The science of beauty

I got a curious response to my post a couple of days ago, about magical and/or supernatural explanations not actually being explanations at all, but a way to stop thinking.

Here's the email:

Dear Mr. Skepto,

You sound pretty worried that you don't have an explanation for everything.  People aren't always explainable!  They do things because they do them.  That's it.  Some people believe weird stuff and some people like the explanations from science.  Just like some people like the Beatles and some people like Beethoven.  It's silly to wear yourself out trying to figure why.

Do you worry about why your loved ones love you?  Maybe it's some chemical thing in their brain, right?  Do you tell your wife that's what love means?  Maybe it's a gene or something that's why I think flowers are pretty.  If so, the explanation is uglier than the flowers are.  I'd rather look at the flowers.

All your scientific explanations do is turn all the good things in life into a chemistry class.  I think they're worth more than calling them brain chemicals.  I'll take religion over science any day.  At least it leaves us with our souls.

Think about it.

L. D.

Well, L. D., thanks for the response.  I find your views interesting -- mostly because they're just about as opposite to the way I see the world as they could be.

But you probably already knew that.

There is a reason why musical tastes exist.  We're nowhere near the point in brain research where we could discern the explanation; but an explanation does exist for why Shostakovich's Prelude & Fugue in E-flat Minor gives me goosebumps (especially in this recording, played by the composer himself!), while Brahms's symphonies might send someone else into raptures but do nothing for me whatsoever.  Nothing just "is because it is."

And I can't fathom how knowing the explanation devalues your appreciation of the thing itself.  Me, I would love to know what's happening in my brain when I hear a piece of music I enjoy.  We're beginning to get some perspective on this, starting with a 2011 study that found that the neurological response to hearing a piece of music we love is similar to the brain's response to sex.

Cool, yes?  I think that's awesome.  How would knowing that make me appreciate music less?

Or sex either?

I find flowers even more beautiful knowing that their shapes and colors evolved to attract pollinators, and understanding a bit about the chemistry of photosynthesis.

Understanding light refraction doesn't make me shrug my shoulders at a rainbow.  And even love -- which L. D. evidently thinks lies entirely in the mystical realm -- is made no less by my knowledge that its underpinning has to do with brain chemistry.  It's like that old song with the verse:

Tell me why the stars do shine
And tell me why the ivy twines
And tell me why the sky is blue,
And I will say why I love you.

A more scientific type added a verse, to wit:

Nuclear fusion is why the stars do shine.
Thigmotropism is why the ivy twines.
Rayleigh scattering is why the sky's so blue,
And testicular hormones are why I love you.

Which I think is not only hilarious, it's a good deal more realistic than attributing it all to souls and people "doing things because they do them."

In short: science itself is beautiful.  Understanding how the world works should do nothing but increase our sense of wonder.  If scientific inquiry isn't accompanied by a sense of "Wow, this is amazing!", you're doing it wrong.  I'll end with a quote from Nobel Prize winning physicist Richard Feynman, who in his 1988 book What Do You Care What Other People Think? had the following to say:

I have a friend who's an artist, and he sometimes takes a view which I don't agree with.  He'll hold up a flower and say, "Look how beautiful it is," and I'll agree.  But then he'll say, "I, as an artist, can see how beautiful a flower is.  But you, as a scientist, take it all apart and it becomes dull."  I think he's kind of nutty…  There are all kinds of interesting questions that come from a knowledge of science, which only adds to the excitement and mystery and awe of a flower.  It only adds.  I don't understand how it subtracts.

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An anodyne against despair

Yesterday, I was discussing with a friend how important it is to find things that lift your spirit. The world has been replete with dismal news lately, and it's all too easy to decide that everything's hopeless -- to become either cynical or despondent.  I know I have to fight that tendency myself, especially considering the topics I frequently address here at Skeptophilia.

It's essential to take a moment, every so often, to step back and recognize that however terrible current events have been, there is still great love, compassion, and wonder in the world.  So I thought I'd take a day off from the continual stream of WTF that the news has become, and consider a few examples of what beauty we humans are capable of.  Think of it as an anodyne against despair, a way to inoculate yourself against losing hope.

Dalai Lama Mandala I, pen/ink/watercolor, by Carol Bloomgarden [Image used with permission]

First, take a look at this video by the Dutch artist Thijme Termaat. He spent two and a half years creating a progressive set of paintings, condensed it into a three-minute video, set it to a piece from Vivaldi's The Four Seasons, and named it Timelapse. Take three minutes and be amazed.

When I was in Boston a while back, I went to the Boston Institute of Contemporary Art, and I lucked out and saw some work by the incredibly creative Rachel Perry Welty. The piece that absolutely captivated me was a twelve-minute video called Karaoke Wrong Number, wherein she took four years' worth of voicemail messages she'd received by accident (i.e., the person had called her number but thought they were leaving a message to someone else entirely), and lip synced to them.  I stood there and watched the entire piece three times in a row -- it's mesmerizing.  The incredible thing about it is that she's able to shift her facial expression and body language to match the voice and message of the person -- it's funny, wry, and at times absolutely uncanny, and illustrates Welty's sheer creative genius.  (You can watch a five-minute clip from it at the link above.)

