28 ms·

I know a military contractor working on some pretty cool stuff, especially back in the day. On one of their projects they had to solve some really gnarly partia

I know a military contractor working on some pretty cool stuff, especially back in the day. On one of their projects they had to solve some really gnarly partial differential equation and weren't really getting anywhere. Since what they actually wanted were values (not the algebraic solution) what they ended up doing is building the equivalent circuit and measured what the voltage and current was in the circuit to get the values that they needed for some completely different domain. I always thought that that way of thinking was pretty neat. Can the same abstraction have a different physical manifestation that's cheap to create? If you kinda squint a bit, it's what we do with computers.

trenchgun 6y ago
Isn't that just analog computing? Or is it something more fancy?
- enriquto 6y ago
  This is analog computing, and it is really cool. Yet, I guess if it corresponds to a circuit it should be more an ODE than a PDE (unless your "circuit" involves large pieces of surface of non-uniform resistivity).
  - 3pt14159 6y ago
    It was a true PDE, not an ODE. The circuit was non-trivial, but though I knew PDEs at the time he told the story, I'd never used them on electronics (only heat / pressure flow, and other physical engineering stuff) so I couldn't really understand what he was saying.
  - jonah-archive 6y ago
    You can definitely do this! Check out Karplus's "Analog Simulation" for examples with conductive fluids and resistance networks: https://archive.org/details/analogsimulation0000karp https://archive.org/details/analogsimulation0000karp
- marcosdumay 6y ago
  Yes. And a numerical calculus software would probably get there faster and with less work.
  - jhayward 6y ago
    and higher precision.
  - enriquto 6y ago
    Numerical solution of PDE is not really a solved problem. If your PDE involves shockwaves or turbulence (which happen for really simple PDEs) then the methods to compute solutions get incredibly fancy. There's no "black box" solution for numerical PDE, as there is for ordinary equations.
    - marcosdumay 6y ago
      If you can solve with an analog computer, without problems with metastability, oscillations or excessive noise, then you can solve it with numeric calculus too. Those computers have much more strict limitations than digital math.
      - 3pt14159 6y ago
        I should call the guy up sometime and get the details about what they were working. It wasn't a run of the mill analog computer, but who knows how novel it really was.
      - klyrs 6y ago
        Your description covers pretty much every quantum computer ever conceived. How certain are you?
        sudosysgen 6y ago
        Not sure you can call any of the actual quantum computers we've made "analog", but if you're talking about the quantum annealment machines, they are generally more limited and take longer than an equivalent supercomputing cluster.
- adamnemecek 6y ago
  It is. I hope it comes back in the photonic form.
curiousgal 6y ago
Banks do that all the time with monte carlo simulation. Can't get a closed form solution? Simulate every possible outcome and aggregate them.
- filmor 6y ago
  This is neither how a Monte-Carlo process works (it's sampling the possible outcomes randomly, not simulating all outcomes), nor what is described here (building a physical system where an observable value is described by the differential equation one is trying to solve).
  - curiousgal 6y ago
    In practice the number of simulated scenarii is quite large which is what I meant by "every". Not rigorous though, I concur. Monte Carlo methods are used to solve partial differential equations, I found both approaches similar in the sense that they look at how the system actually/could behave, instead of looking at the equations solely.
  - stagehn 6y ago
    This is a pedantic response. There isn't an important difference between building a physical system and building a system in code whose generating process is that which you're trying to model. And everyone knew he didn't mean every outcome literally.
- CPLX 6y ago
  You’re talking more about goal-seeking functions right? That’s the one I always see in a finance context.
- seanhunter 6y ago
  Worked in the securities division of a leading investment bank for 8 years including on the equities exotics and hybrids trading desk. And I can confirm that we used to use MC whenever we had something we couldn't price using a closed form method. That said, it's a lot slower and more compute intensive so when you could use a grid pricer or pde solver or whatever people would use that instead. You're not really simulating every outcome, just a "large enough" representative sample. As an aside, my dad was a chemical engineer and Newton-Raphson was his equivalent everything-is-a-nail numerical method. We used to use brent root and monte carlo simulation in the same way. Numerical methods are awesome in general.
jackfoxy 6y ago
Isn't that the basis of analog computing? https://en.wikipedia.org/wiki/Analog_computer https://en.wikipedia.org/wiki/Analog_computer
lopmotr 6y ago
Engineers used to use the shape of a soap bubble to calculate the torsional stiffness or perhaps stress distribution of a non-circular shaft. http://www.newsteelconstruction.com/wp/wp-content/uploads/TechPaper/NSCMar12tech.pdf http://www.newsteelconstruction.com/wp/wp-content/uploads/Te...
