| Topic: |
Science > Physics |
| User: |
"Jack Sarfatti" |
| Date: |
31 Aug 2005 03:02:29 PM |
| Object: |
More on the Illusion of a Classical World |
On Aug 31, 2005, at 12:44 PM, Jack Sarfatti wrote:
"In a general measurement process, we add energy -- e.g. accelerate the
beams, or cause them to impinge on metastable grains of silver salt, or
some other similar scheme. This allows us to enhance the rate of
dissipation - i.e. production of entropy - so that the trajectory of
each piece of the wave function in Hilbert space can satisfy Liouville's
theorem by spreading out in irrelevant variables, but contracting
strongly in certain relevant ones, which have been coupled to the
variables to be measured. The relevant variables, which are normally the
coordinates of some macroscopic, rigid object (a 'pointer'), become
trapped in a 'basin of attraction' which is different for the different
values of the original quantum number... the observer too becomes
entrapped ..."
Measurement in Quantum Theory and the Problem of Complex Systems
Macro-quantum theory with the stiff vacuum order parameter responsible
for gravity and inertia (even in the Newtonian weak curvature limit with
Galilean relativity)
B = (hG/c^3)^1/2d(Goldstone Phase of Vacuum ODLRO Coherence)
is required to describe the "relevant pointer variables." How does that
work?
The small linear vibrations about the stiff local non-unitary vacuum
c-number order parameter dynamical background do obey the approximate
linear unitary Schrodinger equation with nonlocal entanglements in phase
space for complex systems.
"(1) The initial Hamiltonian of our system has a large group G (e.g.
local homogenity and isotropy of a liquid)'
(2) The lowest-energy state, or mean field fixed point, has a lower
symmetry H (as a crystal, with discrete rotation and translational
symmetries.
(3) Hence there is an 'order parameter' describing the state, which has
'phase angles' free to move in a state isomorphic with the factor group G/H.
(4) Interactions enforce generalized rigidity of these phase angles:
there is a (free) energy ~ (Gradient of the order parameter)^2. This
allows dissipationless 'action at a distance' via rigidity,
supercurrents, etc.
(5) Hence all atoms are correlated, in highly non-quantum but very
familiar behavior - WE are broken symmetry objects with quasi-degeneracy
and rigidity ..." P.W. Anderson
AS ABOVE SO BELOW. PWA is here thinking of REAL QUANTA above the surface
of the post-inflationary Higgs Ocean (Vacuum ODLRO) of gravity and
inertia. But the same works BENEATH THE SURFACE of the coherent Higgs
Ocean inside the physical vacuum and this gives us the fabric of
space-time for the objects of the world including ourselves.
On Aug 31, 2005, at 11:45 AM, Jack Sarfatti wrote:
George Chapline Jr (long time protege of Ed Teller) and I have, quite
independently from somewhat different POVs, come to the same general
conclusion (key theme of my http://qedcorp.com/APS/cover.jpg ) on one
key issue. George wrote:
"The validity of the classical equations of motion for macroscopic
length scales is a consequence of having a vacuum state with a 'stiff'
order parameter."
"Transition from quantum to classical information in a superfluid"
Physics Lett A310 p252 (2003).
Chapline says the whole Zurek school of "decoherence" is wrong.
The "stiff order parameter" is what P.W. Anderson calls "generalized
phase rigidity".
Macroscopic space-time physics is local with small entropy only because
of this macro-quantum vacuum coherence. Hal Puthoff & Co do not have the
slightest concept of this in any of their published papers dealing with
metric engineering. I have now elegantly derived Einstein's 1915 theory
of general relativity in a single line, the Ansatz
B = (hG/c^3)^1/2d(Phase of Vacuum Coherence)
http://qedcorp.com/APS/zpf2005.pdf for details.
Therefore there is no "classical world" where h -> 0. If h -> 0 there is
no gravity or inertia. Similarly if c -> infinity, there is no gravity
or inertia even when G =/= 0. This is a very important insight. This
also solves the Schrodinger Cat Paradox.
