The abstract elements introduced so far are still few, but they already allow to delineate a certain ‘abstract space’. Thus there are so far
Abstract elements in current memory (also ‘consciousness’) based on concrete perception,
which then can pass over into stored abstract – and dynamic – elements of potential memory,
further abstract concepts of n.th order in current as well as in potential memory,
Abstract elements in current memory (also ‘consciousness’) based on concrete perception, which function as linguistic elements,
which can then also pass over into stored abstract – and dynamic – elements of potential (linguistic) memory,
likewise abstract linguistic concepts of nth order in actual as well as in potential memory,
abstract relations between abstract linguistic elements and abstract other elements of current as well as potential memory (‘meaning relations’).
linguistic expressions for the description of factual changes and
linguistic expressions for the description of analytic changes.
The generation of abstract linguistic elements thus allows in many ways the description of changes of something given, which (i) is either only ‘described’ as an ‘unconditional’ event or (ii) works with ‘rules of change’, which clearly distinguishes between ‘condition’ and ‘effect’. This second case with change-rules can be related to many varieties of ‘logical inference’. In fact, any known form of ‘logic’ can be ’emulated’ with this general concept of change rules.
This idea, only hinted at here, will be explored in some detail and demonstrated in various applications as we proceed.
Glimpses of an Ontology
Already these few considerations about ‘abstract elements’ show that there are different forms of ‘being’.[1].
In the scheme of FIG. 1, there are those givens in the real external world which can become the trigger of perceptions. However, our brain cannot directly recognize these ‘real givens’, only their ‘effects in the nervous system’: first (i) as ‘perceptual event’, then (ii) as ‘memory construct’ distinguished into (ii.1) ‘current memory (working memory, short-term memory, …) and (ii.2) ‘potential memory’ (long-term memory, various functional classifications, …).”[2]
If one calls the ‘contents’ of perception and current memory ‘conscious’ [3], then the primary form of ‘being’, which we can directly get hold of, would be those ‘conscious contents’, which our brain ‘presents’ to us from all its neuronal calculations. Our ‘current perceptions’ then stand for the ‘reality out there’, although we actually cannot grasp ‘the reality out there’ ‘directly, immediately’, but only ‘mediated, indirectly’.
Insofar as we are ‘aware’ of ‘current contents’ that ‘potential memory’ makes ‘available’ to us (usually called ‘remembering’ in everyday life; as a result, a ‘memory’), we also have some form of ‘primary being’ available, but this primary being need not have any current perceptual counterpart; hence we classify it as ‘only remembered’ or ‘only thought’ or ‘abstract’ without ‘concrete’ perceptual reference.
For the question of the correspondence in content between ‘real givenness’ and ‘perceived givenness’ as well as between ‘perceived givenness’ and ‘remembered givenness’ there are countless findings, all of which indicate that these two relations are not ‘1-to-1’ mappings under the aspect of ‘mapping similarity’. This is due to multiple reasons.
In the case of the perceptual similarity with the triggering real givens, already the interaction between real givens and the respective sense organs plays a role, then the processing of the primary sense data by the sense organ itself as well as by the following processing in the nervous system. The brain works with ‘time slices’, with ‘selection/condensation’ and with ‘interpretation’. The latter results from the ‘echo’ from potential memory that ‘comments’ on current neural events. In addition, different ’emotions’ can influence the perceptual process. [4] The ‘final’ product of transmission, processing, selection, interpretation and emotions is then what we call ‘perceptual content’.
In the case of ‘memory similarity’ the processing of ‘abstracting’ and ‘storing’, the continuous ‘activations’ of memory contents as well as the ‘interactions’ between remembered things indicate that ‘memory contents’ can change significantly in the course of time without the respective person, who is currently remembering, being able to read this from the memory contents themselves. In order to be able to recognize these changes, one needs ‘records’ of preceding points in time (photos, films, protocols, …), which can provide clues to the real circumstances with which one can compare one’s memories.”[5]
As one can see from these considerations, the question of ‘being’ is not a trivial question. Single fragments of perceptions or memories tend to be no 1-to-1 ‘representatives’ of possible real conditions. In addition, there is the high ‘rate of change’ of the real world, not least also by the activities of humans themselves.
COMMENTS
[1] The word ‘being’ is one of the oldest and most popular concepts in philosophy. In the case of European philosophy, the concept of ‘being’ appears in the context of classical Greek philosophy, and spreads through the centuries and millennia throughout Europe and then in those cultures that had/have an exchange of ideas with the European culture. The systematic occupation with the concept ‘being’ the philosophers called and call ‘ontology’. See for this the article ‘Ontology’ in wkp-en: https://en.wikipedia.org/wiki/Ontology .
