I Am a Strange Loop

What I just told is the story at a gross (thermodynamic) level. Nobody who designs combustion engines worries about the fine-grained level — that of molecules. No engineer tries to figure out the exact trajectories of 1023 molecules banging into each other! The locations and velocities of individual molecules are simply irrelevant. All that matters is that they can be counted on to collectively push the piston out. Indeed, it doesn’t matter whether they are molecules of type X or type Y or type Z — pressure is pressure, and that’s all that matters. The explosion — a high-level event — will do its job in heating the gas, and the gas will do its job in pushing the piston. This high-level description of what happens is the only level of description that is relevant, because all the microdetails could be changed and exactly the same thing (at least from the human engineer’s point of view) would still happen.

The Strange Irrelevance of Lower Levels

This idea — that the bottom level, though 100 percent responsible for what is happening, is nonetheless irrelevant to what happens — sounds almost paradoxical, and yet it is an everyday truism. Since I want this to be crystal-clear, let me illustrate it with one more example.

Consider the day when, at age eight, I first heard the fourth étude of Chopin’s Opus 25 on my parents’ record player, and instantly fell in love with it. Now suppose that my mother had placed the needle in the groove a millisecond later. One thing for sure is that all the molecules in the room would have moved completely differently. If you had been one of those molecules, you would have had a wildly different life story. Thanks to that millisecond delay, you would have careened and bashed into completely different molecules in utterly different places, spun off in totally different directions, and on and on, ad infinitum. No matter which molecule you were in the room, your life story would have turned out unimaginably different. But would any of that have made an iota of difference to the life story of the kid listening to the music? No — not the teensiest, tiniest iota of difference. All that would have mattered was that Opus 25, number 4 got transmitted faithfully through the air, and that would most surely have happened. My life story would not have been changed in any way, shape, or form if my mother had put the needle down in the groove a millisecond earlier or later. Or a second earlier or later.

Although the air molecules were crucial mediating agents for a series of high-level events involving a certain kid and a certain piece of music, their precise behavior was not crucial. Indeed, saying it was “not crucial” is a ridiculous understatement. Those air molecules could have done exactly the same kid–music job in an astronomical number of different but humanly indistinguishable fashions. The lower-level laws of their collisions played a role only in that they gave rise to predictable high-level events (propagation of the notes in the Chopin étude to little Douggie’s ear). But the positions, speeds, directions, even the chemical identity of the molecules — all of this was changeable, and the high-level events would have been the same. It would have been the same music to my ears. One can even imagine that the microscopic laws of physics could have been different — what matters is not the detailed laws but merely the fact that they reliably give rise to stable statistical consequences.

Flip a quarter a million times and you’ll very reliably get within one percent of 500,000 heads. Flip a penny the same number of times, and the same statement holds. Use a different coin on every flip — dimes, quarters, new pennies, old pennies, buffalo nickels, silver dollars, you name it — and still you’ll get the same result. Shave your penny so that its outline is hexagonal instead of circular — no difference. Replace the hexagonal outline by an elephant shape. Dip the penny in apple butter before each flip. Bat the penny high into the air with a baseball bat instead of tossing it up. Flip the penny in helium gas instead of air. Do the experiment on Mars instead of Earth. These and countless other variations on the theme will not have any effect on the fact that out of a million tosses, within one percent of 500,000 will wind up heads. That high-level statistical outcome is robust and invariant against the details of the substrate and the microscopic laws governing the flips and bounces; the high-level outcome is insulated and sealed off from the microscopic level. It is a fact in its own right, at its own level.