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jgill
Boulder climber
The high prairie of southern Colorado
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^^^^ zero superfactorial is still 1.
Why doesn't Klaatu get this simple fact?
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healyje
Trad climber
Portland, Oregon
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I consider myself ill-informed in formal matters, but unavoidably curious.
Bayesian? If reckoning from the viewpoint of how many attempts my latest FA project is taking I would say I'm a frequentist. However, given the project has now stretched out over years I fear I must conclude I'm more of an occasionalist.
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WBraun
climber
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zero superfactorial is still 1
Yes, this is one of the most important proofs in mathematics if one can go all the way deep into it.
You will find the ultimate truth there that transcends the material plane including impersonalism ......
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Ed Hartouni
Trad climber
Livermore, CA
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without reading Carroll's book it is hard to guess just why the relatively arcane "crossing symmetry" argument is required.
First off I have to assume Carroll understands what crossing symmetry is, and I don't mean that pejoratively, I had to refresh my memory of what exactly it is... but that is because it is such an unused idea.
In some ways it derives from the actual TCP symmetry, which is fundamental to quantum field theory. And while it is anticipated that this symmetry is ultimately broken, it functions well enough to anchor all that we know.
If you "reverse time," the T operation in the TCP, you have to "reverse" the "CP" operation product too, that is the product of the "C" "Charge conjugation" operator ("+" charge goes to "-") and the "P" "Parity" operator. We have observed "CP" violation in a number of particle decays, first with the K-meson, then the B-meson and finally the D-meson. We also know that "CP" violation is necessary to explain the matter-dominated universe that we live in, yet we don't have a candidate process that provides a large enough violation to explain our universe. No "T" violation has been observed, yet we expect to see it because of the TCP invariance required by QFT.
So it is relatively straight forward to interpret an electron going forward in time is symmetric to a positron going backward in time. Dirac was headed in that direction, Feynman (and to a certain extent Wheeler) made the "interpretation" rigorous. And later, the Feynman diagrams made this idea graphical and visual, so one can draw the Feynman diagram and convey this idea even though the diagram is associated with some integral equation whose expression would vastly confuse most people seeing it.
The "crossing symmetry" tries to take advantage of the TCP symmetry, but runs afoul when trying to relate the kinematics of the "crossed" reactions. Weinberg comments in a footnote "...crossing symmetry is not an ordinary symmetry (it involves an analytic continuation in kinematic variables) and is difficult to use it with any precision for general purposes."
The problem is that "analytic continuation" has not been related to a physical idea, a problem that Heisenberg, the originator of S-Matrix approaches ran into in the 1940s, which Chew writes about in his introduction of his 1961 monograph. Landau contributed his mighty abilities to extend the work, showing that the singularities in the dispersion relations describing the scattering processes were either singularities or branch points in the complex space that they lived in... and the considerable technologies of complex analysis could be applied.
But the physical ideas didn't quite fit, the discreet units of intrinsic angular momentum we call "spin" is a complex continuous parameter, who expresses itself as poles on the real axis and appear to us as discrete quantities... yet the physical interpretation of this complex space doesn't lead to any deeper insight in the physics.
It's just a mathematical tool...
These ideas were the fashion during the 1960s when QFT was not yet up to describing the strong interaction, and it took a decade before both the theory and the experiments were able to describe what was going on... the tools developed in the attempt to side step QFT, S-Matrix theory, Regge Poles, and all that, all find useful application in modern theory, but the promise of explaining the strong interaction physics based on them has long since been considered broken. Who knows, fashion often comes around, and some work on quantum gravity makes use of the ideas.
Trotting out the rather freighted concept of "crossing symmetry" to a philosophy audience to support an argument, without explaining the details, opens the argument up to sever criticism later... and the cute appropriation of a very visual "symbol" (the Feynman diagrams) without explaining the details makes it more fraught.
Unless the argument really needs "crossing symmetry," it boarders on the category of an intellectual "parlor trick"
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jgill
Boulder climber
The high prairie of southern Colorado
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. . . even though the diagram is associated with some integral equation whose expression would vastly confuse most people seeing it
Indeed. Feynman diagram
A primer on analytic continuation in the complex plane:
Example: Consider the series S(z)=1+z+z² + z³ + ..., valid for
|z|<1. The function f(z)= 1/(1-z) extends or analytically continues S(z) to any value of z ≠ 1.
Ed's references of course are to more complicated functions in physics.
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jgill
Boulder climber
The high prairie of southern Colorado
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Yes, this is one of the most important proofs in mathematics if one can go all the way deep into it
You will find the ultimate truth there that transcends the material plane including impersonalism ......
Comments like this bubble up at Cattail Crossing from time to time.
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WBraun
climber
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Humans are different than animals.
The stoopid modern fools say we are animals.
So you like to make up sh!t you know nothing about.
In that case you should kill and hunt humans and eat them just like you slaughter all these animals daily and eat them.
Since you're all animals there's no difference to you loons ......
