a numerical accumulation process that excludes the inconvenient |
Counting is the temporal process of accumulating inclusion markers in a memory for a set of entities.
For each entity identified, a decision is made as to whether or not it suits the purpose of the count to have it included.
If it is included then it is labelled according to a sequential and recursive naming convention.
A cumulative discrete total is thereby acquired when it suits the purpose of the count to stop the counting process.
Counting entities in a chaotic universe, where every entity is perturbed and only approximately related to some presupposed
formal structure, may be neither simple nor painless.
Counting is frequently only estimation.
The supposition that counting is exact just doesn't add up.
There are uncertainties about the exact specifications for the entities being counted, uncertainties about whether all the
entities have been counted and uncertainties about the motives behind the counting.
Counting takes time and there is no guarantee that the first entities you counted will still exist by the time you think you are finished.
Consider the very practical example of counting and removing body hairs.
Firstly, the classification criteria as to which entities to count or not, is normally specified as anything on the surface of
the skin that a pair of tweezers can grab.
They may involve colour exclusions, size, and whether there has been official approval for certain cases to be included or not.
Secondly... since memory alone has proved unreliable... whatever count recorder has been chosen, it must be set to zero
unless distorted totals are required.
Thirdly, a start decision must be made... even if physical pain levels would rather be avoided or certain political procrastinations
Fourthly... once the process is under way... establishing a criterion for deciding if an entity has been counted or
not is vital to the integrity of the exercise.
Specifications for fractional hairs must be rigorously stipulated.
International recommendations are that each hair is plucked out individually and clearly labelled as having been validly included.
Fifthly, the cumulative total counter is incremented.
This is best not done by the pluckee, since variable pain thresholds have been known to disrupt concentration and allow increment omissions.
Lastly, stages four and five are repeated until either no further candidate hairs are available, or an acceptable stop excuse is invoked.
In fact, the stop decision is often difficult to determine if the body is exceedingly hairy and unwaxed, because by the time
every minute and obscure crevice has been processed, there will be new hairs emerging in the regions where the count began.
It should be noted that for a set to be 'countable', there must be a termination to the process.
To claim that a set is countable 'in principle'... if the counting process is started but never terminated...
is to pretend somehow that time is irrelevant.
If you can't finish counting the set then it is not countable.
To initiate a counting process of an 'infinite' number of entities
does not allow the inference or assumption that they are thereby countable.
For a set to have been counted, the stop decision must have been invoked.
Few mathematicians would agree, one imagines,
to allowing their application for promotion to be 'countable' in principle,
although it would take more than the remainder of
the time left for the universe to run its course to
actually get the application 'counted' in the set of applications.