Advanced hair-splitting

FIS Track

Explaining the combinatorics behind theoretical genetics by using extended rules of arithmetic



Karl Javorszky, Clinical Psychologist, Vienna


The main concept of this track is that what is called in a culture “rational thinking” is a cultural agreement that invariably reinforces social hierarchies to the advantage of those who have been traditionally in power. The catechism of what is rational is, in other words, an explanation of the basic principle that what is above is by rights above and that what is below is below because sweet reason and the laws of Nature have caused it to be so. As Orwell has paraphrased what Wittgenstein has formulated exactly: in an “ideal” society, the rules of the language would not allow to state that the rulers are ruling unjustly. The term “unjust” could alone for grammatical reasons not be included in a sentence dealing with the powers-that-be.

The present workshop tries to direct the attention of the participants to some very small details that become visible if one looks into details of properties of logical sentences. The present way we are dealing with concepts of commutativity and associativity, and – before all – order and sequences appears outdated and improvements on it can bring forth deeper insights into the nature of Nature.

Troubles appear the moment we direct your attention to that what the little girl contemplates on Fig. 1 above: two groups of five rabbits are clearly distinguishable to five groups of two rabbits. Yet, one stumbles if one starts discussing a*b ≠ b*a, because it is against the rules to discuss this. Similarly, the rules discourage discussing { a+ bi = ci }, as the rules prescribe focusing on individual instances of a + b = c. Allowing comparisons among collections of logical sentences is made impossible by the insistence of focusing on one instance; this has the effect of ceaselessly comparing individual treesand never having the opportunity to discuss differences among forests.

Great progress in automatization in the last few decades has allowed advances to be made in the observation of small details that were impossible to see by the naked mathematicians’ eyes. We now offer some results of much attention to very small details that have been overlooked so far.

The mechanism unveiled is a highly intricate web of interdependent logical statements relating to a temporal – spatial distribution of matter, much like  a clockwork.

Subjects and scope

We plan to address the following 4 main areas:

1) Concepts Of Order

2) Logical Language

3) Contradictions and compromises

4) Using Strings

To Point 1: Concepts of Order

1.1. Traditional definitions (Platon, Aristoteles, Bruno, Weber)

1.2. Order and Stability (Theories of anarchy, the rule of the savants, supreme leader, divine vs. natural order)

1.3. Monocratic and plutocratic concepts, theories of causation of order

1.4. Order in Logic (incl. new approach: using { < | = | > } )

To Point 2: Logical Language

2.1. Thing and Symbol

2.2. Rational worldview and logical sentences (Wittgenstein)

2.3. Grammatical rules of the language circumscribe possible contents of communication; the rounding error we commit by using commutativity and associativity rules

2.4. Proposed tightening of existing rules and usage of additional rules of the logical language (introducing additional differentiations /=grammatical rules/ among logical sentences /see picture, where a child understands that 2 times 5 is different to 5 times 2/).

To Point 3: Contradictions and compromises

3.1. Order A assigns sequential (linear, “place”) attributes {pi} to elements {ei}. If Order B is different, it  assigns sequential (linear, “place”) attributes {pj} to elements {ei} The resulting contradictions have not been investigated yet in necessary depth.

3.2. To sidestep the contradictions, we assume the set to be neither completely in Order A, nor completely in Order B, but in a transient state, like “goods in transit”. This provides a basic dynamism to the model.

3.3. The process of place changes – how the elements wander from place_previous to place_new – appears as an intricate mechanism based on simple rules, which is actually accessible to humans in everyday situations without undue intellectual strain. This is what we direct your attention to.

3.4. The elaborate and intricate interdependences between amount, place, order and time are simple effects of properties of natural numbers:(Nature appears to use them in the combinatorics behind genetics), are thus acceptable as extended – new? – rules of elementary arithmetic.

To Point 4: Using Strings

4.1. Definition of Strings (collection of properties of elements travelling together during a reorder)

4.2. Strings as permutations (within a string, the elements are numbered sequentially), the parts of strings that are “not-now” and “not-here” as supportive models for concepts of dark matter/energy

4.3. Conflicting assignments of elements to strings (the present state is/can be a transition between which orders?)

4.4. Transient state of the set between two and more possible well-ordered states (constraints and thresholds; masses, levels and distances).


Target groups

The novelty value of the contribution may lie in using a small detail observable during reorders. To this detail no attention has been given so far, probably for lack of powerful accounting devices which one needs to chart the place changes of elements during a reorder.

Time-honoured methods and beliefs have their immanent truths. It is true that a watch, possessing a mass, can well be used as a hammer to hit the nails with while building the Great Edifice of Human Knowledge and Rational Worldview. The target group of this workshop are those who believe that new approaches can bring something worth while.

Important Dates

Submission deadline: 27 February 2015
Notification of acceptance: 20 March 2015