INTERVIEW w/ DANIEL BISS

Though they seem disparate, science and art are inseparable, and, in our current and forthcoming world, it is becoming more and more imperative to promote the merging of these fields. Both deal in the same fundamental concepts: space, time, change, and relationships. They seek out truth in its most abstract form, then attempt to communicate it via a human language. The only difference between the two languages is that one conveys its revelations with numbers, the other visually.

This is That has tried to highlight and promote the disciplines of science, technology, and mathematics, and the creative thinkers who propel them forward. About a year ago, I came across an article in Seed Magazine about a young mathematician named Daniel Biss. Daniel had some imaginative and important things to say about math, and it struck me that his voice would be great to add to the mix of artists and photographers so far interviewed on TisT. I was pleasantly surprised to find out that, in addition to his work as a mathematician, Daniel is also running for State Representative of Illinois.

The following interview took place via email, at the end of May, 2008. Please visit DanielBiss.com for more information.

1. "Things are Defined by Their Connections to Other Things"

This is That: I first learned about you through an article in the March 2007 issue of Seed Magazine. You likened mathematics to art, talking about the aesthetic and abstract qualities of both disciplines, which piqued my interest as both an artist and as (at the time) a math major. You said you were inspired by Braque's quote about how objects exist in terms of their relationships with each other. Can you talk a bit more about this approach to deciphering the world, in terms of math and/or art? How can we use these languages to describe such relationships? In my favorite quote from the article, you said, "When I do math, what I'm trying to do is get closer to reality, to refine this abstract language so that it more closely approximates the way things really are." I think this idea resonates with all creative thinkers, and in this way, there is definitely a link between art and math, where usually they are viewed as opposite extremes.

Daniel Biss: Math is full of instances where it's helpful to think of objects as being defined by the relationships they have to other objects. In the article I meant this quite literally, in the context of viewing the object in a category as "the same" as the functor it represents (this is a reasonable thing to do because of the Yoneda lemma [which allows for an smaller category to relate to objects in the larger, functor category]), but there are lots of less contemporary examples. For example, Dedekind cuts tell us that one of the easiest ways to define a real number is by enumerating the set of rational numbers less than it.

I mention this because it's a pure example of defining an object (a real number) in terms of its relationships to other objects (rational numbers). The fact that one can do this is tautological (indeed, the Yoneda lemma is kind of trivial), but the implications are far-reaching. Objects don't exist in a vacuum. Things are defined by their connections to other things. Life's meaning is embedded in the relationships we have with one another. Oh, sorry—I seem to have accidentally started answering the [forthcoming] political question!

TisT: Your area of research is topology, which deals with, in as few words as possible, the shapes of things. Can you give a brief summary about your work in this field, and its implications? I'd like to know what first pulled you in about this branch of math. It's less number-centric and more abstract, even visually based. Can you talk about what in particular inspired you to go in this direction?

DB: My work in this field has focused on connections between topology, combinatorics, and algebra. For example, I've worked hard to bridge the gap between combinatorial topology (the study of polygons and other finitely-proscribed spaces) and differential topology (the study of shapes using calculus). I'm always attracted to mathematics that makes connections between different fields—maybe that's because I'm more interested in relationships than objects!

I was very drawn in by the first topology class I ever took. I honestly can't say why it is, particularly since high school geometry was never my strong suit.

2. An Unusual, Difficult to Access, But Universal Language

TisT: One of the prevailing sentiments about mathematicians, and mathematics in general, is that it attracts rigorous, austere, even cold personalities—that there's little room for imagination, or spontaneous, creative types. For me, I find this thinking to be woefully handicapped, and I wonder sometimes as to how it became such a popular idea. Do you have any thoughts about why this schism seems so deeply rooted; and going back to question 1, what are your thoughts on overcoming it, or at least reconciling the two disciplines?

DB: I think the schism comes from two things. First, mathematics is the language of the natural sciences, and so mathematicians naturally get lumped in with scientists in most peoples' minds. Second, math as it's often taught at the elementary and secondary levels tends to be pretty rigorous, austere, and cold, and doesn't involve lots of imagination or spontaneity.

Unfortunately, these reasons are actually pretty compelling, in spite of the fact that I agree with your assessment that the conclusion that's drawn is wrong and damaging. As for what to do about it, I think dialog is really important. There aren't a lot of opportunities for mathematicians and artists to interact and share ideas, and that probably has a lot to do with why this misimpressions are allowed to persist.

TisT: I'd like to know a little about your background. You won the Morgan Prize for outstanding undergrad math research—can you tell me a bit about the work you were doing? But more generally, what first attracted you to math and how did your interest and work with it develop?

DB: My Morgan Prize work was on generalizing some basic notions of algebraic topology (fundamental groups, etc.) to some slightly pathological (not necessarily semi-locally simply connected) spaces.

Math was initially a kind of escape for me. I grew up in a family full of musicians, and it became pretty clear by the time I was a teenager that I wasn't going to be a professional musician. Thus, everyone in my family but me shared a calling that came with its own specialized language. I first fell in love with mathematics (thinking about Lebesgue integration over the summer of 1993) because I was drawn to its language, a language that simultaneously seemed unusual and difficult to access and yet universal. In other words, I'd found an expressive language that shared many of the critical features of the language of music, while still being quite different from what my family was doing.

TisT: Where do you see your mathematical work going in the future?

DB: I don't know! :)


















3. Just Solving Math Problems Wasn't Good Enough

TisT: I was surprised and interested to hear about your recent political campaign. Can you talk a bit about how this decision evolved, and where your interest in politics began? I'd like to know your thoughts on how to parallel the lives of a politician and an academic mathematician. How has your mathematical background and training prepared you for a career in politics—has this idea of trying to decipher reality and the relationships between objects influenced your work with society, economics, et. al? How so?

DB: My interest in politics, at least on an abstract level, came from my family. My parents (and other relatives) are very engaged and our household always featured lots of robust discussion about public affairs. However, I never imagined I'd actually run for public office myself.

That decision came much more recently, as a part of an evolution I've gone through in the past seven or so years. As my frustration mounted with the direction our country was headed, I eventually came to feel that it wasn't good enough to just solve math problems; I really needed to somehow get involved and try to impact the direction things were moving.

So I began doing grassroots organizing work for a number of Democratic candidates in the area, and discovered—much to my surprise!—that I really loved this work. And I eventually came to realize that I loved it so much because, in my view, the core problem we face as a society is the lack of participation in public life, and the distance between local communities and the governing process. Grassroots organizing was so satisfying because I was trying to create spaces where people could get involved, connect which each other, and voice their opinions, but I eventually decided that I could more effectively do that as a candidate and eventually as an elected official. Hence this campaign.

It all comes back to thinking about relationships instead of individuals...

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I'd like to thank Daniel Biss and Julie Sweet for their participation and effort with this interview.