Books to read for intuition rather than precision.
hi...@email.com
and Wald for GR. But when I need a good intuitive explanation, I reach
for Burke's Applied Differential Geometry or MTW, respectively.
What are your favorite books for an intuitive approach at an advanced
level in these and other branches of mathematics and physics?
mike.james
news:1115170570.5...@f14g2000cwb.googlegroups.com...
> What are your favorite books for an intuitive approach at an advanced
> level in these and other branches of mathematics and physics?
>
I'd like to throw in an odd one ---- Penrose's Roads to Reality
has helped me with the intuitive part of many areas of physics and maths.
After reading it my ideas of spin, confromal symmetry, some areas of QM,
string theory, complex analysis etc.. are all better developed (I hope :-).
Although its advertised as a book for public/lay person consumption
the level of maths in it is well over the top for that category.
To get anything out of it you need to have done some complex analysis,
differential geometry, GR, QM, QFT and so on and its more like a chat with
postgrad students than a book on popular physics aimed at the lay person.
Reading it isn't quite as good as having a chat with Penrose (I'd imagine)
but
it gets close. :-)
mikej
FrediFizzx
One of my favorites of this type is Christoph Schiller's "Motion
Mountain". Best part is that it is free.
http://www.motionmountain.net/
FrediFizzx
richard miller
"mike.james" <mike....@infomaxgroup.co.uk> wrote in message
news:j6ydndc0VLY...@eclipse.net.uk...
>
snip, snip
> Although its advertised as a book for public/lay person consumption
> the level of maths in it is well over the top for that category.
Too right, but if you have 3rd year undergrad/Msc Physics or Maths, as
below,
>
> To get anything out of it you need to have done some complex analysis,
> differential geometry, GR, QM, QFT and so on and its more like a chat with
> postgrad students than a book on popular physics aimed at the lay person.
>
Absolutely, and damm good it is too on these matters. Almost compulsory
pre-course reading for wannabe post-grads, at least in Theoretical Physics
> Reading it isn't quite as good as having a chat with Penrose (I'd imagine)
> but
> it gets close. :-)
>
He lives down the road from me, never spoken or seen him. Immaterial though.
I wish he'd get the credit Hawking gets.
>
> mikej
>
>
RJM (Richard Miller in 'old money')
Spoonfed
Penrose also wrote Emperor's New Mind which has a pretty good
description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
Quantum Mechanics, and general relativity, and the "arrow of time".
For Relativity, Relativity Visualized, by Lewis Carroll Epstein.
Although you should be warned that the Spacetime Diagram he refers to
is not the Minkowsi Spacetime diagram. He plots (x vs t') instead of
(x vs t) so that he can use pythagorean theorem (x^2 + t'^2)=(x'^2 +
t^2) in place of the spacetime interval. (t^2 - x^2) = (t'^2 - x'^2).
In this "geometry" every particle moves at the speed of light, but
unfortunately incidence relations (collisions) are only preserved on
one horizontal axis. However, his approach to General Relativity
through this method is very powerful, conceptually.
For SR, I've got a few animations, myself, at
www.spoonfedrelativity.com
For thermodynamics, I recommend "Boltzmanns Atom." Mostly historical,
but it really captures the era of the turn of the 20th century, and the
excitement of developing an idea.
For a fast read, with a study of formalism and proof, I recommend
"Uncle Petros and Golbach's Conjecture"
Ralph Hartley
> Penrose also wrote Emperor's New Mind which has a pretty good
> description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
> Quantum Mechanics, and general relativity, and the "arrow of time".
I has a *horrible* description of most of those things.
The conclusions drawn from Goedel's theorem, for example, are completely
backwards.
His discussion of the relationship between QM and the arrow of time was
also problematical.
In this book Penrose has a point to prove, and he doesn't appear willing
to let logical fallacies stand in his way.
I know Penrose is very respected in his field (General Relativity), but
he has some "interesting" views on other subjects.
Ralph Hartley
Nick Maclaren
Spoonfed <jonatha...@spoonfedrelativity.com> wrote:
>
>Penrose also wrote Emperor's New Mind which has a pretty good
>description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
>Quantum Mechanics, and general relativity, and the "arrow of time".
Hmm. I don't know of any mathematician (other than Penrose, of
course) who has much respect for that book. It isn't that Penrose
has said anything that is actually false, so much as he has mixed
up known results with wild speculation in a way that confuses the
layman.
In particular, his claim that the human brain is not subject to a
Goedelian limitation doesn't even have a coherent justification,
though you have to read the book carefully to notice that.
Regards,
Nick Maclaren.
Phillip Helbig---remove CLOTHES to reply
Maclaren) writes:
I've never really bought the Gödelian limitation argument from anyone,
be it Penrose or someone else, except in the trivial form in which it
was originally presented. A lot of stuff is read into it which I think
is unjustified.
Getting back to Penrose, although parts of what he says are speculative,
he DOES distinguish between proved-beyond-a-shadow-of-a-doubt, useful,
tentative, speculative etc. The last I heard from him, at a talk in
Groningen, he was working with Anton Zeilinger to construct an
experiment which could falsify his ideas on quantum mechanics.
bjflanagan
> Penrose also wrote Emperor's New Mind which has a pretty good
> description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
> Quantum Mechanics, and general relativity, and the "arrow of time".
Ralph Hartley
It has a *horrible* description of most of those things.
Flanagan
Well, one can disgree with much of what Penrose has to say, but the
fact is he writes very well for a physicist, and has developed a
natural eloquence to such a degree that it looks easy and even artless.
His lasting contribution in this work and in those that followed
consists in having brought a long and thoroughly embarrassing episode
in intellectual history to an abrupt and comical end. He did this by
asking a simple question, epically awkward in its ramifications.
Of the AI community he asked, in effect, "Where in all the circuitry
and software is the mind?"
He further compounded his error by suggesting that quantum theory has
important things to tell us about the mind.
Well! It just wasn't done. Still, it was Penrose who was saying these
things, and not some Joe Blow no one ever heard of -- that is to say,
me. Actually, Stapp and Lockwood got there first also, but none of us
turned the tide. Penrose did.
Overnight, it was all right for respectable scientists to talk about
consciousness (the "C-word") without indulging in an airy, abysmally
ignorant dismissal of all matters metaphysical.
For several years running, the net lit up with a broad surge of
discussion on the issues, most of it profoundly ill-informed.
Conferences were organized, heated words exchanged. At one point it
seemed as though every flake in Christendom had jumped on the "quantum
mind" bandwagon.
For the ban had been lifted, the fell enchantment dispelled, and the
people babbled happily amongst themselves.
In the midst of all the mirth and chaos, a miracle occurred -- a tiny
bit of real progress was made.
Thus, my children, the place of personal clout in the cognitive
development of the species.
Spoonfed
> >
> >Penrose also wrote Emperor's New Mind which has a pretty good
> >description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
> >Quantum Mechanics, and general relativity, and the "arrow of time".
>
> course) who has much respect for that book. It isn't that Penrose
> has said anything that is actually false, so much as he has mixed
> up known results with wild speculation in a way that confuses the
> layman.
>
> In particular, his claim that the human brain is not subject to a
> Goedelian limitation doesn't even have a coherent justification,
> though you have to read the book carefully to notice that.
>
>
> Nick Maclaren.
That's interesting. I must have missed that point. I thought he was
only saying that he believed that the human brain was better at coming
up with true, useful axioms than a computer could be. Our brains are
limited, but not by nearly the same extent that a Universal Turing
Machine is.
Also, as long as quantum mechanics retains its unknown nature, free
will can never be proven false.
I'm sure there is room enough for scientist with the belief that we
will always have some advantage over digital computers and those who
don't.
Nick Maclaren
Phillip Helbig---remove CLOTHES to reply <hel...@astro.multiCLOTHESvax.de> wrote:
>>
>> In particular, his claim that the human brain is not subject to a
>> Goedelian limitation doesn't even have a coherent justification,
>> though you have to read the book carefully to notice that.
>
>I've never really bought the Gödelian limitation argument from anyone,
>be it Penrose or someone else, except in the trivial form in which it
>was originally presented. A lot of stuff is read into it which I think
>is unjustified.
Please reread what I said.
My point is that we don't know whether other classes of system than
the axiomatic ones Goedel was talking about have the same type of
limitation. In particular, we don't know whether the human brain
does - and to claim that it doesn't without proof or even good
evidence is religion and not science.
>Getting back to Penrose, although parts of what he says are speculative,
>he DOES distinguish between proved-beyond-a-shadow-of-a-doubt, useful,
>tentative, speculative etc. The last I heard from him, at a talk in
>Groningen, he was working with Anton Zeilinger to construct an
>experiment which could falsify his ideas on quantum mechanics.
Not in that book, he doesn't. I looked VERY carefully for any trace
of justification for his claim that the human brain is not subject
to a Goedelian limitation, and found neither evidence nor a clear
statement that it was speculative. Indeed, it was stated as a
known fact.
Don't get me onto A Brief History Of Time, which is similar in a
good many respects, even though the speculations are considerably
more mainstream.
Regards,
Nick Maclaren.
mike.james
"Spoonfed" <jonatha...@spoonfedrelativity.com> wrote in message
news:1115387461....@z14g2000cwz.googlegroups.com...
> hi...@email.com wrote:
> Penrose also wrote Emperor's New Mind which has a pretty good
> description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
> Quantum Mechanics, and general relativity, and the "arrow of time".
Indeed and I almost didn't read the road to reality because of the
"nonsense" in the Emperor's New Mind.
Where it is nonsense or not it isn't really physics whereas the Road is all
physics even when it
goes into Penrose's particular viewpoint on a subject.
You can often tell when he just doesn't like an idea (like more dimensions
that 4). Even though
he attempts to justify his viewpoint with reasons you are left with the
feeling that he just thinks its
obviously wrong.
mikej
Spoonfed
Nick Maclaren wrote:
> My point is that we don't know whether other classes of system than
> the axiomatic ones Goedel was talking about have the same type of
> limitation. In particular, we don't know whether the human brain
> does - and to claim that it doesn't without proof or even good
> evidence is religion and not science.
>
What are these non-axiomatic classes of systems?
[Mod. Note: There is a high chance here of veering off topic.
Please restrict the discussion to physics. -ik]
Thanks,
Jonathan Doolin
Nick Maclaren
Certainly. Please censor this if you feel like it.
Axiomatic systems (in the above sense) are mathematical constructs
that have a set of axioms (i.e. statements that are assumed to be
true) and a set of rules for deducing new statements from ones that
are already known. The latter are essentially the standard rules
of formal logic. See Principia Mathematica (which I have not read
and wouldn't understand) for details. It is possible to invent systems
with different rules, and some mathematicians have done it. Again,
I am not familiar with the details - and it is very off-group.
Physics is based on the rules by which the universe works, and the
mathematics of it is generally assumed to be a particular (but not
yet known) axiomatic system. Perhaps not a finite one, but that
doesn't discourage mathematicians! And note that probabilities are
just another number-like construct. However, it is NOT proven that
the mathematics of physics must be an axiomatic system, to which
results like that of Goedel apply.
What is very clear is that Penrose's claim that the human brain is
not subject to a Goedelian limitation necessarily implies that the
laws of physics are not describable by an axiomatic system (in that
sense). We are a physical construct, after all, and therefore are
bound by the laws of the universe in which we exist. So his theories
imply to we would need an entirely new type of mathematics that
that which we all, er, know and love in order to describe the real
physical laws. And that doesn't mean just new theory ....
An interesting consequence, I think that we will all agree, and
definitely enough to make most people's minds boggle. Mine does, to
be sure. I am absolutely certain that, if Penrose is right, I am
not capable of understanding the relevant physical laws.
Sorry - I did veer off physics a bit - into metaphysics :-)
Regards,
Nick Maclaren.
Ralph Hartley
> Spoonfed wrote:
>
>>Penrose also wrote Emperor's New Mind which has a pretty good
>>description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
>>Quantum Mechanics, and general relativity, and the "arrow of time".
>
> Ralph Hartley:
>> It has a *horrible* description of most of those things.
Flanagan:
> Well, one can disgree with much of what Penrose has to say, but the
> fact is he writes very well for a physicist, and has developed a
> natural eloquence to such a degree that it looks easy and even artless.
>
> His lasting contribution in this work and in those that followed
> consists in having brought a long and thoroughly embarrassing episode
> in intellectual history to an abrupt and comical end.
So far a I can see, what he did was to start one.
Maybe it would be more accurate to say that he perpetuated, or even
resurrected, such an episode. I know that I saw his "Goedel argument",
in almost exactly the same form, in the 1970s. The book I saw it in was
very old at the time.
> He did this by
> asking a simple question, epically awkward in its ramifications.
>
> Of the AI community he asked, in effect, "Where in all the circuitry
> and software is the mind?"
Meaningless questions have ramifications?
I could discuss this, and the previous point, at much greater length,
but that would be outside the charter of this group, so I won't.
> He further compounded his error by suggesting that quantum theory has
> important things to tell us about the mind.
Are you suggesting that making such nonsense believable and respectable
was a *good* thing?
Quantum theory has *nothing* to tell us about "the mind".
Nowadays there is debate about the practicality of building
computational devices that exploit quantum effects. Maybe we can, maybe
we can't. What is *quite* clear is that the human brain is *not* such a
device. Nothing that is composed almost entirely of liquid water ever
can be.
Penrose is at his most damaging when he misrepresents physics to justify
his conclusions. People assume that he should know what he is talking
about. They are correct, he *should* know what he is talking about. That
he repeats meritless arguments for many years is "awkward in its
ramifications".
Just last year I saw him repeat the same bogus argument about Quantum
theory and the arrow of time.
Ralph Hartley
hi...@email.com
after texts not aimed at laymen.
Who would put MTW's "Gravitation" and Burke's "Applied Differential
Geometry" in the "for laymen" category (except as a test or a joke,
that is?)
Does anyone have any favorites of the type I'm wondering about?
Nick Maclaren
bjflanagan <words...@earthlink.net> wrote:
>
>His lasting contribution in this work and in those that followed
>consists in having brought a long and thoroughly embarrassing episode
>in intellectual history to an abrupt and comical end. He did this by
>asking a simple question, epically awkward in its ramifications.
>
>
>Thus, my children, the place of personal clout in the cognitive
>development of the species.
Yes, indeed. An excellent summary. He was late in the day when it
came to asking the question, but previous questions had all been
swept under the carpet. He lifted the carpet and flapped it about,
and all the accumulated dirt went flying into the air.
Regards,
Nick Maclaren.
I.Vecchi
>
> Physics is based on the rules by which the universe works, and the
> mathematics of it is generally assumed to be a particular (but not
> yet known) axiomatic system.
> We are a physical construct, after all, and therefore are
> bound by the laws of the universe in which we exist.
Is it really so?
According to Schroedinger ([1]} "the world is a construct of our
perceptions, sensations and memories", i.e. of the only phenomena that
we can directly experience.
That isn't the same as you are saying, is it?
Regards.
IV
[1] E. Schroedinger, "Mind and Matter", 1958
mike.james
news:1115680820.3...@f14g2000cwb.googlegroups.com...
> Okay. This discussion has been interesting, but I was really asking
> after texts not aimed at laymen.
>
> Who would put MTW's "Gravitation" and Burke's "Applied Differential
> Geometry" in the "for laymen" category (except as a test or a joke,
> that is?)
>
> Does anyone have any favorites of the type I'm wondering about?
Sorry to repeat but Penrose's Roads To Reality isn't in the "laymen"
category despite it saying it is and being in the best sellers list.
It is almost as technical as the two books you list but it isn't as
focused on a single topic - more an overview of interesting topics
in modern physics/mathematical physics - lie groups, fibre bundles,
gauge theory etc...
Just find a copy - open it - look at the number of equations and then
decided if it is a laymans book or not.
mikej
bjflanagan
I could discuss this, and the previous point, at much greater length,
but that would be outside the charter of this group, so I won't."
Yes, the physics of the brain is strictly out of bounds.
> He further compounded his error by suggesting that quantum theory has
important things to tell us about the mind.
"Are you suggesting that making such nonsense believable and
respectable was a *good* thing?"
That comment may have been intended as irony. Are you suggesting that
begging the question is an acceptable form of argument?
"Quantum theory has *nothing* to tell us about 'the mind.'"
Thank you for the benefit of your informed and reasoned analysis.
Dan Schmidt
I haven't read it yet, but Needham's VISUAL COMPLEX ANALYSIS seems like
this kind of book and has gotten rave reviews.
Nick Maclaren
I.Vecchi <vec...@weirdtech.com> wrote:
>Nick Maclaren wrote:
>>
>> Physics is based on the rules by which the universe works, and the
>> mathematics of it is generally assumed to be a particular (but not
>> yet known) axiomatic system.
>..
>> We are a physical construct, after all, and therefore are
>> bound by the laws of the universe in which we exist.
>
>Is it really so?
Most scientists think so, but neo-creationists and similar disagree.
>According to Schroedinger ([1]} "the world is a construct of our
>perceptions, sensations and memories", i.e. of the only phenomena that
>we can directly experience.
>That isn't the same as you are saying, is it?
>
>[1] E. Schroedinger, "Mind and Matter", 1958
No. But what he meant by that is orthogonal to my point, which is
exactly the same whether it refers to the observable universe or the
actual universe underlying that.
What I meant is that we are a physical object - a complex one, to be
sure, but a purely physical construction. What we can prove, and
even imagine, is therefore limited by our initial state (describable
in physical terms even if it is not measurable) and the laws of
physics. So we cannot achieve anything that is impossible under the
aws of physics. And, if the laws of physics can be described as an
axiomatic system (in the Goedelian sense), this includes a complete
analysis of our own theoretical limits. We have no reason to believe
that they are, though it would really blow people's minds if they
are not.
That may seem obvious, but a surprising number of people are not
prepared to accept it.
In particular, most people miss the fact that Penrose's claims are
FAR more radical than either he makes out or is commonly believed.
I cannot make any intelligent judgement on whether he is likely to
be right, but I can comment that he has assuredly not demonstrated
the likelihood of his claims.
Regards,
Nick Maclaren.
Jack....@gmail.com
> >What are your favorite books for an intuitive approach at an
advanced
> >level in these and other branches of mathematics and physics?
Karl Gustafson's Partial Differential Equations and Hilbert Space
Methods.
--
Tana t'mirat,
mjesht=EBr Ardiani
mike.james
news:1115780855.6...@g14g2000cwa.googlegroups.com...
This doesn't sound like the title of a book that has "intuition" within and
there isn't much information on Amazon (one review on .com).
Can you tell us a bit more about it.
mikej
Ardiani
mike.james wrote:
> <Jack....@gmail.com> wrote in message
> news:1115780855.6...@g14g2000cwa.googlegroups.com...
> >
> > Methods.
> >
> > --
> > Tana t'mirat,
> > mjesht=EBr Ardiani
>
> This doesn't sound like the title of a book that has "intuition"
> within and there isn't much information on Amazon (one review on
> .com). Can you tell us a bit more about it.
