Untitled Document In physics the primary object that we are often want to understand is the Hamiltonian111or Lagrangian of a system, denoted by H. Let M be the phase space of our system and so H:M→ℝ:(q,p)↦H(q,p). H gives rise to dynamics through Hamilton’s Equations dqdt=∂H∂p,dpdt=−∂H∂p. (1) While these equations can be thought of as just a system of PDES to be attacked, it is useful to think of them geometrically. ...
What we today call Optics, the study of light, is derived from ancient theories of light and vision, called in ancient Greek ὀπτικός (optikós). In the ancient world the question of what light is was inseparable from the concept of vision. It would be well over a thousand years before any widespread application of our understanding of light would develop (in the form of eyeglasses in 13th cent Italy)1, and even longer before the nature of light itself without reference to vision would be seriously investigated2. ...
What is a scientist? Tautology: When we think of scientists, we should think of all those people throughout history who have practiced science. Those who dedicated some part of their lives to research, either fundamental or applicable, professional or amateur, in what we would today call the Natural Sciences (The modern Social Sciences deserve a separate discussion). In this series of articles, we will attempt to answer this question by focusing by and large on the history of physics, especially the study of light and vision1; beginning with fundamental questions about how we see and culminating (but by no means ending) with modern, Nobel prize winning research. ...
Much ink has been spilt over the difficulty of pinning down exactly what this thing called science actually is[^1]. To avoid doing too much violence to the Philosophers of Science (lest they assault us with their epistemological and metaphysical concerns) we will avoid their heavy-duty conceptual models, the history of optics must remain the primary focus of our limited time and cognition. So, in keeping with the common practice of scientists, we will begin with an approximation. ...