> This is a strange claim since the entire field was founded upon the investigation of potentially (and often actually) infinite computations.
To me, that is not that surprising, although it's a good point.
My view has to do with history of mathematics. People were fascinated with infinities long time before they considered that large but finite systems can be also interesting. I think applications of mathematics, mainly geometry and physics, are responsible too.
The development of more finitist taste in problems (somebody else mentioned the constructivism, which I think is fitting) came with the practical need to do computations and developing algorithms.
So I am not that surprised that one of the early forays into theory of computation are through the lens of infinite, rather than finite.
> Most importantly though, my problem with this kind of discussion is that the question itself is meaningless.
Of course, I forewarned that it's just my view, and you're free to ignore it.
Look, partly why I mention it, it seems rather surprising to me; I would consider infinite structures to be more complicated, in some sense; yet, in the history of mathematics (which lately includes CS, as a study of large but finite), these were studied first. There was nothing that would prevent Ancient Greeks (or Euler) from discovering, say, lambda calculus, or how to do sorting efficiently. Although, it seems in many fields we progress from more complicated to simpler methods, in some way. But I think it's partly precise because the finite is often considered uninteresting by mathematicians, it was overlooked. And that's the philosophical point I am trying to emphasize. Different fields of math perceive (in the way they treat them) the same structures differently, and I gave an example of natural numbers. Another example is the notion of the set cardinality, in most areas of mathematics people only care about countable/uncountable distinction.
To me, that is not that surprising, although it's a good point.
My view has to do with history of mathematics. People were fascinated with infinities long time before they considered that large but finite systems can be also interesting. I think applications of mathematics, mainly geometry and physics, are responsible too.
The development of more finitist taste in problems (somebody else mentioned the constructivism, which I think is fitting) came with the practical need to do computations and developing algorithms.
So I am not that surprised that one of the early forays into theory of computation are through the lens of infinite, rather than finite.
> Most importantly though, my problem with this kind of discussion is that the question itself is meaningless.
Of course, I forewarned that it's just my view, and you're free to ignore it.
Look, partly why I mention it, it seems rather surprising to me; I would consider infinite structures to be more complicated, in some sense; yet, in the history of mathematics (which lately includes CS, as a study of large but finite), these were studied first. There was nothing that would prevent Ancient Greeks (or Euler) from discovering, say, lambda calculus, or how to do sorting efficiently. Although, it seems in many fields we progress from more complicated to simpler methods, in some way. But I think it's partly precise because the finite is often considered uninteresting by mathematicians, it was overlooked. And that's the philosophical point I am trying to emphasize. Different fields of math perceive (in the way they treat them) the same structures differently, and I gave an example of natural numbers. Another example is the notion of the set cardinality, in most areas of mathematics people only care about countable/uncountable distinction.