> mikej
It's a graduate textbook on PDEs, with the physicist and engineer in
mind. Subject matter is bulit by examples, rather than definitions,
using an "intuitive" language (e.g. one can read about regularity of
the solution at the corner of a domain, instead of differentiability of
the solution at the points of discontinuity) and a lot of physical
interpretations (e.g. Green's function method of solving PDEs is
illustrated by singular point source of heat, leading later to the
Dirac's delta function).
It's a textbook that one needs to "work" with, rather than "read and
memorize". This means that in order to understand what's going on, the
reader needs to solve the problems, which are given instead of
definitions. In effect, this makes the reader develop "the feel" for
the various mathematical concepts considered. Later, when new concepts
are introduced, the author goes back to the same problem and attacks it
again, thus repeating without being tedious.
One thing that I felt was forced was the trinity in everything: three
opeators (Laplacian, diffusion, d'Alambertian), three problems
(boundary value, initial value, eigenvalue), three solution methods
(separation of variables, Green's functions, variational method), and
many other threes... But, I guess this was nice from the pedagogical
point of view.
Since I haven't read many books on PDEs, I can't really compare this
book in relation to many other books out there. But, in itself, this
textbook is quite nicely written, with a lot of excercises (some with
solutions), examples from physics (mainly classical), and I think that
it appeals to intuition rather than mathematical exactness (which
doesn't mean that it's missing).
Regards,
--
Tana t'mirat,
mjeshtër Ardiani
achilleas...@yahoo.co.uk
intuition.
Ralph Hartley
> Ralph Hartley wrote:
>> I could discuss this, and the previous point, at much greater
>> length, but that would be outside the charter of this group, so I
>> won't."
>
> Yes, the physics of the brain is strictly out of bounds.
The physics of the brain is in scope, but the philosophy of the mind is
not.
>>> He further compounded his error by suggesting that quantum theory
>>> has important things to tell us about the mind.
>
>> "Are you suggesting that making such nonsense believable and
>> respectable was a *good* thing?"
>
> That comment may have been intended as irony.
You mean *your* comment about "error"?
I'm not sure if you mean to suggest (by irony) that Penrose's argument
is not really an error, or that it was an error, but making it
respectable was a good thing anyway.
Abandoning irony *completely* let me make my position clear.
(1) Penrose's argument that quantum theory has important things to tell
us about the mind is nonsense.
(2) Making nonsense believable and respectable is *not* a good thing.
(3) It would be a bad thing even *if* the conclusion were correct (which
is very unlikely in this case). An invalid argument for a true
proposition is still an invalid argument.
Do you disagree with any of those points? If you disagree with (1), show
me a valid argument that Penrose made (or any valid argument for that
matter).
If you disagree with (2) or (3), we have nothing to discuss.
>> "Quantum theory has *nothing* to tell us about 'the mind.'"
>
> Thank you for the benefit of your informed and reasoned analysis.
You are welcome :-) That was the conclusion. I will repeat the
justification that followed:
Nowadays there is debate about the practicality of building
computational devices that exploit quantum effects. Maybe we can,
maybe we can't. What is *quite* clear is that the human brain is
*not* such a device. Nothing that is composed almost entirely of
liquid water ever can be.
That *is* a statement about the physics of the brain. If you want to
argue with that, go ahead, but be prepared to explain how quantum
effects can matter to a system with a *very* short coherence time and a
*very* long interaction time.
We also have quite a bit of understanding of what a device gains if it
can exploit quantum effects. It may gain the ability to efficiently
solve some otherwise intractable problems. It would *not* gain anything
"non-algorithmic" or anything with obvious relevance to "consciousness"
or "the mind".
Penrose's theses actually requires more than the brain being able to
exploit quantum effects. It requires that quantum mechanics *fail* (in a
rather peculiar way) and that the brain can exploit that failure.
Ralph Hartley
I.Vecchi
Nick Maclaren wrote:
> In article <1115736439.1...@f14g2000cwb.googlegroups.com>,
> I.Vecchi <vec...@weirdtech.com> wrote:
> >Nick Maclaren wrote:
> >>
> >> Physics is based on the rules by which the universe works, and the
> >> mathematics of it is generally assumed to be a particular (but not
> >> yet known) axiomatic system.
> >..
> >> We are a physical construct, after all, and therefore are
> >> bound by the laws of the universe in which we exist.
> >
> >Is it really so?
>
> Most scientists think so, but neo-creationists and similar disagree.
Oh my god! Terrifying company indeed. Especially the all-encompassing
"similar".
>
> >According to Schroedinger ([1]} "the world is a construct of our
> >perceptions, sensations and memories", i.e. of the only phenomena
> >that we can directly experience. That isn't the same as you are
> >saying, is it?
> >
> >[1] E. Schroedinger, "Mind and Matter", 1958
>
> No. But what he meant by that is orthogonal to my point, which is
> exactly the same whether it refers to the observable universe or the
> actual universe underlying that.
Schroedinger is positing our perceptions as the primary entity and he
clearly states that the world is a construct thereof.
You are claiming that we are a physical construct.
I don't see the two statements as orthogonal.
I have trouble grasping why there should be "actual universe
underlying" our peceptions. What does "actual" mean in this setting?
> What I meant is that we are a physical object - a complex one, to be
> sure, but a purely physical construction.
As far as I understand you are postulating an external, "inherently
existing" universe. In my opinion such an assumption is both
unnecessary and unwarranted from a scientific point of view.
> What we can prove, and
> even imagine, is therefore limited by our initial state (describable
> in physical terms even if it is not measurable) and the laws of
> physics. So we cannot achieve anything that is impossible under the
> aws of physics. And, if the laws of physics can be described as an
> axiomatic system (in the Goedelian sense),
that's a pretty big if
> this includes a complete
> analysis of our own theoretical limits. We have no reason to believe
> that they are, though it would really blow people's minds if they
> are not.
>
> That may seem obvious, but a surprising number of people are not
> prepared to accept it.
> In particular, most people miss the fact that Penrose's claims are
> FAR more radical than either he makes out or is commonly believed.
I agree on this.
> I cannot make any intelligent judgement on whether he is likely to
> be right, but I can comment that he has assuredly not demonstrated
> the likelihood of his claims.
The relevant issue, imo, is whether his claims can be tested
experimentally.
Cheers,
IV
Nick Maclaren
In article <1115987280.1...@g44g2000cwa.googlegroups.com>,
"I.Vecchi" <vec...@weirdtech.com> writes:
|>
|> > >According to Schroedinger ([1]} "the world is a construct of our
|> > >perceptions, sensations and memories", i.e. of the only phenomena
|> > >that we can directly experience. That isn't the same as you are
|> > >saying, is it?
|> > >
|> > >[1] E. Schroedinger, "Mind and Matter", 1958
|> >
|> > No. But what he meant by that is orthogonal to my point, which is
|> > exactly the same whether it refers to the observable universe or the
|> > actual universe underlying that.
|>
|> Schroedinger is positing our perceptions as the primary entity and he
|> clearly states that the world is a construct thereof.
In that sentence, he would appear to be doing so, but the book
doesn't support that hypothesis. I am 90% certain that his term
"the world" meant "the world as described by our physical theories".
A very different thing.
However, I have just got the book out of the UL and leafed through
it to check that point. It looks like a good example of a book to
read for intuition rather than precision, so thank you for the
reference.
|> You are claiming that we are a physical construct.
Yes.
|> I don't see the two statements as orthogonal.
No, but they are both orthogonal to my point, which was equally
relevant if it was referring to an actual physical world, the world
as perceived by us, or an imaginary world. If an entity IN any of
those worlds does NOT have a Goedelian limit on its thought
processes, then the laws of that world cannot be described by an
axiomatic system.
|> I have trouble grasping why there should be "actual universe
|> underlying" our peceptions. What does "actual" mean in this
|> setting?
One that exists in reality, as distrinct from being a model that
we have deduced from our perceptions or just plain invented.
|> > What I meant is that we are a physical object - a complex one,
|> > to be sure, but a purely physical construction.
|>
|> As far as I understand you are postulating an external, "inherently
|> existing" universe. In my opinion such an assumption is both
|> unnecessary and unwarranted from a scientific point of view.
Because the converse leads to a ridiculous state. If there is no
external, "inherently existing" universe, then A. Physicist can't
produce evidence that debunks B. Kook's 'theory' is invalid, because
it related to a different universe. If you claim that, despite
there being no external universe, all of our perceptions are
compatible, then I think that you should explain how and why.
The universe I am talking about is the one that we are trying to
model by our physical theories, and discussing on this group. Yes,
I agree that it may be a program in some gigantic supercomputer,
but I am then talking about the rules of the program (i.e. its
functional specification).
|> > And, if the laws of physics can be described as an
|> > axiomatic system (in the Goedelian sense),
|>
|> that's a pretty big if
Yes. And so is the converse. I am not making any judgement about
whether either is true in my point - merely assuming one as a
precondition to explore the consequences.
|> > I cannot make any intelligent judgement on whether he is likely to
|> > be right, but I can comment that he has assuredly not demonstrated
|> > the likelihood of his claims.
|>
|> The relevant issue, imo, is whether his claims can be tested
|> experimentally.
I can't think of how.
Regards,
Nick Maclaren.
r...@maths.tcd.ie
>bjflanagan wrote:
>> Ralph Hartley wrote:
>>>bjflanagan wrote:
>>>> He further compounded his error by suggesting that quantum theory
>>>> has important things to tell us about the mind.
>>
>>> "Are you suggesting that making such nonsense believable and
>>> respectable was a *good* thing?"
>>
>> That comment may have been intended as irony.
>You mean *your* comment about "error"?
>I'm not sure if you mean to suggest (by irony) that Penrose's argument
>is not really an error, or that it was an error, but making it
>respectable was a good thing anyway.
Apparently the two of you have difficulty communicating.
>Abandoning irony *completely* let me make my position clear.
>(1) Penrose's argument that quantum theory has important things to tell
>us about the mind is nonsense.
>(2) Making nonsense believable and respectable is *not* a good thing.
>(3) It would be a bad thing even *if* the conclusion were correct (which
>is very unlikely in this case). An invalid argument for a true
>proposition is still an invalid argument.
>Do you disagree with any of those points? If you disagree with (1), show
>me a valid argument that Penrose made (or any valid argument for that
>matter).
You are fighting against Penrose instead of my namesake. What Brian
was saying was that Penrose's discussion of the subject made it
acceptable for scientists to acknowledge that there is such
a thing as consciousness, even if his actual claims were
speculative, unjustified and incorrect. This was a "good thing"
because previously scientists, and especially physicists,
stood side by side with new age enthusiasts and with those
who oppose all rational enquiry, in condemning any attempt to
think about the mind and its relation to the physical world.
Most of them still do, in fact; I think my cousin is more
optimistic than I.
There was a global prohibition on physicists talking or even thinking
about the mind, and young physicists were trained to sneer at and
insult those who talked or thought about it. Such physicists can
be spotted very easily because when they mention the mind they put
quotation marks around it, to give the reader the impression that
they don't believe it exists, and have contempt for those who do.
This plays an important role in the society of physicists,
as bashing an officially recognised enemy is one way for
a person to maintain their self-esteem. Hence every physicist
can say "I, as a physicist, am superior to all philosophers,"
and will encourage other physicists to adopt the same behaviour,
which they gladly do, since it nurtures their self-esteem. Racism,
hatred of homosexuals and liberals or whoever is officially recognised
as bad in some community, all feed from the same basic impulse.
Tribalism. Savagery.
Physicists who suggest that perhaps the philosophers may have noticed
something that physicists in general haven't, are to be publicly
ridiculed, and all discussion of the subject of philosophy itself
is officially banned, and the ban is implemented in public
discussion arenas. Physics has nothing to do with the mind
because physics has nothing to learn from philosophy, because
philosophers are filthy, dirty, untermenschen.
It wasn't always so; in the seventeenth and eighteenth centuries
many physicists were also philosophers, and, for somebody such as
Descartes or Leibniz, it was crystal clear that there was such a
thing as the mind. The official understanding of physicists today
is that the physical world is all there is, which is the same as
saying that experience doesn't exist. Pointing out that this is
incorrect is officially evil, tantamount to the crime of philosophy,
and whoever talks of experience can be accused of believing in
spirits and immediately classified as a lunatic.
Contempt for philosophers is communicated from physicist to physicist
in the way that racism spreads, but no physicist will admit that
their distate for philosophers was communicated to them in this way,
because each person, in his quest for the respect of his peers,
will try to present an image of himself as a perfect being, unaffected
by social pressures and not in need of any support for his self-esteem.
He will say that he came up with the idea himself, after careful
thought and consideration. Meanwhile, physicists in general are
doomed to remain ignorant of philosophy, except for some of the
"common sense" philosophers such as Russell and Popper.
To demonstrate that this is to the detriment of physicists generally,
I need only draw attention to the epistemology/ontology debate,
which is the same as the Copenhagen/Many-worlds-Bohm-Transactional-
Relational "debate" in physics, which isn't even a debate since
physicists are forbidden from talking about it. The same discussion
has played out again and again among physicists, "Let's talk
about interpretations of quantum mechanics ... Whoops, we're
talking about philosophy. We'd better stop. We're not allowed
to do that." No progress is ever made because thinking and
talking about it is banned.
Again, on the subject of "the mind", I should make it publicly
known that the social rules by which physicists abide say that
it's OK to break the rules of normal rational scientific
discussion when dealing with such filthy philosophers, just as it is
acceptable for a news reporter to exaggerate the dangers of drugs
(it helps keep society safe), or bend the truth in the service of
patriotism. The rules which make science successful are to be
abandoned when they conflict with the "higher good" of giving
philosophers a public trouncing at the hands of physicists.
Hence, if no flaw can be found in their arguments, their
conclusions can be rejected anyway, because they're crazy
fools.
At this point the humble physicist would reflect that physics
has been successful not because of the inherent greatness
of physicists, but because they have traditionally kept well
to the rules of scientific enquiry. It is those rules, not
personal inner greatness, which have kept physics largely immune
from the corrupting influence of emotional motivations. When
a physicist breaks those rules he is abandoning the thing
which had made physics successful, even if he has been trained
to do that by other physicists. If he thinks that inner greatness
or deep insight will make his assertions correct anyway then
he is deluding himself.
>>> "Quantum theory has *nothing* to tell us about 'the mind.'"
>> Thank you for the benefit of your informed and reasoned analysis.
I think Brian's summary of my rant is concise, but, given the
difficulty of communicating about "the mind", I prefer to
be verbose to avoid misunderstanding.
>You are welcome :-) That was the conclusion. I will repeat the
>justification that followed:
[snipped]
Your argument establishes that it is unlikely that quantum
effects play any role in neural information processing. Of
course, it's not conclusively ruled out, but it's fairly unlikely.
I should clarify that there are two different ways
in which quantum effects are unlikely to play a role.
One is that the brain somehow make use of quantum computation,
either inside a neuron at the level of somatic membrane potential
(meaning that the question "Will this neuron fire?" is decided
as the outcome of a quantum computation, after which the consequences
of the firing are classical), or at the level of communication
between neurons, so that the state of one neuron is entangled
with the state of another.
The other is that the "randomness" of quantum mechanics
stops being quite so random inside the brain, and that
when a particle spontaneously adopts a position (as the
Copenhagen interpretation would have it), the position
is specifically tailored to help the animal behave
or perceive.
Now, as you argued and I agreed, these are very unlikely
indeed, but that doesn't justify your original statement:
>>> "Quantum theory has *nothing* to tell us about 'the mind.'"
Rather it says that quantum theory is unlikely to tell us
much about how information is processed by individual
neurons or groups of neurons in the brain.
You might, of course, challenge me to explain how quantum
theory could have something to do with the mind. I would
then be entitled to say that I never claimed that it
did; I merely haven't seen any proof that it doesn't,
and dogmatic (that is, unproved) assertions don't persuade me,
even if they are coupled with emphatic asterisks and
I-don't-even-believe-in-the-mind quotation marks.
But I won't do that; instead I'll tell you how quantum
mechanics might have something to do with the mind, and
I stress that it is only a possibility.
Quantum mechanics appears to very nicely characterize
induction - the basic notion that similar experiments
give similar results. The old problem with induction
was that it remained vague because of the difficulty
involved in measuring the "similarity" of experiments.
Quantum mechanics solves that problem by giving
an explicit mathematical representation of the
experiments. Rotate your apparatus, and there's a
corresponding SO(3) action on your observable
operator. It provides the quantitative element
that was missing from earlier attempts to say
precisely what the principle of induction was.
Also, quantum mechanics is where induction breaks
down. You can't predict the position of the
particle with any more accuracy than |psi^2|,
even in principle. Do the same experiment twice
and you don't get the results.
It's possible that quantum mechanics is a quantitative
formalization of the principle of induction, just
as boolean algebra gives a formalization of deductive
inference (propositional calculus). Now, both inductive
and deductive inferences are done by the mind, so, in
so far as formal logic sets out the rules of correct deductive
thought, quantum mechanics might very well play the
corresponding role for inductive thought.
R.
bjflanagan
Ralph Hartley
The physics of the brain is in scope, but the philosophy of the mind is
not.
Flanagan
What if a mind/brain identity theory holds? What if, as Born said late
in life, physics is philosophy?
Here is what Chalmers, a philosopher, wrote in Sci Am:
"The abstract notion of information, as put forward by Claude E.
Shannon of MIT, is that a of a set of separate states with a basic
structure of similarities and differences between them. We can think of
a 10-bit binary code as an information state, for example. Such
information can be embodied in the physical world. This happens
whenever they correspond to physical states (voltages, say); the
differences between them can be transmitted along some pathway, such as
a telephone line.
We can also find information embodied in conscious experience. The
pattern of color patches in a visual field, for example, can be seen as
analogous to that of pixels covering a display screen. Intriguingly, it
turns out that we find the same information states embodied in
conscious experience and in underlying physical processes in the brain.
The three-dimensional encoding of color spaces, for example, suggests
that the information state in a color experience correspond directly to
an information state in the brain. We might even regard the two states
as distinct aspects of a single information state, which is
simultaneously embodied in both physical processing and conscious
experience. "
David J. Chalmers, "Puzzle of Conscious Experience", Scientific
American, 12/95.
Hartley
I'm not sure if you mean to suggest (by irony) that Penrose's argument
is not really an error, or that it was an error, but making it
respectable was a good thing anyway.
Abandoning irony *completely* let me make my position clear.
(1) Penrose's argument that quantum theory has important things to tell
us about the mind is nonsense.
Flanagan
In another Sci Am article, Freeman Dyson states quite clearly that,
from the perspective of quantum field theory (QFT) everything in the
physical universe is a quantum field: "There is nothing else except
these fields: the whole of the material universe is built of them."
