Making things happen generally takes time; and explaining why something happens generally requires describing the events that led up to it. You can’t make an omelette without breaking eggs – or indeed, without putting those eggs into a pan, applying heat, and waiting for the eggs to cook. Why do we end up with an omelette? Because we took the right actions in the right order. When we explain why things happened the way they did, we usually start by mentioning things that happened beforehand. Earlier explains later – simple, right?

Philosophers of science in recent years have argued that it’s not so simple. There are cases of simultaneous explanation, where something explains something else that happens at the very same moment – for example, the explanation of the temperature of the omelette in terms of the motions of the tiny molecules that make it up. In some approaches to quantum theory, future events – still yet to happen! – can explain why past events occurred. Perhaps most dramatically of all, it has even been suggested – for example, in various theories of quantum gravity – that *time itself* is explained by things outside of time. We’re a long way from ‘earlier explains later’ by this point!

But we don’t need to go to mind-bending new physics to see the variety of explanations in the world around us. One way in which dependence can go beyond the usual pattern of earlier-to-later explanation is by bringing in logical and mathematical elements. The natural world shows a remarkable array of elegant patterns, and if we want to explain them in the deepest way we need to appeal to maths. Consider the hexagonal pattern of cells in a honeycomb. The explanation of why bees build hexagonal honeycombs involves a mathematical fact: hexagons are the most efficient way to divide a flat plane into cells of equal area, while minimizing total length of cell perimeters. Although the bees aren’t of course aware of it, they build hexagonal honeycombs because of the special mathematical properties of hexagons. And although we don’t yet fully understand the explanation of the striking hexagonal cloud that encircles Saturn’s North pole – it’s a controversial question in current planetary science – it seems certain that the special mathematical features of hexagons will play a role in explaining why the cloud is hexagonal as opposed to (say) eleven-sided.

These timeless mathematical explanations go well beyond the natural world and enter into the created world of human artefacts. Hexagons are used extensively in Islamic art, and part of the explanation for this extensive usage involves the special mathematical relationship between hexagons and circles. And many board games make use of a hexagonal grid of tiles, since this grid has the special property that the centres of any two touching tiles are the same distance apart – making moving a piece in any direction equally advantageous to a player, other things equal.

Of course, nobody thinks that any special object, the Ideal Hexagon, is lurking around in the beehive manipulating the bees, or shaping the clouds on Saturn, or whispering in the ears of artists or board-game designers. The way in which mathematics explains these phenomena is altogether unlike the way my breakfast-making efforts explain how an omelette came into being. So how is it possible for mathematics to play such a role in the explanations of natural and created phenomena, if not by giving information about their prior causes? This is a deep problem in philosophy of mathematics, and different theories of the nature of mathematics answer it differently. Nonetheless, theories of explanation need to accommodate the undeniable fact that mathematical truths can help explain the world around us.

Another particularly interesting case of timeless explanation comes up in time travel stories. When there are causal loops around, some action can trigger a chain of events which eventually comes back around to explain why that action happened in the first place. I can build a time machine, take the blueprints back in time and give them to my earlier self, and my handing over the blueprints can then explain how I came to build the time machine in the first place! In such cases, earlier is explaining later but later is also explaining earlier. And there are also apparently timeless forms of explanation at work in the same sorts of cases. If I try to travel back in time and kill my own grandfather, I must fail – not just because I’m a hopeless assassin in general, but because it is a prerequisite of my assassination attempt that I exist in the first place. So, to explain why my grandfather is safe from my evil schemes requires making reference to the whole time-travel scenario – later and earlier are now combining together to explain earlier. These sorts of explanations are fascinating but still poorly understood by philosophers.

At the University of Birmingham, a new project called FraMEPhys aims to come up with a rigorous account of how this kind of timeless explanation works . Funded by the European Research Council, and with particular focus on explanations in physics, FraMEPhys aims to classify the different varieties of explanations that we use in science and in arts, and to better understand how our explanations work in the whole range puzzling cases that go beyond the ordinary causal model. It won’t help us make better omelettes – or even better board games. But it will – hopefully! – help us understand what these creative endeavours have in common.