1989), no. 5, 291--308.
---------------------------------------------------------------
>The author brings brings his point of view better forth in the
book
>
>S.L. Altmann: Rotations, Quaternions, and Double Groups,
>Oxford University Press, Oxford, 1986.
>
>It should be emphasized though that Hamilton's misinterpretation
>was first discussed by Marcel Riesz, in 1958, see page 21 of his
>book "Clifford numbers and spinors", Kluwer 1993 (reprint of
>1958), see publisher's URL:
>
>http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-
2299-1
>
>Hamilton's misinterpretation indeed occurred, but it is rather a
>matter of emphasize, probably a simplification he made in order
>to conform to intellectual limitations of his students (Hamilton
>lectured quaternions several years for classes of 50 students).
>
>Hamilton considered rotations of R^3 in the special case, when
>the vector r, in R^3, to be rotated is orthogonal to the axis of
>rotation, say u in R^3; Hamilton wrote r -> pr, where
>
> p = cos(alpha) + u sin(alpha)
>
>and alpha is the angle of rotation. Hamilton did found the
>so-called conical representation of rotations, as r -> qr/q,
where
>
> q = cos(alpha/2) + u sin(alpha/2)
>
>(p = q^2) as Cayley admitted in his paper of 1845, when the
>result was first published.
>
---------------------------------------------------------------
Certainly your scientific comments are correct. There are a
number of ways to represent biquaternionic operations directly,
as squares, as square roots and such depending on the objective
of the symbology. You have commented on the square root forms
before in a Clifford context. Having said that and not arguing
about whether Hamilton meant conical rotations or planar
rotations as the base operation of his calculus we are talking
about one of the greatest physical scientists in the history of
the world, NO?
How can anyone say ? :
>>Because Hamilton completely misunderstood the way in which
>>quaternions represent rotations in three-dimensional space.
--------------------------------------------------------------
>>>Please! You actually believe this is possible?
was my response to such naivity.
I need to obtain the book by Riesz that you contributed to in a
republication but the historical timing seems strange when you
say that he discovered the "misunderstanding" 100 years after
Hamilton's first publication. This was after years of
publication of detailed extensions of the theories by Tait and a
number of others. There were a number of college texts written
also. I'm sure you know the history and although there was a
massive cover up there still were many people, even in America,
[not Gibbs] who appreciated what Hamilton had done. Does it make
sense that no one but Riesz and Altman could figure out
this "misunderstanding" during all those studies and expositions
over 100 (one hundred) years?
Incidentally, in the book you reference Bolindger from Sweden
also contributed. He has done some brilliant work on direct
applications of the Hamilton type methods to polarization sphere
representations and transformations [polarization fork etc.]
Very powerful!Have you done any similar EM applications anywhere?
Good seeing. JD
---------------------------------------------------------------
>> But certainly a correct modern understanding of quaternions,
>> spinors, and the rest is well within reach of a good
undergraduate
>> student.
>
>I agree. The main obstacle is the doctrine of traditional
syllabus.
>However, an openminded teacher might well be able to teach
>quaternions, in a modern approach, using my book, and the
>relevant chapter on quaternions, as a textbook, see the URL
>http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
>
>> > Incidentally, Hamilton invested the last 25 years of his
works to
>> > documenting Symbolical Geometry [his term] in very simple
terms so you
>> > don't need to take my word for any of these claims.
See "Elements of
>> > Quaternions", William Rowan Hamilton two volume set
completed at his
>> > death in 1865. He starts with the careful meaning of
negative numbers.
>>
>> And I guess that's about as far as you got, eh? And
mathematics hasn't
>> made one iota of progress since 1865, correct?
>>
>> Hamilton unfortunately based his book upon several -
fundamental-
>> conceptual errors which he never overcame. (Exhibit two: how
do you
>> differentiate a function of one quaternion variable?
>
>No. Hamilton did not make errors about differentiating a
>quaternion valued function of a quaternion variable. Instead,
>Hamilton invented Hamilton's operator, called today nabla,
>
> nabla = id/dx + jd/dy +kd/dz.
>
>> This is not so easy
>> to answer, and even today most nonmathematicians don't
understand the
>> importance of even -asking- this question.)
>
>Right, that is not an easy question. In fact, differentiation
of
>complex analytic functions has five different generalization to
>quaternion functions; for a complete discussion, see the Section
>5.8 "Function theory of quaternion variables", pages 74-76, of
>my book "Clifford algebras and spinors", CUP, 1997/98, URL
>http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164.
>
>> Despite Hamilton's brilliant
>> mathematical insights in other areas, when it comes to
quaternions the
>> simple truth is that Gauss, who discovered quaternions a
decade -before-
>> Hamilton, understood them far better than he did.
>
>No. Among Gauss' posthumous papers there was a five-line
>note about linear factorization of a product of two quadratic
>sums, similar to the corresponding complex number formula
>(x^2+y^2)(u^2+v^2) = (xu-yv)^2+(xv+yu)^2. Nothing else.
>That hardly amounts to 'understanding quaternions'.
>
>> Hamilton is a very curious case--- he really did make
unparalleled
>> contributions to mathematical physics as a very young man,
and eventually
>> produced his greatest work (Hamiltonian mechanics) in 1835.
>> Unfortunately, after his discovery of quaternions and their
law of
>> multiplication in 1843, he then slowly and steadily declined
in his
>> intellectual powers until 1850 or so, he was basically a
crank---
>> something which was clear to many of his contemporaries, such
as Josiah
>> Willard Gibbs.
>
>Evidently, you have not read Hamilton's posthumous "Elements of
>Quaternions", but only express a sevond-hand opinion. Your
>remark about Gibbs shows that you have not read Gibbs' book
>of 1901 or his student's lecture notes of 1881-84.
>
>
>
* Sent from RemarQ http://www.remarq.com The Internet's Discussion Network *
The fastest and easiest way to search and participate in Usenet - Free!
jddde...@my-deja.com
You surprise me! I expected that you would either degrade
the Hamilton symbolical geometry accomplishments as
1) nonsense to be laughed auf or 2) old stuff that you had
invented many years previously. I didn't expect that you
would do both simultaneously!
-----------------------------------------------------------------------
>Oh dear me, I must be wrong, because I know so much mathematics I just
>cannot understand how simple the world really is, right?
> >As I study the relations of biquaternions to modern methods related
> >to vectors, matricies, tensors, spinors, twistors, modules, flag
> >spinors, octonions.....I find that all the powers of these methids
> >were developed by Hamilton and every space, every object in a space,
> >and every operator on the objects has an explicit visualization
> >picture which is understandable at the level of grade school
> > geometry by me and my kids and their kids. {It turns out to be
> >mainly circle pictures in complex projective planes as stereo
> >projections from the Hamilton Sphere (HS)!}
>Well, duh! That's exactly what I explained in my own postings years
>ago to this newsgroup. And it's the -Riemann- sphere. Aka the complex
-----------------------------------------------------------------------
Interesting! the scientific meaning of the Hamilton quaternion calculus
is a big mistake; it's all garbage and you invented it! Beautiful!
----------------------------------------------------------------------
Let me summarize the situation. If you knew even a small fraction
of what you THINK you know it would be a spectacular show.
It's why I accurately called you and your opinions about science
"the NAIVE NEW-AGER" many posts ago.
Your historical knowledge is also badly lacking. I guess I shouldn't
have expected that you had any knowledge of the secret socialist club
at Cambridge [ going back forever but only exposed to the world with
the socialist spy revelations about why kids like me had to try to hide
under the schoolroom desk to survive the ablast attacks ] where all
the Cambridge Five were spawned, unless you were there also? You
probably don't know that Rothschild has been exposed as not only
one of the Lordly members of the club along with keynes but the
biggest spy of the Cambridge Five.
----------------------------------------------------------------------
>
> John Maynard Keynes (1883-1946)
>
> I guess Hamilton had available for his use either a time machine or a
> crystal ball, eh?
>
-------------excerpted, see original-----------------------------------
> > to monopolize the intellectual powers of science visualization. He
> > realized they were exploiting his fantastic products and intent on
> > keeping them out of the hands of average people like himself
>
-------------excerpted, see original---------------------------------
> > particularly out on the fringes of the king's men rule like Ireland.
> > Thus he withdrew his most important last 25 years of work from the
> > Cambridge Conspiracy. He published and spoke mainly at Trinity
> > College, Dublin from then on.
>
> And John Maynard Keynes and the Cambridge Conspiracy are responsible
for
> The Great Depression, The Troubles, the Ascent of Winston Churchill,
> Linear Algebra, Vector and Tensor Calculus, and Big Science, the
Decline
> of the Monarchy and the Readership of The Socialist Worker, two World
> Wars, the downfall of Alger Hiss and the Evil Empire, the
cancellation of
> the Superconducting Supercollider, and the Assassination of Presidents
> Lincoln and Kennedy, right? Did I leave anything out?
>
> Oh, right, the fact that Ronald Reagan came down with the Disease That
> Cannot Speak It's Name, yeah, they were responsible for that too.
