[math-fun] "Steampunk" mathematics?
I've just become aware of the concept of "Steampunk", which is an alternate universe in which Babbage-style steam computers actually worked in the 19th Century & thereby changed the world. (Yes, I know; I'm Rip Van Winkling myself; no snarky remarks!) Steampunk today means an exceedingly retro anachronistic concept -- e.g., a spring-wound software-defined digital radio -- so it doesn't actually require steam, per se. https://en.wikipedia.org/wiki/Steampunk Prior to the discovery of the Antikythera Mechanism, any mention of Archimedes in conjunction with geared wheels might have initially seemed "steampunk", but modern X-ray & gamma-ray images and recreations have proved it to be a remarkably sophisticated analog computer. https://en.wikipedia.org/wiki/Antikythera_mechanism Probably one of the coolest "steampunk" exercises of the 20th Century was economist William Phillips's 1949 "MONIC" water-based analog computer which represented the macro economy of the UK (called by one wag "hydraulic Keynesianism"). (Phillips could easily have been the inspiration for the TV series MacGyver -- parodied by SNL's "Gruber" -- as Phillips built all sorts of stuff while a Japanese POW -- including a radio in his shoe.) https://en.wikipedia.org/wiki/William_Phillips_%28economist%29 https://en.wikipedia.org/wiki/MONIAC I would propose that "steampunk mathematics" would be math that Cayley or Hamilton would not only understand, but might have written themselves. No Bourbaki, no axioms of choice, no Goedel (or at least Goedel only in an analog computer world). No Hilbert (especially no Hilbert's Tenth Problem), no quantum theory, very little topology (except early knot theory, thanks to Cayley, etc.). Unfortunately, my emphasis on 19th Century technology leaves out things like relay computers & Strowger switches, which I think would have been understood by, and really appealed to, the Victorians, so long as they don't include vacuum tubes or germanium diodes. I think that a lot of computer graphics technology might have appealed to Cayley & Hamilton -- particularly the use of Hamilton's quaternions for "in-betweening". It is conceivable that _fractal_ graphics, such as some of Gosper's cool pix, would have been understood by Cayley, at least. Cayley was perhaps the first to have notice the chaotic behavior of Newton's method for finding polynomial roots in the complex plane. Computer algebra systems would have been very appealing to Cayley & Hamilton, as the 19th Century mathematicians all seem to have waded through prodigious amounts of symbolic calculations. I'd be interested in any other proposals for "steampunk" mathematics.
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.
There's this wooden ternary calculator from a contemporary of Babbage, who seems to have been denied funding because Babbage's efforts didn't pan out. http://www.mortati.com/glusker/fowler/ ------------ TEA lasers are surprisingly low-tech. They're not directly related to computation, but I'm sure it would make certain things easier. http://www.sparkbangbuzz.com/tealaser/tealaser7.htm Quote: I used to tell people "There is no such thing a true home made laser. There is always a requirement for exotic parts that can only be obtained from a laser manufacturer, and - or there is the requirement to perform exotic high vacuum, glass blowing and gas mixing processes. This would defeat much of the satisfaction of building your own laser." When I read about TEA lasers recently though, that all changed. Here is a laser that is built from aluminum foil, a dielectric and some pieces of aluminum. It is amazing to think of a laser project where a simple 4 to 6 KV DC power supply is the most elaborate component. ------------ Scientific American had an article about analog computation in its June 1985 issue: http://www.softouch.on.ca/kb/data/Scan-130202-0003.pdf ------------ Adi Shamir's TWINKLE factoring device is amusingly analog. http://web.archive.org/web/20010615145445/http://porsche.ls.fi.upm.es/Materi... ------------- The best steampunk comics: The Thrilling Adventures of Babbage and Lovelace! http://sydneypadua.com/2dgoggles/stories/ Girl Genius http://www.girlgeniusonline.com/comic.php?date=20021104 ---------- An excellent site for all things steampunk: http://brassgoggles.co.uk/blog/ http://brassgoggles.co.uk/forum/ On Thu, Sep 11, 2014 at 11:39 AM, Dave Dyer <ddyer@real-me.net> 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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
P.S. Each Babbage/Lovelace comic has at least as many pages of historical notes as pictures! On Thu, Sep 11, 2014 at 12:04 PM, Mike Stay <metaweta@gmail.com> wrote:
There's this wooden ternary calculator from a contemporary of Babbage, who seems to have been denied funding because Babbage's efforts didn't pan out. http://www.mortati.com/glusker/fowler/
------------
TEA lasers are surprisingly low-tech. They're not directly related to computation, but I'm sure it would make certain things easier. http://www.sparkbangbuzz.com/tealaser/tealaser7.htm
Quote:
I used to tell people "There is no such thing a true home made laser. There is always a requirement for exotic parts that can only be obtained from a laser manufacturer, and - or there is the requirement to perform exotic high vacuum, glass blowing and gas mixing processes. This would defeat much of the satisfaction of building your own laser."