[2] On the subject of ‘perception’ and ‘memory’ there is a huge literature in various empirical disciplines. The most important may well be ‘biology’, ‘experimental pschology’ and ‘brain science’; these supplemented by philosophical ‘phenomenology’, and then combinations of these such as ‘neuro-psychology’ or ‘neuro-phenomenology’, etc. In addition there are countless other special disciplines such as ‘linguistics’ and ‘neuro-linguistics’.
[3] A question that remains open is how the concept of ‘consciousness’, which is common in everyday life, is to be placed in this context. Like the concept of ‘being’, the concept of ‘consciousness’ has been and still is very prominent in recent European philosophy, but it has also received strong attention in many empirical disciplines; especially in the field of tension between philosophical phenomenology, psychology and brain research, there is a long and intense debate about what is to be understood by ‘consciousness’. Currently (2023) there is no clear, universally accepted outcome of these discussions. Of the many available working hypotheses, the author of this text considers the connection to the empirical models of ‘current memory’ in close connection with the models of ‘perception’ to be the most comprehensible so far. In this context also the concept of the ‘unconscious’ would be easy to explain. For an overview see the entry ‘consciousness’ in wkp-en: https://en.wikipedia.org/wiki/Consciousness
[4] In everyday life we constantly experience that different people perceive the same real events differently, depending on which ‘mood’ they are in, which current needs they have at the moment, which ‘previous knowledge’ they have, and what their real position to the real situation is, to name just a few factors that can play a role.
[5] Classical examples for the lack of quality of memories have always been ‘testimonies’ to certain events. Testimonies almost never agree ‘1-to-1′, at best ‘structurally’, and even in this there can be ‘deviations’ of varying strength.
In the introduction of the main text it has been underlined that within a sustainable empirical theory it is not only necessary to widen the scope with a maximum of diversity, but at the same time it is also necessary to enable the capability for an optimal prediction about the ‘possible states of a possible future’.
the meaning machinery
In the text after this introduction it has been outlined that between human actors the most powerful tool for the clarification of the given situation — the NOW — is the everyday language with a ‘built in’ potential in every human actor for infinite meanings. This individual internal meaning space as part of the individual cognitive structure is equipped with an ‘abstract – concrete’ meaning structure with the ability to distinguish between ‘true’ and ‘not true’, and furthermore equipped with the ability to ‘play around’ with meanings in a ‘new way’.
COORDINATION
Thus every human actor can generate within his cognitive dimension some states or situations accompanied with potential new processes leading to new states. To share this ‘internal meanings’ with other brains to ‘compare’ properties of the ‘own’ thinking with properties of the thinking of ‘others’ the only chance is to communicate with other human actors mediated by the shared everyday language. If this communication is successful it arises the possibility to ‘coordinate’ the own thinking about states and possible actions with others. A ‘joint undertaking’ is becoming possible.
shared thinking
To simplify the process of communication it is possible, that a human actor does not ‘wait’ until some point in the future to communicate the content of the thinking, but even ‘while the thinking process is going on’ a human actor can ‘translate his thinking’ in language expressions which ‘fit the processed meanings’ as good as possible.Doing this another human actor can observe the language activity, can try to ‘understand’, and can try to ‘respond’ to the observations with his language expressions. Such an ‘interplay’ of expressions in the context of multiple thinking processes can show directly either a ‘congruence’ or a ‘difference’. This can help each participant in the communication to clarify the own thinking. At the same time an exchange of language expressions associated with possible meanings inside the different brains can ‘stimulate’ different kinds of memory and thinking processes and through this the space of shared meanings can be ‘enlarged’.
phenomenal space 1 and 2
Human actors with their ability to construct meaning spaces and the ability to share parts of the meaning space by language communication are embedded with their bodies in a ‘body-external environment’ usual called ‘external world’ or ‘nature’ associated with the property to be ‘real’.