If you don't mind crying, take a look at Kseniya Simonova's stupendous feat of drawing in sand on a light box that brought the whole audience to tears in Ukraine's Got Talent.  It shows the effect of the German invasion on the people of Ukraine during World War II, and packs an emotional punch like nothing I've ever seen before -- especially considering what's happening in Ukraine right now.  It's a perfect example of an artist's ability to distill pain into beauty.

If after that, you want to see something that is pure whimsy to cheer you up, you need to watch the amazing musical marble machine created by Martin Molin of the Swedish band Wintergatan.  Molin created a wild Rube Goldberg machine, powered by a hand crank and 2,000 marbles, that plays a tune he wrote. It's one of those things that you watch, and you just can't quite believe it's real.

If you want to blow your mind further, have a look at this short little video showing one of the crazy three-dimensional sculptures of Japanese mathematician and artist Kokichi Sugihara.  Sugihara specializes in creating optical illusions out of paper -- in this case, a structure that seems to induce marbles to roll uphill.  The weird thing to me is that even when he shows you how it's done -- which he does, about halfway through -- you still can't see it any other way.  It's so cleverly done that our brains simply can't handle it.

Last, for sheer exuberance -- if you're like me, it'll make you laugh and cry at the same time -- check out the short film "Where in the Hell Is Matt?", made by Matt Harding.  Harding set out to film himself dancing in as many different spots on Earth as he could get to, often joined by children, adults, and dogs, all simply expressing how wonderful it is to be alive.  It's set to the heart-wrenchingly gorgeous song "Praan" by Garry Schyman.  The music and the spirit of Harding's project could not blend together more perfectly.

So there you are.  Even when things are bad, people are still creating beautiful, funny, and whimsical things.  They still care about bringing joy into the world, despite the constant barrage of pain, discouragement, and bad news we're subjected to on a daily basis.  I don't know about you, but when I see things like this, it reminds me that humanity isn't as hopeless as it may seem at times.  It recalls the last lines of the beautiful poem "Desiderata," by Max Ehrmann, which never fails to bring me to tears, and which seems like a good place to conclude:

Nurture strength of spirit to shield you in sudden misfortune.  But do not distress yourself with dark imaginings.  Many fears are born of fatigue and loneliness. 

Beyond a wholesome discipline, be gentle with yourself.  You are a child of the universe, no less than the trees and the stars; you have a right to be here. 

And whether or not it is clear to you, no doubt the universe is unfolding as it should.  Therefore be at peace with God, whatever you conceive Him to be.  And whatever your labors and aspirations, in the noisy confusion of life, keep peace in your soul.  With all its sham, drudgery and broken dreams, it is still a beautiful world.  Be cheerful.  Strive to be happy.

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Art, haiku, and Lensa

The injection of AI technology into art has opened up a serious can of worms.

I ran into two examples of this in rapid succession a couple of days ago.  The first came to me by way of a friend who is an artist and writer, and is about the Lensa app -- a wildly-popular AI art interface that can take an image of your face, spruce it up a bit (if it needs it -- mine certainly would), and then create digital art of you as a superhero, model, mythological creature, Renaissance painting, or dozens of other reimaginings of you.  Someone I follow on TikTok posted a sequence of Lensa art based on his face -- and I have to say, they were pretty damn cool-looking.

Yes, but.

The hitch is where all the imagery Lensa is using comes from.  There are credible allegations that the owners of the app are basically shrugging their shoulders at the question.  Artist Rueben Medina had the following to say about it:

I hate being a party pooper but please stop using Lensa and posting your AI art images from it.  I understand if you don't care about the blatant theft of your data the app is doing, lots of things do that.  What you should care about is this: 

The Lensa app uses the Stable Diffusion model to create those AI images.  That model is trained on the Laion database.  That database is full of stolen artwork and sensitive images.  Using Lensa hurts illustrators/photographers in two major ways: 

1. This database was built without consent nor compensation.  That means the work is stolen. 

2. The proliferation of cheap AI art is culturally devaluing the work of illustrators which is already at rock bottom. 

Is there an ethical way to create AI art?  Absolutely.  Databases built on images that artists have opted into and are being compensated for is the first step.  Pretty much none of these AI art apps do that because it would make their business model (Lensa wants $40/yr) unprofitable.

This one hits hard for me because my wife is an artist who shows all over the Northeast, and it has become increasingly difficult for her to sell her pieces at a price that fairly compensates her for her time, skill, and talent -- in part because it's so easy to get mass-produced digital art that gives the impression of high quality at a far lower price.  Carol's work is stunningly original -- you seriously should check out her website -- and while she still has very successful shows, the game is a lot harder than it used to be.

