If you put $••$ marbles with $•••$ marbles, you have $•••••$ marbles total.

There’s potential for foul play, of course. One of your marbles could roll away, and another could crack, and then you’d only have $•••$ marbles.

But there seems to be a general rule in there somewhere, a verity. Absent of foul play, $••$ with $•• •$ is $•••••$. This holds true whether $•$ stands in for marbles, or apples, or trees, or anything that acts like numbers.

This seems self evident. The proof is visual. You can test it out on your fingers. Your brain verified this truth without a second thought, because the brain has been utilizing this truth since the first time a parent had to figure out how to feed five children.

This truth seems so self evident that it hardly seems worth writing down. Why invent symbols like $2$, $3$, $+$, and $=$ to express something so trivial?

And yet, the fact that $•••••••••••••••$ marbles with $••••••••••••••••$ more is $••••••••••••••••••••••••••••••$ is a bit less trivially obvious.

If you run into more than $100$ marbles, you’d best start to know the rules.

This is how the rules of reality work. The fact that $2 + 3 = 5$ seems obvious, almost trivial. Perhaps not worth investigating. But once you’ve investigated the rules, you can figure out how many marbles you have if you start with $16347$ and acquire $2857$ more.

You can’t do that by appealing to your brain’s intuition. If you try to count them up yourself you’ll make a mistake or lose your place long before you reach the answer. If you gave such a problem to a pre-historic human, they’d tell you that generating an accurate answer is impossible.

And yet you can generate an accurate answer, every time. $16347 + 2857 = 19204$.

Learning the rules of things that act like numbers allows you to figure out things that are *far* outside your skill level. It doesn’t matter that you can’t count them out individually. It doesn’t matter that you’d lose your place before you got past the first thousand. Once you know the rules of addition, you can get the right answer *without even touching the marbles.*

A pre-historic human might think that such a skill is useless. Pre-historic humans never had $19204$ mouths to feed. But the ability to handle large numbers has allowed us to create warehouses and run economies. Our intuitions led us to the rules, and the rules themselves let us deduce things that are far outside our experience.

This is the driving force behind civilization.

This is what learning the rules of reality is all about. It’s about being able to answer questions that by all rights should be unanswerable.

We humans can look at a tiny, localized example and apply our intuition until we’ve learned the governing rules. Once we’ve learned those rules, we can look up to the heavens and deduce the true nature of the stars.