Learning as Rediscovery
Because of the possibility of using geometric algebra for the formalisation of physics I have recently read some papers by
David Hestenes, who has played a prominent role not only in developing geometric algebra for application in physics but also
in arguing the case for changes to the way physics is taught to take advantage of the power and simplicity of geometric algebra.
The geometric algebra is not relevant to what I have to say on this page, but there are two other topics addressed by Hestenes
which are.
One is the idea that physics should be regarded as engaged in the construction of models, of which more later.
The other is the idea of learning as rediscovery.
Hestenes argues that when a student learns about science he must (or should?) be engaged in a creative act of rediscovery.
Now I have no idea how true this is in general, or to what extent this is a practical way of thinking of physics teaching,
but it is very relevant to the way in which I approach learning, and I think if I say a few more words about this here, it
might help explain the process of which this page is an evolving snapshot.
I am approaching the study of physics in two complementary ways, both more typical of philosophers than of physicists.
This is typical of my approach to almost any subject matter, but I speak here specifically of physics.
The two "particular" interests which I bring to bear, are first in the formalisation of physics, by which is meant its formalisation in a manner similar to that in which Russell and Whitehead formalised mathematics
in Principia Mathematica, but benefiting from the subsequent development of information technology and a few decades of research
into the use of computers to assist in producing formal proofs.


This perspective immediately transforms the learning of physics into exercise in reformulation or recasting which is itself a creative process, as is illustrated I think by the long period of time which David Hestenes and others
have spent developing geometric algebra and geometric calculus for applications in physics.
The formalisation can of course take advantage of this work, but even in these purely mathematical areas the process of formalisation
invites further development, of which Rob Arthan's construction of GA(∞,∞) is an early example.
This process of formalisation is of independent interest, but not quite enough for me.
The approach to physics via formalisation is undertaken for ulterior motives, of a philosophical character.
It is in part an exploration of the limits of deductive methods, and in part an exploration of what there might be in this
particular direction (if anything) which transcends those limits.
The particular direction being that of physics, that of trying to understand the world from a physical perspective.
Beyond physics here, hints at metaphysics.
This second motivation provides another provocation to reformulation, and in this case reformulations which may be more controversial
than those which arise in formalisation.
In physical theories, at least those which might be called fundamental, intertwine two distinct kinds of element which are
not readily separable.
They provide accurate models of the material world, which are couched in terms which go beyond what might be called the empirical
content of the models, and hence which go beyond what can experimentally be verified.
There seems to be in the practice of physics an acceptance that one may infer to the "best explanation" and that whatever
gains general acceptance must then be a true picture of reality.
Sure enough, some physicists, like Hestenes, do propound a modelling philosophy, but mostly physicists take literally what
I am inclined to call the metaphysical content of their theories.

