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 modeling 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 procedures. The computations could well have proceeded thru innumerable unstable oscillations of chaotic error corruptions and the final values acted upon as it 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 are 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 from now on 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.