>
> > I'm guessing that you read one of the alibis by the Cambridge
> > Conspiracy (CC) for what they did to suppress Hamilton's giant
> > accomplishments. It's even worse than what they did for 50 years to
> > the Heaviside methods. [Eventually they gave up that part of the
> > conspiracy, changed the names to Laplace Transform and pretended
that
> > it never happened.]
>
------------excerpted, see original-------------------------------
Good seeing. JD
Pertti Lounesto
> [cut]
Hamilton wanted to develop a pedagogical approach to
quaternions, and so he deduced the multiplication rules of
quaternions, from his definition of a quaternion as a
quotient of two vectors. This lead him to prefer planar
rotations over conical rotations. And this preference
probably slowed down the acceptance and progress of
quaternions.
Of course, the first to correct Hamilton's mixture of
vectors and bivectors, was Clifford, who presented
the quaternions units i,j,k as products of vectors (not
sitting in the space spanned by i,j,k). But, Clifford did
not emphasize that Hamilton was mistake; such explicit
mentioning of a mistake was written down by M. Riesz.
Of course, Altmann is much clearer and gemetrical than
Riesz, in explaining Hamilton's unfortunate emphasize on
planar rotations.
> Olinde Rodrigues for the composition of rotations
In some sense, Olinde Rodrigues found the spinor
representation of rotaions, in 1840, when he realized
that the half-angle appears in composition of rotations.
> My recollection is also that Gauss definitely
> wrote down the (x,y) notation for complex numbers before Hamilton did.
One could say that Argand placed complex numbers into
the xy-plane before Gauss (Wessel only interpreted i =
sqrt(-1) as a rotation by 90 degrees). But it was Hamilton,
who in (1833) 1835, 1837 wrote a series of papers, where
he began systematic study of complex numbers by
representing them as pairs of complex numbers.
> > Evidently, you have not read Hamilton's posthumous "Elements
> > of Quaternions", but only express a second-hand opinion.
>
> I looked at it last year.
That is good. Hamilton is thourough, and presents a wealth of
new ideas, theories, all in quaternion formalism. The book is
a bit difficult to read, before one is accustomed to the notation,
S(ab) = -a.b and V(ab) = axb, out of which Gibbs extracted his
notations for the scalar product and vector/cross product.
> > Your remark about Gibbs shows that you have not read Gibbs' book of
> > 1901 or his student's lecture notes of 1881-84.
>
> I read that too -last year-! My memory is not perfect but I don't
> think its all -that- bad!
Very good! Gibbs was a great teacher. In particular, he
realized that it is not good to speak to students about the
sums of scalars and vectors, or the formula ab = -a.b+axb.
Almost all ideas and notations of Gibbs are still in use,
expect his dyadic product (nowadays written as a matrix
product of a column vector and a row vector).
jdescript wrote:
> we are talking about one of the greatest physical scientists
> in the history
No doubt. Hamilton's name appers, in two ways, in the
Hamilton operator (nowadays the other is called the Dirac
operator, alhtough the basic idea is Hamilton's).
> I need to obtain the book by Riesz that you contributed to in a
> republication but the historical timing seems strange when you
> say that he discovered the "misunderstanding" 100 years after
> Hamilton's first publication.
Clifford already straightened up Hamilton's misinterpretation
of rotations, or rather misplaced emphasize on planar rotations,
by writing i,j,k as products of vectors, and required that these
i,j,k are not linear combinations of vectors. But, Clifford did
not emphasize that there was a mistake in Hamilton's work.
Such explicit mentioning of a mistake was written first by
M. Riesz, although one can argue that Riesz exaggerated.
> Does it make
> sense that no one but Riesz and Altman could figure out
> this "misunderstanding" during all those studies and expositions
> over 100 (one hundred) years?
It does not, but quaternions, and Clifford algebras, were
largely forgotten for almost 100 years, before they emerged
again in 1970's into the theory of the electron spin, and into
electromagnetism. In particular, in electromagnetism, as
studied in the Minkowski space-time, Gibbs' vector algebra
proved to be insufficient, and there was a ntural need to
rediscover Clifford algebra.
> Incidentally, in the book you reference Bolinder from Sweden
> also contributed. He has done some brilliant work on direct
> applications of the Hamilton type methods to polarization sphere
> representations and transformations [polarization fork etc.]
> Very powerful! Have you done any similar EM applications anywhere?
Yes. Here a web-page of a colleague of mine:
http://www.hut.fi/~ppuska/elmag_alg.html
Richard Herring
> On Sun, 6 Feb 2000 jddde...@my-deja.com wrote:
> > to monopolize the intellectual powers of science visualization. He
> > realized they were exploiting his fantastic products and intent on
> > keeping them out of the hands of average people like himself
> Right, someone who has mastered reading and basic arithmetic by age four,
> Latin, Greek, and Hebrew by age five, had written a Syrian grammar at age
> twelve, had mastered Persian by fourteen, had mastered the mathematical
> methods of Newton, Lagrange and Laplace by age sixteen, and wrote his
> great paper on optics age seventeen--- yup, he sounds like an "average
> person" to me too.
Obviously a "family business mathematician".
> > particularly out on the fringes of the king's men rule like Ireland.
> > Thus he withdrew his most important last 25 years of work from the
> > Cambridge Conspiracy. He published and spoke mainly at Trinity
> > College, Dublin from then on.
> And John Maynard Keynes and the Cambridge Conspiracy are responsible for
> The Great Depression, The Troubles, the Ascent of Winston Churchill,
> Linear Algebra, Vector and Tensor Calculus, and Big Science, the Decline
> of the Monarchy and the Readership of The Socialist Worker, two World
> Wars, the downfall of Alger Hiss and the Evil Empire, the cancellation of
> the Superconducting Supercollider, and the Assassination of Presidents
> Lincoln and Kennedy, right? Did I leave anything out?
The DOJ suit against Microsoft.
> > I'm guessing that you read one of the alibis by the Cambridge
I wonder what the J "Humpty Dumpty" D definition of "alibi" is?
--
Richard "Cambridge graduate" Herring | <richard...@gecm.com>
Pertti Lounesto
> When Tait saw what Vector Analysis had done
> to the HV [Hamilton Visualization] he called it an
> "hermorphadite monster" [maybe this was the first use of
> the French grammar in math!?].
Tait wrote: "Hermaphrodite monster".
Richard Herring
Chris Hillman
On Mon, 7 Feb 2000 jddde...@my-deja.com wrote:
> >Well, duh! That's exactly what I explained in my own postings years
> >ago to this newsgroup. And it's the -Riemann- sphere. Aka the complex
>
> -----------------------------------------------------------------------
>
> Interesting! the scientific meaning of the Hamilton quaternion calculus
> is a big mistake; it's all garbage and you invented it! Beautiful!
>
> ----------------------------------------------------------------------
That's not what I said at all. You obviously didn't look up the postings
in question, in which I was describing well known mathematics and gave
references to various books discussing linear fractional transformations
and the classical groups and spinors and the relation of the quaternion
representation of rotations to reflections in planes and how this relates
to the appearance of half angles. I also discussed the Steenrod twist
algebras. None of these concepts are due to myself, and bits and pieces
of them can be found in many textbooks. I just put the pieces together,
but I have no doubt that many people in mathematics have done the same. My
posts described the most elementary way to understand this stuff correctly
(since anyone who has taken a course in complex variables is sure to have
encountered conformal mapping via Moebius transformations) but as I said,
the two by two complex matrices are not the most efficient notation.
> Your historical knowledge is also badly lacking. I guess I shouldn't
> have expected that you had any knowledge of the secret socialist club
> at Cambridge [ going back forever but only exposed to the world with
> the socialist spy revelations about why kids like me had to try to hide
> under the schoolroom desk to survive the ablast attacks ] where all
> the Cambridge Five were spawned, unless you were there also? You
> probably don't know that Rothschild has been exposed as not only
> one of the Lordly members of the club along with keynes but the
> biggest spy of the Cambridge Five.
(LOL)
You are riot, jd!
james d. hunter
As Donald Snead points out in his sometimes recursively immitating
a scientist way, the MASS of a theory is -not- the same thing as the
WEIGHT of a theory.
In closing, for the minor leaguers in theories of consciousness:
take the load off Annie,
take the load off Annie,
they took the load off Annie,
and put the load right on me, me, me.
------------------------------------
from the theory of "The Weight",
not to be confused with
"waiting for a non-trivial, non-astrological theory of time".
jddde...@my-deja.com
100...@goedel2.math.washington.edu>,
Chris Hillman <hil...@math.washington.edu> wrote:
>
>
> On Mon, 7 Feb 2000 jddde...@my-deja.com wrote:
>
> > >ago to this newsgroup. And it's the -Riemann- sphere. Aka the
complex
> >
> >
> Chris Hillman
>
> Home Page: http://www.math.washington.edu/~hillman/personal.html
>
>
----------------------------------------------------------------------
Believe it or not, I would like to read your comments
because I consider these questions of the highest
importance. How about providing a URL to jump to your
archived material or is it on your web site somewhere?
