You miss the crucial difference between an "analog computer" and a
digital computer: algorithms.
I just explained about
"partitioning." I work in advanced development now, but I used to work in
system design. We were responsible for saying "this goes in analog; this goes
in digital; and this goes in software." It can be the same algorithm in any
case, but some things work better in one domain or the other.
An
analog device (and a DDA – digital differential analyzer – which is its
approximate equivalent using digital technology) is a single-purpose circuit,
built in a space domain, but operating in a time domain.
Be
careful, or you will make the case that regular software is not patentable
because it operates at a higher level of abstraction, but that interpreted
software (e.g. emulating a DDA) might be patentable in some cases, merely
because it emulates a lower level of abstraction.
Most analog
"computers" have changeable wiring, so that the elements can be reused for the
next device, but hardly any have analog switches that allow the elements to
simulate different functions within a single run.
Analog FPGAs
are available. I always see a lot of hand-waving about how the
reconfigurability should affect patentability (btw, I believe that perhaps it
should, but not in the sense most do. Perhaps I should write a paper.) It's
still math, whether you can choose different functions on the fly or
not.
The free variable is always time, although the time can be
ignored when you're interested in the relationship among different functions of
time: element switching would cause serious problems in the free variable, thus
in the function of the analog device.
Yes, "computing" per se
with analog is a challenging problem, which has been overcome in a lot of
(most?) cases by quantizing and using circuits in a fully saturated mode. If
you're going to be that pedantic, you will have to, at some point, acknowledge
that digital computers are analog at the bottom.
In brief, each
analog (or DDA) element is dedicated to one specific purpose at all times of
interest.
There are examples where this is not true, but I'll let
it ride.
In a digital computer, the elements are time-shared — the
adder, for instance, (assuming a single ALU arguendo but without loss of
generality) is used for each summation in the whole run, by multiplexing the
operands into and out of it. All elements of the digital computer are similarly
multiplexed.
True.
The multiplexing is what the
algorithm is about, at this level of discourse: in executing the algorithm, the
multiplexing of the elements follows the math of the
algorithm.
And here we get to the crux of the matter. Yes, the
algorithm handles the multiplexing, but the algorithm also expresses that which
is to be multiplexed. When I write something in Verilog, I can choose to write
"synthesizable" verilog -- that which can be directly translated into hardware
where time (based on a clock tick) is the free variable according to your
reasoning. Or I can write a testbench using Verilog as a purely software
language.
But if I do write synthesizable verilog, it can also be used
directly as software, OR (e.g. for your DDA), I can actually create hardware out
of it. Are you really arguing that the exact same verilog could express a
patentable invention if I used it that way, but not if I used it as
software?
This multiplexing is not feasible in the analog device
(even if the time issue could be resolved), since the characteristics of the
analog signals do not cater to stabilizing the signals when the algorithm would
require them to be stable (i. e., when the particular signal is not an operand
to a computing element).
Yes, it is a lot of effort to "reuse"
analog components, as you state, but it is not impossible, and is actually done
on a regular basis. But that's just an aside.
This stability
requirement is met, in the digital computer, by some storage element (or state
element, if you prefer – depending on the discourse level you're
at).
And, as you know, there are storage elements available in
analog, as well, such as the lowly capacitor (which is, in fact, the basis for
dynamic RAM). BTW, did I mention that all digital is analog, and that, for
example, even a static RAM is implemented with analog transistors operating in a
saturated mode?
The DDA allows for storage, and thus allows the
time variable to be decoupled from real time, but is still a dedicated device.
True, a DDA can be simulated by an algorithm, but that's a simulation, not a
true DDA.
But what happens when the software (what you call a
simulation) actually runs fast enough to control stuff in the real world? Or
what happens when the hardware engineer decides to reuse his expensive
multiplier by adding different registers and making the DDA reconfigurable on
the fly?
From a slightly different perspective: an analog gizmo
uses real-time as the free variable in the computation it's analogizing: it's
really the only free variable that's available to it. The "computing" elements
are distinct in space.
OK, but there is nothing in patent law
that states that time is the only allowed free variable.
A digital
computer 'rotates' the computation into a realm where time is an artifact of the
algorithm (if it appears at all), and uses real-time to follow the algorithm and
make multiple uses of a small number of available computational
facilities.
Sure.
Analog computers inherently
operate in the time domain, where algorithms are irrelevant; digital computers
operate in a more space-like domain, using algorithms.
But I can
code a solution to a problem in Verilog, and then I can run it as hardware or
software. Or I can code a problem as a schematic, and then build it or run a
Spice simulation on it. I know several people say the simulation is not "real"
but we actually package up spice in a package that finds solutions for our
customers more quickly than if they built the hardware.
Yes, the commonly used
meaning of algorithm includes the control path (allowing the multiplexing you
seem to think changes everything), but it also includes the data path. To wave
your hands and try to convince that the algorithm is only the control path is
unhelpful.
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