## Are numbers discrete and time continuous? or is it the other way around?

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?