It follows by a ready consequence that the brain, being a part of the
material universe, just is a collection of [quantum] fields. If an
identity between mind & brain obtains, Dyson's remark would seem to
constrain the solution set quite radically, as you would no doubt
agree. I.e., conscious processes must be field processes: what other
possibility is there, from the physicist's point of view? In this
connection it is interesting to consider that our sensory fields vary
in step with photon fields--a fact subject to experimental
verification. Contrary to prevailing views, it seems quite plausible
(to me, at any rate) that physicists have all kinds of interesting
things to tell us about the mind--if they only knew it. Obviously, such
s development would constitute a major triumph for their science,
although perhaps an unexpected one.
Hartley
Nowadays there is debate about the practicality of building
computational devices that exploit quantum effects. Maybe we can,
maybe we can't. What is *quite* clear is that the human brain is
*not* such a device. Nothing that is composed almost entirely of
liquid water ever can be.
Flanagan
In a quantum universe, all effects are quantum effects, yes? The brain
is mostly water and yet it clearly mediates computations. One can talk
about "higher order" levels of the brain's organization, but the only
level with causal efficacy is the quantum level. (On a reductionist
view, the "higher" levels amount to a kind of shorthand for assemblies
of field processes.)
Hartley
That *is* a statement about the physics of the brain. If you want to
argue with that, go ahead, but be prepared to explain how quantum
effects can matter to a system with a *very* short coherence time and a
*very* long interaction time.
Flanagan
The fractal character of neural nets and their dendritic trees might
suggest self-similarity across spatio-temporal scales. Weyl scaling
might obtain if, as would seem most plausible, the brain's photon
fields are most relevant to what are called conscious processes.
Perhaps neural form follows quantum function? Umezawa, in his nice text
on 'Advanced Field Theory,' seems to suggest something of the kind:
"As we have seen in preceding sections, manifestation of ordered states
is of quantum origin. When we recall that almost all of the macroscopic
ordered states are the result of quantum field theory, it seems natural
to assume that macroscopic ordered states in biological systems are
also created by a similar mechanism."
Hartley
We also have quite a bit of understanding of what a device gains if it
can exploit quantum effects. It may gain the ability to efficiently
solve some otherwise intractable problems. It would *not* gain anything
"non-algorithmic" or anything with obvious relevance to "consciousness"
or "the mind."
Flanagan
Colors and sounds were swept into the dustbin of the mind long ago by
Newton and Galileo. Yet colors and sounds would seem to behave like
physical things, as Mach pointed out; thus, e.g., colors and sounds:
(1) occur in natural spectra;
(2) exhibit crucial symmetries;
(3) depend in a familar way upon phase relations;
(4) respect the laws of projective vector geometry; and
(5) are readily observable.
Weyl is quite explicit regarding #4: "Thus the colors with their
various qualities and intensities fulfill the axioms of vector geometry
if addition is interpreted as mixing; consequently, projective geometry
applies to the color qualities." On his analysis, it seems as though
sounds ought to respect that geometry also:
"Mathematics has introduced the name isomorphic representation for the
relation which according to Helmholtz exists between objects and their
signs. I should like to carry out the precise explanation of this
notion between the points of the projective plane and the color
qualities . . . the projective plane and the color continuum are
isomorphic with one another. Every theorem which is correct in the one
system S_1 is transferred unchanged to the other S_2. A science can
never determine its subject matter except up to an isomorphic
representation. The idea of isomorphism indicates the self-understood,
insurmountable barrier of knowledge. It follows that toward the
"nature" of its objects science maintains complete indifference. This
for example what distinguishes the colors from the points of the
projective plane one can only know in immediate alive intuition . . ."
Weyl arrived at this isomorphism by noting that two colors mixed
together yield another between the two and then mapping this
"betweenness" to a point lying between two others on a line in the
projective plane.
With a color mixture, then, so with a chord:
"To monochromatic light corresponds in the acoustic domain the simple
tone. Out of different kinds of monochromatic light composite light may
be mixed, just as tones combine to a composite sound. This takes place
by superposing simple oscillations of different frequency with definite
intensities." (Weyl)
Dirac, writing about the usual sorts of QM superpositions, points out
several salient features which apply equally well to superpositions of
colors and sounds--which would make a good kind of sense if some sort
of identity should obtain:
"When a state is formed by the superposition of two other states, it
will have properties that are in some vague way intermediate between
those of the original states and that approach more or less closely to
those of either of them according to the greater or less 'weight'
attached to this state in the superposition process. The new state is
completely defined by the two original states when their relative
weights in the superposition process are known, together with a certain
phase difference, the exact meaning of weights and phases being
provided in the general case by the mathematical theory."
Dirac, 'The Principles of Quantum Mechanics,' Oxford, 1958.
I.Vecchi
> In article <1115987280.1...@g44g2000cwa.googlegroups.com>,
> "I.Vecchi" <vec...@weirdtech.com> writes:
> |>
> |> > >According to Schroedinger ([1]} "the world is a construct of our
> |> > >perceptions, sensations and memories", i.e. of the only phenomena
> |> > >that we can directly experience. That isn't the same as you are
> |> > >saying, is it?
> |> > >
> |> > >[1] E. Schroedinger, "Mind and Matter", 1958
> |> >
> |> > No. But what he meant by that is orthogonal to my point, which is
> |> > exactly the same whether it refers to the observable universe or the
> |> > actual universe underlying that.
> |>
> |> Schroedinger is positing our perceptions as the primary entity and he
> |> clearly states that the world is a construct thereof.
>
> In that sentence, he would appear to be doing so, but the book
> doesn't support that hypothesis. I am 90% certain that his term
> "the world" meant "the world as described by our physical theories".
> A very different thing.
Schroedinger elucidates (?) this crucial point in "My view of the
world" where he writes : "In all the world, there is no kind of
framework within which we canfind consciousness in the plural; this is
simply something we
construct because of the spatio-temporal plurality of individuals, but
it is a false construction. Because of it, all philosophy succumbs
again and again to the hopeless conflict between the theoretically
unavoidable acceptance of Berkeleian idealism and its complete
uselessness for understanding the real world."
> However, I have just got the book out of the UL and leafed through
> it to check that point. It looks like a good example of a book to
> read for intuition rather than precision, so thank you for the
> reference.
You are welcome.
OK. This is indeed the crux of the matter.
Indeed any community of observers has a locus of intersubjective
agreement, its very own "reality".
But who's the "we" you are referring to?
Does "we" include the instances of Nick McLaren who saw the cat dead ,
as unitarity dictates, while you saw it alive?
> Yes,
> I agree that it may be a program in some gigantic supercomputer,
> but I am then talking about the rules of the program (i.e. its
> functional specification).
> |> > And, if the laws of physics can be described as an
> |> > axiomatic system (in the Goedelian sense),
> |>
> |> that's a pretty big if
>
> Yes. And so is the converse. I am not making any judgement about
> whether either is true in my point - merely assuming one as a
> precondition to explore the consequences.
>
> |> > I cannot make any intelligent judgement on whether he is likely to
> |> > be right, but I can comment that he has assuredly not demonstrated
> |> > the likelihood of his claims.
> |>
> |> The relevant issue, imo, is whether his claims can be tested
> |> experimentally.
>
> I can't think of how.
I am no fan of Penrose's ideas , but macroscopic superpositions are
already being detected ([1]). When we'll be able to detect superposed
observers (see above) this discussion may reveal itself as more than
philosophical twaddle.
Thank you for your stimulating reply.
IV
Ralph Hartley
> Ralph Hartley <har...@aic.nrl.navy.mil> writes:
>>Abandoning irony *completely* let me make my position clear.
>
>>(1) Penrose's argument that quantum theory has important things to tell
>>us about the mind is nonsense.
>
>>(2) Making nonsense believable and respectable is *not* a good thing.
>
>
> was saying was that Penrose's discussion of the subject made it
> acceptable for scientists to acknowledge that there is such
> a thing as consciousness, even if his actual claims were
> speculative, unjustified and incorrect. This was a "good thing"
So you disagree with (3) then? (Or is that what you think Brian was
saying? The rest of your message implies that you agree with him.)
> because previously scientists, and especially physicists,
> stood side by side with new age enthusiasts and with those
> who oppose all rational enquiry
To consider invalid arguments a good thing under any circumstances, is
to reject rational inquiry.
To fool people into considering a question that they would not otherwise
think about, even if they *should* think about it, is not a good thing.
If nothing else, invalid arguments hide any valid arguments that may
exist, and make their conclusions less respectable among people who
recognize the arguments as invalid.
> The rules which make science successful are to be
> abandoned when they conflict with the "higher good" of giving
> philosophers a public trouncing at the hands of physicists.
But the reverse is OK?
> There was a global prohibition on physicists talking or even thinking
> about the mind
Can you show me something positive that resulted from them doing so, or
even any valid argument that they should?
>[Snipped: I have been indoctrinated]
..
> To demonstrate that this is to the detriment of physicists generally,
> I need only draw attention to the epistemology/ontology debate,
> which is the same as the Copenhagen/Many-worlds-Bohm-Transactional-
> Relational "debate" in physics, which isn't even a debate since
> physicists are forbidden from talking about it. The same discussion
> has played out again and again among physicists, "Let's talk
> about interpretations of quantum mechanics ... Whoops, we're
> talking about philosophy. We'd better stop. We're not allowed
> to do that." No progress is ever made because thinking and
> talking about it is banned.
Here you have cause and effect reversed. Taking about it is "banned"
because no progress is ever made.
This is a question that *every* physicist now alive thinks about at some
time. That little progress has resulted is not a good sign. There is
reason to believe that the kind of progress that physicists can
*use* is very unlikely.
If philosophers have something *new* to add, they should do so. There
*will* be resistance, because we have all had to listen to so much
nonsense already.
> if no flaw can be found in their arguments, their
> conclusions can be rejected anyway, because they're crazy
> fools.
I think your argument could be better made by giving examples of valid
arguments that physicists should be interested in, but reject.
> Your [sniped] argument establishes that it is unlikely that quantum
> effects play any role in neural information processing. Of
> course, it's not conclusively ruled out, but it's fairly unlikely.
>
> I should clarify that there are two different ways
> in which quantum effects are unlikely to play a role.
>
> One is that the brain somehow make use of quantum computation,
..
> The other is that the "randomness" of quantum mechanics
> stops being quite so random inside the brain
..
> Now, as you argued and I agreed, these are very unlikely
> indeed
It is good that you made that clear, since what you agree is unlikely is
Penrose's position.
> but that doesn't justify your original statement:
>
>>>>"Quantum theory has *nothing* to tell us about 'the mind.'"
>
> Rather it says that quantum theory is unlikely to tell us
> much about how information is processed by individual
> neurons or groups of neurons in the brain.
The brain and the mind are closely related, as seen by the fact that
interfering with brain function alters or abolishes consciousness.
One could argue that the mind is simply the function of the brain, in
which case they would be the same thing. I don't need to argue that,
only that the brain and mind are so closely linked that anything closely
related to one must be closely related to the other, in *either* direction.
> You might, of course, challenge me to explain how quantum
> theory could have something to do with the mind. I would
> then be entitled to say that I never claimed that it
> did; I merely haven't seen any proof that it doesn't
I didn't claim that there is no relationship at all, one can find a
relationship between *any* two things, only that it has nothing to
*tell* us. To claim that QM may tell us something about the mind, but
nobody has any idea what, is nonsense. I stretches the meaning of the
word "tell" even farther than we have done already.
Either QM has something to tell us about the mind, and we need only
listen, or it doesn't.
> But I won't do that; instead I'll tell you how quantum
> mechanics might have something to do with the mind, and
> I stress that it is only a possibility.
Do you think you make a valid argument that something could be true, by
showing examples of how it might be, but isn't? Or do you just want to
make an argument without having to defend it?
> Quantum mechanics appears to very nicely characterize
> induction - the basic notion that similar experiments
> give similar results. The old problem with induction
> was that it remained vague because of the difficulty
> involved in measuring the "similarity" of experiments.
> Quantum mechanics solves that problem by giving
> an explicit mathematical representation of the
> experiments. Rotate your apparatus, and there's a
> corresponding SO(3) action on your observable
> operator.
Carefully representing experiments and observables is not part of
quantum mechanics. It applies just as well to classical mechanics. It is
a tool used to do QM, but it is in no way *part* of Quantum mechanics.
A screwdriver can be used as a stabbing weapon, but that does not mean
that screws have something to tell us about ancient warfare.
That's just as well, since induction has been used since the stone age.
Your (non) position would imply that induction was invalid when the
ancients did it, but became valid in the mid 20th century, or perhaps
that induction just wouldn't work in a classical world. That would be
odd since it worked fine in the 10th century when quantum effects were
undetectable.
> Also, quantum mechanics is where induction breaks
> down. You can't predict the position of the
> particle with any more accuracy than |psi^2|,
> even in principle. Do the same experiment twice
> and you don't get the results.
I get the same thing with classical dice (well maybe not the "even in
principle" part, but I don't see how that matters).
> It's possible that quantum mechanics is a quantitative
> formalization of the principle of induction, just
> as boolean algebra gives a formalization of deductive
> inference (propositional calculus).
It would be possible if Quantum Mechanics were anything *like* the
principle of induction. A better candidate for a formalization of the
principle of induction would be Statistical Inference, which is related
to Probability Theory, which *is* related to Quantum Mechanics. :-)
Even if the mathematical descriptions of Quantum Mechanics and induction
were identical, that would not be a direct connection between induction
and Quantum mechanics the physical theory.
Ralph Hartley
r...@maths.tcd.ie
>Flanagan
>What if a mind/brain identity theory holds?
It doesn't; the mind and experience are subjective, while the
brain is objective. Recall that the word subjective refers to
the fact that an experience (for example) can be examined
only by the person having the experience, while the brain
is objective because anybody can examine it if they take the
time to look underneath the skull. This is in contrast to
the widespread notion that subjective simply means "bad".
The brain and the mind are different things for the
reason they they are very obviously different things.
At best you can say that there's a correspondence
of some kind between them, which isn't very strong or
very deep. You might claim, somewhat poetically, that they
are two aspects of the same underlying thing, which is
quite a shift from the original claim that there was
only one thing. Now there are three things, two of which
are "aspects" of the third. This isn't very strong or
deep either; unemployment and inflation are often
aspects of the same underlying economic trouble, but
asserting this fact is very far from claiming that
unemployment and inflation are the same thing.
In the case of the mind and the brain, the only thing which is known
about the third thing is that it is something which has the mind
and the brain as aspects. Apart from the mind and the brain, then
what we know about this thing is nothing at all except that it
is something. This is very vague, and some interpret that as mystery,
and interpret mystery as profundity.
>Here is what Chalmers, a philosopher, wrote in Sci Am:
>"The abstract notion of information, as put forward by Claude E.
>Shannon of MIT, is that a of a set of separate states with a basic
>structure of similarities and differences between them."
No it isn't; as Shannon introduced it, information had to do
with strings of symbols which were sent as messages. The amount
of information provided by a message is the logarithm of
the number of possible messages, assuming that every message
was equiprobable from the point of view of the receiver beforehand.
No "basic structure of similarities and differences" is necessary;
if I have an alphabet of 100 distinct characters, and no measure of how
similar any one is to any other, apart from merely being able to
distinguish between them, then the theory of information works just
fine - the information given by a single symbol is log(100).
>"We can think of
>a 10-bit binary code as an information state, for example. "
No we can't, because we don't know what an information state
is. We know what a 10-bit binary code is because it's a
clear and unambiguous concept. "Information state" is a term
introduced by Chalmers, although he attempts to mislead the
reader into thinking that it was Shannon who introduced it.
If Chalmers means "information", he should say "information".
By saying "information state", he invokes the idea of a "state",
which people understand to mean the condition of a thing. But
what thing is it? What is the information state a state of?
The reader has no idea; Chalmers has given the reader the idea
that, somewhere, there's a Something, associated with the
information, and the reader has no idea what it is except
that it is something.
>"Such
>information can be embodied in the physical world. This happens
>whenever they correspond to physical states (voltages, say); the
>differences between them can be transmitted along some pathway, such as
>a telephone line....
>We can also find information embodied in conscious experience. The
>pattern of color patches in a visual field, for example, can be seen as
>analogous to that of pixels covering a display screen. Intriguingly, it
>turns out that we find the same information states embodied in
>conscious experience and in underlying physical processes in the brain."
It didn't turn out; it was assumed. There are no scientists in white
coats examining "information states embodied in conscious experience".
>"The three-dimensional encoding of color spaces, for example, suggests
>that the information state in a color experience corresponds directly to
>an information state in the brain."
Why does three dimensions have anyting to do with it? Would one
dimension, or none, be any less or more suggestive? Why does
an "encoding of color spaces" suggest anything about the brain?
>"We might even regard the two states
>as distinct aspects of a single information state, which is
>simultaneously embodied in both physical processing and conscious
>experience. "
Here we find why Chalmers introduced the term "information state".
By considering the information which is (presumably) common to
the brain and the mind, and calling it an information state,
he invokes the idea of a Something which it is the state of.
We have no idea what this something is supposed to be, except
that it has something to do with the information in the
brain and the mind. The reader who confuses mystery and profundity
will be suitably impressed.
>Flanagan
>In another Sci Am article, Freeman Dyson states quite clearly that,
>from the perspective of quantum field theory (QFT) everything in the
>physical universe is a quantum field: "There is nothing else except
>these fields: the whole of the material universe is built of them."
If he states it "quite clearly" then it must surely be true.
>It follows by a ready consequence that the brain, being a part of the
>material universe, just is a collection of [quantum] fields.
Even beginning to disentangle the web of confusion here is a daunting
task. You are relying on an argument from authority (in the
form of Freeman Dyson) to establish a point ("There is nothing else except
these fields: the whole of the material universe is built of them")
which is little more than poetry, and is furthermore conditioned
of a specific "perspective" (quantum field theory).
Let me explain something about quantum field theory. It is a
collection of mathematical techniques which attempt to extend
the formalism of quantum mechanics to deal with systems
which have continuous degrees of freedom. It is not the absolute
final truth about what exists, and even when physicists
talk about this or that quantum field as though it were
a physical object, what they are in fact referring to is
a purely mathematical object - a linear operator on a Hilbert
space. You may also hear them talking about virtual or
"off-shell" particles. This kind of talk shouldn't be interpreted
as a statement that these things actually exist and form
the substrate of everything else that exists.
When Freeman Dyson says that from the perspective of quantum field
theory everything in the physical universe is a quantum field, what
he means is that the formalism of quantum field theory deals with
quantum fields and to "solve the system" in quantum field theory
means to determine the time-evolution of these fields. Similarly,
from the perspective of classical mechanics, the universe consists
of a set of coordinates q_i, and momenta, p_i. This isn't a statement
that the coordinates and momenta are what exist. It's a statement
about what mathematical objects the theory deals with.
>Hartley
>Nowadays there is debate about the practicality of building
>computational devices that exploit quantum effects. Maybe we can,
>maybe we can't. What is *quite* clear is that the human brain is
>*not* such a device. Nothing that is composed almost entirely of
>liquid water ever can be.
