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Lex Luthor's Chewing Gum Wrapper and Self Similarity

Explore the concept of self-similarity, from fractals to the behavior of subatomic particles, and discover how it is embedded into the universe. Learn the implications of self-similarity on human consciousness and the universe, as discussed by Gene Hackman's Lex Luthor and Stephen Hawking. Dive into this fascinating concept with this post and learn more about convergent evolution.

Unlocking the Secrets of the Universe with Lex Luthor's Chewing Gum Wrapper

By Michael Levin

Monday, May 8, 2023

In one of the best superhero movies of all time, an for my money one of the best movies of all time, Gene Hackman’s Lex Luthor says, “Some people can read War and Peace and come away thinking it’s a simple adventure story. Others can read the ingredients on a chewing gum wrapper and unlock the secrets of the universe.” That’s absolutely true and some of the wises words ever spoken in media.

The concept is self-similarity. It’s mostly referred to as a characteristic of fractals, a recurring shape at small and big scales. Take a tiny “seed” shape and repeat it at a larger size, drawing the same shape at a slightly different angle so that when you keep doing it, you get the image of the original shape again. We see this in the famous Mandelbrot set, and maybe the most famous example is the Koch snowflake or the fibonacci spiral. But it’s everywhere.

Miss Teschmacher, some people can read War and Peace and come away thinking it’s a simple adventure story. Others can read the ingredients on a chewing gum wrapper and unlock the secrets of the universe.

When you see an “emergent property”, there’s a very good chance that it’s actually a large manifestation of that smaller “seed” shape allowed to run wild. While the flat roundness of planetary orbits and galactic spirals aren’t precisely analogous to electron probability clouds around a nucleus, they are both examples of self-similarity. Round things going into orbit with some other force flattening the orbit into a disk or bending it into an ellipse. These are things you can rely on at any scale.

Human consciousness, the brain, thought and learning and all that is likely a self-similar phenomenon that’s embedded into matter at some smaller scale. Listening to modern physicists talk about the behavior of subatomic particles like electrons and quarks, you’d think they were talking about the behavior of humans. Scale up a little bit an you’ll find cellular automata and epigenetic scientists talking about similar smart behavior at the cellular level. Cells are smart. Their ancestors were 1-celled organisms that had to survive and ended up multicellular.

An process called bifurcation by which something doubles and doubles again eventually kicks-in and you get a multicellular organism. The same thing it seems with the universe, if you believe in the Big Bang and the inflation period. The universe doubled and doubled again and again just like cells dividing and becoming a bigger organism.

A sort of embedded intelligence that we’d call “emergent behavior” exists all around us without it being anything like human consciousness. It reveals itself again and again in things like slime mold, the mycelial network of mushrooms, and the cosmic web of galaxies. All 3 of these examples seem to be able to optimize shortest paths between points, able to solve the O-scale traveling salesperson better than our best supercomputers.

This is the type of thing Gene Hackman’s Luthor is expressing as he talks to Otis about the “real estate scam” he’s pulling off. He’s talking about self-similarity and how it’s a fundamental property of the universe. You can look at many of the things important and meaningful to us in our lives and infer many of the important guiding principles of existence: relationships, orbits, things coming into conflict and colliding, things being attracted to each other, things being repelled by each other, and passing right through each other, being both intact and changed by the experience.

Galaxies can pass right through each other when they collide. The majority of stars can even come out the other side unscathed. But the gravity of the galaxies will be changed forever. Who knows whether beings living on the planets orbiting those stars will be able to survive the change. This is in store for us some 4 billion years from now when the Milky Way and Andromeda galaxies collide. We’ve got as much time to prepare as the Earth existed.

The universe is a self-similar place. It’s a place where the same rules apply at all scales. It is in this spirit that one of my next steps in life is to zero in on those objects and… and… uhm totems? that are around me from which I can draw the most interesting, important and pointed lessons that I can bring to you through this journal.

I guess I’ll just throw in the one that made my brain go in this direction. Do you know those children’s toys that are like elongated water-filled donuts that you can squeeze and the water goes from one side to the other? They’re shaped kinda like a worm where food could go in the hole in the center and come out the other side with the interior being a digestive track. It’s roughly the worm template from which all animals are built. It is also a plausible shape for curved space-time that would neatly wrap-around itself and allow for wormholes and putting the kibosh on certain paradoxes and infinities.

Homer Simpson says so! Homer may not be Lex Luthor, but Stephen Hawking agrees with him and stole his idea. Though in all fairness, the idea of a toroidal universe has been… uh… a-round for a while. Certainly in Sci-Fi if not formally in physics. But it’s another great example and one that finally impressed my kid enough to ask a few follow-up math questions. Woo hoo! (as Homer would say). My Lex Luthor plan is hatching nicely.

And just to capture it, the 2nd self-similarity thing that I noticed, an aspect that is “in all things” that prompted me to write this post, is the concept of language actually being a living, evolving tool. Language is very rarely static in everyday life, with new words and syntax being added all the time. It’s in written languages and visual languages, with memes being a sort of evolving visual language that’s highly compatible with today’s Internet culture.

Without enough time even to read (and imagine the meaning of) headlines, we’re communicating more and more in a condensed visual format that speaks more emotionally, and perhaps powerfully, directly to our more base animal selves, represented by the limbic system and such rockstars as the amygdala and pituitary. I think my amygdala and pituitary love dem emojis and gifs, where my higher order self feels a bit of disgust.

This inventing language as you go is something twins often do with each other. It’s a phenomenon called cryptophasia. In the early days of AI before it got all transformy and generative, when 2 were set talking to each other they rapidly developed their own language that was indecipherable to humans, and as urban legend goes, were quickly turned off for fear of them plotting against their human overlords. But the fact this happens and that it triggers these fears makes strong points again about self-similarity and the power of language.

Hmmm, this self-similarity concept is perhaps the good lead-in for another post sometime on living languages and convergent evolution. We see the same life-templates shapes and behaviors in different species that are not closely related so often, along with the way language evolves. I mean certain jellyfish and cuddlefish use pulsing bands bioluminescence to communicate which isn’t exactly the same as oscillating sound waves in the air, but it’s the same basic idea.

It gives a lot of hope that both our AI machine children aliens and the extraterritorial aliens ones we’re bound to make contact with someday will be able to communicate with us. Let’s just home empathy and compassion are spontaneously recurring self-similar traits as well.