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?

  • Wasn't sure what would make a suitable name for this question. Feel free to rename it if you have something appropriate. Thanks
    – voices
    Mar 29, 2019 at 14:01
  • en.m.wikipedia.org/wiki/Infinite_divisibility#In_physics
    – user37181
    Mar 29, 2019 at 14:28
  • Sounds like a grade schooler's nightmare. Perpetual long division!
    – user4894
    Mar 29, 2019 at 19:44
  • 1
    You are probably referring to Zeno's paradoxes, especially Dichotomy.
    – Conifold
    Mar 30, 2019 at 0:36

2 Answers 2


As has been said, among other thinkers you're talking about Zeno of Alea and his paradoxes. It is the old question of how many angels can dance on the head of a pin, and it leads into the philosophical aspects of the calculus and the existential status of the 'ghosts of departed quantities'. It's a profound and rewarding area of thought with a lot of literature.

It rather suggests our usual idea of objects is flawed. Zeno tried to show this for our usual idea of time and space but the same argument works for objects extended in time and space.


See Aristotle's Physics:

185b8-on Now we say that the continuous is one or that the indivisible is one, or things are said to be one, when the account of their essence is one and the same, as liquor and drink.

If their One is one in the sense of continuous, it is many; for the continuous is divisible ad infinitum.

And Categories:

4b20-on Of quantities some are discrete, others continuous; and some are composed of parts which have position in relation to one another, others are not composed of parts which have position.

Discrete are number and language; continuous are lines, surfaces, bodies, and also, besides these, time and place.

See The Continuum and the Infinitesimal in the Ancient Period.

Aristotle point of view is in strong opposition with that of Ancient Atomists, according to which the universe is composed of physical ‘atoms’ (literally ‘uncuttables’).

  • Sounds like an off-shoot of Zeno's Paradox. Check that out. After you do come back to me for the solution. Cheers, CS
    – user37981
    Mar 29, 2019 at 14:43

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