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PROFESSOR: So now, let me make the first of our technical asides, which you can skip over if you're not interested in the mathematical details or for those of you that have a higher-level, say, upper-level-undergraduate or even graduate-level understanding of transport phenomena and fluid mechanics. I'd like to show you some of the equations that are behind the results that I've been quoting in all the lectures. So in particular, let's derive the Wells curve. So part of that was a theory of drop settling. Here, I will quote a certain result, because the derivation would be a lot longer. Actually, for that, you could refer to my online class 10.50x, which is that if you have a droplet or a particle of a radius R and it is settling under gravity-- so it has a mass m, and the gravitational force is m g, where g is the gravitational acceleration-- then there is a flow of fluid around this object. And relative to the moving object, the flow is going the other w...

PROFESSOR: Let me begin by introducing the subject. The subject is resonances. And we have seen, actually, a little bit of this in the resonant transmission of the Ramsauer-Townsend effect. Because of a resonance phenomenon within the square well obstacle, somehow, for some particular frequencies, for some particular energies, the particles were able to zoom by without experiencing any reflection, whatsoever. So let's begin the subject of resonances by asking a question. If you have the usual potential, the short range potential, which means, that for some distance, R, greater than 0, the potential is 0. Here we put a barrier, and over there could be anything, some potential. We've computed some-- this concept of time delay, there's a formula for the time delay. In fact, it was given by 2 h bar d delta dE, the time delay, 2 h bar d delta dE. And we discussed that this time delay can be positive or it can be negative. If it's positive, it really means a tim...

um let me before I ask you to make out the cards let me get into um the kind of introductory presentation that I wanted to make of course is on the nature of creativity but approached philosophically there are books on that list for instance that are psychology of creativity sum psychoanalytic approaches to the nature of creativity um this is philosophical and in being philosophical it I was going to say transcends but really is fully immersed in all of the different kinds of creativity um one of the questions that you'll be hearing about in a minute is how creativity and science differs or resembles creativity in Fine Arts or and and architecture is always been the in between between science and and the Fine Arts uh so that has its own Niche its own entry into it but philosophy tries to talk in a broader way which makes it uh much much more useless until you know how to apply it but and that's what you can do for your own selves better than I can do for you uh so...