So Penrose does: launching into a pretty detailed introduction to the nuts and bolts of Twistor Theory FROM A GEOMETRIC-mathematical PERSPECTIVE.
You will notice the youtube video has segments. Segment 2 goes in fast. Twistors are explained in segment 3. And...well, to tell the truth, I haven't gotten into the other segments yet! ;-) But I think Penrose gets into some of his other theories and how they more or less relate.
What is remarkable, in my opinion, is that although I have almost none of the math, I can actually follow the majority of the explication pretty well!
And THAT is why I am posting this: in the hope that at least some of you guys will attempt to relax, pay attention, and listen as Penrose lays out the overview of what "Twistors" are and why, and how, he uses them as a mathematical tool to do real hard thinking about the unification of physics from the small to the large, from the Big Bang, to the "Heat Death" at the end of time. And why he feels confident that that end isn't actually the end. Why he says "I don't believe in Inflation"
I'd suggest you start right at the beginning of this. But I think you will find it progresses really quickly to some seriously interesting thinking. And I think that thinking is the SAME SORT OF GEOMETRICAL PERSPECTIVE that Einstein himself said he adopted in coming up with many of his greatest ideas: specifically including General Relativity.
So you are not going to come out of this with a thorough understanding of deep physics. But with a single viewing I think some of you could get a glimpse. And I suspect that with a few more viewings you could get a reasonably solid overview of the strange world which might just provide the next step in Theory of Everything Physics.
FWIW, it would probably be helpful if you have at least a little idea what a "Complex number" is (i + 1, where "i" is the imaginary number otherwise known as the square root of -1). If that bothers you, you are not alone. But since God made the Universe such that everything from radio waves to space flight on up REQUIRES the number i, I suggest you just accept it as a miracle go with it.
And, from there, how complex numbers can be multiplied together to give http://en.wikipedia.org/wiki/Quaternion. (I actually suggest you look for a video explanation and just go with the flow if the whole thing seems to be getting deep too quickly). The basic idea of vectors and how vectors are numbers, too, which means they can be multiplied, too, would also be helpful. And, finally, some recognition that the geometry we learned in mid-school is rectilinear but geometries COULD similarly be mapped onto, say, the surface of a sphere (hyperbolic). And, yes: you CAN say you follow a “straight line” when you travel on along the earth's surface longitudinally or latitudinally. And you can also say, from a different perspective, that when longitudinal paths on the earth are straight, parallel, lines...which just so happen to cross! (horrors!).
Anyway, I think that is all the basic background you need to follow this interview -- which I think makes it remarkable! And, for all I know, you may not even need any background in he items I mentioned directly above.
If you enjoy this, at all, I would appreciate your feedback. FWIW, Curt Jaimungal has a regular podcast in which he interviews leading physicists and other highly scientific-types: "Theories of Everything". But, in this particular interview, being able to SEE Roger Penrose wave his arms as he talks helps considerably with the uptake!
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