Math is Democracy II: Math is Democracy!

I announced a series on math and democracy back in October.

It will deal with a lot of concrete areas. Last time I talked about a case that is before the Supreme Court and will influence voting law throughout the land. In the future I’ll be talking about voting, political participation, technology and who has a say over its development, and of course the classroom.

But I want to properly kick things off with a post that is essentially philosophical. I am here to assert the following proposition:

Math is democracy!

What do I mean?

Democracy — from Greek — literally, “rule by the people.” I am referring to the ideal itself, not any particular system of government. Throughout the world we have various systems attempting to implement this ideal. One can ask questions about the degree of success of these attempts, but that’s not what this post is about. I’m just isolating the ideal — democracy — rule by the people.

Mathematics — from Greek — literally, “learning.” Of all the domains of human inquiry, math occupies a privileged place in terms of our confidence in its conclusions. It is the only field where practitioners regularly express unqualified certainty about its results. We sometimes discuss the wisdom it gives us as some sort of celestial gift (as in Wigner’s classic essay on its applicability to the sciences).

I am about to draw a connection. I expect it is still opaque at this point, but hang on.

If math is a miracle, then there is a second miracle: the divine gift was implanted in each of us, since it springs solely from the universal human capacity for rational thought. The wisdom of mathematics was not given us by way of Mt. Sinai, handed down from on high by somebody with privileged access to The Boss. Although many people think back to childhood and recall inscrutable formulas dispensed by a teacher who mysteriously knew the answer (how did they know??), this memory conceals the real truth, which is that the only place mathematical knowledge comes from is a community of peers reaching some kind of consensus after a period of engaged discussion. Furthermore, at least in principle (if not always in practice), anybody in this community has the right at any time to raise good-faith questions about the logic underlying any of our mathematical knowledge, and the matter is not really settled unless these questions have a good answer.

Thus, the only true source of mathematical authority is the consensus of a community of equals.

The principle of democracy is that this is also the only true source of legitimate political authority.

Broadening further, I offer that the principle of democracy holds that the only source of authority (of any kind) over a community is consensus of that community. So math is literally democracy.

Addendum 3/29/18:

This is edited from the version I posted yesterday, where I used the phrase “functional consensus” instead of “consensus.” This was to acknowledge that in a large-scale community such as a nation, or the international community of mathematics researchers, true consensus is not a viable goal. That said, the “functional” didn’t sit well with me overnight, because I thought it could be taken to suggest some sort of majoritarian principle. To me, majoritarianism is a fatal compromise of the principle of democracy articulated here, and it defeats the purpose of the analogy with math.

The thing about math is that, in principle, if an objection is raised to what is regarded as established fact, then that objection needs to be dealt with. Maybe something was overlooked! In actual practice, it may or may not be, because the question of whether you can get people to pay attention to your objection depends on things like if you’re famous, if you’re well-connected, how much work other people have to do to understand it, etc. But mathematicians’ collective understanding of what we’re doing holds that if somebody raises a new objection to something thought to be well-established, we have to answer it, not ignore it, in order to hold onto the established knowledge. This ideal isn’t attained, but it is still how we think about it.

By the same token, it seems to me that the democratic ideal insists that a minority view has the right to be processed rigorously by the community. I am making a high-level analogy so I’m not getting into what that processing might look like. But the failure of a community to take into account minority constituencies in some way is a failure of democracy.

Addendum 3/31/18:

I want to acknowledge some intellectual debt!

In 2008, I went to the Creating Balance in an Unjust World conference and saw a presentation by Sarah Bertucci, Jason Cushner, and several of their current and former students, entitled Consensus is the Answer Key: Empowerment in the Math Classroom. The presentation was on using consensus as the source of mathematical knowledge in the classroom. Later (in 2009?), I visited the school in Vermont where Jason and Sarah were then teaching, and saw Jason’s class. (Random aside: I also met Jasmine Walker!) The ideas have shaped how I saw both mathematics and the classroom ever since. You can see their clear imprint above (and in many of the things I’ve written on this blog over the years).

In about 2010, I was having a conversation with Jay Gillen of the Baltimore Algebra Project. At the time, I was preparing to apply to graduate school in math. Jay asked me many questions about how I thought about the math classroom and the subject itself. At some point he paused and said, “Everything you love about math is what free people love about democracy.” This comment has been continuously blowing my mind for 8 years, and again you can see its clear imprint in the above.

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The dental hygiene mode of thinking and talking about race

So back in January I promised a pair of posts entitled “Visibility/Invisibility of Brown Brilliance.” Part I went up almost right away, but Part II has proven to be a lot of work. I tried to bang it out a couple times but got stuck in questions of exactly how personal I wanted to get. So I shelved it until after I finished and defended my PhD thesis.