- ghj 6y ago
  Soap film is also used to solve the steiner problem: https://www.youtube.com/watch?v=dAyDi1aa40E https://www.youtube.com/watch?v=dAyDi1aa40E
kens 6y ago
I've been doing some restoration on an analog computer. While it seems bizarre now to solve a problem with analog circuits instead of a digital computer, analog computers were a reasonable approach until about the 1970s. The basic idea of an analog computer is you use op amps to sum voltages. Integration is easy, by adding a capacitor. By hooking up op amps, capacitors, and resistors (usually with a plugboard), you can quickly and easily solve differential equations. (Surprisingly, multiplication by a non-constant value is hard with an analog computer.) The nice thing about analog computers is they gave the answer almost instantaneously. You could turn the dials and experiment with different parameters interactively. A digital computer in 1970, on the other hand, might take minutes to solve the same equation. This also made analog computers useful for real-time applications such as flight simulators. A big problem with analog computers is that the accuracy is limited by your components. If you want 0.1% accuracy, you need expensive 0.1% resistors and capacitors. With a digital computer, you can get as many bits of accuracy as you want using cheap components. Basically, Moore's law killed off analog computers.
- TrackerFF 6y ago
  Just fire up any older electronics textbook, and they'll probably have examples of integrator and summing circuits solving differential equations. At least that's what we had in our control (engineering) books.
  - sudosysgen 6y ago
    In my dad's Calculus II equivalent class in Morocco, one of the question in their exam was to built the circuit to solve a given differential equation. Pretty neat! That being said, that exam was substantially shorter and easier than the Cal II exam I had to take!
- qppo 6y ago
  > multiplication by a non-constant value is hard with an analog computer Researching this topic also qualifies you to write technobabble for sci-fi movies. Like "operational trans impedance amplifier."
andrewjl 6y ago
Is this something an FPGA or something similar could do? Would be interesting to know of any home-brew attempts at this out there.
- bashinator 6y ago
  I wonder how difficult it would be to re-purpose a modular analog audio synthesizer for this. Since they're direct descendants of analog computers in the first place.
  - andrewjl 6y ago
    There are ASICs out there that simulate analog synths, such Universal Audio. Brings to mind some interesting pure software approaches if that were the case.
- klyrs 6y ago
  Do you mean FPAA? Totally a thing. https://en.m.wikipedia.org/wiki/Field-programmable_analog_array https://en.m.wikipedia.org/wiki/Field-programmable_analog_ar...
  - XMPPwocky 6y ago
    FPAAs don't really exist as products you can buy, as far as I know (unlike FPGAs, which are a very mature technology to the point that I suspect there's nontrivial (say, >5%) odds the average HN reader owns something with a FPGA in it somewhere.))
  - andrewjl 6y ago
    I didn't know about this. It's curious that the article mentions that recently (2016) improved FPAAs were demonstrated. Perhaps an opportunity where there wasn't one before.
dzolob 6y ago
I knew a guy who built specific surfaces with plaster and threw marbles at them to find some special solutions to nonlinear mechanics problems. He thought of himself as an experimental mathematician.
jiggawatts 6y ago
There is practically no scenario where a digital computer couldn't do better if what you wanted was a numerical result and not a symbolic one. It's simply criminal how underutilised the technique of Automatic Differentiation is! It can solve incredibly complex differentials to machine precision, good numerical stability, and minimal tuning or hand-holding. Lots of these "difficult" problems aren't, it's just that people aren't aware of the solution because it's not commonly taught in a University setting. Automatic Differentiation is one of those techniques that's "boring" and "numerical", so there are no courses that teach it.
- ampdepolymerase 6y ago
  Doesn't literally every optimisation and ML class teaches it nowadays?
  - jiggawatts 6y ago
    Actually, no! You would think so, but again, it's a boring numerical technique so it is all too often sidelined in favour of the more "flashy" symbolic techniques. An awful lot of tertiary education has been caught up in the publish-or-perish mentality. Unfortunately for AD, it is not "impressive". Differentiating hideously difficult expressions symbolically is impressive. Publishing a paper packed full of enormous, scary looking expressions is impressive. Merely saying that "we used AD and it worked just fine" is unimpressive. For decades now we've been incentivizing intellectual wankery over practical utility.
    - lambdatronics 6y ago
      Here's an example from my field: "The derivatives of the finite-build coils are computed -- with almost no additional effort from the authors -- using automatic differentiation." Well, what kind of scientist are you, if you are too lazy to take derivatives? /sarcasm http://meetings.aps.org/Meeting/DPP20/Session/BP14.32 http://meetings.aps.org/Meeting/DPP20/Session/BP14.32
- theemathas 6y ago
Loranubi 6y ago
Also see Optical Fourier co-processors for a similar example.

