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> Cognitive Physics, What [i]could[/i] physics rationally be?
Raphie Frank
Posted: Nov 21 2007, 06:19 AM


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IT'S ALL A QUESTION OF FRAMING...

Is it a Buttercup?

User posted image

Full Pic Here
http://www.flickr.com/photos/artivist/3366...in/photostream/

Or a Woman Dressed to the Nines?

User posted image

Full Pic Here:
http://www.flickr.com/photos/artivist/3366...in/photostream/

Same picture, two different framings with two different meanings. Something to think about, perhaps...


==================================================

"TANTEXTUALLY" SPEAKING...

That first pic up there, incidentally, was associated with a post I did over on Friendster a little less than a year ago (December 27th, 2006). The key line of note...

"Web 3.0 will be what WE make it in 2007 in what I hope Time Magazine will next year dub 'The Year of Community.'"
http://boojummy.blogs.friendster.com/snipe...nk_you_to_.html

The jury is still out on the notion of "Community", but Edward O. Wilson's concept of "Consilience" aka "The Unity of Knowledge" sure has come a mighty long way in 2007, from Frank Tipler down in New Orleans announcing he had proven the existence of the "Cosmological Singularity..."

SEE...
The Physics of Christianity
http://www.randomhouse.com/catalog/display...40&view=excerpt

... to Garrett Lisi's recent paper "An Exceptionally Simple Theory of Everything" that uses the E8 Lie Group to bring gravity out of the orphan cold and into the classical fold...

SEE...
Einstein on a snowboard
http://www.timesonline.co.uk/tol/news/uk/s...icle2889309.ece

==================================================

Ah... perhaps not so "TANTEXTUAL" after all. "One" Reality, perhaps, but many, many approaches...

Best,
Raphie

P.S. Oh. and we won't go into numerology for the moment, but there was indeed a numerological reason for suggesting 2007 as the possible year of "Community." Numerology may or may not be what the Brits call "boll*x," but the belief that people have in it is what Jung would have called "psychological fact." For my part I've a notion or two, one of which I call "Evolutionary Semiotics" and another one of which I call "Social Resonance." More on those another time...

P.P.S. For the record, I sincerely question Tipler's interpretive capacities. He may be a bit "too" blinded by the light.

This post has been edited by Raphie Frank on Nov 21 2007, 06:24 AM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Isee
Posted: Nov 21 2007, 08:13 AM


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Hi Rahpie Frank,

Thanks for all the info. I especially like the stuff from " From the Stanford Encyclopedia of Logic" and " The Physic of Christianity".
It is the same topic of measurement. One is converted for general teaching and the other is converted for religous.

The problem with physic is the problem of understanding what measurement means. Measurement is base on the notion of intelligence. One is artificial and one is natural. The natural one is said to be regenerative or have the power to repair itself. This is what I think M-theory is. But the 11D of M-theory break into the many 10D Quantum Gravity. Many, but only sensory perception is the natural aspect of measurement. The other are Heterotic or fake measurement. Fake here means it is artificial or man made. It is not the 4D/ physicist's brain that is fake but the probe or the instrumentation of science. For example the LHC is a probe. And who or what invented it. Watch how Quantum Gravity works when the image of the explosion is projected to the 4D brain. That is embeding all right.
If one look at how M-Theory is structure there is already a place for Garrett Lisi E8 theory.
So, a warning from Cognitive Physics. Don't declared anything yet! dry.gif
Anyway I'm going to take a Thanksgiving break. I hope to hear from SteveA soon. I'll be back in a week. Happy Thanksgiving for those in the USA. rolleyes.gif
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Raphie Frank
Posted: Nov 23 2007, 08:40 PM


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PHYSICAL - QUANTUM ENTANGLEMENT
=========================
via Wikipedia
http://en.wikipedia.org/wiki/Quantum_entanglement

Quantum entanglement is a quantum mechanical phenomenon in which the quantum states of two or more objects have to be described with reference to each other, even though the individual objects may be spatially separated. This leads to correlations between observable physical properties of the systems.

For example, it is possible to prepare two particles in a single quantum state such that when one is observed to be spin-up, the other one will always be observed to be spin-down and vice versa, this despite the fact that it is impossible to predict, according to quantum mechanics, which set of measurements will be observed. As a result, measurements performed on one system seem to be instantaneously influencing other systems entangled with it. But quantum entanglement does not enable the transmission of classical information faster than the speed of light (see discussion in next section below).