>Flanagan
>In a quantum universe, all effects are quantum effects, yes?
Quantum mechanics is a formalism which can be used to predict the
values of measurable quantities. An effect is called a quantum
effect if that formalism needs to be used to predict or explain
that effect. Hence not all effects are quantum effects, the Coriolis
effect being an example of a completely classical effect (explainable
using classical mechanics). The expression "quantum universe" is
poetry.
>The brain
>is mostly water and yet it clearly mediates computations. One can talk
>about "higher order" levels of the brain's organization, but the only
>level with causal efficacy is the quantum level.
There is no such thing as a "level with causal efficacy". The
brain does what it does, and we may or may not need to use
the formalism of quantum mechanics to predict what it does.
For the purpose of predicting whether a muscle will move, it
is unlikely that the formalism of quantum mechanics will be
necessary, since the Hodgkin-Huxley equations (perhaps the
most successful application of differential equations in
biology) work extremely well for characterizing the
properties of spiking neurons.
It may turn out that the quantum formalism will need to be used
somewhere if we want to predict some number to some number of decimal
places. The same is true of an internal combustion engine.
>Hartley
>That *is* a statement about the physics of the brain. If you want to
>argue with that, go ahead, but be prepared to explain how quantum
>effects can matter to a system with a *very* short coherence time and a
>*very* long interaction time.
>Flanagan
>The fractal character of neural nets and their dendritic trees might
>suggest self-similarity across spatio-temporal scales.
Are you familiar with the works of Igor and Grichka Bogdanov?
>Weyl scaling
>might obtain if, as would seem most plausible, the brain's photon
>fields are most relevant to what are called conscious processes.
>Perhaps neural form follows quantum function? Umezawa, in his nice text
>on 'Advanced Field Theory,' seems to suggest something of the kind:
>"As we have seen in preceding sections, manifestation of ordered states
>is of quantum origin. When we recall that almost all of the macroscopic
>ordered states are the result of quantum field theory, it seems natural
>to assume that macroscopic ordered states in biological systems are
>also created by a similar mechanism."
It doesn't seem natural to me. Do the "macroscopic ordered states"
he's talking about refer to superconductivity and superfluidity?
These are accounted for (at low temperatures) by QFTs, but
there's no Bose-Einstein condensation going on in biological
systems. The order that we see in biological systems is the
result of evolution. Quantum field theory is not necessary to
understand evolution.
BJ on colours:
>(4) respect the laws of projective vector geometry; and
>(5) are readily observable.
>Weyl is quite explicit regarding #4: "Thus the colors with their
>various qualities and intensities fulfill the axioms of vector geometry
>if addition is interpreted as mixing; consequently, projective geometry
>applies to the color qualities." On his analysis, it seems as though
>sounds ought to respect that geometry also:
>"Mathematics has introduced the name isomorphic representation for the
>relation which according to Helmholtz exists between objects and their
>signs. I should like to carry out the precise explanation of this
>notion between the points of the projective plane and the color
>qualities . . . the projective plane and the color continuum are
>isomorphic with one another. Every theorem which is correct in the one
>system S_1 is transferred unchanged to the other S_2."
Weyl is incorrect. What is at issue here is the set of colours which
share a given intensity. At a particular intensity, there is
one shade of grey, one bluest colour, one greenest colour and
one reddest colour. Leaving out some details, the (+++)-octant
of a three dimensional space can be identified with the
manifold of all possible colours, with the axes corresponding
to red, green and blue.
Hence the colour purple with an overall intensity, I, will lie at
a point (I/2, 0, I/2). The purples of various different brightnesses
lie along the line which you can get by substituting various different
values of I above. Since, in this sense, the hue of purple, meaning
the colour purple without regard to its shade (or brightness),
corresponds to a line going through the origin, the set of hues
is like the set of lines going through the origin, which is called
RP2 or the real projective plane. Weyl omits the fact that only
a convex section of RP2 actually corresponds to visible colours:
only positive brighnesses are possible, and so these lines
are really only half-lines. These go from the origin into the
(+++) octant and do not extend backwards past black into some kind of
anti-colour in the (---) octant.
What's the result of all this? The manifold of hues actually
has the topology of a disc. It is simply connected, unlike
RP2. This means that you can draw a circle (or rather, closed curve)
on RP2 which can't be continuously shrunk to a single point. RP2
is like a sphere, except that every point is "the same" as its
antipodal point. You can draw the closed curve on RP2 by starting
at one point and ending at the antipodal point, which is (by
construction) the same as your starting point. This curve
can't be shrunk to zero, in the same way that a circle drawn around
the hole in a torus can't be shrunk to zero. In this sense,
RP2 has a hole in it.
It would be very exciting indeed to discover that the manifold of
hues (or the manifold of colours, for that matter), had a hole like
this, as Weyl says it does, but it doesn't. Draw a circle with
different colours at different points along the circle, with the
property that the colour changes continuously around the circle,
keeping the overall brightness of the colours constant. This is a
map from the circle into the manifold of hues. To see this, note
that, for each point, theta, on the circle, S1, you have chosen a
colour, f(theta); all the intensities are the same. Hence f:S1 ->
M, where M is the manifold of hues. Now, notice that each hue
can fade to grey continuously until the entire circle is grey. To
see this, let the colour at a point, theta, at time t be given by:
f(theta,t)=(1-t/2)f(theta,0)+(t/2)f'(theta,0)
where f'(theta,0) is the complementary colour to f(theta,0). At time
1, the entire circle has, at every point, an equal mixture of
a colour with its complementary colour. That is, the entire
circle is grey and so the image of the circle on the colour
manifold is a single point. This recipe works if you want to
talk about the manifold of hues. For the manifold of colours,
where the intensity can vary around the circle, instead use the map:
f(theta,t)=(1-t)f(theta,0)
And watch the entire circle fade to black at time 1.
>Dirac, writing about the usual sorts of QM superpositions, points out
>several salient features which apply equally well to superpositions of
>colors and sounds--which would make a good kind of sense if some sort
>of identity should obtain:
>"When a state is formed by the superposition of two other states, it
>will have properties that are in some vague way intermediate between
>those of the original states and that approach more or less closely to
>those of either of them according to the greater or less 'weight'
>attached to this state in the superposition process. The new state is
>completely defined by the two original states when their relative
>weights in the superposition process are known, together with a certain
>phase difference, the exact meaning of weights and phases being
>provided in the general case by the mathematical theory."
>Dirac, 'The Principles of Quantum Mechanics,' Oxford, 1958.
Now, you want to "identify" colours with quantum states, based on
the fact that they can be added together to form mixtures. Let
me make two objections:
1. When mixing quantum states, there is a very important
phase to be taken into account: |up> + |down> is very
different from |up> - |down>. When adding colours there
is no corresponding phase.
2. Coloured light can be mixed with other coloured light
by shining both lights onto a common surface. If you want
to keep the intensity constant you can dim both lights
as you mix them. This is a way of defining "addition of colours" -
A + B means the colour that you would see if you shone
A-coloured light and B-coloured light onto the same white
screen. Or you could try using inks and lightening by adding
white. Either way, neither of these methods of adding light
are "mental", by which I mean that, if I have never played
with lights or ink, and I have never seen purple, then
showing me a picture with red in one place and blue in
another place will not reveal to me what purple looks like.
The addition has to be performed outside me.
I have seen purple, and I think it looks more like blue
or red than like green, suggesting that I may have
some kind of a built-in distance function for the
manifold of hues (or it could have come from the
fact that blue things look purple from certain
angles or in certain lights - that is, from
experience), but I don't have any ability to
add colours together in my head. All my understanding
of colour mixing comes from experience of experimenting
with coloured lights and inks.
What you want to do is say that the experience of
seeing colours is the same as a quantum state, based
on a shared additive property, but the fact is that it
is not the experiences of seeing colours which
can be added together; only the lights and inks
are added.
R.
bjflanagan
What if a mind/brain identity theory holds?
>It doesn't; the mind and experience are subjective, while the
brain is objective.
The "objective" is the result of intersubjective agreement.
"I believe that the first step in the setting of a "real external
world" is the formation of the concept of bodily objects and of bodily
objects of various kinds. Out of the multitude of our sense experiences
we take, mentally and arbitrarily, certain repeatedly occurring
complexes of sense impression (partly in conjunction with sense
impressions which are interpreted as signs for sense experiences of
others), and we attribute to them a meaning-the meaning of the bodily
object. Considered logically this concept is not identical with the
totality of sense impressions referred to; but it is an arbitrary
creation of the human (or animal) mind. On the other hand, the concept
owes its meaning and its justification exclusively to the totality of
the sense impressions which we associate with it." (Einstein)
R
>The brain and the mind are different things for the
reason they they are very obviously different things.
Flanagan
Just as it is obvious that the sun goes around the earth.
R
>At best you can say that there's a correspondence
of some kind between them, which isn't very strong or
very deep.
Flanagan
No, I can say that an identity obtains between them. If you think this
is neither strong nor deep, one might suspect that your comments
reflect more nearly on your understanding.
>Here is what Chalmers, a philosopher, wrote in Sci Am:
>"The abstract notion of information, as put forward by Claude E.
>Shannon of MIT, is that a of a set of separate states with a basic
>structure of similarities and differences between them."
R
No it isn't; as Shannon introduced it, information had to do
with strings of symbols which were sent as messages.
Flanagan
You might want to contact Hawking & Bekenstein, who are suffering under
the illusion that information theory applies to black holes.
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html
>We can also find information embodied in conscious experience. The
>pattern of color patches in a visual field, for example, can be seen
as
>analogous to that of pixels covering a display screen. Intriguingly,
it
>turns out that we find the same information states embodied in
>conscious experience and in underlying physical processes in the
brain."
R
It didn't turn out; it was assumed. There are no scientists in white
coats examining "information states embodied in conscious experience".
Flanagan
You might want to read Grassmann, Maxwell and Schrodinger on the
subject:
http://www.spie.org/web/abstracts/oepress/MS77.html
>"The three-dimensional encoding of color spaces, for example, suggests
>that the information state in a color experience corresponds directly
to
>an information state in the brain."
R
Why does three dimensions have anyting to do with it? Would one
dimension, or none, be any less or more suggestive? Why does
an "encoding of color spaces" suggest anything about the brain?
Flanagan
Maxwell makes this point. If one assigns R, G & B to the principal axes
of a unit sphere, then combinations of the associated vectors
"generate" all the other colors. Using the unit ball, one can account
for weights assigned to the vectors.
Where A is any color, -A is then "A rotated 180 degrees" or "A
reflected through the origin." If zero is assigned to "no light" or
"darkness," then we recover a familiar fact from phenomenology: A +
(-A) = 0. (This also applies to sound, of course, since there also two
waves 180 degrees out of phase cancel one another.) This interpretation
completes the vector space and recapitulates the group behavior of
colors under mixing. I am rather pleased to have figured out the former
point, as it seems to have escaped Schrodinger, who was more of a
mathematician than I will ever be.
>"We might even regard the two states
>as distinct aspects of a single information state, which is
>simultaneously embodied in both physical processing and conscious
>experience. "
R
Here we find why Chalmers introduced the term "information state".
By considering the information which is (presumably) common to
the brain and the mind, and calling it an information state,
he invokes the idea of a Something which it is the state of.
We have no idea what this something is supposed to be, except
that it has something to do with the information in the
brain and the mind. The reader who confuses mystery and profundity
will be suitably impressed.
Flanagan
When the path forward seems obscure, experience has shown that
following the math often turns out to be fruitful. Chalmers is no
mystery monger, and your dismissive remarks impress no one.
>Flanagan
>In another Sci Am article, Freeman Dyson states quite clearly that,
>from the perspective of quantum field theory (QFT) everything in the
>physical universe is a quantum field: "There is nothing else except
>these fields: the whole of the material universe is built of them."
R
If he states it "quite clearly" then it must surely be true.
Flanagan
Similarly, knocking down straw men is of no interest whatever.
>It follows by a ready consequence that the brain, being a part of the
>material universe, just is a collection of [quantum] fields.
R
Even beginning to disentangle the web of confusion here is a daunting
task. You are relying on an argument from authority (in the
form of Freeman Dyson) to establish a point ("There is nothing else
except
these fields: the whole of the material universe is built of them")
which is little more than poetry, and is furthermore conditioned
of a specific "perspective" (quantum field theory).
Flanagan
I am not relying on authority. Dyson simply made the point with
beautiful clarity. To say that all material things consist of fields is
to clarify the situation quite radically, and so I suggest the
confusion is all on your end. To say that QFT is little more than
poetry is really quite interesting and I must congratulate you on your
degree of intellectual probity.
R
Let me explain something about quantum field theory. It is a
collection of mathematical techniques which attempt to extend
the formalism of quantum mechanics to deal with systems
which have continuous degrees of freedom. It is not the absolute
final truth about what exists, and even when physicists
talk about this or that quantum field as though it were
a physical object, what they are in fact referring to is
a purely mathematical object [...]
Flanagan
O, so the EM field is a purely mathematical object. What a very
interesting point of view. Funny, that this object should correspond so
well with the world of observation.
Ralph Hartley
> bjflanagan <words...@earthlink.net> writes:
>
>>What if a mind/brain identity theory holds?
>
> It doesn't; the mind and experience are subjective, while the
> brain is objective. Recall that the word subjective refers to
> the fact that an experience (for example) can be examined
> only by the person having the experience, while the brain
> is objective because anybody can examine it if they take the
> time to look underneath the skull. This is in contrast to
> the widespread notion that subjective simply means "bad".
Perhaps this notion results at least in part from the notion that
subjective means "arbitrary". In general it does not. A subjective
effect can be rigidly determined.
I have argued in an old thread
(http://groups-beta.google.com/group/sci.physics.research/msg/13a0fc1679fd3fb4?hl=en)
that Quantum wave function collapse can be viewed as a subjective effect
in much the same way as visual perspective. Both are observer dependent,
but determined by an objective rule.
That doesn't mean Quantum mechanics tells us anything about the mind,
any more than perspective does. Perhaps less, because our visual systems
have evolved to handle perspective, but not quantum effects.
> The brain and the mind are different things for the
> reason they they are very obviously different things.
> At best you can say that there's a correspondence
> of some kind between them, which isn't very strong or
> very deep.
The correspondence is quite strong, and getting stronger rapidly. This
is not the work of Physicists or Philosophers, but Physiologists. There
are now quite powerful tools for studying the relationship between
subjective states and functional states of the brain.
Generally they involve recording brain activity while the subject
performs a mental task. MRI records the activity of different brain
areas, and is non-invasive. Electrode arrays (in animals) simultaneously
record the activity of many neurons.
You can tell a lot about what a monkey intends, or even believes, if you
record enough.
It may be impossible in principle to *experience* another person's
subjective states, but that does not mean we can't *detect* them.
One might argue that we are detecting the neural correlates of
subjective states, not the states themselves. That is a distinction
without a difference. If A and B are %100 correlated, and you detect B,
then you indirectly detect A. That would be true even if A were nothing
but an interpretation of B.
> You might claim, somewhat poetically, that they
> are two aspects of the same underlying thing, which is
> quite a shift from the original claim that there was
> only one thing. Now there are three things, two of which
> are "aspects" of the third.
The "third" thing could be one of the original two.
> In the case of the mind and the brain, the only thing which is known
> about the third thing is that it is something which has the mind
> and the brain as aspects.
The obvious thing that the mind and brain could be aspects of is the brain.
Saying that the mind is an aspect of the brain does not introduce any
"third thing". Of course, the brain is an aspect of the brain as well,
but that would be an odd thing to say.
>>It follows by a ready consequence that the brain, being a part of the
>>material universe, just is a collection of [quantum] fields.
>
> Even beginning to disentangle the web of confusion here is a daunting
> task.
Too daunting for me.
>>In a quantum universe, all effects are quantum effects, yes?
Though false, that is at least a coherent statement. I couldn't make any
sense at all of most of the rest.
Ralph Hartley
Ralph Hartley
> Ralph Hartley
>> The physics of the brain is in scope, but the philosophy of the mind is
>> not.
>
Then it would be in scope, and the physical fact that Quantum effects
cannot contribute to brain function would settle the matter.
You could argue that it isn't true, but not (as another poster did) that
it doesn't matter.
> In a quantum universe, all effects are quantum effects, yes?
Not really. Effects may be indirect consequences of quantum effects,
without *being* quantum effects.
The price of coffee is not a quantum effect. Quantum mechanics has
*nothing* to tell us about the price of coffee.
>> be prepared to explain how quantum
>> effects can matter to a system with a *very* short coherence time and a
>> *very* long interaction time.
>
> The fractal character of neural nets and their dendritic trees might
> suggest self-similarity across spatio-temporal scales. Weyl scaling
> might obtain if, as would seem most plausible, the brain's photon
> fields are most relevant to what are called conscious processes.
That doesn't make any sense.
Ralph Hartley
bjflanagan
The correspondence is quite strong, and getting stronger rapidly. This
is not the work of Physicists or Philosophers, but Physiologists.
Flanagan
The facts are otherwise:
"It is just like the mathematics of the addition of vectors, where (a,
b, c ) are the components of one vector, and (a', b', c' ) are those of
another vector, and the new light Z is then the "sum" of the vectors.
This subject has always appealed to physicists and mathematicians. In
fact, Schr=F6dinger wrote a wonderful paper on color vision in which he
developed this theory of vector analysis as applied to the mixing of
colors." (Feynman, 'Lectures')
As Weinberg relates in his nice little essay, "Elementary particles and
the laws of physics," (Cambridge) we are all reductionists in the sense
that we would be very suspicious of any scientific theory which does
not reduce to physics.
Colors and sounds are inherently simple things and presented to us as
vectors in a manifold. Where in physiology do we find objects of like
simplicity? (Aside from your brain, I mean.)
"When we're asked "What do 'red', 'blue', 'black', 'white' mean?" we
can, of course, immediately point to things which have these
colours,--but that's all we can do: our ability to explain their
meaning goes no further."
(Wittgenstein, 'Tractatus')
"Thus 'this is red,' 'this is earlier than that,' are atomic
propositions."
Russell & Whitehead, 'PM'
"... so few and far between are the occasions for forming notions whose
specialisations make up a continuous manifoldness, that the only simple
notions whose specialisations form a multiply extended manifoldness are
the positions of perceived objects and colors." (Riemann)
http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Geom/WKCGeom.html
"The characteristic of an n-dimensional manifold is that each of the
elements composing it (in our examples, single points, conditions of a
gas, colours, tones) may be specified by the giving of n quantities,
the 'co-ordinates,' which are continuous functions within the
manifold." (Weyl)
"This is the characteristic mathematical property of a classical field:
it is an undefined something which exists throughout a volume of space
and which is described by sets of numbers, each set denoting the field
strength and direction at a single point in the space." (Dyson)
Nick Maclaren
bjflanagan <words...@earthlink.net> writes:
|>
|> R
|> No it isn't; as Shannon introduced it, information had to do
|> with strings of symbols which were sent as messages.
|>
|> Flanagan
|> You might want to contact Hawking & Bekenstein, who are suffering under
|> the illusion that information theory applies to black holes.
