Re: [math-fun] "Steampunk" mathematics?
HGB>I guess the Galton box qualifies as a mechanical calculator for a Gaussian: https://en.wikipedia.org/wiki/Bean_machine Also, Fredkin's billiard ball computer: https://en.wikipedia.org/wiki/Billiard-ball_computer And then there's those wonderful 1960's mechanical desktop "calculators"; I recall seeing one in the 1950's multiply two large numbers; they were amazing to watch! <HGB Even from a distance. The Friden (and I think, Marchant) machines had a column of 10 togglable keys for each of 10 digit positions, and a 20 digit accumulator carriage that chugged back and forth. The Friden I used in 1961 to Monte-Carlo submarine kill probabilities(!) could also take the 10 digit square root of the 20 digits in the accumulator. Unless the carriage was too close to an immovable object, whereupon you enjoyed the screech of stripping gears, and a multihundred dollar, multiday repair job. HGB> Some of IBM's early punch card machines were deliciously electromechanical, < and LOUD (and plugboard programmable) HGB> with grease everywhere. Also, some of their disk drives and printers I used in the 1960's had _hydraulic_ mechanisms; the IBM CE's looked more like car mechanics than computer engineers! And UNIVAC CEs were more like shipyard workers than car mechanics. UNIVAC tape drives were frightening. And the 1206 CPU, built like a bank vault, though solid state, required such deafeningly ferocious cooling that you could Bernoulli-levitate a football in the vertical exhaust. --rwg Also, selected Stanford AI alumni have coffee tables made from Librascope disk platters. At 11:39 AM 9/11/2014, Dave Dyer wrote: I nominate Turing's analog computer to find zeta function zeros, described in the Hodges biography. Also, obviously, the concept of physically realizing Turing machines using punched tape and mechanical reader/writer mechanisms. <
Who needs billiard balls when you have soldier crabs? http://www.technologyreview.com/view/427494/computer-scientists-build-comput... A billiard-ball computer was on display in the lobby of MIT's Stata Center a couple of weeks ago. It was fun to run it once, but we didn't have time to learn to reset it. Feeding the balls through a second time was boring, as the machine was in, and stayed in, the halt state. Who can beat elephants pulling on ropes 1200 years ago to calculate navigation parameters in binary? It must be true, it was in Scientific American. http://ftp.math.utah.edu/pub/tex/bib/sciam1980.html#Anonymous:1988:ARP The full article isn't as easily found online as it was years ago. "An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney" (v 258 no. 4, April, 1988) On Thu, Sep 11, 2014 at 4:49 PM, Bill Gosper <billgosper@gmail.com> wrote:
HGB>I guess the Galton box qualifies as a mechanical calculator for a Gaussian: https://en.wikipedia.org/wiki/Bean_machine
Also, Fredkin's billiard ball computer: https://en.wikipedia.org/wiki/Billiard-ball_computer
And then there's those wonderful 1960's mechanical desktop "calculators"; I recall seeing one in the 1950's multiply two large numbers; they were amazing to watch! <HGB
Even from a distance. The Friden (and I think, Marchant) machines had a column of 10 togglable keys for each of 10 digit positions, and a 20 digit accumulator carriage that chugged back and forth. The Friden I used in 1961 to Monte-Carlo submarine kill probabilities(!) could also take the 10 digit square root of the 20 digits in the accumulator. Unless the carriage was too close to an immovable object, whereupon you enjoyed the screech of stripping gears, and a multihundred dollar, multiday repair job.
HGB> Some of IBM's early punch card machines were deliciously electromechanical, < and LOUD (and plugboard programmable) HGB> with grease everywhere. Also, some of their disk drives and printers I used in the 1960's had _hydraulic_ mechanisms; the IBM CE's looked more like car mechanics than computer engineers!
And UNIVAC CEs were more like shipyard workers than car mechanics. UNIVAC tape drives were frightening.
And the 1206 CPU, built like a bank vault, though solid state, required such
deafeningly ferocious cooling that you could Bernoulli-levitate a football
in the vertical exhaust.
--rwg
Also, selected Stanford AI alumni have coffee tables made from Librascope
disk platters.
At 11:39 AM 9/11/2014, Dave Dyer wrote:
I nominate Turing's analog computer to find zeta function zeros, described in the Hodges biography.
Also, obviously, the concept of physically realizing Turing machines using punched tape and mechanical reader/writer mechanisms.
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You did notice that this article was in the April issue, right? --Dan On Sep 11, 2014, at 5:33 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
Who can beat elephants pulling on ropes 1200 years ago to calculate navigation parameters in binary? It must be true, it was in Scientific American.
http://ftp.math.utah.edu/pub/tex/bib/sciam1980.html#Anonymous:1988:ARP
The full article isn't as easily found online as it was years ago. "An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney"
I did notice both the date and the name, Apraphul. I was referred to the article by a guy who had not noticed and was enthusiastic about that "piece of history". He was predictably embarrassed when I pointed out his error. On Thu, Sep 11, 2014 at 8:53 PM, Dan Asimov <dasimov@earthlink.net> wrote:
You did notice that this article was in the April issue, right?
