These days I volunteer to tutor once at week at the local county community college on topics ranging from math to physics, and even engineering. I do not know what exactly to expect when I go for a tutoring session because the students I deal with are somewhat random and the range of subject matter quite broad. It is a bit of an adventure for me because it has been quite a while since I dealt with the basics on these subjects. I find myself trying to remember things from 30 to 40 years back, and often am reminded that I have forgotten more than I remember. It is indeed also a learning process for me, where I am learning to interact with students for the first time even as I am recalling fundamentals from the old days, and where I am trying to find a way to get a point across even in the midst of my uncertainty so that they can understand it. It also seems that the tools that the students use for learning, including the computer software and even the TI calculator, are different from what I am used to, and this is something that I need to adapt to. I sometimes encounter students who have not even seen a textbook on the subject they are studying. My approach most often is to explain things and work my way through problems on a piece of paper so that students can follow what is going on. At the end I try to make sure that my answer is indeed correct because I am never too sure, and also because I can make mistakes when trying to do things too quickly. Most students seem to appreciate the approach. So far so good…

Most of the questions I have dealt with so far have been on topics in math, but I will sometimes get a question in physics. I have to deal with these questions more carefully because of the rustiness of my brain. Luckily, almost all the questions I have gotten so far in this context have been related to Classical Newtonian Mechanics, a topic that seems somewhat intuitive to me. Most often I can work things out from first principles.

I was presented with the following problem yesterday. There is heavy block of wood of a certain mass sitting on a frictionless table . The block of wood is attached to a spring on one side that is fixed to a wall. You are given the constant that will describe the behavior of the spring. A bullet of a certain mass is fired into the block of wood from the opposite side of the spring, and it hits the block with a certain velocity. The question was about the maximum displacement of the block of wood under these conditions. The figure below represents the physical setup.

I am not going to solve the problem here, but will only note that the primary issue that I mentally debated as I was trying to help the student was whether one should use the principle of conservation of momentum or the principle of conservation of energy in order to address the problem. With the help of the student I figured out that one has to use the principle of conservation of momentum, but it was only after coming home and doing some more research on the Internet that I convinced myself of why I could not use the principle of conservation of energy. (This is how far behind I have fallen on the topic of physics!)

Anyway, I spent so much time thinking about this topic yesterday that it seems to have gotten into my head. It was towards early morning, when I was deep in my dreams, dreams which can often be entangled and confusing and easy to forget, that the problem confronted me in a different way. In these dreams I found myself in some unknown place with railroad tracks that happened to be not too far away. I saw the signals for the railroad tracks out of the corner of my eye, and one of the two signals had turned green. Before too long, a massive railroad locomotive was thundering past projecting power. The next instant in my dream I noticed that in addition to the freight cars that the locomotive was pulling, there was this solitary freight car in front of it. But, goodness me, the freight car was not attached to the locomotive!! It was being pushed in front of it in a free manner. This cannot be safe, I remember thinking to myself! The next thing that happened in my dream was that the freight car had derailed and crashed. I do not remember if I woke up soon after.

I think my dream was related to both my tutoring experience the previous day and the fact that the weekend before we had walked on the C&O canal towpath beside some active railroad tracks near Point of Rocks. The neurons in my brain were doing a dance of some sort connecting different independent strands of thought even as I slept.

Coming back to Newton, how many of you know that he was one of the inventors of calculus. This guy was simply amazing when it comes to the range of topics he covered. I have also mentioned his work on Gravity in an earlier blog.

In one way or other, newton in related to every branch of mathematics.

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Almost everyone knows newton was one of the inventors of calculus.. But how many of us know Newton is the inventor of Binomial theorem?

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Yeah, he was the one who generalized the binominal theorem for non-integers. I find it fascinating that this leads us directly to the concept of infinite series.

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