On Aug 30, 2005, at 6:37 PM, Jack Sarfatti wrote:
Also the key new idea which only I and George Chapline, Jr have gotten
(quite independently and with key differences of detail) is that Gravity
and Inertia are EMERGENT from the COHERENT PHASE of the charge-neutral
VACUUM ODLRO field. Probably the same one that in the standard model
SU(2)hypercharge that gives the small inertia ~ Mev of the leptons and
the quarks via the Yukawa coupling before the quarks confine where their
kinetic energy gives most of the hadronic mass ~ Gev. That is the key to
metric engineering that neither Woodward not Puthoff & Co are yet even
able to conceive of. Once you realize, which they do not, that the
vacuum has a coherent phase that determines the shape of the space-time
fabric, then the next step is obvious, MODULATE THE PHASE (Josephson
effect). Woodward, Puthoff et-al simply ASSUME gravity equations. I
actually derive Einstein's GR from a deeper substratum i.e.
B = (hG/c^3)^1/2d(Vacuum ODLRO Phase)
for the non-trivial piece of the Einstein-Cartan tetrad field, that
Rovelli in "Quantum Gravity" calls the fundamental gravity field.
On Aug 30, 2005, at 5:40 PM, Jack Sarfatti wrote:
On Aug 30, 2005, at 4:31 PM, Jack Sarfatti wrote:
We agree on that.
On Aug 30, 2005, at 1:00 PM, George Chapline wrote:
Very good; the existence of ODLRO has nothing to do with the problem of
wave-function collapse, which can and usually occurs in systems without
ODLRO. On the other hand, I do believe that the existence of ODLRO in
the vacuum state explains why the ordinary macroscopic world looks
classical. In this respect everything Zurek has said is wrong.
george"
First of all the Forward gedankenexperiment (that he copied from Hermann
Bondi - I was at Bondi's Cornell Lectures on this BTW on top floor of
Newman Nuclear Labs when I was working for Hans Bethe & Tommy Gold) is
simply a primitive version of Alcubierre's warp drive i.e. it is a
timelike geodesic drive. Zero g-force ( G. Trimble's "G-Engine" & P.
Hill's "acceleration field") zero time-dilation globally
faster-than-light without ANY LOCAL MOVEMENT as in Jacques Vallee's
"Fastwalker" etc. See my book Super Cosmos for the details.
On Aug 30, 2005, at 12:17 AM, james f woodward wrote:
On Mon, 29 Aug 2005 08:16:13 -0700 Jack Sarfatti <sarfatti@pacbell.net>
writes:
As I've said all along, your bec fudge may turn out to be right. And
certainly there's no harm in trying to square GRT and the Standard
Model. But I don't think that that's the key to solving the transport
problems explicitly. It seems to me that finding something overlooked in
the area of inertia -- the real problem in this business -- is the best
way to
proceed. Hence, Mach's principle. And, ironically as it turns out, just
SRT. :-) And there's now even some experimental evidence. . . .
It's quite obvious in my theory how warp drive works - it's essentially
the negative matter propulsion in Robert Forward's paper. Negative
pressure positive zero point energy density = "negative matter", when
combines with positive pressure negative zero point energy density in
the right configuration (e.g. Alcubierre's metric) does it all. Inertia
plays no role at all. The mass cancels out of the geodesic. The whole
point is to control the timelike geodesic on which the craft free floats.
Well, as I see it, there are two problems with the physics of what you
say. First, you give absolutely no math from which simple
electrical/electronic circuits can be designed to implement the creation
with claimed EM induction fields of the exotic matter (negative mass)
needed to make a Forward type of device or generate an Alcubierre metric.
You are garbling theoretical physics with engineering applied physics.
Also you have sidestepped the key error in your general conception
shared, oddly enough, by Hal Puthoff.
First, one's theoretical ideas must be clear and consistent, though
never complete (Godel). No engineering implementation will work if the
theory is no good.