trenchgun 6y ago

Isn't that just analog computing? Or is it something more fancy?

enriquto 6y ago
This is analog computing, and it is really cool. Yet, I guess if it corresponds to a circuit it should be more an ODE than a PDE (unless your "circuit" involves large pieces of surface of non-uniform resistivity).
- 3pt14159 6y ago
  It was a true PDE, not an ODE. The circuit was non-trivial, but though I knew PDEs at the time he told the story, I'd never used them on electronics (only heat / pressure flow, and other physical engineering stuff) so I couldn't really understand what he was saying.
- jonah-archive 6y ago
  You can definitely do this! Check out Karplus's "Analog Simulation" for examples with conductive fluids and resistance networks: https://archive.org/details/analogsimulation0000karp https://archive.org/details/analogsimulation0000karp
marcosdumay 6y ago
Yes. And a numerical calculus software would probably get there faster and with less work.
- jhayward 6y ago
  and higher precision.
- enriquto 6y ago
  Numerical solution of PDE is not really a solved problem. If your PDE involves shockwaves or turbulence (which happen for really simple PDEs) then the methods to compute solutions get incredibly fancy. There's no "black box" solution for numerical PDE, as there is for ordinary equations.
  - marcosdumay 6y ago
    If you can solve with an analog computer, without problems with metastability, oscillations or excessive noise, then you can solve it with numeric calculus too. Those computers have much more strict limitations than digital math.
    - 3pt14159 6y ago
      I should call the guy up sometime and get the details about what they were working. It wasn't a run of the mill analog computer, but who knows how novel it really was.
    - klyrs 6y ago
      Your description covers pretty much every quantum computer ever conceived. How certain are you?
      - sudosysgen 6y ago
        Not sure you can call any of the actual quantum computers we've made "analog", but if you're talking about the quantum annealment machines, they are generally more limited and take longer than an equivalent supercomputing cluster.
adamnemecek 6y ago
It is. I hope it comes back in the photonic form.

curiousgal 6y ago

Banks do that all the time with monte carlo simulation. Can't get a closed form solution? Simulate every possible outcome and aggregate them.

filmor 6y ago
This is neither how a Monte-Carlo process works (it's sampling the possible outcomes randomly, not simulating all outcomes), nor what is described here (building a physical system where an observable value is described by the differential equation one is trying to solve).
- curiousgal 6y ago
  In practice the number of simulated scenarii is quite large which is what I meant by "every". Not rigorous though, I concur. Monte Carlo methods are used to solve partial differential equations, I found both approaches similar in the sense that they look at how the system actually/could behave, instead of looking at the equations solely.
- stagehn 6y ago
  This is a pedantic response. There isn't an important difference between building a physical system and building a system in code whose generating process is that which you're trying to model. And everyone knew he didn't mean every outcome literally.
CPLX 6y ago
You’re talking more about goal-seeking functions right? That’s the one I always see in a finance context.
seanhunter 6y ago
Worked in the securities division of a leading investment bank for 8 years including on the equities exotics and hybrids trading desk. And I can confirm that we used to use MC whenever we had something we couldn't price using a closed form method. That said, it's a lot slower and more compute intensive so when you could use a grid pricer or pde solver or whatever people would use that instead. You're not really simulating every outcome, just a "large enough" representative sample. As an aside, my dad was a chemical engineer and Newton-Raphson was his equivalent everything-is-a-nail numerical method. We used to use brent root and monte carlo simulation in the same way. Numerical methods are awesome in general.

jackfoxy 6y ago

Isn't that the basis of analog computing? https://en.wikipedia.org/wiki/Analog_computer https://en.wikipedia.org/wiki/Analog_computer

lopmotr 6y ago

Engineers used to use the shape of a soap bubble to calculate the torsional stiffness or perhaps stress distribution of a non-circular shaft. http://www.newsteelconstruction.com/wp/wp-content/uploads/TechPaper/NSCMar12tech.pdf http://www.newsteelconstruction.com/wp/wp-content/uploads/Te...

