Mathematics as the basis for leftist reasoning


Chris Mooney of the Inquiring Minds podcast interviewed Jordan Ellenberg about his book How Not to Be Wrong: The Power of Mathematical Thinking, and in a fascinating accompanying post, Mooney investigates whether mathematics are "liberal." His argument is that liberal thought is characterized by "wishy washy" uncertainty and that math professors tend to vote left:

For instance, Ellenberg is big on busting tendencies towards what he calls "false linearity" in our thinking—and not afraid to use political examples to make his point. Early in the book, he takes on a Cato Institute scholar who wrote a 2010 blog post about health care entitled, "Why Is Obama Trying to Make America More Like Sweden When Swedes Are Trying to Be Less Like Sweden?" As Ellenberg explains, the whole conceit of this argument, the mental model involved, is linear in nature. He includes this amusing hand-drawn figure in the book (one of many) to illustrate the point:


If the United States and Sweden are both on a straight line, one end of which is prosperity and one end of which is a "Black Pit of Socialism," then of course the US should move away from socialism and towards higher prosperity—and Sweden should too. "But if you take one second to think about that consciously, that's obviously not true," Ellenberg explains.

Suppose instead that the two countries are located on a curve, one where prosperity peaks at some degree of socialism/"Swedishness" that is greater than that of the United States but also less than that of Sweden, but declines when you have too much socialism—or too little of it. More like this:

"There's such a thing as taxing too little, and there's such a thing as taxing too much, and there's kind of a Goldilocks point where it's just right, somewhere in between," Ellenberg says. "And so there's no contradiction to say that, maybe the US should have more of a welfare state than it does, and maybe Sweden should have less of a welfare state than it does."

Of course, as Stephen Colbert has reminded us, "Reality has a well-known liberal bias."

How Not to Be Wrong: The Power of Mathematical Thinking,

Is Math Liberal? [Chris Mooney/Mother Jones]

Notable Replies

  1. There is no logic in the argument that maths is liberal because maths professors are.

    But I'm sure there is more to it than that.

    That aside the above illustration shows why partisan two party politics will always fail as the linear (I call it black and white) view is always to say the opposite of your argument is purely wrong.
    It amazes me that the modern western liberal centerist politics never acknowledge the benefits of both capitalism and socialism in the same argument.

  2. The Laffer curve of Swedishness?

  3. The example used in the OP is curious.

    As the example itself notes, if US and Sweden are on a straight line, then CATO may be right and it may be rational to move away from the Sweden model.

    But if the alternative example of the curve is correct, then it would make sense for both countries to shift in direction.

    What we would really need, however, is some way of determining which model is correct. All Cory and the OP seem to do is posit that simply because there are alternative ways of describing a problem that any given way of describing it is likely wrong (which may be trivially true, but is not all that helpful).

  4. Ygret says:

    They're not saying there are alternative ways of describing a problem they're saying that one way is ridiculously simplified to the point it is worse than useless, and the other provides an example of why that way is useless. Its an important point because the truth is that in the US so much is done wrong because of an anti-intellectual bias that insists on simplifying complex issues until they turn to nonsense.

    Take for example the notion that government accounting is just like a business or home. The idea appears to have a certain linear logic to it, but its flat wrong. Governments print money. Homes and businesses don't. If governments don't print money then there is no money, so governments HAVE TO run deficits in order for us to have money to spend and create an economy. Those two facts completely annihilate the "common sense" meme that most Americans believe. This leads to all sorts of perverse and terrible outcomes for the vast majority of the American citizenry. I'd go so far as to say that linear thinking is destroying our country and the world. The way simpletons mock global warming because there was a big snowstorm in early Spring, or something, is symptomatic of the problem. In other words stupidity reins when linear thought is applied to complex problems. And the left is constantly accused of "wishy-washy" thinking because we don't always give pat and simple, linear answers and our solutions often have a counter-intuitive quality.

    And in response to another comment above, the fact that mathematicians are liberal doesn't prove that liberals are correct on every issue, but it does strongly suggest it wink.

  5. Hmm... The point that I got from the article wasn't so much that the curve is linear or parabolic, it's that we need to think about what is the most appropriate curve.

    I think it was Douglas Hofstadter (of Gödel, Escher, Bach, an Eternal Golden Braid fame) who suggested that when considering an action, or law, or what have you, some helpful questions are:

    What if everybody did it?
    What if no one did it?
    What if half the people did it?
    What if a few people did it?
    What if most people did it?

    One way to look at this in terms of this article is that it helps to determine the order of the equation needed to model the decision.

    "What if no one/everyone/half the people tortured people?" gives a very different answer than "What if no one/everyone/half the people drove on the right side of the road?"

    The first question suggests a linear relation and a plot going from liberal democracy at one end to "Black Pit of Torturous Hell" may well be appropriate.

    On the second question, it does't matter which side is chosen, as long as everyone agrees to the same side. The shape of the solution is fundamentally different.

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