Which, by the way: defended! You may now address me as “MF Doctor.”

Also, I’m on twitter now, and plan on actually using it.

So, anyway, looking forward to finishing Part II. But I realized it might help to more explicitly create the frame for the type of conversation I want to have. I got added impetus by reading Yen Duong’s sweet and brave post the other day, entitled Am I Racist?

In it, Yen describes going to a football game with her spouse, and noticing that she perceives the white players as younger than the black players. She connects this with a 2014 study showing that white male police officers and white female undergraduates tend to overestimate the ages, and underestimate the innocence, of black boys aged 10 and up. She asks her spouse if she is being racist. He recoils and insists she’s not.

What came up for me was the critical, critical importance of being able to talk about the way that living in this world and this country, with all their glorious and sordid history, distorts our perceptions of each other based on race, without getting sidetracked by a conversation about whether or not we are good people.

I think something really beautiful and important was said about this some years ago by Jay Smooth. I’ve linked the below video twice before, but let me make it the focus this time.

The main idea:

Being a good person, with respect to race (and more generally), is like being a clean person. It’s not something you are or not, it’s a practice. Like dental hygiene.

The world we have inherited has racial “dirt” everywhere — tendencies to misperceive each other accrete in our minds, like plaque on our teeth, daily, just from living life in this world. The root causes of this fact were in place long before anyone alive today was born. So when we notice one of these accretions in ourselves, or have it pointed out to us, the question of whether that makes us a bad person is a red herring. It doesn’t: these accretions are inevitable, for everyone. The right question is how to train ourselves to perceive each other more clearly.

The video:

Watch this right now. I’ll wait.

What I want to add:

Two things.

1) In the video, Jay says, “There are many things in our day-to-day lives that lead us toward developing little pockets of prejudice.”

I think one aspect of the racial “dental hygiene” he’s calling for is the search for awareness and understanding of these processes. My major purpose in writing the Visibility/Invisibility of Brown Brilliance posts is to call attention to the subtlety and effectiveness with which our media and cultural environment, whether by design or not, programs us to underestimate the minds of the black and brown Americans among us. (How could I not have noticed, before Queen of Katwe and Hidden Figures were announced, that I’d practically never seen a movie centered on the brainy pursuits of a brainy black woman, despite the many brainy black women in my life?)

But for the benefit of those reading who are unsure what is being referred to, here is a very concretely documented example:

Here is a twitter user comparing Google image searches of the phrases ‘three black teenagers’ vs. ‘three white teenagers’, turning up mugshots in the former case and cutesy, wholesome stock photos in the latter.

This is the “dirt.” It is going to get on us, every day. The question is what to do with it.

2) I love Yen for her reflectiveness about the football players and the study. This is what the “dental hygiene” looks like — this is how you do it.

I also relate to her spouse. If somebody (even your partner) is calling your partner a bad name, you defend! BUT, I have the feeling that trying to reassure Yen she wasn’t being racist was pulling them both away from the good stuff. Look, a study of hundreds of cops and college kids found that on average they tended to overestimate black boys’ ages a dramatic amount. Presumably, lots and lots of people do this. I bet I do it. What are we then going to do? Take note, and look for ways to do a better job? Or, waste energy trying to prove the improbability that we’re somehow immune from this poison?

Again, I feel him. And I don’t blame him. The issue is that our cultural understanding of how to be a good person is so limited. An alien watching video of lots of Americans talking publicly about race would surely conclude that we believe that good people are never prejudiced and if you ever have a prejudiced thought, you’re bad. In the language of the video, the “tonsils paradigm of race discourse” — “I can’t be prejudiced, I had my prejudice removed in 2005!” We would all grant that this is absurd, abstractly, and yet we have an anxiety meltdown, or get angry and defensive, at the slightest suggestion of prejudice — what other conclusion could our hypothetical alien come to?

This limited frame makes it impossible to attend to a racially problematic habit of thought without implying that you’re a bad person. This forces us to hide the dirt. Then we just get dirtier and dirtier and keep hiding it.

I’m offering Jay’s video as an alternative frame. What if instead of hiding our racial dirt we were trading ideas about how to deal with it? Working on better and better “toothbrushes” for our stereotypes?

On that note — above I mentioned Google image searches as a quick and concrete measure of the “dirtiness” of our environment of racial images — here is a “toothbrush” that was designed in response. A photo / video / poetry art piece by 19-yr-old Myles Loftin, addressing these images. Enjoy!