Part of the problem is how good the AI has gotten.  And it's not just visual art that is under attack.  Right after I ran into the Lensa sequence on TikTok and saw Rueben Medina's impassioned plea not to use it, I stumbled across a paper in the journal Computers in Human Behavior describing an AI program that can produce haiku, a stylized seventeen-syllable form originating in Japan that often deals with finding beauty in nature, and evokes the emotions of serenity, peace, wistfulness, and nostalgia.

The authors write:

To determine the general characteristics of the beauty experience across object kinds, Brielmann et al. (2021) proposed eleven dimensions that have been considered by prominent philosophers of aesthetics (pleasure, wishing to continue the experience, feeling alive, feeling that the experience is beautiful to everyone, number of felt connections to the experience, longing, feeling free of desire, mind wandering, surprise, wanting to understand the experience more, and feeling that the experience tells a story) and eight dimensions conveyed by psychologists (complexity, arousal or excitement, learning from the experience, wanting to understand, harmony in variety, meaningfulness, exceeding one's expectation, and interest).  In accordance with [this scheme], these dimensions were used to identify factors that delineate the experience of beauty in human-made and AI-generated haiku.

It is both fascinating and disquieting that the software produced haiku so authentic-sounding that a panel of readers couldn't tell them apart from ones written by humans.

"It was interesting that the evaluators found it challenging to distinguish between the haiku penned by humans and those generated by AI," said Yoshiyuki Ueda, who co-authored the paper, in an interview with Science Daily.  "Our results suggest that the ability of AI in the field of haiku creation has taken a leap forward, entering the realm of collaborating with humans to produce more creative works. Realizing [this] will lead people to re-evaluate their appreciation of AI art."

Yes, but.

[Image licensed under the Creative Commons Damian Putica, A.I Generated Artwork of a teenage boy and teenage girl, CC BY-SA 4.0]

I am very much of the opinion that the perception of beauty in any art form -- be it visual arts, writing, music, dance, theater, or anything else -- occurs because of the establishment of a link between the producer of the art and the consumer.  (I dealt with this a while back, in a post called "The Creative Relationship," about our unstoppable tendency to read our own experience into what we see and hear.)  But what happens when one side of that relationship is a piece of software?  Does that matter?  As a writer, I find this a troubling prospect, to say the least.  I know we're not nearly there yet; haiku is a simple, highly rule-based form, which novels are clearly not.  (I don't mean haiku is simple to do well, just that the rules governing the form are simple.)  Having an AI write a creditable haiku is bound to be a lot easier than having it write a novel.  But as we've seen so many times before, once we have proof of concept, the rest is just tinkering; the software tends to improve really quickly once it's shown that the capability is there.

As a novelist, I would have a serious concern about being superseded by a story-generating computer that could create novels as well as I can.

The whole thing raises questions not only about the ethics of using human creators' work as a springboard for AI-based mass production, but about what exactly creativity means, and whether it matters who -- or what -- is doing the creating.  I don't have any easy answers; my emotional reaction against the possibility of what my wife and I both do being supplanted by computer-generated content may not mean very much.

But I think all of us -- both creators and consumers -- better think long and hard about these issues, and soon.

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A hostile beauty

William Shatner, of Star Trek fame, wrote some profoundly moving words in his book Boldly Go, about his experience riding into space on Jeff Bezos's Blue Origin shuttle:

I love the mystery of the universe.  I love all the questions that have come to us over thousands of years of exploration and hypotheses.  Stars exploding years ago, their light traveling to us years later; black holes absorbing energy; satellites showing us entire galaxies in areas thought to be devoid of matter entirely… all of that has thrilled me for years… but when I looked in the opposite direction, into space, there was no mystery, no majestic awe to behold... all I saw was death.

I saw a cold, dark, black emptiness.  It was unlike any blackness you can see or feel on Earth.  It was deep, enveloping, all-encompassing.  I turned back toward the light of home.  I could see the curvature of Earth, the beige of the desert, the white of the clouds and the blue of the sky.  It was life.  Nurturing, sustaining, life.  Mother Earth.  Gaia.  And I was leaving her.

Everything I had thought was wrong.  Everything I had expected to see was wrong.

I had thought that going into space would be the ultimate catharsis of that connection I had been looking for between all living things—that being up there would be the next beautiful step to understanding the harmony of the universe.  In the film Contact, when Jodie Foster’s character goes to space and looks out into the heavens, she lets out an astonished whisper, "They should’ve sent a poet."  I had a different experience, because I discovered that the beauty isn’t out there, it’s down here, with all of us.

He's right in one sense; the vast majority of the universe is intrinsically hostile to life.  It's why I've always found the Strong Anthropic Principle a little funny.  The Strong Anthropic Principle claims that the physical constants which are, as far as we currently understand, not derivable from anything else -- such as the strength of the four fundamental forces, the masses of the subatomic particles, the speed of light, the fine structure constant, and so on -- were set with those values in order to make the universe accommodate matter and energy as we know it, and ultimately, life.  The words they use are "fine tuned."  If any of those constants were even a little bit different, life would be impossible.

