Photons don't even know to
travel in straight lines. However if there is nothing between the source and detector, light appears to travel in straight lines. So next you might try looking at lining-up and curling-up for a source and detector with nothing in the space separating them. Again you have to guess – but an intelligent guess – as to the most significant paths and then model that with the triplets.
Here only the contributions from the central area add much to the resultant – contributions from paths with waypoints far from the centre line curl up. Again you have recovered an empirical law: that light travels in straight lines. But once again you now have a theoretical reason why this is the case – it's no longer just to be accepted as fact.
But there is a wrinkle, which you can explore. It does look as if you can ignore all paths apart from those defined by a hole around the centreline. A commonly fruitful way of thinking in physics is to take things to extremes – so now try making the hole smaller by adding a barrier. In two dimensions on screen that will be a slit.