[math-fun] Non-electronic analogue computers
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots? That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation. As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer? Jim Propp
There is an excellent book for this, Walter J. Karplus, Analog Simulation: Solution of Field Equations, 1958. Almost certainly out of print, but worth looking up.
On Jan 29, 2018, at 1:09 PM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
https://en.wikipedia.org/wiki/Hydraulic_analogy http://www.msipos.info/news-feed/2016/2/4/the-fascinating-and-forgotten-worl... On Mon, Jan 29, 2018 at 6:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp _______________________________________________ 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.math.ucr.edu/~mike http://reperiendi.wordpress.com
On Jan 29, 2018, at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots? Jim, you have to go beyond linear components to make a computer. For example, static friction that breaks down at some force threshold might help you make a diode.
-Veit
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
Veit is right: if you want a general-purpose computer, you need nonlinear elements. But if you want a special-purpose computer for solving a restricted class of problems, linear elements might suffice. Jim On Mon, Jan 29, 2018 at 11:27 AM, Veit Elser <ve10@cornell.edu> wrote:
On Jan 29, 2018, at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots? Jim, you have to go beyond linear components to make a computer. For example, static friction that breaks down at some force threshold might help you make a diode.
-Veit
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Actually, now that I've thought a little harder about what I'm after, namely a cool exhibit for the Museum of Mathematics, whose core audience consists of kids who haven't seen calculus, I realize that what I want is an analogue system for solving ALGEBRAIC equations, as opposed to DIFFERENTIAL equations. So I'm asking for a lot less! As an example of the kind of thing that might be suitable, check out Mark Levi's recent proposal for hydrostatic solution of polynomial equations: https://sinews.siam.org/Details-Page/a-water-based-solution-of-polynomial-eq... Jim Propp On Mon, Jan 29, 2018 at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
It sounds like you should show them linkages: https://en.wikipedia.org/wiki/Kempe%27s_universality_theorem - Cris
On Jan 29, 2018, at 11:09 AM, James Propp <jamespropp@gmail.com> wrote:
Actually, now that I've thought a little harder about what I'm after, namely a cool exhibit for the Museum of Mathematics, whose core audience consists of kids who haven't seen calculus, I realize that what I want is an analogue system for solving ALGEBRAIC equations, as opposed to DIFFERENTIAL equations.
So I'm asking for a lot less!
As an example of the kind of thing that might be suitable, check out Mark Levi's recent proposal for hydrostatic solution of polynomial equations:
https://sinews.siam.org/Details-Page/a-water-based-solution-of-polynomial-eq...
Jim Propp
On Mon, Jan 29, 2018 at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Gitton's water clock implemented a counter using tanks and siphons. http://www.marcdatabase.com/~lemur/dm-gitton.html#logictheory I saw a version of this at the Deutsches Museum in Munich. Here's a different design for water-based circuits: https://www.youtube.com/watch?v=6qP9HfUOCN4&t=10m3s On Mon, Jan 29, 2018 at 12:36 PM, Cris Moore <moore@santafe.edu> wrote:
It sounds like you should show them linkages: https://en.wikipedia.org/wiki/Kempe%27s_universality_theorem
- Cris
On Jan 29, 2018, at 11:09 AM, James Propp <jamespropp@gmail.com> wrote:
Actually, now that I've thought a little harder about what I'm after, namely a cool exhibit for the Museum of Mathematics, whose core audience consists of kids who haven't seen calculus, I realize that what I want is an analogue system for solving ALGEBRAIC equations, as opposed to DIFFERENTIAL equations.
So I'm asking for a lot less!
As an example of the kind of thing that might be suitable, check out Mark Levi's recent proposal for hydrostatic solution of polynomial equations:
https://sinews.siam.org/Details-Page/a-water-based-solution-of-polynomial-eq...
Jim Propp
On Mon, Jan 29, 2018 at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
_______________________________________________ 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.math.ucr.edu/~mike http://reperiendi.wordpress.com
Here's someone's copy of his clock: https://c1.staticflickr.com/3/2907/14489121635_19f4c45d82_b.jpg On Mon, Jan 29, 2018 at 12:58 PM, Mike Stay <metaweta@gmail.com> wrote:
Gitton's water clock implemented a counter using tanks and siphons. http://www.marcdatabase.com/~lemur/dm-gitton.html#logictheory I saw a version of this at the Deutsches Museum in Munich.
Here's a different design for water-based circuits: https://www.youtube.com/watch?v=6qP9HfUOCN4&t=10m3s
On Mon, Jan 29, 2018 at 12:36 PM, Cris Moore <moore@santafe.edu> wrote:
It sounds like you should show them linkages: https://en.wikipedia.org/wiki/Kempe%27s_universality_theorem
- Cris
On Jan 29, 2018, at 11:09 AM, James Propp <jamespropp@gmail.com> wrote:
Actually, now that I've thought a little harder about what I'm after, namely a cool exhibit for the Museum of Mathematics, whose core audience consists of kids who haven't seen calculus, I realize that what I want is an analogue system for solving ALGEBRAIC equations, as opposed to DIFFERENTIAL equations.
So I'm asking for a lot less!
As an example of the kind of thing that might be suitable, check out Mark Levi's recent proposal for hydrostatic solution of polynomial equations:
https://sinews.siam.org/Details-Page/a-water-based-solution-of-polynomial-eq...
Jim Propp
On Mon, Jan 29, 2018 at 8:09 AM, James Propp <jamespropp@gmail.com> wrote:
Anyone know of any good designs for an easy-to-make analogue computer based on springs, masses, and dashpots?
That is, we want a supply of easily-interconnectable components that we can combine in ways that correspond to a prescribed differential equation, so that the behavior of the system will be a solution of the equation.
As I recall, there’s also a way to get hydraulic analogues of LRC networks (though I forget what the three sorts of components are called); is there a good design for a hydraulic computer?
Jim Propp
_______________________________________________ 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.math.ucr.edu/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://www.math.ucr.edu/~mike http://reperiendi.wordpress.com
participants (5)
-
Cris Moore -
James Propp -
Mike Stay -
Tom Knight -
Veit Elser