Typically, the argument progresses from "fine tuning" to "implies a fine tuner" to "implies God."

This whole line of thought, though, ignores three things.  First, of course we live in a universe that has the physical constants set such that life is possible; if they weren't, we wouldn't be here to discuss the matter.  (This is called the Weak Anthropic Principle.)  Second, when I said those constants are not derivable from anything else, you should place the emphasis on the phrase that came before it; as far as we currently understand.  It may be that physicists will eventually find a Grand Unified Theory showing that some -- perhaps all -- of the physical constants are what they are because of a single fundamental principle stating that they aren't arbitrary after all, that they couldn't have any other values.

Third, as Shatner points out, most of the universe -- even most of the Earth, honestly -- is pretty fucking hostile to life as it is.

But I question his statement that this makes the universe any less beautiful.  I was in Iceland this summer and got to see an erupting volcano -- the whole nine yards, with jets of orange lava fountaining up and cascading down the side of the cinder cone.  I could feel the heat on my face from where I stood, about a hundred meters away; much closer, and my skin would have blistered.  The sulfur fumes were only made tolerable by the fact that it was a windy day.  The hillside beneath my feet was vibrating, the air filled with a roar like thunder.  Standing there, I was in no doubt at all about my own frailty.

It was also incredibly, devastatingly beautiful.

I was thinking about the beauty of the universe -- as unquestionably inimical as it is to our kind -- when I saw images from the Hubble Space Telescope of the Cat's Eye Nebula, along with a visualization of what it would look like close up, created by a team led by Ryan Clairemont of Stanford University:

The spirals are thought to be caused by two stars in the center of the nebula orbiting around each other, each emitting a pair of plasma jets that have been twisted by the stars' motion in the fashion of the jets of water sprayed from a spinning garden sprinkler.  But whatever the cause of the pattern, I was immediately struck by its awe-inspiring beauty.

I've never been to space, and I don't mean to gainsay Shatner's experience.  But I find the vast immensity of space to be beautiful even though I know my own existence in it is all but insignificant.  I can look up at the autumn constellations, as I did last night -- Perseus and Andromeda, Pegasus and Pisces and Aquarius -- and appreciate the beauty of those stars glittering in the night sky from the warm safety of my home planet.  Maybe some of them have planets harboring their own frail, fragile life forms, who just like us are dependent on the searing fires of their host stars to survive, and just like us look up into the night sky with awe and wonder.

Frightening?  Sure.  Dangerous, savage, unpredictable?  Undeniable.

But also deeply, overwhelmingly beautiful.

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The most beautiful brain network

A couple of weeks ago, I wrote a piece here at Skeptophilia about some fascinating new research suggesting that there are links between our perceptions of artistic, musical, and mathematical beauty, and expressed some puzzlement about how those could possibly connect.  In one of those lovely near-synchronicities that happen sometimes, today I happened upon some new(er) research showing what the underlying connection might be -- in one single region of the brain.

In a paper published this week in the Proceedings of the National Academy of Sciences, a team made up of Edward A. Vessel and Ayse Ilkay Isik (of the Max Planck Institute), Amy M. Belfi (of the Missouri University of Science and Technology), Jonathan L. Stahl (of Ohio State University), and G. Gabrielle Starr (of Pomona College) showed that with different sorts of visual stimuli, our sense of aesthetic pleasure comes from activation of a part of the brain called the default-mode network.  The authors write:

Despite being highly subjective, aesthetic experiences are powerful moments of interaction with one’s surroundings, shaping behavior, mood, beliefs, and even a sense of self.  The default-mode network (DMN), which sits atop the cortical hierarchy and has been implicated in self-referential processing, is typically suppressed when a person engages with the external environment.  Yet not only is the DMN surprisingly engaged when one finds a visual artwork aesthetically moving, here we present evidence that the DMN also represents aesthetic appeal in a manner that generalizes across visual aesthetic domains, such as artworks, landscapes, or architecture.  This stands in contrast to ventral occipitotemporal cortex (VOT), which represents the content of what we see, but does not contain domain-general information about aesthetic appeal.

Using fMRI studies, the researchers compared the responses of the brains of volunteers to three types of visual stimuli; art, architecture, and photographs of natural landscapes.  The responses of the visual cortices of the test subjects showed great variation between these three different types -- evidently the brain's effort to categorize and interpret what it's seeing, so it's no great surprise that you'd respond differently while seeing the Mona Lisa than you would looking at Chartres Cathedral.

What was surprising, though, is that while viewing visual stimuli the test subjects found aesthetically pleasing, all of them had a high response in the default-mode network, which is usually associated with contemplation, imagination, self-reflection, and inward thought.  It's uncertain if the DMN actually encodes the basics of aesthetic response, but this certainly suggests a critical role.  "We don't know yet if DMN actually computes this representation," said Edward Vessel, lead author of the paper, in an interview in EurekAlert.  "But it clearly has access to abstract information about whether we find an experience aesthetically appealing or not."