Incidentally, another way to say your apparent mistake
is that the vector being described is not a displacment
vector but an axial vector. An axial vector is the cross
product of two displacment vectors but it's visual
meaning is such that it can't be arbitrarily translated
[only along it's own axis] in space like a displacment
vector which you don't think Hamilton knew how to rotate.
If it is translated it's visual meanuing changes. In
Hamilton's methods vector displacment or translation
is not the simple add another displacment vector as you
apparently assume. Since you know conformal
transformations think of how translation in the complex
plane is compounded with two reflections to get the
displacment. What you are doing with c#s there is
equivalent to what the quaternions do with the sequence
carefully treated.
Thanks. JD
jddescr...@my-deja.com
richard...@gecm.com wrote:
> In article <Pine.OSF.4.21.0002051939560.30469-
100...@goedel1.math.washington.edu>, Chris Hillman
(hil...@math.washington.edu) wrote:
>
> > > On Sun, 6 Feb 2000 jddde...@my-deja.com wrote:
>
> > > to monopolize the intellectual powers of science visualization. He
> > > realized they were exploiting his fantastic products and intent on
> > > keeping them out of the hands of average people like himself
>
>
> Right, someone who has mastered reading and basic arithmetic by age
four,
> > Latin, Greek, and Hebrew by age five, had written a Syrian grammar
at age
> > twelve, had mastered Persian by fourteen, had mastered the
mathematical
> > methods of Newton, Lagrange and Laplace by age sixteen, and wrote
his
> > great paper on optics age seventeen--- yup, he sounds like
an "average
> > person" to me too.
>
> Obviously a "family business mathematician".
>
-----------------------------------------------------------------------
Thanks for reminding me of William Rowan Hamilton's
status as a family business scientist. Of course
everyone, but Chris!, wants to claim him as one of
them so you call him a mathematician but he was a
natural scientist describing the physical world and
particularly astronomical observations with a strong
bias to developing a universal language of description
that he called symbolical geometry and involved all
mechanics and optics[characteristic functions].
The reason you seem to have such a big problem with
"average guys" who bootstrap themselves to the top
family business scientists in the world like Feynman,
and Hamilton, and Teller, and ...is because you take
the king's men view that everyone who isn't of royal
blood or isn't annointed/appointed by some social
manipulator (socman) = king's men AUTHORITY is part of
the masses. The American idea [read the DECLARATION] is
that WE [Wealth Engine] are all inherently equal and we
can bootstrap our way to what ever SOUL [Self Ownership
of yoUr Life] we are willing to effort for/invest in.
I'll just mention a few examples of the SIGNATURE
products that the Hamilton family business produced. If
you really care read the Graves history of Hamilton and
the Hamilton families. Of course his main product is
"Elements of Quaternions" published after his death by
his son. As this thread reflects it is still so far
advanced that many, not just Chris!, still don't know
what he did with this SIGNATURE product. He was very
proud of several other similar products he produced and
sold as a family business scientist. One was a game
involving an icosehedron puzzle. Another was a game related
to Hamilton bridge crossings without repitition. He
developed a special symbology to solve the puzzles with
paper and pencil. Another example of his foundation
innovations is the process of the hodograph. You haven't
heard about it? EXACTLY! Did you hear about the CC
[Cambridge Conspiracy] which Chris played into?
Of course, this has nothing to do with gender since it is
an individual mind effort. Ayn Rand is a female example of
such an "average guy" who made herself = bootstrapped
herself into the greatest(?) philosopher of human history.
----------------------------------------------------------------------
> > > particularly out on the fringes of the king's men rule like
Ireland.
> > > Thus he withdrew his most important last 25 years of work from the
> > > Cambridge Conspiracy. He published and spoke mainly at Trinity
> > > College, Dublin from then on.
>
> > And John Maynard Keynes and the Cambridge Conspiracy are
responsible for
> > The Great Depression, The Troubles, the Ascent of Winston Churchill,
> > Linear Algebra, Vector and Tensor Calculus, and Big Science, the
Decline
> > of the Monarchy and the Readership of The Socialist Worker, two
World
> > Wars, the downfall of Alger Hiss and the Evil Empire, the
cancellation of
> > the Superconducting Supercollider, and the Assassination of
Presidents
> > Lincoln and Kennedy, right? Did I leave anything out?
>
> The DOJ suit against Microsoft.
>
> > > I'm guessing that you read one of the alibis by the Cambridge
>
> --------excerpted, see original--------------------------------------
You signed yourself as a graduate of Cambridge
University. Maybe you could tell US to what extent
you saw the influences of the secret socialist club
where the Cambridge Five and keynes belonged leak
over into the policies of covering up visualization
for the "average guy". Do you know about the cover
up of the Heaviside breakthroughs for 50 years? You
are aware of the Spycatcher revelations I'm sure.
Those revelations and the book "The Fifth Man" show
how all the ablast secrets were passed by and to
Rothschild and the russian socialists studying there
under Rutherford in the 20s and 30s. Can you say
anything about the CC {Cambridge Conspiracy}?
-----------------------------------------------------------------------
Good seeing. JD
jddescr...@my-deja.com
> > Chris Hillman wrote:
> >
> > Actually, my comments were based upon knowledge of exactly what
> > quaternions (and spinor representations) are really all about, and
> > knowledge of the precise conceptual errors made by Hamilton. I
know you
> > won't benefit from this reference, but for the benefit of others
who will,
> > I'll mention the very clear article
> >
> > Simon L. Altmann,
> > Hamilton, Rodrigues, and the Quaternion Scandal.
> > Math. Mag. 62 (1989), no. 5, 291--308.
>
> The author brings brings his point of view better forth in the book
>
> S.L. Altmann: Rotations, Quaternions, and Double Groups,
> Oxford University Press, Oxford, 1986.
>
> It should be emphasized though that Hamilton's misinterpretation
> was first discussed by Marcel Riesz, in 1958, see page 21 of his
> book "Clifford numbers and spinors", Kluwer 1993 (reprint of
> 1958), see publisher's URL:
>
> http://kapis.www.wkap.nl/kapis/CGI-BIN/WORLD/book.htm?0-7923-2299-1
>
> Hamilton's misinterpretation indeed occurred, but it is rather a
> matter of emphasize, probably a simplification he made in order
> to conform to intellectual limitations of his students (Hamilton
> lectured quaternions several years for classes of 50 students).
>
> Hamilton considered rotations of R^3 in the special case, when
> the vector r, in R^3, to be rotated is orthogonal to the axis of
> rotation, say u in R^3; Hamilton wrote r -> pr, where
>
> p = cos(alpha) + u sin(alpha)
>
> and alpha is the angle of rotation. Hamilton did found the
> so-called conical representation of rotations, as r -> qr/q, where
>
> q = cos(alpha/2) + u sin(alpha/2)
>
> (p = q^2) as Cayley admitted in his paper of 1845, when the
> result was first published.
>
> ----------excerpted, see original-----------------------------------
I'm going to ask a question and although I know I'm not
using the right mathematician terminology maybe you can
read between the lines and see what I don't understand.
This last expression that you use for a quaternion[cone
operator] is very good but as you say there are many other
ways to express it. This example seems to illustrate that
Hamilton's treatment of the scalar and vector parts
simultaneously was the right way and not a mistake as you
comment that Gibbs thought. The key thing is that the unit
vector u is a Hamilton meaning of vector. Gibbs would call
it the cross product of two displacment "vectors" or an
axial "vector". Since it visually represents a rotation axis
it can not be arbitrartily translated and retain it's meaning
but only along itself. Hamilton would say u^2 = -1 (correct?).
Hamilton was very proud of his invention of biquaternions that
retained all the visual expansion properties of Euler complex
variable functions as long as sequence is treated carefully.
I would call this a functional property. Explicitly we can
define spaces that correspond to square functions of a
quaternion, to exponential functions of quaternions, to
inversions of quaternions,...and in each case the results are
more quaternions. In a foundation sense the square space and
the square root spaces are the most fundamental pictures. All
the results are different distinct quaternions but they all
have explicit visual pictures. Then by using the Hamilton
(Cayley) characteristic function argument ALL known series
expansions of functions including the Mobious transforms can be
understood visually. Tait said one of the foundation reasons
that they work so well is because of associativity which was
lost with the Gibbs dyadic approach and dot/cross products.
[Is it also lost with Clifford extensions ?] Gibbs justified
his approach on pedegogic grounds [easier to memorize] but in
reality he lost the associative property of biquaternions.
Associativity shows up as indifference to whether combinations
are done left or right or in general where the brackets are
placed in a total sequence. Thus;
(Q1 * Q2 * Q3) = (( Q1 * Q2 ) * Q3) = (Q1 * ( Q2 * Q3 )).
What am I missing in these considerations?
---------------------------------------------------------------------
Good seeing. JD
Richard Herring
> Richard Herring wrote:
> >
> > In article <87g524$9b4$1...@nnrp1.deja.com>, jimh...@my-deja.com wrote:
> > > richard...@gecm.com wrote:
> > > > In article <3899C886...@jhuapl.edu>, james d. hunter
> > > (jim.h...@jhuapl.edu) wrote:
> > > > > Richard Herring wrote:
> > > >
> > > > "Force equals rate of change of momentum"
> > > >
> > > > Good. Now, how far can you throw it?
