 I once saw a guy on Netflix whose limericks went to line 6. He never did know how far they should go, and he never did bother to fix them at all. Does this video make you a little uncomfortable? What about this one? How about this? Almost, almost, ahhh! All humans have, to a greater or lesser extent, an awareness and inclination for order, regularity, harmony, that sort of thing. By the time we're one year old, human babies exhibit a clear preference for symmetrical patterns over asymmetrical ones. Many evolutionary biologists have chalked that instinctive affinity for symmetry up to mate selection. If you're trying to find a sexual partner who will give your offspring the best possible genes and the best possible chance at survival, you probably don't want to pick the one that can only swim in small circles. That might explain why we share that preference with a huge number of very different animals. Lies, fish, birds, bees, chickens, gemspock, almost every creature that we've tested has exhibited a significant preference for visual patterns and mating partners that are bilaterally symmetric. But as these alternately frustrating or satisfying jive collections illustrate all too well, humans have a special appreciation for order and regularity that isn't restricted to bilateral symmetry or wanting to get close to Ryan Gosling. Maybe it's some sort of development of that deep evolutionary desire for a lover with matching ears, or maybe it's another aspect of our psychology altogether. But it's definitely there, and it definitely affects how we think about the world. Of course, it's not like humans only want order. We also appreciate deliberate departures from it. Asymmetry is visually interesting. Syncopation, tension, and discord makes music engaging to listen to. But if you leave an unresolved chord progression just hanging, GAH! Importantly, it's not a purely cultural thing either. Autistic children who haven't even learned how to speak yet will arrange objects at regular intervals in order of size, or stack cans of food or toys together. There's something instinctive in their brains that urges them to impose order on their environment, and when I see something like this, I think that I kind of feel it too. Weirdly, that instinct for regularity has served us very well in our efforts to understand the universe. Numerous great scientists, including Newton and Galileo, and other luminaries like Bach or Aristotle, have cited a guiding principle of beauty and elegance in their work. Einstein is notorious for the very spiritual way in which he viewed the laws of the universe as having some sort of intrinsic elegance in order to them, a feeling which motivated much of his life. He once said, if I hadn't an absolute faith in the harmony of creation, I wouldn't have tried for 30 years to express it in a mathematical formula. Scientists are supposedly dedicated to sterilizing their theories of any personal bias or wishful thinking, but everyone seems kind of okay with what seems to be a purely aesthetic valuation that prettier laws are more likely to be true. And weirdly, that's often the case. Wonder is positively overflowing with structures, processes, and principles which seem custom-built to appeal to that instinct for order and symmetry. Crystal lattices, DNA, the symmetry of subatomic particles, very simple physics equations with nice whole-number exponents. There's no real reason that any of this stuff should be pretty, but it frequently is. It's no wonder that Einstein and many other brilliant people would feel rapturous about the abundance of orderliness in our universe. But there's a problem with just abandoning ourselves to the ecstasies of things fitting perfectly into other things. If we're paying close enough attention, that beauty that we have such an appreciation for has its limits. I'm not even talking about those annoying real-world practical divergences from symmetry and order because things don't go quite the way that they're supposed to. Even in the perfectly harmonious world of pure abstractions, untainted by the grossness of the physical world, there's still some things that feel the way that this sounds. Speaking of music, let's start there. Pythagoras was an ancient Greek philosopher. You probably know the theory about triangles that bears his name, even though he didn't discover it. But he did discover an elegant, beautiful relationship between the ratios of the lengths of strings and the musical notes that those strings produced. Divide a string in half and you get an octave. Divide it into two thirds and you get a fifth. Divide it into three quarters and you get a third. Play the three of them together and you have a major chord. Lovely. You can build a whole chromatic scale this way just by multiplying some starting tone by ratios. Start with C. Add a fifth and get a G. Take two thirds of that and get a D. Do it again and get an A and so on and so on. But when you finally wrap around to C again in some other register, you get this note. Which is like a C, but not quite. There are all sorts of different methods for building musical scales out of ratios between notes, but they're all a little bit off. The modern equal temperament tuning, which was discovered in the 20th century and is built on the square root of two, which will become relevant in a second, is used to tune everything from pianos to xylophones, and it's designed to make the differences between the notes and what they're supposed to be nearly indistinguishable in every key. But if you play a C and E and a G, it's never going to be really perfectly harmonious. Despite his issues with scale tuning, Pythagoras inspired a whole cult of followers who were dedicated to his precept that the universe was built out of integers and ratios of integers, the Pythagoreans. They also had some weird ideas about beans and sex, which I won't get into here. We're just going to focus on the numbers thing. There's an almost certainly apocryphal story about Hipposus of Metapontum, a Pythagorean from around 500 BC, who was supposedly drowned for revealing something that was utterly scandalous to the order. The eponymous Pythagorean theorem is pretty simple. If you make a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. A squared plus B squared equals C squared. The Babylonians and Egyptians got there way before Pythagoras did. But Hipposus discovered something interesting. If you make both of the sides a length of one, that makes the length of the hypotenuse, by the Pythagorean theorem, the square root of two. And he didn't need a lot of math from that point to prove that there's no way to write the square root of two as a ratio of two integers. It's an irrational number, a number which, by definition, has no such representation. Written as a decimal, it just goes on forever, never repeating, never terminating, just unending chaos. It's a Pythagorean's worst nightmare, and you can get there through a pretty straightforward application of the Pythagorean theorem. No wonder they drowned it. Goethe's incompleteness theorem, the dollar auction paradox. Even in the pure and unsullied realm of mathematics, we run into several of these immensely unsatisfying truths. They seem to be built into the most perfect abstract systems that humans can come up with. And when you start talking about the real world again, they don't go away, and in some cases things get even worse. There are many natural phenomena that aren't really as beautiful or elegant as we might imagine them being. For example, DNA seems like a gorgeous, nearly computer-like method for storing and replicating genetic information. But it has this problem. If you put two T's next to each other, all it takes is a little bit of UV light and it causes kinks in the structure that can lead to cancer. Man, many people find the physical impossibility of a perpetual motion machine frustrating, along with the nearly impossible amount of computation necessary to calculate the motion of just three bodies in space. And looping back to our friend Einstein, he had a really hard time accepting the unintuitive and kind of gross probabilistic weirdness that is inherent to quantum mechanics, even though some of the most robustly demonstrated science humanity has ever produced. I think that there's probably a decent lesson in that. The deeply coded human love for regularity in order has driven many brilliant people to incredible heights of discovery, whispering that a simple and elegant explanation must lurk behind the seemingly random noise of the messy world's operation. But it's probably worth remembering that it's not a capital L law of the cosmos, the way that we might like to think it is. Sometimes, despite all of our desires for something to be perfect and complete, it's just where has the love of patterns and regularity served you well? Where has it led you astray? Please leave a comment below and let me know what you think. Thank you very much for watching. Don't forget to subscribe, like, share, and don't stop thunking.