The Power of Analogs
The Power of Analogs
Bernd Ulmann
10-DEC-2010
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The Power of Analogs – Bernd Ulmann
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1. What it is (not) about?
What it is (not) about?
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The Power of Analogs – Bernd Ulmann
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What it is not about?
1. What it is (not) about?
. . . it’s not about ”The Analogs”, a Polish street punk band. . .
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What it is not about?
1. What it is (not) about?
. . . it’s also not about the ”Dueling Analogs”, a web comic by
Steve Napierski1 :
1
I would like to thank Steve for his permission to use the above comic strip
for this talk.
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What it is about, then?
1. What it is (not) about?
Since we will not talk about Polish street punk or Dueling Analogs
(which, by the way, are both rather funny); what, then, is the
theme of this talk?
It is about models – so called analogs – and their (future) use in
simulation and computation.
We will distinguish direct and indirect analogs (like soap bubbles
for minimal surfaces and electrical circuits simulating a mechanical
system).
The art of analog computation/simulation has been largely
forgotten (like Atari’s ET game mentioned in the Dueling Analogs
comic) but this technology has enough potential to rise again to
new heights in the future employing state of the art devices like
FPGAs etc.
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Direct Analogies
1. What it is (not) about?
We are not interested in direct analogies although these are very
powerful, too – NASA has a program called Extreme Analogs:
(Cf. http://www.nasa.gov/exploration/analogs/)
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Indirect Analogies
1. What it is (not) about?
What we are interested in are indirect analogies like this one (but
with more modern technology) showing an analog computer setup
to compute airflow around a Joukowski air foil:
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Indirect Analogies
1. What it is (not) about?
To create an indirect analog of a given problem the following steps
will be executed:
Create a mathematical description of the problem – this will
normally yield (coupled) differential equations.
Transform these equations into a corresponding computer
setup (a circuit consisting of basic elements like adders,
integrators, multipliers etc.).
Setup this circuit on an analog computer thus transforming it
into a model of the initial problem.
The resulting model, the analog will now behave like the problem
described initially. In contrast to a memory programmed digital
computer the analog computer changes its structure according to
the problem that is to be solved while the digital computer keeps
its structure and only the algorithm stored in memory will change.
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An Example
1. What it is (not) about?
Let us have a look at an example – the Lorenz attractor that is
described by the following three DEQs:
dx
dt
dy
dt
dz
dt
= σ(y − x)
= x(ρ − z) − y
= xy − βz
The resulting circuit looks like this:
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An Example
1. What it is (not) about?
This yields to the following computer setup:
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An Example
1. What it is (not) about?
The result of a computer run:
How did this technology evolve? Why was it forgotten and what
might the future bring?
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2. The Early Days
The Early Days
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Gears from the Greeks
2. The Early Days
The mechanism of Antikythera is the first mechanical analog
computer ever – it dates back to 150 BC:
(Cf. http://upload.wikimedia.org/wikipedia/commons/6/66/NAMA Machine d%27Anticythre 1.jpg.)
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Gears from the Greeks
2. The Early Days
What could this lump of gears do2 ?
It could calculate sidereal, synodic, draconic and anomalistic
lunar cycles.
It took into account the first lunar anomaly (the moon’s
velocity is higher in its perigee compared with its apogee).
It predicted lunar and solar ecplises and it even predicted if an
ecplise would be visible or not (day/night).
. . . and more. . . (much?)
Isn’t that impressive – accomplishing all of that with nothing more
than cleverly arranged gears?
For those interested, there is a simulation of this mechanism
described in [McCarthy 2009].
2
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Cf. [McCarthy 2009].
The Power of Analogs – Bernd Ulmann
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Solving DEQs
2. The Early Days
About 2000 years later, in 1876, Lord Kelvin developed the idea of
using mechanical analogs to solve differential equations – his
feedback scheme became the workhorse of the zenith of analog
computation in the mid 20th century.
He discovered that a string of integrators in conjunction with other
elements could be used to solve DEQs3 :
[. . . ] it seems to me very remarkable that the general
differential equation of the second order with variable
coefficients may be rigorously, and in a single process
solved by a machine.
Unfortunately, he did not build a real machine which would have
become the world’s first mechanical differential analyzer.
3
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Cf. [Thomson 1876].
The Power of Analogs – Bernd Ulmann
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Polyphemus
2. The Early Days
Another 62 years later, George A. Philbrick
developed Polyphemus, the first electronic
training simulator.
The picture on the left shows a Polyphemus
setup with an illustrated process-control
model involving a two-stage liquid bath with
steam and cold water inflowsa .
a
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Cf. [Holst 1982][p. 152].