--Dan
On Sep 11, 2014, at 5:33 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
Who can beat elephants pulling on ropes 1200 years ago to calculate navigation parameters in binary? It must be true, it was in Scientific American.
http://ftp.math.utah.edu/pub/tex/bib/sciam1980.html#Anonymous:1988:ARP
The full article isn't as easily found online as it was years ago. "An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney"
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Yes! But speaking less seriously, I wonder if the two-toed sloth (also a primate) has developed the binary system. --Dan On Sep 12, 2014, at 11:33 AM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
I did notice both the date and the name, Apraphul. I was referred to the article by a guy who had not noticed and was enthusiastic about that "piece of history". He was predictably embarrassed when I pointed out his error.
On Thu, Sep 11, 2014 at 8:53 PM, Dan Asimov <dasimov@earthlink.net> wrote:
You did notice that this article was in the April issue, right?
--Dan
On Sep 11, 2014, at 5:33 PM, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
Who can beat elephants pulling on ropes 1200 years ago to calculate navigation parameters in binary? It must be true, it was in Scientific American.
http://ftp.math.utah.edu/pub/tex/bib/sciam1980.html#Anonymous:1988:ARP
The full article isn't as easily found online as it was years ago. "An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney"
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Correction: Apparently sloths are *not* primates. Not sure where I thought I knew that from. --Dan On Sep 12, 2014, at 11:41 AM, Dan Asimov <dasimov@earthlink.net> wrote:
But speaking less seriously, I wonder if the two-toed sloth (also a primate) has developed the binary system.
--Dan
On Fri, Sep 12, 2014 at 11:41 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Yes!
But speaking less seriously, I wonder if the two-toed sloth (also a primate) has developed the binary system.
http://en.wikipedia.org/wiki/Footfall -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Sorry, that wiki page doesn't make it clear, but the elephant-like aliens have multiply split trunks and use a binary system. On Fri, Sep 12, 2014 at 11:54 AM, Mike Stay <metaweta@gmail.com> wrote:
On Fri, Sep 12, 2014 at 11:41 AM, Dan Asimov <dasimov@earthlink.net> wrote:
Yes!
But speaking less seriously, I wonder if the two-toed sloth (also a primate) has developed the binary system.
http://en.wikipedia.org/wiki/Footfall -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Jeff Caldwell: "The full article isn't as easily found online as it was years ago. 'An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney' (v 258 no. 4, April, 1988)" It appears in Dewdney's 1990 'The Magic Machine' compilation. I've put a scan of it here: http://chesswanks.com/txt/TAW/
Thank you, Hans. I enjoyed rereading the article. On Thu, Sep 11, 2014 at 11:33 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
Jeff Caldwell: "The full article isn't as easily found online as it was years ago. 'An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney' (v 258 no. 4, April, 1988)"
It appears in Dewdney's 1990 'The Magic Machine' compilation. I've put a scan of it here:
http://chesswanks.com/txt/TAW/
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On 9/12/14, Warren D Smith <warren.wds@gmail.com> wrote:
In a V-vertex E-edge graph...
What string-machine salesman Lunnon forgot to say, is that enormous edge-length integers, N bits long, would require an exponentially large budget to purchase the string, plus the thing would gravitationally collapse into a black hole.
If the edge lengths were selected from a BOUNDED set of integers only, though, then Lunnon's "string machine" for all shortest paths would work... it takes O(E+V) steps to build it, then to solve the A-B shortest path problem requires effort (force, energy expenditure versus friction, also time if you have bounded power source) of order O(E+V) to pull on that much weight.
Meanwhile the conventional computer has a linear time algorithm O(V+E) for single source, all destinations, shortest paths (assuming bounded nonnegative integer edge lengths), then constant time lookups... so, sorry, Lunnon+string has not really beat conventional computers.
SWASC is not restricted to a single "source" (starting town)! WFL
A nicer try was made by Ken Steiglitz who once invented a machine made of rigid parts to solve NP-complete problems instantly. (Some part can move, or not, if the SAT problem has solution, or not.) Really, though, it won't work, albeit the physical reasons for the failure are a bit subtle and were not understood by KS himself.
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On 9/12/14, Jeff Caldwell <jeffrey.d.caldwell@gmail.com> wrote:
Thank you, Hans. I enjoyed rereading the article.
On Thu, Sep 11, 2014 at 11:33 PM, Hans Havermann <gladhobo@teksavvy.com> wrote:
Jeff Caldwell: "The full article isn't as easily found online as it was years ago. 'An ancient rope-and-pulley computer is unearthed in the jungle of Apraphul By A. K. Dewdney' (v 258 no. 4, April, 1988)"
It appears in Dewdney's 1990 'The Magic Machine' compilation. I've put a scan of it here:
http://chesswanks.com/txt/TAW/
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participants (6)
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Bill Gosper -
Dan Asimov -
Fred Lunnon -
Hans Havermann -
Jeff Caldwell -
Mike Stay