> >
> > > If you are so into logic and categories, you should know
> > > that you need a theory of TRUTH before you can ask
> > > questions like that.
> >
> > OK. And how much will that theory weigh?
> As Donald Snead points out in his sometimes recursively immitating
> a scientist way, the MASS of a theory is -not- the same thing as the
> WEIGHT of a theory.
Thank you for the well-deserved correction.
In turn I should remind readers that by "mass of a theory" you
are referring to the quantity which is invariant under Lorentz
transformation, not the so-called "relativistic mass of a theory".
--
Richard Herring | <richard...@gecm.com>
Richard Herring
> On Mon, 7 Feb 2000 jddde...@my-deja.com wrote:
[sorry about the double quotes, I haven't seen the original yet]
>
> > Your historical knowledge is also badly lacking. I guess I shouldn't
> > have expected that you had any knowledge of the secret socialist club
> > at Cambridge [ going back forever but only exposed to the world with
> > the socialist spy revelations about why kids like me had to try to hide
> > under the schoolroom desk to survive the ablast attacks ] where all
> > the Cambridge Five were spawned, unless you were there also? You
> > probably don't know that Rothschild has been exposed as not only
> > one of the Lordly members of the club along with keynes but the
> > biggest spy of the Cambridge Five.
Do you think JD is confusing the hundreds of Apostles
(wow, really big secret, with dozens of books written about them)
with the handful of Cambridge spies who happened to be members?
Shock horror revelation: J C Maxwell was one, too.
> (LOL)
> You are riot, jd!
Seconded.
--
Richard "went to D D Maclean's old college" Herring
Pertti Lounesto
> Pertti Lounesto <Pertti....@hit.fi> wrote:
>
>> Penrose has introduced
>>
>> 1. Penrose tribar (impossible figure),
>> 2. Penrose tile (non-periodic filling of the plane by polygons),
>> 3. Penrose transform (by integrals),
>> 4. Penrose twistor (conformal spinors),
>>
>> or labelled these concpets by his name. At least
>> the last concept, twistor, is a hoax. See the book
>> http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164,
>> in particular the chapter on the conformal groups
>> "Moebius transformations and Vahlen matrices",
>> pages 244-254.
>
> Are you giving us a preview of your next book? I can't find
> twistors mentioned explicitly in this chapter of your book.
No, I don't have really time, and the audience in
sci.physics lacks knowledge of modern methods of
physics, so much so that only very elementary
matters can be discussed.
> I know there is an extensive literature on twistors
> apparently mainly by Penrose students.
Yes, twistor approach has not been accepted outside
of Penrose's students.
> Have you found some defects in this
> approach similar to your previous comments about the Atiyah
> period 8 works and triality?
No, twistor formalism seems so clumsy, and
artificial, that it is not worth much effort.
The number of publications (of students of
Penrose) on twistors has been declining, now
that Penrose is getting older.
> Is it possible to compare
> conformal spinors and Dirac double spinors and your flag pole
> spinors all as biquaternion objects or operators?
It is possible to build up a correspondence
between conformal spinors and Dirac doule spinors.
A pair of biquaternions can be put to a
correspondence with Dirac bispinors (ala G"ursey).
> In the referenced chapter you use some very suggestive
> visualization terminology like stretch and translate and
> inversion and transversion which all relate to compounding
> reflections in Hamilton biquaternion terminology. What about
> the various visual invariants like cross ratio and the relation
> to the Mobious transforms you describe?
These have been discussed by Lars Ahfors.
> Will these topics be in your next book?
No.
Chris Hillman
On Tue, 8 Feb 2000 jddde...@my-deja.com wrote:
> Believe it or not, I would like to read your comments because I
> consider these questions of the highest importance. How about
> providing a URL to jump to your archived material or is it on your web
> site somewhere?
Naturally my archived material is on my web site; see url below and follow
the links.
The posts on quaternions, SU(2) and the appearance of the night sky as
seen in "real proper time" by an arbitrarily moving relativistic observer
are mostly archived in Deja News, however, under "Night Sky" or something
like that. This turned out to be rather tricky: I was thinking in terms
of acceleration using a one parameter subgroup whereas Steve V was
thinking in terms of decomposing each Lorentz transformation into a boost
composed with a rotation. This leads to rather different descriptions of
what the observer would actually see and reconciling these two viewpoints
led to a long discussion in which it eventually turned out that they are
not mutually inconsistent after all: both viewpoints are correct.
> Since you know conformal transformations think of how translation in
> the complex plane is compounded with two reflections to get the
> displacment. What you are doing with c#s there is equivalent to what
> the quaternions do with the sequence carefully treated.
Since you didn't write down any math, I can only guess what you are
talking about, but it sounds as if you are saying that the representation
X -> Q X Q^(-1)
where X is a Hermitian matrix
[ t+x y+iz ]
X = [ y-iz t-x ] det X = t^2 - x^2 - y^2 - z^2
and where Q is in SU(2), is equivalent to conjugation by unit norm
quaternions, r -> q r q^(-1) where
r = ix + jy + kz, x^2 + y^2 + z^2 = 1
If so, that is quite correct. As I said, the chief advantage of the
matrix group formulation is that connection with concepts encountered by
undergraduate students in a complex variables and "abstract" linear
algebra course such as linear fractional transformations, conformal
transformations, the Riemann sphere, determinants and Hermitian and
special unitary matrices, is transparent. I also discussed how this is
related to the "geometric Hopf fibration"
SO(2) >--> SU(2) -->> S^2
or
S^1 >--> S^3 -->> S^2
Here, SU(2), the group of unit norm quaternions, may be identified with
the unit sphere in E^4, namely S^3, and the quaternions of form r above
may be identified with S^2, the "space of directions" in E^3, which is the
double cover of the "space of one dimensional subspaces", namely RP^2.
The group SU(2) is the universal cover (a double cover) of the rotation
group SO(3).
I also tried to use this beautiful stuff as one the simplest nontrivial
examples where the power of Lie theory is plainly apparent, by introducing
the Lie product in a natural way and giving expressions for "infinitesimal
rotations" and "infinitesimal conjugations", working only with the power
series for the matrix exponential. I also tried to explain how the
Steenrod twist algebra and the matrix exponential allows one to generalize
the Euler expression
z = r e^(i theta)
to quaternions and their close relatives, the two by two real matrices,
another four dimensional real algebra (almost but not quite a division
algebra; it is a Cayley-Dickson algebra with a multiplicative norm) which
is associated with the geometry of E^(2,2) rather than E^4. Finally, the
group of Moebius transformations PSL_2(C) turns out to be isometric to the
proper orthochronous Lorentz group SO+(1,3), i.e. the component of the
identity transformation; there are three other algebraic cosets, i.e.
topological components in the full Lorentz group O(1,3).
I also gave several advanced undergraduate textbooks which discuss various
pieces of this wonderful stuff.
A small part of these posts is included in the FAQ and one of my archived
posts summarizes some of this stuff. Of course, it is much more vivid if
one can draw pictures. Someday Nathan and I might convert parts of the
FAQ into a format which includes gif images, but that is a project for the
distant future :-/
Chris Hillman
Oops!
On Tue, 8 Feb 2000, I wrote:
> Since you didn't write down any math, I can only guess what you are
> talking about, but it sounds as if you are saying that the representation
>
> X -> Q X Q^(-1)
>
> where X is a Hermitian matrix
>
> [ t+x y+iz ]
> X = [ y-iz t-x ] det X = t^2 - x^2 - y^2 - z^2
>
> and where Q is in SU(2), is equivalent to conjugation by unit norm
> quaternions, r -> q r q^(-1) where
>
> r = ix + jy + kz, x^2 + y^2 + z^2 = 1
>
> If so, that is quite correct.
Oh dear. Obviously, I meant to kill of t in X above before saying this.
Oh well. This is rather technical stuff and since I have been thinking
about quite different stuff lately, I would have to look up my own notes
to remember all the details. Hopefully I didn't get anything else wrong
in my hasty summary.
I should also have mentioned that exponentiating the Lie algebra of a
uniparameter subgroup yields that subgroup; the Lie theory way of saying
z = r e^(i theta)
is that so(2) is the Lie algebra of SO(2):
exp t [ 0 1 ] = [ cos t sin t ] = a rotation about a particular axis
[ -1 0 ] [ -sin t cos t ]
and so(1,1) is the Lie algebra of SO(1,1):
exp t [ 0 1 ] = [ cosh t sinh t ] = a boost in particular direction
[ 1 0 ] [ sinh t cosh t ]
Then, the Steenrod twist algebra nicely generalizes this principle to give
a simple and beautiful formula for a rotation through a given angle about
a given rotation axis (x,y,z), completely analogous to a "realified"
version of
z -> z e^(i t)
Richard Herring
I see your amateur psychoanalysis knows no bounds.
