Take the PAIN out of math part 2

Counting, really? Doesnt everybody know all about counting?

Aaron Horak


No, there’s actually a lot to learn here.

As I said in part 1, I will be keeping in mind the question “do we need math”?

I am going to start with a very basic approach here, but bear with me, it will get interesting. There are no shortcuts on the path to mastering mathematics.

So… what is counting? I mean, you can point to a dozen eggs and say, “one, two, three… twelve” but how is that different than pointing to them and saying “A, B, C… L”? Or is there a real difference? Think about that a second.

Math is many things, it’s a science, an art, a language, a journey, a destination. It helps us think, decide, and pursue truth. Counting, the most basic form of math, is a language. It uses words and symbols to describe reality.

Let’s say you have a number of sheep in your pasture. There are wild animals in your area, so each evening, when you bring them into their pen, you have your daughter make a mark on the ground each time one enters the pen. ||||| ||||| |||

Then you compare those marks to permanent marks you made on a board months ago. If they match, all the sheep are safely home.

What actually happened here, is that your daughter counted the sheep, and you counted her marks! Seems pretty primitive, but really, you don’t need any more than that to count thirteen sheep.

In modern terms, we would say that her marks are in a one-to-one correspondence with the sheep. Each sheep has one mark, each mark has one sheep. One to one. Your marks are in one-to-one correspondence with her marks and, by transitivity, with the sheep. This is primitive counting.

When it comes to counting

Its plain to see

You don’t always need 1, 2, or 3

Okay then, why do we need anything beyond marks in the dirt and on a board? Well, what if you had 649 sheep? That’s an awful lot of marks! (And a lot of sheep😁) Also, being able to represent numbers with symbols allows us to decide how many sheep we have left if we sell 57 sheep, and then buy 14 more.

So yes, at least being able to count and represent numbers with symbols would seem to be math that we need! In fact, we need it so much, that people all over the world came up with various…



Aaron Horak

Hello! I have many interests, including science fiction, real science, writing, and math. I hope to contribute much here. I have a BS and MS in mathematics.