No, that was correct. Shannon information is precisely about that,
but it turned out to be merely part of a larger field. A lot of
statistics is based on a different viewpoint of information theory,
and Kolmogorov had a lot to do with both aspects.
I don't have a clue what Hawking etc. mean by information, but I
am pretty sure that it is a viewpoint very different from both
that of Shannon and the statistical one. Information theory is a
remarkably Protean field.
Regards,
Nick Maclaren.
r...@maths.tcd.ie
>r...@maths.tcd.ie wrote:
>> Ralph Hartley <har...@aic.nrl.navy.mil> writes:
>>>Abandoning irony *completely* let me make my position clear.
>> ...
>>>(3) It would be a bad thing even *if* the conclusion were correct [...].
>>>An invalid argument for a true
>>>proposition is still an invalid argument.
>>
>> What Brian
>> was saying was that Penrose's discussion of the subject made it
>> acceptable for scientists to acknowledge that there is such
>> a thing as consciousness, even if his actual claims were
>> speculative, unjustified and incorrect. This was a "good thing"
>So you disagree with (3) then? (Or is that what you think Brian was
>saying? The rest of your message implies that you agree with him.)
I was explaining what Brian was saying. To say whether Penrose's
arguments about the mind were are good thing or a bad thing
would require either making a value judgment or asking whether
they are likely to hinder or help progress towards a specific
goal. With regard to value judgments and morality, I don't
think Penrose was being in any way dishonest; he most likely
believes that what he argued was correct. In this sense I
don't think Penrose should be morally condemned. With regard
to progress towards a goal, which was the sense in which Brian
meant it was a good thing, I consider it highly unlikely
that the social effect, of Penrose setting an example by
talking about the mind, will inspire any genius to make
progress on any issue at all.
>> because previously scientists, and especially physicists,
>> stood side by side with new age enthusiasts and with those
>> who oppose all rational enquiry
>To consider invalid arguments a good thing under any circumstances, is
>to reject rational inquiry.
>To fool people into considering a question that they would not otherwise
>think about, even if they *should* think about it, is not a good thing.
>If nothing else, invalid arguments hide any valid arguments that may
>exist, and make their conclusions less respectable among people who
>recognize the arguments as invalid.
I fully agree.
>> The rules which make science successful are to be
>> abandoned when they conflict with the "higher good" of giving
>> philosophers a public trouncing at the hands of physicists.
>But the reverse is OK?
I concern myself with the ethics of public trouncings only
in the following regard. The inclination to dispence such
trouncings and avoid suffering them is motivated by a desire
to increase and maintain one's self-respect and the respect
of one's peers. This motivation, in so far as it has any
effect at all on a person's behaviour, can only serve to
conflict with the motivation to explain one's own position
and understand the position of the person with whom one
is debating. If the goal is to achieve a better understanding
of the subject matter oneself, or to help others achieve
a better understanding, then the motivation which underlies
trouncings can only be detrimental to achieving the goal.
I am not saying that one should neglect the desire for
self-respect and the respect of one's peers. Rather,
the source of self-respect should be the knowledge
that one adheres honestly to the rules of inquiry
and debates the actual points at hand rather than
seeking merely to humiliate the opponent. A person
who does this will earn the respect of whoever's
respect is worth having.
This is not an attempt to moralize or imply that
this is a lesson you need to learn. It is just
a statement of my views about public trouncing,
which I give because you asked for them.
>> There was a global prohibition on physicists talking or even thinking
>> about the mind
>Can you show me something positive that resulted from them doing so, or
>even any valid argument that they should?
I will do this in another thread.
>> You might, of course, challenge me to explain how quantum
>> theory could have something to do with the mind. I would
>> then be entitled to say that I never claimed that it
>> did; I merely haven't seen any proof that it doesn't
>I didn't claim that there is no relationship at all, one can find a
>relationship between *any* two things, only that it has nothing to
>*tell* us. To claim that QM may tell us something about the mind, but
>nobody has any idea what, is nonsense. I stretches the meaning of the
>word "tell" even farther than we have done already.
>Either QM has something to tell us about the mind, and we need only
>listen, or it doesn't.
I misunderstood you, then. My interpretation of your assertion
was that quantum mechanics will never have any relevance to
questions about the mind. You were apparently making the
weaker statement that quantum mechanics doesn't tell us anything
clear about the mind right now. I agree with this weaker
statement.
>> But I won't do that; instead I'll tell you how quantum
>> mechanics might have something to do with the mind, and
>> I stress that it is only a possibility.
>Do you think you make a valid argument that something could be true, by
>showing examples of how it might be, but isn't? Or do you just want to
>make an argument without having to defend it?
My original understanding (which was incorrect) was that
you were asserting something of the form "P is false",
without proof, where P was the statement that quantum
mechanics could someday turn out to have something to
say about the mind. In order to draw attention to the
fact that this was unproven, I had merely to demonstrate
that P was possible. To assert that P was true would
have required a proof which I don't have.
>> Quantum mechanics appears to very nicely characterize
>> induction - the basic notion that similar experiments
>> give similar results. The old problem with induction
>> was that it remained vague because of the difficulty
>> involved in measuring the "similarity" of experiments.
>> Quantum mechanics solves that problem by giving
>> an explicit mathematical representation of the
>> experiments. Rotate your apparatus, and there's a
>> corresponding SO(3) action on your observable
>> operator.
>Carefully representing experiments and observables is not part of
>quantum mechanics. It applies just as well to classical mechanics. It is
>a tool used to do QM, but it is in no way *part* of Quantum mechanics.
I don't understand why you are emphasising "part".
>A screwdriver can be used as a stabbing weapon, but that does not mean
>that screws have something to tell us about ancient warfare.
I don't see the relevance of this.
>That's just as well, since induction has been used since the stone age.
>Your (non) position would imply that induction was invalid when the
>ancients did it, but became valid in the mid 20th century, or perhaps
>that induction just wouldn't work in a classical world. That would be
>odd since it worked fine in the 10th century when quantum effects were
>undetectable.
If I were to believe that QM is a formalisation of induction (which
I don't, although I consider it a possibility), I would in no
way be led to conclude that induction didn't work before the
discovery of quantum mechanics. Before the formalisation of
symbolic logic, logical reasoning worked just fine; it
wasn't invalid. This is the same situation.
>> Also, quantum mechanics is where induction breaks
>> down. You can't predict the position of the
>> particle with any more accuracy than |psi^2|,
>> even in principle. Do the same experiment twice
>> and you don't get the same results.
>I get the same thing with classical dice (well maybe not the "even in
>principle" part, but I don't see how that matters).
It's the "even in principle" part that makes the difference.
With die rolling and coin tossing, sufficient control of the
initial conditions would allow you to get the same result
when you repeat the experiment. The old principle of
induction "Do the same experiment; get the same result"
still holds true. With quantum mechanics, it fails.
>> It's possible that quantum mechanics is a quantitative
>> formalization of the principle of induction, just
>> as boolean algebra gives a formalization of deductive
>> inference (propositional calculus).
>It would be possible if Quantum Mechanics were anything *like* the
>principle of induction. A better candidate for a formalization of the
>principle of induction would be Statistical Inference, which is related
>to Probability Theory, which *is* related to Quantum Mechanics. :-)
Statistical inference and probability theory are completely
mathematical disciplines. As such, they place no constraint
upon the behaviour of the world and their theorems hold
regardless of what experiments give what results.
In order for quantum mechanics or induction to be true, the
world has to behave a specific way. They both say something
nontrivial about the results of experiments.
R.
jcgon...@yahoo.com
> (1) Penrose's argument that quantum theory has important things to
tell
> us about the mind is nonsense.
>
> (2) Making nonsense believable and respectable is *not* a good thing.
>
> is very unlikely in this case). An invalid argument for a true
> proposition is still an invalid argument.
>
show
> me a valid argument that Penrose made (or any valid argument for that
> matter).
Penrose gets mind biology help from Stuart Hameroff so Penrose's ideas
are not just about physics. Hameroff and Chalmers the philosopher
(mentioned here earlier) are directors for the University of Arizona's
Center for Consciousness Studies. Chalmers is actually not set on any
particular idea for consciousness, he explores lots of ideas (even mine
for a few minutes at Quantum Mind 2003). I like the following Tony
Smith ideas which include Penrose's ideas:
http://www.valdostamuseum.org/hamsmith/QuantumMind2003.html
John
http://home.comcast.net/~jcgonsowski/psychophysics/index.html
(Any goofiness is my fault not the fault of my sources)
r...@maths.tcd.ie
>bjflanagan writes:
>What if a mind/brain identity theory holds?
>>It doesn't; the mind and experience are subjective, while the
>brain is objective.
>The "objective" is the result of intersubjective agreement.
Sure; but you cannot have intersubjective agreement about certain
things. The experience that I have when I see the colour blue,
for example, is something that I cannot compare to the experience
that other people have when they look at the same object. For
all I know, they might have the experience that I call seeing
red when they look at it, but have always known that experience
by the name of blue. Whether this is the case or not cannot be
settled by studying either their behaviour or their brain.
>R (O'Flanagan)
>>The brain and the mind are different things for the
>reason they they are very obviously different things.
>Flanagan
>Just as it is obvious that the sun goes around the earth.
Perhaps I was using rhetoric. I retract the remark quoted
above.
>R
>>At best you can say that there's a correspondence
>of some kind between them, which isn't very strong or
>very deep.
>Flanagan
>No, I can say that an identity obtains between them. If you think this
>is neither strong nor deep, one might suspect that your comments
>reflect more nearly on your understanding.
You apparently didn't understand my objection. It was a purely
logical objection, by which I mean that it uses a theorem
from logic (by which I mean first order predicate calculus).
Actually, it applies only in first order theories with identity,
but this is a complication which isn't important for our
purposes.
The theorem is:
Let x and y be objects and P and Q be properties such that for
all z, Pz=>~Qz and Qz=>~Pz. Then Px & Qy => ~x=y.
Here, ~ denotes logical not, and Px means that x has the
property P. The proof of the theorem is left as an
exercise for the reader with too much time on his hands.
Now, the theorem applies to the case when x is any
physical object or process in the brain, y is an
experience (such as the experience of seeing blue),
P is the property "can be examined by more than one
person" and Q is the property "can be examined by
only one person" (namely the experiencer).
From these considerations, it is concluded that
an identity between any physical object or process
and experience is ruled out on purely logical
grounds. They simply cannot be the "same thing"
because they have different properties. At best
you can say that there is a relationship between
them and try to clarify that relationship.
>>Here is what Chalmers, a philosopher, wrote in Sci Am:
>>"The abstract notion of information, as put forward by Claude E.
>>Shannon of MIT, is that a of a set of separate states with a basic
>>structure of similarities and differences between them."
>R
>No it isn't; as Shannon introduced it, information had to do
>with strings of symbols which were sent as messages.
>Flanagan
>You might want to contact Hawking & Bekenstein, who are suffering under
>the illusion that information theory applies to black holes.
Both Chalmers and I were referring to Shannon's introduction
of the notion of information. Chalmers gave an inaccurate
description of what Shannon said. I pointed this out. You
responded by attempting to give the impression that I had
said information theory didn't apply to certain systems.
I never said or implied that.
>>"The three-dimensional encoding of color spaces, for example, suggests
>>that the information state in a color experience corresponds directly
>to
>>an information state in the brain."
>R
>Why does three dimensions have anything to do with it? Would one
>dimension, or none, be any less or more suggestive? Why does
>an "encoding of color spaces" suggest anything about the brain?
>Flanagan
>Maxwell makes this point. If one assigns R, G & B to the principal axes
>of a unit sphere, then combinations of the associated vectors
>"generate" all the other colors. Using the unit ball, one can account
>for weights assigned to the vectors.
>Where A is any color, -A is then "A rotated 180 degrees" or "A
>reflected through the origin." If zero is assigned to "no light" or
>"darkness," then we recover a familiar fact from phenomenology: A +
>(-A) = 0.
Now, once again I'd like to draw your attention to the distinction
between the experience of seeing a colour, and the wave associated
with coloured light. Only the latter satisfies the rules of
vector addition.
>(This also applies to sound, of course, since there also two
>waves 180 degrees out of phase cancel one another.) This interpretation
>completes the vector space and recapitulates the group behavior of
>colors under mixing. I am rather pleased to have figured out the former
>point, as it seems to have escaped Schrodinger, who was more of a
>mathematician than I will ever be.
It's a pity that you didn't reply to my objections to your theory
that the experience of seeing colour is identical to a quantum
field:
>> 1. When mixing quantum states, there is a very important
>> phase to be taken into account: |up> + |down> is very
>> different from |up> - |down>. When adding colours there
>> is no corresponding phase.
>>
>> 2. ... What you want to do is say that the experience of
>> seeing colours is the same as a quantum state, based
>> on a shared additive property, but the fact is that it
>> is not the experiences of seeing colours which
>> can be added together; only the lights and inks
>> are added.
Your response to this would have been much more interesting
than the irrelevant points you did respond to.
>>Flanagan
>>In another Sci Am article, Freeman Dyson states quite clearly that,
>>from the perspective of quantum field theory (QFT) everything in the
>>physical universe is a quantum field: "There is nothing else except
>>these fields: the whole of the material universe is built of them."
..
>>It follows by a ready consequence that the brain, being a part of the
>>material universe, just is a collection of [quantum] fields.
>R
>Even beginning to disentangle the web of confusion here is a daunting
>task. You are relying on an argument from authority (in the
>form of Freeman Dyson) to establish a point ("There is nothing else
>except
>these fields: the whole of the material universe is built of them")
>which is little more than poetry, and is furthermore conditioned
>on a specific "perspective" (quantum field theory).
>Flanagan
>I am not relying on authority. Dyson simply made the point with
>beautiful clarity. To say that all material things consist of fields is
>to clarify the situation quite radically, and so I suggest the
>confusion is all on your end. To say that QFT is little more than
>poetry is really quite interesting and I must congratulate you on your
>degree of intellectual probity.
What I said was little more than poetry was the claim: "There is
nothing else except these fields: the whole of the material universe
is built of them". You responded as though I had said that QFT was
poetry, which I didn't say.
>R
>Let me explain something about quantum field theory. It is a
>collection of mathematical techniques which attempt to extend
>the formalism of quantum mechanics to deal with systems
>which have continuous degrees of freedom. It is not the absolute
>final truth about what exists, and even when physicists
>talk about this or that quantum field as though it were
>a physical object, what they are in fact referring to is
>a purely mathematical object [...]
>Flanagan
>O, so the EM field is a purely mathematical object. What a very
>interesting point of view. Funny, that this object should correspond so
>well with the world of observation.
My spider senses detect that you are trying to ridicule me. Let
me respond by clarifying the situation. There are certain
mathematical objects, such as numbers and linear operators
on Hilbert spaces. I might use these mathematical objects
in the course of doing a physical experiment. For example,
I might use a number to denote how many metres one object
is from another object. You might call this a coordinate.
In classical mechanics, the aim is to predict the values
of the coordinates at future times. From this solution,
I can infer the future locations of the objects in the
experiment. When I do a different type of experiment,
say, scattering two particles against one another and
detecting the resulting particles, I use a different
set of mathematical objects, linear operators on a
Hilbert space. A set of such linear operators which is
indexed by a continuous variable is called a quantum
field. This is a purely mathematical object. You
might say that there is something physical which
coresponds to the mathematical object. Maybe, but
it is the mathematical object which is "quantum".
R.
bjflanagan
|> You might want to contact Hawking & Bekenstein, who are suffering
under the illusion that information theory applies to black holes
Maclaren
No, that was correct.
Flanagan
Yes, I know that was correct. I predicted the existence of Hawking
radiation when I was 16, several years before Hawking. I am simply
trying to be more patient than I have been in the past, but don't know
how much longer I can hold out.
There is a direct inverse relation between information & entropy, which
can be found in Shannon:
http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
See also:
quant-ph/0311049
bjflanagan
>> The physics of the brain is in scope, but the philosophy of the mind
is
>> not.
Flanagan
> What if a mind/brain identity theory holds?
Hartley
Then it would be in scope, and the physical fact that Quantum effects
cannot contribute to brain function would settle the matter.
Flanagan
If you say so, it must be true.
> In a quantum universe, all effects are quantum effects, yes?
Hartley
Not really. Effects may be indirect consequences of quantum effects,
without *being* quantum effects.
The price of coffee is not a quantum effect. Quantum mechanics has
*nothing* to tell us about the price of coffee.
Flanagan
O? What about the conservation laws? And the symmetries related thereto
by Noether?
Are transistors not quantum devices? Are they not a more apposite case
than the price of coffee?
Hartley
>> be prepared to explain how quantum
>> effects can matter to a system with a *very* short coherence time
and a
>> *very* long interaction time.
> The fractal character of neural nets and their dendritic trees might
> suggest self-similarity across spatio-temporal scales. Weyl scaling
> might obtain if, as would seem most plausible, the brain's photon
> fields are most relevant to what are called conscious processes.
Hartley
That doesn't make any sense.
Flanagan
So you say.
Tim Josling
> ... I don't
> think Penrose was being in any way dishonest; he most likely
> believes that what he argued was correct. In this sense I
> don't think Penrose should be morally condemned.
I think though that he can be justly criticised for using his authority
as a physicist and mathematician as cover for his speculations about the
mind.
As far as I can see, from what he says and from his list of references,
he does not seem to have sufficiently informed himself about either the
philosophy or physiology of the mind/brain. As a result his speculations
are naive.
Tim Josling
bjflanagan
>What if a mind/brain identity theory holds?
>brain is objective.
>The "objective" is the result of intersubjective agreement.
Sure; but you cannot have intersubjective agreement about certain
things. The experience that I have when I see the colour blue,
for example, is something that I cannot compare to the experience
that other people have when they look at the same object.
Flanagan
Well, why don't you explain that to the judge the next time you run a
red light? If we both respond by saying "red" when presented with a
novel stimulus that others agree is red, then we have all the
intersubjective agreement we need -- a case which finds a telling
parallel in the measuring sticks and clocks of relativity. I.e., space
and time have subjective aspects, too, but we get around that by
agreeing on objective standards, as is done when constructing color
monitors and TV screens.
http://www.cs.rit.edu/~ncs/color/t_convert.html
R.
For all I know, they might have the experience that I call seeing
red when they look at it, but have always known that experience
by the name of blue. Whether this is the case or not cannot be
settled by studying either their behaviour or their brain.
Flanagan
Yes, and for all I know, you may see a meter where I see a centimeter.
Occam's razor applies: if our brains are built along the same lines,
and we both say "meter" when presented with a measuring stick of that
length, then the simplest explanation is that we both see a meter.
>R
>>At best you can say that there's a correspondence
>of some kind between them, which isn't very strong or
>very deep.
