The study of physics has driven us to the positivist conception of physics. We can never understand what events are, but must limit ourselves to describing the pattern of events in mathematical terms: no other aim is possible .... the final harvest will always be a sheaf of mathematical formulae. (Sir James Jeans)
How can it be that mathematics, a product of human thought independent of experience, is so admirably adapted to the objects of reality? (Albert Einstein)
Mathematics has the completely false reputation of yielding infallible conclusions. Its infallibility is nothing but identity. Two times two is not four, but it is just two times two, and that is what we call four for short. But four is nothing new at all. And thus it goes on and on in its conclusions, except that in the higher formulas the identity fades out of sight. (Johann Wolfgang Von Goethe)
Lecture Five found us [re]examining the concept of energy, momentarily reflecting on the fact that it is, at heart, a defined rather than measured quantity. So the principle of the Conservation of Energy is, simply, the statement that humanity has stumbled onto some number that happens to never change for the universe. This is a direct consequence that the laws of physics do not appear to change with time.
This conservation law leads directly to the development of the First Law: dU = dq + dw. We reminded ourselves of the differences between state and path functions -- a distinction which will be key to later developments. Further, the idea of work and generalized force was developed, enumerating six or seven examples to be used in subsequent lectures.