As Danny and I had already discussed offline, John McCarthy et al have described how to implement Steve Gray's solution via a giant game of billiards with Kuiper object cue balls. Gene's tidal deceleration might be handled by noncircular gears feeding a differential. The solution Danny posted (which is only good to 1.5 lsd, sorry) models n bodies with 4 n + 2 gears and no gear fanout, only shaft fanout. A partial solution using two gear fanouts, but lacking Earth and Mars, is 149 293 157 --- --- --- = 29.5350888532671 +.3 lsd 12 83 233 149 293 103 143 (--- ---) --- --- = 87.969257189543 +1 lsd 12 83 41 179 149 152 293 (---) --- --- = 224.700799133144 -.7 lsd 12 107 23 (Don't see how to reuse 293.) <Inter Venerem et Jovem planetas quaeremus.> 149 259 259 174 (--- --) --- --- --- = 4332.82012915184 +.1 lsd 12 83 13 31 149 259 259 321 183 (--- --- --- ---) --- --- = 10755.6986497112 +1 lsd 12 83 13 31 136 The idea here is to spend five gears followed by three. One avenue I didn't explore is to handle one or more intermediate planets with shaft fanout. --rwg ULTONIAN LUNATION, PRICELESS ECLIPSERS, TIME-SHARINGS MISSING-EARTH ASTROMETRIC MERITOCRATS
My solution? Did I forget doing something noteworthy? Or is there another Steve Gray? But I have that name copyrighted! (I did suggest using rockets to make planetary periods easier to deal with.) The Original Steve Gray ----- Original Message ----- From: "R. William Gosper" <rwg@osots.com> To: <math-fun@mailman.xmission.com> Sent: Wednesday, February 09, 2005 2:07 PM Subject: [math-fun] 10,000 year gear train
As Danny and I had already discussed offline, John McCarthy et al have described how to implement Steve Gray's solution via a giant game of billiards with Kuiper object cue balls. Gene's tidal deceleration might be handled by noncircular gears feeding a differential.
This subject reminds me that at Gathering for Gardner 6 was a psycho- mechanic named Arthur Ganson who had connected the merrily spinning shaft of a big motor to a long string of 100:1 gearboxes, with the final output shaft firmly planted in a concrete wall. I suggested as a future project a group of protruding arms performing the candle dance rotation with a proffered horizontal tray, but so far haven't heard back. This is understandable, since his immediate project was to connect the shaft of a hefty (but unmoored) motor around to the back of its own housing via 1:1 bevel gears. Presumably this reached infinite angular velocity and sucked him into a time warp. Or maybe he was just overcome with fumes from the incinerated windings. With ratios other than 1:1 (perhaps via a simple pair of chains and sprockets), this gizmo might actually do something interesting. Or maybe 1:1 with a fluid coupling?? What a great auto shop project for a school with a lot of insurance. --rwg IODOMETRIC MOTORICIDE INCINERATES ANCIENTRIES CREATININES
This guy is artist-in-residence at MIT, and there's a permanent exhibit of his work at the MIT museum -- which is decidedly worth a visit, if you're in the area. --Michael Kleber On Thu, 10 Feb 2005 11:11:27 -0800 (PST), R. William Gosper <rwg@osots.com> wrote:
This subject reminds me that at Gathering for Gardner 6 was a psycho- mechanic named Arthur Ganson who had connected the merrily spinning shaft of a big motor to a long string of 100:1 gearboxes, with the final output shaft firmly planted in a concrete wall. I suggested as a future project a group of protruding arms performing the candle dance rotation with a proffered horizontal tray, but so far haven't heard back. This is understandable, since his immediate project was to connect the shaft of a hefty (but unmoored) motor around to the back of its own housing via 1:1 bevel gears. Presumably this reached infinite angular velocity and sucked him into a time warp. Or maybe he was just overcome with fumes from the incinerated windings. With ratios other than 1:1 (perhaps via a simple pair of chains and sprockets), this gizmo might actually do something interesting. Or maybe 1:1 with a fluid coupling?? What a great auto shop project for a school with a lot of insurance. --rwg IODOMETRIC MOTORICIDE INCINERATES ANCIENTRIES CREATININES
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-- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
I can highly recommend this DVD by Arthur Ganson. I bought it at G4G6. My kids (9 and 6) love it http://www.arthurganson.com/pages/DVD.html Having provided this public service, I will take this opportunity to plug my paper on how the Sprague Grundy theory of impartial combinatorial games generalizes to misere play via commutative semigroups and the "indistinguishability quotient" construction: http://arxiv.org/abs/math.CO/0501315 I've computed a semigroup presentation for the misere quotient of Dawson's Chess to heap size 30. It has 128 elements and 19 distinguishable P position types. Maybe someone can figure out the algebraic theory of the misere mex rule, which seems to be related to ideal extensions, and this presentation can be extended to a complete analysis. More info here http://www.plambeck.org/oldhtml/mathematics/games/misere/ Thane Plambeck http://www.plambeck.org/ehome.htm Michael Kleber wrote:
This guy is artist-in-residence at MIT, and there's a permanent exhibit of his work at the MIT museum -- which is decidedly worth a visit, if you're in the area.
