Sorry! Did you say the beauty of mathematics?
Those of you that read this blog fairly regularly know that from time to time I drift away from all things dog and potter in the garden of simply fascinating ideas.
Such is the case today.
It is an article on mathematics that was sent to me by Jim Goodbrod. He had read it in The New York Times in April.
Read it and see if you, too, find it as fascinating as I did!
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The World’s Most Beautiful Mathematical Equation
I was doing KenKen, a math puzzle, on a plane recently when a fellow passenger asked why I bothered. I said I did it for the beauty.
O.K., I’ll admit it’s a silly game: You have to make the numbers within the grid obey certain mathematical constraints, and when they do, all the pieces fit nicely together and you get this rush of harmony and order.
Still, it makes me wonder what it is about mathematical thinking that is so elegant and aesthetically appealing. Is it the internal logic? The unique mix of simplicity and explanatory power? Or perhaps just its pure intellectual beauty?
I’ve loved math since I was a kid because it felt like a big game and because it seemed like the laziest thing you could do mentally. After all, how many facts do you need to remember to do math?
Later in college, I got excited by physics, which I guess you could say is just a grand exercise in applying math to understand the universe. My roommate, a brainy math major, used to bait me, saying that I never really understood the math I was using. I would counter that he never understood what on Earth the math he studied was good for.
We were both right, but he’d be happy to know that I’ve come around to his side: Math is beautiful on a purely abstract level, quite apart from its ability to explain the world.
We all know that art, music and nature are beautiful. They command the senses and incite emotion. Their impact is swift and visceral. How can a mathematical idea inspire the same feelings?
Well, for one thing, there is something very appealing about the notion of universal truth — especially at a time when people entertain the absurd idea of alternative facts. The Pythagorean theorem still holds, and pi is a transcendental number that will describe all perfect circles for all time.
But our brains also appear to respond to mathematical beauty as they do to other beautiful experiences.
In a 2014 study, Semir Zeki, a neuroscientist at University College London, and other researchers used fM.R.I. scanners to observe the brains of 15 mathematicians while they were thinking about various equations. The subjects were shown 60 mathematical formulas two weeks before they were scanned and during and after the scan. They were also asked to rate their level of understanding of each equation and their subjective emotional response to it, from ugly to beautiful.
The researchers found a strong correlation between finding an equation beautiful and activation of the medial orbitofrontal cortex, a region of the prefrontal cortex just behind the eyes. This is the same area that has been shown to light up when people find music or art beautiful, so it seems to be a common neural signature of aesthetic experience.
Geeks, take heart: While you can’t see or hear mathematical ideas, they too are capable of arousing a sense of beauty.
No doubt you’d like to know which equation won the beauty contest. It was the so-called Euler’s identity, which is a deceptively spare but profound equation that links five fundamental mathematical constants: a mix of real and imaginary numbers that combine to make zero. And the ugliest? Ramanujan’s infinite series for the reciprocal of pi — a clunky equation, even to this non-mathematician.
While mathematicians were more likely to find formulas beautiful if they understood them well, the correlation was not perfect, so the researchers were able to show that the observed brain activation was a result of the experience of beauty apart from meaning. This makes sense, in that there were equations that subjects understood completely yet found ugly.
Now, the medial orbitofrontal cortex is also active when we find something pleasurable or rewarding, which isn’t surprising either, since you’d expect beautiful experiences to be both.
My love of math originated in the physical world. My father, an insatiably curious guy and electrical engineer, used to build things with me — crystal radios, electric generators, all kinds of exciting contraptions.
One summer evening I found him tinkering with a mysterious metal box in the garage. It was a prototype of a ruby laser. When he flicked the switch, a brilliant thin red light shot out of the laser and up into the night sky.
“How far does it go?” I asked. “To infinity,” he said and added, smiling, “or further.”
I was awe-struck. I still am.
Richard A. Friedman is a professor of clinical psychiatry and the director of the psychopharmacology clinic at the Weill Cornell Medical College, and a contributing opinion writer.
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While my understanding of mathematics is average, to say the best, I did identify with the idea spelt out a few paragraphs above. This one:
….. so the researchers were able to show that the observed brain activation was a result of the experience of beauty apart from meaning.
Because it took me back to looking up at the night sky out at sea well away from land.
Did I understand the meaning of what I was looking up at? Of course not! Did I experience beauty? Beyond what I could put into words!
If only I had been blessed with the gift of knowing numbers, I would have considered a career in the sciences.
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But I bet you have a great interest in the sciences!
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I do! That is my analytical nature.
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Not a difficult guess on my part!
