Innumerable as the Starrs of Night,
Or Starrs of Morning,
Dew-drops, which the Sun
on every leaf and every flouer
Beauty is truth, truth beauty,
— that is all
Ye know on earth, and all
ye need to know.
E = M
Energy is eternal delight.
Impearls: 2002-12-01 Archive
Archimedes and the Infinite
To paraphrase Yoda in George Lucas's Star Wars: “Always in motion is the past.”
It might be thought that our knowledge of the ancient world (at least the better known periods and aspects of it) would have mostly shaken into a settled shape by now. It's true that much information about the past is well and reliably known; in vast areas of concern, however (intellectual history, as an example), there remain crucial gaps, some of which are only now being partially filled in, with details sometimes importantly different from what had been presumed to be there before.
Mathematician and philosopher of science Jacob Bronowski put it like this: 1
This principle is exemplified in the appreciation of one of antiquity's most brilliant minds, Archimedes (one of a handful through history whose achievements may be said to lie on a par with those of modern giants Newton and Einstein).
The story of the recovery of Archimedes' great work Method of Mechanical Theorems in 1906 after more than 2,000 years is remarkable enough, but the tale is not yet ended!
Now after nearly another 100 years further progress has recently been made, and the results are illuminating.
Life and work
Born circa 290-280 B.C. in the Greek city of Syracuse in Sicily, dying in the Roman sack of that city in 212-211 B.C. during the Second Punic War, Archimedes is most famous today as the great ancient Greek inventor and mathematician. In antiquity, Archimedes was also well known as a superb astronomer.
In a recent piece, “Proof, Amazement, and the Unexpected” in the journal Science, Stanford professor Reviel Netz characterizes Archimedes' mathematical contributions. 2
Books such as Euclid's Elements have come down to us by way of numerous Greek and Arabic manuscripts, but, as Carl Boyer points out in his excellent History of Mathematics, the connecting link to Archimedes' works is thin. Boyer writes: 3
Misconceptions of his work — and Archimedes' Method
The dearth in availability of Archimedes' works over much of the past two millennia has, as one might expect, led to errors in the appreciation of the body of his work. Boyer writes:
Gerald Toomer of Brown University assesses Archimedes' Method, as it was known during the twentieth century. 4
The Method: discovery and recovery, lost and found again
The story of the recovery of Archimedes' Method of Mechanical Theorems is a terrific example, in my view, of how our comprehension of the past can even at this late date be dramatically changed by new discoveries, which may hinge on the merest chance. Quoting Boyer again:
No sooner had Archimedes' Method been almost miraculously recovered in 1906, but it was lost again (or stolen), disappearing for most of the rest of the century. Fortunately for Archimedean scholarship of the twentieth century, the palimpsest had been photographed before being lost, allowing Heiberg to perform his remarkable feat.
Archimedes and the Infinite
Netz proceeds to the heart of the matter: the remarkable results recently obtaining from the re-recovery of the original manuscript in 1998.
1 J. Bronowski, The Common Sense of Science, Harvard University Press, Cambridge, Massachusetts, 1963; pp. 117-118.
2 Reviel Netz (Assistant Professor of Classics, Stanford University), “Proof, Amazement, and the Unexpected” (link requires subscription or pay per view), Science (1 Nov 2002), Vol. 298, No. 5595, pp. 967-968.
3 Carl B. Boyer (Professor of Mathematics, Brooklyn College), A History of Mathematics, Second Edition, revised by Uta C. Merzbach, John Wiley & Sons, Inc., New York, 1991, ISBN 0-471-09763-2 or 0-471-54397-7 (pbk); pp. 136-137, 139.
4 Gerald J. Toomer (Professor of the History of Mathematics, Brown University, Providence, Rhode Island), “Archimedes,” Encyclopædia Britannica, CD 1997, Encyclopaedia Britannica, Inc.
Impearls: 2002-12-01 Archive
Taken stupidest quote
U.S. government black project's captive German scientist, in Steven Spielberg's Taken episode 2:
Anyone who's glanced at a few of the books entertaining the possibility of interstellar travel (covering such topics as the amount of fuel vs. payload needed to get a vessel to the stars) can see what a terrific boner is being pulled here. In brief, if you have to carry your fuel along with you (as in ordinary rockets), even using nuclear or antimatter powered spaceships, the payload achievable is an extremely tiny fraction of the size of the entire ship, with required fuel occupying almost all of it. Needless to say, a vast ship full of antimatter (and normal matter) fuel equals a stupendous amount of energy.
Ramscoops or ground-laser illuminated lightsails offer significant escape from these limitations, because you don't have to carry (most of) the fuel along with you. Even using these approaches, however, the amount of portable energy that must be carried on an interstellar ship is immense.
Beyond straightforward acceleration-deceleration means of getting to the stars, even if suggested approaches for bypassing the great distances between the stars turn out to be feasible (hypotheticals such as wormholes or “hyperspace”), who says the amount of energy needed to make use of such methods would be small? If opening up a wormhole requires, say, artificial creation of a black hole massive enough not to crush “passengers” passing through its event horizon (i.e., much-much larger than a stellar-mass black hole), then the physical energy requirements for interstellar travel via wormholes would be truly gigantic!
Coming at it from the other direction, one must consider the question of how much “energy,” if that's the right term, is needed in principle to “reach inside a man's mind and give him the images that are lurking there.” The “scientist” providing the Taken quote tosses it off as if of course! the energy required would be huge. How much energy, though, did it take for the Voyager spacecraft to send images into the minds of Earthlings across billions of miles of space from the planet Neptune? A few watts of power in Voyager's transmitter?
In the scene in Taken to which the above quote refers, the alien stood only a few feet from a human into whose brain he fed “the images that are lurking there.” How much “energy” would that take? How much energy under optimum conditions would it take to send a TV signal across a few feet? Microwatts, at a guess?
Whether any signal transmitted could be received is another matter. If a reception mechanism is already present in the human brain (which if telepathy exists — a big if — there must be; or if “synchronicity” is the way that telepathy works, that too will do for an explanation), in either case, once again, watts or microwatts (or even less, in the case of synchronicity) should suffice. If there is no reception mechanism already present in the brain, however (or no synchronicity), then even an infinitude of power might not do.
In the situation where humans do not already come equipped with a “transmission image receptor” mechanism, the easiest way to get such a reception system implanted, in my view, would simply be to waft a “designer virus” across the intervening space (once again, a few feet, given the premise of the story), which infecting the intended individual, would cause a suitable receptor system to be grown, perhaps in his or her brain. How much “energy” does it take to waft a tiny virus (far smaller than anthrax spores) across a few feet of space?
Once a suitable reception mechanism is present in the intended recipient, images should, once again, be transmittable using minimal energy. Of course, if a continuing transmission link isn't needed, the viruses themselves could carry all the images or other data desired without any subsequent energy requirements.
However, the words Spielberg later in that same episode of Taken also places in the mouth of that “German scientist,” are if anything even stupider than the above quote!
I don't know about Spielberg.
UPDATE: 2002-12-22 01:30 UT: More fundamental Taken stupidity.
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