Improvising... Music and Math

For Sunday reflection, from Stephon Alexander’s “The Jazz of Physics”:

“Humans are the only creatures that can discover advanced mathematics, and the only creatures that can create and formalize music. If the beauty and physics of the universe, and the beauty and physics of music are linked, the links exist uniquely in human brains… What makes us uniquely able to do what nonhuman brains cannot: appreciate music and understand mathematics? And to create new things under the sun: compose, improvise, discover new mathematical facts about the universe?   

 “A few musicians, like Coltrane, have an uncanny ability to improvise, to find the hidden patterns and regularities underlying harmonic forms and to use those insights to generate brand-new kinds of melodic sequences. And a few scientists, like Einstein, can find regularities that have eluded even other great scientists — such as taking the Maxwell equations and reducing them into a single unifying formulation.”

Taking In the Forest From Above...

(via Wikipedia)

As most have heard by now, Robert Langlands, at age 81 (and it’s always great to hear of an 81-year-old mathematician receiving an award! ;), is the winner of the 2018 Abel Prize in mathematics.  Robert’s work, the Langlands Program, is fascinating even if all you grasp is the broad outline of what it attempts to do, without much understanding of its complex details.  Here are 3 of the general audience pieces already out on this momentous occasion:

Alex Bellos in The Guardian:

https://www.theguardian.com/science/alexs-adventures-in-numberland/2018/mar/20/abel-prize-2018-robert-langlands-wins-for-unified-theory-of-maths

Kevin Hartnett at Quanta:

https://www.quantamagazine.org/robert-langlands-mathematical-visionary-wins-the-abel-prize-20180320/

Davide Castelvecchi for Nature:

https://www.nature.com/articles/d41586-018-03423-x

I suspect over the next week there will be additional excellent articles appearing on this subject (I may or may not add other links here as they come along.)

Added:

For those with the background, a longer, more technical piece from AMS here:

https://blogs.ams.org/beyondreviews/2018/03/20/robert-p-langlands-receives-the-abel-prize/

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For any who've never read it, or are unfamiliar with it, Ed Frenkel's "Love and Math: The Heart of Hidden Reality" introduces readers, to the Langlands Program, Ed's specialty.

And rightly or wrongly, this whole unification of mathematics notion, reminds me of a favorite quote from Keith Devlin I’ve used multiple times before (from an interview he once did for the NPR program “On Being” — and, not meant to imply anything about his own specific knowledge of Langlands):

"...that's when I became a mathematician; that's what I stumbled on at age 15 or 16 when here I was learning all this mathematics because I needed it. I had a utilitarian view of mathematics. I was learning it because I needed to solve the equations because I was going to be solving them in physics. And then, at the age of about 16 or 17, it all fit because it all came together in my mind. It was no longer this disjointed collection of techniques you could use to solve problems. It all fell into place, into this wonderful landscape. It was as if I'd been stumbling around in a forest, and suddenly I've climbed to the top of a tree and looked out and thought, this is the most beautiful place in the world. You can't tell it when you're down in the trees, which I had been, but the moment you reach an elevation where it all falls into place and you can see the whole topographic display in front of you, then the beauty is incredible. And the moment I discovered it, I said, um, I want to study mathematics. And I've been studying it ever since."

(...not sure of the specific credit for creation of this fun map, that has been passed around a lot, or I'd give credit?)

Bernie's Self-control...

Sunday reflection:

"[Walter] Mischel has priceless videos from some of the early experiments that demonstrate the difficulty kids had in exerting self-control. There is one kid I am particularly curious about. He was in the toughest setup, in which the bigger prize, three delicious Oreo cookies, was sitting right in front of him. After a brief wait, he could not stand it anymore. But rather than ring the bell, he carefully opened each cookie, licked out the yummy white filling, and then put the cookie back together, arranging the three cookies as best he could to avoid detection. In my imagination, this kid grows up to be Bernie Madoff."

                                                             -- Richard Thaler in "Misbehaving"

Robots Creating Robots

If you missed Terry Gross's "Fresh Air" episode yesterday on artificial intelligence, it's worth a listen here, when you get a chance:
https://www.npr.org/2018/03/15/593863645/robots-are-now-creating-new-robots-tech-reporter-says

A Sad Pi Day

In honor of Stephen Hawking today I’ll just link to perhaps my favorite Hawking story (granted it’s probably more of a Sean Carroll story). Most science buffs likely already know it, but in case you’ve missed it over the years:

https://www.preposterousuniverse.com/blog/2012/01/08/happy-birthday-stephen-hawking/

[ADDENDUM: this morning Sean tweeted out the audio version of this story told originally for "Story Collider":
https://www.storycollider.org/stories/2016/1/1/sean-carroll-what-would-stephen-hawking-do ]

Additionally, here’s an older lecture Dr. Hawking published in Plus Magazine about his work:

https://plus.maths.org/content/stephen-hawkings-60-years-nutshell

Math Story-Collider

H/T to Jim Propp for pointing out this current 'Story Collider' edition offering up two quite different narratives (with important messages) from Ken Ono and Piper Harron:

https://www.storycollider.org/stories/2018/3/5/in-honor-of-pi-day-stories-about-math

Transcripts of the talks are also presented, but give the under-15-min. talks a listen if you have the time.

"the distilled essence of who we are"

Paul Lockhart expounds:

“And I'll go even further and say that mathematics, this art of abstract pattern-making — even more than storytelling, painting, or music -- is our most quintessentially human art form. This is what our brains do, whether we like it or not. We are biochemical pattern-recognition machines and mathematics is nothing less than the distilled essence of who we are.” 

In Honor Of...

In honor of International Women's Day a few links I’ve posted here before, but seem especially appropriate for today:

http://unexpectedtheatre.org/video.htm

https://www.womendomath.org

https://sites.google.com/site/awmmath/home

…and Evelyn Lamb maintains this list of female math tweeters:

https://twitter.com/evelynjlamb/lists/mathy-ladies

Lastly, a little nostalgia:

Video Games Versus Boredom

Sunday reflection:

“Every maker of video games knows something that the makers of curriculum don't seem to understand. You'll never see a video game being advertised as being easy. Kids who do not like school will tell you it's not because it's too hard. It's because it's boring.”

— Seymour Papert