| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
14 May 2005 05:34:38 PM |
| Object: |
Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
From Osher Doctorow
COPYRIGHT NOTICE
Randall-Sundrum, Einstein-Gauss-Bonnet, and PI
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005
Randall-Sundrum theory (Lisa Randall of MIT and Raman Sundrum of Johns
Hopkins) is either Kaluza-Klein or Superstring theory without
compactification of the extra dimensions, while Einstein-Gauss-Bonnet
theory basically incorporates and keeps track of an
Einstein-Gauss-Bonnet or Gauss-Bonnet term in the equations which
generalizes the original total Gaussian curvature of differential
geometry which becomes more negative as the number of holes increases
and analogously with the number of oriented caps except that a plane
has Gaussian curvature 0 and a sphere has Gaussian curvature +1.
At present, Randall-Sundrum theory seems to be accepted by most
physicists and mathematicians who accept Kaluza-Klein and/or
Superstring/Brane theories, while Einstein-Gauss-Bonnet theory was
originally technically part of the Kaluza-Klein theory but the term is
now used by that name for a curvature-related term in other theories
including Randall-Sundrum. Lisa Randall herself has called her theory
alternatively "warped geomery in extra dimensions," ScienceWatch
July-August 2001 "MIT's Lisa Randall: two branes are better than one,"
www.sciencewatch.com.
I'll try to continue this shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
14 May 2005 05:41:10 PM |
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From Osher Doctorow
Take a look at hep-th/0202009, hep-th/0010093 in arXiv, Borcherds
seminar notes uncut by Scott Carnahan under the name Borcherds seminar
(2004 at Berkeley), BRST formalism in Wikipedia, and also "Fadeev-Popov
ghost" and "First class constraint" there, and I'll try to continue
shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
14 May 2005 08:05:50 PM |
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From Osher Doctorow
I should mention that Randall-Sundrum theory also adds branes in the
modern sense to Kaluza-Klein theory.
Probable Influence (PI) would have led to both Randall-Sundrum and
Kaluza-Klein and also to Brane Theories much more quickly than they
actually either developed or took hold (the latter case for
Kaluza-Klein mostly) because PI embodies something which should really
be regarded as an Axiom:
Axiom of PI. Low Probability Events/Processes include those with
highest Probable Causation/Probable Influence.
So what do we make of Einstein's Principle of Verification - roughly
speaking, that what you see is what you get? In my own opinion, the
Axiom of PI should be roughly time-indexed for human beings: in a
person's lifetime of about 70 years average or slightly more, there are
roughly one or two low probability events/processes of extremely high
probable causation/probable influence at any time which have not been
observed and which should be searched for by intensive research
programs - excluding merely finding particles to conform with previous
predictions.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 01:00:51 AM |
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From Osher Doctorow
Actually, the Principle of Verification seems to have a longer history
than Einstein, although he was one of the first to use it in physics.
See under those keywords (Principle of Verification) on the internet
and also under keywords Logical Positivism.
I'm going to turn next to rather deep relationships of PI and
probability in general to Randall-Sundrum and the Einstein-Gauss-Bonnet
term and Kaluza-Klein. See "An alternative to compactification" by
Lisa Randall and Raman Sundrum, Phys. Rev. Lett. 84 (1999) 4690 and
arXiv:hep-th/9906064 v1 8 Jun 1999 to which I'll refer.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 01:46:55 AM |
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From Osher Doctorow
Some authors trace the Principle of Verification to David Hume, who in
his Enquiry Concerning Human Understanding asserted roughly that
divinity and school metaphysics books contain neither abstract logical
reasoning about quantity or number nor experimental reasoning
concerning existence and matters of fact and so should be burned
because they contain nothing but sophistry and illusion.
Hume was quite smart, but he didn't have the opportunity to read later
books such as Orwell's Animal Farm and 1984 where dictatorships
literally burned books that didn't appeal to their political and
sociocultural or other orientations, which probably would have made him
much more cautious. In fact, Hitler and Stalin and Mao and most other
genocidal leaders were quite definite about not allowing books or
pamphlets or discussion on any type of politics or economics or even
socioculture different from the leaders' views, so that while Hume had
some usefulness in urging people not to proliferate axioms "randomly"
just because they liked them, there seems to be an equal danger at
least in preventing people from exploring new axioms in whatever
direction (random or not) that interests them.
Einstein's particular orientation toward the Principle of Verification
was largely associated with the ideas of the Vienna Circle which
included A. J. Ayer, Tarski, von Neumann, Quine, Godel. Tarski to some
extent and Godel to a considerable extent would eventually go beyond
the restrictions of the principle and even turn philosophy upside down
not to mention mathematics and other subjects.
Einstein was a Creative Genius in physics, as was Erwin Schrodinger
from Vienna, but neither was exceptional in philosophy and both were
rather Ingenious Imitators in probability-statistics. This is almost
totally incomprehensible to modern Mainstream physics elitists who are
Ingenious Imitators themselves, and who use a rather interesting
version of the Principle of Verification that goes something like this:
Physics theory goes upward in a rising spiral and there is only one
accurate theory at any time which is a generalization of previous
theories and all other theories will and do and have collapsed via
"survival of the fittest theory". Orwell and Ray Bradbury would
undoubtedly have something sarcastic to say about this, but we already
find traces of this view in Werner Heisenberg and the
teacher-turned-politician Himmler and Nietzche and Marx and Lenin and
Mao and Stalin and Hitler.
It is admittedly a difficult field of inquiry to examine oneself.
Psychoanalysts have been some of the very few who have done it for a
long time, and they're not good at communicating with other Academic
disciplines (though they haven't gotten good receptions from the
pervasive Mainstream Bureaucracies in Academia). Some psychoanalysts
are also wrong period. I like Melanie Klein and the Kleinian school of
psychoanalysis especially, and Freud had a lot of great insights
although he made some great errors.
