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. As I looked at the illustration, I started to feel the molecules bouncing around me and a sense of a chaotic infinity expanding out into space - for a moment, I was somewhere else.
No one had told me that understanding science could feel like traveling to another planet. Many works talk about traveling to other scientific worlds - for an example, read Tim Urban’s wonderful post on the ‘The Big and the Small’. But no one had told me that you could inhabit them. I always thought that ideas from textbooks should map to strings of characters running through my head, or the ‘vague background feeling of thinking’. I didn’t realize that thinking about science could feel like running around in the best virtual reality game ever designed.
It took me a long time to turn that brief, overwhelming experience of a crowded cell into an experience I could stay with for a few minutes or even an hour, and to connect it with thought experiments that generated insight. I’ll describe that journey a bit more here, in detail, as I’d like to learn from others who can relate to these experiences.
My second step towards this state came over a decade later, in 2019, and involved realizing the link between the feeling of ‘being in another world’ and the tradition of doing thought experiments in physics. I remember, I was watching a Nima Arkani-Hamed lecture (‘Morality of Fundamental Physics’) on my laptop while posted up at a cafe on Divisadero street, and it was starting to get dark and cold, but I couldn’t leave because the lecture was so good. I’d felt despair at the lack of science-feeling in my life amid the weirdness of San Francisco courtier culture and watching Nima talk was an antidote to that.
In the lecture, Nima described the importance of units - how you could hold the weight of a star in your mind in terms of numbers of neutrons, and this might change your intuition about what it would do - 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. It’s there, it’s really there. I fell into a daze. I think I got ice cream after, just feeling elation at the world I was living in. I spent days staring at objects and inferring around how many atoms they had and then feeling like those atoms were really there. But then I didn’t know what to do with that sensation, so it started to fade away.
The third step was linking this feeling of ‘seeing an object, associating it with a certain number of atoms, and then feeling the presence of those atoms’ - I called it ‘atom glasses’ - with the narrative context of doing a thought experiment inside a cell.
For context, I’d always struggled with biology - hated it passionately, in fact - for how little it lent itself to thinking. Reading a biology textbook or badly-written paper, I had to link together either arbitrary geometric shapes that represented proteins, or to place obviously incorrect concepts into logical frameworks and believe the results (antioxidants certainly were not single-handedly ‘causing’ aging in some absolute way, we had no idea what was happening, but I was supposed to eat this fact from a paper at that level of resolution and infer something else with it somehow?).
This picture of biology changed for me in 2020, while I was in the middle of a pandemic road trip. I’d just pulled over for a call with mentor where they were described a meditation-style exercise to help with emotional regulation - you imagine an object, like an orange, positioned right in front of you and try to ‘see’ it with increasing detail, imaging the color, shape, taste, and rotating it, etc. That was the first concept I needed.
I was pondering it when I remembered - a year earlier - lying on a mattress in the warm, stuffy attic of the group house I lived in and watching clips of Iron Man, where Tony Stark talked to Jarvis, pulling up diagrams and manipulating them with just his hands. Lying there, watching Tony expand an atom over and over, I’d wanted so badly to build something like that for myself - to be able to draw my hands apart and have a mechanical diagram I was working on suddenly become room-sized. And then my brain put two things together and it was like - I could just do that inside my brain, I could use the atom glasses - the feeling of being on a different log scale - and this new skill of 'seeing’ more complex objects visually, and what I knew about a cell to render a picture of it and then feel like I was really there, inside a holographic display. I literally pulled over a few hours later at a random truckstop at night, and recorded a video talking through the experience so I wouldn’t forget. I remember ‘feeling’ being next to a mitochondria, and wondering about its composition with an intensity and specificity I hadn’t felt before. I started asking new questions, ones I wouldn’t otherwise have known to ask.
Having this perspective was hugely motivating, and I felt consumed, hunting down new information about biology, numbers I had previously struggled to care about. It sparked an obsession with a new hallowed resource of facts about the cell - book.bionumbers.org. I tried to memorize enough numbers that I could do 30 minute-long thought experiments without exiting the state, first asking how many receptors were on a membrane, then how dense they were, then looking at how ions were going in and out and their concentration - you could follow a story endlessly, it seemed.
I learned a lot, doing these thought experiments. They showed me how much more useful some mental models were than others - energy should be measured in kBT! It was so obvious that was the best way to think about things, 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. For a while, I worked with my dear friend and collaborator, Joanne Peng, to turn these types of thought experiments into an online syllabus. We didn’t release it, but I’m more proud of the work we did and the concepts we discovered while working on that syllabus than of many of the other, longer projects I’ve worked on.
I was amazed at how much moving my body freely through space was important, for complete immersion in the land of the cell. I couldn’t feel the state sitting at a desk - it was embodied, so I normally got there running or dancing around a grassy, abandoned field. Music was so important to me then - 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 the inverse square law really feels, how when you're nanoscale electrical forces dominate and gravity fades away, how you're always bombarded, how dark it is, how quantum things become more important. How diffusion works until it doesn't. How weird that the cell ran mostly on passive diffusion, there were no orderly grid-like rows for information to flow through, like 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? What was in front of me? How fast was I moving? What would I do next?
Unfortunately, this skill is not that useful if you want to make scientific breakthroughs, in the absence of the other 99% of rote work - like, it doesn't magically solve all problems, doesn't analyze RNA-seq data for you. It is super helpful for hypothesis generation or trying to understand 'what might be happening' - but you could probably solve a lot of science without it. I think it in relation to (at least) biology is a bit different from a certain period of physics in this regard - physics probably really required this for a while.
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 - it's just the feeling. Nothing to do with solving the most important problems in science. 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.
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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 undersatnding - 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.