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There is a mathematics of similarities and directions that’s different from the mathematics of numbers.

“The idea is to go from numbers to information to understanding.”
– Hans Rosling, physician

I’m no mathematician and, chances are, you aren’t either.

Some conspiracy theories are more likely than others, and I think most have some truth. One of the least plausible conspiracy theories is that forces have conspired to make us mathematically stupid. Yet here we are: mathematically stupid.

Maybe it’s more about thinking and less about math. We are thinking-disabled, and there definitely is a conspiracy keeping us so. In that plan, math is hyper-logical thinking pressed on children to keep them from developing.

Mathematics has little to do with numbers. It has a lot to do with equations, but not the kind of equations you think. It’s not about establishing equality in formulas; it’s about establishing the equality of concepts. Numbers are just the nuts and bolts of mathematics. Nuts and bolts won’t make that happen if you can’t envision the relationships between things.

Numbers

“If you don’t know your numbers, you don’t know your business.”
– Marcus Lemonis, businessman, television personality and philanthropist

Numbers measure. If you want to make precise comparisons, you need to measure. You need to measure if you want to establish absolute equality. But if you’re more interested in similarity and growth, you don’t.

Math is taught as a machine for measuring. If ideas were architecture, then math is taught as the craft of driving nails. And for twelve years in school, children are drilled, over and over, on how to drive nails.

In the nineteenth century, children were taught to shovel coal. In the twentieth century, they were taught to add numbers. Now, in the early twenty-first century, school still teaches children how to drive ideas, not how to design them.

This form of teaching is increasingly irrelevant. As artificial intelligence makes clear, it’s no longer building machines that’s important, it’s designing them. Math will play a role, but at a higher level.

Ideas

If you’re going to think, then it’s imperative that you’re able to compare ideas. That’s because small differences can lead to big changes, and if your discernment is poor, and your awareness is dull, then you’ll be mixed up. There is definitely a conspiracy against thinking. We see this in every organization: the media, entertainment, work, law, advertising, and social trends.

Maybe our dominant political structures will continue to need non thinking workers. Outside-the-box thinking is discouraged in most animal colonies, and human colonies are rarely an exception. Religion is an example of constrained human thinking that’s for the betterment of all… except when it’s not. And the more we need non-thinkers, the more mathematics will continue to be mis-taught.

To be clear, mathematics is not taught badly, it’s taught wrongly. Students are intentionally misdirected. That’s the conspiracy part of it, but even if you don’t believe that, realize that what’s taught is wrong. Mathematics is not about numbers, it’s about ideas.

Metaphors

I’m a metaphorician, but since there’s no science of metaphor, there’s no such thing. There are similarities between ideas, and these similarities form bridges. The metaphorical connections between ideas are often paths to their extension. That’s because we invent all our ideas and they all come out of the same soup.

Mathematics offers many useful metaphors, but you wouldn’t know it if all you know about math is numbers and equations. I want to introduce some of these metaphors. This does not involve numbers. The equalities are metaphorical.

Math puts numbers to qualities, and refines qualities into categories like shape, texture, direction, progression, and destination. We can categorize shapes by the number of significant holes they have. We can describe textures by the size and shape of extensions. To compare directions, we must define a reference system. And to describe a destination, we need to say whether things will change on our way to it.

But to ascribe a quantity to something that does not have it, you need imagination. A metaphor will connect things that are otherwise dissimilar. We can say a car is like a submarine that travels through air, or that a towel is like a sheet covered with a forest of tiny fur trees.

Equality

Equality is the foundation of measure, judgment, and mathematics. Let there be hard and soft equalities and a range of in-betweens. Equality is just the counterpart of difference and, if you know the difference, then you can restate the equality.

We rarely see things as equals because we’re more attuned to differences. Our nervous systems are designed to notice differences and to amplify them. Most of what we perceive as large differences are small ones, but the closer things get to equal, the more we refine our sense of difference.

We set our expectations based on the largest differences we see. Maybe that’s why people find thriller and horror movies relaxing. By stretching our sense of difference, they make the differences of normal life demand less of our attention, and we relax.

Linear and Logarithmic Measures

While we mostly see in terms of lines—direct proportions, linear progressions, ratios, and changes in the same direction—we mostly perceive things in terms of logarithms. Logarithms measure changes in terms of powers of 10, not in terms of equal measure.

We cook using equal measures—liters, pounds, cups, and grams—but we see distances in terms of things that are 10, 100, and 1000 times farther away. We call it “perspective” but it’s really logarithmic. The same with illumination. What we perceive as being twice as bright really provides 10 times more surface radiance (or lux). What we see as four times as bright, radiates 100 times more light.

We might say, “At this rate, that will take forever.” And this is a perfect example of how much better our thinking would be if we were more adept at measuring things. Something that takes “forever” is more likely a progression in which each step takes longer to complete than the last.

We could say, “A solid relationship takes years to develop.” Or we could say, “A solid relationship takes a dozen steps where each step takes twice as long as the one before it.” The first description doesn’t tell us much and isn’t optimistic. The second description says much more about relationships and also reflects something about ourselves.

Progression: A Vector

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