When I read about TEA lasers recently though, that all changed. Here is a laser that is built from aluminum foil, a dielectric and some pieces of aluminum. It is amazing to think of a laser project where a simple 4 to 6 KV DC power supply is the most elaborate component.
------------
Scientific American had an article about analog computation in its June 1985 issue: http://www.softouch.on.ca/kb/data/Scan-130202-0003.pdf
------------
Adi Shamir's TWINKLE factoring device is amusingly analog. http://web.archive.org/web/20010615145445/http://porsche.ls.fi.upm.es/Materi...
-------------
The best steampunk comics:
The Thrilling Adventures of Babbage and Lovelace! http://sydneypadua.com/2dgoggles/stories/
Girl Genius http://www.girlgeniusonline.com/comic.php?date=20021104
----------
An excellent site for all things steampunk: http://brassgoggles.co.uk/blog/ http://brassgoggles.co.uk/forum/
On Thu, Sep 11, 2014 at 11:39 AM, Dave Dyer <ddyer@real-me.net> 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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- 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
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! Some of IBM's early punch card machines were deliciously electromechanical, 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! 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.
(This story isn't really relevant, but it comes to mind, and it isn't one I've told before.) When I was a boy and my father worked as a lawyer in Manhattan, he would sometimes let me visit his office. There were some electro-mechanical calculators there, but one was the crown jewel: in addition to addition, subtraction, and multiplication, it could also do ... division! One evening I did what any curious proto-mathematician would do, and tasked it with dividing something by 0. Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! It began printing out repeated subtractions, advancing the platen several times a second. I quickly shut it off. When I turned it on, it resumed the calculation. Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! I shut it off again and left the room. I assume that the next person who turned the calculator on got a nasty surprise. I have no idea what might have eventually been required to reset the device and make it useable again. Jim Propp On Thu, Sep 11, 2014 at 4:12 PM, Henry Baker <hbaker1@pipeline.com> wrote:
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!
Some of IBM's early punch card machines were deliciously electromechanical, 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!
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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I had the same experience 60 years ago in Singapore. The machine couldn't be used. You had to send for the man! R. On Thu, 11 Sep 2014, James Propp wrote:
(This story isn't really relevant, but it comes to mind, and it isn't one I've told before.)
When I was a boy and my father worked as a lawyer in Manhattan, he would sometimes let me visit his office. There were some electro-mechanical calculators there, but one was the crown jewel: in addition to addition, subtraction, and multiplication, it could also do ... division!
One evening I did what any curious proto-mathematician would do, and tasked it with dividing something by 0.
Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! It began printing out repeated subtractions, advancing the platen several times a second.
I quickly shut it off. When I turned it on, it resumed the calculation. Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! I shut it off again and left the room.
I assume that the next person who turned the calculator on got a nasty surprise.
I have no idea what might have eventually been required to reset the device and make it useable again.
Jim Propp
On Thu, Sep 11, 2014 at 4:12 PM, Henry Baker <hbaker1@pipeline.com> wrote:
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!
Some of IBM's early punch card machines were deliciously electromechanical, 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!
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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
I used to divide by 0 all the time on the Marchant calculators. They could be unwedged, though I can't quite remember how. Maybe there was a Stop key. -- Gene
________________________________ From: rkg <rkg@cpsc.ucalgary.ca> To: math-fun <math-fun@mailman.xmission.com> Sent: Thursday, September 11, 2014 1:43 PM Subject: Re: [math-fun] "Steampunk" mathematics?
I had the same experience 60 years ago in Singapore. The machine couldn't be used. You had to send for the man! R.
On Thu, 11 Sep 2014, James Propp wrote:
(This story isn't really relevant, but it comes to mind, and it isn't one I've told before.)
When I was a boy and my father worked as a lawyer in Manhattan, he would sometimes let me visit his office. There were some electro-mechanical calculators there, but one was the crown jewel: in addition to addition, subtraction, and multiplication, it could also do ... division!
