The Beauty of Dependability

why the 2 + 2 = 5 brigade still enrages me

My Forest Green Hoodie

Forest green and purple are my favorite colors. I own a forest green hoodie that says 2 + 2 = 4. I got a dirty look from someone in line at the post office earlier today—a look that suggested to me she knew damn well why I was wearing it, and the story behind it. Perhaps I was projecting, but I don’t think so. This is a cobalt blue area, where many people still stay home as much as possible, in terror of catching COVID, so many people around here are very, very online.

Many of you will remember that during the summer of 2020, several arenas of media, particularly Twitter, were overtaken by 2 + 2 = 5 discourse. I’m still angry about that. Before I go into how the Woke brigade that perpetrated that lie was doing something far more evil than it may seem, I want to share with you why, in my view, mathematics is so important to our humanity.

Yes, it’s how the bridges don’t collapse and the computers compute, and is crucial for so much else that we rely on. But that’s why it’s important for our lives, not why it’s important for our humanity.

Mathematics is the root of how we understand symmetry, and therefore beauty. It is also far more accessible than most people think. Let me show you what I mean.

Prime, Indeed

Prime numbers are very special. They are numbers that can only be evenly divided by 1 and themselves. 10 can be evenly divided by 1, 2, 5, or 10 and is therefore not prime; 5 is only divisible by 1 and 5, and is prime. Here are the prime numbers under 100, on a colorful chart:

The study of prime numbers is ancient and glorious. Euclid proved that there are infinite prime numbers about 300 years BC. They fascinate nerds of all stripes, even today, and there are many subsets of primes. Sexy primes are primes separated by 6 (like 41 and 47, or 53 and 59). Cousin primes are primes separated by 4 (like 19 and 23, or 67 and 71).

There is one, and only one, prime with two cousins: 7.

Yes, only one. I am 100% sure. I can say this with total certitude, betting anything you can name on it — everything I own, both kidneys, the lives of all the people I love most.

How can I know?

Any prime with two cousins would mean this scenario is true: three numbers in a sequence where the middle number (let’s call it p) is prime, p-4 is prime, and p+4 is prime.

You can see that this is true for 7. 7 is prime, 7-4 is prime, and 7+4 is prime. Our sequence is: 3, 7, 11.

To make our example simpler to follow, let’s focus on the first number. We would need to find three numbers where the first number (let’s call it n) is prime, n+4 is prime, and n+8 is prime.

As you can see, this fits with our 3, 7, 11 example. n=3. 3 is prime, and n+4 is prime, and n+8 is prime. 3, 7, 11.

Here is a fact about ALL numbers. In EVERY case, a number is either: evenly divisible by 3 (like 3, 9, 15, etc.); divisible by 3 with a remainder of 2 (like 8, 17, or 35); or divisible by 3 with a remainder of 1 (like 10, 19, or 28). There are no other possibilities.

Let’s return to our n, n+4, n+8 and see if it’s possible for them to all be prime if they are anything other than 3, 7, 11.

If n is not 3 and it is prime, then it is only divisible by 1 or itself. Therefore, since it is not 3 in our hypothetical, it MUST have a remainder of 1 or 2.

If n has a remainder of 1, then n+8 cannot be prime, because n+8 would be divisible by 3. 1 + 8 = 9 and 9 is divisible by 3.

If n has a remainder of 2, then n+4 cannot be prime, because n+4 would be divisible by 3. 2 + 4 = 6 and 6 is divisible by 3.

Thus there is one, and only one, situation where n, n+4, and n+8 are all prime, and that is 3, 7, and 11. 100% of the time, any other attempt to find two cousin primes will fail, because at least one number in any sequence of n, n+4, and n+8 will be divisible by 3. Thus the only one that works for all of them to be prime is the one that includes 3.

By the way, all you people who think you “just can’t understand” mathematics?

You just understood a number theory proof. Number theory is something I took for the first time as a senior mathematics major in university.

See? I told you it was more accessible than you think!

The Foundation of Reality

Where else in life can you be absolutely certain of anything? What else is so dependable? What else requires no faith or trust or hope, just the beauty of pure logic? What else is never going to change?

What the Woke Brigade Tried to Do

James Lindsay has a really excellent recounting and analysis of the story of how the Woke brigade tried to muddy these waters, so I won’t rehash it here. Suffice it to say: there are now many academics, particularly teachers, who are proudly telling their students that 2 + 2 is sometimes 5, just to “own the cons.” They are lying, and lying in a way most evil and egregious. They are taking the certainty and dependability of reality itself away from kids by teaching them that mathematics is just like anything else: it depends on how you look at it; it changes with the wind; it’s culturally and context-dependent; blah, blah blah.

In so doing, they are truly hurting underprivileged and marginalized communities the most. The Woke recite this bromide about everything under the sun (“….of course, this affects Black and Brown bodies disproportionately…”) and it’s rarely true. This time, it is. Kids who grow up poor or marginalized, as I did (and yes, non-white kids do fall into that category disproportionately) need to know the power of mathematics. Mathematical excellence is a game-changer for employment, for opening other doors, for understanding the world.

Just as importantly, it is a game-changer for personal development and happiness. Getting good at math requires patience, persistence, work ethic, logic, and many other qualities that cross-pollinate into all areas of life.

Understanding mathematics is understanding the structure of reality.

Undermining the ability of children to trust that structure is egregiously unethical, a sickness that rises to the level of evil.

2 + 2 = 4, not 5. Some of us will die on this hill. And the scowling lady at the post office is just going to have to be okay with that.

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