Originally featured this fascinating article was first published on Quanta Magazine.
In the movie Oppenheimer, Niels Bohr challenges the physicist early in his career:
Bohr: Algebra is like sheet music. The important thing isn’t “can you read music?” It’s “can you hear it?” Can you hear the music, Robert?
Oppenheimer: Yes, I can.
I may not hear the algebra, but I sense the machine.
Even before I laid hands on my first computer, a Radio Shack TRS-80 in the 1970s, I could almost envision its operations. I would write basic programs on paper, feeling the machine I was yet to possess processing each step. When I finally key in the program, I almost missed not being able to witness the internal processes.
Even today, I do not visualize or hear the machine, yet it sings to me; I sense it humming along, updating variables, looping, branching, searching, until it reaches its destination, providing an answer. To me, a program is not static code; it embodies a lively creature following my directions to a (hopefully) successful conclusion. Although I am aware that computers don’t physically function this way, my metaphorical machine continues.
Once you delve into the realm of computation, you begin to perceive its presence everywhere. For instance, sending a letter via the postal service. By placing an addressed and stamped envelope in a mailbox, it somehow reaches the recipient’s mailbox. This process is computational—a chain of operations moving the letter from one point to another until it reaches its final stop. This routing system resembles what occurs with electronic mail or any data transmitted via the internet. Viewing the world through this lens might appear strange, but as Friedrich Nietzsche is quoted to have said, “Those who were seen dancing were thought to be insane by those who could not hear the music.”
This inherent sense of a functioning machine can introduce a computational perspective to virtually any phenomenon, even the seemingly enigmatic concept of randomness. A seemingly random event, like a coin toss, can be completely defined by a sophisticated computational process yielding an unpredictable outcome of heads or tails. This outcome is influenced by multiple variables: the force, angle, and height of the flip; the weight, diameter, thickness, and mass distribution of the coin; air resistance; gravity; the surface hardness on which it lands; and more. This applies to shuffling cards, rolling dice, spinning a roulette wheel, or generating “random” numbers on a computer—each involves executing a deliberately complex function. None of these processes are truly random.
This concept traces back centuries. In 1814, in his Philosophical Essay on Probabilities, Pierre-Simon Laplace originally discussed an intellect, now recognized as Laplace’s demon, capable of foreseeing these outcomes: