Cohen does a wonderful treatment of how Newton went about
determining the masses and densities of the planets and our Sun. It is also
interesting to me that Newton's quantitative work was plagued with numerical
issues, but his qualitative work or symbolical work was spot on. His methods
were correct.
The takeaway I feel is that being taught and being able to
reproduce the proper method is extremely important. By being able to do that,
you are able to refine your result closer and closer to the truth as you gain
more understanding. This can be seen between the different releases of Newton
where the errors become less and less and the work simpler as a result. Cohen
goes into detail for these to show Newton's process of refinement.
For students and teachers, it is very important to get the
method correct. A good foundation is required to be able to move forward in
understanding of the more advanced topics. With a sufficient methodology, it is
possible to move forward and continue to make refinements as you go.
To tie this back to what DiSessa has said on p-prims and
their applications, this would probably be akin to choosing the proper p-prim
that is being invoked. To simplify it further, it would be like making sure
that you are starting at the actual beginning or at least the same area.
Perhaps it would also be reassuring to students to point out
that even a great mind like Newton's had to do multiple refinements .
I. Bernard Cohen, "Newton's determination of the masses and densities of the Sun, Jupiter, Saturn, and the Earth," Archive for History of Exact Sciences, Vol. 53, pages 83-95 (1998)
