noel emits
a wonderful wooden reason
The unarticulated assumption in this 'paradox' is that there is a discrete event, an isolated system, with definable beginning and end points.
Or rather that such a thing can be said to 'exist'.
This is implicit in the notion that there is a point in time when you can say you have a 'full cone', the moment the experiment begins. So you are allowing for a beginning.
In doing this you are then for the purposes of the experiment treating that moment as the 'beginning of time'.
The 'end of time' as then defined as the moment that the conditions that define the end of the experiment are met. In this case that the water has no depth and / or surface area.
So this is the entire scope of the experiment. It must 'happen', otherwise there is no experiment, it never begins!
The event 'happens', it has beginning and end points, this defines its existence.
The 'trouble' comes when you measure its progress through time 'fractally'. In that sense it will apear to be eternal.
This happens because the mathematical stance you are taking to analyse it is that of being at a relative point 'outside' time.
But if the observer is included as part of the system, or relative to it, then the temporal relationship is less than infinite, the ratio of rate of motion through time is less than 0:1.
I suggest then that the apparent 'error' is in the original assumption - i.e. that such a thing as a discrete event or isolated system can be said to to exist apart from an observer, or even to exist at all.
So does this mean that time has no beginning and no end?
And whence the second law of thermodynamics?
Or rather that such a thing can be said to 'exist'.
This is implicit in the notion that there is a point in time when you can say you have a 'full cone', the moment the experiment begins. So you are allowing for a beginning.
In doing this you are then for the purposes of the experiment treating that moment as the 'beginning of time'.
The 'end of time' as then defined as the moment that the conditions that define the end of the experiment are met. In this case that the water has no depth and / or surface area.
So this is the entire scope of the experiment. It must 'happen', otherwise there is no experiment, it never begins!
The event 'happens', it has beginning and end points, this defines its existence.
The 'trouble' comes when you measure its progress through time 'fractally'. In that sense it will apear to be eternal.
This happens because the mathematical stance you are taking to analyse it is that of being at a relative point 'outside' time.
But if the observer is included as part of the system, or relative to it, then the temporal relationship is less than infinite, the ratio of rate of motion through time is less than 0:1.
I suggest then that the apparent 'error' is in the original assumption - i.e. that such a thing as a discrete event or isolated system can be said to to exist apart from an observer, or even to exist at all.
So does this mean that time has no beginning and no end?
And whence the second law of thermodynamics?
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