I'll close this particular posting by reminding people that Einstein
was a Creative Genius in physics and in relating physics to geometry
(although he had help in that from his friend Professor Marcel
Grossman, a geometer), but was a total dud in philosophy and
probability-statistics. So is Pavel Hajek a Creative Genius in fuzzy
multivalued logics (see his Metamathematics of Fuzzy Logics, Kluwer:
Dordrecht 1998, which I ceaselessly recommend except for his mediocre
probability chapter). He is in the Czech Republic computer science
bureaucracy. His 1998 volume reveals a "total dud" in probability.
But nobody said that Creative Geniuses know everything. Do you think
that Beethoven was a great physicist or that Mozart was a great
astronomer? I think that it takes an Ingenious Imitator or Mediocre
person to believe that Creative Geniuses are universal in all
disciplines and are know-it-alls in all disciplines or even most
disciplines. Perhaps the Dalai Lama had the last word when he
remarked in slightly different language that certain Mediocre people
and Ingenious Imitators are especially bad at history. That's the
bottom line: they can neither analyze themselves nor others (the latter
especially via history and its interpretations). They are destined to
repeat past mistakes, learn few lessons from the past. But then, the
Dalai Lama would himself be ousted by the Principle of Verification!
What goes around, comes around.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 08:05:21 AM |
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From Osher Doctorow
Randall-Sundrum theory comes in two forms, one with two "parallel"
branes separated by a non-compact 5th dimensional space that may
contain also the other dimensions of Superstring theory, the other with
one brane embedded in a higher dimensional but non-compact space. We
live on one brane, and gravity mostly lives on a second brane if that
brane exists or else in the spacetime outside our brane. Gravity is
weak on our brane and strong elsewhere.
PI does have something important to say about this. If
Randall-Sundrum theory maintains that the intermediate spacetime
between the two branes is the "whole super-universe" of all dimensions,
then this is impossible since the whole universe does not have
probability zero. In fact, the probable influence of the whole
universe A on any event B is:
1) P(A-->B) = 1 + P(AB) - P(A) = 1 + P(B) - 1 = P(B)
since the probability of the whole universe A is 1 on a scale of 0 to
1. On the contrary, any subset C of any event B, and any set C of
probability 0 has probable influence 1 on B, because:
2) P(C-->B) = 1 + P(BC) - P(C) = 1 + P(C) - P(C) = 1
However, there is an aspect of two branes that can save Randall-Sundrum
theory, namely if the two branes are actually two dimensions and the
separating spacetime does not contain those dimensions. In that case,
the separating spacetime lacks the full dimensions of the universe and
therefore has both Lebesgue measure and probability 0.
Can a brane be a dimension in the spacetime sense? Yes, although to
be a brane in the technical definition of physics it should have
various tension properties where appropriate (for example in matter
other than 0-branes or point particles, although it might have
something analogous to tension even there).
I'll try to continue this soon.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 08:22:07 AM |
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From Osher Doctorow
It is possible, of course, that although the two branes are whole
dimensions, they are finite in extent. The "interdimensional"
spacetime would then surround those branes/dimensions and yet not
partake in their dimensionality, a curious scenario indeed.
Is there something wrong about "impossible" events and the null set
(both of which have probability 0) having probable influence 1 on any
event? Not for people familiar with logic, where false propositions
imply any other proposition. Intuitively, if an event is either
impossible or null, then it "differs maximally" from any non-impossible
non-null event, which can be regarded as a form of probable influence.
The idea can then be generalized to the relationships between two
impossible and/or null events.
In the one-brane Randall-Sundrum theory, there has to be a similar
restriction on the dimensionality of the off-brane spacetime and the
brane has to be a dimension.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 08:56:29 AM |
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From Osher Doctorow
I mentioned earlier that some researchers in these fields consider that
geometry follows the uniform distribution and matter follows in some
sense an "opposite" distribution. Is this true?
I don't think that geometry really assigns equal probability or
probability density to all points. Until recently, nobody thought that
it assigns probabilities at all to anything. It has turned out in PI
(Probable Influence) Theory that Probable Influence has both geometric
and matter/energy relationships and that any continuous distribution
can be assigned to any geometric object provided that continuous random
variables are found on a volume of space(time) containing the geometric
object in question. For one or two or zero dimensional spacetimes,
"volume" is to be understood as referring to length or area or whatever
respectively.
A more interesting question is whether probability could actually be
identical with mass except for scales (which could be remedied by
normalization and a dimensional constant). I think that probability
doesn't equal mass precisely because, among other things, the probable
influence or probable causation is a probability but not a mass.
However, it is conceivable that certain "elementary events" are such
that probability equals mass for them. If we have an event A which is
not of form "C influences B" for some sets C, B different from A, and
if A is not null or impossible, then conceivably there is some universe
in which the mass of A equals the probability of A, and similarly for
all such events A. Whether that universe is ours is somewhat doubtful
intuitively but perhaps not impossible. In quantum theory, we have
probabilities of wave-particles or particle-fields or string-fields
being found in particular volumes of space(time) via the Schrodinger
equation, but those probabilities are not taken as equal to masses of
objects (it would be interesting to see what happens if they were). In
classical physics outside thermodynamics and statistical mechanics and
PI and a few other models, probabilities tend to be either ignored or
hypothetically taken as 1 for laws of nature and 0 for impossible
events/processes.
Most of the above is for continuous events/processes/random variables.
For their discrete cousins, the situation is even more "disorganized",
which perhaps consoles only those who thrive on thinking about the
"heat death" of the universe.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 12:40:38 PM |
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From Osher Doctorow
Is there a loophole from the above results via Fairly Frequent or Very
Frequent Event probabilities (respectively conditional probability and
independent probability)? No.
