What is more fundamental than a bit? The short answer is that I cannot think of a more fundamental notion than the notion of a bit (i.e., a binary attribute). Both philosophically and psychologically the notion of a binary attribute (e.g., exists or not, true or false, here or there, now or later, important or not, etc) seems to precede any thought or discussion.
Still, I recall a brief exchange with a physicist who was sitting next to me listening to a panel discussion on Theoretical Computer Science and Physics (which took place in the early 1990s): They [the TCS guys] talk as if a bit is as fundamental as an electron - he told me with amazement. That's of course wrong, a bit is far more fundamental - I answered to his even greater amazement. Needless to say, he did not talk to me during the rest of the panel...
An electron is merely a specific model of a specific phenomena. It is a very important model, but how can you compare its importance to the importance of the notion of a model? But, then, all models are built of binary attributes.
This reminds me of a drive from MIT to Providence that Shafi and me made in the mid-1980's. We stopped in a diner on the way, got some food and coffee, and then Shafi asked the attendant Do you have the notion of a refill? The answer was: Yes, we do have refills, but what is a notion?
Indeed, people may use notions without having a notion of a notion, and likewise they may think of bits without a clear conceptualizing of the pure notion of a bit. In both cases, these notions exist before we conceptualize them; these notions are preconditions to any conceptualization.
Admittingly, bits are not what computer science is about. Bits are static objects, whereas computer science is about processes in which the values of bits are changed. But, again, the notion of a process is quite a fundamental one; it is linked to the notion of change, and more accurately to the notion of a rational change - that is, a change that can be conceptualized as evolving gradually via a sequence of applications of simple rules. Here we can stop: We just reached the notion of computation.
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