A numerical estimation results when a counting process is initiated, but uncertainties exists with respect to inclusion criteria, time windows and technological capabilities. It is a cumulative count with a suggested error variation associated with it. Counting, even though it is often paraded and portrayed as being mathematically precise, is in fact frequently only numerical estimation. Counting is an operation which is a practical procedure for much of everyday life... as long as the entities are simply identified, have a longevity which is stable during the count-time, and the numbers involved are only in the tens. Counting the number of graduations on a measurement scale is usually linear, uncomplicated and readily verified by rechecking. Counting the number of water condensation droplets on a spiderweb is topologically complex, open to dispute as to what constitutes a droplet and quite difficult to confirm. Trying to count the number of individuals during a large-scale population census is essentially impossible... because of the difficulties in trying to cope with the chaos of unpredictable circumstances... and can never be any more than an estimation.

Elementary practical learning experience tends to encourage the idea that there is an exact and unique number associated with example sets. Early teaching exercises carefully avoid ambiguous situations, in order to promote the supposedly analytic and rational properties of numbers and mathematics. Objects with similar characteristics and life-spans... like fingers and toes and wooden blocks... are grouped and counted in such a manner that the final count is contrived to always be the same. Without careful inclusion criteria defined however, numerical certitude quickly becomes precarious. Thus the cumulative count of the fingers and toes of a normal... whatever that is... human might be either 18 or 20 depending upon whether the thumbs were counted as fingers or not. When the life-spans of the entities being counted are significantly shorter than the time-span allocated to perform the count, then only an estimation of their numbers is possible. Spending time trying to count water droplets on a cobweb... which is subject to ongoing wind gusts... could result in a large total for the count, no droplets left at the end, and no way of checking unless some sort of video record had been made of the whole process. The final count might have some meaning, but it certainly won't be an estimate of how many droplets actually exist at the end of the count. Education encourages the erroneous supposition that counting is exact.

The technology available to the counter is of vital importance. Gardeners can count pumpkin seeds without any technological assistance, but not rainfall or fungal spores. Physics researchers can count the number of papers they have published without any special equipment, but not elementary particles like electrons or photons. When a technology is used to count entities the result is almost inevitably an estimation. Simple rulers estimate the length of your piece of string. Thermometers estimate the temperature of your fruit-wine fermentation. Stopwatches estimate the longevity of New-Year resolutions. The financial computers estimate your bank balance to the nearest basic unit. Even digital systems... like counting the number of bottles produced by a glass factory... can never be error free. An estimation is the result when counting is assisted by a technology. As well as admitting that a count is an estimation, some attempt is usually made to quantify the uncertainty of the count so as to indicate its accuracy. Thus the error by which a total might vary must itself be estimated. Extrapolated away from the seeming security of small conceptual sets of entities, counting mutates into a chaos of indeterminate fuzzy estimations with estimations of fuzziness.