This suggests to me a couple of interesting directions this research could go.  Obviously, it'd be intriguing to find out of the DMN is also active with other types of aesthetic appreciation (such as musical and mathematical aesthetics, the subject of the previous research).  What I'd find even more fascinating, though, is to see if there's a difference in the activity of the DMN depending upon how strongly the individual is aesthetically moved.  Those responses are so highly individual that finding a biological underpinning would be amazingly cool.  Why, for example, was my wife moved to tears while looking at paintings in a Van Gogh exhibition we attended a couple of years ago in New York City?  Why do I find Édouard Manet's 1882 masterpiece A Bar at the Folies-Bergère so emotionally evocative, while a lot of other art from the same period doesn't really grab me one way or the other?

[Image is in the Public Domain]

So this could be a window into finding out -- at least from a neurological standpoint -- how our brain modulates our aesthetic response.  The "why," of course, is more inscrutable -- demonstrating in an fMRI that I go into rapture hearing Stravinsky's Firebird isn't telling me anything I didn't already know, after all, and doesn't answer why I don't have the same response hearing Rachmaninoff's Piano Concerto #2.

But at least finding a neurological basis for such judgments would be a step forward.  The Vessel et al. research is a fascinating first step into understanding the sweetest of human behaviors -- our perception of beauty in the world around us.

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This week's Skeptophilia book recommendation made the cut more because I'd like to see what others think of it than because it bowled me over: Jacques Vallée's Passport to Magonia.

Vallée is an interesting fellow, and certainly comes with credentials; he has an M.S. in astrophysics from the University of Lille and a Ph.D. in computer science from Northwestern University.  He's at various times been an astronomer, a computer scientist, and a venture capitalist, and apparently was quite successful at all three.  But if you know his name, it's probably because of his connection to something else -- UFOs.

Vallée became interested in UFOs early, when he was 16 and saw one in his home town of Pontoise, France.  After earning his degree in astrophysics, he veered off into the study of the paranormal, especially allegations of alien visitation, associating himself with some pretty reputable folks (J. Allen Hynek, for example) and some seriously questionable ones (like the fraudulent Israeli spoon-bender, Uri Geller).

Vallée didn't really get the proof he was looking for (of course, because if he had we'd probably all know about it), but his decades of research compiles literally hundreds -- perhaps thousands -- of alleged sightings and abductions.  And that's what Passport to Magonia is about.  To Vallée's credit, he doesn't try to explain them -- he doesn't have a favorite hypothesis he's trying to convince you of -- he simply says that there are two things that are significant: (1) the number of claims from otherwise reliable and sane folks is too high for there not to be something to it; and (2) the similarity between the claims, going all the way back to medieval claims of abductions by spirits and "elementals," is great enough to be significant.

I'm not saying I necessarily agree with him, but his book is lucid and fascinating, and the case studies he cites make for pretty interesting reading.  I'd be curious to see what other Skeptophiles think of his work.

[Note: if you purchase this book using the image/link below, part of the proceeds goes to support Skeptophilia!]

Is there in truth no beauty?

Today's post is about an odd little piece of research that appeared in the journal Cognition this week, tying together a number of disparate realms -- mathematics, music, art, and the neuroscience of perception.

The study, by Samuel Johnson and Stefan Steinerberger (of the University of Bath and Yale University, respectively), looks at the fascinating question of how our perception of beauty carries across different expressions of the human creative impulse.  I've been interested in this topic for some time, especially with respect to music.  (Artistically, I have the aesthetic sensibilities that God gave gravel, and when my wife and our cultured friends talk art, I usually just keep my mouth shut and nod sagely.)

But the perception of beauty in music has intrigued me ever since my first realization that some pieces of music that thrilled me to the core left other people completely cold, and vice versa.  I have a good friend who, while we agree on many things, has about as opposite tastes to me in classical music as one could possibly have.  He adores Brahms, Mahler, Tchaikovsky, and Rachmaninoff, whereas I don't really care for any of them, and in fact could live happily forever without hearing a piece of Brahms's music again.  My tastes run more to Bach and Scarlatti... and Shostakovich, Stravinsky, and Prokofiev.  (What the link is between those two groups of composers, I have no idea.)

What Johnson and Steinerberger did, though, was to link up people's views of the aesthetic merit of art and music with their perception of beauty in mathematics.  Don't laugh, you non-math types; if you do any digging amongst the writings of mathematicians, you'll find plenty of references to theorems or proofs as being "elegant" or "beautiful," and a while back I did a piece on the claim that Euler's Identity, one of the most curious statements of mathematics, was so beautiful that it is a proof of the hand of the divine.  (To see how far mathematicians will engage in such aesthetic commentary on mathematical theorems, Paul Nahin calls Euler's Identity "the gold standard for mathematical beauty," and Keith Devlin of Stanford University states, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence.")