ghj 6y ago
Soap film is also used to solve the steiner problem: https://www.youtube.com/watch?v=dAyDi1aa40E https://www.youtube.com/watch?v=dAyDi1aa40E

kens 6y ago

I've been doing some restoration on an analog computer. While it seems bizarre now to solve a problem with analog circuits instead of a digital computer, analog computers were a reasonable approach until about the 1970s. The basic idea of an analog computer is you use op amps to sum voltages. Integration is easy, by adding a capacitor. By hooking up op amps, capacitors, and resistors (usually with a plugboard), you can quickly and easily solve differential equations. (Surprisingly, multiplication by a non-constant value is hard with an analog computer.) The nice thing about analog computers is they gave the answer almost instantaneously. You could turn the dials and experiment with different parameters interactively. A digital computer in 1970, on the other hand, might take minutes to solve the same equation. This also made analog computers useful for real-time applications such as flight simulators. A big problem with analog computers is that the accuracy is limited by your components. If you want 0.1% accuracy, you need expensive 0.1% resistors and capacitors. With a digital computer, you can get as many bits of accuracy as you want using cheap components. Basically, Moore's law killed off analog computers.

TrackerFF 6y ago
Just fire up any older electronics textbook, and they'll probably have examples of integrator and summing circuits solving differential equations. At least that's what we had in our control (engineering) books.
- sudosysgen 6y ago
  In my dad's Calculus II equivalent class in Morocco, one of the question in their exam was to built the circuit to solve a given differential equation. Pretty neat! That being said, that exam was substantially shorter and easier than the Cal II exam I had to take!
qppo 6y ago
> multiplication by a non-constant value is hard with an analog computer Researching this topic also qualifies you to write technobabble for sci-fi movies. Like "operational trans impedance amplifier."

andrewjl 6y ago

Is this something an FPGA or something similar could do? Would be interesting to know of any home-brew attempts at this out there.

bashinator 6y ago
I wonder how difficult it would be to re-purpose a modular analog audio synthesizer for this. Since they're direct descendants of analog computers in the first place.
- andrewjl 6y ago
  There are ASICs out there that simulate analog synths, such Universal Audio. Brings to mind some interesting pure software approaches if that were the case.
klyrs 6y ago
Do you mean FPAA? Totally a thing. https://en.m.wikipedia.org/wiki/Field-programmable_analog_array https://en.m.wikipedia.org/wiki/Field-programmable_analog_ar...
- XMPPwocky 6y ago
  FPAAs don't really exist as products you can buy, as far as I know (unlike FPGAs, which are a very mature technology to the point that I suspect there's nontrivial (say, >5%) odds the average HN reader owns something with a FPGA in it somewhere.))
- andrewjl 6y ago
  I didn't know about this. It's curious that the article mentions that recently (2016) improved FPAAs were demonstrated. Perhaps an opportunity where there wasn't one before.

dzolob 6y ago

I knew a guy who built specific surfaces with plaster and threw marbles at them to find some special solutions to nonlinear mechanics problems. He thought of himself as an experimental mathematician.

jiggawatts 6y ago

There is practically no scenario where a digital computer couldn't do better if what you wanted was a numerical result and not a symbolic one. It's simply criminal how underutilised the technique of Automatic Differentiation is! It can solve incredibly complex differentials to machine precision, good numerical stability, and minimal tuning or hand-holding. Lots of these "difficult" problems aren't, it's just that people aren't aware of the solution because it's not commonly taught in a University setting. Automatic Differentiation is one of those techniques that's "boring" and "numerical", so there are no courses that teach it.

ampdepolymerase 6y ago
Doesn't literally every optimisation and ML class teaches it nowadays?
- jiggawatts 6y ago
  Actually, no! You would think so, but again, it's a boring numerical technique so it is all too often sidelined in favour of the more "flashy" symbolic techniques. An awful lot of tertiary education has been caught up in the publish-or-perish mentality. Unfortunately for AD, it is not "impressive". Differentiating hideously difficult expressions symbolically is impressive. Publishing a paper packed full of enormous, scary looking expressions is impressive. Merely saying that "we used AD and it worked just fine" is unimpressive. For decades now we've been incentivizing intellectual wankery over practical utility.
  - lambdatronics 6y ago
    Here's an example from my field: "The derivatives of the finite-build coils are computed -- with almost no additional effort from the authors -- using automatic differentiation." Well, what kind of scientist are you, if you are too lazy to take derivatives? /sarcasm http://meetings.aps.org/Meeting/DPP20/Session/BP14.32 http://meetings.aps.org/Meeting/DPP20/Session/BP14.32
theemathas 6y ago

Loranubi 6y ago

Also see Optical Fourier co-processors for a similar example.