Lucretius deduces the existence of atoms and void from the complex world of perceptible compounds around us. He therefore next has to show that those compounds can be formed from the endless stock of imperceptible particles. Once more, he bombards us with examples and comparisons from the world around us. One of his neatest analogies, used on more than one occasion, is between the letters in words and the atoms in compounds: with just a little rearranging, letters can form different words (Lucretius's first example, ligna atque ignes, means "bits of wood and fires", and has been translated variously as "firs and fires", "conifers and fires" and "beams and flames"), and so, too, atoms can form seemingly very different compounds.

The atoms have shape and weight, but no other qualities – in a fine, biting argument, Lucretius pictures the consequences of atoms having any other characteristics: imperceptible particles howling with laughter or sobbing their hearts out. The shapes of atoms within compounds explain the characteristic traits and behaviours of those compounds: things that taste sweet are predominantly made of smoother atoms, whereas bitter-tasting things are made mostly from hooked ones that tear at our sense organs as we eat or drink them; liquids must be made of rounder atoms to flow and stones from atoms that are closely hooked together. There thus must be many different shapes of atoms; but though greatly varied, they cannot be infinite in variety: the only way to vary shape is to add a piece, on which model if there were infinite different types of shape for atoms, some atoms would be big enough to be seen, which we know isn't the case.

Every compound contains an array of different types of atom, the prime example of which is the Earth, which must contain a huge variety to be able to sustain the huge variety of life it supports. But not every type of atomic combination is possible: if it were, we would have monsters – Lucretius uses familiar mythological examples such as centaurs and the chimera, but also an otherwise unfamiliar half-human, half-tree hybrid, a strange precursor to Tolkien's ents – roaming among us, which we can see isn't so. There are fixed seeds for plants, fixed parents for animal species, and living things assimilate from whatever they feed on only those atoms suitable for nourishing them. There is thus an order to the world that means the sky and the sea are kept separate in just the same way as animals curled up together on the ground have separate bodies.

But this order has to be created somehow, and it is in that creative mechanism we find a form of chaos. Although, of course, we can't perceive it, the atoms that make up the universe are in constant motion (Lucretius points us to the dust we can see flying about in a sunbeam as an example of particles moving violently that we nevertheless barely perceive). A principle of the Epicurean and therefore the Lucretian universe is that matter, through its intrinsic weight, moves downwards. This might lead us to suppose that atoms simply drop in straight channels, and thus never meet. But for compounds to form, atoms must do exactly that: collide and then, when colliding with something suitable, form a compound. To facilitate this creative clashing of atoms Epicureanism had a concept very unusual in antiquity (Lucretius's is the only surviving full explanation of it): the atomic swerve. As atoms fall there exists the possibility that they can swerve – only very slightly – instead of falling in an utterly straight line. This swerve allowed the first meetings of atoms and so the creation of the universe around us. Its existence is proved by the successfully formed compound entities around us, but also, argues Lucretius, by the free will we can feel we possess but that a world of atoms falling in straight lines would seem to disbar (because the predictable movements of the atoms, hitting each other at set angles and bouncing off in predictable directions, would make our actions predetermined from the first atomic bounce). Lucretius, sadly, doesn't make clear precisely what role swerving atoms play in free will, but the swerve's importance to the Epicurean view of the universe does come across from the poem.

Ridiculed in antiquity because it is uncaused (the most shameful thing a philosopher can say, according to Cicero, is that something can come about without any cause), the swerve has more recently been put forward as the precursor to Heisenberg's uncertainty principle and an image for the spark that lit the renaissance's blue touch paper. One simple idea explains both the existence of the world around us and our ability to act freely within it: uncaused, and unobservable, but undoubtedly ingenious.

• The subheading of this article was changed on 11 February 2013. It originally referred to a "swerve atom" rather than "atomic swerve". This has now been corrected