> Luckily, with today’s electronic technology it is possible to build integrated circuits containing not only the basic computing elements but also a crossbar that can be programmed from an attached digital computer, thus eliminating the rat’s nest of wires altogether.
This is the most important paragraph in the entire article.
Analog Computers can be made very small. It'd take an ASIC, but the 741 OpAmp was less than 100 transistors. A more modern OpAmp might be under 1000 transistors... although noise issues would be abound.
Bernd Ulmann has developed a methodology that performs non-trivial computations (such as: http://analogparadigm.com/downloads/alpaca_4.pdf), but its still hand-programmed by connecting wires together.
If it were digitally programmed with a digital crossbar switch (consisting of CMOS Analog Gates instead), then it'd be controllable by a real computer.
I think what Ulmann is arguing here... is to use analog computers as a "differential equation accelerator". Perform a lot of computations in the digital world, but if you need to simulate a differential equation, then simulate it on an analog circuit instead.
And there are a large number of interesting mathematical problems that are described as differential equations.
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The main issues, as far as I can see, would be the multiplier, logarithm, and exponential functions. IIRC, these are created using a bipolar transistor... and modern manufacturing doesn't really mix BJT with MOSFET.
I mean, IGBT transistors exist, but modern computers are basically MOSFET all the way down. MOSFETs would be able to make a lot of things though: digital potentiometers / variable resistors... the crossbar switch, capacitors, resistors, and OpAmps.
And all of those can simulate addition, subtraction, derivatives and integrals. More than enough to build a "differential equation accelerator" that the author proposes.
This is the most important paragraph in the entire article.
Analog Computers can be made very small. It'd take an ASIC, but the 741 OpAmp was less than 100 transistors. A more modern OpAmp might be under 1000 transistors... although noise issues would be abound.
Bernd Ulmann has developed a methodology that performs non-trivial computations (such as: http://analogparadigm.com/downloads/alpaca_4.pdf), but its still hand-programmed by connecting wires together.
If it were digitally programmed with a digital crossbar switch (consisting of CMOS Analog Gates instead), then it'd be controllable by a real computer.
I think what Ulmann is arguing here... is to use analog computers as a "differential equation accelerator". Perform a lot of computations in the digital world, but if you need to simulate a differential equation, then simulate it on an analog circuit instead.
And there are a large number of interesting mathematical problems that are described as differential equations.
-----------------
The main issues, as far as I can see, would be the multiplier, logarithm, and exponential functions. IIRC, these are created using a bipolar transistor... and modern manufacturing doesn't really mix BJT with MOSFET.
I mean, IGBT transistors exist, but modern computers are basically MOSFET all the way down. MOSFETs would be able to make a lot of things though: digital potentiometers / variable resistors... the crossbar switch, capacitors, resistors, and OpAmps.
And all of those can simulate addition, subtraction, derivatives and integrals. More than enough to build a "differential equation accelerator" that the author proposes.