Digital Logic and Metaphysics
Throughout the past two weeks' classes, we have discussed computers' fundamental architecture, and how we might think of such low-level computation through a metaphysical lens. Below are circuit diagrams for a 2-Bit Adder and a 2-Bit Subtractor, both of which are simple logical circuits fundamental to digital computation. I'll then share my thoughts on low-level computation as it relates to metaphysics, and consider how we might think about computers through a metaphysical lens.
2-Bit Adder
- Input: 4 bits.
- X1: The '1s place' bit of our 2-digit binary number X.
- X2: The '2s place' bit of our 2-digit binary number X.
- Y1: The '1s place' bit of our 2-digit binary number Y.
- Y2: The '2s place' bit of our 2-digit binary number Y.
- Half Adder: Takes 2 input bits A, B. Outputs the sum and carry of X+Y.
- Full Adder: Takes 3 input bits A, B, C. Outputs the sum and carry of X+Y+C.
- Output: 3 bits, together representing the 3-digit sum of X+Y.
Thus, the Half Adder calculates the first bit of the output and a carry. That carry, as well as the 2s places of X & Y, are sent to the Full Adder, which then calculates bits two and three.
2-Bit Subtractor
This layout also functions near-identically to the 2-Bit Adder, with 'borrow' bits instead of carry bits.
Additionally, there are only 2 output bits; the borrow bit leading out from the Full Subtractor goes unused. This is because that borrow bit would only be activated if the 'Y' input was greater than the 'X' input, a scenario which this 2-bit subtractor does not account for. (It operates under the assumption that X > Y).
Metaphysics
In class, we discussed what one might consider a computer, (or what one might
consider not to be a computer).
A question that particularly highlighted this dilemma was the following: "is a
computer that is turned off still a computer?
What about a computer that is broken?"
The immediate issue is this: we are already presuming that the "not-computer" we're
talking about
is, at least in some regard, a computer; (the question refers to this not-computer
as a computer).
In class, we reached the conclusion that there must be two definitions of a
computer, (or perhaps more):
a colloquial definition of a computer, and a strict, mathematical definition of a
computer.
Perhaps, from the mathematical angle, a broken computer is not a computer.
But if I were to say
"I'm getting my computer fixed over the weekend," you wouldn't be confused by the
notion
of a "broken computer."
This distinction resolves the issues proposed by the readings. Is a computer made of
crabs a computer?
What about a set of ropes and pullies? What if a slime mold was involved? All of
these examples certainly
have 'computery' properties, but fail to live up to the prototypical definition that
we live by in the day-to-day.
Perhaps even the simple circuits shown above are, in a sense, 'computers.' But they
are
most certainly not 'computer computers;' they are not what most people think
of as
computers.
An ancient rope-and-pulley computer is unearthed in the jungle of apraphul. (1995). Humour the Computer. https://doi.org/10.7551/mitpress/3615.003.0054
Gunji, Y.-P., Nishiyama, Y., Adamatzky, A., Simos, T. E., Psihoyios, G., Tsitouras, Ch., & Anastassi, Z. (2011). Robust soldier Crab Ball Gate. AIP Conference Proceedings, 995–998. https://doi.org/10.1063/1.3637777
Lu, J., & Lopes, P. (2022). Integrating living organisms in devices to implement care-based interactions. Proceedings of the 35th Annual ACM Symposium on User Interface Software and Technology, 1–13. https://doi.org/10.1145/3526113.3545629