# Newton's model

[From Bill Powers (951121.2230 MST)]

Bruce Abbott (951121.2105 EST)

You seem to have missed one. One line of thinking current in
physics says that the appearance of forces "acting at a distance"
is mediated by an exchange of subatomic particles between the
interacting bodies.

True. There was another: Descartes proposed that space was filled with
little vortices, and that apparent actions at a distance were mediated
by chains of direct collisions among these vortices.

What Newton proposed was a _model_ that accounted for the phenomenon
of gravitation.

This merely follows from the observations. If every object
attracts every other object according to its mass and inversely
with the square of its distance, then if you divide an object into
two equal masses, each will attract the other (at a given distance)
with a force half that of the original mass.

No forces between remote objects have ever been observed. The behavior
of the objects has been observed, but the forces are part of a model of
invisible mechanisms. The essence of Newton's Law was not only proposing
an inverse-square distance law involving a product of masses, but the
idea that all materials were equivalent in terms of a property called
"mass," also part of the model. The first "If" in your second sentence
above is the proposal that constitutes the model. The second "if" is
simply a deduction from the model, and assumes that all mass is the same
with respect to gravitational phenomena.

The deduction is not strictly true; it depends on how you divide the
object. If you slice it at right angles to the line joining the objects,
there will be a nearer half and a farther half, and the attraction will
be different for the two halves. That's another deduction from the
model.

The hard part, which Newton achieved, was to develop the
mathematics that would allow one to derive the observed
gravitational attraction from the sum of the pulls of the
individual particles.

I would say that the hard part was coming up with the inverse-square
relationship, and deciding to use the product of the masses in the
numerator (rather than, say, the sum or some other function). These
features of the model were not derived from observations. They were
guesses.

From this one could show, for example, that the gravitational pull
of a spherical mass could be represented as if originating from a
point at its center (if I recall correctly). But what does this
add to the empirical observation that g = m/d2?

That is NOT an empirical observation; it is an invented model. Newtonm
did not _observe_ the law of gravitation; he _invented_ it. The
expression is more properly g = Gm/d^2, where G is the universal
gravitational constant, determined by measuring or assuming g, m, and d
and calculating G from observations. The formula itself is not a result
of observation. Nobody has ever varied g, G, m, and d and shown that
they fit the proposed relationship. The only way to test the model is to
assume its truth, evaluate the constants, and use it to predict the
behavior of objects subject to gravitational effects. If the predictions
accurately match observed behaviors, we accept the model as being true
(as true as any model gets).

Now you are claiming that Newton proposed a model from which
gravitation could be deduced, which is clearly wrong. He proposed
a way to apply the empirical law to get the gravitational effect of
objects composed of nonuniformly distributed masses.

This is part of our basic disagreement. What Newton did was to propose
something that had never been observed: the dependency of acceleration
on the masses involved and the distances between them. He even had to
define "mass," another invented entity, as the ratio of force to
acceleration. Mass itself is unobservable: it is a relationship between
two quantities, but of those two, only acceleration is measurable in a
free-moving body. Thus all predictions about free-moving bodies based on
Newton's model have to be tested in terms of acceleration, velocity (the
first time integral of acceleration) or position (the second time-
integral of acceleration). Force and mass remain parts of the underlying
model, and are not individually measurable for a free-moving body. The
only way to measure mass is to measure the force required to restrain an
object from moving under a known gravitational acceleration; the only
way to measure the gravitational acceleration is to measure the force
required to restrain a known mass; the only way to measure force is to
measure the acceleration of a known mass. Given any two you can
calculate the third, but there is no way to measure all three
independently. Of the three, only acceleration is related to other basic
physical measurements, distance and time.

Newton proposed a model from which the acceleration of objects toward
each other could be quantitatively deduced. That mutual acceleration is
what we call "gravitation:" objects gravitate toward each other. The
quantitative deduction from the model matched observed celestial motions
very exactly, and terrestrial accelerations somewhat less accurately;
that is why we keep the model.

And Newton did not posit any underlying organization of which
gravitational attraction is the observable consequence. What it
comes down to is this: for Newton, gravitational attraction is a
property of objects with mass. Why this is so, he had no idea. Not
a clue. He said so.

