Algorithms and external notations

[Peter Cariani, 960314, 1200]

Bill Powers 3/13/96 wrote:

When you apply a force to a mass, you get an acceleration. We represent
this relationship as f = ma. But what is it that makes the mass
accelerate when the force is applied? It is not the algorithm, f = ma.
The symbols f, m, and a stand for measurements -- i.e., perceptions. The
perceptions are not what create the behavior. In fact, even f, m, and a
are themselves perceptual representations of some external sea of
variables and interactions which can't possibly be as simple as the
symbols that we use to speak about them. What f=ma does is to _impose
order_ on our experiences. It simplifies our interactions with the
external world, making them comprehensible. But our symbolic
representations of the world no more make it work than the words "200-
horsepower engine" make a car run.

Yes. I think the symbols that we use allow us to order our perceptions in
such a way so as to permit us to carry out a reliable sequence of
behaviors (symbol manipulations). So mathematical operations are a
means by which we can reliably replicate sequences of behaviors to
achieve consistent ends, across repetitions and observers. These
behaviors are all contingent upon our previous perceptions and
vice-versa --the use of discrete symbols makes these looping sequences
extremely reliable.

I think of mathematical notations and operations as one means
of externalizing chains of thoughts so as to make them more reliable.
When they are sufficiently reliable and explicit to permit
many different observer-participants to replicate our results
without (apparent) ambiguity or error, then I am willing to call them
"computations" and "algorithms".

And yes, simulated fires do not burn us. Aristotle made similar
criticisms of Pythagorean theories of the motions of planets.
Pattee and I tried over and over to convey the distinction
between symbolic representations and material
process to the Alife community, but with only limited success.

Peter Cariani