QUALITATIVE APPROXIMATIONS? - QUANTUM ENTANGLEMENT
======================================
Telos: The Revival of an Aristotelian Concept in Present Day Ethics
MICHAEL HAUSKELLER

Aristotle thought, in unison with some contemporary bioethicists,40 that every organism has its own kind of good, and although he could give no reason for this apart from the intuition that whatever it is ‘for the sake of which’ all the parts that make up a particular organism are made and conjoined, must be good, the intuition itself is as plausible as it is possible for any intuition about what is good, or bad.
http://www.pubmedcentral.nih.gov/articlere...i?artid=1351104

COMMENT: This, of course, does not include the concept of non-locality. For that, it is far better to reference R.D. Laing and his work with schizophrenics. Mike Maran, in his play, "Did You Used to Be R.D. Laing?" a pretty amazing play I saw here in NYC tells in faux first-person narrative of how Laing came to many of his recognitions regarding interdependency. While staffed on a psychiatry ward he noticed that the patients seemed to -- my description not his -- almost choreograph their movements in relation to one another.

On Google Books, you can download Laing's work...

The Divided Self: An Existential Study in Sanity and Madness
http://books.google.com/books?id=f2Dz6n0eT...dCJCpF0#PPA7,M1

... and here is a link to the website of Mike Maran, a very talented, engaging and very convincing storyteller
http://www.mikemaran.com/

Also related is the work of David Bohm. See...

David Bohm and the Implicate Order

excerpt...
... while there he worked at the Lawrence Radiation Laboratory where, after receiving his doctorate in 1943, he began what was to become his landmark work on plasmas (a plasma is a gas containing a high density of electrons and positive ions). Bohm was surprised to find that once electrons were in a plasma, they stopped behaving like individuals and started behaving as if they were part of a larger and interconnected whole. He later remarked that he frequently had the impression that the sea of electrons was in some sense alive.
http://www.theosophy-nw.org/theosnw/science/prat-boh.htm


user posted image

RELATED POST
from "the Verdict On Intelligent Design"

TYC'S ITHACA CHANGES THE AUDIENCES' WAY OF SEEING THINGS
(regarding a modern dance piece scored by Anestis Logothetis)
http://forum.physorg.com/index.php?showtop...ndpost&p=285372

This post has been edited by Raphie Frank on Nov 23 2007, 08:46 PM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Zarabtul
Posted: Nov 23 2007, 09:09 PM


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Physics to me has always been the underlying result of everything. Basically it is randomness at it's best. Physics when we make all the connections can solve anything and just because it isn't plain as day sometimes it does still work.


Lord Elf,

Zacharia_Andrew_Pain


--------------------
Andrew Strasser

A.K.A......The Godfather of Epileptics.


Google works.
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Isee
Posted: Nov 27 2007, 06:16 PM


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This is nice.
http://fqxi.org/community/forum.php?action=topic&id=107

What?
Garrett Lisi said "String theory is about add on by hand."
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Raphie Frank
Posted: Nov 28 2007, 12:31 AM


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KAPREKAR NUMBERS

1, 9, 45, 55, 99, 297, 703, 999 , 2223, 2728, 4879, 4950, 5050, 5292, 7272, 7777, 9999, 17344, 22222, 38962, 77778, 82656, 95121, 99999, 142857, 148149, 181819, 187110, 208495, 318682, 329967, 351352, 356643, 390313, 461539, 466830, 499500, 500500, 533170

ex.

9^2 = 81
9 = 8 + 1

45^2 = 2025
45 = 20 + 25

55^2 = 3025
55 = 30 + 25

Hopefully the concept is clear? :-)

How about Powers of ten?

10^2 = 100
10 = 10 + 0

Well, this doesn't fly, unfortunately, under the definition of the term as the official "definition" via Wikipedia posits that

========================================
"a Kaprekar number for a given base is a non-negative integer, the representation of whose square in that base can be split into two parts that add up to the original number again."
========================================

There are, however, looser interpretations of the Kaprekar Series that include the powers of 10. Incidentally, as per the work of D. E. Iannucci, in binary, all even perfect numbers are Kaprekar numbers.

More on Wikipedia
http://en.wikipedia.org/wiki/Kaprekar_number

And fom the Online Encyclopedia of Integer Sequences, links to the various Kaprekar series...

http://www.research.att.com/~njas/sequences/A006886

=============================================

The Kaprekar "Constants" (i.e. the Kaprekar Routine") are where this series really gets interesting because of it's cyclical nature.

