Posted on 09/10/2005 7:27:37 PM PDT by snarks_when_bored
Fascinating interview. I read the whole thing without falling asleep, and I'm not math-minded. I saw the title and don't know why I read it.
I had a linear algebra professor who drilled into me the meaning of the Null Space endlessly. At the end of the course I had about as much understanding of null spaces as I had from any Marxist explaining the meaning of the Negation of the Negation. I have nothing, non, no, nada, naught, or ought to do with intellectuals anymore. There ain't nutting there.
I'll bet you remember whether or not the nullspace of a linear map is ever the empty set.
Our first-graders are being taught Euler's formula?
Unfortunately for us, I believe that Hironaka was talking about his Japanese first-graders.
Yes I agree:) That's why I was saying "we're in trouble".
Thanks for posting the interview.
(smile) I missed your original point. Dang.
Here is how you can make a singularity. You take some manifold, grab some part of it, crush it to a point, and that’s a singularity. So the singularity itself has a geometry. Stephen Hawking has said that in a black hole there is another universe. A singularity is like that: if you really look inside it, then you see a big universe. So the problem of dealing with singularities is that the singularity is just one point, but it has many, many things in it. Now, to see what is in it, you must blow it up, magnify it, and make it smooth, and then you can see the whole picture. That’s resolution of singularities. What Mori does is he creates a singularity by collapsing something.
This is quite an interesting feature of human nature. To my way of thinking, humans are different from other animals in that humans have a notion of infinity. They never see infinity, they never live infinitely, and even the universe may not last infinitely long. But humans cannot live without the idea of infinity.
This is the reason that people create religions. Religions say that the world is much longer and the universe is much bigger than you can reach within a lifetime. So then you feel better. Infinity is like a belief. If you have a belief in infinity or eternity, you feel happier.
I guess we do have to stop and smell the roses.
Nice quotes. I was impressed with Hironaka's way of expressing himself, even about his difficult-to-understand work.
It's not your fault, I didn't make my point very clear. Have a good night.
Cheers!
The part about Italian algebraic geometry reminded me that I took a course in algebraic geometry from an Italian professor. He was a great guy and liked anyone who had an interest in geometry. When the students had a discussion with him about problems or research; if you were wrong about something he would not pounce on you and rip you to shreds as most other professors would. He would say something like "You are totally wrong but essentially correct !!"
I have a desire to try number theory. This time for real.
"Once more into the breach, dear friends!"
Math ping.
From a cursory reading of his approach, it would seem he is trying to use images of the global projected on the local.
An extraordinaly admirable ideal, and potentially giving us great insight, but it strikes me already that there are probably an infinite number of spaces and functions that could give us the same projection.
I spent alot of time then, and now, in topology.
And I have pinged you often, and frequently, with my ideas about your posts.
When I was a young child, living in a quonset hut in Conesus, NY, I remember wondering why is there only three dimensions? My answer at that time was "because that's all we need"
And I recall my father talking to my mother about some kind of test I took, and my mother saying "Oh, my God!" (We were very poor) and it had something to do with my IQ test.
Which, the last test I took, was 158
And one of my most bittersweet memories is my professor, Ernst. R. Ranucci, in college, who taught "Advanced Plane Geometry". He was by no means a great methematician, by he was tremendous in being a problem solver, he loved heuristics. I was eating lunch with a fellow classmate and commented that he must hate my guts by now. The classmate said, "Dave, you got it all wrong, he told me that in his thirty years of teaching high school and college math, you are the most creative student he ever met!
So tell me, give me some assurance, that the path that is being followed will yield the answer. I dare you. I dare your pretentiousness.
Out of the mouths of babes...
The next revolution in physics will be dramatically different from what has come before. It stands to reason that the obvious has been discovered.
Nice post. Thanks. :-)
Your Italian professor had a streak of kindness in him. But he was probably thinking (as most math profs do), "If you can't do the problems, you don't understand the material."
Singularity bookmark!
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