I have no "problem" with such people. A good deal of my
own work is based on Hamiltonian optics, for example.
What I do object to is your attempt to hijack these
people to your own political agenda, whatever it is,
by pasting that emotive but semantically void "family
business" label on them.
[...]
> > > And John Maynard Keynes and the Cambridge Conspiracy are responsible for
> > > The Great Depression, The Troubles, the Ascent of Winston Churchill,
> > > Linear Algebra, Vector and Tensor Calculus, and Big Science, the
> Decline of the Monarchy and the Readership of The Socialist Worker, two
> World Wars, the downfall of Alger Hiss and the Evil Empire, the
> cancellation of the Superconducting Supercollider, and the Assassination of
> Presidents Lincoln and Kennedy, right? Did I leave anything out?
> >
> > The DOJ suit against Microsoft.
> >
> You signed yourself as a graduate of Cambridge
> University. Maybe you could tell US to what extent
> you saw the influences of the secret socialist club
You think James Clerk Maxwell was a socialist?
> where the Cambridge Five and keynes belonged leak
> over into the policies of covering up visualization
> for the "average guy".
What policies would those be?
> Do you know about the cover
> up of the Heaviside breakthroughs for 50 years?
No. Go on, tell us.
> You
> are aware of the Spycatcher revelations I'm sure.
> Those revelations and the book "The Fifth Man" show
> how all the ablast secrets were passed by and to
> Rothschild and the russian socialists studying there
> under Rutherford in the 20s and 30s.
Would you think any Russians studying there in the 20s and 30s
(and I can only think of one) would still be in Cambridge,
post 1945?
> Can you say
> anything about the CC {Cambridge Conspiracy}?
Of course not. My lips are sealed.
--
Richard "quarter-blue, 1978" Herring
Pertti Lounesto
> Pertti Lounesto <Pertti....@hit.fi> wrote:
>
> > > Chris Hillman wrote:
> > >
> > > I'll mention the very clear article
> > >
> > > Simon L. Altmann,
> > > Hamilton, Rodrigues, and the Quaternion Scandal.
> > > Math. Mag. 62 (1989), no. 5, 291--308.
>
> >
Already Clifford, 1878, pointed out that i,j,k can be
considered products of vectors, say e1,e2,e3, so that
i = e2e3, j = e3e1, k = e1e2 and so that i,j,k are not
real linear combinations of e1,e2,e3 (and e1,e2,e3 are
not real linear combinations of i,j,k). In his paper of
1878, Clifford assumed that e1^2 = e2^2 = e3^2 = -1.
Later, in a posthumous paper of 1882, Clifford assumed
that e1^2 = e2^2 = e3^2 = 1. So, Clifford was a forerunner
of Marcel Riesz, in emphasizing that Hamilton's i,j,k are
not really vectors (= generators of translations), but
bivectors (= generators of rotations).
Gibbs' contribution was to extract, out of Hamilton's
quaternion calculus, today's vector algebra, by teaching
to his students only a part of quaternion theory, with a
small modification. In particular, Gibbs refused to sum
up scalars and vectors.
> Tait said one of the foundation reasons
> that they work so well is because of associativity which was
> lost with the Gibbs dyadic approach and dot/cross products.
> [Is it also lost with Clifford extensions ?]
Right, associativity is a very practical thing in formal
computations, with a number of advantages. Gibbs'
vector algebra is not associative, but Clifford algebra
is (the Clifford product). Also the exterior product
(which can be derived from the Clifford poduct) is
associative. However, contraction is not associative.
> Gibbs justified
> his approach on pedegogic grounds [easier to memorize] but in
> reality he lost the associative property of biquaternions.
Gibbs' formalism was easier to students, who already
had difficulties to understand that vectors are not scalars
(so complete separation of scalars and vectors was
easier to teach to students).
> Associativity shows up as indifference to whether combinations
> are done left or right or in general where the brackets are
> placed in a total sequence. Thus;
>
> (Q1 * Q2 * Q3) = (( Q1 * Q2 ) * Q3) = (Q1 * ( Q2 * Q3 )).
>
> What am I missing in these considerations?
Go on asking. If I have time, I will try to supply an
answer. Of course, you are already more advanced
than most posters in sci.physics.
Robert Low
> jdescrtipt wrote:
> > I know there is an extensive literature on twistors
> > apparently mainly by Penrose students.
> Yes, twistor approach has not been accepted outside
> of Penrose's students.
Your polemics are getting the better of you again.
I don't think anybody could really classify Michael Atiyah,
Nigel Hitchin, Yuri Manin, RO Wells, Ed Witten or TJ Willmore
as Penrose's students. They have all used twistorial methods
(primarily in the context of self-dual complex
Riemannian geomety, to a lesser extent in mathematical
physics).
Unless, of course, you choose to define anybody who finds
twistors useful as a student of Penrose. That would work :-)
> No, twistor formalism seems so clumsy, and
> artificial, that it is not worth much effort.
Horses for courses. And I don't think anybody will
deny that it hasn't been as fruitful in physics as
was originally hoped, though there has been a lot
of work done on integrable systems, and on certain
problems within GR such as the problem of the definition
of mass, and the asymptotic structure of space-times.
But there has been quite a lot of work on complex
differential geometry sparked of by twistor theory,
by no means all of it by Penrose's students, and also on
various other areas of maths, such as representation
theory.
Nobody is telling you to eat it, but you might refrain
from claiming that the reasons you don't like it are
that it tastes bad and has no nutritional value.
Pertti Lounesto
> Pertti Lounesto wrote:
> > jdescrtipt wrote:
> > > I know there is an extensive literature on twistors
> > > apparently mainly by Penrose students.
> > Yes, twistor approach has not been accepted outside
> > of Penrose's students.
>
> Your polemics are getting the better of you again.
>
> I don't think anybody could really classify Michael Atiyah,
> Nigel Hitchin, Yuri Manin, RO Wells, Ed Witten or TJ Willmore
> as Penrose's students. They have all used twistorial methods
> (primarily in the context of self-dual complex
> Riemannian geomety, to a lesser extent in mathematical
> physics).
You are right: There was some initial enthusiasm about
twistors, also by good mathematicians, but lately the
torch has been crumbled on mainly by Penrose's students.
Of course, since twistors are conformal spinors, but do
have some _additional_ structure, it is important to keep
an eye on twistors.
Chris Hillman
On Tue, 8 Feb 2000, Robert Low wrote:
> Pertti Lounesto wrote:
> > jdescrtipt wrote:
> > > I know there is an extensive literature on twistors
> > > apparently mainly by Penrose students.
> > Yes, twistor approach has not been accepted outside
> > of Penrose's students.
>
> Your polemics are getting the better of you again.
>
> I don't think anybody could really classify Michael Atiyah,
> Nigel Hitchin, Yuri Manin, RO Wells, Ed Witten or TJ Willmore
> as Penrose's students. They have all used twistorial methods
> (primarily in the context of self-dual complex
> Riemannian geomety, to a lesser extent in mathematical
> physics).
Add Robin Graham of our very own UW math department to the list of
non-Penrose students who have worked on the mathematical side of twistor
theory. And as a matter of fact, he was worked with Ed Witten on that
aspect of his own work, I think. And darn, I was so busy talking to my
visiting collaborator that I -forgot- to go to Ed Witten's talk on "Black
Holes, SuperString Theory, and Holography" yesterday. So I can't give my
promised report on what Witten has to say about that.
> Nobody is telling you to eat it, but you might refrain
> from claiming that the reasons you don't like it are
> that it tastes bad and has no nutritional value.
I'll second that.
Pertti Lounesto
> > Nobody is telling you to eat it, but you might refrain
> > from claiming that the reasons you don't like it are
> > that it tastes bad and has no nutritional value.
>
> I'll second that.
Hm. Does that mean that Chris is telling me to eat twistors?
Lets be objective: After introduction of a new idea, there
often is a first wave of interest. In the case of twistors,
the wave was pretty high. But it soon fell flat. And the
fact that mathematicians of the first rank participated in
scrutinizing twistor theory, although only for a short while,
shows that the wave was rather empty.
I admit, of course, that my negative opinion of Penrose's
twistor theory is influenced by Penrose's clumsy approach
to spinors (= the van der Waerden - Infeld index notation),
which led Penrose to invent twistors.
Chris Hillman
On Tue, 8 Feb 2000, Pertti Lounesto wrote:
> Chris Hillman wrote:
>
> > > Nobody is telling you to eat it, but you might refrain
> > > from claiming that the reasons you don't like it are
> > > that it tastes bad and has no nutritional value.
> >
> > I'll second that.
>
> Hm. Does that mean that Chris is telling me to eat twistors?
It means that I was seconding Robert Low's suggestion that you refrain
from claiming that twistors have no value. It would be more fair to say
that as twistor theory has led to some interesting mathematics and that
the utility in physics is not clear.
> Lets be objective: After introduction of a new idea, there often is a
> first wave of interest. In the case of twistors, the wave was pretty
> high. But it soon fell flat. And the fact that mathematicians of the
> first rank participated in scrutinizing twistor theory, although only
> for a short while, shows that the wave was rather empty.