For the technical version, see...
http://mathworld.wolfram.com/KaprekarRoutine.html

Or to make it a bit more fun, see...

Mudd Math Fun Facts
==============
Take any four digit number (whose digits are not all identical), and do the following:

Rearrange the string of digits to form the largest and smallest 4-digit numbers possible.

Take these two numbers and subtract the smaller number from the larger.

Use the number you obtain and repeat the above process.

What happens if you repeat the above process over and over? Let's see...

Suppose we choose the number 3141.

4311-1134=3177.
7731-1377=6354.
6543-3456=3087.
8730-0378=8352.
8532-2358=6174.
7641-1467=6174...

The process eventually hits 6174 and then stays there!
http://www.math.hmc.edu/funfacts/ffiles/10002.5-8.shtml

The 3-digit Kaprekar constant is 495, in similar vein, a point worth making in relation to the number 496, the third (by current definition) perfect number, and a number not unrelated to striing theory.

Best,
Raphie

P.S. "Lisi's inspiration lies in the most elegant and intricate shape known to mathematics, called E8 - a complex, eight-dimensional mathematical pattern with 248 points first found in 1887, but only fully understood by mathematicians this year after workings, that, if written out in tiny print, would cover an area the size of Manhattan."

From the Daily Telegraph:

Surfer dude stuns physicists with theory of everything
http://www.telegraph.co.uk/earth/main.jhtm.../scisurf114.xml

248 * 2, of course, is 496, and 2n-1 = 495, which is quite interesting in relation to Pythagorean triples, but I'll save that for another post...

This post has been edited by Raphie Frank on Nov 28 2007, 12:43 AM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Raphie Frank
Posted: Nov 28 2007, 01:34 AM


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PYTHAGOREAN TRIPLES #1

As a followup to that last post on Kaprekar numbers:

248 * 2, as I mentioned in the previous post = 496, the third perfect number (not unrelated to string theory), and 2n-1 = 495, the 3-digit Kaprekar Constant, cyclical in nature

In relation to Pythagorean triples that 2n-1 comes up again, via the following identity, where F = Fibonacci Number.

a^ + b^2 = c^2

a = F_(n-1)
b = F_(n)
c = sqrt F_(2n-1)

by substitution...

F_(n-1)^2 + F_(n)^2 = F_(2n-1)

c, it so happens, falls in between = a^2 and b^2. I termed it a "Fibonacci half-step" a while back but there may be a better name for it.

F_(n-1)^2 < sqrt F_(2n-1)< F_(n)^2

OR

a^2 < c < b^2

===================================================

RATIO-WISE, as for the interval that separates these terms, and someone may wish to check up on my arithmetic here, but it is not uninteresting with regards to polyedra, the Pentagon etc.

a^2 * 1.1755705 = c

... where 1.1755705 = the length of one side of a Pentagon = sqrt (5-sqrt(5))/2 = sqrt (3 - phi) = sqrt (1 + (1/phi)^2)

c * (1.37638192) = b^2

... where 1.37638192 = 1/(tan 36 degrees) = cotangent (pi / 5) = 1.37638192

... which is the inverse of this identity.

user posted image

cotangent (pi/5), equivalent to tan 54 degrees, also arises with regards to the formula for the area of a pentagon and the volume of a dodecahedron (see http://www.shlomifish.org/MathVentures/dodeca.html )

Best,
Raphie

A related post on "Relative Zeroes"

see Erratum first...
http://forum.physorg.com/index.php?showtop...ndpost&p=274699
then...
http://forum.physorg.com/index.php?showtop...ndpost&p=274675

Best.
Raphie

RELATED LINK:

Exact Trigonometric Constants:
http://en.wikipedia.org/wiki/Exact_trigonometric_constants

This post has been edited by Raphie Frank on Nov 28 2007, 02:27 AM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Isee
Posted: Nov 28 2007, 08:08 AM


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What I been doing in this thread was talking about Metrology and how it is base on intelligent. It seems to me that String theory got all the right stuff, including closed strings and open strings. I am not a string theorist but I see the logic in it. I think that closed strings describe living objects while open strings describe dead objects.

So, let us focus on the meaning of dead and alive or what it means to put something by hand. The living part of the universe is said to be deterministic or hand pick. The dead part is said to be by accident or through random actions. For example if someone fall down on the ground that would be by accident or at that moment it is undetermind or simply dead. An accidental fall is different than a control fall. For example if I sit down on a chair or an airplane comes for a landing that would be a control fall or it is deterministic and plan out to be like so.

