Continuum Hypothesis via Scott Aaronson

 

Bored with the headlines, folks?... Is election news getting you down?... Or the blitz of political ads scraping on your last nerve?... Is that what's buggin' you, kiddies??? 

Well, OK, this won’t be everyone’s cup-a-tea, or fun distraction, but in a longish post (first of multiple) Scott Aaronson tackles the independence of the Continuum Hypothesis:

https://www.scottaaronson.com/blog/?p=4974

I knew it would be a great read when he started off with this quote from Bertrand Russell:

 ;)

“in adolescence, I hated life and was continually on the verge of suicide, from which, however, I was restrained by the desire to know more mathematics.”

Something for the Young, the Older, and the Conspiracy Theorist

A few items you may have already seen, but if not...:


1) Sherlock-Holmes-wannabes are still trying to figure out who "Satoshi Nakamoto," creator of Bitcoin really is. The NY Times piece below draws an unconvincing (I think) link to the former proprietor of the Silk Road website. The guessing game may be more fun than learning the true identity will ever be.

http://tinyurl.com/otavjw3

2) Another great post from MathMunch covering several matters, but what most interested me (because I'd not heard of it) is a Scrabble-like game called "Numenko" that helps young people learn/practice arithmetic:

http://mathmunch.org/2013/11/04/numenko-turning-square-and-toilet-paper/

3) And finally, my favorite recent read from the Web, the always excellent Natalie Wolchover attempts to explain (better than I've ever seen done before, though still a tough-read) two different approaches to solving the infinity "continuum" problem:

https://www.simonsfoundation.org/quanta/20131126-to-settle-infinity-question-a-new-law-of-logic/

Set aside some brain-time to take in this account of "forcing axioms" versus "V = ultimate L".

Wow! The Continuum Hypothesis Solved???...

...well, I doubt it, but what do I know: Apparently a major Berkeley mathematician/set theorist, Hugh Woodin, using a "radically stronger logical structure" known as "ultimate L," believes he has accomplished what no one has been able to do in well over a century, and demonstrate that Gödel's Cantor's Continuum Hypothesis is true (essentially, that there exist no infinite sets lying between the set of integers and the set of real numbers -- of course it still all hinges on the initial axiomatic system one adapts):

http://www.newscientist.com/article/mg21128231.400-ultimate-logic-to-infinity-and-beyond.html?full=true

(Coincidentally, this fascinating article is from Richard Elwes who I was just highlighting a few days back.)

If you're not interested in infinity or sets, skip this article; otherwise, dive in!

Poincare and the Continuum

From "Mathematics Rising" blog: 

"...mathematics is not built entirely on logic.  It lives somewhere between thought-governed ideal realities and physical realities created by the senses.  As such, it may be able to provide its own unique view of cognition itself.  It may be said that cognitive processes unfold themselves into mathematical insights."

Read the entire post on the essence of mathematics here:

http://mathrising.com/?p=335