So it's not far-fetched to claim that some people see the same kind of beauty in mathematics that many of us do in art and music.  And Johnson and Steinerberger wanted to find out if there's a connection between the three.

They took four theorems from mathematics -- the sum of an infinite geometric series, Gauss’s summation trick for positive integers, the pigeonhole principle, and a geometric proof of a Faulhaber formula.  They used four pieces of music -- Schubert’s Moment Musical No. 4, D 780 (Op. 94), Bach’s Fugue from Toccata in E Minor (BWV 914), Beethoven’s Diabelli Variations (Op. 120), and Shostakovich’s Prelude in D-flat major (Op.87 No. 15) -- and four landscape paintings, Looking Down Yosemite Valley, California and A Storm in the Rocky Mountains, Mt. Rosalie by Albert Bierstadt, The Hay Wain by John Constable, and The Heart of the Andes by Frederic Edwin Church.

Looking Down Yosemite Valley, California by Albert Bierstadt (1864) [Image is in the Public Domain]

Test subjects were then assigned a series of three rather strange tasks -- to match the music to the mathematical theorems based on how similar they were aesthetically; to pair the art and the theorems the same way; and to rate each of the theorems and the pieces of art and music on nine criteria (seriousness, universality, profundity, novelty, clarity, simplicity, elegance, intricacy, and sophistication).

My immediate reaction to reading this was that I can't see any connection between artistic, musical, and mathematical beauty, at least in the sense that you would look at a landscape painting and be immediately struck the same way as you were by Gauss's summation trick.  I understand finding beauty in each realm, but I can't fathom how they could be connected in any sort of one-to-one correspondence.

But strangely, they seem to be.  The correspondences drawn between art and math and between music and math were remarkably similar across test subjects, as were the rankings given to each, especially on the criteria of elegance, profundity, and clarity.  Whatever it is that gave me such a frisson of wonder when I first came across the formula for the sum of an infinite geometric series -- and yes, that did actually happen, because it's freakin' cool -- causes a consistently similar reaction in people not only seeing art or listening to music, but seeing particular pieces of art or hearing particular pieces of music.

"Laypeople not only had similar intuitions about the beauty of math as they did about the beauty of art but also had similar intuitions about beauty as each other," Johnson said.  "In other words, there was consensus about what makes something beautiful, regardless of modality."

"I’d like to see our study done again but with different pieces of music, different proofs, different artwork,” said Steinerberger.  "We demonstrated this phenomenon, but we don’t know the limits of it.  Where does it stop existing?  Does it have to be classical music?  Do the paintings have to be of the natural world, which is highly aesthetic?"

Which are excellent questions.  For myself, I have incredibly eclectic tastes in music (as evidenced by putting my iPod on "shuffle," and inducing musical whiplash by going directly from a Bach partita to Nine Inch Nails).  Is there some correspondence there -- are other aficionados of Stravinsky also more likely to listen to Linkin Park?  Is there a connection between people who love mathematics and particular styles of music?

And what's going on in our brains when these judgments are being made?

As with much good scientific research, the Johnson/Steinerberger study raises as many questions as it answers.  We still don't know where aesthetic perception comes from, nor why it varies so much from person to person.  But as this study shows, there are some remarkable (and unexpected) similarities in how we perceive beauty.

And that is, in and of itself, kind of beautiful.

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This week's Skeptophilia book recommendation is a classic: James Loewen's Lies My Teacher Told Me.  Loewen's work is an indictment not specifically of the educational system, but of our culture's determination to sanitize our own history and present our historical figures as if they were pristine pillars of virtue.

The reality is -- as reality always is -- more complex and more interesting.  The leaders of the past were human, and ran the gamut of praiseworthiness.  Some had their sordid sides.  Some were a strange mix of admirable and reprehensible.  But what is certain is that we're not doing our children, nor ourselves, any favors by rewriting history to make America and Americans look faultless.  We owe our citizens the duty of being honest, even about the parts of history that we'd rather not admit to.

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An anodyne against despair

Yesterday, I was discussing with one of my colleagues how important it is to find things that lift your spirit.  The world has been replete with dismal news lately, and it's all too easy to decide that everything's hopeless -- to become either cynical or despondent.  I know I have to fight that tendency myself, especially considering the topics I frequently address here at Skeptophilia.

It's essential to take a moment, every so often, to step back and recognize that however terrible current events have been, there is still great love, compassion, and wonder in the world.  So I thought I'd take a day off from the continual stream of WTF that the news has become, and consider a few examples of what beauty we humans are capable of.  Think of it as an anodyne against despair, a way to inoculate yourself against losing hope.

Dalai Lama Mandala I, pen/ink/watercolor, by Carol Bloomgarden [image used with permission]

First, take a look at this video by the Dutch artist Thijme Termaat.  He spent two and a half years creating a progressive set of paintings, condensed it into a three-minute video, set it to a piece from Vivaldi's The Four Seasons, and named it Timelapse.  Take three minutes and be amazed.

