Math is Democracy II: Math is Democracy! Wednesday, Mar 28 2018 

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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Math is Democracy I: The Citizen and the Gerrymander Friday, Oct 20 2017 

I am intending a series of my typically long, elaborate blog posts entitled Math is Democracy. The ideas have been brewing for years although they have been rapidly expanding and taking on new urgency since January. I alluded to this intention previously.

I wasn’t ready to start it yet, but I feel I must. I was reading the oral arguments in Gill v Whitford, the Wisconsin partisan gerrymandering case currently before the Supreme Court. I had to stop and have a moment when I read this:

CHIEF JUSTICE ROBERTS: Mr. Smith, I’m going to follow an example of one of my colleagues and lay out for you as concisely as I can what — what is the main problem for me and give you an opportunity to address it.

I would think if these — if the claim is allowed to proceed, there will naturally be a lot of these claims raised around the country. Politics is a very important driving force and those claims will be raised.

And every one of them will come here for a decision on the merits. These cases are not within our discretionary jurisdiction. They’re the mandatory jurisdiction. We will have to decide in every case whether the Democrats win or the Republicans win. So it’s going to be a problem here across the board.

And if you’re the intelligent man on the street and the Court issues a decision, and let’s say, okay, the Democrats win, and that person will say: “Well, why did the Democrats win?” And the answer is going to be because EG was greater than 7 percent, where EG is the sigma of party X wasted votes minus the sigma of party Y wasted votes over the sigma of party X votes plus party Y votes.

And the intelligent man on the street is going to say that’s a bunch of baloney. It must be because the Supreme Court preferred the Democrats over the Republicans. And that’s going to come out one case after another as these cases are brought in every state.

And that is going to cause very serious harm to the status and integrity of the decisions of this Court in the eyes of the country.

Now, there’s a lot here one could react to.[1] But the main thing I reacted to was this:

The Chief Justice of the highest court in the land thinks Americans don’t feel empowered to judge an argument on the merits if there’s math involved.

You know what? He’s probably right about that.

But this situation is very, very wrong.

Math is being used increasingly to make decisions governing our lives, for good or ill. Increasingly sophisticated math.[2] The instance most familiar to readers of this blog is probably teacher value-added scores, but the many various uses share this: they are not accountable to the public.

One reason the Wisconsin case is so hot is because the process that led to the map currently being challenged included a lot of fancy mathematical modeling intended to make the Republican legislative majority as bomb-proof as possible — an effort that appears to have worked really well. That the map was drawn with this goal and these tools is not a controversial point in the case. This was a use of math by legislators aimed at becoming less accountable to the public.

What I’m getting at: math is a species of power, and it’s a species that multiple antidemocratic forces are using, very effectively. And it’s a kind of power that citizens, by and large, totally lack.

So, the game is unfair. We the People are supposed to be able to participate in public decision-making. That’s the heart of democracy. But math is increasingly becoming a kind of secret key to power that, if the Chief Justice is right, We the People mostly don’t have. As soon as there’s math involved, we can’t even participate in debates about the very consequential choices that are being made. In which case, nobody who wants to use the power of math (for good or ill!) needs to be accountable to us.

I mean, this was true before the explosion of data-science driven business and governmental practices Cathy writes about, or the computer-assisted 2010-11 legislative redistricting.[3] But now it is more intensely true than ever.

What this leaves me with is that doing our jobs well as math educators is completely urgent for democracy. Every kid we leave traumatized and alienated from formulas and data analysis is a citizen that doesn’t have a voice.

Don’t let anybody tell you it doesn’t matter.

Notes:

[1] For example: This author at ThinkProgress thinks Roberts has a lot of nerve claiming to be concerned with the perception that the court is partisan when he has so consistently voted along partisan lines in landmark cases. This author at WaPo thinks it’s not legitimate for the Court to be considering its public perception in the first place. I am personally inclined to believe that Roberts is earnestly concerned about the court’s reputation and that his question was earnest (mostly because of his surprising and apparently similarly-motivated vote in NFIB v Sebelius), although I do think that the fact that he doesn’t appear to be equally concerned with the perception of partisanship if the court does not “allow the claim to proceed” reflects a rather striking partisan limitation in his image of the “intelligent man on the street.” I know plenty of intelligent men, and women, who would be inclined to conclude that he himself is a partisan hack on the basis of the above quotation alone.

[2] Shout out to Cathy O’Neil.

[3] This seems like a good moment to acknowledge the deep debt of my thinking here to Bob Moses, who has been on this tip for a long time. Also, there is some relationship to the work of math educators in the Freirean tradition such as Marilyn Frankenstein and Rico Gutstein, though I can’t take the time now to figure out exactly what it is.