Science > Physics > Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes
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Science > Physics |
| User: |
"OsherD" |
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24 Feb 2006 02:01:55 AM |
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Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes |
From Osher Doctorow
Engineering control/feedback is extremely concrete and yet also
extremely abstract in slightly different aspects, and is of course
(Probable) Causal, and this characterizes arguably
Combinatorics/Arithmetic/Number Theory, Probability-Statistics, Physics
Intuition/Experiment, Differential Equations and Inequalities, Real and
Complex and Functional Analysis including Measure and Integration,
Logic, and Geometry and Topology without Algebra.
But here we come to what looks at first like a curiosity, namely that
in Combinatorics/Airthmetic/Number Theory, which derives its heavy
concreteness from human counting of objects which is almost
"omnipresent", one doesn't count "Universal Constants" other than
something like pi (circumference divided by diameter of circle) or e of
which the former really expresses ratios of length-like properties of
an object of a special type and the latter is just the zero value of a
far more general function useful elsewhere.
Arguably, what isn't counted or (Probably) Causal or logical or
experimental/observed lacks plausibility as a "fundamental" constituent
of physics, and both the "finite" speed of light and the Planck
constant lack plausibility as "fundamental" constituents on this basis.
There is one other thing that arguably should be included as
"fundamental" in physics: the essences of geometry and topology insofar
as they apply to the real physical world, namely (a)
continuity/connectedness and (b) discontinuity/disconnection in a
continuous environment. Note carefully that (b) describes
holes/handles in topology, because holes don't make sense except as
interruptions of continuous and connected objects. We don't observe or
perceive "discrete topologies" or "discrete universes" except as
fictitious or abstract pictures on paper. When Loop Quantum Gravity
(LQG) claims that the Universe is fundamentally discrete at the
microscopic level, it is violating these ideas.
There is a way of "violating" Continuity/Connection in theory but not
in practice so to speak, namely "discretizing" what is really
continuous in order to computerize it. Computers are very useful for
rapid calculations and rapid "mechanical" results including numerical
solutions. But this doesn't make what they are doing "fundamental".
From this viewpoint, the quantum itself which is discrete can be
explained as an approximation for a more theoretical version of "rapid
computing". The most plausible explanation is that the remoteness of
the microscopic quantum domain from direct human
perception/observation/direct experiment has changed measurement itself
from continuous to approximate/discrete. This could be rephrased as a
"phase change" from macroscopic to microscopic phase. Quantum
physicists could then claim to justify themselves as representing the
"other (discrete) phase," but there we come to a very deep fact, namely
that we really only know our own (continuous) phase fundamentally
unless and until we ever reach the other one if any.
Ultimately, I suspect, physics will go back to the fundamental nature
of the macroscopic rather than the microscopic realm. We are already
arguably seeing signs of that. When physicists wonder why
discrete-based theories are yielding relatively fewer and fewer
predictions and practical applications, they should keep this in mind.
Osher Doctorow
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| User: "Caught You" |
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| Title: Re: Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes |
24 Feb 2006 10:36:08 AM |
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"OsherD" <> wrote in message
news:1140768115.690771.114180@j33g2000cwa.googlegroups.com...
From Osher Doctorow
Engineering control/feedback is extremely concrete and yet also
extremely abstract in slightly different aspects, and is of course
(Probable) Causal, and this characterizes arguably
Combinatorics/Arithmetic/Number Theory, Probability-Statistics, Physics
Intuition/Experiment, Differential Equations and Inequalities, Real and
Complex and Functional Analysis including Measure and Integration,
Logic, and Geometry and Topology without Algebra.
techno-babble, and poor too. Put Michael Jackson in there somewhere.
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| User: "OsherD" |
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| Title: Re: Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes |
25 Feb 2006 12:39:05 AM |
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From Osher Doctorow
Caught You of invalid.com (where trolls usually come from) typed:
techno-babble, and poor too. Put Michael Jackson in there somewhere
What can one say to the birth-defect-because-mother-was-on-heavy-dope
crowd? I hope that you overcome your childhood.
Osher
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| User: "OsherD" |
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| Title: Re: Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes |
24 Feb 2006 02:22:06 AM |
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From Osher Doctorow
Here we come to a surprise.
Readers who have looked up my postings in detail on sci.physics and
sci.stat.math and geometry.research and elsewhere, and possibly one or
two of my publications, will notice that Probable Influence/Causation
is always used with Continuous Random Variables rather than Discrete
ones, which I usually explain as a "simplifying" assumption.
But from the arguments of this thread, it isn't just a simplifying
assumption. Continuous random variables and their probability
distributions (normal/Gaussian, uniform, gamma including chi-square and
exponential, F and t and Cauchy and beta and power distributions, etc.)
really are arguably fundamental, and the discrete distributions like
binomial, hypergeometric, Bernoulli, equiprobable, multinomial,
Poisson, geometric, etc., are arguably approximations to the continuous
ones.
So we come finally to a question like: what about a random variable X
which takes on an allegedly constant finite value c, the "speed of
light"? It assigns all its probability to a single point/value c, and
so is not continuous but discrete. From this thread, it arguably is
not fundamental but only approximates reality, either as an extremely
large number "approximating" infinity (as a mathematician I don't like
this expression's lack of rigor, but it conveys the English sense that
the extremely large numbers are Rarer and Rarer in our experiences) or
as a boundary of human/animal visual perception.
So at the boundary of the "light cone", a continuous relative of the
old X = c, let us say Y in [c - epsilon, c + epsilon] for small
positive epsilon, seems plausible and may well be the random variable
or even a deterministic variable which describes tunnelling through the
light cone. It is a simple picture, and as so often, simplicity seems
to be the direction to proceed.
Osher Doctorow
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| User: "Caught You" |
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| Title: Re: Causation/Causality, Memory, and Convolution 14: Universal Constant Paradoxes |
24 Feb 2006 10:41:11 AM |
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"OsherD" <> wrote in message
news:1140769326.438084.190660@i40g2000cwc.googlegroups.com...
From Osher Doctorow
Here we come to a surprise.
Readers who have looked up my postings in detail on sci.physics and
sci.stat.math and geometry.research and elsewhere, and possibly one or
two of my publications, will notice that Probable Influence/Causation
is always used with Continuous Random Variables rather than Discrete
ones, which I usually explain as a "simplifying" assumption.
But from the arguments of this thread, it isn't just a simplifying
assumption. Continuous random variables and their probability
distributions (normal/Gaussian, uniform, gamma including chi-square and
exponential, F and t and Cauchy and beta and power distributions, etc.)
really are arguably fundamental, and the discrete distributions like
binomial, hypergeometric, Bernoulli, equiprobable, multinomial,
Poisson, geometric, etc., are arguably approximations to the continuous
ones.
No, they are not.
So we come finally to a question like: what about a random variable X
which takes on an allegedly constant finite value c, the "speed of
light"?
Then it is not a random variable anymore, is it?
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