Beauty and Pattern in Math and Science

@swamidass got me thinking about beauty last night in his interview. And I have in the last months watched a few interviews with theoretical physicists who argued about beauty, what it has to do with their work, and if they’re too obsessed with it.

This morning I came across two particularly beautiful things in my news feed (below).

  1. And it got me thinking: what do scientists individually find beautiful in nature or in math?

  2. And what do scientists or others here find beautiful that someone like me, who is not a scientist, would probably never encounter?

  3. Does/did it make your career more enjoyable?

Feel free to comment on the videos too. Happy to read any comments from those more familiar with these topics than me (that’s everyone here probably).

Kepler, Platonic Solids, and Penrose Tiling

Even though I watched this week ago, still sharing ICYMI. Because it’s also on platonic solids and cool.


https://www.quantamagazine.org/mathematicians-report-new-discovery-about-the-dodecahedron-20200831/
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For my own part I wonder what it is about beauty @swamidass finds so perplexing on evolution. There are many ways evolution can account for humans finding things beautiful, be they music, physical appearance, landscapes, or mathematical relationships.

The first thing to note is that the perception of beauty is subject to large degrees of variation like all other biological traits, as some individuals are moved by it more than others(and we even some times completely disagree on whether something is beautiful or not, so the range of emotions covers all the way from universal agreement to noise).
And then there’s the fact that at least some kinds of attraction to beauty are adaptive. That implies others can simply be byproducts of neurological circuitry that control our attraction to certain patterns.

You might say something like evolution doesn’t explain the degree to which you find something beautiful, like some equation you find so beautiful it moves you to tears, and I just have to ask, why not? Supposing that emotional reaction to some pattern is a byproduct of adaptive feelings of attraction, how strongly should that feeling register to you if it was an evolutionary byproduct?

You might say byproducts are sort of ad-hoc explanations that can account for anything, but we have to concede the human mind has byproduct reactions to things. Take the example of sensing a strong pain or itch in a phantom limb. That’s a byproduct of how our brain and mind works, regardless of whether we evolved or we were designed, and the feeling can be intense and appears absolutely real to the people who have it.

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Where beauty comes from is one conversation, but I wasn’t really looking for a philosophical discussion. I was actually more interested in what each scientist finds particularly interesting or beautiful in their work. I don’t care whether you think the feeling is evolved or designed :slight_smile: Either way, it’s interesting. I had never heard of Penrose tilings before - the concept of a beautiful pattern that’s not repetitive is fascinating in its own right.

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I understand. My comment wasn’t meant to spark a debate so I’ll be fine with just leaving the question of the origin of beauty aside.

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Not exactly what you are talking about, but I remember reading an article a number of years back, in The New Yorker IIRC, that spoke to a number of people who were among the absolute elite in a number of non-artistic fields. It included athletes like Wayne Gretzky and Tony Gwynn, a neurosurgeon and I think mathematicians and scientists were included.

What they had in common was that they spoke of their work in aesthetic terms, that they found a sense of beauty in a particular mathematical problem or surgical procedure, the flow of the other players during a game or the trajectory of a pitch as it met the swing of the bat. The thesis of the article was that it was this that separated the people at the upper echelon of a field, the Hall of Famers or Nobel Laureates, from the other people who are still at an extremely high level of achievement but just not quite at that level.

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Yes, this is what I was referring to! What do scientists at a high level get to see that’s aesthetically pleasing that they could explain in layman’s terms? I would also be interested in researching these things to better understand the “art” in science. I’m really noticing that there’s a lot out there to find beauty in. @Rumraket

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I’m imagining if we were visited by aliens who did not have art or music. How would we convey to them what we experience when we look at a Rembrandt or listen to a Schubert piano sonata? I have no idea.

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See if they seem to be capable of emotional responses when trying to communicate - frustration, joy, etc. Then show the painting or play the music. See what happens.

Then go from there. I have to figure out how to communicate my emotions to my husband who has autism who misunderstands me a lot. LOL, this doesn’t seem like a hard problem to me.

