THE OKSIMO CASE as SUBJECT FOR PHILOSOPHY OF SCIENCE. Part 4. Describing Change

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  ENVSP 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 P1, P2, … which have durations between about 50 – 700 milliseconds and which are organized as 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 P0 and those abstracted structures A(P) coming out of preceding time slices interacting in many various ways with other available abstracted structures:  Diff(A(P0), A(P)) = Δint. Usually we assume automatically that the perceived internal change Δint 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 Δint as Δext = Diff(S, S’). As psychological tests can  reveal  this automatic (unconscious) assumption that a perceived change Δint corresponds to a real external change Δext must not be the case. There is a real difference between Δint, Δext and on account of this difference there exists the possibility that we can detect an 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 ES={e1, e2, …, en }. This general assumption is valid for all real states S, which results in the fact that a series of real states S1, S2, …, Sn is conceivable where every such real state Si can be associated with a set of expressions Ei which contain individual expressions ei which represent according to the presupposed meaning function φ certain aspects/ properties Pi of the corresponding real situation Si.  Thus, if two consecutive real states Si, Si+1 are include perceived  differences  indicated by some properties then it is possible to express these differences by corresponding expressions ei as part of the whole set of expressions Ei and Ei+1. If e.g. in the successor of Si one property px expressed by ex  is missing which is present in Si then the corresponding set Ei+1 should not include the expression ex. Or if the successor state Si+1 contains a property py expressed by the expression ey which is not yet given in Si then this fact too indicates a difference. Thus the differing pair (Si, Si+1)  could correspond to the pair (Ei, Ei+1) with ex as part of Ei but not any more in Ei+1 and the expression ey not part of Ei but then in Ei+1.

The general schema could be described as:

Si+1 = Si -{px} + {py} (the real dimension)

Ei+1 = Ei – {ex} + {ey} (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 Ahum which are using a language L.
  • The group generates a decidable description of S as a set of expressions ELS following the rules of language L.
  • Thus we have symbolicarticulation(S, Ahum) = ELS
  • The group of human actors defines a finite set of change rules X which describe which expressions Eminus should be removed from ES and which expressions Eplus should be added to ES to get the successor state  ES‘ represented in a symbolic space:
  • ES‘ = ES – 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 ES saying: COND ⊆ ES. 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 ES of  S as follows:
  • applychange: S x ES x {ξ}    —> ES
  • There can be more than only one change rule ξ as a finite set X = {ξ1, ξ2, …, ξn}. They have all to be applied in a random order. Thus we get:
  • applychange: S x ES x X   —> ES‘ or applychange(S,ES,X) = ES
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  ES. 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 ES but also for a finite number of other possible state descriptions ES* then one could repeat the application of the change rules X* several times by using the last outcome desribing ES‘ to make ES‘ to the new actual state description ES. Proceeding in this way we can generate a whole sequence of state decriptions: <ES.0, ES.1, …, ES.n> where for each pair (ES.i, ES.i+1) it holds that  applychange(Si,ES.i,X) = ES.i+1

Such a repetitive application of the applychange() rule we call here a simulation: S x ES x X   —> <ES.0, ES.1, …, ES.n> with the condition  for each pair (ES.i, ES.i+1) that it holds that  applychange(Si,ES.i,X) = ES.i+1also written as: simulation(S , ES, X) = <ES.0, ES.1, …, ES.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.

 

THE OKSIMO CASE as SUBJECT FOR PHILOSOPHY OF SCIENCE. Part 1

eJournal: uffmm.org
ISSN 2567-6458, 22.March – 23.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.

THE OKSIMO EVENT SPACE

The characterization of the oksimo software paradigm starts with an informal characterization  of the oksimo software event space.

EVENT SPACE

An event space is a space which can be filled up by observable events fitting to the species-specific internal processed environment representations [1], [2] here called internal environments [ENVint]. Thus the same external environment [ENV] can be represented in the presence of  10 different species  in 10 different internal formats. Thus the expression ‘environment’ [ENV] is an abstract concept assuming an objective reality which is common to all living species but indeed it is processed by every species in a species-specific way.

In a human culture the usual point of view [ENVhum] is simultaneous with all the other points of views [ENVa] of all the other other species a.

In the ideal case it would be possible to translate all species-specific views ENVa into a symbolic representation which in turn could then be translated into the human point of view ENVhum. Then — in the ideal case — we could define the term environment [ENV] as the sum of all the different species-specific views translated in a human specific language: ∑ENVa = ENV.

But, because such a generalized view of the environment is until today not really possible by  practical reasons we will use here for the beginning only expressions related to the human specific point of view [ENVhum] using as language an ordinary language [L], here  the English language [LEN]. Every scientific language — e.g. the language of physics — is understood here as a sub language of the ordinary language.

