Steven Pinker -- How the Mind Works - Hampshire High Italian ...

Thinking Machines 119You might think it is easy to put compositionality in a neural network:just turn on the units for "baby," "eats," and "slug." But if that was all thathappened in your mind, you would be in a fog as to whether the baby atethe slug, the slug ate the baby, or the baby and the slug ate. The conceptsmust be assigned to roles (what logicians call "arguments"): who is theeater, who is the eaten.Perhaps, then, one could dedicate a node to each combination o^tonceptsand roles. There would be a baby-eats-slug node and a^rfug-eatsbabynode. The brain contains a massive number of neuron^ one mightthink, so why not do it that way? One reason not to isihat there is massiveand then there is really massive. The number orcombinations growsexponentially with their allowable size, setting>erfr a combinatorial explosionwhose numbers surpass even our mo^generous guess of the brain'scapacity. According to legend, the vizjefaissa Ben Dahir claimed a humblereward from King Shirham^mdia for inventing the game of chess.All he asked for was a grajjyrjf wheat to be placed on the first square of achessboard, two graips^r wheat on the second, four on the third, and soon. Well before tirey reached the sixty-fourth square the king discoveredhe had unwittingly committed all the wheat in his kingdom. The rewardamounfea to four trillion bushels, the world's wheat production for twothotfsand years. Similarly, the combinatorics of thought can overwhelmthe number of neurons in the brain. A hundred million trillion sentencemeanings cannot be squeezed into a brain with a hundred billion neuronsif each meaning must have its own neuron.But even if they did fit, a complex thought is surely not stored whole,one thought per neuron. The clues come from the way our thoughts arerelated to one another. Imagine that each thought had its own unit. Therewould have to be separate units for the baby eating the slug, the slugeating the baby, the chicken eating the slug, the chicken eating the baby,the slug eating the chicken, the baby seeing the slug, the slug seeing thebaby, the chicken seeing the slug, and so on. Units have to be assigned toall of these thoughts and many more; any human being capable of thinkingthe thought that the baby saw the chicken is also capable of thinkingthe thought that the chicken saw the baby. But there is something suspiciousabout this inventory of thought-units; it is shot through with coincidences.Over and over again we have babies eating, slugs eating, babiesseeing, slugs seeing, and so on. The thoughts perfectly slot themselvesinto the rows, columns, layers, hyper-rows, hyper-columns, and hyperlayersof a vast matrix. But this striking pattern is baffling if thoughts are