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. While pointing to a David Goodsell-style illustration of molecules inside a cell, I was struck by how strange the world in the image was - the physics were totally different from my normal world, and the molecules were jam-packed, right on top of each other!
Suddenly, my heart stopped, and I had a realization. These molecules (or, molecules similar to them) were really there, somewhere in space. The realization grew - I was looking at an illustration, but it was telling me about a world just as real as my world except smaller. As I stared, I started to feel the molecules bouncing around me, and to feel in my chest a sense of being in a chaotic infinity expanding out into space. For a moment, I was somewhere else.
It took me a long time to turn that brief, overwhelming experience of being in a crowded cell into an experience I could stay with for a few minutes or even an hour, and to connect it to thought experiments that generated insight. I’ll describe that journey a bit more here, and would love to hear from you if you’ve experienced similar states.
My second step towards this state came over a decade later, in 2019, and involved making a link between the feeling of ‘being in another world’ and the feeling of doing a physics thought experiment. I remember watching a Nima Arkani-Hamed lecture (‘Morality of Fundamental Physics’) on my laptop while studying at a cafe on Divisadero street, as it got dark and cold outside. Nima was describing the importance of units - how seeing the weight of a star as a certain number of neutrons as opposed to thinking of it in grams allowed you to think about it differently, because you could ‘see’ the star as a collection of that number of neutrons, and what that number of neutrons might 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. I felt overwhelmed, and had a rapidly repeating sense of ‘it’s there, it’s really there’, referring to that ‘other world’ in which the atoms existed and which in that moment I felt so viscerally. I fell into a daze, got ice cream, and just wandered around feeling elated to live in this world with such magical properties. 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 next, and the sensation started to fade away.
The third step I took toward exploring the feeling of being in a scientific world was linking this feeling of ‘seeing an object, associating it with a certain number of atoms, and then feeling the presence of those atoms’ with the narrative context of doing a thought experiment inside a cell.
For context, until that point in my life, I’d struggled with biology. I hated how little biology lent itself to thinking. Reading a biology textbook or badly-written paper, I had to either link together rbitrary geometric shapes that represented proteins or 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 on a holographic display them with just his hands. 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 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.
Tim Urban’s wonderful post The Big and the Small perfectly illustrates this phenomenon