**eJournal: uffmm.org
ISSN 2567-6458, 24.March – 24.March 2021
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de**

##### CONTEXT

This text is part of a philosophy of science analysis of the case of the oksimo software (oksimo.com). A specification of the oksimo software from an engineering point of view can be found in four consecutive posts dedicated to the HMI-Analysis for this software.

##### CHANGE

AS described in part 1 of the philosophy of science analysis of the oksimo behavior space it is here assumed — following the ideas of von Uexküll — that every biological species SP embedded in a real environment ENV transforms this environment in its *species specific internal representation ENV _{SP }*which is no 1-to-1 mapping. Furthermore we know from modern Biology and brain research that the human brain cuts its sensory perceptions P into

*time-slices P*which have durations between about 50 – 700 milliseconds and which are organized as

_{1}, P_{2}, …*multi-modal structures*for further processing. The results of this processing are different kinds of

*abstracted structures*which represent — not in a 1-to-1 fashion — different aspects of a given situation S which in the moment of being processed and then

*being stored*is not any longer actual, ‘not now’, but ‘

*gone*‘, ‘

*past*‘.

Thus if we as human actors are speaking about *change* then we are primarily speaking about the *difference* which our brain can compute comparing the *actual* situation S being kept in an *actual time-slice P _{0}* and those

*abstracted structures A(P)*coming out of preceding time slices interacting in many various ways with other available abstracted structures:

*Diff(A(P*Usually we

_{0}), A(P)) = Δ_{int}.*assume*

*automatically*that the perceived internal change

*Δ*corresponds to a change in the actual situation S leading to a follow-up situation S’ which differs with regard to the species specific perception represented in

_{int}*Δ*=

_{int}as Δ_{ext}*Diff(S, S’)*. As psychological tests can reveal this automatic (unconscious) assumption that a

*perceived change Δ*corresponds to a

_{int }*real external change Δ*must not be the case. There is a

_{ext}*real difference*between

*Δ*

_{int}_{,}

*Δ*and on account of this difference there exists the possibility that we can detect an

_{ext}*error*comparing our ideas with the real world environment. Otherwise — in the absence of an error — a congruence can be interpreted as a

*confirmation*of our ideas.

##### EXPRESSIONS CAN FOLLOW REAL PROPERTIES

As described in the preceding posts about a decidable *start state S* and a *vision V *it is possible to map a perceived actual situation S in a set of expressions E_{S}={e_{1}, e_{2}, …, e_{n} }. This general assumption is valid for all real states S, which results in the fact that a *series of real states S _{1}, S_{2}, …, S_{n }is *conceivable where every such real state S

_{i}can be associated with a

*set of expressions*E

_{i}which contain individual expressions e

_{i}which represent according to the presupposed meaning function φ certain aspects/ properties P

_{i}of the corresponding real situation S

_{i}. Thus, if two consecutive real states S

_{i}, S

_{i+1}are include perceived differences indicated by some properties then it is possible to express these differences by corresponding expressions e

_{i}as part of the whole set of expressions E

_{i}and E

_{i+1}. If e.g. in the successor of S

_{i}one property p

_{x}expressed by e

_{x}is missing which is present in S

_{i}then the corresponding set E

_{i+1}should not include the expression e

_{x}. Or if the successor state S

_{i+1}contains a property p

_{y}expressed by the expression e

_{y}which is not yet given in S

_{i}then this fact too indicates a difference. Thus the differing pair (S

_{i}, S

_{i+1}) could correspond to the pair (E

_{i}, E

_{i+1}) with e

_{x}as part of E

_{i}but not any more in E

_{i+1}and the expression e

_{y}not part of E

_{i}but then in E

_{i+1}.

The general schema could be described as:

S_{i+1} = S_{i} -{p_{x}} + {p_{y}} (the real dimension)

E_{i+1} = E_{i} – {e_{x}} + {e_{y}} (the symbolic dimension)

Between the *real* dimension and the *symbolic* dimension is the *body* with the *brain* offering all the neural processing which is necessary to enable such complex mappings. This can bne expressed by the following pragmatic recipe:

**symbolicarticulation: S x body[brain] —> E**

**symbolicarticulation(S,body[brain]) = E**

Having a body with a brain embedded in an actual (real) situation S the body (with the brain) can produce symbolic expressions corresponding to certain properties of the situation S.

##### DESCRIBING CHANGE

Assuming that symbolic articulation is possible and that there is some *regular mapping* between an actual situation S and a set of expressions E it is conceivable to describe the generation of two successive actual states S, S’ as follows:

###### Apply a Change Rule ξ of X

- We have a given
*actual situation S.* - We have a
*group of human actors A*which are using a language L._{hum} - The group generates a
*decidable description*of S as a*set of expressions E*following the rules of language L.^{L}_{S} - Thus we have
*symbolicarticulation(S, A*_{hum}) = E^{L}_{S} - The group of human actors defines a
*finite set of change rules X*which describe which expressions*Eminus*should be*removed*from E_{S}and which expressions*Eplus*should be*added*to E_{S}to get the successor state E_{S}‘ represented in a symbolic space: - E
_{S}*‘ =*E_{S }*– Eminus + Eplus .*An individual change rule ξ of X has the format: - IF COND THEN with probability π REMOVE Eminus and ADD Eplus.
- COND is a set of expressions which shall be a
*subset*of the given set E_{S }saying: COND ⊆ E_{S}. If this condition is*satisfied (fulfilled)*then the rule can be applied following probability π. - Thus applying a change rule ξ to a given state S means to operate on the corresponding set of expressions E
_{S}of S as follows: - applychange: S x E
_{S}x {ξ} —> E_{S}‘ - There can be more than only one change rule ξ as a finite set X = {ξ
_{1}, ξ_{2}, …, ξ_{n}}. They have all to be applied in a random order. Thus we get: - applychange: S x E
_{S}x X —> E_{S}‘ or applychange(S,E_{S},X) = E_{S}‘

###### Simulation

If one has a *given actual* state S with a finite set of *change rules X* we know now how to apply this finite set of change rules X to a *given* state description E_{S}. But if we would *enlarge* the set of change rules X in a way that this set X* not only contains rules for the given actual state description E_{S} but also for a finite number of other *possible* state descriptions E_{S}* then one could *repeat* the application of the change rules X* several times by using the last outcome desribing E_{S}‘ to make E_{S}‘ to the *new actual state description E _{S}*. Proceeding in this way we can generate a whole

*sequence*of state decriptions: <

*E*.

_{S}_{0},

*E*.

_{S}_{1}, …,

*E*.

_{S}_{n}> where for each pair (

*E*.

_{S}_{i},

*E*.

_{S}_{i+1}) it holds that

*applychange(S*

_{i},E_{S.i},X) = E_{S.i+1}Such a *repetitive application* of the applychange() rule we call here a *simulation: *S x E_{S} x X —> <*E _{S}*.

_{0},

*E*.

_{S}_{1}, …,

*E*.

_{S}_{n}> with the condition for each pair (

*E*.

_{S}_{i},

*E*.

_{S}_{i+1}) that it holds that

*applychange(S*also written as:

_{i},E_{S.i},X) = E_{S.i+1}*simulation(S , E*

_{S, }X) = <E_{S}._{0}, E_{S}._{1}, …, E_{S}._{n}>.A device which can operate a simulation is called a *simulator* ∑. A simulator is either a *human actor* or a *computer* with an appropriate algorithm.