The Power of Analogs – Bernd Ulmann
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Polyphemus
2. The Early Days
This drawing of Philbrick’s Electronic Control Analyzer gives an
impression of Polyphemus’ inner workings4 :
4
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Cf. [Holst 1982][p. 151].
The Power of Analogs – Bernd Ulmann
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Hoelzer’s Analog Computers
2. The Early Days
Parallel to Philbrick, Helmut Hoelzer developed another analog
computer – in fact he developed two:
The so called Mischgeraet, was the world’s first on-board
computer and was used in the guidance section of the V2
rocket.
A truly general purpose electronic analog computer, used by
NASA in rocket development at Redstone Arsenal, up through
the late 1950s.
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The Mischgeraet
2. The Early Days
The Mischgeraet5 :
5
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Photo by Adri de Keijzer.
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Hoelzer’s Analog Computer
2. The Early Days
Hoelzer’s analog computer as it appeared at the end of WWII6 :
6
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Source: NASA, Marshall Space Flight Center.
The Power of Analogs – Bernd Ulmann
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3. The Zenith
The Zenith
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Large Scale Analog Computing
3. The Zenith
Analog computing gained a lot of interest after WWII especially in
areas like high performance air planes and space flight etc.
NASA had some of the largest analog computer centers from
about 1950 and well into the 70s.
During this time analog computing transformed from an arcane
technology into the backbone of our technological culture.
Especially in test pilot circles analog computing and simulation was
not taken seriously. After all, what could these guys wearing white
lab coats and fiddling with slide rules teach pilots about handling a
real aircraft?
A lot. . .
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Analog Flight Simulation
3. The Zenith
Using analog computer systems like this7
high performance planes like the Bell X2 were successfully
simulated. Initially this dismayed the pilots who regarded it is
certainly not the ”Right Stuff”. Dick Day remembers8 :
Well, the simulator was a new device that has never
been used previously for training or flight planning. Most
pilots had, in fact, expressed a certain amount of distrust
in the device.
7
8
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Cf. [EAI].
Cf. [Waltman 2000][p. 138 f.].
The Power of Analogs – Bernd Ulmann
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Mel Apt’s X2 Flight
3. The Zenith
In a particular impressive example, it was shown by simulation that
the X2 would become unstable at around Mach 3.0 under certain
circumstances9 :
We showed [Mel Apt (the test pilot)] if he increased
AOA [(angle of attack)] to about 5 degrees, he would
start losing directional stability. He’d start this, and due
to adverse aileron, he’d put in stick one way and the
plane would yaw the other way[. . . ]
Maybe due to the distrust of pilots concerning analog simulation
techniques Mel Apt nevertheless did the maneuver mentioned
above when he ran out of fuel and tried to head back to the
base. . . Apt did not survive (as predicted). . .
9
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Cf. [Waltman 2000][p. 138 f.]
The Power of Analogs – Bernd Ulmann
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Mel Apt’s X2 Flight
3. The Zenith
Mal Apt in the cockpit of the X2:
(Cf. http://upload.wikimedia.org/wikipedia/commons/2/2f/Captain Mel Apt in Bell X-2 1956.jpg.)
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Mel Apt’s X2 Flight
3. The Zenith
The end of this flight which boosted the trust in analog computing:
(Cf. [Merlin, Moore 2008][p. 20].)
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The Zenith
3. The Zenith
In the following years electronic analog computers reached their
zenith – without their help the technological achievements of the
1960s, 1970s and later would have not been possible. These
machines were used most prominently in the following areas:
Flight simulation and space flight
Optimization of processes
Process control and simulation
Chemistry (reaction kinetics, . . . )
Biology and medicine (metabolism research, immunology,
neuro science etc.)
Power plant planning, scheduling, power grid simulations, . . .
Mechanical systems (rail road cars, street cars etc.)
Military applications (embedded control, simulations,
research, . . . )
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The Power of Analogs
3. The Zenith
What was the advantage of analog computing that led to this wide
spread use?
Programming an analog computer is close to the problem to
be solved and not abstract as traditional algorithmic
approaches.
Analog computers offer an uniquely high amount of
interactivity.
Analog computers are highly parallel machines thus surpassing
even modern memory programmed digital computers in terms
of parallelism and maybe even in terms of sheer computing
power.
Analog computers do not have a von Neumann-bottleneck
since they change their structure according to a problem
without needing memory.
Analog computers can be easily expanded – if a problem
grows larger the computer can grow with the problem.
