Sunday, August 30, 2020

Cantor and Infinity

Georg Cantor was obsessed with the Infinity, in a mystical sense. His attempts to understand Infinity led to new ideas in Mathematics which have contributed foundational ideas to Computer Science.


Anonymous said...

What's up with the bombastic soundtrack?

Einstein's legacy was so popularly overwhelming in the latter half of the 20th Century that a number of great minds have been largely overlooked. Cantor is one of those and I would add Reimann.

But Cantor's thought processes were so unique as to indicate the work of an idiot savant or maybe divine inspiration. Cantor's insights give me hope that someday, someone will crack the physics of the singularity. Probably impossible - the mind of God not knowable to the human mind - but numbering the infinities was thought ridiculous not that long ago.

Pastorius said...

First, I am not a math guy, so I struggle with the subject.

I am a Philosophy guy.

I became aware of Cantor's work by reading The Fabric of Reality, by the Physicist David Deutsch, and from reading Infinity and More by David Foster Wallace.

You know, Einstein was a kind of savant, more than likely, Asperger's.

I was once invited to visit the Athanaeum Club at CalTech in Pasadena, CA. I was invited by the Club Manager. While I was there, he took me on a tour of the Club. He took me to the Einstein Suite which is the room where Albert Einstein lived.

Einstein had clearly made a big impression on the people of the Club. They were still passing down stories.

The story I found interesting was that, Einstein would go out for a morning walk in the garden to think. The Club Manager took me along the route to the Garden. As I recall it, we went around a corner, and then another corner. There were some hedges, and around that second corner, there was a bench. The manager said, this is where Einstein would sit down and spend his time thinking. And then at the end of the day, someone would have to come out here and get him, because he wouldn't remember how to get back. Either that or he was just so lost in thought, he had not noticed what time it was.

That a man who is widely considered to be the greatest genius of the 20th century couldn't remember to go home, or how to get home, when it was no more than 100 yards away, tells me he had to have been some sort of Autistic.

Anyway, it could also be true of Cantor, but I believe Cantor was a mystic, like Spinoza.

The thing I find interesting about Cantor is that the pursuit of defining Infinity (which in itself sounds insane), and incompleteness led to ideas that are foundational in AI technology.

I find something mystical in that. What is of note is that, when man wants to Create in his own image, he must deal with where his ideas bump up against the ineffable. I believe that, ultimately, man is going to find out his "AI" is soul-less, and that there is something magical about being a human being, something ineffable, there is a chooser behind the brain, which is not to be captured by science.

Anonymous said...

Pasto: interesting commentary. I hate that Einstein has so many detractors today and I didn't want to give a negative impression. He just "consumed most of the Oxygen in the Room" so to speak. Also, I misspelled Riemann above. My German isn't bad but my dyslexia is better LOL.

Anonymous said...

Also I will look into the books you referenced. Thanks.

Pastorius said...

I am not sure, but I think Infinity and More is not considered highly.

The Fabric of Reality is, to my mind, an absolutely amazing book. It has changed the way I see the world.

And, by the way, I don't know German at all, though what little I have learned about the intricacies of translation is via reading multiple versions of Nietzsche and Rilke, and trying to understand the deviations.