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And if they don’t get it, then our experience would be similar to that of a mathematician who tries to convey to us the beauty of a mathematical formula that we are unable to appreciate.

That’s an interesting take on the question. Of course, it is not unheard of for autistic people to be very accomplished at math or other subjects.

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I suppose some people would do that. But I don’t give up if I really want to know something or want someone to understand something.

My husband is horrible at math except counting and adding in his head which he’s really good at. I’m not sure how your comment is relevant to what I’m saying. I’m just explaining that I am required to be quite persistent and stubborn at explaining how a certain thing makes me feel to make my marriage work. So it doesn’t make sense to me that varied intelligent creatures couldn’t find a way to communicate eventually.

As you can tell, if I think someone doesn’t understand something, I’ll be persistent until I’m quite certain they don’t want to understand what I’m saying. And even then, I’ll probably still make sure it’s not a communication problem. I have a harder time understanding when my communicating is just horrible because I’ve misunderstood something or I just write gibberish.

I think all of our reactions to beauty are a feeling of some type - joy, wonder, sadness, jealousy, etc. If intelligent beings exist, it seems they’d rely on some kind of feeling to filter information.

But I suppose in my worldview, I can’t imagine creatures that don’t have feelings. We visited a zoo once, where a cockatoo was extremely jealous and would squawk anytime we turned our attention to the macaw in the cage next to its. We recognize feelings even in animals.

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I find organisms and their interactions sometimes beautiful, but the word I would use more generally is fascinating.

Depends on if you’ve every been to Australia, Botswana, Peru, etc. I like watching birds I’ve never seen before, especially if they belong to families or orders I’ve never seen before.

Sadly, my career has been entirely in the lab, where the organisms look like small tubes of clear liquid. But phylogeny is fascinating too, so we persist. Finding out something nobody knows yet is fun too.

"There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been and are being evolved.”

That actually brought tears to my eyes as I typed it.

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I’d say that beauty is about as big a puzzle for evolution as is suffering and evil for theology. Which is to say, they aren’t ultimate problems for either, though they certainly raise a whole lot of interesting questions. And the answers we give aren’t fully stable.

I’m sure you can give an account of beauty from evolution, and I’m sure also I could find boundary cases that unsettle the simple accounts. Perhaps Beauty is just is a spandrel, or maybe the mathematics of beauty gives us strong rationale for why aesthetics on one scale will transfer to other scales, and even previously unseen worlds. That might even be a fruitful place of further inquiry.

The key point though is that the objection to God because of all the suffering and death in an ancient earth is comically one sided. Some how we have to take into account all the life and joy that couldn’t be contained in a young earth, but fills beyond imagination the old earth. It seems the only serious arguments against God from an old earth would have to deal with both sides of the coin, not just one.

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Examples? This does sound fascinating.

I’ve not had the opportunity to travel much outside the U.S. Just barely into Canada. I’ve been to Hawaii 4 times, if that counts as exotic. I did enjoy noticing the species there. I got to visit the observatory on the Big Island. I want to go back after studying the stars to know what I was looking at.

Thank you for answering all my questions. That’s beautifully written. Who wrote the quote?

I knew I liked you. I love the word grandeur.

One of my favorite poems. Maybe you will appreciate the avian references? Sadly I have a book of his poetry from my college days, and I haven’t read the thing. It has to go on my reading list.

God’s Grandeur - Gerard Manley Hopkins

The world is charged with the grandeur of God.
It will flame out, like shining from shook foil;
It gathers to a greatness, like the ooze of oil
Crushed. Why do men then now not reck his rod?
Generations have trod, have trod, have trod;
And all is seared with trade; bleared, smeared with toil;
And wears man’s smudge and shares man’s smell: the soil
Is bare now, nor can foot feel, being shod.
And for all this, nature is never spent;
There lives the dearest freshness deep down things;
And though the last lights off the black West went
Oh, morning, at the brown brink eastward, springs —
Because the Holy Ghost over the bent
World broods with warm breast and with ah! bright wings.