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Very nice! I have always considered myself as standing in the doorway of math. Enjoyed arithmetical computations as a kid, loved plane geometry in high school. But got lost in the depth of real statistical analysis. That was the stuff that convinced me math wasn’t my field. Nonetheless, in writing about markets over the years for Reuters, I did get to know and enjoy the Fibonacci Progression and the Golden Mean. I did Sudokus for while, but had to quit because filling in the little boxes was too painful for the arthritis in my hands. Thanks for the fun read!
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Tony, you lift the lid on what sounded like an interesting occupation. Can’t resist asking if it has left you with a greater insight into the behavior of said markets than the average person?
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Absolutely. I wrote about markets for 20 years for Reuters. When I left them I taught Journalism for a while, then worked for a philanthropy writing in their investment department. I moved from there to managing their bond investments. It’s like writing about a sport for 20 years and then being asked to come play. It was great.
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How very interesting! I stumbled into journalism when I was living in Australia in 1968-1969. Working freelance for the Finnish magazine KotiPosti. Certain that’s where my love of writing was born.
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I stumbled into journalism, too. I took a finance degree expecting to go into commerce, but always loved reading and writing. I actually wrote for men’s magazines for the first five years of my career. Became a ‘journalist’ after that. It’s all writing, though. Funny how life works out. Now I am a health writer and that is my life, only for the past seven plus years since starting the blog.
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“Funny how life works out.” isn’t the half of it!! Best wishes!
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Its a foreign language to me, but one I appreciate!
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Bet it’s not that foreign!
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I agree with Val… It’s all Greek to me, but the letters are pretty 🙂
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John, likewise, don’t believe you!
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I was never the brightest spark at school when it came to Maths Paul.. In fact I was considered quite dim.. But managed never to come bottom.. 😉
Maths is fascinating and Did you get to see the film.. Hidden Figures? about the woman who helped put rockets and men in space and bring them back safely through their shear genius in Maths.. Great film..
When you look around in Nature.. Everything is Maths.. An interesting article I am sure will find of interest is here on the BBC website
http://www.bbc.co.uk/news/magazine-14305667 🙂 Natures hidden Prime Number Code.. 🙂
Thanks Paul for making my grey matter work today.. 🙂
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Hadn’t even heard about that film! (Must get out more!) But a quick search showed it was released just last December. One to watch fairly soon me thinks.
Then your link to that BBC News item – fascinating. So much to learn. So little time!
Sue, what a fabulous contribution from you. Thank you!
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🙂 we try to see a film now once a month of one of our choosing at the cinema.. Its amazing what you can fit in as we get older.. One wonders how we ever found time to work a full time job. 😉
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Or stay on top of 13 acres, a decent sized house and look after 18 animals, not counting the deer, write a blog, and endless other things! And fib! Because we don’t stay on top of it all!
I was always told that these are going to be the quieter end times of our lives!! Fat chance!
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Hehe.. But it keeps us going Paul.. And we wouldn’t have it any other way would we.. LOL. 🙂
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Not at all! (Just crossed my mind as to whether you and your husband ever make it across to the West? For if you did, we could offer you a nice English cup of tea! 😍 )
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Bless you both Paul and Jean.. 🙂 That is a most generous offer.. One should never pass up the chance of a cuppa.. 🙂 At the moment we have not got our flying Wings on.. 🙂 Preferring to explore more of the UK these past couple of years.. And Scotland beckons to us next week.. 😉 So Haggis is on the menu .. 🙂 and no doubt a wee dram for Hubby.. 🙂 😉 But if ever I should be in your neck of the woods Paul.. I will be sure to let you and Jean know to put the Kettle on.. 😉 ❤ Many thanks
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And I’m sure you read my offer of a cuppa as including coming to stay with us! But Scotland is a precious part of the UK!
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I did indeed Paul and I so thank you both for that gracious offer my friend.. 🙂 You do not know what that means… So thank you so much again my friends.. You are both indeed very dear to me.. 🙂
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Mutually felt!
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🙂 😀
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I actually did a semester on Sacred Geometry in college. I also love Physics, esp the quantum variety. Have you read Loren Eisley’s “Star Thrower?” I bet you’d love his writing, if you haven’t run across it. I’m a straight-up liberal arts person, but I do love the elegance of math.
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I hadn’t previously heard of Loren Eisley but a quick web search brought this up: http://www.eiseley.org/Star_Thrower_Cook.pdf
I shall be reading that a little later on.
Many thanks for your contribution. It joins so many others today that have really been fascinating to read!
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Now been read and, yes, incredibly powerful prose.
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Oh, he’s wonderful. He has written many interesting books, but Star Thrower remains my favorite 😉 Also and surely you know of Fritjof Capra’s The Tao of Physics? xoxoxo
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The name is familiar but I can’t recall it in detail. Sign of the timed for me these days!!
But I will look up the details without doubt!
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🙂
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Somehow aesthetics don’t come to mind right off the bat when I see mathematical equations. Frustration on the other hand does. LOL
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Each to their own! And your response is perfectly understandable.
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