That's "objective"?
I think this is your subjective judgement and I think it is inaccurate.
First rate mathematicians continue to work on the mathematical side. Of
course people I consider to be "first rate" might not count as first rate
in your book, so we're back to "subjective" judgements again.
> I admit, of course, that my negative opinion of Penrose's twistor
> theory is influenced by Penrose's clumsy approach to spinors (= the
> van der Waerden - Infeld index notation), which led Penrose to invent
> twistors.
Since I also happen to dislike that notation, perhaps we can let things
rest here, on a note of agreement.
james d. hunter
>
> In article <389F8630...@jhuapl.edu>, james d. hunter (jim.h...@jhuapl.edu) wrote:
> > Richard Herring wrote:
> > >
> > > In article <87g524$9b4$1...@nnrp1.deja.com>, jimh...@my-deja.com wrote:
> > > > richard...@gecm.com wrote:
> > > > > In article <3899C886...@jhuapl.edu>, james d. hunter
> > > > (jim.h...@jhuapl.edu) wrote:
> > > > > > Richard Herring wrote:
> > > > >
> > > > > "Force equals rate of change of momentum"
> > > > >
> > > > > Good. Now, how far can you throw it?
> > >
> > > > If you are so into logic and categories, you should know
> > > > that you need a theory of TRUTH before you can ask
> > > > questions like that.
> > >
> > > OK. And how much will that theory weigh?
>
> > As Donald Snead points out in his sometimes recursively immitating
> > a scientist way, the MASS of a theory is -not- the same thing as the
> > WEIGHT of a theory.
>
> Thank you for the well-deserved correction.
>
> In turn I should remind readers that by "mass of a theory" you
> are referring to the quantity which is invariant under Lorentz
> transformation, not the so-called "relativistic mass of a theory".
No not really, I believe with theories of consciousness,
there are preferred reference frames.
jdescript
r...@gmrc.gecm.com (Richard Herring) wrote:
>In article <87omd8$572$1...@nnrp1.deja.com>, jddescript_deja@my-
deja.com wrote:
>> In article <87majo$cj9$3...@miranda.gmrc.gecm.com>,
>> richard...@gecm.com wrote:
>
>> > In article <Pine.OSF.4.21.0002051939560.30469-
>> 100...@goedel1.math.washington.edu>, Chris Hillman
>> (hil...@math.washington.edu) wrote:
>> >
>> > Right, someone who has mastered reading and basic
arithmetic by age
>> four,
>> > > Latin, Greek, and Hebrew by age five, had written a
Syrian grammar
>> at age
>> > > twelve, had mastered Persian by fourteen, had mastered the
>> mathematical
>> > > methods of Newton, Lagrange and Laplace by age sixteen,
and wrote
>> his
>> > > great paper on optics age seventeen--- yup, he sounds like
>> an "average
>> > > person" to me too.
>> >
>> > Obviously a "family business mathematician".
>> >
>> --------------------------------------------------------------
>> Thanks for reminding me of William Rowan Hamilton's
>> status as a family business scientist. Of course
>> everyone, but Chris!, wants to claim him as one of
>> them so you call him a mathematician but he was a
>> natural scientist describing the physical world and
>> particularly astronomical observations with a strong
>> bias to developing a universal language of description
>> that he called symbolical geometry and involved all
>> mechanics and optics[characteristic functions].
>
>> The reason you seem to have such a big problem with
>> "average guys" who bootstrap themselves to the top
>> family business scientists in the world like Feynman,
>> and Hamilton, and Teller, and
>
>I see your amateur psychoanalysis knows no bounds.
>I have no "problem" with such people. A good deal of my
>own work is based on Hamiltonian optics, for example.
>
>What I do object to is your attempt to hijack these
>people to your own political agenda, whatever it is,
>by pasting that emotive but semantically void "family
>business" label on them.
>
>[...]
>
>> > > And John Maynard Keynes and the Cambridge Conspiracy are
responsible for
>> > > The Great Depression, The Troubles, the Ascent of Winston
Churchill,
>> > > Linear Algebra, Vector and Tensor Calculus, and Big
Science, the
>> Decline of the Monarchy and the Readership of The Socialist
Worker, two
>> World Wars, the downfall of Alger Hiss and the Evil Empire,
the
>> cancellation of the Superconducting Supercollider, and the
Assassination of
>> Presidents Lincoln and Kennedy, right? Did I leave anything
out?
>> >
>> > The DOJ suit against Microsoft.
>> >
>> You signed yourself as a graduate of Cambridge
>> University. Maybe you could tell US to what extent
>> you saw the influences of the secret socialist club
>
>You think James Clerk Maxwell was a socialist?
>
>> where the Cambridge Five and keynes belonged leak
>> over into the policies of covering up visualization
>> for the "average guy".
>
>What policies would those be?
>
>> Do you know about the cover
>> up of the Heaviside breakthroughs for 50 years?
>
>No. Go on, tell us.
>
>> You
>> are aware of the Spycatcher revelations I'm sure.
>> Those revelations and the book "The Fifth Man" show
>> how all the ablast secrets were passed by and to
>> Rothschild and the russian socialists studying there
>> under Rutherford in the 20s and 30s.
>
>Would you think any Russians studying there in the 20s and 30s
>(and I can only think of one) would still be in Cambridge,
>post 1945?
>
>> Can you say
>> anything about the CC {Cambridge Conspiracy}?
>
>Of course not. My lips are sealed.
>
>--
>Richard "quarter-blue, 1978" Herring
>
>
----------------------------------------------------------------
You certainly are quick footed at avoiding the
issues aren't you? I'm going to assume that it
is the newsgroup format that causes you to lose
track of what is being discussed and provide some
detail.
Reference the well known CC (Cambridge Conspiracy)
to cover up the scientific breakthroughs of one
of the best family business scientist in British
history; Oliver Heaviside; He is a very illuminating
case since he was an English subject throughout his
life work so the cover-up of his work couldn't just
be due to being out on the fringes of the kingdom
like possibly Hamilton, Maxwell, Tait,.... He is a
famous case because of the concerted attempts by the
CC to devalue his work. Books have been written about
him because of the enormous importance of his
discoveries particularly in electromagnetics and
specifically in terms of distorsionless transmission
of signals by soliton type signals(gauss pulses} in
underwater cables. What I said before that Chris was
argueing against was:
----------------------------------------------------------------
I'm guessing that you read one of the alibis by the Cambridge
Conspiracy (CC) for what they did to suppress Hamilton's giant
accomplishments. It's even worse than what they did for 50 years
to the Heaviside methods.
[Eventually they gave up that part of the conspiracy, changed
the names to Laplace Transform and pretended that it never
happened.] An example that you might have seen is "Rotations,
Quaternions and Double Groups" by S. L. Altmann. They have so
covered up Hamilton's giant accomplishments in visualization
that I recommend this book to people even though warning them
that it is an alibi for the CC. By carefully screening the
material you can still learn some of Hamilton's breakthroughs.
---------------------------------------------------------------
Heaviside lived in dire poverty his entire life because he
wouldn't bow down to the king's men of the CC. A few people
respected his work, such as Kelvin and a popular magazine for
ameuture electronics people.
----------------------------------------------------------------
The idea that you can't distinguish the "average guy"
who developes signature products by enormous and risky
investments in personal learning from the
authoritartian manipulators (authman) or king's men is
hard to understand. Can't you distinguish free people
signature products from the authorized king's men
corpconspiracy plastic phony balony rapcrap casino sleeze
trinkets? The distinction is very clear in America. Maybe
it's the fact that you weren't watching very carefully
when you were at Cambridge.
---------------------------------------------------------------
Your history problems are similar to Chris when the
topic of how the CC suppression of the HV [ Hamilton
Visualization ] relates to the socialist keynes.
Chris thought there could be no connection because
Hamilton completed his work in the mid 1800s and
keynes wasn't even born then. Obviously Chris didn't
know about the secret sociaslist club at Cambridge
that spawned all the Cambridge Five besides keynes.
You clear the whole secret group [Apostles] because
you know one member who was a good person. You
probably think that when the king's men recognize a
good family business scientist like Euler or Berry
or...that clears the king's men of the KMS [ Kings
Men Spirit] manipulations. Please! that is as naive
as the Chris claim that one of the greatest physical
scientists in world history(Hamilton) made a mistake
about how displacment vectors are rotated in three
dimensions. Similarly your claim that the russian
socialist spies who studied under Rutherford at
Cambridge in the 20s and 30s weren't still around in
WW II. You are right, they weren't. They had been
called back to Moscow by stalin to build a duplicate
nuclear facility to prepare for building the ablast.
This only after they had all been interconnected to
the top king's men of Britain by their connections to
Rothschild in this secret socialist club that your
mouth is sealed about. Rothschild , LORD Victor
Rothschild, was able to get all the key Cambridge Five;
including Blunt directly in the castle, into top spy
positions in the British king's men structure of MI 5
and 6, including postings to America. Read the
"Spycatcher" expose and "The Fifth Man" expose or any
of the more recent exposures of the SSS = Secret
Socialist State of the BS [British Socialists]
king's men.
