*Idle thoughts and unanswerable questions on a Saturday morning:*

The *Number System* seems to be continuous and infinite but every *number* seems to be discrete. But if any* number *is also infinitely divisible it must also be continuous. So are* numbers* simultaneously both discrete and continuous?

Or is a *number* just a label? Perhaps a *number* – if just a label and representing a singularity – is discrete and the divisibility of a number is actually undefined. It is *number difference* – not a *number* – which is infinitely divisible. So – for example – the number 10, as a label, is not divisible — it is the number difference between 10 and some reference number (10-0) which is. So is our *Number System* then a discrete thing and made up of an infinite and continuous quantity of *number differences* with each *number difference* being discrete? It would then be rational for there to be an infinity of discrete *Number Systems*.

So perhaps *numbers* don’t exist. Only *number differences* do and the *numbers* are their labels.

A* length* or* distance* can appear to be discrete but every *length* is infinitely divisible – within itself – and so must also be continuous – within it’s discrete self! But *length* is *spatial* *position* *difference. So length *is to* position *as *number difference* is to* numbers*. And can there be an infinite number of *spatial positions* in our discrete but infinite universe (our *Spatial System*) giving an infinite number of *lengths* – each discrete but infinitely divisible and continuous within itself? Is *Spatial System* to *position* which is to *length* as our *Number System* is to* numbers* which are to *number differences?*

Does what seems to hold for a* Number System *and a* Spatial System *also apply to a* Time System?*

*Time* appears infinitely divisible and so must be continuous? But that does not seem right. It is not *Time* but *time interval *(time difference or duration) within our *Time System* which is infinitely divisible. Can our *Time System* then be something discrete? If discrete, there must be a start and an end to our *Time System*. And perhaps there are many other *Time Systems *– an infinity of them. Perhaps* Change* comes before our *Time System* starts and *Stasis* comes before *Change*. Or is *Change* just another label for our particular *Time System*? Any *time interval* within our *Time System* can however seem to be a discrete thing and yet it remains infinitely divisible within that interval. Can it be so that within our particular *Time System* (as one of many) *time intervals* are discrete and *Time* represents labels which mark the end points of the intervals?

Is it then so that

**A Number System gives numbers as labels which lead to number differences**

**as**

**A Spatial System gives position labels which lead to length**

**as**

**A Time System (Change?) gives Time labels which lead to time intervals?**

An infinity of discrete* Time Systems* perhaps and we inhabit one such which we can call *Change*? And in our *Time System*, *time intervals* are discrete but infinitely divisible. So is our discrete *Time System* then an infinite and continuous succession of discrete *time intervals *where* Time *provides labels for the end points of the intervals*?* But the past is unreachable and the future never comes and the present is over before it has begun.

Is a *Life System* then discrete and just one of an infinite number? Where each *Life System* is continuous within itself?

Tags: Change, length, number, Number system, position, Spatial System, Stasis, Time, time interval, Time System, unanswerable questions