When I was in Boston a while back, I went to the Boston Institute of Contemporary Art, and I lucked out and saw some work by the incredibly creative Rachel Perry Welty.  The piece that absolutely captivated me was a twelve-minute video called Karaoke Wrong Number, wherein she took four years' worth of voicemail messages she'd received by accident (i.e., the person had called her number but thought they were leaving a message to someone else entirely), and lip synced to them.  I stood there and watched the entire piece three times in a row -- it's mesmerizing.  The incredible thing about it is that she's able to shift her facial expression and body language to match the voice and message of the person -- it's funny, wry, and at times absolutely uncanny, and illustrates Welty's sheer creative genius.  (You can watch a five-minute clip from it at the link above.)

If you don't mind crying, take a look at Kseniya Simonova's stupendous feat of drawing in sand on a light box that brought the whole audience to tears in Ukraine's Got Talent.  It shows the effect of the German invasion on the people of Ukraine during World War II, and packs an emotional punch like nothing I've ever seen before.

If after that, you want to see something that is pure whimsy to cheer you up, you need to watch the amazing musical marble machine created by Martin Molin of the Swedish band Wintergatan.  Molin created a wild Rube Goldberg machine, powered by a hand crank and 2,000 marbles, that plays a tune he wrote.  It's one of those things that you watch, and you just can't quite believe it's real.

If you want to blow your mind further, have a look at this short little video showing one of the crazy three-dimensional sculptures of Japanese mathematician and artist Kokichi Sugihara.  Sugihara specializes in creating optical illusions out of paper -- in this case, a structure that seems to induce marbles to roll uphill.  The weird thing to me is that even when he shows you how it's done -- which he does, about halfway through -- I still can't see it any other way.  It's so cleverly done that my brain simply can't handle it.

Last, for sheer exuberance -- if you're like me, it'll make you laugh and cry at the same time -- check out the short film "Where in the Hell Is Matt?", made by Matt Harding.  Harding set out to film himself dancing in as many different spots on Earth as he could get to, often joined by children, adults, and dogs, all simply expressing how wonderful it is to be alive.  It's set to the heart-wrenchingly gorgeous song "Praan" by Garry Schyman.  The music and the spirit of Harding's project could not blend together more perfectly.

So there you are.  Even when things are bad, people are still creating beautiful, funny, and whimsical things.  They still care about bringing joy into the world, despite the constant barrage of pain, discouragement, and bad news we're subjected to on a daily basis.  I don't know about you, but when I see things like this, it reminds me that humanity isn't as hopeless as it may seem at times.  It recalls the last lines of the beautiful poem "Desiderata," by Max Ehrmann, which never fails to bring me to tears, and which seems like a good place to conclude:

Nurture strength of spirit to shield you in sudden misfortune.  But do not distress yourself with dark imaginings. Many fears are born of fatigue and loneliness. 

Beyond a wholesome discipline, be gentle with yourself.  You are a child of the universe, no less than the trees and the stars; you have a right to be here. 

And whether or not it is clear to you, no doubt the universe is unfolding as it should.  Therefore be at peace with God, whatever you conceive Him to be.  And whatever your labors and aspirations, in the noisy confusion of life, keep peace in your soul.  With all its sham, drudgery and broken dreams, it is still a beautiful world.  Be cheerful.  Strive to be happy.

The science of beauty

I got a curious response to my post yesterday about finding out that my previously-held explanation for why people become conspiracy theorists was probably wrong.

Here's the email:

Dear Mr. Skepto, 

You sound pretty worried that you don't have an explanation for everything.  People aren't always explainable!  They do things because they do them.  That's it.  Some people believe weird stuff and some people like the explanations from science.  Just like some people like the Beatles and some people like Beethoven.  It's silly to wear yourself out trying to figure why. 

Do you worry about why your loved ones love you?  Maybe it's some chemical thing in their brain, right?  Do you tell your wife that's what love means?  Maybe it's a gene or something that's why I think flowers are pretty.  If so, the explanation is uglier than the flowers are.  I'd rather look at the flowers. 

All your scientific explanations do is turn all the good things in life into a chemistry class.  I think they're worth more than calling them brain chemicals.  I'll take religion over science any day.  At least it leaves us with our souls. 

Think about it. 

L. D.

Well, L. D., thanks for the response.  I find your views interesting -- mostly because they're just about as opposite to the way I see the world as they could be.

But you probably already knew that.

There is a reason why musical tastes exist.  We're nowhere near the point in brain research where we could discern the explanation; but an explanation does exist for why Shostakovich's Waltz #2 gives me goosebumps, while Chopin's waltzes do nothing for me whatsoever.  Nothing just "is because it is."

And I can't fathom how knowing the explanation devalues your appreciation of the thing itself.  Me, I would love to know what's happening in my brain when I hear a piece of music I enjoy.  We're beginning to get some perspective on this, starting with a 2011 study that found that the neurological response to hearing a piece of music we love is similar to the brain's response to sex.