----------------------------------------------------------------
Good seeing. JD
--------------------------------------------------------------
Bruce Scott TOK
>
>> Your historical knowledge is also badly lacking. I guess I shouldn't
>> have expected that you had any knowledge of the secret socialist club
>> at Cambridge [ going back forever but only exposed to the world with
>> the socialist spy revelations about why kids like me had to try to hide
>> under the schoolroom desk to survive the ablast attacks ] where all
>> the Cambridge Five were spawned, unless you were there also? You
>> probably don't know that Rothschild has been exposed as not only
>> one of the Lordly members of the club along with keynes but the
>> biggest spy of the Cambridge Five.
JD, do you get this from LaRouche, or from somewhere else?
In article <Pine.OSF.4.21.00020...@goedel2.math.washington.edu>,
Chris Hillman <hil...@math.washington.edu> wrote:
>(LOL)
>
>You are riot, jd!
Interesting to see these conspiracy comments in the midst of a discussion
about mathematics, isn't it? One should know that these always do
damage to one's credibility, even if they are right!
--
cu,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
jddescr...@my-deja.com
Pertti....@hit.fi wrote:
> > jdescrtipt wrote:
-------------excerpted, see original---------------------------------
>
> > I know there is an extensive literature on twistors
> > apparently mainly by Penrose students.
>
> Yes, twistor approach has not been accepted outside
> of Penrose's students.
>
> > Have you found some defects in this
> > approach similar to your previous comments about the Atiyah
> > period 8 works and triality?
>
> No, twistor formalism seems so clumsy, and
> artificial, that it is not worth much effort.
> The number of publications (of students of
> Penrose) on twistors has been declining, now
> that Penrose is getting older.
>
> > Is it possible to compare
> > conformal spinors and Dirac double spinors and your flag pole
> > spinors all as biquaternion objects or operators?
>
> It is possible to build up a correspondence
> between conformal spinors and Dirac doule spinors.
> A pair of biquaternions can be put to a
> correspondence with Dirac bispinors (ala G"ursey).
>
----------------excerpted, see original------------------------------
I'm begining to think that this discussion about
the biquaternions/spinors has greater overall
importance than I previously realized. Dirac was
a special expert on biquaternions and although he
changed the names to bra/ket/Hilbert space I'm
wondering if the pictures of biquaternions (cone
objects and operators) don't apply directly to the
bra/ket meanings including when quantum spin
(isotropic spin) is modeled. With unit quaternions
(versors or right versors) the conjugate just means
a reversal of the rotation axis direction and
corresponds (in the correct space) to the inverse
operator. I'm still confused about when we have a
double cover and when we have biquaternions that
are divisors of zero [but I'm thinking that all the
pictures probably carry over directly]. I'm trying
to relate your flag pole spinors; Chapter twelve of
your book "Clifford Algebras and Spinors", Cambridge
University Press to a representation of Berry Phase?
It's related to twistors is it also related to spinors?
Good seeing. JD
----------------------------------------------------------------------
Pertti Lounesto
> I'm trying
> to relate your flag pole spinors; Chapter twelve of
> your book "Clifford Algebras and Spinors", Cambridge
> University Press to a representation of Berry Phase?
> It's related to twistors is it also related to spinors?
The Chapter 12 "Flags, poles and dipoles" of my book
"Clifford numbers and spinors", Cambridge UP, 1997/98,
http://www.cup.cam.ac.uk/Scripts/webbook.asp?isbn=0521599164,
is not related to Penrose's twistors or Berry Phase.
For spinors, Penrose's introduce a visualization
method, called the "flags and poles". There a
Majorana spinor was put in correspondence with
a pole on the light-cone and a flag on that pole
and tangent to the light-cone. Penrose's flag
then turned 180 degrees in a full turn of the space.
Weyl spinors just have a pole.
In Chapter 12 of my book, I review Penrose's
flag-pole approach to Majorana spinors, in more
geometrical setting, and go much further. I classify
spinors by their bilinear coviariants (observables),
and find that between the Majorana, Weyl and Dirac
spinors there resides a new class of spinors.
I predict that there should be a new particle
corresponding to these new spinors, called
flag-dipole spinors (Greg Trayling, Windsor,
has proposed that my new particles are related
to the quark confinement). However, up till
now physicist has taken the task of detecting
my new particles. I guess the main reason is
lack of knowledge of mathematics among physicists.
No mathematician has taken the task decode
and understand my Chapter 12. I guess the
reason here is the same as for physicists.
Chuck Stewart
Anderson deal with perps like Faroe, The Angel Clan, and Judge
Death... Judge Kitty has to deal with:... Jaded Nondescript...)
jddescrip...@aol.com.invalid (jdescript) wrote in
<11aaf29c...@usw-ex0104-026.remarq.com>:
<endless babble snipped>
The crime is being obliquely obtuse.
The penalty is 90 days in the killfile.
(The Isocube door shuts with a metallic *plonk*)
--
Chuck Stewart
"Anime-style catgirls: Threat? Menace? Or just studying
algebra?"
JMFBAH
Date: Tue, Feb 8, 2000 11:56 EST
Message-id: <87phr3...@subds.rzg.mpg.de>
>>On Mon, 7 Feb 2000 jddde...@my-deja.com wrote:
>>
>>> Your historical knowledge is also badly lacking. I guess I shouldn't
>>> have expected that you had any knowledge of the secret socialist club
>>> at Cambridge [ going back forever but only exposed to the world with
>>> the socialist spy revelations about why kids like me had to try to hide
>>> under the schoolroom desk to survive the ablast attacks ] where all
>>> the Cambridge Five were spawned, unless you were there also? You
>>> probably don't know that Rothschild has been exposed as not only
>>> one of the Lordly members of the club along with keynes but the
>>> biggest spy of the Cambridge Five.
>JD, do you get this from LaRouche, or from somewhere else?
Oh, he gets it from somewhere else.
/BAH
john baez
> And last but not least, Pertti omitted any mention of Penrose's greatest
> contributions to science (in my view), namely his introduction of
> conformal compactification (global analysis of solutions to the EFE)
> and his proof of several of the singularity theorems which played such a
> crucial role in fostering the development of gtr.
Yes, I'd guess that his work on the singularity theorems is the most
important stuff he's done.
john baez
>Unfortunately, as far as I know, Penrose has been unable to suggest a
>plausible experiment, or at least, to persuade any biophysicists to try to
>perform an experiment.
On a somewhat different line, Penrose *has* proposed some plausible
experiments to test his hypothesis of the gravitationally induced
collapse of the wavefunction, and he's talking to some experimentalists
to see if the experiment can be done.
Chris Hillman
Interesting. Would this involve an experiment in an Earthbound
laboratory? How would it work?
Nathan Urban
> On 10 Feb 2000, john baez wrote:
> > On a somewhat different line, Penrose *has* proposed some plausible
> > experiments to test his hypothesis of the gravitationally induced
> > collapse of the wavefunction, [...]
> Interesting. Would this involve an experiment in an Earthbound laboratory?
The one he's been talking about recently is spacebound. Here is one of
his talks on it, with slides and audio:
http://cosmos.nirvana.phys.psu.edu/online/Html/Seminars/Fall1999/Penrose/
(Time dilation notwithstanding, the talk was actually on October 25,
not October 52.)
I seem to recall him mentioning something about some earthbound
experiments that someone at one of the California schools had proposed,
I think involving neutron interferometry. But I could be misremembering.
jddescr...@my-deja.com
100...@goedel2.math.washington.edu>,
> talking about, but it sounds as if you are saying that the
representation
>
> X -> Q X Q^(-1)
>
> where X is a Hermitian matrix
>
> [ t+x y+iz ]
> X = [ y-iz t-x ] det X = t^2 - x^2 - y^2 - z^2
>
> and where Q is in SU(2), is equivalent to conjugation by unit norm
> quaternions, r -> q r q^(-1) where
>
> r = ix + jy + kz, x^2 + y^2 + z^2 = 1
>
> matrix group formulation is that connection with concepts encountered
by
> undergraduate students in a complex variables and "abstract" linear
> algebra course such as linear fractional transformations, conformal
> transformations, the Riemann sphere, determinants and Hermitian and
> special unitary matrices, is transparent. I also discussed how this
is
> related to the "geometric Hopf fibration"
>
> SO(2) >--> SU(2) -->> S^2
>
> or
>
> S^1 >--> S^3 -->> S^2
>
> Here, SU(2), the group of unit norm quaternions, may be identified
with
> the unit sphere in E^4, namely S^3, and the quaternions of form r
above
is the
> double cover of the "space of one dimensional subspaces", namely
RP^2.
> The group SU(2) is the universal cover (a double cover) of the
rotation
> group SO(3).