The key error you and Hal make, independent of any machine
implementation, is that you want to change the inertia for flight
purposes. Suppose you did it - best possible scenario, then you will
change the e/m ratios of the leptons and hadrons with disastrous
effects. BTW this is in my book Super Cosmos, though only Hal is
mentioned not you I recall?
http://qedcorp.com/APS/cover.jpg
Metric engineering is the control of the timelike geodesic of the
Unconventional Flying Machine. For you to ask me to provide a detailed
blueprint all on my own in less than 3 years of getting the main idea is
silly. It's like asking Einstein for a blueprint of a nuclear reactor in
1906.
I gave you the basic equation for one kind of design I have in mind (in
early stages)
/\zpf ~ (Length Scale)^-1(Surface Density of Anyon ODLRO)^1/2Cos(Phase
Difference)
e.g. Phase Difference = 2pi(Magnetic Flux/Magnetic Flux Quantum)
through a non-simply connected inductive nano-loop of anyon condensate
in the thin film "painted" on the fuselage. The core enclosed by the
nano-loop is normal material.
Guv + /\zpfguv = 0
is the basic equation for the (anti) gravity influence of the nano-loop
on its immediate space that it occupies. So this is the beginning of a
gendankenexperiment. It's not the only possibility.
Obviously, that's the most important problem. Everyone's known at least
since the mid-'90s about the Forward system and Alcubierre metric you
cite. Figuring out how to produce them with the technical means
available to us is the problem.
So you think you have solved it? Do you think anyone in Puthoff's group
has solved it? I say I am the closest of anyone so far - and, of course,
I could be wrong.
The second problem relates to your claim that inertia has nothing to do
with the issue. Yes, it is true that the total mass of a Forward type
device is zero. And it is also true that one mass attracts the other,
while the other mass repells the first -- leading to the system
accelerating off in a direction along their line of centers. And there
is no violation of energy or momentum conservation because the total mass
of the system is zero.
Yes, we agree on that.
However, consider the question: What is the rate of the acceleration of
the system as it motors off? I think that inertia still does play an
important roll in the process you claim to be the embodiment of
revolutionary transport. And since you're relying on the force of
gravitational attraction/repulsion between the two components of the
Forward type system, the accelerations involved are hardly going to be
head turning, even if you could build it. :-)
No, INERTIA PLAYS NO ROLE! Also you simply do not understand the
equations I wrote down. The zero point energy density bending of
space-time is INCREDIBLY STRONG! The problem is not how weak it is, but
how strong it is - and one must be careful not to make a WMD! I think
you are very confused here. You do not seem to understand the
equivalence principle and neither BTW does Hal Puthoff, Eric Davis or
anyone in his group. Of course, I know you can all mouth the words but
you have not really understood it intuitively and how it applies to the
problem. You keep thinking gravity force. You are thinking Newtonian.
There is NO GRAVITY FORCE in Einstein's General Relativity. You are not
thinking GEOMETRODYNAMICALLY!
Even in Newton's theory
mg = -GMm/r^2
m the mass of the craft cancels out of the problem!
The effective GM in my theory is
GM = c^2/\zpf4pir^2&r
where I approximate the saucer fuselage by a thin shell of radius r and
thickness &r tiled with tiny anyon nano-loop local oscillators threaded
by controllable magnetic flux.
The whole idea is to vary the Phase Difference around the spherical
shell in accord with the Alcubierre "exotic matter" distribution. Note
that Phase between -pi/2 and pi/2 gives repulsive dark energy and Phase
outside that interval gives attractive dark matter.
.
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| User: "" |
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| Title: Re: More on the Illusion of a Classical World |
31 Aug 2005 05:34:14 PM |
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First, one's theoretical ideas must be clear and consistent, though
never complete (Godel).
************
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts. Sorry. Other than that,
all your ideas are correct.
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| User: "Tom Roberts" |
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| Title: Re: More on the Illusion of a Classical World |
31 Aug 2005 05:54:35 PM |
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wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Thoughts clearly satisfy that, and Goedel's theorem applies. That is,
there are true but unprovable thoughts, just as there are true but
unprovable statements in mathematical logic.