>Flanagan
>No, I can say that an identity obtains between them. If you think this
>is neither strong nor deep, one might suspect that your comments
>reflect more nearly on your understanding.
R
You apparently didn't understand my objection. It was a purely
logical objection, by which I mean that it uses a theorem
from logic (by which I mean first order predicate calculus).
[intoductory matter deleted]
>From these considerations, it is concluded that
an identity between any physical object or process
and experience is ruled out on purely logical
grounds. They simply cannot be the "same thing"
because they have different properties. At best
you can say that there is a relationship between
them and try to clarify that relationship.
Flanagan
This is an empirical issue and begs the question. How did you determine
that mind & brain do not have the same properties? As Einstein, Wigner
& Weyl all explain, the "physical" is a theoretical construct whereby
we make sense of the regularities of "mental" experience. If the
theoretical construct does not do justice to experience, it is the
construct which is called into question.
"The immediately experienced is subjective but absolute; no matter how
cloudy it may be, in this cloudiness it is something given thus and not
otherwise. To the contrary, the objective world which we continually
take into account in our practical life and which science tries to
crystallize into clarity is necessarily relative; to be represented by
some definite thing (numbers or other symbols) only after a system of
coordinates has been arbitrarily introduced into the world. [...] We
said at an earlier place, that every difference in experience must be
founded on a difference of the objective conditions; we can now add: in
such a difference of the objective conditions as is invariant with
regard to coordinate transformations, a difference that cannot be made
to vanish by a mere change of the coordinate system used. . . . Who
desires the absolute, must take subjectivity, the ego for which things
exist, into the bargain; who is urged towards the objective cannot
escape from the problem of relativity!" (Weyl)
It is highly instructive to consider the invariance of color under a
"change of the coordinate system used."
>>Here is what Chalmers, a philosopher, wrote in Sci Am:
>>"The abstract notion of information, as put forward by Claude E.
>>Shannon of MIT, is that a of a set of separate states with a basic
>>structure of similarities and differences between them."
>R
>No it isn't; as Shannon introduced it, information had to do
>with strings of symbols which were sent as messages.
>Flanagan
>You might want to contact Hawking & Bekenstein, who are suffering
under
>the illusion that information theory applies to black holes.
R
Both Chalmers and I were referring to Shannon's introduction
of the notion of information. Chalmers gave an inaccurate
description of what Shannon said.
Flanagan
I suggest you revisit what Shannon wrote:
cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
>>"The three-dimensional encoding of color spaces, for example,
suggests
>>that the information state in a color experience corresponds directly
>to
>>an information state in the brain."
>R
>Why does three dimensions have anything to do with it? Would one
>dimension, or none, be any less or more suggestive? Why does
>an "encoding of color spaces" suggest anything about the brain?
>Flanagan
>Maxwell makes this point. If one assigns R, G & B to the principal
axes
>of a unit sphere, then combinations of the associated vectors
>"generate" all the other colors. Using the unit ball, one can account
>for weights assigned to the vectors.
>Where A is any color, -A is then "A rotated 180 degrees" or "A
>reflected through the origin." If zero is assigned to "no light" or
>"darkness," then we recover a familiar fact from phenomenology: A +
>(-A) = 0.
R
Now, once again I'd like to draw your attention to the distinction
between the experience of seeing a colour, and the wave associated
with coloured light. Only the latter satisfies the rules of vector
addition.
Flanagan
Well, you're simply mistaken. Red at 620nm added to green at 540 nm is
indistinguishable from yellow at 580 nm. On the vector model I sketched
in, there is a precise correspondence between what is experienced and
what the model predicts.
>(This also applies to sound, of course, since there also two
>waves 180 degrees out of phase cancel one another.) This
interpretation
>completes the vector space and recapitulates the group behavior of
>colors under mixing. I am rather pleased to have figured out the
former
>point, as it seems to have escaped Schrodinger, who was more of a
>mathematician than I will ever be.
R
It's a pity that you didn't reply to my objections to your theory
that the experience of seeing colour is identical to a quantum
field:
Flanagan
It's a pity you don't think instead of simply regurgitating the
received wisdom.
>> 1. When mixing quantum states, there is a very important
>> phase to be taken into account: |up> + |down> is very
>> different from |up> - |down>. When adding colours there
>> is no corresponding phase.
Flanagan
Photons of the same color (tone) but 180 degrees out of phase cancel.
So how is there no corresponding phase?
R
>> 2. ... What you want to do is say that the experience of
>> seeing colours is the same as a quantum state, based
>> on a shared additive property, but the fact is that it
>> is not the experiences of seeing colours which
>> can be added together; only the lights and inks
>> are added.
Flanagan
O, so there is no corresponding perception?
R
My spider senses detect that you are trying to ridicule me. Let
me respond by clarifying the situation. There are certain
mathematical objects, such as numbers and linear operators
on Hilbert spaces. I might use these mathematical objects
in the course of doing a physical experiment.
Flanagan
Yes, and mapping color vectors to the unit sphere (ball) allows us to
use the same matrix machinery to rotate those vectors when the color
changes. We can thus capture an insight due to Helmholtz: "Similar
light produces, under like conditions, a like sensation of color." A
change of condition then maps to an operator. In the trivial case where
no change occurs, the identity operator gives us the same color x: I(x)
= x. In the more interesting case where a Doppler shift occurs, the
Hamiltonian rotates x by a determined number of degrees corresponding
to the change in energy of the photon. The invariance of color under
change of coordinates leads us directly to Noether, which is really
quite interesting.
R
A set of such linear operators which is
indexed by a continuous variable is called a quantum
field. This is a purely mathematical object. You
might say that there is something physical which
corresponds to the mathematical object. Maybe, but
it is the mathematical object which is "quantum".
Flanagan
You may wish to apprise the larger community of physicists of your
discovery, most of whom believe that the universe is quantum and that
the formalism has been developed to reflect this understanding.
And now I really have to get back to work. Good bye.
Ralph Hartley
> With regard to value judgments and morality, I don't
> think Penrose was being in any way dishonest; he most likely
> believes that what he argued was correct. In this sense I
> don't think Penrose should be morally condemned.
I have no doubt at all that he is sincere, and believes his own
arguments, but I don't consider that enough.
When making an argument there is obligation to consider, and to
disclose, its weaknesses. It is wrong (in the ethics of science) to make
arguments you know or *should* know are invalid.
Now we all fail at this sometimes, but when one writes books for
"popular" consumption, and make the same argument for years, one should
be expected to be held to a higher standard than a usenet post.
Sir Roger is, by all accounts, a very smart guy. He has been making the
same arguments to large audiences for a long time. It stretches my
credulity to believe that he could not understand their problems if he
wanted to.
Even so, his books would do little harm if they came with warning
labels, so when they are mentioned I apply one.
> Ralph Hartley <har...@aic.nrl.navy.mil> writes:
>> Quantum Mechanis has nothing to tell us about the mind.
..
>>I didn't claim that there is no relationship at all
..
> I misunderstood you, then. My interpretation of your assertion
> was that quantum mechanics will never have any relevance to
> questions about the mind.
If I had intended to say, "quantum mechanics will never have any
relevance to any questions about the mind", that's what I would have said.
Do you agree with the statement "Quantum mechanics has nothing to tell
us about the price of coffee"?
Interpreted the way you interpreted my previous statement, I couldn't
prove that either.
I could have said, "Quantum mechanics in not likely enough to have
enough to tell us about the mind to be worth thinking about," but that's
just too long a sentence.
> If I were to believe that QM is a formalisation of induction (which
> I don't, although I consider it a possibility)
There are far too many possibilities for smart people like you to waste
time considering them all.
>>>It's possible that quantum mechanics is a quantitative
>>>formalization of the principle of induction, just
>>>as boolean algebra gives a formalization of deductive
>>>inference (propositional calculus).
>
>>It would be possible if Quantum Mechanics were anything *like* the
>>principle of induction. A better candidate for a formalization of the
>>principle of induction would be Statistical Inference, which is related
>>to Probability Theory, which *is* related to Quantum Mechanics. :-)
>
> Statistical inference and probability theory are completely
> mathematical disciplines.
A formalization of a principle *should* be a completely mathematical
thing. Boolean algebra is the same.
> As such, they place no constraint
> upon the behaviour of the world and their theorems hold
> regardless of what experiments give what results.
As would any theorems of formalized induction. The theorems would be
true even in a world in which induction is useless. Of course, in such a
world what experiments give what results wouldn't tell you anything at all.
> In order for quantum mechanics or induction to be true, the
> world has to behave a specific way. They both say something
> nontrivial about the results of experiments.
But they don't say the *same* nontrivial thing. There are possible
worlds in which induction works, but not quantum mechanics. I'm pretty
sure the reverse is true as well.
Ralph Hartley
mark...@yahoo.com
> The physics of the brain is in scope, but the philosophy of the mind
is
> not.
The question can be refined to a single proposition which can
(ultimately) be put to the test. The relevant question is: is the
infrastructure that comprises your ego a classical or quantum state?
If the former, then it should be theoretically possible to replicate
the state (i.e. "upload" it). If the latter, then given the inability
to carry out non-detructive replication of any quantum state, then any
transference of the brain's state will necessarily be destructive of
the original. In that case, what makes you an instance of "you" is
essentially unique.
Charles Francis
>>> The rules which make science successful are to be
>>> abandoned when they conflict with the "higher good" of giving
>>> philosophers a public trouncing at the hands of physicists.
>
>>But the reverse is OK?
>
>I concern myself with the ethics of public trouncings only in the
>following regard. The inclination to dispence such trouncings and avoid
>suffering them is motivated by a desire to increase and maintain one's
>self-respect and the respect of one's peers. This motivation, in so far
>as it has any effect at all on a person's behaviour, can only serve to
>conflict with the motivation to explain one's own position and
>understand the position of the person with whom one is debating. If the
>goal is to achieve a better understanding of the subject matter
>oneself, or to help others achieve a better understanding, then the
>motivation which underlies trouncings can only be detrimental to
>achieving the goal.
So does the fact that you, presumably, enjoyed trouncing physicists who
dismiss philosophy, and I enjoyed reading it, indicate that we are on
the route to a better understanding, or merely that we seek to increase
and maintain our self respect over those physicists whom we despise? And
if these physicists are to be enlightened in such matters, how is the
trouncing to help?
>I am not saying that one should neglect the desire for self-respect and
>the respect of one's peers. Rather, the source of self-respect should
>be the knowledge that one adheres honestly to the rules of inquiry and
>debates the actual points at hand rather than seeking merely to
>humiliate the opponent. A person who does this will earn the respect of
>whoever's respect is worth having.
I suspect that is optimistic. If one adheres to the rules of inquiry and
honestly demonstrates someone wrong, that person will still become
hardened in their views and hostile to corrections.
>
Regards
--
Charles Francis
r...@maths.tcd.ie
>In message <d6hinq$1a3p$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>>> The rules which make science successful are to be
>>>> abandoned when they conflict with the "higher good" of giving
>>>> philosophers a public trouncing at the hands of physicists.
>>
>>I concern myself with the ethics of public trouncings only in the
>>following regard.
>>... If the
>>goal is to achieve a better understanding of the subject matter
>>oneself, or to help others achieve a better understanding, then the
>>motivation which underlies trouncings can only be detrimental to
>>achieving the goal.
>So does the fact that you, presumably, enjoyed trouncing physicists who
>dismiss philosophy, and I enjoyed reading it, indicate that we are on
>the route to a better understanding, or merely that we seek to increase
>and maintain our self respect over those physicists whom we despise? And
>if these physicists are to be enlightened in such matters, how is the
>trouncing to help?
Unfortunately, as you are aware, nobody likes to be told that they're
wrong, and, in this case, it's worse, because this is a public
discussion group, and so the respect of one's peers is on the line.
In such a circumstance, any time anybody is corrected by anybody
else, it will look like a public trouncing. This is an inherent
problem with any form of discussion in public.
In my case, I didn't produce my rant just to stand at the top
of a mountain and beat my chest while proclaiming myself
the king of the world. I actually think physicists are the
best hope in the sense that they understand rigour without
devoting all of their thought to mathematics. In that sense,
they have an opportunity to be cured of their mental diseases,
because when things are pointed out to them, they at least
have the inclination to look first for what makes sense. If
I tried to convince a racist, for example, that his hatred
for whoever he hates is unjustified, even ridiculous, he
would pay no attention at all to the question of whether
I was making any sense, but would interpret it purely
in terms of whether, from his point of view, I was a
good person or an enemy.
Although I replied to Ralph, the message was intended for
every physicist, and I think Ralph demonstrated that
physicists are generally reasonable people, by responding
not with personal attacks or an attempt to misrepresent
what I was saying, but with an honest question about
whether thinking about the mind was worth the effort. I
would not have expected such a reasonable response had
I attempted to attack a meme which had infected a non-physicist.
>>I am not saying that one should neglect the desire for self-respect and
>>the respect of one's peers. Rather, the source of self-respect should
>>be the knowledge that one adheres honestly to the rules of inquiry and
>>debates the actual points at hand rather than seeking merely to
>>humiliate the opponent. A person who does this will earn the respect of
>>whoever's respect is worth having.
>I suspect that is optimistic. If one adheres to the rules of inquiry and
>honestly demonstrates someone wrong, that person will still become
>hardened in their views and hostile to corrections.
Most likely, but their training as a physicist, and their
acknowledgement of the rules of rational debate are intended
to counter this inclination. If it were as bad as you say
in every case, then there would be no point in discussing
anything at all, because the only thing we would expect
would be childish bickering. Debate becomes useful only
when people are mature enough to be able to publicly
change their mind without becoming so embarrassed that
they consider the person who corrected them as their
enemy. That requires some trust in the maturity of the
audience as well, since the immature person will consider
a person who changes their mind to be one who is likely
to be wrong. We need to recognise that the people who
change their mind when presented with a coherent argument
are more worthy of respect than those who don't, since
they thereby demonstrate the ability to learn.
As it is, my rant was worth producing because many physicists,
although they will find it offensive, will at least recognise that
I have a point. The purpose was not to humiliate anybody, but
to explain. People who see debate in a physics newsgroup
in terms of winners and losers are missing the entire point
of communication, which is not supposed to be merely another
form of fighting, but is supposed to enable people to share
information.
This, unfortuantely, inevitably becomes a slightly hostile affair
when the information is "You're all infected with a mental disease,"
because the mental disease has been through a process of evolution,
and has acquired defenses, in the form of preprogrammed emotional
responses to something which should properly evoke no emotion at
all, since it is a purely scholastic, if philosophical, matter. In
order to cure a person of such a disease, one must understand it
very well, and anticipate its response to your attacks, which was
what I did.
Most of the time the defenses are impenetrable, as is the case when
somebody has had a religion spread to them. Physicists, however,
have, if not a special form of defense, at least a way in which
they can be cured, through reason, although even reason will not
cure religion, since it has faith, which teaches that reason should
be ignored when it conflicts with belief. Patriotism, in contrast,
is a less-evolved meme, and doesn't preach faith, so you might
expect that a sufficiently reasonable patriotic physicist could be
cured of this meme if one took the time to prepare the attack
well. I don't think this is worth the effort, though, since I
don't think it would be of much benefit to physics to do this.
R.
r...@maths.tcd.ie
>r...@maths.tcd.ie wrote:
>> With regard to value judgments and morality, I don't
>> think Penrose was being in any way dishonest; he most likely
>> believes that what he argued was correct. In this sense I
>> don't think Penrose should be morally condemned.
>I have no doubt at all that he is sincere, and believes his own
>arguments, but I don't consider that enough.
>When making an argument there is obligation to consider, and to
>disclose, its weaknesses. It is wrong (in the ethics of science) to make
>arguments you know or *should* know are invalid.
I agree, although it's a little difficult to be aware of what one
should know, but doesn't. Almost by definition, if one should know
something but doesn't, one has done something wrong.
>Sir Roger is, by all accounts, a very smart guy. He has been making the
>same arguments to large audiences for a long time. It stretches my
>credulity to believe that he could not understand their problems if he
>wanted to.
I think he does, but gets additional psychological support from
various places, like the fact that the mass of a tubulin molecule
gives a wavefunction collapse at around the right timescale
if you calculate it using his gravitational wavefunction collapse
formula. There are probably other factors of which he is more
aware than we which give him more confidence about his ideas.
>>> Quantum Mechanics has nothing to tell us about the mind.
>..
>>>I didn't claim that there is no relationship at all
>..
>> I misunderstood you, then. My interpretation of your assertion
>> was that quantum mechanics will never have any relevance to
>> questions about the mind.
>If I had intended to say, "quantum mechanics will never have any
>relevance to any questions about the mind", that's what I would have said.
OK.
>Do you agree with the statement "Quantum mechanics has nothing to tell
>us about the price of coffee"?
Yes.
>> If I were to believe that QM is a formalisation of induction (which
>> I don't, although I consider it a possibility)
>There are far too many possibilities for smart people like you to waste
>time considering them all.
Yes, so I consider the ones which I regard as more likely
than others, but I'm careful not to start believing them.
>>>>It's possible that quantum mechanics is a quantitative
>>>>formalization of the principle of induction, just
>>>>as boolean algebra gives a formalization of deductive
>>>>inference (propositional calculus).
>>
>>>It would be possible if Quantum Mechanics were anything *like* the
>>>principle of induction. A better candidate for a formalization of the
>>>principle of induction would be Statistical Inference, which is related
>>>to Probability Theory, which *is* related to Quantum Mechanics. :-)
>>
>> Statistical inference and probability theory are completely
>> mathematical disciplines.
>A formalization of a principle *should* be a completely mathematical
>thing. Boolean algebra is the same.
Yes, of course.
>> As such, they place no constraint
>> upon the behaviour of the world and their theorems hold
>> regardless of what experiments give what results.
>As would any theorems of formalized induction. The theorems would be
>true even in a world in which induction is useless. Of course, in such a
>world what experiments give what results wouldn't tell you anything at all.
Yes, but the statements "Quantum mechanics accurately describes the
statistics of measurement results" and "The principle of
induction accurately describes the statistics of measurement
results" both place constraints on the statistics of
measurement results. Probability theory, in contrast, only
has something to say about measurement results if one
introduces a model for the process generating the results.
That is, probability theory alone says nothing about the
results of experiments, but becomes applicable if one
introduces an extra hypothesis about the measurement
results. Similarly, statistical inference alone says
nothing a priori about the results of measurements,
but becomes relevant when one introduces additional
hypotheses regarding the things to be inferred.
>> In order for quantum mechanics or induction to be true, the
>> world has to behave a specific way. They both say something
>> nontrivial about the results of experiments.
>But they don't say the *same* nontrivial thing. There are possible
>worlds in which induction works, but not quantum mechanics. I'm pretty
>sure the reverse is true as well.
