bigideas

In the last Big Ideas we talked about Anthony Giddens’s view of modernity as involving, in part, an abstraction of space and time from our immediate environment. The railway timetable, for example, is able to refer to places and times distant from where we are, and perhaps places and times at which nothing particular happens. This, Giddens thinks, is something new.

Giddens isn’t talking about a physical theory here but an attitude towards space and time. Look at the timetable again — it contains times but, in general, no dates. As such each entry represents a potentially infinite series of moments in the future at which a train is expected to depart from a certain place. Such a view requires a general sense that we live in a fixed, permanently-existing “grid” of space-time. This view is attributable, at least in part, to Isaac Newton, who in the 17th century, and near to the beginning of modern mathematical physics, stands at the a point that’s a decent candidate for being the beginning of the modern world.

Newton’s physics was made possible by the previous invention by Descartes of co-ordinate geometry. Descartes gave us the idea that space can be considered as a regular grid, and any point in the grid can be references by three co-ordinates. In school (and in some real-life problems) you can just use two co-ordinates, restricting yourself to a flat surface. In higher mathematics you might use more co-ordinates.

The number of co-ordinates you need to identify your position in space tells you how many dimensions your space has. We live in a three-dimensional space because we need three co-ordinates to find a point in it — longitude, latitude and altitude are one way to do it.

Newton’s key metaphysical statement about space is probably this one, from the Scholiumto the Definitions in the Principia Mathematica:

Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; such is the dimension of a subterraneous, an aerial, or celestial space, determined by its position in respect of the earth. Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be continually changed.

As usual with Newton, he gives a nice concrete example to help us see what he means; when the earth moves through absolute space its atmosphere moves with it, in absolute terms, even though relative to us the atmosphere, fortunately, appears to stay where it is. This privileging of “relative space” over “absolute space” would, of course, be inverted in the twentieth century by Einstein, but that’s another story.

This is slightly ironic because Descartes, who gave Newton the tool to describe absolute space and use it to do calculations, actually would have disagreed strenuously with Newton’s metaphysics. For Descartes, space is defined by the motions of bodies and time is defined by change. An empty space or, similarly, a time during which nothing happens are equally unthinkable. This attitude is exactly where the famous controversy over the vacuum comes from. In Newton’s universe a vacuum is perfectly possible, since space is there even if matter isn’t. For Descartes, and a long tradition preceding him, space is just an abstraction we use to talk about where matter is, and space without stuff is unthinkable.

This isn’t just Newton the scientist flirting with philosophy in that typically renaissancy interdisciplinary sort of way that wouldn’t be tolerated today. The development of the calculus by Newton and his followers relied, for its justification, on this idea of absolute space. Even today, students learn vector calculus in a co-ordinate system that they (rightly) call “Cartesian”, although as an idea about what space is really like it’s more properly “Newtonian”. A discussion of the extent to which pure mathematical ideas about “space” imply, when applied to the real world, certain metaphysical commitments would be a fascinating, if delicate project. But it’s clear that the mathematics that engineers and physicists use today sprang from this very specific notion that Newton names “absolute space”.

What’s this got to do with modernity? Well, as Nathan outlined at the event in July, Giddens takes the view that modernity is, in part, characterised by an abstraction of space and time away from our immediate surroundings. We talk now about locations that are far away, and that we may not really know the exact location of. That goes for “locations” in time as well as in space.

Modern space-time contrasts with mediaeval space-time in the exact sense that Newton’s metaphysics contrasts with the tradition Descartes follows. Institutionally, mediaeval space-time can be relative because mediaeval lives and projects tend to be fairly localised. In the 10th century, you didn’t need to know how to fly to LA. You needed to know how to get from England to Jerusalem, say, but that was accomplished by a long, slow journey composed of many short legs.

I’m sceptical about this idea of mediaeval life, but I’m paraphrasing a second-hand paraphrase of Giddens, so you can blame me for it rather than him. The point is that this Newtonian space-time locates all of us — every human being, and everything a human being might take an interest in — in a standard, uniform grid. This grid functions like an institution, to enable us to organise things and achieve much greater effects than we could alone.

One thing we asked at the event was whether modernity ended at the beginning of the twentieth century, and postmodernity began. If so then the Einteinian, relativistic revolution might provide a good metaphor for that, but it would only be, like the points made above about Newtonian space, a metaphor. Quite enough nonsense has been talked over the years about relativism, so at this point I’ll shut up. I will mention, though, that the philosopher and sometime mathematician Henri Bergson disagreed powerfully with both the Newtonian and Einsteinian models of time, preferring a more mediaeval model of time as change. That’s interesting because Bergson was a towering figure in French philosophy in the twentieth century, and is considered by many to be one of the forefathers of postmodernism. Perhaps there’s something in this idea that modernity, in the large, is bound up with basic metaphysics of space and time.

Newton’s definitions of absolute space and time are set out in a Scholium in the Principia Mathematica, which is helpfully available in HTML form. Einstein wrote a lay person’s guide to relativity which, although lucid and admirable in intent, is the source of much misunderstanding. Robert Geroch attempted a treatment that tries to do better justice to the theory without the mathematics. In the end, though, it’s all hand-waving without doing the maths.The image of the Cartesian grid is from Wikimedia Commons. The GPS co-ordinates are courtesy of LaertesCTB.