Cool, yes?  I think that's awesome.  How would knowing that make me appreciate music less?

Or sex either?

I find flowers even more beautiful knowing that their shapes and colors evolved to attract pollinators, and understanding a bit about the chemistry of photosynthesis.

[image courtesy of the Wikimedia Commons]

Understanding light refraction doesn't make me shrug my shoulders at a rainbow.  And even love -- which L. D. evidently thinks lies entirely in the mystical realm -- is made no less by my knowledge that its underpinning has to do with brain chemistry.  It's like that old song with the verse:

Tell me why the stars do shine
And tell me why the ivy twines
And tell me why the sky is blue,
And I will say why I love you.

A more scientific type added a verse, to wit:

Nuclear fusion is why the stars do shine.
Thigmotropism is why the ivy twines.
Rayleigh scattering is why the sky's so blue,
And testicular hormones are why I love you.

Which I think is a good deal more realistic than attributing it all to souls and people "doing things because they do them."

In short: science itself is beautiful.  Understanding how the world works should do nothing but increase our sense of wonder.  If scientific inquiry isn't accompanied by a sense of "Wow, this is amazing!", you're doing it wrong.  I'll end with a quote from Nobel Prize winning physicist Richard Feynman, who in his 1988 book What Do You Care What Other People Think? had the following to say:

I have a friend who's an artist, and he sometimes takes a view which I don't agree with.  He'll hold up a flower and say, "Look how beautiful it is," and I'll agree.  But then he'll say, "I, as an artist, can see how beautiful a flower is.  But you, as a scientist, take it all apart and it becomes dull."  I think he's kind of nutty. …  There are all kinds of interesting questions that come from a knowledge of science, which only adds to the excitement and mystery and awe of a flower.  It only adds.  I don't understand how it subtracts.

Euler's identity, and seeing the divine in mathematics

Yesterday I ran into a "proof of the existence of god" I'd never seen before; the idea that there are mathematical patterns that suggest the hand of a deity.

One of the most popular patterns that religiously-inclined mathematicians point to is "Euler's identity:"

And on the surface of it, it does seem kind of odd.  "e" is the base of the natural logarithms; "i," the square root of -1, and thus the fundamental unit of imaginary numbers; pi, the ratio between the circumference of a circle and its diameter.  That they exist in this relationship is certainly non-intuitive, and the non-intuitive often makes us sit back, and go, "Wow."

Euler's identity isn't the only such set of patterns, though.  A gentleman named Vasilios Gardiakos goes through a good many mathematical gyrations to show that god wrote his signature in number patterns, including the presence of "Pythagorean triplets" in the decimal expansion of pi.  (A "Pythagorean triplet" is a set of three integers that solve the Pythagorean theorem, that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.  The most famous one is 3, 4, and 5.)

Gardiakos's messing about seems to me to stray a little too close to numerology for my comfort.  If you've already have decided that number patterns Mean Something, and you're willing to use any pattern you find, you're already off to a good start.  Add to that the fact that he was searching for patterns in decimal expansions that are infinite (pi, e, and √2), and it's a sure bet that given enough time, you'll come across whatever you need.

The use of the Euler identity, though, is a little harder to answer.  It certainly seems... well, perfect.  It relates five fundamental constants in mathematics -- e, pi, i, 1 and 0 -- in one simple, elegant equation.  And the mathematicians themselves have waxed rhapsodic over it.  Mathematician and writer Paul Nahin calls it "the gold standard for mathematical beauty."  Mathematician Keith Devlin of Stanford University states, "Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence."

Which is all well and good, but does it prove anything beyond a fascinating and complex mathematical relationship?  First of all, the fact that it's true might be non-intuitive, but it is hardly a coincidence.  For a lucid explanation of why Euler's identity works, you have to go no further than the Wikipedia page on the subject, which leads us step-by-step through a proof of how it was constructed.

And honestly, all of the theologizing over beautiful theorems in mathematics seems to me to turn on one rather awkward question; if you are claiming that Euler's identity, or any other mathematical pattern, proves the existence of god, you are implying that had god wanted, he could have made the math work differently.  God exists -- we get Euler's identity and various patterns of numbers in the decimal expansion of pi.  God doesn't exist -- we don't.

So then, can you conceive of a mathematical system in which Euler's identity is a false statement?  Because if not, then god (should he exist) was apparently constrained to creating a universe where Euler's identity was true, and the god/no god models end up looking exactly the same.

Kind of a poor proof, honestly.

What this sort of thing seems like, to me, is an extension of the Argument from Incredulity: "I don't really understand how this could be true, so it must be god."  Understanding Euler's identity does require that you know a good bit of mathematics; easier, maybe, just to marvel at its beauty, and attribute that beauty to a deity.

For me, I'd rather just try to understand the reality, which is marvelous enough as it is, and worth reveling in a little.  It might be time to break out Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid and K. C. Cole's The Universe and the Teacup again.