I agree with both of these, but for different reasons. It is logically
possible for induction to work without quantum mechanics working
because the principle of induction is vaguer than quantum mechanics
and hence weaker. The actual world that we live in is one in
which quantum mechanics works (apparently), but induction does
not work absolutely. It works exactly as far as quantum mechanics
does, and no further.
I should explain this more clearly. The principle of induction
alone is pretty vague, saying that the more similar the
experiments are the more similar the results should be. No hint
is given, in this statement alone, that it might break down
at some point, where you can do two experiments which are
identical as far as it is possible to determine in principle,
but which give different results. Quantum mechanics tells
us that the principle of induction fails; with certain
experiments, it is impossible, even in principle, to know,
for example, where a particle will be found to more accuracy
than |psi^2|. Hence, ours is a world in which QM works but
induction, at least its naive formulation, fails at a certain
point.
On the other hand, in so far as quantum mechanics does
work, induction also works. That is, quantum mechanics
gives us some information about the results of experiments.
Prepare the system in a state |psi>, let the eigenvectors
of the observable operator corresponding to the experiment
be |e_i>, with corresponding eigenvalues e_i, and the
probability of getting e_i as a result is |<psi|e_i>|^2.
Repeat the experiment with the same initial state and
QM says the probabilities of the e_i are the same the second
time around. That is, in so far as induction says "Do
the same experiment twice and you'll probably get the same results",
quantum mechanics says this isn't quite right, but replaces
it with "the probabilities of the results are the same both
times".
Imagine what it would be like if induction didn't work
at all. Experiments would give random results, and the
information we would have in advance of an experiment
about the result would be zero. Now, suppose the
amount of information given by the result of the experiment
is I=I1 + I2, where I1 is what quantum mechanics tells us
and I2 is the "surprise" when we get the final result. In
a world where induction didn't work at all, we would
know nothing in advance about the result and so I1 would have
to be zero, that is, quantum mechanics would be able to
tell us nothing about the result.
So, you can't have a possible world in which quantum mechanics works
just fine but induction doesn't work at all. In our world, induction
works exactly as well as quantum mechanics and no better.
R.
r...@maths.tcd.ie
>>bjflanagan writes:
>>What if a mind/brain identity theory holds?
>>>It doesn't; the mind and experience are subjective, while the
>>brain is objective.
>>The "objective" is the result of intersubjective agreement.
>Sure; but you cannot have intersubjective agreement about certain
>things. The experience that I have when I see the colour blue,
>for example, is something that I cannot compare to the experience
>that other people have when they look at the same object.
>Flanagan
>Well, why don't you explain that to the judge the next time you run a
>red light?
What I said above does not lead to the conclusion that a person
would misinterpret traffic signals. You responded as though it
did. In fact, the misinterpretation that you displayed is so
easy to avoid, and difficult to fall into, that it leads me
to the conclusion that you deliberately pretended to have
misinterpreted me in this way, to give you the opportunity
to respond with your pugnacious comment, by which you
presumed to show your wisdom. Shame on you.
>If we both respond by saying "red" when presented with a
>novel stimulus that others agree is red, then we have all the
>intersubjective agreement we need -- a case which finds a telling
>parallel in the measuring sticks and clocks of relativity. I.e., space
>and time have subjective aspects, too, but we get around that by
>agreeing on objective standards, as is done when constructing color
>monitors and TV screens.
This more coherent response shows that you in fact understood
very well what I was saying, if not its significance. Yes, for
practical purposes we never need to compare one person's
experience of seeing a red object with another's. Whatever
experience you have when seeing red is associated with
the word "red" and with certain traffic rules in your mind,
and that allows you to avoid ending up before a judge, even
if the particular experience that you associate with the
word "red" differs from everybody else's. This is true and
I don't deny it.
However, we are not here concerned with practical purposes, because
you want to say something about the experience of seeing colours,
namely that it is "the same thing as" a certain physical process
or object. Hence the intersubjective agreement that you referred
to is to be considered not with regard to traffic lights, but
with regard to the experience of seeing colours. Now I claimed,
and you didn't deny, that there can be no intersubjective
agreement about whether what I call blue and what you call
blue are the same experience. You instead said that it didn't
matter for practical purposes. I agree that it doesn't matter
for practical purposes, but for philosophical purposes, we have to
regard the experience of seeing blue as subjective, and recognise
that physical processes and events are objective, and that
they therefore cannot be the same thing.
>R.
>For all I know, they might have the experience that I call seeing
>red when they look at it, but have always known that experience
>by the name of blue. Whether this is the case or not cannot be
>settled by studying either their behaviour or their brain.
>Flanagan
>Yes, and for all I know, you may see a meter where I see a centimeter.
>Occam's razor applies: if our brains are built along the same lines,
>and we both say "meter" when presented with a measuring stick of that
>length, then the simplest explanation is that we both see a meter.
You are invoking Occam's razor to establish the point that, if
we somehow could compare my experience of blue to yours, we
would most likely agree that they are the same. This may or
may not be true, but is irrelevant to the point I was making.
The important point is that they cannot be compared, even
in principle, and this is a property of the experience of
seeing a colour, a property which we call subjectivity,
and a property which physical processes and events lack.
>>R
>>>At best you can say that there's a correspondence
>>of some kind between them, which isn't very strong or
>>very deep.
>Flanagan
>This is an empirical issue and begs the question. How did you determine
>that mind & brain do not have the same properties?
And the answer is that we do so empirically. We notice, from
experience, that the brain is a physical object, and its
properties, as a physical object, are objective. We notice
that experiences are experienced only by the experiencer,
and are thus subjective. Then we notice that subjective is
the opposite of objective. Then we realise that the brain
and the mind cannot be the same thing.
>As Einstein, Wigner
>& Weyl all explain, the "physical" is a theoretical construct whereby
>we make sense of the regularities of "mental" experience. If the
>theoretical construct does not do justice to experience, it is the
>construct which is called into question.
Yes indeed, but the mental constructs which we build, the concepts
which we use, must, in order for us not to confuse ourselves,
remain clear and distinct, and we should not "identify" one
with another when they refer to different things. If I identify
"mind" with "brain" as you want to, then when I look underneath
somebody's skull, I would find myself saying that I see their
mind. That would not be correct. I agree with Wigner and Einstein
about the status of the physical and its relation to the
mental, and I recognize that an immediate consequence of this
is that we cannot "identify" the "mental" experience with
the physical, because that would be to "identify" mental
experience with a theoretical construct which arises in
experience as a tool to characterize regularities of that
experience. Nobody should confuse their thoughts with the
things that they are thinking about.
>>>Here is what Chalmers, a philosopher, wrote in Sci Am:
>>>"The abstract notion of information, as put forward by Claude E.
>>>Shannon of MIT, is that a of a set of separate states with a basic
>>>structure of similarities and differences between them."
..
>R
>Both Chalmers and I were referring to Shannon's introduction
>of the notion of information. Chalmers gave an inaccurate
>description of what Shannon said.
>Flanagan
>I suggest you revisit what Shannon wrote:
>cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf
I did, just before I declared that Chalmers had misrepresented him.
If there's a section that I missed in that paper where Shannon
mentions an "information state", or "a set of separate states with
a basic structure of similarities and differences between them",
then I'd be grateful if you could point it out to me.
>R
>Now, once again I'd like to draw your attention to the distinction
>between the experience of seeing a colour, and the wave associated
>with coloured light. Only the latter satisfies the rules of vector
>addition.
>Flanagan
>Well, you're simply mistaken. Red at 620nm added to green at 540 nm is
>indistinguishable from yellow at 580 nm. On the vector model I sketched
>in, there is a precise correspondence between what is experienced and
>what the model predicts.
I find it difficult to believe that you still don't understand what
I've been saying. The addition of red light to green light is a
mixture of light, achieved by shining the red and the green light
into the same region of space. It is not an addition of the experiences
of red and green. The experience that I have when viewing this
mixture may be indistinguishable from the experience that I have
when I see monochromatic yellow light, indicating that the two types
of light (mixed red/green light and yellow light) have the same
effect on my sensory apparatus, but that does not mean that any
addition of experiences has taken place, which is what you are
trying to suggest.
>R
>It's a pity that you didn't reply to my objections to your theory
>that the experience of seeing colour is identical to a quantum
>field:
>Flanagan
>It's a pity you don't think instead of simply regurgitating the
>received wisdom.
But that is little more than an insult. Shame on you again.
>>> 1. When mixing quantum states, there is a very important
>>> phase to be taken into account: |up> + |down> is very
>>> different from |up> - |down>. When adding colours there
>>> is no corresponding phase.
>Flanagan
>Photons of the same color (tone) but 180 degrees out of phase cancel.
>So how is there no corresponding phase?
My apologies for not being clearer. You are talking about addition
of experiences, claiming that the experience of seeing one colour
can be added to the experience of seeing another colour, and you
do this because you want to identify the experience of seeing
colour with a quantum state. Because of this, when I said
"When adding colours there is no corresponding phase", I was
using "colour" to refer to the experience of seeing colour. Your
statement that "Photons of the same color (tone) but 180 degrees
out of phase cancel" clearly refers not to the experience of
seeing colour, but to the addition of waves to waves. It is
not news that waves can be added together.
>R
>>> 2. ... What you want to do is say that the experience of
>>> seeing colours is the same as a quantum state, based
>>> on a shared additive property, but the fact is that it
>>> is not the experiences of seeing colours which
>>> can be added together; only the lights and inks
>>> are added.
>Flanagan
>O, so there is no corresponding perception?
There is the experience of seeing red and the experience of
seeing green. There is the experience of seeing yellow, which
can be induced by mixing red light to green light, or red
ink and green ink. This is not the addition of the experience
of seeing red with the experience of seeing green. You can
say that the perception of yellow "corresponds" to the mixed
light if you like, but there is no corresponding "addition"
of perceptions.
>R
>A set of such linear operators which is
>indexed by a continuous variable is called a quantum
>field. This is a purely mathematical object. You
>might say that there is something physical which
>corresponds to the mathematical object. Maybe, but
>it is the mathematical object which is "quantum".
>Flanagan
>You may wish to apprise the larger community of physicists of your
>discovery, most of whom believe that the universe is quantum and that
>the formalism has been developed to reflect this understanding.
More sarcasm. Shame on you again.
>And now I really have to get back to work. Good bye.
Good bye.
R.
Charles Francis
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
One will find the same message in mystic philosophy of course, delusion
is the natural human condition, and takes a fair bit of escaping, if
anyone can escape at all.
>because the mental disease has been through a process of evolution,
>and has acquired defenses, in the form of preprogrammed emotional
>responses to something which should properly evoke no emotion at
>all, since it is a purely scholastic, if philosophical, matter. In
>order to cure a person of such a disease, one must understand it
>very well, and anticipate its response to your attacks, which was
>what I did.
>
>Most of the time the defenses are impenetrable, as is the case when
>somebody has had a religion spread to them. Physicists, however,
>have, if not a special form of defense, at least a way in which
>they can be cured, through reason, although even reason will not
>cure religion, since it has faith, which teaches that reason should
>be ignored when it conflicts with belief. Patriotism, in contrast,
>is a less-evolved meme, and doesn't preach faith, so you might
>expect that a sufficiently reasonable patriotic physicist could be
>cured of this meme if one took the time to prepare the attack
>well. I don't think this is worth the effort, though, since I
>don't think it would be of much benefit to physics to do this.
Much of what you say I agree with, but I don't think the training of
physicists has much to do with anything. As a mathematician my initial
attempts at learning qm were thwarted by canonical quantisation, a
process which I still regard as replacing mathematical argument with an
irrational recipe, and which I cannot justify from the correctness of
the mathematical structure so produced. Unfortunately I think the use of
such recipes trains physicists in precisely the opposite way from the
one which you suggest. By and large only those who can treat physics as
magical recipes for experimental results are likely to make enough
progress at an early stage of there careers to move to positions of
authority.
What I do think is that, rather than by training, there are a small
number of people who innately value the search for scientific truth
above self esteem, and who are more than usually ready to dismiss
preconceptions.
Regards
--
Charles Francis
Ralph Hartley
> Yes, but the statements "Quantum mechanics accurately describes the
> statistics of measurement results" and "The principle of
> induction accurately describes the statistics of measurement
> results" both place constraints on the statistics of
> measurement results. Probability theory, in contrast, only
> has something to say about measurement results if one
> introduces a model for the process generating the results.
> That is, probability theory alone says nothing about the
> results of experiments, but becomes applicable if one
> introduces an extra hypothesis about the measurement
> results.
Quantum mechanics alone does not tell you anything about the results of
experiments either. Just as probability theory requires a distribution,
quantum mechanics needs at least a Hamiltonian (or something equivalent,
depending on the formulation being used).
Fortunately, we seem to inhabit a world in which both QM and induction
apply, so we can use induction to figure out at least some of the
missing information.
> Ralph Hartley <har...@aic.nrl.navy.mil> writes:
>>... they [QM and induction] don't say the *same* nontrivial thing. There are possible
>>worlds in which induction works, but not quantum mechanics. I'm pretty
>>sure the reverse is true as well.
>
> ... It is logically
> possible for induction to work without quantum mechanics working
> because the principle of induction is vaguer than quantum mechanics
> and hence weaker.
Furthermore it is by induction that we discovered QM. If induction was
dependent on QM, I'm not sure that would make sense. In a world in which
induction did not work, it would be impossible to tell if QM worked or
not (or anything else).
> Imagine what it would be like if induction didn't work
> at all. Experiments would give random results, and the
> information we would have in advance of an experiment
> about the result would be zero. Now, suppose the
> amount of information given by the result of the experiment
> is I=I1 + I2, where I1 is what quantum mechanics tells us
> and I2 is the "surprise" when we get the final result. In
> a world where induction didn't work at all, we would
> know nothing in advance about the result and so I1 would have
> to be zero, that is, quantum mechanics would be able to
> tell us nothing about the result.
Just so. In a world in which induction does not work, QM would tell us
nothing.
Let's try constructing a toy world.
Assume you can make a sequence of experiments. For each experiment you
choose an N bit number E_t, make a 1 bit "guess" G_t, and get back a one
bit result R_t = w(E_t,t). Your goal is to be able to correctly guess as
many results as possible.
Consider this game in which the results are produced by some process
equivalent to a fair coin, and independent of the experiment E_t. In
this case you can never do better than chance. Induction doesn't help.
You can guess 1 every time, or 0, or you can flip a coin, it doesn't
matter. Your guesses will be right half the time.
This is the same regardless of how the process producing the results
works. It can be quantum or classical. It can even be a predetermined
function of t and E_t.
In this world quantum mechanics indeed gives no information.
We can construct worlds in which induction (and/or QM) does work by
putting restrictions on how the results are produced.
For example, we could require that the result be produced by a circuit
(or a quantum circuit) with at most X gates, or by a program of length
at most X. Induction will work in this world, but as X increases it will
get harder.
These toy worlds may not be much like ours, but if one of them has a
certain combination of properties, then you *can* have a possible world
with those properties.
Ralph Hartley
r...@maths.tcd.ie
>In message <d6ntvf$14fk$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>>People who see debate in a physics newsgroup
>>in terms of winners and losers are missing the entire point
>>of communication, which is not supposed to be merely another
>>form of fighting, but is supposed to enable people to share
>>information.
>>
>>This, unfortuantely, inevitably becomes a slightly hostile affair
>>when the information is "You're all infected with a mental disease,"
>One will find the same message in mystic philosophy of course, delusion
>is the natural human condition, and takes a fair bit of escaping, if
>anyone can escape at all.
It needs introspection, and a willingness to admit that, since
many great minds have been led into thinking absurd things,
we should check the things that we ourselves believe for
absurdness, not according to our own likes and dislikes,
or what, in our personal opinion, is likely or unlikely,
but according to some objective standard, such as what
we can actually prove or what experimental results are
actually confirmed. Theoretical physics is the field
where this introspection is needed.
>Much of what you say I agree with, but I don't think the training of
>physicists has much to do with anything. As a mathematician my initial
>attempts at learning qm were thwarted by canonical quantisation, a
>process which I still regard as replacing mathematical argument with an
>irrational recipe, and which I cannot justify from the correctness of
>the mathematical structure so produced. Unfortunately I think the use of
>such recipes trains physicists in precisely the opposite way from the
>one which you suggest. By and large only those who can treat physics as
>magical recipes for experimental results are likely to make enough
>progress at an early stage of there careers to move to positions of
>authority.
Exactly. Quantum mechanics is the only serious part of theoretical
physics where we have a magical formula that just works for
no apparent reason.
>What I do think is that, rather than by training, there are a small
>number of people who innately value the search for scientific truth
>above self esteem, and who are more than usually ready to dismiss
>preconceptions.
A very small number indeed.
R.
Alf P. Steinbach
>
> (1) Penrose's argument that quantum theory has important things to tell
>
> (2) Making nonsense believable and respectable is *not* a good thing.
>
> (3) It would be a bad thing even *if* the conclusion were correct (which
> is very unlikely in this case). An invalid argument for a true
> proposition is still an invalid argument.
I agree with all three points, except the use of the word "unlikely", which
IMO is too categorical and unfounded.
> Nowadays there is debate about the practicality of building
> computational devices that exploit quantum effects. Maybe we can,
> maybe we can't. What is *quite* clear is that the human brain is
> *not* such a device. Nothing that is composed almost entirely of
> liquid water ever can be.
That argument doesn't seem to hold water.
The flaws in Penrose's arguments do not mean that quantum effects do
not have importance for the functioning of a biological brain. There is
much that is not well-understood even at the physics level. E.g., as I
recall (and this is from Penrose... :-)), how a noble gas such as Xenon --
a chemically non-reactive gas -- can work effectively as an analgesic.
In the face of that kind of unmapped territory I don't think one should
be too categorical in stating what could possibly be in that territory.
Or not.
In short, it seems to me that you're committing the same kind of error as
Penrose did: "X must be true or false because that's what I feel".
--
A: Because it messes up the order in which people normally read text.
Q: Why is it such a bad thing?
A: Top-posting.
Q: What is the most annoying thing on usenet and in e-mail?
Charles Francis
<har...@aic.nrl.navy.mil> writes
>> Imagine what it would be like if induction didn't work
>> at all. Experiments would give random results, and the
>> information we would have in advance of an experiment
>> about the result would be zero. Now, suppose the
>> amount of information given by the result of the experiment
>> is I=I1 + I2, where I1 is what quantum mechanics tells us
>> and I2 is the "surprise" when we get the final result. In
>> a world where induction didn't work at all, we would
>> know nothing in advance about the result and so I1 would have
>> to be zero, that is, quantum mechanics would be able to
>> tell us nothing about the result.
>
>Just so. In a world in which induction does not work, QM would tell us
>nothing.
>
necessarily the case that we need induction. Einstein showed by thought
experiments that certain laws of relativity are necessary because of the
way in which we go about measuring things. Likewise, as rof has pointed
out, we do not need induction for the probabilistic part of quantum
theory.