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It’s from this book:

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It’s the very last sentence in The Origin of Species.

Too many to chose. All you have to do is look. A couple off the top of my head: golden eagle courtship flight; American white pelicans forming a circle around a school of fish and dipping their beaks in the water simultaneously; tiger beetles flying away as you approach but always landing facing in your direction as a challenge.

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Great topic, thanks!!!

I find lots of things beautiful in nature. I am drawn mostly to beauty in the biological world and in the geological world. In the biological world, I see beauty in things that were designed for that purpose: ornamentation in plants and animals, of the kind that is designed to attract other animals (mates and/or pollinators). This to me is the kind of beauty that seems to serve no purpose, and is different from pattern and design. Flowers, colors, etc. There are some jaw-dropping images and descriptions of beauty in birds, and these are the main topic of a recent very interesting book (The Evolution of Beauty) by Richard Prum that specifically puts beauty at the center of thought about evolution. His emphasis in that book is controversial and even tedious but the universe of beauty in birds is astounding.

But I am also drawn to both “design” (especially protein nanomachines like voltage-gated ion channels and ATP synthase) and to grand visions of biology and geology, such as tree-covered mountains that unfold one ecosystem after another as you ascend them. Being a biologist has significantly heightened my enjoyment of these things, and it takes effort for me to resist the impulse to babble ecstatically about “sky islands” and evolution when my car-mates just want to enjoy the view.

For some reason I am less drawn to regular pattern and to symmetry. Probably a personality defect.

This most definitely makes my career more enjoyable. All day, my work is about the biological world. I do know how very lucky I am.

Much of the beauty that I see day-to-day is a collaboration between human minds and the creative power of the universe. Specifically, I find images of brain circuits to be among the most beautiful things I see in my work. But these images are enhancements of various kinds: the circuits themselves don’t look like that. This could launch us into a discussion of how perception and beauty are both creations of minds and brains, but I’m not up for that. I’ll just say that I do see a difference between the images in this Picture Show and the images in this gallery of the sky islands of Arizona.

Which leads me to the final relevant answer to your excellent questions: I am most inspired by the creativity of humans. This applies very much to science, since it takes creativity and imagination to do great science. I think “inspiration” is pretty closely related to the wonder we feel when we talk about “beauty,” so it seems to belong here too.

Thanks for the topic, and thanks for coming to my TED talk :slight_smile:

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To pull this together @thoughtful, that quote was by Charles Darwin, and he was describing evolution as God’s way of creating endless forms, which was far more beautiful than a fixed and limited number of “kinds.” Typing that quote brought an atheist biologist to tears as he reflected on his work shuffling clear tubes of liquid to categorize endless varieties of birds.

We do find beauty in the most unexpected places, do we not?

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I don’t know anyone who makes such a simplistic argument. Maybe you do.

If your argument is that a god who created X units of suffering is absolved by creating Y units of beauty, then you are simply presenting a particular version of a god. For me, there is no amount of beauty, no amount of “life and joy,” that rescues a god from the crime of inspiring Deuteronomy 20 or of the myriad evils his name is attached to in modern America. This simply means, I think, that your god is different, somehow designed to escape responsibility, and that’s fine. But he sure isn’t helped by strawmen, and that’s what your argument here is. In short: it’s trivial to make a serious argument “against God from an old earth.” All one has to do is expect different things from that god than you seem to.

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It is pretty common among YECs arguing against an old earth.

Perhaps. Though I don’t think this is what I’m saying. The problem of evil is a larger conversation, as is the question “what is good?”.

I think all believers would be united in saying that there’s endless potential for beauty no matter how God created - especially since heaven will be eternal, in God’s image we create endless worship and beauty. But even YEC believe God used evolution to create various forms. My kids definitely don’t look the same as me. I find beauty in eye color. My youngest has sea glass gray blue eyes, flecked with some brown and green, which is pretty amazing since I liked sea glass before he was born. I wonder where they came from. Well, from his parents, but neither of us really has eye color like that. My husband’s are brown and mine are green-blue.

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