One of the triumphs of technology has been the development of computing machines which have succeeded in displacing human numeracy skills with ignorant reverence. Fingers and toes have been freed up again for the counting of intelligence quotients. Just as plants and animals have inspired attitudes... ranging from the grossly pragmatic to the absurdly religious... so are numerical computations merely practical modelling to some, but mindlessly venerated by others. The computation rules for manipulating numbers are determined analytically and then rules for manipulating numerals are devised. For the relatively small number-base sets in use, an awareness can manipulate the visualized entity sets and hence devise numerical rules which will enable the manipulation of very large numbers. Computers are then programmed with these numerical rules, thus removing the necessity for individuals to guide and monitor the phases of the process. Incomprehensibly numerous computations are now performed during progressively briefer intervals of time. More and more individuals... in diversifying activities... basically have no idea whatsoever as to what was involved in the computational procedures programmed into the computer. Not the faintest idea. Yet a significant proportion of their decision-making is based on tabulated ranks of ecclesiastical digits... manufactured from dubious start values, and processed thru innumerable iterations, truncations and uncertified routines. The computations could well have proceeded thru countless unstable oscillations of chaotic error corruptions, before the final values are acted upon as if they had cosmic significance.

One marginal benefit of the exponential increases in computational power, is to shift conceptual ideas of numbers away from supposing them to be some sort of existential entities, towards a recognition that they can be thought of as being no more than computational consequences with computational relationships with other computations. As increasingly elaborate computational procedures have been mathematically devised, so identifiably different patterns of numerical representation have emerged. Thus for example, starting with any numeral N₁... except psychotic zero as usual... compute the value of N₂ = N₁/2 + 1/N₁... ( ie add half of it to its reciprocal )... and then repeat the process with the resulting number over and over again. The pattern of numerals that emerges never repeats, has no end and starts either as the sequence of digits +1.4142135... or the sequence of digits -1.4142135...
This so-called 'irrational' number does not exist anywhere as a fairy-like spirit but deserves its given specific name of 'the square root of 2' simply because of the unique behavioural properties it exhibits with respect to other computations. In the same way numerals like 'π' and 'e' have resulted from other computational procedures. They have no ontological existence at all but acquire their intrinsic importance from their wide range of interactive numerical-behavioural properties. Computation has now become so devoid of significant cost that, as well as the supposedly useful calculations being spewed out, there will be more pointless, useless, unknown and unmonitored calculations performed on computing machines every nano-second, than all the human calculations ever performed during the evolution of the species.

Computations are very often performed as part of a numerical model in order to promote an opinion. Sometimes such opinions can be verified... as when a bridge is constructed to test the computed opinion of an engineer, that the structure can withstand its design specifications. On the other hand, an amateur astronomer could assume the published values of the sun and earth radii as 695950km and 6371km respectively, perform the computation (695950)³ ÷ (6371)³, and then promulgate the opinion that the volume of the sun was about 1,303,500 times the volume of the earth. For opinions like this, there is no possible way of ever checking such a claim directly.