EVENTS

An event [EV] within an event space [ENVa] is a change [X] which can be observed at least from the  members of that species [SP] a which is part of that environment ENV which enables  a species-specific event space [ENVa]. Possibly there can be other actors around in the environment ENV from different species with their specific event space [ENVa] where the content of the different event spaces  can possible   overlap with regard to  certain events.

A behavior is some observable movement of the body of some actor.

Changes X can be associated with certain behavior of certain actors or with non-actor conditions.

Thus when there are some human or non-human  actors in an environment which are moving than they show a behavior which can eventually be associated with some observable changes.

CHANGE

Besides being   associated with observable events in the (species specific) environment the expression  change is understood here as a kind of inner state in an actor which can compare past (stored) states Spast with an actual state SnowIf the past and actual state differ in some observable aspect Diff(Spast, Snow) ≠ 0, then there exists some change X, or Diff(Spast, Snow) = X. Usually the actor perceiving a change X will assume that this internal structure represents something external to the brain, but this must not necessarily be the case. It is of help if there are other human actors which confirm such a change perception although even this does not guarantee that there really is a  change occurring. In the real world it is possible that a whole group of human actors can have a wrong interpretation.

SYMBOLIC COMMUNICATION AND MEANING

It is a specialty of human actors — to some degree shared by other non-human biological actors — that they not only can built up internal representations ENVint of the reality external to the  brain (the body itself or the world beyond the body) which are mostly unconscious, partially conscious, but also they can built up structures of expressions of an internal language Lint which can be mimicked to a high degree by expressions in the body-external environment ENV called expressions of an ordinary language L.

For this to work one  has  to assume that there exists an internal mapping from internal representations ENVint into the expressions of the internal language   Lint as

meaning : ENVint <—> Lint.

and

speaking: Lint —> L

hearing: Lint <— L

Thus human actors can use their ordinary language L to activate internal encodings/ decodings with regard to the internal representations ENVint  gained so far. This is called here symbolic communication.

NO SPEECH ACTS

To classify the occurrences of symbolic expressions during a symbolic communication  is a nearly infinite undertaking. First impressions of the unsolvability of such a classification task can be gained if one reads the Philosophical Investigations of Ludwig Wittgenstein. [5] Later trials from different philosophers and scientists  — e.g. under the heading of speech acts [4] — can  not fully convince until today.

Instead of assuming here a complete scientific framework to classify  occurrences of symbolic expressions of an ordinary language L we will only look to some examples and discuss these.

KINDS OF EXPRESSIONS

In what follows we will look to some selected examples of symbolic expressions and discuss these.

(Decidable) Concrete Expressions [(D)CE]

It is assumed here that two human actors A and B  speaking the same ordinary language L  are capable in a concrete situation S to describe objects  OBJ and properties PROP of this situation in a way, that the hearer of a concrete expression E can decide whether the encoded meaning of that expression produced by the speaker is part of the observable situation S or not.

Thus, if A and B are together in a room with a wooden  white table and there is a enough light for an observation then   B can understand what A is saying if he states ‘There is a white wooden table.

To understand means here that both human actors are able to perceive the wooden white table as an object with properties, their brains will transform these external signals into internal neural signals forming an inner — not 1-to-1 — representation ENVint which can further be mapped by the learned meaning function into expressions of the inner language Lint and mapped further — by the speaker — into the external expressions of the learned ordinary language L and if the hearer can hear these spoken expressions he can translate the external expressions into the internal expressions which can be mapped onto the learned internal representations ENVint. In everyday situations there exists a high probability that the hearer then can respond with a spoken ‘Yes, that’s true’.

If this happens that some human actor is uttering a symbolic expression with regard to some observable property of the external environment  and the other human actor does respond with a confirmation then such an utterance is called here a decidable symbolic expression of the ordinary language L. In this case one can classify such an expression  as being true. Otherwise the expression  is classified as being not true.

The case of being not true is not a simple case. Being not true can mean: (i) it is actually simply not given; (ii) it is conceivable that the meaning could become true if the external situation would be  different; (iii) it is — in the light of the accessible knowledge — not conceivable that the meaning could become true in any situation; (iv) the meaning is to fuzzy to decided which case (i) – (iii) fits.

Cognitive Abstraction Processes

Before we talk about (Undecidable) Universal Expressions [(U)UE] it has to clarified that the internal mappings in a human actor are not only non-1-to-1 mappings but they are additionally automatic transformation processes of the kind that concrete perceptions of concrete environmental matters are automatically transformed by the brain into different kinds of states which are abstracted states using the concrete incoming signals as a  trigger either to start a new abstracted state or to modify an existing abstracted state. Given such abstracted states there exist a multitude of other neural processes to process these abstracted states further embedded  in numerous  different relationships.

