Just how big is it?

[Snowhog]

"Mr Qq, I'm impressed, very clever, too clever, so clever that I can't see what is really going on at the detail level, thank you, please sit down now, and can anyone present a proof I can understand?"

OMG! That is absolutely priceless!!

[SteveRiley]

I majored in algebraic topology, if that tells you anything.

What is that, like equations across the land or something?

"Let X be the height of this mountain, and Y be the depth of the valley below. If Alice navigates within 90% of the distance between X and Y, how fast can Bob refold his map?"

[Snowhog]

...how fast can Bob refold his map?"

Depends on whether or not the Mad Hatter has invited Bob over for tea.

[HalationEffect]

I haven't followed mathematics lately.

HalationEffect: "Paul Halmos is another name with which I'm unfamiliar (but I see from his Wikipedia page that he worked with John von Neumann, who I very much have heard of)."

I also worked with Halmos ... as a struggling graduate student taking his Real Analysis course :-)
I once presented a short, 3-line insightful proof to a complex, delicate theorem by abstracting to a higher-level operator space and using a fixed point property of Hilbert spaces. His response was simple, "Mr Qq, I'm impressed, very clever, too clever, so clever that I can't see what is really going on at the detail level, thank you, please sit down now, and can anyone present a proof I can understand?" He was right, of course, I didn't really understand the theorem at a meaningful level; to me it was just another opportunity to abstract some pure, clean math out of it. (I majored in algebraic topology, if that tells you anything.)

Awesome! So, because I've communicated with you here at KFN, that means there are only three degrees of separation between me and von Neumann

Algebraic topology... I know those words separately, but together, not so much. I took a look at the Wikipedia page on the subject... and wow, I've seen some arcane wiki pages in my time, but that takes the cake! I mean, the page is (allegedly) written in English, but it may as well have been Greek. The only thing I came away from it with was a vague sense that it might tie in with a personal gut-feeling of mine (which doesn't really deserve to be raised to the level of a hypothesis) that all aspects of reality from the quantum foam up, are nested layers of abstraction.

"Hell is other people." -- you would like Bukowski

I expect you may know that it is a quote from Sartre's play "No Exit" As I'm somewhat of a depressive hermit, no surprise that I'd latch onto that particular line. It really resonates with me.

[woodsmoke]

How BIG....BIG....IS...it!? lol

On the last episode of "Suites"...the two "heroine" secretaries were .....talking about a guy...

and one of them held her fingers up and started "spreading the tips of fingers apart".... and after about....
humoungous inches....

walked off.



woodsmoke

[Qqmike]

The most embarrassing thing about being a topologist, yes, is explaining why you don't know geography. Not this: http://en.wikipedia.org/wiki/Topography But this: http://en.wikipedia.org/wiki/Algebraic_topology. I know you know. If "nested layers of abstraction" turns you on, yes, algebraic topology is one neat place to hang your hat. I liked topology, I liked abstract algebra (that is not the algebra most people think of), http://en.wikipedia.org/wiki/Abstract_algebra , so when I saw you could investigate abstract topological spaces using algebraic structures, that was the thing for me.

"Hell is other people." from No Exit, yes I had forgotten that actually. Looks like I've come full circle, from Sartre in college to the drunken Bukowski! "As I'm somewhat of a depressive hermit, no surprise that I'd latch onto that particular line. It really resonates with me." As I say, H-E, you might like Bukowski, his poems are best (vs novels). So many readers have thanked Bukowski for giving them something they could relate to, to hang on to, to help them get through the craziness of modern life, but Bukowski would say, Yes, that's nice, but who the hell am I supposed to read to help ME?!

And as to my Halmos story, this: "... can anyone present a proof I can understand?," as I'm sure you might already surmise, of course Halmos understood my proof but exaggerated with some humor to encourage a naive approach, starting with a solid, basic understanding of what is REALLY going on at the detail level of the spaces involved, rather than to whip out some sexy function-theoretic sledge hammer as I did (but it did impress my fellow students and I think also Dr. Halmos may have raised one eyebrow however slightly).

Halmos had an interesting habit. On the first day of class he said he wanted to know each of us. He asked each person to say his name. Then he scheduled a F2F in his office with each student. He also took a Polaroid or three of the class, marked a sheet of paper with our names (in bijective correspondence with the seating at the photo), and returned to the next class in two days to call us each by name and for the rest of the semester. As he said, that was his "photographic" memory at work. He had a good sense of humor, was friendly, walked everywhere, carrying a walking cane, always wore a hat.