It is easy to prove that:
Theorem. P(A-->B) > = P(B|A) > = P(B)
where the first inequality always holds for P(A) not 0 and the second
inequality holds for all positively statistically quadrant dependent
events (roughly speaking events that increase together
probabilistically).
Proof. P(A-->B) > = P(B|A) iff 1 + P(AB) - P(A) > = P(AB)/P(A) for
P(A) not 0, iff 1 + P(AB)[1 - 1/P(A)] > = P(A) iff 1 - P(A) > =
P(AB)[1/P(A) - 1] =[ P(AB)/P(A)][1 - P(A)] iff P(AB)/P(A) < = 1 and the
latter holds from monotonicity of probability since AB is a subset of A
so that P(AB) < = P(A). The second inequality says P(AB)/P(A) > = P(B)
which holds iff P(AB) > = P(A)P(B) which is the definition of
positively statistically quadrant dependent events for P(A) not 0.
Q.E.D.
Hence P(B|A) very high implies that P(A-->B) is very high and similarly
P(B) very high implies that P(A-->B) is very high, and in particularly
P(B|A) or P(B) = 1 implies that P(A-->B) = 1, so for considering very
high relationship events in the sense of conditional or independence
probabilities it is enough to consider P(A-->B) very large or equal to
1 events.
But do P(B|A) very close to 1 and/or P(B) very close to 1 indicate any
similar situation physically to P(A-->B) close to 1? Yes, because they
are all probability analogs of fuzzy multivalued logical (FML)
implications, respectively Product/Goguen, Godel, and
Lukaciewicz/Rational Pavelka, and any two of these generate the
generalized Boolean algebra in FML. So even though P(B|A) is only
called the "probability of B given A" in conditional
probability-statistics including Bayesian probability statistically, it
is conceptually the same type of relationship as "probable influence"
or "probable correlation" P(A-->B) where the latter is especially
applicable to Rare Events.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 03:46:15 PM |
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From Osher Doctorow
If mass equals probability for example in the Schrodinger equation,
then since mass occurs in all terms of the Schrodinger equation except
the "Laplacian" (space partial derivative) term, the Schrodinger
equation becomes literally a probability equation rather than a
deterministic equation. In modern terminology, this is called a
stochastic (i.e., probability) equation.
It still leaves the question of why we have:
1) ww* = P
where w is the wave function and P is probability of finding the
particle-wave in a volume of space via the Born probability
interpretation. If P = m, then we get:
2) ww* = m
The wave function w is then something like a complex "square root" of
mass although technically square root is the wrong name since complex
numbers have square roots different from the type indicated here. In
any case, the wave-particle duality is resolved since the wave function
as well as the particle/string are now of the nature of mass. The
particle-field duality of Quantum Field Theory (QFT) is explained in
what Cao (1997) calls its "substantial" aspect (with regard to field)
since the field has the nature of mass. The nature of string theory
is explained since not only does a vibrating string generate a mass but
the wave thereby generated has the nature of a mass and so does the
little string. The equation E = hv for v frequency is also now
interpreted as obtaining its frequency v from the vibrating mass "in"
E. E = mc^2 = hv now links mass to frequency and thereby to strings in
an unexpected way.
Yet puzzles remain even in the Schrodinger equation which now contains
spatially differentiated masses, temporally differentiated mass,
non-differentiated mass, or to be more precise a combination of
non-differentiated mass and differentiated wave-function-mass and
wave-conjugate-function-mass.
I am not claiming that PI requires the wave function to be a "complex
mass" in this posting, but merely pursuing what would happen in that
scenario. The possibility, recall, arose in an earlier posting here.
The Einstein Field Equation becomes even more curious if some analog of
the mass interpretation carries over. It says roughly but fairly
closely that matter generates curvature of space and vice versa. But
in the string interpretation curvature could be considered proportional
to tension so that the Einstein Field Equation says roughly but rather
closely:
3) Energy = Mass = Curvature of Space = String/Brane Tension
So why does mass get bigger as the speed of light is approached in
Special Relativity (SR)? It vibrates more roughly speaking from (3).
This suggests that despite remarkable accuracy, the factor sqrt(1 -
v^2/c^2) is an approximation and that vibration "breaks down" very
close to light speed, that is to say that the SR is a model which
breaks down at light speed.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 04:19:51 PM |
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From Osher Doctorow
Now let's look at a misuse of probability in Randall and Sundrum
(1999), hep-th/9906064, a major paper of theirs referenced earlier.
Their paper is largely concerned to establish things like the
improbabiity of low-energy brane processes leading to strong
gravitational interactions at large coordinate z. While this leading
"can" happen, it "almost never" does. Consulting the massless
graviton's wave function, for example, they obtain this probability as
10^(-18).
This is a misinterpretation of probability and even of statistics. The
lower the probability, the greater the probable influence for Rare
Events. Obviously, 10^(-18) as a probability (if accurate) would
identify a Rare Event. It does not identify a statistical test of a
hypthesis since no hypothesis was stated and none seems plausible. In
statistics, research hypotheses are "accepted" if null hypotheses
("opposites" of research hypotheses in a sense) are rejected at for
example .05 or .01 levels of significance, meaning that the probability
of obtaining a result as extreme or more extreme than the one obtained
is less than .05 or.01. It is true that so-called p-value statistics
is often used nowadays in the behavioral sciences and social sciences,
in which the actual obtained probability corresponding to the sample is
simply stated and still should be less than .05 though without
committing oneself as to whether .05 is small enough in a sense. But
the whole thing has no meaning without a research and null hypothesis.
The research and null hypotheses are what "generate" a probability
distribution or curve (pdf, cdf - probability density and cumulative
probability distribution functions, or for discrete random variables
probability mass and cumulative probability distribution functions).