Thus the assumed internal language Lint does not map the neural processes  which are processing the concrete events as such but the processed abstracted states! Language expressions as such can never be related directly to concrete material because this concrete material  has no direct  neural basis.  What works — completely unconsciously — is that the brain can detect that an actual neural pattern nn has some similarity with a  given abstracted structure NN  and that then this concrete pattern nn  is internally classified as an instance of NN. That means we can recognize that a perceived concrete matter nn is in ‘the light of’ our available (unconscious) knowledge an NN, but we cannot argue explicitly why. The decision has been processed automatically (unconsciously), but we can become aware of the result of this unconscious process.

Universal (Undecidable) Expressions [U(U)E]

Let us repeat the expression ‘There is a white wooden table‘ which has been used before as an example of a concrete decidable expression.

If one looks to the different parts of this expression then the partial expressions ‘white’, ‘wooden’, ‘table’ can be mapped by a learned meaning function φ into abstracted structures which are the result of internal processing. This means there can be countable infinite many concrete instances in the external environment ENV which can be understood as being white. The same holds for the expressions ‘wooden’ and ‘table’. Thus the expressions ‘white’, ‘wooden’, ‘table’ are all related to abstracted structures and therefor they have to be classified as universal expressions which as such are — strictly speaking —  not decidable because they can be true in many concrete situations with different concrete matters. Or take it otherwise: an expression with a meaning function φ pointing to an abstracted structure is asymmetric: one expression can be related to many different perceivable concrete matters but certain members of  a set of different perceived concrete matters can be related to one and the same abstracted structure on account of similarities based on properties embedded in the perceived concrete matter and being part of the abstracted structure.

In a cognitive point of view one can describe these matters such that the expression — like ‘table’ — which is pointing to a cognitive  abstracted structure ‘T’ includes a set of properties Π and every concrete perceived structure ‘t’ (caused e.g. by some concrete matter in our environment which we would classify as a ‘table’) must have a ‘certain amount’ of properties Π* that one can say that the properties  Π* are entailed in the set of properties Π of the abstracted structure T, thus Π* ⊆ Π. In what circumstances some speaker-hearer will say that something perceived concrete ‘is’ a table or ‘is not’ a table will depend from the learning history of this speaker-hearer. A child in the beginning of learning a language L can perhaps call something   a ‘chair’ and the parents will correct the child and will perhaps  say ‘no, this is table’.

Thus the expression ‘There is a white wooden table‘ as such is not true or false because it is not clear which set of concrete perceptions shall be derived from the possible internal meaning mappings, but if a concrete situation S is given with a concrete object with concrete properties then a speaker can ‘translate’ his/ her concrete perceptions with his learned meaning function φ into a composed expression using universal expressions.  In such a situation where the speaker is  part of  the real situation S he/ she  can recognize that the given situation is an  instance of the abstracted structures encoded in the used expression. And recognizing this being an instance interprets the universal expression in a way  that makes the universal expression fitting to a real given situation. And thereby the universal expression is transformed by interpretation with φ into a concrete decidable expression.

SUMMING UP

Thus the decisive moment of turning undecidable universal expressions U(U)E into decidable concrete expressions (D)CE is a human actor A behaving as a speaker-hearer of the used  language L. Without a speaker-hearer every universal expressions is undefined and neither true nor false.

makedecidable :  S x Ahum x E —> E x {true, false}

This reads as follows: If you want to know whether an expression E is concrete and as being concrete is  ‘true’ or ‘false’ then ask  a human actor Ahum which is part of a concrete situation S and the human actor shall  answer whether the expression E can be interpreted such that E can be classified being either ‘true’ or ‘false’.

The function ‘makedecidable()’ is therefore  the description (like a ‘recipe’) of a real process in the real world with real actors. The important factors in this description are the meaning functions inside the participating human actors. Although it is not possible to describe these meaning functions directly one can check their behavior and one can define an abstract model which describes the observable behavior of speaker-hearer of the language L. This is an empirical model and represents the typical case of behavioral models used in psychology, biology, sociology etc.

SOURCES

[1] Jakob Johann Freiherr von Uexküll (German: [ˈʏkskʏl])(1864 – 1944) https://en.wikipedia.org/wiki/Jakob_Johann_von_Uexk%C3%BCll

[2] Jakob von Uexküll, 1909, Umwelt und Innenwelt der Tiere. Berlin: J. Springer. (Download: https://ia802708.us.archive.org/13/items/umweltundinnenwe00uexk/umweltundinnenwe00uexk.pdf )

[3] Wikipedia EN, Speech acts: https://en.wikipedia.org/wiki/Speech_act

[4] Ludwig Josef Johann Wittgenstein ( 1889 – 1951): https://en.wikipedia.org/wiki/Ludwig_Wittgenstein

[5] Ludwig Wittgenstein, 1953: Philosophische Untersuchungen [PU], 1953: Philosophical Investigations [PI], translated by G. E. M. Anscombe /* For more details see: https://en.wikipedia.org/wiki/Philosophical_Investigations */