--Michael Kleber
On Thu, 10 Feb 2005 11:11:27 -0800 (PST), R. William Gosper <rwg@osots.com> wrote:
This subject reminds me that at Gathering for Gardner 6 was a psycho- mechanic named Arthur Ganson who had connected the merrily spinning shaft of a big motor to a long string of 100:1 gearboxes, with the final output shaft firmly planted in a concrete wall. I suggested as a future project a group of protruding arms performing the candle dance rotation with a proffered horizontal tray, but so far haven't heard back. This is understandable, since his immediate project was to connect the shaft of a hefty (but unmoored) motor around to the back of its own housing via 1:1 bevel gears. Presumably this reached infinite angular velocity and sucked him into a time warp. Or maybe he was just overcome with fumes from the incinerated windings. With ratios other than 1:1 (perhaps via a simple pair of chains and sprockets), this gizmo might actually do something interesting. Or maybe 1:1 with a fluid coupling?? What a great auto shop project for a school with a lot of insurance. --rwg IODOMETRIC MOTORICIDE INCINERATES ANCIENTRIES CREATININES
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Maybe Google or somebody could commission a children's museum exhibit in the form of Ganson's futernity machine extended to a length of fifty 100:1 gearboxes. The boxes would be labeled with the powers of 10 and Conway names, and signs would label the first few shafts with, e.g., "x turns per second," "x turns per minute," ..., "... years," "... millennia," galactic rotations,..., solar nova consumes Earth, universe runs out of gas (with a gratuitous universal joint as an inside joke), ..., googol. --rwg ANCESTORED SECOND-RATE TERASECOND STREAMLINES RAIMENTLESS ETERNALISMS
This is reminiscent of the scene in "Forbidden Planet" in which the Krell power meters go off scale. There are many many of them, and it is explained that each represents ten times the power of the previous. On Feb 11, 2005, at 7:50 PM, R. William Gosper wrote:
Maybe Google or somebody could commission a children's museum exhibit in the form of Ganson's futernity machine extended to a length of fifty 100:1 gearboxes. The boxes would be labeled with the powers of 10 and Conway names, and signs would label the first few shafts with, e.g., "x turns per second," "x turns per minute," ..., "... years," "... millennia," galactic rotations,..., solar nova consumes Earth, universe runs out of gas (with a gratuitous universal joint as an inside joke), ..., googol. --rwg ANCESTORED SECOND-RATE TERASECOND STREAMLINES RAIMENTLESS ETERNALISMS
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I seem to recall that the (very impressive) light panels on the larger IBM 360 machines included lights for the real-time clock, and the leftmost lights were only ever turned on during "lamp test" mode, since the clocks (probably) never made it that far. Perhaps someone else remembers the details better than me. At 04:50 PM 2/11/2005, R. William Gosper wrote:
Maybe Google or somebody could commission a children's museum exhibit in the form of Ganson's futernity machine extended to a length of fifty 100:1 gearboxes. The boxes would be labeled with the powers of 10 and Conway names, and signs would label the first few shafts with, e.g., "x turns per second," "x turns per minute," ..., "... years," "... millennia," galactic rotations,..., solar nova consumes Earth, universe runs out of gas (with a gratuitous universal joint as an inside joke), ..., googol. --rwg ANCESTORED SECOND-RATE TERASECOND STREAMLINES RAIMENTLESS ETERNALISMS
participants (6)
-
Henry Baker -
Michael Kleber -
R. William Gosper -
Steve Gray -
Thane Plambeck -
Tom Knight