I’ve always thought it would be cool to have a tattoo. No, not “cool”; satisfying. To have a symbol that I like, that is meaningful to me, that I can carry around with me. I would put one on each wrist, because I would see them often, it’s a nice blank spot, and my hands are symbolic of my interaction with the rest of the world.

I am a person who is very interested in and aesthetically aligned with finding things that are singularly good in some way. What is the optimal way to make choices? What is the truth underlying all other truths? What is the best possible future? The most important thing? So when I think about getting a tattoo for myself, I don’t just think of getting a pretty design, or a character from a show, or a commemoration of a past event. I think, what is one message that I fully love? What symbol most represents me? What would be optimal to remind myself of so often?

I could look at it and take regular pleasure in the meaning of the thing. People I meet could ask about it, and I would get to excitedly tell them about the cool meaningful thing.

There are so many great things it could be: the earth; the earliest known writing; neurons; a depiction of Turing machines; of infinity, of an infinite future, of unbounded potential; of striving; of cooperation between sentient beings.

But, I don’t have one yet. And it’s because, well, I haven’t found the “right” thing. I haven’t found a concrete, visual expression of something that passes my bar for being permanently part of my experience.

I know, I know — “you’ll never find the perfect thing”, “nothing’s perfect”, “you’re missing the point of tattoos”, “don’t let the perfect get in the way of the good” etc. etc. But… I don’t think I’m falling into the failure mode that you might be imagining. I don’t feel anxious about getting something and then not liking it later. I’m not sure that there is a perfect thing. I just haven’t thought of anything that really excites me. If 50 years go by and I still don’t have a tattoo, I don’t think I’m going to regret it. I think I’ll just think, “well, I didn’t find the right thing, and that’s perfectly okay”.

But something occurred to me today; an alternative framing. I was pacing around my apartment, trying to make progress on my research. I was thinking about how, if an entity receives two different inputs, what does it mean when it takes two different actions, versus the same action? What does it mean when it takes two different actions, but which result in the same outcome? And at the same time, I was thinking about my cool coworker friend who helped me decide to get my ears pierced, and who also has lots of cool tattoos. I looked at my arms and thought about how I don’t have tattoos. And I thought; me not having a tattoo is one of the ways the world can look. What does it mean about the difference between this world and the one where I do have tattoos?

And then, I had the sense that it meant something positive rather than something negative. That it was the result of an action rather than an inaction. That is to say: I have a tattoo. The fact that I have not yet found a suitable symbol is a meaningful and enduring fact about me. The nothingness emblazoned on my arms is a direct causal effect of my continued search. I can look at my arms, and instead of thinking “maybe I should have gotten Turing machines tattooed there years ago”, I can think “there it is, there’s the symbol to myself that I am one who searches, one who is not satisfied”. And in fact that’s essentially what I do think when I look at my arms. Because when I think, “I still wish I had a tattoo” my immediate next thought is, “let’s think harder about what it could be”, which causes me to start thinking about potential essential expressions of ultimate meaning. This is essentially identical to thinking, “I still wish I understood the most important things… let’s keep trying to understand them”.

In almost all of modern mathematics, the objects of discourse are ultimately defined in terms of what are called sets. The number 5 is the set containing the numbers 1 through 4. A function is a set of pairs (where a pair is a set of two things), where the first thing (itself some kind of set) in each pair gets mapped to the second thing (another set) in the pair, et cetera. But if everything is in terms of sets, where does it bottom out? The empty set. The empty set is a perfectly valid set; it has no elements. Because nothing is in it, you don’t need to have a pre-existing type of object in order to define the empty set. You can start there.

So that’s my tattoo; the empty tattoo.¹ It represents everything I’ve found so far that’s perfect; nothing. The fact that nothing is in it is meaningful, because I have been searching. There are other people who have no tattoo and who have not been searching. You can’t tell us apart by looking, but that’s okay, because I know who I am.

1. Of course, many people have a tattoo of the empty set itself. But, well, that doesn’t feel right for me. The set containing only the empty set is different from the empty set itself. ↩︎