One evening I did what any curious proto-mathematician would do, and tasked it with dividing something by 0.
Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! It began printing out repeated subtractions, advancing the platen several times a second.
I quickly shut it off. When I turned it on, it resumed the calculation. Ka-CHUNK! Ka-CHUNK! Ka-CHUNK! I shut it off again and left the room.
I assume that the next person who turned the calculator on got a nasty surprise.
I have no idea what might have eventually been required to reset the device and make it useable again.
Jim Propp
On Thu, Sep 11, 2014 at 4:12 PM, Henry Baker <hbaker1@pipeline.com> wrote:
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!
Some of IBM's early punch card machines were deliciously electromechanical, 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!
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.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Partial function; no value returned. -- Gene
________________________________ From: Dan Asimov <dasimov@earthlink.net> To: Eugene Salamin <gene_salamin@yahoo.com>; math-fun <math-fun@mailman.xmission.com> Sent: Thursday, September 11, 2014 1:55 PM Subject: Re: [math-fun] "Steampunk" mathematics?
I've long been curious: What was the answer?
--Dan
On Sep 11, 2014, at 1:49 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I used to divide by 0 all the time on the Marchant calculators.
I had Marchant calculators at Cal Tech in the 60's. The answer to dividing by zero was often a service call. It just kept on chugging and there was no obvious reset mechanism without taking off the cover. --Rich -----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Thursday, September 11, 2014 4:55 PM To: Eugene Salamin; math-fun Subject: Re: [math-fun] "Steampunk" mathematics? I've long been curious: What was the answer? --Dan On Sep 11, 2014, at 1:49 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I used to divide by 0 all the time on the Marchant calculators.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The calculators I did this to were easily stopped. Maybe a different brand. -- Gene
________________________________ From: Richard E. Howard <rich@richardehoward.com> To: 'math-fun' <math-fun@mailman.xmission.com> Sent: Thursday, September 11, 2014 6:45 PM Subject: Re: [math-fun] "Steampunk" mathematics?
I had Marchant calculators at Cal Tech in the 60's.
The answer to dividing by zero was often a service call.
It just kept on chugging and there was no obvious reset mechanism without taking off the cover.
--Rich -----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Thursday, September 11, 2014 4:55 PM To: Eugene Salamin; math-fun Subject: Re: [math-fun] "Steampunk" mathematics?
I've long been curious: What was the answer?
--Dan
On Sep 11, 2014, at 1:49 PM, Eugene Salamin via math-fun <math-fun@mailman.xmission.com> wrote:
I used to divide by 0 all the time on the Marchant calculators.
There's Lehmer's bicycle sieve: http://en.wikipedia.org/wiki/Lehmer_sieve Victor On Thu, Sep 11, 2014 at 2:23 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I've just become aware of the concept of "Steampunk", which is an alternate universe in which Babbage-style steam computers actually worked in the 19th Century & thereby changed the world. (Yes, I know; I'm Rip Van Winkling myself; no snarky remarks!)
Steampunk today means an exceedingly retro anachronistic concept -- e.g., a spring-wound software-defined digital radio -- so it doesn't actually require steam, per se.
https://en.wikipedia.org/wiki/Steampunk
Prior to the discovery of the Antikythera Mechanism, any mention of Archimedes in conjunction with geared wheels might have initially seemed "steampunk", but modern X-ray & gamma-ray images and recreations have proved it to be a remarkably sophisticated analog computer.
https://en.wikipedia.org/wiki/Antikythera_mechanism
Probably one of the coolest "steampunk" exercises of the 20th Century was economist William Phillips's 1949 "MONIC" water-based analog computer which represented the macro economy of the UK (called by one wag "hydraulic Keynesianism").
(Phillips could easily have been the inspiration for the TV series MacGyver -- parodied by SNL's "Gruber" -- as Phillips built all sorts of stuff while a Japanese POW -- including a radio in his shoe.)
https://en.wikipedia.org/wiki/William_Phillips_%28economist%29
https://en.wikipedia.org/wiki/MONIAC
I would propose that "steampunk mathematics" would be math that Cayley or Hamilton would not only understand, but might have written themselves.
No Bourbaki, no axioms of choice, no Goedel (or at least Goedel only in an analog computer world). No Hilbert (especially no Hilbert's Tenth Problem), no quantum theory, very little topology (except early knot theory, thanks to Cayley, etc.).
