I just noticed a post on the Differential Geometry Forum asking about the topological meaning of Chern numbers. The question seems a little vague. Still it could lead to interesting explanations and repartee. I am willing to start things off but perhaps you should check it first and demand...
I am really objecting here to censorship. I understand that it is a fine line but people come here to learn and to start dialogues that lead to understanding. It seems to me that a Mentor or whatever you are should consider that first.
By the way answering questions with links e.g. to Wikipedia...
That is baloney. But fine. Close the thread. Please close all of my posts that have no references e.g. in the Mathematics Forums. For instance, I just posted some exercises in the Differential Geometry Forum that used the definition of a covariant derivative without a reference. It is not my...
You are confusing me and don't know what you are getting at. The first time I saw these problems was in an old engineering book from the 1920's. That was 40 years ago. Are you asking me to spend a few years trying to find another copy of that book? If you want to go on a jihad why not just...
Hitting a baseball in the sweet spot on a baseball bat gives the best rebound and does not twist the handle of the bat in the hitter's hand. How is this spot and its behavior described in Mechanics?
A similar question: The bumper on a pool table is at a height so that the pool ball does not...
A related question came up when talking with my brother. If you get Covid-19 after the first vaccination shot but before the booster could one consider it to be a substitute for the booster?
One might ask whether the pathology from the post first shot Covid infection would be short term and...
Some exercises for post #5 on the definition of the induced covariant derivative in the cotangent bundle,
##(∇_{X}ω)(Y)=X⋅ω(Y) -ω(∇_{X}Y)##
Show that
1) ##∇_{X}ω## is an element of the cotangent space at each point of the manifold.
2) Given a tangent vector ##X_{p}## at a point ##p##...
Visualization is a prized exercise among mathematicians. Often visualizations brings life to definitions and serve in many cases as a way to understand them. It is worth risking a mistake.
I also think that with long study, one gets an intuitive sense of a subject, a feeling of familiarity and a sense of what can and cannot be right. When visualization is possible it makes this much easier but it is still there without it.
Mathematical spaces are often defined as the natural domains in which phenomena can be described. For instance phase spaces are the mathematical domains of Mechanical systems. Their dimensionally derives from the number of degrees of freedom of a mechanical system e.g. the phase space of a...
Thinking about the formation of Pangea and then its subsequent separation into separate continents, if one thinks of this as flows along convection currents in the mantle then it would seem that the direction of these currents reversed. If this is true, what are the dynamics of this convection...
So modern research describes plate tectonics in terms of differential equations? I would like to understand that. Reference?
Also while recreating past plate configurations seems to be based on empirical modeling, projecting forward to future configurations would presumably not be. Would this...
I have been trying to learn about the geology of the western United States since recently moving to New Mexico. There are many videos and articles on line that explain the present and the past both in terms of tectonic plate movements. But the ones I have looked at do not describe why tectonic...