Understanding as an art
I'll never forget the first time I entered a different world.
I was 11, in the kitchen of our house in New Zealand, explaining a concept from ‘Molecular Biology of the Cell’ to my dad. Cynthia Kenyon had given me the book, so it was a sacred object. I was pointing to a David Goodsell-style illustration of molecules crowded inside a cell. I’d never seen anything like it - they were all so jam-packed, right on top of each other! What a riotous place!
My heart stopped. These molecules were really there. I was looking at an illustration, but it was telling me about a world just as real as my world except smaller. I started to feel the molecules bouncing around me, that I was in a chaotic infinity expanding out into space. For a moment, I was somewhere else.
That day opened a portal I would step through a decade later, when I learned to feel quantitative facts in the same way. I was watching a Nima Arkani-Hamed lecture* at a cafe on Divisadero street, as it got dark and cold outside. Nima described the importance of units - that you should visualize the weight of a star in numbers of neutrons - and when I finally had to leave I walked outside and stared at a manhole cover and suddenly my brain yelled THAT IS AROUND 10^10 ATOMS ACROSS, AND THOSE ATOMS ARE REALLY THERE, and the feeling of ‘seeing another world’ came rushing back. I felt overwhelmed, and had a rapidly repeating sense of ‘it’s there, it’s really there’. I spent days staring at objects, inferring how many atoms they had, and then feeling those atoms were really there. But I didn’t know what to do next, and the sensation started to fade away.
I learned how to stay in the world and go on adventures. During a 2020 pandemic roadtrip, I was practicing a meditation exercise to calm down - visualizing an orange in my mind, then rotating and peeling it. It reminded me of Iron Man scenes, where Tony Stark used a holographic display to manipulate engineering diagrams, and how I’d longed to think in a similar embodied way. My brain suddenly put these experiences together - I could enter another world by believing in the reality of a fact, visualize and manipulate the molecules in that scene as I had done in meditation, and parameterize the world with the quantitative facts I knew so that exploring it was as accurate and useful as the engineering diagrams Stark was manipulating. I tried doing this with a mitochondrion and was amazed at how visceral it felt, and how immediately curious I was about how it worked - I wondered how many receptors were on the surface, how many ions were passing through, and in my mind the answers I guessed changed the picture I was looking at.
These thought experiments turned me from someone who learned what biology was from textbooks into someone who thought through feeling the cell. When you were flying through a cell quickly, some mental models were more ‘natural’ than others - energy should be measured in kBT! It fit clearly, when you were constantly being bumped by the kinetic motion of molecules, or you were counting how many ATP you needed to shove a molecule through a membrane.
Traveling to other worlds felt inextricably related to dance. I couldn’t feel the state sitting at a desk - it came when I danced in endless, green parks. The feeling came most when I went to a park and blasted music through earphones, dancing and riding the waves high until the visions came - atoms whirling around, running at me and accelerating as they got closer so they taught me about how to feel the surprise of the inverse square law, how when you're nanoscale electrical forces dominate and gravity fades away, how you're always bombarded, how dark it is. How diffusion works until it doesn't, how different that chaos was from the orderly grid-like rows you’d see in a computer. I died and came back to life in that world so many times - eliminated in a collision, bumping into things. I'd close my eyes and the theater would light up - where was I? How big, how small? How fast was I moving? What would I do next?
Transcendent experiences like this deeply confuse me, because they don’t solve all of your problems. They won’t produce a scientific breakthrough in the absence of the other 99% of rote work - you’ll still need to analyze that RNA-seq data to find your novel target. They help with hypothesis generation and insight, but are plausibly less important in biology today than they were historically in physics.
But still, I long for this feeling. I know it's out there, in other worlds. I'm looking for it in math, right now.
And there's a funny thing - more than discovery, I just want the feeling. I just want to travel to other worlds, like the character Paprika in the title sequence of the Satoshi Kon film. Jumping between different realities. I want this, all the time. It's not practical. In the future, who will care about human understanding? But I care - I want to live many lives, in other worlds, where the rules are stranger and more intimate than they are here. More than anything else, the varieties of scientific and mathematical experience are my portal to that. I miss them so much in this ordinary world, when the portals close.
____
Credit to my collaborator Joanne Peng, for the work we did together on Tiny Machines (a project which synthesized many of the experiences we co-generated and which are described in the above essay - in particular, a lot of work internalizing book.bionumbers.org, generating thought experiments, and playtesting the narratives on volunteers). Joanne’s extraordinary imagination, maestro-level visualization ability, and unbounded enthusiasm and energy for the purest parts of this and similar projects remain deeply inspiring to me. We never published the website we made, but it’s beautiful, and I hope it or something like it sees the light of day sometime.
*I am no longer sure which lecture this was - it is possibly this one. I’d separately highly recommend his “Morality of Fundamental Physics” lecture, should you ever feel dispirited about life.
Questions I am curious about, for those who like chatting about this stuff:
How do these states relate to meditation? In the presence of meditation, should one pursue the ‘feeling’ of awe in isolation of structure or scientific content? Is it stubbornness, which drives me to want this feeling to come from the magical laws underlying reality, instead of just trying to summon it arbitrarily? Why aren’t meditators excellent mathematicians (I know about Shinzen, but like, you have to do extra stuff to learn about mathematical structure alongside meditation, I don’t think it gives you those objects, just makes you calm enough to interact with them better?). I would love to hear from any scientist-meditators about this. I wonder a lot about which path is more sacred, although that’s possibly an incredibly silly question.
To what degree can computers, technology (really, ML) help us understand this more? To what degree will they make this skill purely aesthetic? Could one ‘see’ the Newton’s laws of biology (which I increasingly despair will not be as simple as Newton’s laws) if one had access to more computational power through a BCI, somehow?
I’ve increasingly found that, when I ‘really want to get something done’ in every day work, I’ll often instead of visualization just do subconscious processing - so, the thing comes, but you don’t see how it comes and it’s not like you spend a ton of time in it. I’ve been wondering how many latent spaces are likely to be consistent with human understanding - is the cell just particularly lucky, because it can be explored so literally? How often should one expect to ‘usefully’ use this type of experience? Currently trying to understand this in the context of math.
Additional reading:
I think the ‘Martians’ had high school teachers that did a bunch of embodied work like this, have heard refs to i.e. teachers telling the kids to weigh different objects to get a visceral sense of them.
Einstein’s high school and thought experiments are very interesting in this regard.
Terrence Tao talks about embodied stuff a bit (i.e. wriggling on the floor to visualize a concept), but I wish I could read a lot more from him about it.
James Somers’ stunning essay and Niko McCarty both write so well about the atom level view in biology. Rob Philips and Ron Milo are, of course, original gods in this regard and I am eternally grateful to them for creating book.bionumbers.org.
Tim Urban’s wonderful post The Big and the Small perfectly illustrates this phenomenon