But when we seek to apply simply the constraints which we can find on
experiment the mathematical structure becomes constrained. So
constrained in fact that we do not know how to satisfy it and combine
general relativity and qm. In fact we cannot even resolve all the issues
for a special relativistic theory.
I do not believe that the physical universe can be inconsistent, and
therefore I believe it must be describable by a consistent mathematical
structure. I very much doubt that much induction will be left once we
have found such a mathematical structure.
Regards
--
Charles Francis
r...@maths.tcd.ie
Quantum mechanics, considered as a recipe for predicting the
reults of future measurements, works better than chance
only if induction works better than chance.
You didn't deny this, but instead hypothesised a "real world",
which was invisible, but contained the "process producing
the results", and supposed that quantum mechanics could work
there, and hence still "work" even though induction didn't.
It was, or should have been, clear that when I was referring
to quantum mechanics I meant the formalism which is used to
assign probabilities to measurement results, not "what's
going on in the real world". If the former works, meaning
allows you to predict meaurement results better than
chance, then induction also works.
R.
Charles Francis
>Charles Francis <cha...@clef.demon.co.uk> writes:
>
>>In message <d6ntvf$14fk$1...@lanczos.maths.tcd.ie>, r...@maths.tcd.ie writes
>
>>>People who see debate in a physics newsgroup
>>>in terms of winners and losers are missing the entire point
>>>of communication, which is not supposed to be merely another
>>>form of fighting, but is supposed to enable people to share
>>>information.
>>>
>>>This, unfortuantely, inevitably becomes a slightly hostile affair
>>>when the information is "You're all infected with a mental disease,"
>
>>One will find the same message in mystic philosophy of course, delusion
>>is the natural human condition, and takes a fair bit of escaping, if
>>anyone can escape at all.
>
>It needs introspection, and a willingness to admit that, since
>many great minds have been led into thinking absurd things,
>we should check the things that we ourselves believe for
>absurdness, not according to our own likes and dislikes,
>or what, in our personal opinion, is likely or unlikely,
>but according to some objective standard, such as what
>we can actually prove or what experimental results are
>actually confirmed. Theoretical physics is the field
>where this introspection is needed.
Indeed, but given the human capacity for self delusion, how are we to
know whether or not we have succeeded in applying an objective standard.
Both mathematics and experimental results provide such a standard, but
Priestley believed in Phlogiston even after producing oxygen, and I know
no means other than the 'personal' opinion of other mathematicians to
ensure there is no mistake in mathematical argument.
>
>>Much of what you say I agree with, but I don't think the training of
>>physicists has much to do with anything. As a mathematician my initial
>>attempts at learning qm were thwarted by canonical quantisation, a
>>process which I still regard as replacing mathematical argument with an
>>irrational recipe, and which I cannot justify from the correctness of
>>the mathematical structure so produced. Unfortunately I think the use of
>>such recipes trains physicists in precisely the opposite way from the
>>one which you suggest. By and large only those who can treat physics as
>>magical recipes for experimental results are likely to make enough
>>progress at an early stage of there careers to move to positions of
>>authority.
>
>Exactly. Quantum mechanics is the only serious part of theoretical
>physics where we have a magical formula that just works for
>no apparent reason.
>
>>What I do think is that, rather than by training, there are a small
>>number of people who innately value the search for scientific truth
>>above self esteem, and who are more than usually ready to dismiss
>>preconceptions.
>
>A very small number indeed.
>
>R.
>
Regards
--
Charles Francis
John Baez
Nick Maclaren <nm...@cus.cam.ac.uk> wrote:
>In article <1115387461....@z14g2000cwz.googlegroups.com>,
>Spoonfed <jonatha...@spoonfedrelativity.com> wrote:
>>Penrose also wrote Emperor's New Mind which has a pretty good
>>description of Goedel's Theorem, the Mandelbrot set, thermodynamics,
>>Quantum Mechanics, and general relativity, and the "arrow of time".
Yes!
>Hmm. I don't know of any mathematician (other than Penrose, of
>course) who has much respect for that book.
It's a mixed bag. I completely agree with "Spoonfed" on the
good point of this book.
>In particular, his claim that the human brain is not subject to a
>Goedelian limitation doesn't even have a coherent justification,
>though you have to read the book carefully to notice that.
I completely agree with you on that. So, people should read this
book but take all the stuff about artificial intelligence with a
whopping mountain of salt.
It's a pity Penrose wrote a book that one has to treat with caution
this way, by mixing up excellent explanations of widely accepted
stuff with idiosyncractic theories that few scientists agree with.
But, if one knows this, one can figure out how to deal with it.
For people who want to get started developing their physics
intuition, I recommend reading some history:
Robert P. Crease and Charles C. Mann, The Second Creation:
Makers of the Revolution in Twentieth-Century Physics,
Rutgers University Press, New Brunswick, NJ, 1996.
and for more detail, these:
Emilio Segre, From Falling Bodies to Radio Waves: Classical Physicists
and Their Discoveries, W. H. Freeman, New York, 1984.
Emilio Segre, From X-Rays to Quarks: Modern Physicists and Their
Discoveries, W. H. Freeman, San Francisco, 1980.
Abraham Pais, Inward Bound: of Matter and Forces in the Physical
World, Clarendon Press, New York, 1986.
Marcel LeBel
>
> You didn't deny this, but instead hypothesised a "real world",
> which was invisible, but contained the "process producing
> the results", and supposed that quantum mechanics could work
> there, and hence still "work" even though induction didn't.
>
warning sign! Do you have any idea of what you are doing or even of
what you want? Sure, there is (A) a real universe out there made of
some mush substance with its built-in processes and causes. Then there
is (B)our reality which is a total construct, which is how we experience
the variations this mush has to offer given the way we are built, our
size and the way we think. An then there is (C)our scientific analysis
of our experience of that mush. So you see, you are a long way from
being able to say what is, and what is not about that mush. So, what is
it that you want? Do you want to understand what the universe is made of
and how it works by itself?(It does) To that question there is a single
possible answer and you need an ontological analysis for that. If not,
what is it that you are trying to do? ????? I suggest an ontological
analysis of (C) in order to elucidate (A), which will come back as
understanding, not experiencing. There is some good in understanding
(you know)that we can apply to (C) and in turn physically turn into
stuff in (A).
Philosophy is just that; standing back for a moment and asking yourself
where you are and what you are trying to achieve. Good luck!.
suggestion applies to both parties.
le...@muontailpig.com ------- remove particle
MML
Ralph Hartley
> Exactly. Quantum mechanics is the only serious part of theoretical
> physics where we have a magical formula that just works for
> no apparent reason.
Where have you been for the last 400 years?
"F=ma" is a magical formula that just works for no apparent reason.
*All* of theoretical physics consists of either magical formulas that
just work for no apparent reason, or magical formulas that work as a
consequence of other magical formulas working.
There may be people who think that quantum mechanics, or Newton's laws,
or *any* physical law, could be derived from first principles, without
knowing the results ahead of time, but that is not so.
Where do we get all these magical formulas? We build theories, test with
experiment, and try the simple ones first. I can't claim to know, on a
fundamental level, why *that* formula works, but we've had very good
luck with it.
Ralph Hartley
Mike Helland
> >
> > You didn't deny this, but instead hypothesised a "real world",
> > which was invisible, but contained the "process producing
> > the results", and supposed that quantum mechanics could work
> > there, and hence still "work" even though induction didn't.
> >
> This is like watching someone bathing in quicksand right in front of the
> warning sign! Do you have any idea of what you are doing or even of
> what you want? Sure, there is (A) a real universe out there made of
> some mush substance with its built-in processes and causes. Then there
> is (B)our reality which is a total construct, which is how we experience
> the variations this mush has to offer given the way we are built, our
> size and the way we think. An then there is (C)our scientific analysis
> of our experience of that mush.
Would it perhaps be adequate if we defined (B) as observation
(experiment) and (C) as knowledge (theory) ?
I suggest this because using your terms you've separated our experience
of the universe and our knowledge of the universe, while it seems to me
that our experience of the universe is defined by both our observations
and our knowledge, as they are deeply intertwined in the memetic
networks of our brians.
Or so it seems to me.
Another way to say this is, there is the universal ontological domain.
In the universal ontological domain there is a neural network of memes.
These memes are an axiomatic system of truths that as a whole, define a
relative ontological domain.
Our relative ontological domain is defined by knowledge, both a
posteriori (empirical) and a priori (mathematical, metaphysical).
>From what you've said, you seem to be setting the two apart. I think
that's a mistake.
<snip>
Charles Francis
<har...@aic.nrl.navy.mil> writes
>r...@maths.tcd.ie wrote:
>> Exactly. Quantum mechanics is the only serious part of theoretical
>> physics where we have a magical formula that just works for
>> no apparent reason.
>
>
Wrong example. It works because it is the definition of force. No magic
about a definitional truism. But you miss the point. Qm is normally
found from classical mechanics by following a seemingly irrational
recipe, quantisation. Newtonian mechanics is found from an empirical
law, namely conservation of momentum.
>
>*All* of theoretical physics consists of either magical formulas that
>just work for no apparent reason, or magical formulas that work as a
>consequence of other magical formulas working.
>
>There may be people who think that quantum mechanics, or Newton's laws,
>or *any* physical law, could be derived from first principles, without
>knowing the results ahead of time, but that is not so.
Can you rigorously justify this assertion, bearing in mind that "it has
not been done yet" is not the same as "it cannot be done".
>
Regards
--
Charles Francis
Marcel LeBel
I did this on purpose because that is the way it is. Either you see the
stars and the moon at the same moment (our perceptual reality) or you
analyze it and consider them away in time from you and from each other
( knowledge of the real universe). Since you logically can't have both,
you have to choose ... and this is why they are two separate
groups of information, different by what they are and how they were
acquired or produced.
MM
le...@muontailpig.com ------ remove particle
Nick Maclaren
Charles Francis <cha...@clef.demon.co.uk> writes:
|> In message <d7ksut$gka$1...@ra.nrl.navy.mil>, Ralph Hartley
|> <har...@aic.nrl.navy.mil> writes
|> >
|> >just work for no apparent reason, or magical formulas that work as a
|> >consequence of other magical formulas working.
|> >
|> >There may be people who think that quantum mechanics, or Newton's laws,
|> >or *any* physical law, could be derived from first principles, without
|> >knowing the results ahead of time, but that is not so.
|>
|> Can you rigorously justify this assertion, bearing in mind that "it has
|> not been done yet" is not the same as "it cannot be done".
I can.
All systems derived from first principles fall into the category
of pure mathematics. Whether they match the behaviour of the
'physical universe' (a concept somewhat alien to the purest of
mathematicians) or not is entirely coincidental, and regarded as
a little bit vulgar (i.e. as applied mathematics) by the extreme
purists.
For every system that can be invented that is compatible with the
physical universe, many others can be invented that are not. If
you are allowing only derivation from first principles, there is
no way to tell which of these systems (if any) will match the
purported physical universe - or, indeed, whether there is any
physical universe to match, let alone a unique one.
Regards,
Nick Maclaren.
Ralph Hartley
> <har...@aic.nrl.navy.mil> writes:
>>"F=ma" is a magical formula that just works for no apparent reason.
>
> Wrong example. It works because it is the definition of force.
That isn't the *original* definition of force. Force and mass where both
known for thousands of years during which F=ma was not known. Do you
think that they could have discovered Newtons laws if they had bothered
to look up the definitions? :-) Of course not, the definition was
different then.
If you have enough trust in the rule (we do) you can *re*define force so
that it is true by definition (we have). It is the definition of force
because it works, not the other way around.
> Newtonian mechanics is found from an empirical
> law, namely conservation of momentum.
Empirical law = something that just works for no apparent reason.
>>There may be people who think that quantum mechanics, or Newton's laws,
>>or *any* physical law, could be derived from first principles, without
>>knowing the results ahead of time, but that is not so.
>
> Can you rigorously justify this assertion, bearing in mind that "it has
> not been done yet" is not the same as "it cannot be done".
Because there is more than one logically consistent world. Not even a
finite number.
You need experiment to distinguish this world from all the other
consistent worlds.
One could, in hindsight, find a (relatively) small set of principles,
from which all the rest can be derived. One could then convince oneself
that that set consists of only "first" principles, but that wouldn't
make it so. There are many other sets of "first principles" that the
world could have been based on, but isn't.
Ralph Hartley
Charles Francis
<har...@aic.nrl.navy.mil> writes
>Charles Francis wrote:
>> <har...@aic.nrl.navy.mil> writes:
>>>"F=ma" is a magical formula that just works for no apparent reason.
>>
>> Wrong example. It works because it is the definition of force.
>
>That isn't the *original* definition of force. Force and mass where both
>known for thousands of years during which F=ma was not known. Do you
>think that they could have discovered Newtons laws if they had bothered
>to look up the definitions? :-) Of course not, the definition was
>different then.
>
>If you have enough trust in the rule (we do) you can *re*define force so
>that it is true by definition (we have). It is the definition of force
>because it works, not the other way around.
>
>> Newtonian mechanics is found from an empirical
>> law, namely conservation of momentum.
>
>Empirical law = something that just works for no apparent reason.
But at a deeper level there is a reason, that we can only study physical
law on the assumption that it is always and everywhere the same.
Conservation of momentum follows from that.
>
>>>There may be people who think that quantum mechanics, or Newton's laws,
>>>or *any* physical law, could be derived from first principles, without
>>>knowing the results ahead of time, but that is not so.
>>
>> Can you rigorously justify this assertion, bearing in mind that "it has
>> not been done yet" is not the same as "it cannot be done".
>
>Because there is more than one logically consistent world. Not even a
>finite number.
At the moment there is not even one. And I will not allow as distinct
arbitrary parameters with no observational consequences.
>
>
>One could, in hindsight, find a (relatively) small set of principles,
>from which all the rest can be derived. One could then convince oneself
>that that set consists of only "first" principles, but that wouldn't
>make it so. There are many other sets of "first principles" that the
>world could have been based on, but isn't.
>
First principles have to consist of measurement processes. We live in a
universe in which we can define a metre in such and such a way.
Regards
--
Charles Francis
Charles Francis
<nm...@cus.cam.ac.uk> writes
>In article <sdGZBTMJ...@clef.demon.co.uk>,
>Charles Francis <cha...@clef.demon.co.uk> writes:
>|> In message <d7ksut$gka$1...@ra.nrl.navy.mil>, Ralph Hartley
>|> <har...@aic.nrl.navy.mil> writes
>|> >
>|> >*All* of theoretical physics consists of either magical formulas that
>|> >just work for no apparent reason, or magical formulas that work as a
>|> >consequence of other magical formulas working.
>|> >
>|> >There may be people who think that quantum mechanics, or Newton's laws,
>|> >or *any* physical law, could be derived from first principles, without
>|> >knowing the results ahead of time, but that is not so.
>|>
>|> Can you rigorously justify this assertion, bearing in mind that "it has
>|> not been done yet" is not the same as "it cannot be done".
>
>I can.
>
>All systems derived from first principles fall into the category
>of pure mathematics. Whether they match the behaviour of the
>'physical universe' (a concept somewhat alien to the purest of
>mathematicians) or not is entirely coincidental, and regarded as
>a little bit vulgar (i.e. as applied mathematics) by the extreme
>purists.
>
>For every system that can be invented that is compatible with the
>physical universe, many others can be invented that are not.
At the moment we do not even have one system compatible with the
physical universe.
> If
>you are allowing only derivation from first principles, there is
>no way to tell which of these systems (if any) will match the
>purported physical universe - or, indeed, whether there is any
>physical universe to match, let alone a unique one.
>
Of course one must allow observation as well as pure mathematical
reason. And to establish first principles in science we must have
definitional procedures to define physical units. Einstein looked at the
definitional procedures for coordinates in space and time and showed
that they uniquely lead to the laws of relativity. So we do not have
complete freedom to choose axiomatic systems, but are constrained to
those which allow us to carry out procedures for measurement of time and
position. If we can also build into the system quantum measurement
procedures we start to become so constrained as to find the Dirac
equation, and actual physical properties of matter. If one eliminates
from consideration theories with no measurable properties, I see no
reason not to think that a model could be effectively unique.
Regards
--
Charles Francis
Nick Maclaren
In article <xGZMMOFn...@clef.demon.co.uk>,
Charles Francis <cha...@clef.demon.co.uk> writes:
|> >
|> >For every system that can be invented that is compatible with the
|> >physical universe, many others can be invented that are not.
|>
|> physical universe.
True. But we did :-) We still do have systems that are compatible
within their domain of validity.
|> Of course one must allow observation as well as pure mathematical
|> reason. And to establish first principles in science we must have
|> definitional procedures to define physical units. Einstein looked at the
|> definitional procedures for coordinates in space and time and showed
|> that they uniquely lead to the laws of relativity. ...
Only partially. Yes, the Lorentz transformations are the unique
solution to certain observations about motion and associated
assumptions, but that is also true of Newton's laws of motion.
There are always two problems with this:
If we can't match everything, then the choice of which
assumptions to regard as sacrosanct is arbitrary. Wttness the
argument between the Quantum Mechanicists and General relativists
over how long an electron takes to tunnel through a gap.
There will always be uncertainty beyond the point at which
we have real observations, because of models that are equivalent
(to measured accuracy) within that range but different thereafter.
Such as exp(t^2/2) versus 1/sqrt(1-t^2).
But I doubt that we disagree.
Regards,
Nick Maclaren.
Charles Francis
<nm...@cus.cam.ac.uk> writes
>
>In article <xGZMMOFn...@clef.demon.co.uk>,
>Charles Francis <cha...@clef.demon.co.uk> writes:
>|> >
>|> >For every system that can be invented that is compatible with the
>|> >physical universe, many others can be invented that are not.
>|>
>|> At the moment we do not even have one system compatible with the
>|> physical universe.
>
>True. But we did :-) We still do have systems that are compatible
>within their domain of validity.
>
>|> Of course one must allow observation as well as pure mathematical
>|> reason. And to establish first principles in science we must have
>|> definitional procedures to define physical units. Einstein looked at the
>|> definitional procedures for coordinates in space and time and showed
>|> that they uniquely lead to the laws of relativity. ...
>
>Only partially. Yes, the Lorentz transformations are the unique
>solution to certain observations about motion and associated
>assumptions, but that is also true of Newton's laws of motion.
>There are always two problems with this:
>
> If we can't match everything, then the choice of which
>assumptions to regard as sacrosanct is arbitrary.
Yes, but I am talking about definitions, not assumptions. Definitions
are arbitrary, but they are necessarily valid provided that they are
consistent, which in physics means consistent with observation as well
as logically consistent. Lorentz transformations are not merely the
solution to certain observations about motion. They are the logically
necessary result of the defining physical procedures which we use to
determine coordinate systems. The only observation which we need is to
state that we can physically carry out those procedures. When we cannot
carry out those procedures there is no definition of space-time. And
indeed there are situations in which we cannot carry out such
procedures; namely quantum mechanical situations, wherein measurement of
coordinates fundamentally changes the situation..
Regards
--
Charles Francis