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WBraun
climber
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Hey .... those my lines!!!! :-)
Plagiarism and copy cat!!!!
Muwhahaha ......
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jogill
climber
Colorado
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5!=120. But 0!=1, 0!!=1!=1, 0!!!=1!!=1!=1, 0!!!!=1, 0!!!!!=1
Klaatu stupid. Gort smart. Gort command saucer; Klaatu change oil.
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MH2
Boulder climber
Andy Cairns
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Kel Cheris is brevetted to General and sent to rid the Fortress of Scattered Needles of enemies whose heretical calendar threatens to cause rot in consensus mechanics. Good thing she's a brilliant number theorist.
Ninefox Gambit
Yoon Ha Lee
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jgill
Boulder climber
The high prairie of southern Colorado
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Klaatu barada nikto
means:
"Klaatu's babe is now Gort's doll."
Meanwhile, Klaatu toils on trying to understand 0!!!!!. (Look closely at the photo of him at the blackboard)
If his intellect fails the task, meditation should work!
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High Fructose Corn Spirit
Gym climber
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Thanks, Ed, for the reply.
A lot of your post re crossing symmetry goes over my head but I think I get the gist of it. I cited it only because it was an item I wasn't familiar with as part of Carroll's chapter conversation.
I hope I didn't give any impression that crossing symmetry was a major component of Carroll's book. It wasn't. Thanks again.
....
In part, this hints to how easily Carroll - and his "poetic naturalism" approach - can be misinterprettted by the public...
[Click to View YouTube Video]
https://youtu.be/3AMCcYnAsdQ
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jgill
Boulder climber
The high prairie of southern Colorado
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In 1954 I was a high school student taking physics and I wrote a short report on a popularized article I read about positrons being interpreted as electrons going backward in time. Needless to say I hadn't a clue about the details, but the physics teacher liked it!
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MikeL
Social climber
Southern Arizona
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Duck: In that case you should kill and hunt humans and eat them just like you slaughter all these animals daily and eat them.
In Southeastern Cherokee literature, the following has been claimed:
————————
In the old days the members of the brute creation were gifted with speech, and dwelt in amity with the human race. The increase of humanity, however, crowded the animals into the forests and desert places of the earth, and upon the invention of lethal weapons, man commenced the wholesale slaughter of the beasts for the sake of their flesh and skins, and trod upon the lesser animals with contempt. The animals, driven to despair, resolved upon retributive measure. The first to meet where the bears, headed by old White Bear, their chief. After several speakers had denounced mankind for the bloodthirsty behavior, war was unanimously decided upon, and the nature of human weapons was discussed. It was discovered that the bow and arrow were the principal human weapons, and it was resolved to fashion a specimen to see if they could not turn man’s weapons against him. A piece of wood suitable for the purpose was procured, and one of the bears sacrificed himself to provide them with gut for the bowstring. After the bow was completed it was discovered that the claws of the bears spoiled their shooting. One of the bears, however, cut his claws, and succeeded in hitting the mark. But the chief, the old White Bear, interposed with the remark that the claws were necessary to climb trees with, and that all would have to starve if they were to cut them off.
The next council was held by the deer, under their chief, Little Deer. They resolved to inflict rheumatism upon every hunter who should slay one of them unless he asked a pardon in a suitable manner. They gave notice of this decision to the nearest settlement of Indians, and instructed them on how to make propitiation when forced by necessity to kill one of the deer folk. So when a deer is slain by a hunter, the Little Deer runs to the spot, and bending over the blood stains, asks the spirit of the deer if it has heard the prayer of the hunter for pardon. If the reply is yes, all is well, and the Little deer departs; but if the response is in the negative, he tracks the hunter until he is in his cabin and strikes him with rheumatism, so that he becomes a helpless cripple. Sometimes hunters who have not learned the proper formula for pardon attempt to turn aside the Little Deer from his pursuit by building fire behind them in the trail.
The fishes and reptiles then held a joint council, and arranged to haunt those human beings who tormented them, with hideous dreams of serpents twining around them, and of eating fish which had become decayed.
Lastly, the birds and insects, with the smaller animals, gathered together for a similar purpose, the grub worm presiding over the meeting. Each in turn expressed an opinion, and the consensus was against mankind. They devised and named various diseases.
When the plants, which were friendly to man, heard what had been arranged by the animals, they determined to frustrate their evil designs. Each tree, scrub, herb, down even to the grasses and mosses, agreed to furnish a remedy for some of the diseases named. Thus did medicine come into being, and thus the plants came to furnish the antidote to counteract the evil wrought by the revengeful animals.
(. . . cited in Lewis Spence, “Cherokees”, in “Hastings Encyclopedia of Religion and Ethics,” vol 3, p. 505)
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jgill
Boulder climber
The high prairie of southern Colorado
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Interesting and well-executed new series on NBC about time travel:
Timeless
Anyone here watch the SyFy Channel's 12 Monkeys ?
I'm a sucker for this kind of stuff.
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