Accounting is not a science
There is an old joke about the mafia boss, who needs a new accountant. Proband 1 is asked: how much is 2+2? Answer: 4. Next candidate: How much is 2+2? Answer: anything between 3 and 5. No good. Next candidate, same question. Answer: whatever you wish, boss. He gets hired. More traditional approaches to accounting disqualify the art from being a science, as there is no room for error. Accounting embodies all that Wittgenstein stood for: true statements that rely on each other and are invariably inherently – grammatically – correct, otherwise it would not be accounting but spaghetti. Science, like philosophy, deals with such, what is presently unknown, while trying to explore, understand, qualify and quantify it. There is room for error in philosophy and science, which room does not exist in an ideal Wittgenstein set of sentences. Among tautologies, nothing can turn out to be otherwise. Theoretical genetics has forced us to leave the traditional understanding of what a number is and where it is placed. Its place has been heretofore inseparably fused with its value, form, appearance, properties and associations. By repeatedly sorting, one denies the connection, naively believed to be inherent, of a value with its place. What is a king, if he is among beggars? Can the Captain of Koepenick be represented in a numeric tale? Are some changes more problematic than others? One never knows, what hidden revolutionary instincts slumber deep in the hearth of an individual. Maybe mathematicians are not so much given to overthrowing age-old agreements, definitions, rules and conventions. Biologists, however, should maintain the idea of sudden, *deus ex machina* type improvements, as tools of evolution by mutation and variation. It could well be, that a rupture from its place of a number does introduce a new species of counting. If numbers are no more married to their place, where are they then? Here, accounting helps. We know that they cannot simply disappear; furthermore, we add them up and expect grand totals that match. We add them up actually twice, once according to place occupied and once as carriers of symbols. This one can only do, if one switches to cycles as units of counting. Accounting in units of cycles may sound more complicated than it is in actual practice. Classical logic degenerates into the special case of a plane across the number line: as the ever-present moment of “now”, which is eternal, because it is timeless. In this cross-section of time, the rules of Wittgenstein apply. The actual content of the “now” is one of the varieties made possible by its neighbours, the predecessor and the successor. The intermediate state of actual (real, existing, true) state does have a-priori rules in it. These are given by the fact that the predecessor and the successor states are ordered. If we take the table we have constructed with (a,b) and watch the process of reordering between the two sorted states <set sorted on AB> vs. <set sorted on BA>, then we see that the collection is subject to very potent sets of restrictions, on what can be where. Knowing the end state allows building estimates about what is missing, that is: yet to come. Cycles are of a great help here, as they are successions, ordered in specific ways. Of that, what has happened before, human intelligence can confer, what will happen next. That, what we deduct, is different to that, what we observe. The former is meta-physic to the latter’s physic, meaning to the latter’s message. Learning is basically an ability to improve the efficacy of predictions. To be able to imagine the continuation of partly finished cycles, periods and rhythms is to be able to respond intelligently. One enters a territory here, which separates accounting from predicting the future. Classical logic will not speak about the future, because the future is not tautologic. Seen, however, as an exercise in combinatorics, one may be able to construct – at least, theoretically – all true sentences that can be consistently said about up to 136 objects. In this hypothetical case, whichever state the set is in, possible predecessors and successors of this state can be established. Taking the most probable of among the possible next steps, the system begins a walk. It is then possible to find such walks that are a closed loop. If the version is included, that some facts that relate to the sequence of arguments restrict the ways commutative assemblies can be contemporary, and that the configuration of symbols of commutative assemblies restricts the ways arguments can be sequenced: in this case theoretical genetics has been made accessible to a Wittgenstein type logical discourse, reduced to tautologies and probabilities, that is: predictions, which are again part of the art of accounting.
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