And all one does is reject a hypothesis subject to a particular
probability distribution holding - in other words, you reject not only
a population mean (expectation) or variance or correlation or other
value which is the non-desired value or range of values, but your
results also only "confirm" the alternative hypothesis in the class of
probability distributions of the type proposed (the normal/Gaussian,
Student's t, F distribution, and chi-square distribution being the most
common ones proposed, but certainly not the only possible ones!).
Can we salvage Randall-Sundrum? I think so. The argument for
Mainstream probability-statistics tests would be something like this:
state the null hypothesis (a certain range of values of a random
variable which the researcher "doesn't want to hold") and some rather
common probability distribution (the normal/Gaussian is quite common,
though it has several disadvantages which never make anything as "sure"
as one would think). Then obtaining a probability of 10^(-18) would
reject the null hypothesis and yield the research ("alternative")
hypothesis at a p-value of 10^(-18), but only provided that
normal/Gaussian distributions really hold for the problem. Nobody can
ever really disprove the latter absolutely or prove it absolutely.
There are "goodness of fit" tests, but again they involve tiny p-values
that are often even harder to establish, and again there are
probability distribution assumptions. In fact, in a goodness-of-fit
test, you literally reject only one parameter (mean, variance, etc.) of
one specific member of a family of probability distributions period, at
some p-value. That leaves a theoretically infinite number of members
of the normal/Gaussian family (in fact, an uncountable number) that
could still hold!
Readers can see why I maintain that "the one true theory" doesn't
really apply at any time, although there are several additional
reasons. Probability has a sobering effect on megalomania. It brings
us back to the multiplicity and alternative nature of Reality.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 04:45:15 PM |
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From Osher Doctorow
Hooke's Law of Sir Robert Hooke (1678) who preceded Sir Isaac Newton at
least in published research says:
1) F = kx
with k the force constant or stiffness coefficient of a spring. This
is generalized in physics with regard to elasticity (stress, strain).
So we have:
2) F = ma = kx
classically, and therefore:
3) m = kx/a
The potential energy (elastic potential energy) of the stretched spring
P.E. is classically:
4) P.E. = (1/2)kx^2
and since kx = ma from (3), (4) can be rewritten:
5) P.E. = (1/2)Fx
which since x is the extension above the normal no-load length has the
form:
6) E = wLF
with L (length) = x and w = 1/2 and E entirely potential.
Could anybody interpret w = 1/2? Hint: the uniform probability
distribution on [0, 1] or (0, 1) has probability density function (pdf)
fX(x) = 1, cumulative distribution function FX(x) = x, population mean
(expectation or expected value) 1/2.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 05:07:32 PM |
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From Osher Doctorow
The one-dimensional wave equation of a vibrating string is:
1) Dtt(u) = c^2Dxx(u)
where Dtt is the second partial derivative of u(x, t) with respect to
time t and Dxx is the second partial derivative of u(x, t) with respect
to position x, where the string is horizontally (along x) stretched but
can be in arbitrary position vertically (y) to begin with and y = u(x,
t) gives its vertical displacement u as a function of coordinates x and
y.
For a two-dimensional wave equation of a vibrating membrane:
2) Dtt(u) = c^2 (Dxx(u) + Dyy(u))
where c^2 is the tension divided by the density.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 07:33:27 PM |
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From Osher Doctorow
Notice that nonparametric tests in statistics don't dispense with the
problem of either null vs research (alternative) hypotheses or using
probability distributions - although probability distributions are used
in a way that is more applicable to Randall-Sundrum theory, namely
instead of assuming a particular probability distribution one evaluates
results by a known form of the statistics (measurement and/or
aggregated/transformed measurement types) obtained. Once again, null
vs research hypotheses are of critical importance. Also, the
measurements have to be of particular known types and certain side
conditions must be known usually such as sample size, etc. For
example, measurements could be in or transformed to ranked order, sums,
sample medians, etc.
Osher Doctorow
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| User: "Lady Chatterly" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 09:15:27 PM |
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In article <1116203607.861457.245500@g49g2000cwa.googlegroups.com>
OsherD <mdoctorow@comcast.net> wrote:
Notice that nonparametric tests in statistics don't dispense with the
problem of either null vs research (alternative) hypotheses or using
probability distributions - although probability distributions are used
in a way that is more applicable to Randall-Sundrum theory, namely
instead of assuming a particular probability distribution one evaluates
results by a known form of the statistics (measurement and/or
aggregated/transformed measurement types) obtained. Once again, null
vs research hypotheses are of critical importance. Also, the
measurements have to be of particular known types and certain side
conditions must be known usually such as sample size, etc. For
example, measurements could be in or transformed to ranked order, sums,
sample medians, etc.
These are peano 's axioms for number theory.
Osher Doctorow
Oh puh-leeze. Grow up.
--
Lady Chatterly
"Attn: Lady Chatterly. Please repeat your answer to my question. My
server dropped in less than an hour. Thank you." -- Fourdogs
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 08:38:33 PM |
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From Osher Doctorow
Immaterial, irrelevant, and indecisive. Now I know what the "y" in
your first and last names stand for.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
15 May 2005 09:05:40 PM |
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From Osher Doctorow
I should remark at this point that it would be nice if MIT (where Lisa
Randall is Professor) and Johns Hopkins U (Maryland, where Sundrum is
Professor) or even Lisa's former associates at U.C. Berkeley or
Princeton U. had learned probability-statistics just because Einstein,
Schrodinger, Bohr, and Heisenberg didn't, but apparently the errors of
history are destined to repeat themselves when physicists are afraid to
learn history of science, philosophy of science, and mathematics beyond
the first few courses (other than the current fads of math subjects).