>
> I also tried to use this beautiful stuff as one the simplest
nontrivial
> examples where the power of Lie theory is plainly apparent, by
introducing
> the Lie product in a natural way and giving expressions
for "infinitesimal
> rotations" and "infinitesimal conjugations", working only with the
power
> series for the matrix exponential. I also tried to explain how the
> Steenrod twist algebra and the matrix exponential allows one to
generalize
> the Euler expression
>
>
matrices,
> another four dimensional real algebra (almost but not quite a division
> algebra; it is a Cayley-Dickson algebra with a multiplicative norm)
which
> is associated with the geometry of E^(2,2) rather than E^4. Finally,
the
> group of Moebius transformations PSL_2(C) turns out to be isometric
to the
> proper orthochronous Lorentz group SO+(1,3), i.e. the component of the
> identity transformation; there are three other algebraic cosets, i.e.
> topological components in the full Lorentz group O(1,3).
>
> I also gave several advanced undergraduate textbooks which discuss
various
> pieces of this wonderful stuff.
>
> A small part of these posts is included in the FAQ and one of my
archived
> posts summarizes some of this stuff. Of course, it is much more
vivid if
> one can draw pictures. Someday Nathan and I might convert parts of
the
> FAQ into a format which includes gif images, but that is a project
for the
> distant future :-/
>
----------------------------------------------------------------------
Thanks for the comments. I'm studying them in hope
of expressing my simple approach to quaternions in
correct mathematical language. I'm also using the
Pertti Lounesto book "Clifford Algebras and Spinors".
When I checked your site I found a one paragraph
"Geometry of Two by Two Real Matrices" under your
Eprints. With a detailed search I found a few things
under "night sky" but not these transformations. Could
you give a few other key wordas and the approximate
time when you wrote them?
Earlier when I wrote:
> I'm applying the Hamilton methods of biquaternions
> [the Hamilton Visualization = HV ]
you responded with;
Did you listen to word any of us were saying? Hamilton
made a serious conceptual error in the use of quaternions
in representing rotations in E^3 and then proceeded to go
further and further wrong from there.
There is no such thing as "Hamilton visualization", btw,
except in your dreams.
---------------------------------------------------------------------
Strange! I must be dreaming now as I look at the two
volume hard cover version of "Elements of Quaternions"
sitting on the shelf. If you look at it carefully some
day think of the effort that Hamilton invested, not
only to invent the approach but, to write it all out in
detail with pen and paper. This second edition was
published in 1899 and contains a number of geometric
appendices of Hamilton's work by Charles Jasper Jolly,
professor of Astronomy and Royal Astronomer of Ireland.
Obviously another scientist mistaken about the importance
of quaternions who would never know what Altman knew some
60 years later. You should ask Pertti Lounesto about the
amount of work that Hamilton did to produce the HV;
monumental and I and my family appreciate it greatly.
While you and Altman were rolling on the floor laufing
about Hamilton's "irish problem" Hamilton was a family
business scientist, having three children and devoting
the last 25 years of his work to producing the HV
extension of geometry for people around the world. He
knew exactly how important it was and I believe he also
knew they would try to cover it up. If you know anything
about the King's Men of Science (KMS) clubs than you will
realize how those who envied the Hamilton accomplishments
exagerated one incident at a public party to run down
his life work.
Again when you look at the "ELEMENTS" note that most of
the drawings are done by Hamilton as the intersections of
cones and a sphere, the Hamilton Sphere(HS). This was long
before Riemann worked out layered and cut complex variable
surfaces on his sphere. I don't know the details but I
suspect that the Poincare Sphere was derived by Poincare
from the quaternion square space of the HS.
Thanks again. JD
Robert Low
> While you and Altman were rolling on the floor laufing
> about Hamilton's "irish problem" Hamilton was a family
> business scientist,
See
http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Hamilton.html
Such was his collison with the vile conspiracy of
socialists controlling all aspects of academic
life, he had to settle for being Astronomer Royal
throughout his professional life, and was
only elected to be the first ever foreign
member of the National Academy of the Sciences
of the USA shortly before his death. It's tough
being an unappreciated outsider whose work is
suppressed.
Chris Hillman
On Fri, 11 Feb 2000 jddescr...@my-deja.com wrote:
> With a detailed search I found a few things under "night sky" but not
> these transformations. Could you give a few other key wordas and the
> approximate time when you wrote them?
I can't remember the title of the thread, but it was a VERY long one.
Try searching under one of the author names, "Steve Vandevender", in
sci.physics.relativity. The thread extended over several months. Maybe
Tom Roberts or Nathan Urban or another regular poster who contributed will
recall more detail. You'll need to read the -entire- thread to get the
good stuff. Expect to spend several days wading through it all.
> This second edition was published in 1899 and contains a number of
> geometric appendices of Hamilton's work by Charles Jasper Jolly,
> professor of Astronomy and Royal Astronomer of Ireland.
Are you sure he wasn't a mole?
> Obviously another scientist mistaken about the importance of
> quaternions who would never know what Altman knew some 60 years later.
Or else an Irish double agent run by the Cambridge Five.
> You should ask Pertti Lounesto about the amount of work that Hamilton
> did to produce the HV; monumental and I and my family appreciate it
> greatly.
What are you implying here? That you are a family member of the Oxford
Conspiracy? Or would that be the Trinity College (Dublin) Conspiracy?
> While you and Altman were rolling on the floor laufing about
> Hamilton's "irish problem" Hamilton was a family business scientist,
I am laufing right now. If S1DNeY HARR1S were J0hNNY CARS0N, then you'd
be J0HN BeLUSH1!
> If you know anything about the King's Men of Science (KMS) clubs
Nope, but wasn't there a movie called "King of Hearts"? Anyone who's seen
that will know why you remind me of it :-/
> than you will realize how those who envied the Hamilton
> accomplishments exagerated one incident at a public party to run down
> his life work.
You mean that time that Hamilton got so plastered he took part in a Monty
Python skit? (He played the parrot, IIRC.)
> Again when you look at the "ELEMENTS" note that most of the drawings
> are done by Hamilton
Wow, you mean Hamilton illustrated Eucl1d?!
> This was long before Riemann worked out layered and cut complex
> variable surfaces on his sphere.
Even worse, it has recently been discovered that the "Tevye-Mendel-Baruch
sandwich theorem" should really be called the "Riemann layer cake
theorem". Carcinogenic food dye is optional but highly reccommended in
lecture hall demonstrations of this theorem.
> I don't know the details but I suspect that the Poincare Sphere
Don't you mean the Soviet Sphere?
jddescr...@my-deja.com
Robert Low <mtx...@coventry.ac.uk> wrote:
> jddescr...@my-deja.com wrote:
>
> > While you and Altman were rolling on the floor laufing
> > about Hamilton's "irish problem" Hamilton was a family
> > business scientist,
>
>
> http://www-history.mcs.st-
andrews.ac.uk/history/Mathematicians/Hamilton.html
>
> Such was his collison with the vile conspiracy of
> socialists controlling all aspects of academic
> life, he had to settle for being Astronomer Royal
> throughout his professional life, and was
> only elected to be the first ever foreign
> member of the National Academy of the Sciences
> of the USA shortly before his death. It's tough
> being an unappreciated outsider whose work is
> suppressed.
>
> --
> Rob. http://www.mis.coventry.ac.uk/~mtx014/
>
--------------------------------------------------------------------
You have totally missed the point. See Chris's earlier
description of Hamilton which is the Altman type alibi
for the suppression of the HV [ Hamilton Visualiaztion
= Elements of Quaternions published in 1866 the year
after his death by his son]. Roughly the description
goes; he was a brilliant child prodigy who became
Astronomer Royal of Ireland at something like 21 and was
knighted at about age 30 after having done the optics and
mechanics and conical refraction work. He also was in
fairly close contact with the big island and involved in
scientific societies and such. You have to realize the
status of Ireland for the king's men of science [KMS] in
those times.
See Chris's story. Supposedly Hamilton now [in the last 25
years of his work from age 35 on] becomes a big drinker out
chasing the girls and disippates all his science genius.
This is the story told by the promoters of the French grammar
approach to science and those who suppressed the HV from me
and my family and other average students all over the world.
Even the very best scientists often have fallen for this alibi
of the HV suppression. When Professor Berry rediscovered the
HV in the quantum mechanics context of Berry Phase he
presented a number of papers on precursors to his discovery
in the area of geometric phase including as far back as Gauss.
I corresponded with him because he didn't mention and didn't
realize the connection to the HV. He had never heard about it
in the Scotish schools where he was trained even though Maxwell
and Tait[both Scotish] were experts in the HV and wrote on it
extensively. Of course Professor Berry knew all about the
Hamilton characteristic function of optics and mechanics called
the HAMILTONIAN which had been completed when Hamilton was in
contact with the big island before the suppression of the HV.
The truth of what happened, as I can see it, is that Hamilton
knew the king's men were going to suppress his vast
accomplishments in science visualization and thus withdrew his
work from them for the last 25 years and did it in a form that
would live forever. See Pertti Lounesto's comment about what was
involve in the production of "Elements of Quaternions".
The work totally speaks for itself.
Good seeing. JD
------------------------------------------------------------------------