Recent content by Cruikshank

Experiments gather data. Then we have to think about the data and make models, concepts, constructs, theories. We have to decide what the basic objects are. That's choosing an ontology. Newton stipulated absolute space, absolute time, masses, and forces, and then built a structure using...

Dale, if you are happy without thinking about philosophy, more power to you. For myself, I can't do physics without it. To me the whole *point* of physics is to understand the real world. So yes, the definition of "real" is vitally important. If physics is not about reality then I'm not...

Khashishi, exactly. Stress in a transparent solid can be measured by measuring forces on the exterior, by measuring strains, by looking at the optical deformations, etc, so Bridgman says that stress is a real thing. He claims that there is only one way to detect an electric field, and that is...

I'm reading The Logic of Modern Physics by P.W. Bridgman (1927). He states an operational definition of reality: something is a "good construct" if it has a one to one correspondence with a physical situation defined by observations, but it isn't "real" until it has multiple...

Part of physics is philosophy, of necessity. I enjoyed An Introduction to the Philosophy of Physics by Marc Lange, for raising good questions, and pointing out how physicists are doing some philosophy whether they want to or not. When building a theory, you have to choose an ontology--declare...

Thank you both for your replies, As I learned it, there are atomic orbitals such as 1s, 2s, 2p, etc for each atom. One system for adjusting orbitals due to the presence of other atoms is the "hybrid atomic orbitals": sp, sp2, sp3, sp3d, and sp3d2 (and I've heard that sp3d3 exists for IF7.)...

I am a professional math and science tutor, primarily focused on math and physics. I used to tutor organic chemistry but gave it up because I didn't want to study orgo an hour per week for the rest of my life. I like general chemistry and have no trouble with most topics, but the way of...

Thank you, micromass! I will study those. That looks like exactly what I wanted. (By the way, I believe my counts are low because I merged points which only appear together. I will reexamine the cases.)

Just for fun, I tried enumerating the topologies on n points, for small n. I found that if the space X consists of 1 point, there is only one topology, and for n = 2, there are four topologies, although two are "isomorphic" in some sense. For n = 3, I I found 26 topologies, of 7 types. For n...

Read Lighthill's Introduction to Fourier Analysis and Generalized Functions Make sure to review Taylor Series and the Remainder theorem

I also am interested in such things. I've been a tutor for many years and students are pestering me to go online so I can tutor them after they move away. Hunting for more threads on this topic...

Your question doesn't match the question in your title, but okay, I'll take a guess. I've wondered similar things, and one idea that occurred to me is that someone who really wanted to expand their repertoire in the early days of calculus could simply take lots of functions, find their first...

My first instinct is to say, "all those extra field lines inside the coil have to go *somewhere*, so yes it increases, and by the same multiplier. That still sounds right after a minute of reflection. I've never learned any formulas for ferromagnetism, though.

I believe there is no loss of generality. There are three sets, X, A and B. We are given A and B, and that phi is a monomorphism from A to B. X is introduced as a tool to show a = a'. If it is true for X, it is true for any other X, because a and a' are elements of A, not X. Whether a = a'...

KE = sum of 1/2 mv2. Can any of those terms be negative? Or, imagine covering the whole system with a curtain or box and treating it as one object of total mass M and velocity V. P=MV, while KE= 1/2MV2+ KE(within system, relative to the center of mass) If KE = 0, what does that imply? Assume...