Correct. The fact of gravitation is observational. We observe
gravitation as an acceleration of objects toward other objects. But we
do not observe the forces or the masses. We imagine them. We say that
because the objects accelerate toward each other, there must be a force
pushing them together. Because they do not fly instantly together, we
imagine that there must be something resisting the acceleration, which
we call mass. But we have no direct way of knowing that there _is_ a
force pushing them together or a mass restraining their movements. Force
and mass are part of a plausible model that accounts for the actual
observations. This model has been very carefully and extensively tested,
and so far it has worked as nearly as we can measure, for macroscopic
objects and in the absence of other influences such as magnetism and
electrostatic fields. But it is still a model.

I have always felt that psychologists have not understood the extent to
which physics is based on models, and how few kinds of actual
observations there are. We can measure time intervals between events,
length, angular and linear accelerations and their integrals, positions
of meter needles and numbers on digital readouts, and a few other things
on a short list. All the rest derives from models and deductions from
models. Every label on a meter-face refers to a model of unobservable
processes. Physics itself is a testimony to the power of the model-based
kind of explanation. But what was the first thing that scientific
psychologists said, thinking they were emulating physics? "Don't guess
about what's going on inside." That was a tremendous mistake.

···

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Best,

Bill P.

[From Bruce Abbott (951122.1455 EST)]

Bill Powers (951121.2230 MST)]

Bruce Abbott (951121.2105 EST)

You seem to have missed one. One line of thinking current in
physics says that the appearance of forces "acting at a distance"
is mediated by an exchange of subatomic particles between the
interacting bodies.

True. There was another: Descartes proposed that space was filled with
little vortices, and that apparent actions at a distance were mediated
by chains of direct collisions among these vortices.

Ah, you are implying that these ideas have equivalent merit. Interesting.

No forces between remote objects have ever been observed. The behavior
of the objects has been observed, but the forces are part of a model of
invisible mechanisms. The essence of Newton's Law was not only proposing
an inverse-square distance law involving a product of masses, but the
idea that all materials were equivalent in terms of a property called
"mass," also part of the model. The first "If" in your second sentence
above is the proposal that constitutes the model. The second "if" is
simply a deduction from the model, and assumes that all mass is the same
with respect to gravitational phenomena.

Where did Newton get these ideas, if not from data?

The formula itself is not a result
of observation.

From what first principles was it derived? Did they spring into Newton's

mind with no empirical support?

Nobody has ever varied g, G, m, and d and shown that
they fit the proposed relationship.

Nobody CAN vary G, but certainly m and d have been manipulated and g
measured. I seem to recall this being done using a torsion-spring system
and copper spheres.

But I think we are still miscommunicating. I'm not out to show that
reinforcement theorists early in this century succeeded in developing a
Newtonian-style model. What I'm doing (among other things) is trying to
understand where things went wrong, back there at the beginnings of
psychology as a science, and perhaps develop a reasonable explanation why.
I don't think it's enough to claim that psychologists back then were poorly
educated in the methods of physics; I don't know that there is evidence of
that. Herman Helmholtz and Ernst Mach were both top-flight physicists, yet,
although both contributed to sensory psychology, neither developed models of
sensation or behavior of the sort Newton did for physics. Why not? They
certainly knew how to apply Newton's methods. What was missing? Gustov
Fechner was a physicist and an expert mathematician; Wilhelm Wundt was a
physiologist well grounded in the physical sciences. Why didn't they
develop the kinds of models Newton did, within the realm of psychological
phenomena?

Are there other possible reasons that should be explored? One suggestion I
have made is that the database on which to build a model was much firmer for
Newton than the meager information available to late 19th century
psychologists and physiologists. Newton may have been a genius, but his
ideas did not spring from nothing. He had to have a basis for them.
Perhaps this basis was lacking in psychology. Newton had over 2000 years of
observation and previous theory to draw on, plus some very recently obtained
quantitative data. What did Helmholtz, Mach, Fechner, Wundt, Pavlov, or
Thorndike have to draw on? Anecdotes, introspection, and philosophical
speculation. Had Newton been a psychologist, on what would he have based
his models of mind and behavior, at the end of the 19th century?

By the way, you didn't comment on the physicists' use of terms like
"magnet," and the parallel I noted between that use and the term
"reinforcer." If there's some fundamental difference between these uses,
I'm not seeing it. What is it?

Regards,

Bruce