Simple example:
This statement is not provable in system S.
is indeed true but unprovable in system S, for any S that is a system of
deductive reasoning sufficiently complex to express this statement.
Quite clearly S can be the set of valid English statements and deductive
reasoning (which for me is the set of all my thoughts that are subject
to any sort of proof).
As Douglas Hofstadter has shown so delightfully, there is an
infinite regress of such statements -- see his book
_Goedel,_Escher,_Bach_.
Tom Roberts tjroberts@lucent.com
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| User: "Bilge" |
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| Title: Re: More on the Illusion of a Classical World |
02 Sep 2005 04:11:55 AM |
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Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
A proof was given by tarski, but I don't have the reference handy.
I'm guessing that extends to geometry in general, since from what I
recall, euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
.
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| User: "Schoenfeld" |
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| Title: Re: More on the Illusion of a Classical World |
02 Sep 2005 06:34:14 AM |
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Bilge wrote:
Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
That's false. Euclid's parallel postulate is undecidable.
[...]
euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
Not so. Geometry has a very strong and fundamental algebraic structure.
Take for example the geometry of R^2 describable entirely by the
algebraic closure of the reals. Similarly, n-dimensional real vector
spaces can be described by graded algebras having the usual inner
product but also with defined grassman outer product. Clifford Alegbras
with real scalars are good examples of this. These are not pathalogical
structures, but rather extremely useful both practically and
theoretically.
.
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| User: "Bob Cain" |
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| Title: Re: More on the Illusion of a Classical World |
05 Sep 2005 02:17:48 AM |
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Schoenfeld wrote:
Bilge wrote:
Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
That's false. Euclid's parallel postulate is undecidable.
You don't decide posulates, silly. They're what's given.
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
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| User: "Schoenfeld" |
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| Title: Re: More on the Illusion of a Classical World |
05 Sep 2005 06:22:10 AM |
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Bob Cain wrote:
Schoenfeld wrote:
Bilge wrote:
Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
That's false. Euclid's parallel postulate is undecidable.
You don't decide posulates, silly. They're what's given.
You misread, inferred things all wrong, and then misspoke. Euclid's
"absolute geometry" used only the first four postulates for the first
28 propositions of the Elements. He was forced to invoke the parallel
postulate on the 29th, but he and most most mathematicians after him
believed said postulate was a mere theorem. It's undecidability was
eventually proven.
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
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| User: "" |
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| Title: Re: More on the Illusion of a Classical World |
07 Sep 2005 12:44:11 PM |
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Schoenfeld wrote:
Bilge wrote:
Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
That's false. Euclid's parallel postulate is undecidable.
No it's not undecidable in the Godel sense, it's just *independent*.
Godel's work implies that a TRUE statement inside the system cannot be
proven, but the parallel postulate is not true or false within the
given system. That's how it was explained to me at least.
[...]
euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
Not so. Geometry has a very strong and fundamental algebraic structure.
Take for example the geometry of R^2 describable entirely by the
algebraic closure of the reals. Similarly, n-dimensional real vector
spaces can be described by graded algebras having the usual inner
product but also with defined grassman outer product. Clifford Alegbras
with real scalars are good examples of this. These are not pathalogical
structures, but rather extremely useful both practically and
theoretically.
Can you define a 'successor' in algebras you've described? Being
algebraically robust doesn't imply some sort of omnialgebraic structure
and may be missing some key component which prevents Godel's arguments
from holding. It's not that it lacks all algebraic structure, just the
important one needed for Godel to work in paticular.
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| User: "Schoenfeld" |
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| Title: Re: More on the Illusion of a Classical World |
08 Sep 2005 08:58:02 AM |
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wrote:
Schoenfeld wrote:
Bilge wrote:
Tom Roberts:
donstockbauer@hotmail.com wrote:
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
That's false. Euclid's parallel postulate is undecidable.