Fortunately, Randall and Sundrum seem to have very good physics
intuition - arguably Creative Genius level. Of course, Princeton
can't be characterized by a short association with one person, and
hopefully they are at this very moment learning probability and
statistics :>)
I want to turn momentarily to the curious indications that gravitation
comes from outside our universe or our 3 + 1 dimensional spacetime.
That is what Kaluza-Klein, Superstring/Brane theory, and
Randall-Sundrum theory seem to be converging on, and
Einstein-Gauss-Bonnet term/theory also.
On the one hand we have Loop Quantum Gravity (LQG) plugging its way
along by demolishing continuity and providing not the faintest clue
about gravitation and mass, and on the other hand we have the above
mentioned theories indicating that gravitation and perhaps mass come
from the "outside". Once again, we seem to be getting a better
picture from non-LQG theories, though nobody wants to literally destroy
LQG, just make them one of the alternatives rather than the survivor of
the fittest so to speak.
If somebody will look back at my mass-generating threads, the idea
seems to be that mass and/or energy push their way from outside inward
also at various key eras involving acceleration and/or expansion.
Look outside the box. Everybody seems to say this, but few know how.
Bureaucracies look inward at themselves but use perception and emotion
without cognition. They are face-oriented and appearance-oriented even
though looking at each other. They lack reality-orientation. This
keeps them in the box. Creative Geniuses look outside the box. They
look at the Individual in each Plurality (not only their own) and at
the Pluralities to which each Individual belongs (not only their own
ones). They are reality-oriented.
Get Real.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 12:06:58 AM |
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From Osher Doctorow
ArXiv has several hundred entries under the keyword "Review" or
"review", and one interesting one is "Brane world of warp geometry: an
introductory review," by Yoonbai Kim, Chong Oh Lee, Ilbong Lee of
Sungkyunkwan U, Korea, arXiv:hep-th/0307023 v2 26 Apr 2004.
One of their first comments in the introduction of their paper is that:
"A fine tuning of m_bare up to 16 digits like m_bare =
-9.99999999999999989 x 10^18 GeV is nonsense in any rational science,"
from which they go on to say that they need "an additional physical
principle to protect physical results from the above nonsensical fine
tuning." This is the second page of their paper.
This 10^(16) reminds me of 10^(-18) in a recent posting in this thread,
and a few words need to be said in defense of very small probabilities
and very small positive numbers.
The reason why most people don't see very small positive numbers or
probabilities much is that almost nobody figured out a motivation to
look at them until rather recently. Still, General Relativity people
should not knock the very small numbers of their Quantum Theory
relatives! The latter don't criticize small length/distance units and
indeed seem to cherish them, so they in turn should presumably cherish
small probabilities. But probability only recently entered physics as
time goes, and in the case of quantum theory it entered rather
backwards as I have described.
Large probabilities seem to cause rejoicing in many scientific
scenarios, and small probabilities are OK there and also in
mathematical probability-statistics as long as they're roughly slightly
below .05 or .01 or even .001. Something like .0000001 starts people
looking over their shoulder rather guiltily to figure out what they did
wrong. Perhaps the computer did one of its idiotic roundings?
Actually, if there are roughly 6-7 billion people on Earth today, I
would estimate the probability of a Creative Genius being chosen
randomly from this number on one attempt as roughly the ratio:
1) 10^4/(6.5 x 10^9) (if there are 10,000 Creative Genius alive today)
which is less than 1/100,000. The probability of a Creative Genius
being either born or coming to "fruition" (if Creative Genius is
developed rather than born) in any particular hour or even day is
arguably of the order of 10^(-16). Yet can anybody think of many more
important events or processes not only for Knowledge but for both the
Individual and Pluralities? I suspect that the answer is No, even if
Lisa Randall were answering.
This only scratches the surface. Two reasons why you may not see very
small positive numbers often outside Quantum Theory is that dividing by
them and taking logarithms of them causes "blow-ups" of various types.
This has major dangers in conditional probability and in Shannon
information/entropy theory near events of probability 0. You can find
a lot of my discussions on those in the archives of sci.stat.math and
elsewhere.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 12:51:55 AM |
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From Osher Doctorow
If Randall-Sundrum theory is correct, then I suggest that we start
looking for the explanations of anomalies, paradoxes, and similar
things in higher dimensions especially with regard to forces, masses,
energies.
One example that occurs to me almost immediately is the rather
non-intuitive model currently used in elementary particle physics and
accepted as an approximation by most quantum theorists regarding
force-carrying bosons. The rough picture is that of two USA football
players (where throwing the ball is permitted) going through life
passing (throwing) the ball between each other except that the ball
"disappears" after it's passed.
Even the model which I suggested in earlier work, of two wave-particles
or field-particles overlapping partly when transmitting the force (in
their wave or field parts) and then separating is much more intuitive
than the passing football scenario.
If Randall-Sundrum theory points the way, an even better idea is that
the force is transmitted at least partly through the force dimension of
the relevant force and that we observe the interface and once the force
is transmitted the interface just "closes". We have matter-filled
dimensions and energy-filled dimensions available as theoretical
constructs. Why not force-filled dimensions?
There are supposed to be 4 basic elementary forces: electromagnetic,
weak nuclear, strong nuclear, and gravitation, with an electroweak
combination of the first two. There are 3 observable space dimensions
and 1 "clock" time dimension. Since gravitation is basically
associated with the 5th dimension, 3 + 1 time + 1 gravitational force
is 5 dimensions. Suppose that electromagnetic force adds one
dimension, giving 6 dimensions. The weak nuclear force adds one
dimension, giving 7 dimensions. The strong nuclear force adds one
dimension, giving 8 dimensions. I already indicated that a second time
dimension is plausible in this or the last thread, giving 9 dimensions.