Equipped with a body with multiple different kinds of ‘sensors’ some of the environmental properties can stimulate these sensors which in turn send neuronal signals to the embedded brain. The first stage of the ‘processing of sensor signals’ is usually called ‘perception’. Perception is not a passive 1-to-1 mapping of signals into the brain but it is already a highly sophisticated processing where the ‘raw signals’ of the sensors — which already are doing some processing on their own — are ‘transformed’ into more complex signals which the human actor in its perception does perceive as ‘features’, ‘properties’, ‘figures’, ‘patterns’ etc. which usually are called ‘phenomena’. They all together are called ‘phenomenal space’. In a ‘naive thinking’ this phenomenal space is taken ‘as the external world directly’. During life a human actor can learn — this must not happen! –, that the ‘phenomenal space’ is a ‘derived space’ triggered by an ‘assumed outside world’ which ’causes’ by its properties the sensors to react in a certain way. But the ‘actual nature’ of the outside world is not really known. Let us call the unknown outside world of properties ‘phenomenal space 1’ and the derived phenomenal space inside the body-brain ‘phenomenal space 2’.
TIMELY ORDERING
Due to the availability of the phenomenal space 2 the different human actors can try to ‘explore’ the ‘unknown assumed real world’ based on the available phenomena.
If one takes a wider look to the working of the brain of a human actor one can detect that the processing of the brain of the phenomenal space is using additional mechanisms:
The phenomenal space is organized in ‘time slices’ of a certain fixed duration. The ‘content’ of a time slice during the time window (t,t’) will be ‘overwritten’ during the next time slice (t’,t”) by those phenomena, which are then ‘actual’, which are then constituting the NOW. The phenomena from the time window before (t’,t”) can become ‘stored’ in some other parts of the brain usually called ‘memory’.
The ‘storing’ of phenomena in parts of the brain called ‘memory’ happens in a highly sophisticated way enabling ‘abstract structures’ with an ‘interface’ for ‘concrete properties’ typical for the phenomenal space, and which can become associated with other ‘content’ of the memory.
It is an astonishing ability of the memory to enable an ‘ordering’ of memory contents related to situations as having occurred ‘before’ or ‘after’ some other property. Therefore the ‘content of the memory’ can represent collections of ‘stored NOWs’, which can be ‘ordered’ in a ‘sequence of NOWs’, and thereby the ‘dimension of time’ appears as a ‘framing property’ of ‘remembered phenomena’.
Based on this capability to organize remembered phenomena in ‘sequences of states’ representing a so-called ‘timely order’ the brain can ‘operate’ on such sequences in various ways. It can e.g. ‘compare’ two states in such a sequence whether these are ‘the same’ or whether they are ‘different’. A difference points to a ‘change’ in the phenomenal space. Longer sequences — even including changes — can perhaps show up as ‘repetitions’ compared to ‘earlier’ sequences. Such ‘repeating sequences’ can perhaps represent a ‘pattern’ pointing to some ‘hidden factors’ responsible for the pattern.
formal representations [1]
Based on a rather sophisticated internal processing structure every human actor has the capability to compose language descriptions which can ‘represent’ with the aid of sets of language expressions different kinds of local situations. Every expression can represent some ‘meaning’ which is encoded in every human actor in an individual manner. Such a language encoding can partially becoming ‘standardized’ by shared language learning in typical everyday living situations. To that extend as language encodings (the assumed meaning) is shared between different human actors they can use this common meaning space to communicate their experience.
Based on the built-in property of abstract knowledge to have an interface to ‘more concrete’ meanings, which finally can be related to ‘concrete perceptual phenomena’ available in the sensual perceptions, every human actor can ‘check’ whether an actual meaning seems to have an ‘actual correspondence’ to some properties in the ‘real environment’. If this phenomenal setting in the phenomenal space 2 with a correspondence to the sensual perceptions is encoded in a language expression E then usually it is told that the ‘meaning of E’ is true; otherwise not.
Because the perceptual interface to an assumed real world is common to all human actors they can ‘synchronize’ their perceptions by sharing the related encoded language expressions.
If a group of human actors sharing a real situation agrees about a ‘set of language expressions’ in the sens that each expression is assumed to be ‘true’, then one can assume, that every expression ‘represents’ some encoded meanings which are related to the shared empirical situation, and therefore the expressions represent ‘properties of the assumed real world’. Such kinds of ‘meaning constructions’ can be further ‘supported’ by the usage of ‘standardized procedures’ called ‘measurement procedures’.
Under this assumption one can infer, that a ‘change in the realm of real world properties’ has to be encoded in a ‘new language expression’ associated with the ‘new real world properties’ and has to be included in the set of expressions describing an actual situation. At the same time it can happen, that an expression of the actual set of expressions is becoming ‘outdated’ because the properties, this expression has encoded, are gone. Thus, the overall ‘dynamics of a set of expressions representing an actual set of real world properties’ can be realized as follows:
Agree on a first set of expression to be a ‘true’ description of a given set of real world properties.
