It strikes me that there is something to be said about mathematics and politics that goes beyond just numbers.  Mathematics, because it is a logical system, guards against some kinds of sloppy thinking that can get in the way or be exploited in propaganda.  Here are a few examples.

1. Not every function is bounded or even linear.

I’m starting here because it came up in a previous discussion of climate change. Damage from climate change is not bounded or even linear.  The world just gets that much farther from what human civilization was built to deal with.

Destruction from climate change increases exponentially with the concentration of carbon dioxide in the atmosphere.  As noted there is no such thing as a “new normal” or even a price limit for the damage done by a ton of CO2.   So there is no alternative to preemptive action, hard as that is for any society to achieve.

2. Negative numbers are just as real as positive ones.

In our national budgets positive expenditure are discussed in terms of things bought:  for infrastructure, education, healthcare, safety net.  Deficits are abstractions: possible effects on the financing costs for the national debt for example.  In fact deficits are negatives of things bought—things not bought.  They have to be evaluated by tradeoff of what that money was spent on versus what now isn’t going to be bought—for infrastructure, education, healthcare, safety net.

3. You can’t understand a function of two variables without looking at values for both.

It may seem obvious, but it is still worth stating: if you have a function of two variables, you can’t understand anything by looking at variation in one.  Performance of Trump’s golden dome depends on how well the new defense handles the offense coming at it.  We already had a much-touted proposal like that under Reagan—his Star Wars.  That was an expensive program that sounded great and went absolutely nowhere—no successful tests even of highly-simplified versions!

We’re told the time has come to build another one, because defensive capabilities have increased so much that it’s time to finish Reagan’s job.  To my knowledge, no one has said a single word about what has changed with the offense.

4. You have to be able to learn from applicable results in different contexts.

This may seem abstract, but some of the greatest advances in mathematics have been made by recognizing that results in one area can be brought to bear on seemingly different classes of problems.  Life is like that, just generally.  You have to understand how things work, so you can apply what you know to new problems.

What have we as humans learned about how a society should function?  Most of all that chaos is a bad thing.  If we are going to live together successfully, we need rules of behavior and at least mutual tolerance.  There is also some notion of caring for the weak as an essential part of social cohesion.  That is built into essentially all successful cultures and all religions, because chaos is unstable, exhausting, and dangerous. It also undermines the stability needed for economic growth and prosperity.

For international relations we have nonetheless chosen to ignore that experience, on the grounds that of course we are going to win, rule the world, and steal everything of value from everyone else. That’s not new as motivation, but it is precisely the mentality that our species has learned is self-destructive.  Christianity has a few apt quotes:  “As a man sows so shall he reap” or more to the point “For they have sown the wind, and they shall reap the whirlwind”.

 In a age of proliferating nuclear weapons and accelerating climate change, that’s not something you want to think about too much.

5. There is one more relevant point:  not all functions are continuous.

It is natural to believe in continuity, that the features of one’s current life are somehow normal and can be relied upon.  That is felt as reality, not complacency.

But history has shown over and over again that there are no guarantees.  It’s all up to us.