Unfortunately, my emphasis on 19th Century technology leaves out things like relay computers & Strowger switches, which I think would have been understood by, and really appealed to, the Victorians, so long as they don't include vacuum tubes or germanium diodes.
I think that a lot of computer graphics technology might have appealed to Cayley & Hamilton -- particularly the use of Hamilton's quaternions for "in-betweening".
It is conceivable that _fractal_ graphics, such as some of Gosper's cool pix, would have been understood by Cayley, at least. Cayley was perhaps the first to have notice the chaotic behavior of Newton's method for finding polynomial roots in the complex plane.
Computer algebra systems would have been very appealing to Cayley & Hamilton, as the 19th Century mathematicians all seem to have waded through prodigious amounts of symbolic calculations.
I'd be interested in any other proposals for "steampunk" mathematics.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify? Best, jj P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
Only have the copy (and bib.tiera.ru is down ) http://books.google.de/books?hl=de&lr=&id=0--3rcO7dMYC&oi=fnd&pg=PR5&dq="The+Book+of+Numbers"+Conway&ots=-cSHFYoQrH&sig=0orNe79DvsERJ1CkIeVwNCoXKec might allow you to see the pages in question. Best, jj * Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 18:02]:
I've never heard of it. Does anyone have a pdf of these pages?
At 12:02 AM 9/12/2014, Joerg Arndt wrote:
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
There's a mention of this on the second page of http://arxiv.org/pdf/physics/0308017.pdf --- it's not clear that it achieves anything that the classical "soup-plate trick" does not. WFL On 9/12/14, Henry Baker <hbaker1@pipeline.com> wrote:
I've never heard of it. Does anyone have a pdf of these pages?
At 12:02 AM 9/12/2014, Joerg Arndt wrote:
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course. Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns. Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull. Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short. Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats. WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model. Charles Greathouse Analyst/Programmer Case Western Reserve University On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Setting up only needs to be done once (in principle); then you can find as many shortest-paths as you like in constant time each. WFL On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Sure, just like you could make a table of all shortest paths and then spend only constant time for each. What's the best batch complexity for finding all shortest paths? Charles Greathouse Analyst/Programmer Case Western Reserve University On Fri, Sep 12, 2014 at 11:55 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Setting up only needs to be done once (in principle); then you can find as many shortest-paths as you like in constant time each. WFL
On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
So the wax-and-string model takes amortised constant time, whereas Dijkstra takes amortised linear time. http://en.wikipedia.org/wiki/Amortized_analysis Sincerely, Adam P. Goucher
Sent: Friday, September 12, 2014 at 5:10 PM From: "Charles Greathouse" <charles.greathouse@case.edu> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] "Steampunk" mathematics?
Sure, just like you could make a table of all shortest paths and then spend only constant time for each. What's the best batch complexity for finding all shortest paths?
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 11:55 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Setting up only needs to be done once (in principle); then you can find as many shortest-paths as you like in constant time each. WFL
On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Has to be at least O(V^2) on a serial processor at any rate, because there are that many routes. WFL On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sure, just like you could make a table of all shortest paths and then spend only constant time for each. What's the best batch complexity for finding all shortest paths?
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 11:55 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Setting up only needs to be done once (in principle); then you can find as many shortest-paths as you like in constant time each. WFL
On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]:
[...]
I'd be interested in any other proposals for "steampunk" mathematics.
[...]
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
http://en.wikipedia.org/wiki/Bead_sort On Fri, Sep 12, 2014 at 10:18 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Has to be at least O(V^2) on a serial processor at any rate, because there are that many routes. WFL
On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sure, just like you could make a table of all shortest paths and then spend only constant time for each. What's the best batch complexity for finding all shortest paths?
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 11:55 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
Setting up only needs to be done once (in principle); then you can find as many shortest-paths as you like in constant time each. WFL
On 9/12/14, Charles Greathouse <charles.greathouse@case.edu> wrote:
Sounds like O(E + V) to me, unless you assume that the input is in the form of a wax-and-string model.
Charles Greathouse Analyst/Programmer Case Western Reserve University
On Fri, Sep 12, 2014 at 10:51 AM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
* Henry Baker <hbaker1@pipeline.com> [Sep 12. 2014 08:17]: > [...] > > I'd be interested in any other proposals for "steampunk" > mathematics. > > [...] >
Does the "quaternion machine" described on pp.232-234 in the "Book of numbers" by Conway/Guy qualify?
