Joon Yun explains how human brains use a compressive scale to process numbers, giving high detail to small quantities and low detail to large ones. This matches how Sumerian and Aboriginal cultures counted, and why we misjudge big numbers. Teaching linear math instead creates bad decisions.
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So the math that we all use was invented in several civilizations, independent of each other. And I think it emerged because linear math became necessary as a function of transactions. We'll go over that in a second. So the Sumerian math, the Mesopotamian math, the Chinese math, all have linear basis. Mm-hmm. And that's what we're taught in school. And the linear mathematicians will tell you that the difference between the number 10 and 1 is identical to the difference between the numbers 100 and 91, right? They say it's 9. Well, let me tell you how nature would look at this. Here's the difference between 10 pebbles and 1 pebble. And does that look the same to you as the difference between 100 pebbles and 91 pebbles? No. No. No. So in this case, it's actually the ratio that matters. So in linear math, we're taught these are identical. In natural math, we realize these are completely different things. In fact, if you were to take away numbers and just place, let's say, chips, here's how a modern student would place the chips on a scale of 1 to 100. They would place it this way. Right? There's 1 in 10. That's 91 in 100. This is the linear scale, right? Well, it turns out, if you go to people that are untrained in modern math, this is how they would space quantities. So this next data was taken from Aborigines. This is how they space quantities. Remember, they have no math system. It just— this is how, when you ask them to space pebbles on a 0 to 1 or 1 to 100 scale, here's how they do it. In fact, this is also how American children do it before they enter preschool. So we're all wired to be able to do this. Let's just call it compound thinking, for the lack of a better word. And then we're trained into linear math. So think about the scale I just showed you. The best way to describe what we just saw is a compressive scale. Our minds were wired to think in a compressive scale. What I mean by compressive scale is there's high resolution at low numbers, right? You can see bigger spaces, and low resolution at high numbers. Why in the world would our brains be wired— To see the details. In this way? Why high resolution? Why can we discriminate between low numbers and we can't discriminate between high numbers in the natural world? Well, the first reason is because it's relevant. Low numbers connote scarcity, and it makes a huge difference whether you can tell there's 3 bananas or 2 bananas when you're making your choices, right? It makes no difference if you can discriminate difference between high numbers. 100 bananas versus 91, who cares? It's not relevant, right? So nature has wired in this ability to discriminate at low resolution and low numbers and have no resolution at high numbers. The second reason is Pareto's Law. Have you guys heard of Pareto's Law? The vast majority of things in nature happen infrequently. So most things happen at very low numbers. Very few things occur at high numbers. The third reason is— the third reason for the compressive scale is that you can compact a lot of information in a small amount of space. So the way our senses work, our hearing, our vision, everything works on a compressive scale. Kind of like the Richter scale, you can pack a lot of information on the Richter scale, whereas if you had to depict seismographic information in a linear scale, it would go from here to the moon, right? So that's the third beauty of a compressive scale. It's highly efficient in terms of storing and processing and displaying information. So I was driving home one day, and I realized, wow, even lampposts, when you really think about it, is a compressive scale. And this is nothing more than— Trees. What we used to see in nature? Trees. So when a lion is between the 2nd and 3rd tree, that's really relevant, right? It's about to get you. When the lion is between the 100th tree and the 101st, who cares? It's far away. So nature has wired in this capacity to do compressive scale thinking. And yet, because of the linear math we're taught, sometimes it could actually cause a lot of confusion. We can make the wrong decisions.