We're trying for 11. How about a "consciousness" or "cognitive" force
as 10 and a "perception" force as 11? Concerning the perception
force, for example, it certainly has been indirectly motivated by the
curious observer interactions with experiments in quantum theory.
Perception and cognition are key in psychology and at least perception
in biology (I suspect that cognition is also applicable there at least
in part).
Could these dimensions be even further increased? If we're trying for
26, the next "feasible" number of dimensions, we need 15 more. What
about 4 mass dimensions to correspond to the 4 forces, 4 energy
dimensions to correspond to these. That gives us 8 out of 15. We need
7 more. If we added 8 "anti-mass" and "anti-energy" dimensions, we'd
have 1 too many. Take away the second time dimension. That's 26.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 01:29:26 AM |
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From Osher Doctorow
I have nothing against octonions - some of my best friends are
octonions :>)
In fact, I have defended Clifford algebra in Professor Hestenes'
interpretation (of Arizona State U.) as geometric calculus or spacetime
calculus (sometimes rather unfortunately called spacetime algebra).
But there comes a point where, just as algebra is too abstract and
"unreal", so too is geometry too abstract and "unreal". Perhaps that
is why they seem to get along so well, although geometry is generally
far better.
But physics needs to lead the way when geometry starts acting like
another algebra. What is so terribly bothersome about Tony Smith's
and John Baez' enumerations of octonions and all their descendents and
ancestors and modifications and variations unto the last degree of
non-commutativity, non-associativity, or non-anything, is the terrible
boredom of it all for me!
There are enumerators and there are explorers/discoverers. When
exploration and discovery and invention starts getting like filing mail
into pigeonholes or sorting papers into shelves or books into shelves,
then I think that the problem is likely to be not oneself but the job.
Some of you will never leave octonions so to speak, and good for you!
No viewpoint except Violence-Orientation and Ignorance-Orientation (the
desire to not know) should be banished. There is a wealth of things to
be discovered with octonions and spinors and tensors and quaternions.
I hope to meet octonions in particular again relatively soon, but not
quite as soon as John Baez does. It is all a matter of timing.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 03:35:22 PM |
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From Osher Doctorow
Let's improve the Elementary Particle Physics model of how fermions
exchange bosons to transmit forces using the particle-field or
wave-particle notion combined with the notion that forces are
transmitted through a higher dimension (analogously to what happens
with gravitation in Randall-Sundrum more or less).
Instead of regarding a fermion as emitting a force-carrying boson which
will hit a second fermion, we ask one question: how can a wave-particle
emit anything without expanding at least its wave part?
It can't under most intuitively plausible scenarios, so we have this
picture: the fermion expands its wave or field part toward the second
fermion. We already know from earlier threads that expanding objects
can expand to different degrees and at different speeds in different
directions simultaneously, so there's nothing wrong with a "focused
wave" in general.
Ordinarily, we could just imagine the wave expanding through 3
dimensional space and 1 dimensional time (3 + 1 spacetime for short),
but the wave gets endowed with a force quality or push/pull which it
didn't have before (a fermion not being a force, and we're using
fermion for the wave-particle). Either we have to regard the fermion
as exerting some "volition" type push on its own wave part through 3 +
1 spacetime, or the fermion can just expand its wave part in the
direction of the force dimension. The latter only requires that the
fermion can "orient" itself, which is intuitively roughly like an
observer seeing something or perceiving something in a particular
direction. This in turn is what intuitively moves or expands the wave
part into the force dimension, endowing it with a force, while its
projection simultaneously expands through 3 + 1 spacetime. The wave
part then pushes or pulls the other fermion when it hits it (remember
science fiction tractor beams!) and extricates itself assuming no
entanglement by contracting back to the first fermion.
An especially nice thing about the above is that there is no "virtual
particle" which doesn't really make logical sense when you think about
it and is at best intuitively ambiguous.
Just as a mass gets "painted the color mass" so to speak by contacting
the Higgs field, so fermions become forcelike (formerly called
force-carrying bosons) by contacting the force dimension.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 03:50:25 PM |
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From Osher Doctorow
The force dimension (each fundamental force having its own dimension,
although these dimensions could change and even merge at the
unification level) in this theory is regarded as having a quality
somewhat like that of a fully packed mass or energy dimension. The
latter two dimensions exert a "pressure to explode" that results in
intermittent penetration of 3 + 1 spacetime from objects in those
dimensions. The force dimension has something analogous with a
built-in "push-pull" gradient or tendency. Its "language" or "logic"
is to push-pull objects around. It doesn't have to explode. Push-pull
tendency is already an "explosive" tendency in a way, but "controlled"
rather than intermittent. A fermion has to send its wave or field part
into the push-pull dimension to get this quality, and it is
simultaneously directed toward the second fermion, and after pushing or
pulling the second fermion its task is done and it contracts back to
the first fermion.
As a friend of mine used to say in the British Foreign Office, "it's
all done with mirrors." :>)
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 04:21:44 PM |
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From Osher Doctorow
So we come again to the question: is there an Observer or Perception
dimension? I think so.
The above theory isn't the only one in which something important occurs
via an "Observer" or "Perception" property which happens to be
attributed to fermions. One of the biggest anomalies or paradoxes of
physics is Quantum Strangeness, in which the way the experiment is made
(open or closed hole or slit) affects the wave/particle's choice of
paths.
I have to leave, and I'll try to continue this shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 05:42:35 PM |
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From Osher Doctorow
A Perception dimension or Observer dimension has to be treated
delicately because of its possible misuse among other things. Science
doesn't work if everybody proliferate their own axioms and postulates
to conform with their opinions or intuitions. Moreover, I think that
science and most branches and topics even in mathematics are basically
Reality-oriented - they don't regard the Real world as arbitrary
depending on the whims of people's opinions and intuitions. And
they're correct in this in my opinion.