Best, jj
P.S.: I recall building such a TEA laser. Turned out to be quite fiddly (very sensitive to the exact geometry).
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
You can cut a string into N lengths in constant time, independent of N? :-) Brent On 9/12/2014 7:51 AM, Fred Lunnon wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
As I pointed out earlier, "constant time" applies only to look-up. [Though when working out against resistance, I have observed that stretching the arms does tend to slow down somewhat with repetition ...] Set-up has to take time at least order #edges, whether on SWASC or on boring old serial computer, because that's the number of data variables. WFL On 9/12/14, meekerdb <meekerdb@verizon.net> wrote:
You can cut a string into N lengths in constant time, independent of N? :-)
Brent
On 9/12/2014 7:51 AM, Fred Lunnon wrote:
The SWASC (Sealing-Wax and String Computer) had a walk on and trip up part when I discussed finding shortest paths between towns on a road-map in my Algorithms course.
Set-up: (1) Cut the string into segments representing town-to-town distances; (2) Join the ends together with wax blobs representing towns.
Operation: (3) Grasp start and finish towns in left and right hand resp. (4) Pull.
Output: (5) The straight line of string gives the shortest route. Unless you pulled too hard. Or your arms were too short.
Performance: constant time: knocking Dijkstra's algorithm into a cocked hat. Along with itself when it overheats.
WFL
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Does this qualify: http://arxiv.org/abs/1106.0423 ? Victor On Thu, Sep 11, 2014 at 2:23 PM, Henry Baker <hbaker1@pipeline.com> wrote:
I've just become aware of the concept of "Steampunk", which is an alternate universe in which Babbage-style steam computers actually worked in the 19th Century & thereby changed the world. (Yes, I know; I'm Rip Van Winkling myself; no snarky remarks!)
Steampunk today means an exceedingly retro anachronistic concept -- e.g., a spring-wound software-defined digital radio -- so it doesn't actually require steam, per se.
https://en.wikipedia.org/wiki/Steampunk
Prior to the discovery of the Antikythera Mechanism, any mention of Archimedes in conjunction with geared wheels might have initially seemed "steampunk", but modern X-ray & gamma-ray images and recreations have proved it to be a remarkably sophisticated analog computer.
https://en.wikipedia.org/wiki/Antikythera_mechanism
Probably one of the coolest "steampunk" exercises of the 20th Century was economist William Phillips's 1949 "MONIC" water-based analog computer which represented the macro economy of the UK (called by one wag "hydraulic Keynesianism").
(Phillips could easily have been the inspiration for the TV series MacGyver -- parodied by SNL's "Gruber" -- as Phillips built all sorts of stuff while a Japanese POW -- including a radio in his shoe.)
https://en.wikipedia.org/wiki/William_Phillips_%28economist%29
https://en.wikipedia.org/wiki/MONIAC
I would propose that "steampunk mathematics" would be math that Cayley or Hamilton would not only understand, but might have written themselves.
No Bourbaki, no axioms of choice, no Goedel (or at least Goedel only in an analog computer world). No Hilbert (especially no Hilbert's Tenth Problem), no quantum theory, very little topology (except early knot theory, thanks to Cayley, etc.).
Unfortunately, my emphasis on 19th Century technology leaves out things like relay computers & Strowger switches, which I think would have been understood by, and really appealed to, the Victorians, so long as they don't include vacuum tubes or germanium diodes.
I think that a lot of computer graphics technology might have appealed to Cayley & Hamilton -- particularly the use of Hamilton's quaternions for "in-betweening".
It is conceivable that _fractal_ graphics, such as some of Gosper's cool pix, would have been understood by Cayley, at least. Cayley was perhaps the first to have notice the chaotic behavior of Newton's method for finding polynomial roots in the complex plane.
Computer algebra systems would have been very appealing to Cayley & Hamilton, as the 19th Century mathematicians all seem to have waded through prodigious amounts of symbolic calculations.
I'd be interested in any other proposals for "steampunk" mathematics.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (14)
-
Adam P. Goucher -
Charles Greathouse -
Dan Asimov -
Dave Dyer -
Eugene Salamin -
Fred Lunnon -
Henry Baker -
James Propp -
Joerg Arndt -
meekerdb -
Mike Stay -
Richard E. Howard -
rkg -
Victor Miller