[From Bill Powers (951121.1240 MST)]
Bruce Abbott (951121.1110 EST) --
I can well understand Newton's frustration over his treatment by
those reviewers and the editor, who clearly were demanding of him
details that were neither necessary to the theory nor possible for
him to supply in his day. Gravitation could only be inferred from
empirical observation; it could not be deduced from mechanism.
It's more frustrating than that. Gravitation _is_ an empirical
observation. Newton hypothesized no cause; only Einstein has ever
proposed one (distortion of space). Gravitation is a behavior (moving
toward something), just as rotation is a behavior (moving around
something). "Gravity" is a folk term meaning the cause of gravitation;
it does not refer to anything real. If we were unable to account for
rotation, I suppose someone would invent "rotatity."
What Newton proposed was a _model_ that accounted for the phenomenon of
gravitation. He said that each particle of matter is subject to an
apparent force in the direction of each other particle in the universe
in the way described by his formula. By summing all the calculated
forces between each particle of one object and each particle of another
object, the net force could be computed; This computed force could then
be compared with the actual force necessary to maintain a planet in its
observed orbit, or to make an object accelerate downward toward the
center of the Earth (in a vacuum).
This was a proposed model and not an empirical observation. Nobody ever
actually observes all the forces due to all the pairwise interactions of
particles and adds them up vectorially. Those forces are computed from a
Newton's situation was very much like those of the reinforcement
theorists of the twentieth century, although Newton had the
advantage of studying a much simpler system whose empirical
relationships were easily measured and stable across a wide variety
of conditions. Both built their theoretical system on an empirical
relationship. Newton refers to the "process of gravitation,"
reinforcement theorists to the "process of reinforcement." Neither
theory requires the theorist to explain the process itself; both
then use the empirically-inferred process to explain other
phenomena in which the process appears to operate.
The difference between Newton and the reinforcement theorists is that
Newton proposed a model from which gravitation could be deduced, while
the reinforcement theorists did not proposed a model from which
reinforcement could be deduced. Newton's law is not a generalization
from observations: it is a leap of the imagination that goes beyond what
anyone had been able to observe, and indeed contradicts all earthly
measurements made in an atmosphere.
The reinforcement theorists remained at the level of gross observation,
not positing any underlying organization of which reinforcement is the
observable consequence. Furthermore, reinforcement theorists did what
Newton refused to do: they proposed a cause of the phenomenon of
reinforcement, a cause which is seen in the term "reinforcer." The name
of the process has become a noun; one variable involved in the process
has become an agency, just as the Earth becomes an agency when it is
said to "attract" objects to itself.
Newton was able to provide a quantitative model of great power,
beginning with that simple relationship between gravitational
attraction, mass, and distance. The reinforcement theorists went
searching for an equally stable relationship from which the
"attraction" of the reinforcer could be computed. ... What they
found was a bewildering complexity of relationships involving such
factors as delay-to-reinforcement, amount, "establishing
operations," extra-experimental sources of reinforcement, response
"cost," and on and on.
Newton would have been in exactly the same fix if he had used the same
empirical approach. By studying the way objects fly through the air and
fall to earth, he, too, would have come up with a bewildering complexity
of relationships involving such factors as composition, weight, shape,
orientation, moving parts, wind velocity, air temperature, extra-
experimental sources of force, delayed effects, collisions, and so on.
This is the state in which the science of ballistics was _before_
When Newton's explanation for the behavior of projectiles finally
replaced all the earlier conjectures, it still did not explain the
behavior of projectiles. What it did was to show that the actual
behavior departed from the Newtonian path for reasons that had nothing
to do with the basic phenomenon of gravitation. All the departures were
due to forces that arose from other causes, such as friction with the
air and dynamic air pressure distributions. Before Newton's model, all
these phenomena were treated as a single problem; for all anyone knew,
every empirical fact about flying objects was as important as every
other fact. After Newton, one giant part of the problem was simply
removed and counted as solved; this totally changed the nature of the
remaining problems. The reason that the feather and the cannonball did
not reach the ground at the same time had nothing to do with
gravitation; it had to do with air resistance.
If reinforcement theorists failed to achieve results comparable to
Newton's, it was not because they failed to adopt his approach.
Newton was a modeler. Reinforcement theorists are not. To me, that makes
their approaches completely different.
And Newton used simultaneous equations correctly.