Math Mojo vrs. Anti-intellectualism

This is the second post in a series about counter-intuition.

(View the first post about counter-intuition here.)

When I ask many elementary school teachers if they teach that you can’t divide by zero, they say, “Of course.”

When I ask them why, things get a little murkier. Usually they will grasp for an answer, like, “Because you can’t divide by nothing. That just makes sense.” Which is meaningless and irrelevant, and is certainly not the answer.

It’s sort of scary that people who are trained to teach our children don’t know the first rule of learning – if you don’t know something that you need to, face up to it, and learn it.

There is a sad tendency for us to want to say we know something more than we want to know it. That is a learned trait. We learn it from ignorant parents who make fun of us when we are young, from a school system that uses grades more to judge us than to help us, and from our peers who in their infinite insecurity need to make fun of anyone who does something wrong, just so we won’t notice their faults.

Our schools train us to want to have “the right answer” more than to want to understand anything. Face it, most of the school experience is about tests. There may be some exceptional teachers that go beyond that, but “No Child Left Behind” has had that become even rarer than it was previously.

This degrades the quest for true knowledge. If you constantly have to pretend you know something that you don’t, you’ll never get to the point of maturity where you finally have to go and learn it. Then, to keep from being found out as an ignoramus, you’ll have to make fun of people who understand more than you do.

Look at your average political talk show host, for example. Raving at things they don’t understand, and decrying “elite intellectuals.” It’s basically a cry for help from them from their own ignorance, but disguised as “political analysis.”

They are hiding in their “anti-intellectual” comfort zone. They are threatened by what they don’t understand. This is the main problem. Admitting you don’t understand something is the first step towards freedom. Freedom from rigidity of thought, freedom from superstition, freedom from ignorance. Once you can imagine that you don’t understand something, you are free to go about finding out an answer, of if one can even be had.
Posturing that you have an answer to what can’t really be known is the depths of slavery of the mind to the will of other, equally ignorant minds.

Imagine if we still believed things like throwing a virgin into the volcano will appease the gods? That sounds ridiculous, but there are people who spout equally silly things today. And a large portion of the population believes them, because, “anyone can see that it’s true.”

It is appalling that in the U.S., anti-intellectualism is actually praised by part of the population. What is the deal – “Don’t be smart like them – be dumb like us?”

An intellectual approach (which does not mean some effete, elite attitude – after all, intellect is not based on emotion) would be, “Let’s look at the facts regardless if they are comfortable or not, and form some opinion from what we can prove, and change or reject the opinion as we find out more facts. And let’s try to use logic to convince those who don’t agree with us. But if their facts and opinions make more sense, we can change our opinions.”

The anti-intellectual approach (which generally does mean some attitude, because this approach is based on ‘gut’ emotions) would be, “Let’s form an opinion based on making us feel comfortable with what we don’t understand, and then we’ll try to find some facts to fit them, and change or reject the facts if they don’t fit our opinions. Oh, yeah, and let’s get real mad at anyone who doesn’t accept our opinions. And if their facts make more sense than our opinions, let’s just deny their facts.”

That is no way to run your mind, your country, your society, or anything else. It is just the same as denying that the Earth revolves around the Sun.

Knowledge isn’t something to be afraid of, nor is it something to be proud of. It is just something to be curious about. Curiosity ends when you think you know the answer, but you don’t care why it is true – you just know “…because…”

Don’t let curiosity end for you. Ever. As the Chinese say, “Curiosity is the best teacher.”

Want to know the real scoop on division by zero (in arithmetic)?
Check out:

Why We Don’t Divide By Zero in Arithmetic
and
Division by zero

By the way, Occam’s Razor is not only a tenet of Math Mojo, it is one of the things that guides mathematics. Math and logic are not the same. Math doesn’t always have to be logical (really? How counter-intuitive), but it always must have logical consistency.

The next post in this series will be a real-life and current example of how people intentionally or ignorantly deny and distort facts by starting with opinions.

One more note – don’t confuse intellectualism with academic elitism. Most populists do that to confuse you. Academic elitism is just another form of  ”everybody knows.” “Everybody knows that if you went to Hahvahd, like me ,you ah superior.” Of course the opposite is not true either. Just because someone went to an elite school doesn’t mean he or she is an elitist. Stick with the facts – don’t let where someone went (or didn’t go) to school impress you. Judge their arguments on the merits, and leave the populism and elitism to the slobs and the snobs.