This doesn't mean that science or mathematics "spirals upward" in time
and that only one of several alternative theories is correct at any
time in the modern era. Reality may be contained party in different
theories so to speak, and different theories may give different
insights into reality. So there is room for very much difference of
emphasis, difference of opinion about what is important or even what is
better. The only thing that there isn't room for is proliferating
axioms without considerable indications of how and why they relate to
Reality.
I''ll try to continue this shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 06:56:26 PM |
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From Osher Doctorow
Let's look at the question of whether mass equals probability or
something related to probability again.
In this context, recall gravitational potential energy near the surface
of the earth:
1) P.E. = mgh
Aristotle introduced the idea of potential versus kinetic, and much of
probability is reminiscent of what is intuitively "potential," as when
we say: "what's this person's potential for success," when we mean
"what''s the probability that this person will succeed."
The equation (1) is so elementary that we tend to forget it. There's
also:
2) P.E. = -Gm1m2/r
for the gravitational potential energy of a mass m2 at distance r from
mass m or of the system as a whole. The gravitational potential GP is
considered to be the gravitational potential energy per unit mass:
3) GP = -Gm1/r
by dividing P.E. of (2) by m2.
In both (1) and (3) we see the relationship of a "potentiality" in a
probabilistic sense to a mass, with the remaining factor being some
function of length or distance L (h or r). Likewise for the potential
energy of a stretched spring:
4) P.E. = (1/2)kx^2
where the stiffness coefficient k comes from F = kx (Hooke's law) and
so mass and length (x) enter again.
One could say that in these simple classical scenarios that a big part
of energy, namely potential energy E_p, is proportional to mass times
length or the inverse of length L:
5) E_p = kmL^a
where k is some constant and a is either 1 or -1 or 2 depending on the
scenario.
So the equation:
6) E = wLF
with ww* = P (probability) or even w = constant and F = ma with a
constant (not the last a above) starts looking more plausible in these
scenarios.
It turns out that probability is also closely related to kinetic
energy, but that doesn't spoil the similarities because probability
itself might be of two types: potential and kinetic.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
16 May 2005 08:39:12 PM |
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From Osher Doctorow
If there is a dimension of Perception, then we don't have to invoke the
idea that so much trial and error or even so much time was required for
life to evolve. The earliest matter if not radiation presumably had
some degree of entry into the Perception dimension, and life forms
developed an "unusual" ability to traverse that dimension. What could
have taken a very long time was the chemistry and geology and
biochemistry to support land-mobile and ocean-mobile life forms.
I'll try to be back soon.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
17 May 2005 01:12:48 AM |
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From Osher Doctorow
Thought Experiments and Physics Intuition involve Perception as well as
Cognition. If you don't believe this, try a Thought Experiment under
instructions not to try to perceive anything and to scream every time
you perceive something whether or not you try to. Ditto for Cognition.
If those words are too vague, try respectively "sensing something" or
"thinking something". You will probably end up screaming the whole
time if you are foolish enough to try this Thought Experiment, but even
thinking about it will probably convince you.
Mathematical and Quantitative-oriented psychologists have been using
the logistic model (logistic differential equation and logistic
probability distribution) in Perception for quite a few years for
various reasons including intuition, theoretical reasons such as the
item response theory/Rasch model assumptions and background (see under
Rasch as a keyword on the internet or under Item Response Theory), etc.
There are admittedly a few competing methods in Perception including
Thom's Catastrophe Theory, and as in physics the philosophical and
logical analysis of competing theories is only beginning.
One interesting study accessible on the internet is "Perception and
valuation of risk reduction as a public and private good: investigating
methodological issues of contingent valuation of UV risks in New
Zealand," Roy Brouwer, Ian J. Bateman, Caroline Saunders, and Ian H.
Langford, CSERGE Working Paper GEC 99-06 (Centre for Social and
Economic Research on the Global Environment). The authors are with U.
of East Anglia and/or University Colege London and/or Lincoln U. New
Zealand. You can also find it under keywords "logistic perception" or
"logistic models of perception".
The Brouwer et al study above tried to figure out why New Zealanders in
certain contexts exposed themselves to sunburn even though skin cancers
are a major problem there (per capita morbidity and mortality rates are
among the highest in the world). It turns out that they tend to like
appearances of people who are brown or tanned among other things. The
emphasis was on people's perceptions. 359 people were interviewed.
The logistic probability or logit model was used. A whole bunch of
people so to speak didn't want to pay money even for the research study
to which many objected not to mention for improving the situation on
the grounds of already paying too much for taxes and so on. New
Zealand's politics, incidentally, is currently on the far left,
opposite to Australia's, but apparently life doesn't qualify as a far
leftist goal in much of the sample selected although this wasn't one of
the research questions.
I'll take this opportunity to mention that Cognition and Perception
differ. In the New Zealand study above, one might well have asked
whether people who believe in Underdogs or Humanity necessarily believe
in life. Surprisingly, I have my doubts even though logically life is
usually considered part of the definition of humanity. Lots of people
seem to believe in Humanity as an amorphous "everybody" that somehow
always contains themselves but not the people they dislike (which is
already a contradiction, but there you are). Underdogs are also
notoriously relative. The same people who claim that "your Terrorist
is my Liberation hero" also tend to have a curious belief that "your
Victimizer is my Victim," which, assuming that most people know the
difference between being hit on the head repeatedly with a steel pipe
or not, is roughly equivalent to not being able to tell Right from
Wrong in the definition of legal insanity.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
17 May 2005 07:38:01 AM |
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From Osher Doctorow
If only we had a dimensional laboratory - or do we? Let's see.