The living part of the universe is said to be theoritically reasonable while the dead part of the universe is said to be physically reasonable. So, to be physically reasonable you have to be dead. laugh.gif

Obviously most things are physically reasonable because they are mostly dead objects randomly bouncing off each other. The outcome of this is dead, decay, destruction, and disorder. But too much disorder can also bring order or the living form. This is not a hand pick but pure statistical outcome.

Obviously the scientific method is never be physically reasonable. It all about deterministic, hand pick, probe it, and see what happen. Planning and probing for answere is anti-nature. This include experimental result from LHC. Also you don't see the LHC rise up by chance/statistic? Someone must built it.

Now, what part of GL theory that is not hand pick?



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Raphie Frank
Posted: Nov 28 2007, 10:21 AM


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Dear Isee,

You write...

"Obviously the scientific method is never be physically reasonable."

That's a bit like saying a styrofoam cup is not a part of nature, don't you think? I'm not sure one can make such an arbitrary distinction. If humans are a part of the Cosmos (i.e. a part of the "natural") and if the laws of physics apply to humans, then all consequence and "product" of their existence is therefore also natural and eminently "reasonable."

Perhaps you might wish to define your terms a bit more precisely, if only so that we may have a common reference point of understanding?

Best,
Raphie

This post has been edited by Raphie Frank on Nov 28 2007, 10:22 AM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Isee
Posted: Nov 28 2007, 04:06 PM


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O.K
Let say a rock fall off a mountain clif and hit the ground.
Is that physically reasonable?
My answere is yes. It's by chance/statistic that the rock fall and hit the ground.

What if someone was under the falling rock and got kill without anyone noticing?
Again this is physically reasonable. From the perspective of the falling rock that person was dead a long time ago. And again accident, chance, and statistic play all the roll.

What if that someone spot the falling rock by using their sensory, and move out of harms way. Is this physically reasonable?
According to my definition this is not physically reasonable. The person has used a method of detection to escape dead/accident. In other words he/she completely change the outcome. But is this part of reality? Yes. This is why I think we need to properly define what we means by chance/statistic verses testing or detection.

It looks to me that GL theory is base on Quantum Gravity but one that is split into cosmology rather than biology. Yes they are part of reality and experimentally verifiable but if one where to claim theory of everything then what?
I see a differant between the fabric of reality for biology than cosmology. One can repair itself but the other can't. And also don't forget about the role of metrology in all of this.

Maybe more explanation, but have to go.
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Isee
Posted: Nov 29 2007, 09:11 AM


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The dead and the living is very close together. I have proposed that we should looked at it in term of white frame, gray frame, and black frame.
White frame is what is known or proven or already happened. It is the past state.
Black frame is unknown or undetectable, it is beyond your event horizon, it is waiting to happen. It is the future state.
The gray frame is when you combined the white frame and the black frame or combine the known and unknown. Or combine past and future and get the present state.
In term of sensory perception one just let in light reflected of a sample through the eyes and into the brain. The brain hold the definition standard inwhich it compared incoming frame to get a gray frame. The gray frame is a threshold for image recognition. The threshold can be adjusted by the light source or the brain cell itself. One must understand that beyond sensory perception is accident waiting to happened.
In practice, the brain invent. Sensory perception inspected and feedback info to the cell membrane that this is one possible way to go. So, life kind of evolve with this probing and testing the environment. It's a learning curve. biggrin.gif
In AI like the HONDA ASIMO is trying hard to be human. But if one looked at where he get his brain and sensors from and how it is made we need another AI. Electron optic inspection machine. Notice that sensory perception and electron optic are using small amount of energy to illuminate the sample while the LHC is doing a 100% destruction probing methology.
In any case the future is ambigous until observed. That also apply to this new E8 theory. I don't think it is a hit or miss kind of thing. I always believe in such things as a learning curve.
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Raphie Frank
Posted: Nov 29 2007, 10:55 AM


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Dear Isee,

Let me suggest that you add in OBSERVER POV.

The past can be thought of as a series of "Data Points" in geographical strata-like formation through time wherein the issue of INTERPRETATION (i.e the "gray") becomes key. What happened 10 zillion years ago? We don't know, but can make educated guesses. Similarly, history is told by those who tell the most convincing stories, not by those who are necessarily "correct;" and in Rashomon fashion (Rashomon was a Kurosawa film about four people with conflicting accounts about a murder) two observers to the same event may come away with two completely different interpretations, or, in the case of Rashomon, four different interpretations.

