Your ancestors may not have had the toolset you do when it came to avoiding mental stumbling blocks or your immense cultural inheritance, but their minds worked in much the same way. The people who thought the world rested on the back of a great tortoise or who thought dancing would make it rain - they had the same brain as you; that is to say, they had the same blueprint in their DNA for making brains. So a baby born into their world was about the same as one born into yours. Evolution is so slow that not enough has changed in the way brains are made to tell much of a difference between you and a person from ten thousand years ago. That means that from gods in burning chariots to elves making cookies in trees, people long ago believed in all sorts of silly things thanks to the same faulty reasoning you deal with today. They, too, were fueled by a desire to make sense of reality and to answer the age-old question: “What, exactly, is happening here?” Instead of letting that question hang in the air, your distant relatives tended to go ahead and answer it, and they kept answering it over and over again, with newer yet equally dumb ideas because of one of the most profoundly difficult obstacles humans have faced since we started chipping away at flint to make heads for spears. This malfunction of the mind is called the common belief fallacy.
Before we had a method for examining reality, the truth was a slippery fish, which is why your ancestors were so dumb. So dumb, in fact, that for a very long time people got smarter in a slow, meandering, and unreliable sort of way until human beings finally invented and adopted a tool with which to dig their way out of the giant hole of stupid into which they kept falling. The hole here is a metaphor for self-delusion. Your great-great-great-grandparents didn’t really keep falling into giant holes, at least not in numbers large enough to justify a book on the topic. The tool here is also a metaphor. I’m talking about the scientific method. Your ancestors invented the scientific method because the common belief fallacy renders your default strategies for making sense of the world generally awful and prone to error. Why do bees like flowers? What causes snow? Where do babies come from? Every explanation in every tribe, city, and nation was as good as the next, even if it was completely made up. Even worse, once an explanation was woven into a culture, it would often become the official explanation for many lifetimes. “What is thunder?” a child might have asked. “Oh, that’s the giant snow crab in the sky falling off his bed,” a shaman would have explained, and that would have been good enough for everyone until they all had their own kids and eventually died of dysentery. That hamster wheel of limited knowledge kept spinning until the scientific method caught on. Even then, there was a long way to go and lots of cobwebs to be cleared from common sense.
People learned that science, as a tool, as a lens to create an upside-down way of looking at the world, made life better. Your natural tendency is to start from a conclusion and work backward to confirm your assumptions, but the scientific method drives down the wrong side of the road and tries to disconfirm your assumptions. A couple of centuries back people began to catch on to the fact that looking for disconfirming evidence was a better way to conduct research than proceeding from common belief. They saw that eliminating suspicions caused the outline of the truth to emerge. Once your forefathers and foremothers realized that this approach generated results, in a few generations your species went from burning witches and drinking mercury to mapping the human genome and playing golf on the moon.
When you have zero evidence, every assumption is basically equal. You prefer to see causes rather than effects, signals in the noise, patterns in the randomness. You prefer easy-to-understand stories, and thus turn everything in life into a narrative so that complicated problems become easy. Scientists work to remove the narrative, to boil it away, leaving behind only the raw facts. Those data sit there naked and exposed so they can be reflected upon and rearranged by each new visitor. Scientists will speculate, and they will argue, but the data they extract from observation will not budge. They may not even make sense for a hundred years or more, but thanks to the scientific method, the stories, full of biases and fallacies, will crash against the facts and recede into history.
A writer’s work is the product of laziness, you see. A writer’s work essentially consists of taking his mind off things, of thinking about something else, of daydreaming, of not being in any hurry to go to sleep but to imagine something … And then comes the actual writing, and that’s his trade. That is, I don’t think the two things are incompatible. Besides, I think that when one is writing something that’s more or less good, one doesn’t feel it to be a chore; one feels it to be a form of amusement. A form of amusement that doesn’t exclude the use of intelligence, just as chess doesn’t exclude it.
Mirror symmetry is an example of a duality, which occurs when two seemingly different systems are isomorphic in a non-trivial way. The non-triviality of mirror symmetry involves quantum corrections. It’s like the Fourier transform, where “local” in one domain translates to “global”—something requiring information from over the whole space—in the other domain.
Under a local/global isomorphism, complicated quantities get mapped to simple ones in the dual domain. For this reason the discovery of duality symmetries has revolutionized our understanding of quantum theories and string theory.
summer school on mirror symmetry (liberally edited)
Thinking about local-global dualities gave me another idea about my model-sketch of knowledge, ignorance & expectation.
You didn’t smile, not really —
but the way your eyes squinted
said “today” like
there could be no other time.
No, I am not enlightened. Let me be very clear on that matter.
The nature of all things is enlightenment but until we come to know and abide in our...