After an agreed period of time one has to check whether (i) the encoded meaning of an expression is gone or (ii) whether a new real world property has appeared which seems to be ‘important’ but is not yet encoded in a language expression of the set. Depending from this check either (i) one has to delete those expressions which are no longer ‘true’ or (ii) one has to introduce new expressions for the new real world properties.
In a strictly ‘observational approach’ the human actors are only observing the course of events after some — regular or spontaneous –time span, making their observations (‘measurements’) and compare these observations with their last ‘true description’ of the actual situation. Following this pattern of behavior they can deduce from the series of true descriptions <D1, D2, …, Dn> for every pair of descriptions (Di,Di+1) a ‘difference description’ as a ‘rule’ in the following way: (i) IF x is a subset of expressions in Di+1, which are not yet members of the set of expressions in Di, THEN ‘add’ these expressions to the set of expressions in Di. (ii) IF y is a subset of expressions in Di, which are no more members of the set of expressions in Di+1, THEN ‘delete’ these expressions from the set of expressions in Di. (iii) Construct a ‘condition-set’ of expressions as subset of Di, which has to be fulfilled to apply (i) and (ii).
Doing this for every pair of descriptions then one is getting a set of ‘change rules’ X which can be used, to ‘generate’ — starting with the first description D0 — all the follow-up descriptions only by ‘applying a change rule Xi‘ to the last generated description.
This first purely observational approach works, but every change rule Xi in this set of change rules X can be very ‘singular’ pointing to a true singularity in the mathematical sense, because there is not ‘common rule’ to predict this singularity.
It would be desirable to ‘dig into possible hidden factors’ which are responsible for the observed changes but they would allow to ‘reduce the number’ of individual change rules of X. But for such a ‘rule-compression’ there exists from the outset no usable knowledge. Such a reduction will only be possible if a certain amount of research work will be done hopefully to discover the hidden factors.
All the change rules which could be found through such observational processes can in the future be re-used to explore possible outcomes for selected situations.
COMMENTS
[1] For the final format of this section I have got important suggestions from René Thom by reading the introduction of his book “Structural Stability and Morphogenesis: An Outline of a General Theory of Models” (1972, 1989). See my review post HERE : https://www.uffmm.org/2022/08/22/rene-thom-structural-stability-and-morphogenesis-an-outline-of-a-general-theory-of-models-original-french-edition-1972-updated-by-the-author-and-translated-into-english-by-d-h-fowler-1989/
In a preceding post I have outline the concept of an empirical theory based on a text from Popper 1971. In his article Popper points to a minimal structure of what he is calling an empirical theory. A closer investigation of his texts reveals many questions which should be clarified for a more concrete application of his concept of an empirical theory.
In this post it will be attempted to elaborate the concept of an empirical theory more concretely from a theoretical point of view as well as from an application point of view.
A Minimal Concept of an Empirical Theory
Empirical Basis
As starting point as well as a reference for testing does Popper assume an ’empirical basis’. The question arises what this means.
In the texts examined so far from Popper this is not well described. Thus in this text some ‘assumptions/ hypotheses’ will be formulated to describe some framework which should be able to ‘explain’ what an empirical basis is and how it works.
Experts
Those, who usually are building theories, are scientists, are experts. For a general concept of an ’empirical theory’ it is assumed here that every citizen is a ‘natural expert’.
Environment
Natural experts are living in ‘natural environments’ as part of the planet earth, as part of the solar system, as part of the whole universe.
Language
Experts ‘cooperate’ by using some ‘common language’. Here the ‘English language’ is used; many hundreds of other languages are possible.
