Fuzzy Thinking

The mathematics under the appliances is older than the appliances. In 1965, an electrical engineer at Berkeley named Lotfi Zadeh published a paper on what he called fuzzy sets. Classical set theory asks a yes-or-no question: is this thing a member of the set, or not? Zadeh proposed sets with degrees of membership. A fifty-year-old is, say, 0.6 a member of the set "old" — not fully in, not fully out. Truth, on this view, comes in shades between zero and one, and most interesting statements about the world live somewhere in the middle.

Kosko presses this into a claim about reality itself. Consider a glass of water with a bacterium in it. Is the water clean? Half a bacterium? A thousand? Somewhere along that line "clean" stops being true, but there is no crisp point where it flips. The same holds for tall, bald, rich, dangerous — nearly every word we use to carve up experience. The sharp categories of ordinary logic are, he argues, an idealization we impose. The mist is the territory; the crisp line is the map we drew for convenience.

The bridge from philosophy to product runs through a technique with an ungainly name: the fuzzy approximation of a system. A fuzzy machine doesn't need equations describing how a helicopter flies or how cement cures. It needs rules of thumb, the kind an expert operator carries in their head. "If the load is heavy and very dirty, run a long cycle." "If the train is close to the platform and moving fast, brake hard." A handful of such rules, each covering a fuzzy patch of possibilities, can be stitched together to control something genuinely complicated.

The mechanism has three moves. First, fuzzification: the machine reads a sensor — water is 40 percent murky — and translates that number into fuzzy words. Then it fires its rules, all of them at once, each contributing its bit of advice weighted by how well the situation matches it. Finally, defuzzification: it blends the competing recommendations back into a single crisp action, a specific cycle length or brake pressure. Kosko shows that with enough rules a fuzzy system can approximate any smooth behavior at all — a result he treats as the engineering heart of the book.

Having sold the machines, Kosko turns to the argument he most wants to win, and it is a quarrel with two and a half millennia of Western thinking. The habit of splitting everything into A and not-A has a name and a father: Aristotle, and his law of the excluded middle. A thing either is or is not; there is no third option. That law became load-bearing for logic, mathematics, science, and eventually the digital computer, which is nothing but a vast machine of ones and zeros, true and false, all the way down.

Kosko's provocation is that this inheritance, for all it built, quietly filtered out most of reality. The world it describes well is the world of counting and of ideal geometry — the places where things really are discrete. But rooms, faces, risks, opinions and emotions don't come in ones and zeros, and forcing them into that mold means throwing away information at the very first step. He sees a cultural fork here: where Western engineering clung to the crisp and treated the fuzzy as sloppy, Japanese firms, less bound to the Aristotelian reflex, were willing to build in the gray — and shipped the smarter products because of it.

The washing machine that opened the book turns out to have been the small, deliberate face of a large claim. Sasaki's appliance washed better not because it computed harder but because it was permitted to hesitate — to judge a load "fairly dirty" and act accordingly. Multiply that permission across cameras, cars, brakes and grids, and you get Kosko's promised flood of smarter machines: devices that stopped rounding the world to true or false and started reasoning in the shades where the world actually lives.