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4. Now
Now
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The Decline
4. Now
Despite these advantages the decline of analog computers started
in the 1970s for a number of reasons:
Memory programmed digital computers became fast enough
to compete at least with small and medium analog computers
in terms of computing power.
Memory programmed digital machines became simpler and
thus cheaper each month while analog computers continued
being highly complex machines – expensive and hard to
maintain and run.
Digital computers offered more flexibility due to time sharing
etc. which allowed a better utilization of the machines.
Over time, the expertise in analog computing was lost –
abstract algorithmic approaches which are adapted to the
machines won over analog approaches which were adapted to
the problems to be solved.
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A Dream Machine
4. Now
Now that analog computing is largely a forgotten art, its particular
advantages are still too precious to relinquish – imagine a machine
consisting of
an off-the-shelf x86-workstation and
additional extension cards containing digital implementations
of typical analog computer elements.
Such a machine would easily outperform even most of todays
traditional parallel computers due to the inherent fine grain
parallelism in analog problem solving.
Even without specialized hardware, analog computing would be a
great basis to generate code for highly parallel architectures like
graphic cards.
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A Dream Machine
4. Now
Such a digital implementation of analog computer parts is nothing
new – first attempts were done in the form of DDAs10 like
MADDIDA, built by Northtrop at about 1950 (cf. [Reed 2006])
or TRICE (cf. [Ameling 1963]).
A modern direct implementation could use FPGAs for example
while another approach could use highly parallel computers like the
Green Arrays GA144 chip11 which contains 144 independent
F18A processors – each of which might implement a group of
traditional analog computing elements thus forming high level
building blocks12 .
10
Digital Differential Analyzer
Cf. [Green Array 2010].
12
This approach would renew interest in the Hannauer matrix – cf.
[Hannauer 1968].
11
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A Dream Machine
4. Now
Why would one want to build such a machine?
It would be ideally suited to tackle dynamic systems of all
kinds (mechanics, electronics, biology, nuclear physics, . . . ) –
just as a traditional electronic analog computer but without
its drawbacks.
It could possibly deliver more computing power for the buck in
these areas than traditional parallel digital computers.
Programming this system would be based mainly on the
DEQs describing the problem to be solved, simplifying
programming substantially.
It could be a great tool in education due to its high
performance and possible high interactivity.
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Thank You
4. Now
Thank you for your interest!
The author can be reached at
ulmann@analogmuseum.org
The author would like to thank Scott Kelbell, Dr. Reinhard
Steffens and Arno Jacobs for valuable suggestions and corrections
to this talk.
Personal note: If you have any old analog computing equipment,
documentation etc. looking for a good new home, please contact
the author.
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5. Bibliography
Bibliography
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Bibliography
5. Bibliography
[Ameling 1963] W. Ameling, ”Aufbau und Arbeitsweise des
Hybrid-Rechners TRICE”, in Elektronische Rechenanlagen, 5
(1963), Heft 1., pp. 28 – 41
[EAI] N. N., PACE 231R analog computer, Electronic Associates,
Inc., Long Branch, New Jersey, Bulletin No. AC 6007
[Green Array 2010] N. N., ”Green Array GA144 – 144-Computer
Chip”, http://www.greenarraychips.com/home/documents/
greg/PB001-100503-GA144-1-10.pdf
[Hannauer 1968] George Hannauer, Stored Program Concept for
Analog Computers, EAI Project 320009, NASA Order
NAS8-21228, 1968
[Holst 1982] Per A. Holst, ”George A. Philbick and Polyphemus –
The First Electronic Training Simulator”, in Annals of the History
of Computing, Vol. 4, Number 2, April 1982, pp. 143 – 156
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Bibliography
5. Bibliography
[McCarthy 2009] Jerry McCarthy, ”Der Mechanismus von
Antikythera”, in Tagungsband, 15. Internationales Treffen der
Rechenschiebersammler und 4. Symposium zur Entwicklung der
Rechentechnik, Universitaet Greifswald, 2009, pp. 55 – 64
[Merlin, Moore 2008] Peter W. Merlin, Tony Moore, X-Plane
Crashes, Specialty Press, 2008
[Reed 2006] Irving S. Reed, ”The Dawn of the Computer Age”, in
Engineering & Science, No. 1, 2006, pp. 7 – 12
[Thomson 1876] William Thomson, ”Mechanical integration of
linear differential equations of the second order with variable
coefficients”, Proceedings of the Royal Society, Vol. 24, No. 167,
1876, pp. 269 – 270
[Waltman 2000] Gene L. Waltman, Black Magic and Gremlins:
Analog Flight Simulations at NASA’s Flight Research Center,
NASA SP-2000-4520, 2000
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