No unthinkables (I think)

A fashionable sound, made by some: “Why yes, science explains a lot, but some day we might run into things the human mind simply cannot comprehend. Things too complex, too alien, for our puny minds to process. We’ll be up the creek with no paddle then, no mistake.”

There’s nothing wrong with saying that as “might”; but for some reason I don’t think that’s a particularly likely may-be.

For a part this is because I study mathematics. Mathematics is, to be blunt about it, mad insane complicated stuff. The way mathematics is written is outright inhuman. This is unavoidable. Have you ever seen a Greek mathematics text, or one from old Babylon or Egypt? I have glimpsed a few, and they are enough to give anyone seizures. The reason: the old ones wrote things out in human terms: “Five is an odd number. Let us add the square of the first number to it, and divide the sum by four. The resulting number is divisible by four.”

That kind of writing becomes a near-meaningless torrent of tepid jabbering with a longer calculation. Modern mathematics done that way would kill a million trees, and then the poor sods that chose to learn things written that ungainly, slow, too human way. A modern mathematician would never write anything like that; no, she would write 4 \mid (5+a^2)/4 and be done with it.

Likewise, mathematicians do not write out their jabberings; they define new terms to stand for longer strings (“We say an integer in odd if it is not divisible by two”), often “forget” the original details and use their new terms as if they were the most basic ones they had, and build even more complex abstractions from the initial ones (“We say an integer n is outright peculiar if it is odd and $n/2$ is odd”). Best of all, mathematicians do not deal with single cases (“Let’s look at the number five”); they try to speak as generally as they can (“Let n be an odd integer”). This means that when a mathematician speaks, she as often as not speaks of literally endless multitudes, giving by a limited exhibition truths about logical worlds without end.

Mathematics is the art of finding medium-difficult ways to talk about extra-difficult things. Science is the same. It has to be, because we human beings are basically nose-picking grub eaters, evolved creatures without any special means except our wits. We’re bad with the extremes of time, space, energy, and the like; anything that’s not like our ancestral savanna tends to be something that trips us unless we are extra careful. And that’s why we don’t determine the intelligence of people by asking them outright how smart they feel; in the words of St. Gregory of the Knife, everybody lies.

Our lies and fumbles are built in, all the way from the Dunning-Kruger effect to how we tend to see faces wherever we can, and faces of gods if we believe in them. Much of science is mechanisms to counter this, to keep us from believing what ain’t true but seems so to us dullards. We’re old friends with trying our damnedest to think the hard-to-think and the supposedly unthinkable. (Oh, and don’t mention probability. I suspect orang-outans are better with probability than we, because surely they can’t be any worse.)

Though I admit I am no perfect mind, just a semi-orang-outan, and furthermore one officially unschooled in serious scientific thought, I personally think it’s unlikely our descendants will ever run into anything that is too difficult to grasp. It might be something that needs to be divided into many chunks — the times of one mind grasping all human discoveries is past, which is both happy and sad — and it might need a lot of time to develop the necessary layers of abstraction and analysis, not to mention the statistically rare insights — but I don’t really believe in unthinkable things, though they are possible. And if we humans don’t succeed, we may eventually give birth to machines and hybrids that are better thinkers than we evolution escapees.

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