The future, meanwhile, at least from our time-bound perspective, can be conceived of as a "probability distribution," and is thus "quantum" in nature. Again issues of interpretation (the "gray") come into play, but doubly so, because in this case it is the data points themselves that are in question as well as one's ability, based upon historical experience and ability to accurately assess the current state (the "Now") and how they will impact one another going forward, to correctly analyze how events will "play out."

Best,
Raphie

RELATED:

Wolfgang Iser & Reader-Response Theory
------------------------------------------------
Iser compared the output of the "author" to the placing of stars in the sky. He or she (or "it") can SUGGEST the "constellations" of perception, but there will always be a "gray" area.

More about Iser...
http://www.litencyc.com/php/speople.php?rec=true&UID=2316

Rashomon (film)
----------------------
Rashomon... is a 1950 Japanese film directed by Akira Kurosawa, working in close collaboration with cinematographer Kazuo Miyagawa. It stars Toshiro Mifune, Machiko Kyo and Masayuki Mori. The film is based on two stories by Ryunosuke Akutagawa ("Rashomon" provides the setting, while "In a Grove" provides the characters and plot). Rashomon can be said to have introduced Kurosawa and Japanese cinema to Western audiences, and is considered one of his masterpieces.

The film has an unusual narrative structure that reflects the impossibility of obtaining the truth about an event when there are conflicting witness accounts. In English and other languages, 'Rashomon' has become a byword for any situation in which the truth of an event is difficult to verify due to the conflicting accounts of different witnesses. In psychology, the film has lent its name to the 'Rashomon effect'.
http://en.wikipedia.org/wiki/Rashomon_%28film%29

Rashomon effect
----------------------
The Rashomon effect is the effect of the subjectivity of perception on recollection, by which observers of an event are able to produce substantially different but equally plausible accounts of it. A useful demonstration of the use of this principle in scientific understanding can be found in the article "The Rashoman Effect: When Ethnographers Disagree," by Karl Heider (American Anthropologist, March 1988, Vol. 90 No. 1, pp. 73-81).

It is named for Akira Kurosawa's film Rashomon, in which a crime witnessed by four individuals is described in four mutually contradictory ways. The film is based on two short stories by Ry?nosuke Akutagawa, "Rash?mon" (for the setting) and "Yabu no naka", otherwise known as "In a Grove" (for the story line).
http://en.wikipedia.org/wiki/Rashomon_effect

===================================================

In very loose manner, Ramsey Theory, which deals with the inevitably of "order," is also not at all unrelated to the issue of interpretation (the "gray") as the question then becomes WHOSE order and WHICH properties?

Ramsey Theory
--------------------
Ramsey theory, named for Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear. Problems in Ramsey theory typically ask a question of the form: how many elements of some structure must there be to guarantee that a particular property will hold? An oft-quoted slogan for the subject is "complete disorder is impossible" (T. S. Motzkin).
http://en.wikipedia.org/wiki/Ramsey_theory

This post has been edited by Raphie Frank on Nov 29 2007, 11:13 AM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Raphie Frank
Posted: Nov 29 2007, 11:26 AM


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Dear Isee,

The below is related to the discussion of metrology which, for those unaware of the term...

---------------------------------------------
Metrology (from Greek 'metron' (measure), and 'logos' (study of)) is the science of measurement. Metrology includes all theoretical and practical aspects of measurement.
---------------------------------------------

from the thread...
The Fine Structure Constant As Fractal Construct?, A "Physio-theoretical" Exploration
http://forum.physorg.com/index.php?showtopic=19245

A FEW GUIDING HYPOTHESES/ASSUMPTIONS REGARDING THE BELOW "NUMEROLOGICALLY" DERIVED "PHYSIO-THEORETICAL" APPROXIMATIONS FOR ALPHA:

3) All truly "Fundamental" Constants are dimensionless by definition. They only seem to be not so RELATIVE to our "somewhat" arbitrarily chosen units of measurement, but...

4) IF the Laws of physics apply to ALL things in the known Universe, including human patterns of perception and organization on all levels from the individual psyche to the world collective, and including a progressive component THROUGH TIME, then such laws apply also to the development and evolution of our units of measure. In theory, then, such measurements approach, but never reach some optimal "mean."


Best,
Raphie

This post has been edited by Raphie Frank on Nov 29 2007, 12:00 PM


--------------------
Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Raphie Frank
Posted: Nov 29 2007, 11:54 AM


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Modular arithmetic

(from Wikipedia)
http://en.wikipedia.org/wiki/Modular_arithmetic

Modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value — the modulus. Modular arithmetic was introduced by Carl Friedrich Gauss in his book Disquisitiones Arithmeticae, published in 1801.

