A selection of the best from recent issues of the Philosopher

From Zeno to Einstein

Philosophers have puzzled over this question for as many years as any other problem. Space is after all, both fundamental and inexplicable. In Plato's dialogue, the Timaeus, which kicks off Hugget's book, it is described as that 'which exists and cannot be destroyed', that which 'provides a location for all things that come into being'. Everything in the universe is scattered through space, 'like grain that is sifted by winnowing sieves or other such implements' the dense and heavy elements here, the light and rare elements there. But like the soul, space can be only indirectly observed, apparent only through the physical effects associated with it. But like the soul too, somehow at the same time separate and distinct from them. 

That said, Hugget then launches into lecture mode, (the book is unashamedly based on his series of faculty courses). What is logic, what is metaphysics? Who was Plato? When did he live? It is in places rather inelegant, and at times too rather dull. But the writing is as clear as a book aimed at mathematicians and physicists is likely to be, and the readings themselves are a treasure trove. 

We are introduced to Euclid's Elements, which were the first attempt to found reasoning on clearly stated self-evident assumptions, and whose geometrical proofs set the style for the future of philosophising. Zeno is well represented by not only his paradoxes but some rather rarer fragments from Simplicius and Aristotle as well. 

And Aristotle leads the next chapter with extracts from his Physics . Descartes' view of space and time follows on, with extracts from The Principles of Philosophy, and Newton's reaction and response from On the Gravity and Equilibrium of Fluids. Newton argues that Descartes' system would have some absurd consequences, with God, for example, trying to rotate the Earth one way, the starry heaven the other. As if this were not enough, Newton adds, after a long spiel of objections, 'if space had ever not existed, God at that time would have been nowhere; and hence he either created space later (in which he was not himself), or else, which is not less repugnant to reason, he created his own ubiquity'. Newton says we can imagine there being nothing in space, but not imagine space itself not existing. If God destroyed the world, the space it was in would surely remain. 

Which of course leads on to Newton's monumental Principia, including his axioms 'the three Laws of Motion'. Huggett then discusses the conflict between theories, like Newton's so-called 'absolute' space and time, (everywhere, always, unchanging) and relative spaces. 

Which, he is quick to remind the reader, is not the same as relativistic space, which is Einstein's much later notion. Relative space is summed up by Descartes' celebrated illustration of the sailor on the ship, who does not change his position relative to the cabin or the ship, but is nonetheless moving relative to the shore. The ship is a possible frame of reference for describing motion, the shore is another. 

Absolute space supposes that ultimately there is just one true frame of reference, and all the relative motions can be explained within it. Newton tried to demonstrate that there was an 'Absolute Space' framework by whirling a bucket round on a rope - but that is a story the reader must go to the book for! 

Relationism, as Huggett likes to call it, is taken further with an exchange between Messers Leibniz and Clarke, in which concepts of 'other universes' and 'kinematic shift' make their appearance. Berkeley and Mach take up the bucket problem together, at least in Hugget's book, as in fact they lived a good century apart from one another. Galileo attempts a messy compromise, allowing unmeasurable absolute velocity, but preserving absolute acceleration, and Kant's Critique of Pure Reason is used both to show the importance of left and right handedness and the geometry of mirror images, as well as to introduce non-Euclidean geometry. 

This last is taken further by Poincaré, who is increasingly preoccupied with the behaviour of light, and thus it is that at last we arrive at Einstein and the Problem of Space, Ether and the Field in Physics. Einstein serves to unite the theories too, by being prepared to go back through history, and consider the psychological roots of our notions of space and time 

But not much further forward, and although assuredly the book is complex enough for several years study, it is slightly anti-climatic to be left at the end of it with the sense of having looked at only the 'out-of-date' theories, and been deprived of consideration of the new ones.