Machine, a Heap of Gestures

While out hiking, you come across a strange installation by the side of the trail. A bag filled with black and white rocks, all of comparable size, lies near a sign. Beneath the sign, the ground is marked with a row of ten square boxes, each about thirty centimeters on a side. On each of the last three boxes, the ones furthest to the right, rests a black rock.

The sign lists a series of strange actions to be carried out. Intrigued, you decide to put them into practice:

1. Stand on the box furthest to the right. Go to instruction 2.

2. Examine the box you are standing on:

• If you see a black rock in the box, take it between your fingers, slip it into the bag, then immediately grab a white rock and set it down in the same box. Then move one box to the left, to carry out instruction 2 once again.
• If you see a white rock in the box, put it away in the bag, take a black rock out of it and place it in the same spot. You are done! Continue your hike, see you soon.
• If you see no rock in the box, draw a black rock from the bag and place it in that same box. Continue your hike, you are done.

Having carefully carried out each action, you contemplate the row: four rocks now follow one another. The three original black rocks have been replaced by white rocks, while at the left end a new black rock sits enthroned. You continue your hike, respecting the instructions to the very end.

The following year, on vacation in the same region, you pass by the same spot again. You had forgotten the strange installation, which is nonetheless still there. This time, there are five rocks on the boxes, at the right of the row. From left to right, there is: a black one, a white one, and then three more black ones. The instructions, still on the same sign, have not changed. The bag is still there, filled with black and white rocks. You repeat the experiment; the intrigue takes hold of you once more. You stand at the far right, respecting instruction 1. After replacing three black rocks with white rocks – according to the first case indicated by instruction 2 – as you move toward the left, you replace the white rock that was initially there with a black rock, as indicated by the second case contemplated by instruction 2. Having finished this last manipulation, the sign with the instructions invites you to continue your hike. You look, and you try to remember the final state of the arrangement: a black rock at the far left (the rock that was already there), followed by another black rock to its right, followed in turn by three other rocks, now white.

Intrigued, you do not continue your hike. You decide to do the exercise again, in the hope of understanding its meaning, of discovering the nature of this strange game.

This time, it is easier: starting at the far right, as instruction 1 indicates, you simply had to replace the last white rock with a black one, in accordance with the second case of instruction 2. Result: still five rocks; the first two remain black, followed by two white rocks, and a last rock at the far right, now black.

A little confused and frustrated, without having understood the meaning of the installation, you continue your hike. You may not come back to this trail next year.

Back from vacation, you tell a friend about the strange experience you have lived through again and again. Your friend is a computer scientist. You no longer remember the instructions, but you do recall the configurations of rocks you found and those you left behind. Your friend takes out a pen and grabs a napkin (you are in a restaurant, and computer scientists always carry a pen). If the black rocks are “ones” and the white ones “zeros” – as your friend explains – the very first time, you found 111, and left 1000 behind as you went away. On your second time along the trail, a year later, you had found 10111, and on finishing the instructions, you had left 11000. Then, on the third run, starting from 11000, you left 11001. You see it now: this is the binary system you learned at school, long ago. At your first encounter with the installation, you had found a seven and left an eight; the second time, you had found a twenty-three and left a twenty-four; then, starting from that twenty-four, you left a twenty-five. You have “lived” an algorithm that, for any given number, adds one unit to it. “Strange, isn’t it, how a computer works!” – your friend laughs. It makes you think of using an abacus…

But your felt sense of the experience is not exhausted: something else remains. These black and white rocks, a good ten centimeters or so in diameter, were not insignificant: handling them truly called upon your body. It also took you a certain amount of time to carry out these operations, even though this was the simplest algorithm there is. In reality, those that operate within a computer are infinitely more complex. You then have the impression of having felt the energy expenditure associated with the digital, which clashes with the apparent lightness you associate with this “cloud” technology.

“What would have happened if I had found ten black rocks, filling all the boxes?” – you ask your friend. He answers: “Overflow!” The memory’s capacity being exceeded, the program stops, the memory empties: it does not have an infinite capacity.

You had never seen a computer from this angle, with programs that are successions of gestures – taking, grasping, slipping, putting away, drawing, moving forward, moving back, placing –, affected by the resistance that the matter to be handled offers them, requiring an irreducible execution time…