I recall a story about a philosopher who proposed an idea that everything is essentially perpetually divisible. That is to say, you can divide a whole into two halves and for each half (regarded as new wholes), divide into two more halves ad infinitum.
The analogy used was a cake or bread or some food or other quantifiable object to be split into equal parts.
I think the lesson, or the question, or the hypothesis of the thought experiment was basically that everything is composed of smaller components and there was no lower limit; no matter how small the pieces get, You can't divide to zero. With a fine enough instrument, you can keep going and going, and never reach a certain point where matter just vanishes. It perhaps presents some interesting implications regarding concepts like atomism and relativity.
It was supposedly from before the advent of modern microscopy and particle physics. I thought it was attributed to either Socrates, Plato, or Aristotle, but I can't find any evidence of it and the key words are a bit vague to build a strong search query. I keep coming up with unrelated information on things like Socrates' Analogy of the Divided Line (as told by Plato) and Aristotles Categories, Division of Science, Division of the Soul, etc.
My question is: Does anybody recognize who or what I'm talking about? What is this story (theory/idea/whatever) known as? And who is it attributed to?