There are a lot of people in the world. About is 7.036 billion, actually [USCB]. If we assume we can get to know someone in a cursory 30 second chat, assuming we all spoke the same language, it would take about 6700 years for everyone to meet and greet everyone else even if we assume rigid 30 second time periods, no time for sleep, no eating or drinking (or at least none that interferes with talking) and instant switching from one partner to the next.

Even if we allowed for a mere 3 seconds for changeover between each conversation, that would still tack on another 660 years. Giving everyone eight hours of sleep would tack on another 2300 years or so. Giving everyone an hour time to bathe, brush their teeth, and so forth is good for another 290 or so. Grand total: 9950 years–and that’s still assuming that say, robots are doing all the labor to sustain our industries, agriculture, and the giant conveyor belt never, ever breaks down and always functions perfectly.

The result is that, if humans lived for ten thousand years, and everyone did nothing but meet other people, we would still spend 99.995% of our lifetimes meeting other people. This also assumes, of course, that the birthrate is zero. But let’s divide it instead by the average human lifespan of 69.6 years [World Bank]. The result is about 143–yes, that means that if you had 143 average human lifetimes, you might be able to have a single, thirty-second conversation with every person *currently* alive on the planet as of this instant.

Obviously, then, anyone proposing a system by which we base our actions exclusively on personal relationships would be laughed out of town by anyone who had thought about it for longer than about five minutes. Some kind of compromise has to be made, and our rather curious brains, having evolved as they did to help us maintain relationships among comparatively small social groups of primates, provide us with a surprisingly functional but somewhat problematic solution.

Stereotyping: This brilliant shortcut lets us establish correlative relationships between superficially similar things, which has obvious benefits. If you see someone eat a brightly colored frog and die, you are more than likely going to benefit from avoiding the consumption of the whole category of brightly colored frogs. If say, you are living in a tribe among others and the possibility of violent conflict exists, you are more likely than not to benefit from associating their phenotypical features, clothing, language, and mannerisms with danger or at least the unknown of which you should be wary. So on, and so forth.

Where we start to get into trouble is that while these correspondences are easy to establish, they are difficult to break without a great deal of effort. The mechanisms themselves are quite intricate, and as a I am no neuroscientist I will not attempt to explain them, but the upshot is that what is in actuality a useful approximation can be unintentionally conflated with a bit of guaranteed predictive information. This actually would not even be a problem if a “stereotype” was established with an arbitrary but large degree of precision and applied only with respect to things that met the specific definitions, but that would be antithetical to the purpose of our rather fuzzy system of categorizations.

They are of value specifically because they allow us to benefit from prior knowledge even when dealing with novel situations. Learning by analogy might be the best use we have for these ‘fuzzy’ correspondences. Math, science, and art all rely on establishing correspondences to our previous experience and constructing mental tools of ever-increasing complexity.

A very young child can be said to be starting on mathematics when they establish the line of demarcation between a single discrete object and a group of them. The child continues by learning the words that correspond to specific discrete quantities and learns to place them in order, learning to count from one to two, two to three, and so on. From there it’s a hop, skip, and jump to addition. Subtraction is only addition in reverse, multiplication only addition of group quantities. When we divide, we are splitting a quantity into groups and the problem can be framed as a ratio with fractions. All math problems inherently possess at least one variable, and algebra is just learning to break up a single problem into smaller discrete parts and manipulate those parts. Once we have that, we can look at the relationships between real world shapes and equations with geometry.

When we look closely at a story, the fuzzy correspondences are being made use of any time something happens in the text that we have not personally experienced. When Cervantes’ Don Quixote charges the giants, explosions of neurochemicals construct the notional realities of the errant knight’s tale–he is able to charge the great four-armed beasts never seen on Earth because we have had the experience both of seeing something and having been mistaken and having felt something we wanted to be true even if cold reality stonily folded its arms. We are Sancho Panza, observing Quixote with bemused, if phlegmatic, marvel. We have never been in these situations, but nevertheless a string of correlations forms the connective tissue that allows us to use language to grasp something of value and meaning from the story.

I submit, therefore, that the problem with stereotypes is only that they underlie so much of our accomplishment both as individuals and as a species, that we forget sometimes to confine them to their proper category–probabilistic approximations  useful only in providing a general estimate that allows us to act without freezing, but that can and very often are imprecise, inaccurate, or even outright mistaken. If we remain willing to juggle people between our categories, shift those categories around, re-write their boundaries, or even dispose of them entirely if we find too much evidence against them–we will not go too far afield to treat our fellow humans decently even if we do not know them personally.