Applications
--------------
Modular arithmetic is referenced in number theory, group theory, ring theory, abstract algebra, cryptography, computer science, chemistry and the visual and musical arts.

It is one of the foundations of number theory, touching on almost every aspect of its study, and provides key examples for group theory, ring theory and abstract algebra.

In cryptography, modular arithmetic directly underpins public key systems such as RSA and Diffie-Hellman, as well as providing finite fields which underlie elliptic curves, and is used in a variety of symmetric key algorithms including AES, IDEA, and RC4.

In computer science, modular arithmetic is often applied in bitwise operations and other operations involving fixed-width, cyclic data structures. The modulo operation, as implemented in many programming languages and calculators, is an application of modular arithmetic that is often used in this context.

In chemistry, the last digit of the CAS registry number (a number which is unique for each chemical compound) is a check digit, which is calculated by taking the last digit of the first two parts of the CAS registry number times 1, the next digit times 2, the next digit times 3 etc., adding all these up and computing the sum modulo 10.

In the visual arts, modular arithmetic can be used to create artistic patterns based on the multiplication and addition tables modulo n (see external link, below).

In music, arithmetic modulo 12 is used in the consideration of the system of twelve-tone equal temperament, where octave and enharmonic equivalency occurs (that is, pitches in a 1:2 or 2:1 ratio are equivalent, and C-sharp is considered the same as D-flat).

The method of casting out nines offers a quick check of decimal arithmetic computations performed by hand. It is based on modular arithmetic modulo 9, and specifically on the crucial property that 10 : 1 (mod 9).

More generally, modular arithmetic also has application in disciplines such as law (see e.g., apportionment), economics, (see e.g., game theory) and other areas of the social sciences, where proportional division and allocation of resources plays a central part of the analysis.

Some neurologists (see e.g., Oliver Sacks) theorize that so-called autistic savants utilize an "innate" modular arithmetic to compute such complex problems as what day of the week a distant date will fall on.

==========================================================

Speaking of which, Andrew Wiles used mod 32 in his proof of Fermat's Last Theorem

See...

Fermat's Last Theorem: Proof for n=5: Key Lemma 1
http://fermatslasttheorem.blogspot.com/200...for-n5-key.html

Best,
Raphie

This post has been edited by Raphie Frank on Nov 29 2007, 11:56 AM


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Reality is always bending itself for us. sometimes it bends itself to amuse us, sometimes to teach us, sometimes to confuse us. It bends itself overtly and covertly. the bending takes many different forms -- sometimes visual, sometimes spiritual, sometimes we feel vertigo that has nothing to do with any physical circumstances... - Egg Theorem
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Isee
Posted: Nov 30 2007, 04:06 PM


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Hi Raphie Frank,
The the Observer POV is a source of confusion. This is the reason why we have physic. For example math could be verything or nothing but when you add physic to it, physic FORCE math to be useful. laugh.gif
In life you can't force any human or animal to see what you see. Only fundimentalist do that kind of stuff. Why do we see things different? It's because we all have different DEFINITION STANDARD and RESOLUTION STANDARD.

So, physic force unity and accuracy. I never thought physicists would fight over theories, but they do. Sometime it can get real ugly like the recent E8 theory verses String theory. I reason reality and physic like so;

If Newtonian physic is usefull and proven to worked then it is part of my reality.
If Relativity physic is usefull and proven to worked then it is part of my reality.
If Quantum physic is usefull and proven to worked then it is part of my reality.
Now, the unify theories or higher theories are a bit confusing because you are dealing with the act of measurement and membrane creation. But I can see here the logic of String theory where Gravity can move from dimensions to dimensions. It's not that it moves but how precise and exact you wants your calculation to be. Or how precise you wants your measurement to be. Quantum Gravity deal with measuremt and verification thus when you do measurement you know exactly the state of the system at that time. This is where you know your theory works or not. The 11D memembrane has to live or die according to the outcome of your measurement. It had no choice. Like Relativity has to use Newtonian Gravity, it has no choice.

Thus, what the Law of Physic is saying is that it's all about what ever works that is the reality of it. And what ever that doesn't work you can blame on Mother nature or Quantum nature. It's just that you did not think about that one.

Hmm..... I keep using String for my argument. I did not put E8 in my logic but it is within the Quantum Gravity level.
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