Analog Computers

Yeah I remember reading the chatter about FPAA's back in the 90's.

It seemed like an exciting idea, but it never took off perhaps because the kind of accuracy that makes it worthwhile was not achievable?

I got some FPAA chips I assume you're referring to, the ones I've got are Anadigm ones, I need to get round to using them. The downside is the ones I've got, simply make use of switched capacitors for creation of filters, so there will be some form of discretization in the temporal domain I guess.

> 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.

-----------------

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.

I recall checking a few years ago, and it would have taken about 40,000 high-end GPUs to match the common estimates of the computing power of the brain. It's no doubt much lower now.

The problem is that it takes far more than raw computing power to make AI. We have sufficient computing power but we don't know how to use it, not even close.

As for how it's measured, it's basically a matter of guesstimating the computing power of a single neuron based on its inputs, outputs, and the computation it appears to do to map between them, and then multiplying by the number of neurons in the brain. This is horribly imprecise so estimates vary a lot (describing it as "38" gives the estimate way too much credit, should probably say 10 or 100 instead) but they're probably in the very rough ballpark.

I always hear such things from EE's. So, what's your thoughts on stuff like this in terms of analog "always" being more expensive or power hungry:

http://www.cisl.columbia.edu/grads/gcowan/vlsianalog.pdf

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.325...

Now, I won't argue with cheaper to develop since analog is manual with a lot of issues to contend with. I'm just wondering if there are more applications that can get huge speedups at lower power or cost than digital. I know the ASIC makers in power-sensitive spaces are already moving parts of their chips to analog for power reduction. That's what mixed-signal people tell me anyway: the specifics are often secret. So, I have to dig into CompSci looking for what they've tried.