No it's not undecidable in the Godel sense, it's just *independent*.
Godel's work implies that a TRUE statement inside the system cannot be
proven, but the parallel postulate is not true or false within the
given system. That's how it was explained to me at least.
Euclids 5'th parallel postulate is undecidable from the previous 4.
This is a well-known fact.
SIDE NOTE:It is interesting to compare this with today's continuum
hypothesis, which is also undecidable.
[...]
euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
Not so. Geometry has a very strong and fundamental algebraic structure.
Take for example the geometry of R^2 describable entirely by the
algebraic closure of the reals. Similarly, n-dimensional real vector
spaces can be described by graded algebras having the usual inner
product but also with defined grassman outer product. Clifford Alegbras
with real scalars are good examples of this. These are not pathalogical
structures, but rather extremely useful both practically and
theoretically.
Can you define a 'successor' in algebras you've described?
Yes, in various ways. One could for example consider linearly DEPENDENT
orthonormal basis vectors from infinite dimensional Hilbert space.
Being
algebraically robust doesn't imply some sort of omnialgebraic structure
and may be missing some key component which prevents Godel's arguments
from holding. It's not that it lacks all algebraic structure, just the
important one needed for Godel to work in paticular.
Consistent axiomatic formulations for integers, reals are known.
Godel's first theorem doesn't apply to them. One of course can
formulate a consistent geometry categorically dual to Euclidean
geometry, but that is not EUCLIDEAN geometry. More likely than not,
said geometry would be a pathological structure.
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| User: "Bob Cain" |
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| Title: Re: More on the Illusion of a Classical World |
09 Sep 2005 01:53:04 AM |
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Schoenfeld wrote:
Euclids 5'th parallel postulate is undecidable from the previous 4.
This is a well-known fact.
As is the fourth from the previous three. So what?
Bob
--
"Things should be described as simply as possible, but no
simpler."
A. Einstein
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| User: "" |
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| Title: Re: More on the Illusion of a Classical World |
12 Sep 2005 03:55:14 PM |
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wrote:
That's false. Euclid's parallel postulate is undecidable.
No it's not undecidable in the Godel sense,
There is no such thing as a "Goedel sense", you made up that term. A
theorem is undecideable within a theory if it can neither be proven
true or false from the theory.
Euclid's 5th postulate is undecideable from the theory containing only
the other 4 postulates.
The only thing Goedel did was show that arithmetic is not finitely
axiomatizable as a 1st order theory -- which is a completely separate
issue from the question of what undecideability is; and has nothing to
do with anything being discussed here.
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| User: "Shmuel Seymour J. Metz" |
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| Title: Re: More on the Illusion of a Classical World |
06 Sep 2005 07:08:48 AM |
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In <slrndhg8v2.94h.>, on
09/02/2005
at 09:11 AM, (Bilge) said:
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
A proof was given by tarski, but I don't have the reference handy.
I'm guessing that extends to geometry in general, since from what I
recall, euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
Yes you can. Pick two distinct arbitrary points and label them as 0
and 1. They define a line, and they define a model of N whose
successor function is extending by the length between the two points.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to
.
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| User: "Herman Rubin" |
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| Title: Re: More on the Illusion of a Classical World |
07 Sep 2005 10:39:59 AM |
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In article <431d94e1$17$fuzhry+tra$mr2ice@news.patriot.net>,
Shmuel (Seymour J.) Metz <spamtrap@library.lspace.org.invalid> wrote:
In <slrndhg8v2.94h. >, on
09/02/2005
at 09:11 AM, (Bilge) said:
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
A proof was given by tarski, but I don't have the reference handy.
I'm guessing that extends to geometry in general, since from what I
recall, euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
Yes you can. Pick two distinct arbitrary points and label them as 0
and 1. They define a line, and they define a model of N whose
successor function is extending by the length between the two points.