When we fall asleep, our perceptions and cognitions ordinarily diminish
to "close to zero" except for some cyclical aspects of REM vs non-REM
sleep in which dreaming alternates with not dreaming. Our spatial
motions diminish to close to zero. Our sense of time diminishes to
close to zero but we actually do experience the sense of a rapid
passage of time usually and an interesting thing happens in reality -
we do find that the clock records a passage of time that is "roughly as
large as would be predicted by the sensation of rapid passage of time"
in various respects.
And we have a certain tendency to solve problems during sleep in
physics and in mathematics at least. Why?
Let's explore this further. What happens to our kinetic and potential
energies, to our mass, to our forces? There is relatively little
kinetic energy although if I recall correctly it increases somewhat
during the dreaming parts of the alternating cycles. Forces tend to
decrease since there is relatively little acceleration barring
nightmares or similar events. Mass doesn't seem to alter much.
If we solve problems during sleep in physics and in mathematics (think
of the occasions if any where you were trying to solve one for a long
time before going to sleep and thought of the answer upon awakening
almost immediately), we arguably could be using physics intuition or
mathematics intuition.
But no dimensional change of significance was involved except time and
some curious aspects of dreaming cycles. I have argued before quite
considerably (see sci.stat.math, geometry.research, etc.) that time or
change in time is Birkhoff causation and that Probable Influence is
closely related to Birkhoff causation, so there we seem to have the
causation part or probable causation part of problem-solving in sleep.
In dreaming, we have internal representations of "important" spacetime
events or problems without the distraction of other "noiselike"
spacetime events, although we also may have utter nonsense (in a
sense). Let's consider only those internal representations or
thoughts/"pictures" that involve real issues during the prior awake
states. To the extent that we have insight thereby into how things
"work" without equations or inequalities, I think that we are using
physics intuition. To the extent corresponding to equations or
inequalities, I think that we are using mathematics intuition. In
both cases, the connection to Reality via the spacetime representations
of the outside world or its past is essential. In both cases, the
connection to the abstract via time/(probable) causation is essential,
and arguably physics intuition is connected also to the perception
dimension or its representation while mathematics intuition is
connected also to the cognition/logic dimension or its representation.
I'll try to continue this soon.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
17 May 2005 08:05:20 AM |
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From Osher Doctorow
I should mention one caution here. Both physicists and mathematicians
can have nightmares of problem-solving in what subjectively seem to be
"infinite loops". It's probably not a good idea to make a habit of
problem-solving before going to sleep, at least for an hour or two
before. It's not intuitively so much the subjective impressions of
nightmares that are worrisome as the possible physical and mental
effects.
On the positive side, we seem to have an ideal recipe for
problem-solving in physics, mathematics, and engineering. For those
who know some game theory and/or linear programming, the "winning game"
seems to involve staying in the intersection of the dimensions of
spacetime, matter, energy, force, perception, cognition with an
emphasis on the time/(probable) causation part of space-time and on the
Reality part of space at least. But since we are often in the
intersection of these dimensions if we assume that they exist, it would
be more accurate to say that we need to specifically focus our
attention on these dimensions via perception or its representation and
cognition or its representation. Ingenious Imitation and Mediocrity
involve in my opinion lack of attention to these dimensions which is
usually habitual for people who fall into those categories. Creative
Genius in this theory is a new habit that arises from Ingenious
Imitation and even Mediocrity when people start paying habitual
attention to these dimensions via perception/cognition or their
"representations" in thinking/dreams/thought-experiments/daydreams.
Even then, familiarity with past research is usually a good idea even
only from the viewpoint of not repeating past mistakes and learning new
habits that benefit the process. But there is some tradeoff there.
You can spend your life in one corner of problem-solving, calculating
the number of pigeonholes required to put mail in and sort it. Or you
can try to solve world-class problems. Most of us have to spend much
time somewhere in between, but I suspect that in the process of trying
to solve world-class problems we are winning the game of Life and
Knowledge, while in calculating and sorting pigeonholes we lose that
game.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
17 May 2005 08:22:11 AM |
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From Osher Doctorow
Now take a look at "Relativistic constraints on the structure of
fundamental forces," by E. Comay (Tel Aviv University School of Physics
and Astronomy), arXiv:physics/0503020 v1 2 Mar 2005, especially the
three requirements that shold be satisfied by a relativistic force (p.
10). That should bring us back to the literature if anything can.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Randall-Sundrum, Einstein-Gauss-Bonnet, and PI |
17 May 2005 10:29:12 AM |
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From Osher Doctorow
Engineers have a claim on "Reality-orientation" in a sense because they
are usually so into problem-solving, and it turns out that in
dimensional analysis they are way ahead of us all (somewhat reminiscent
of the bumper-sticker: "I may be slow, but I'm way ahead of you.").
You've all heard of the MLT (mass, length, time) dimensional system,
and probably the MLTQ (Q for dimension of (electric) charge) and MLT
theta (theta for temperature) systems, but engineers have used force
and various types of energy besides temperature including heat in
dimensional systems and even dimensionless ratios. See for example H.
A. Becker's (Queen's University, Ontario Canada Dept. of Chemical
Engineering) Dimensionless Parameters Theory and Methodology, WIley:
N.Y. 1976; E. de St. Q. & M. de St. Q. Isaacson (U. K.) Dimensional
Methods in Engineering and Physics, Wiley: N.Y. 1975.
In fact, it turns out that some of our best friends are ratios of
forces including the Reynolds number/ratio, the Froude ratio/number,
Strouhal ratio/number, Stokes ratio/number, Euler ratio/number,
cavitation ratio/number, wall friction coefficient, friction factor,
drag coefficient, Weber ratio/nymber, Bond ratio/number, capillary
ratio (Becker pp. 28-29). Are they important in Reality? Heck, yes!
The Isaacsons even have found a use for an MLTH theta system of units
and others.
Osher Doctorow
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