|August Kekulé chemistry
One atom of carbon usually bonds to four hydrogen atoms, but benzene has only one hydrogen for each of its six carbons. The remaining bonds must be consumed in its structure; otherwise, benzene would stick to everything, or fall apart, which is not its observable behavior. The six carbons use their three remaining bonds to hold on to each other, but the arrangement was unknown, until it came in a daydream to August Kekulé, of a snake forming a circle by biting its own tail, which is strange because a snake has only its mouth for grasping. I’d rather the dream were of a monkey grabbing with both hands and feet. It may be difficult to distinguish the dream from the waking interpretation. Put six carbons in a ring, join them hand to hand, and let each grab the hand of a hydrogen. This still leaves one hand per carbon. Given a circular symmetry, various cross bonds had been proposed, but Kekulé realized alternating carbon-to-carbon bonds were doubled. The carbons grasp two hands on one side only.
Discovery and proof
Discovery and proof follow independent paths in the mind. Mathematicians leap to conjectures that may take years to reach by means of proof. No one can say why the idea pops into the mind of one and not another, except that one must ponder the problem. There are methods, but none are sufficient. Some say genius is dreaming, but a dream is effortless and unconvincing, whereas the opposite is true of the tedious and pedantic.
I learned to unlock and lock the Chinese ring puzzles my uncle bought for me in San Francisco Chinatown. Then I started linking triangular with circular, and large with small, until every pair was linked with all the other pairs to the extent that every ring fit in all the others in a single mass of snakes writhing in a perpetual metal orgy.