Listening to Freakonomics s11e16 there was some commentary about “if the world was run by mathematicians it’d be so logical.”

What an absurd statement.

I’ll just focus on two ways this is wrong. The first is that mathematics is irrational through omission.

Irrational Through Omission

To model something with math (or in any formal system), you must first convert it to something that can be expressed in a mathematical system. The model, constructed by a human, will omit details and variables that complicate the math too much or do not appear to be relevant. As the jokes goes, if you ask a physicist the shape of a cow he’ll tell you its a sphere.

Given that we must omit details to be able to express things in a mathematical language, the model can end up being irrational (when looked at in the broader context) due to these omissions.

We also are guilty of omission not just via simplification but also through own ignorance. Are mathematicians omniscient and thus know all variables to consider when building their models such that their models will be perfect?

Math Cannot Confer Value

Is it ever right to sacrifice an individual’s rights for the greater good? To kill a righteous man to save 100. This isn’t a mathematical question. It is a moral one. And as a moral question it is an aesthetic question with no foundation in logic.

Now do note that you can make moral questions scientific questions by positing a goal for an organism and then understanding the best things that the organism can do to achieve that goal. But see even here we must posit something arbitrary. That arbitrary thing being a goal. My goal might be life of myself and others. Your goal might be life of yourself and death of all others.

If there was such a thing as “the greater good”, what would that even be? Each individual makes their own value judgments. Will you collect all individuals, ascertain exactly what they value now, determine the overlap, sacrafice the rest? Do individuals even know what they value? Can they communicate it accurately? Is the greatest good even aligned with that which is valued by the most?

Luckily there’s no such thing as the greater good. An appeal to the greater good is, at best, an abdication of responsibility. At worst, a theft of natural rights.