In Tarski's approach, one has the real numbers already,
so it is not even necessary to do such as defining points
and lines. So one can start with TRYING to define integers
by
0 is an integer
if x is an integer, x+1 is the successor of x
and is an integer
but there is no ARITHMETIC method to define the set of
all integers.
If one could identify the integers, and apply induction,
Godel's theorem would apply.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558
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| User: "Zeb Glittering" |
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| Title: Re: More on the Illusion of a Classical World |
02 Sep 2005 07:39:47 AM |
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In article <slrndhg8v2.94h.dubious@radioactivex.lebesque-al.net>,
dubious@radioactivex.lebesque-al.net says...
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
A proof was given by tarski, but I don't have the reference handy.
I'm guessing that extends to geometry in general, since from what I
recall, euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
I didn't know that. I am excited to learn this. Presumably geometry escapes
Godel because is does not include the 'Axiom of Infinity'. I strongly suspect
that infinity is an imaginary concept, that is to say that infinity cannot be
observed in the Universe. (This is not the same as saying it isn't useful.)
Has Godel's theory been proven to rest upon the inclusion of the 'Axiom of
Infinity' ?
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| User: "Shmuel Seymour J. Metz" |
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| Title: Re: More on the Illusion of a Classical World |
06 Sep 2005 07:10:11 AM |
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In <df9h6j$d1p$1@news7.svr.pol.co.uk>, on 09/02/2005
at 12:39 PM, (Zeb Glittering) said:
I didn't know that. I am excited to learn this. Presumably geometry
escapes Godel because is does not include the 'Axiom of Infinity'.
Euclidean Geometry includes an equivalent. There are finite
geometries, which, of course, don't.
--
Shmuel (Seymour J.) Metz, SysProg and JOAT <http://patriot.net/~shmuel>
Unsolicited bulk E-mail subject to legal action. I reserve the
right to publicly post or ridicule any abusive E-mail. Reply to
domain Patriot dot net user shmuel+news to contact me. Do not
reply to
.
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| User: "bernardz" |
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| Title: Re: More on the Illusion of a Classical World |
04 Sep 2005 08:29:50 PM |
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Zeb Glittering wrote:
In article <slrndhg8v2.94h.dubious@radioactivex.lebesque-al.net>,
dubious@radioactivex.lebesque-al.net says...
Surprisingly, godel's theorem doesn't apply to euclidean geometry.
A proof was given by tarski, but I don't have the reference handy.
I'm guessing that extends to geometry in general, since from what I
recall, euclidean geometry escapes because it lacks the arithmetic
structure, i.e., you can't define things like the successor of a
number within the system.
I didn't know that. I am excited to learn this. Presumably geometry escap=
es
Godel because is does not include the 'Axiom of Infinity'. I strongly sus=
pect
that infinity is an imaginary concept, that is to say that infinity canno=
t be
observed in the Universe. (This is not the same as saying it isn't useful=
..)
Has Godel's theory been proven to rest upon the inclusion of the 'Axiom of
Infinity' ?
Try the following for a fairly good discussion on the issues.
en.wikipedia.org/wiki/G=F6del's_incompleteness_theorem
Ultimately if we ever do find the *ultimate equations* to escape the
GIT, physics may have to be rewritten into geometry.
It is a issue that excited me as well for quite awhile too.
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| User: "BernardZ" |
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| Title: Re: More on the Illusion of a Classical World |
01 Sep 2005 06:20:35 AM |
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In article <LyqRe.3386$v83.2452@newssvr33.news.prodigy.com>,
tjroberts@lucent.com says...
Godel's Theorem applies only to the system of mathematics as defined in
the Principia Mathematica, not to thoughts.
Actually, I'm pretty sure it applies to _any_ system of deductive
reasoning that is at least "as large" as the usual mathematical logic.
Actually there are several mathematical systems where Godel's theorem do
not apply eg Presburger arithmetic and the theory of the real field as
we are not counting numbers. Maybe physics may one day have to be
rewritten into these types of mathematical systems.
--
Ask yourself, what would God think of your ideals, religion and beliefs?
Observations of Bernard - No 83
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