D vs C

Everything can be, in a sense, quantified. Time is, of course, not an exception. We are all familiar with the meassurment of time, and humanity has createad increiasingly percice devices to keep track of it. And we all like to think that time is universal an idea that has long since been proven wrong.

But then, one comes to ask: what is time?

The 'flow' of time is relative to one's position and velocity, that is, the magnitude of that flow in relation to the 'flow' of space. But the direction of time is not relative, at least as far as we know, and definetely as far as normal, everyday, life is concerned. The 'direction' of the flow of time is indeed universal: no one has a neighbour who's clocks run backwards; a rather fortunate situation indeed, for it allows us to avoid aditional problems when trespassing into our neighbours backyard to fetch a ball.

There is one first concept I'd like to explain today: discrete vs. continous. Let us forget for now the math related to it. We can think of time going in two directions, one of them impossible to achieve, but only two direction, forward and backwards. We can't think of an intermediate direction, beteeen forward and backwards... nor can we think of another direction, say... further from forward than what backwards is. How ever, it is easy to imagine a spot between your house and your workplace, or a spot past your workplace in the direction you take every morning to get to work. And between any two of those four spots, you can easily imagine one more inbetween, and so on. But the same cannot be told about the possible directions one can imagine time to have.

The directions we can imagine time to have form a discrete set: forward and backward. The spots on a map form a continous set: every two points on the map have not one, but a infinte amount of them inbetween.

A mathmatician would argue that continuity is a property of functions, not of sets, that perhaps I'm trying to refer to a set being infinite, or rather complete. That is a correct remark. Continuity is indeed a property of functions. And ofcouse one can mess arround and define continous functions in non-complete and even finite sets.

But lets forget that for a moment I said!

It is the concepts which are discrete and continous, and we therefore cannot create a 'nice' relation between the two of them. Supose your neightbour has his clocks going backwards... as you aproach the wall that separates both houses you clock is still running forward, and once you hop that fence, all of a sudden it is running backwards. An aburbt change of direction, abrubt ofcourse if we consider time to be continous. These two concepts can not be put together, related, in a nice mater, one without this abrubt changes.