Shared Goal (Changes, Time, Measuring, Successive States)
For cooperation it is necessary to have a ‘shared goal’. A ‘goal’ is an ‘idea’ about a possible state in the ‘future’ which is ‘somehow different’ to the given actual situation. Such a future state can be approached by some ‘process’, a series of possible ‘states’, which usually are characterized by ‘changes’ manifested by ‘differences’ between successive states. The concept of a ‘process’, a ‘sequence of states’, implies some concept of ‘time’. And time needs a concept of ‘measuring time’. ‘Measuring’ means basically to ‘compare something to be measured’ (the target) with ‘some given standard’ (the measuring unit). Thus to measure the height of a body one can compare it with some object called a ‘meter’ and then one states that the target (the height of the body) is 1,8 times as large as the given standard (the meter object). In case of time it was during many thousand years customary to use the ‘cycles of the sun’ to define the concept (‘unit’) of a ‘day’ and a ‘night’. Based on this one could ‘count’ the days as one day, two days, etc. and one could introduce further units like a ‘week’ by defining ‘One week compares to seven days’, or ‘one month compares to 30 days’, etc. This reveals that one needs some more concepts like ‘counting’, and associated with this implicitly then the concept of a ‘number’ (like ‘1’, ‘2’, …, ’12’, …) . Later the measuring of time has been delegated to ‘time machines’ (called ‘clocks’) producing mechanically ‘time units’ and then one could be ‘more precise’. But having more than one clock generates the need for ‘synchronizing’ different clocks at different locations. This challenge continues until today. Having a time machine called ‘clock’ one can define a ‘state’ only by relating the state to an ‘agreed time window’ = (t1,t2), which allows the description of states in a successive timely order: the state in the time-window (t1,t2) is ‘before’ the time-window (t2,t3). Then one can try to describe the properties of a given natural environment correlated with a certain time-window, e.g. saying that the ‘observed’ height of a body in time-window w1 was 1.8 m, in a later time window w6 the height was still 1.8 m. In this case no changes could be observed. If one would have observed at w6 1.9 m, then a difference is occurring by comparing two successive states.
Example: A County
Here we will assume as an example for a natural environment a ‘county’ in Germany called ‘Main-Kinzig Kreis’ (‘Kreis’ = ‘county’), abbreviated ‘MKK’. We are interested in the ‘number of citizens’ which are living in this county during a certain time-window, here the year 2018 = (1.January 2018, 31.December 2018). According to the statistical office of the state of Hessen, to which the MKK county belongs, the number of citizens in the MKK during 2018 was ‘418.950’.(cf. [2])
Observing the Number of Citizens
One can ask in which sense the number ‘418.950’ can be understood as an ‘observation statement’? If we understand ‘observation’ as the everyday expression for ‘measuring’, then we are looking for a ‘procedure’ which allows us to ‘produce’ this number ‘418.950’ associated with the unit ‘number of citizens during a year’. As everybody can immediately realize no single person can simply observe all citizens of that county. To ‘count’ all citizens in the county one had to ‘travel’ to all places in the county where citizens are living and count every person. Such a travelling would need some time. This can easily need more than 40 years working 24 hours a day. Thus, this procedure would not work. A different approach could be to find citizens in every of the 24 cities in the MKK [1] to help in this counting-procedure. To manage this and enable some ‘quality’ for the counting, this could perhaps work. An interesting experiment. Here we ‘believe’ in the number of citizens delivered by the statistical office of the state of Hessen [2], but keeping some reservation for the question how ‘good’ this number really is. Thus our ‘observation statement’ would be: “In the year 2018 418.950 citizens have been counted in the MKK (according to the information of the statistical office of the state of Hessen)” This observation statement lacks a complete account of the procedure, how this counting really happened.
Concrete and Abstract Words
There are interesting details in this observation statement. In this observation statement we notice words like ‘citizen’ and ‘MKK’. To talk about ‘citizens’ is not a talk about some objects in the direct environment. What we can directly observe are concrete bodies which we have learned to ‘classify’ as ‘humans’, enriched for example with ‘properties’ like ‘man’, ‘woman’, ‘child’, ‘elderly person’, neighbor’ and the like. Bu to classify someone as a ‘citizen’ deserves knowledge about some official procedure of ‘registering as a citizen’ at a municipal administration recorded in some certified document. Thus the word ‘citizen’ has a ‘meaning’ which needs some ‘concrete procedure to get the needed information’. Thus ‘citizen’ is not a ‘simple word’ but a ‘more abstract word’ with regard to the associated meaning. The same holds for the word ‘MKK’ short for ‘Main-Kinzig Kreis’. At a first glance ‘MKK’ appears as a ‘name’ for some entity. But this entity cannot directly be observed too. One component of the ‘meaning’ of the name ‘MKK’ is a ‘real geographical region’, whose exact geographic extensions have been ‘measured’ by official institutions marked in an ‘official map’ of the state of Hessen. This region is associated with an official document of the state of Hessen telling, that this geographical region has to be understood s a ‘county’ with the name MKK. There exist more official documents defining what is meant with the word ‘county’. Thus the word ‘MKK’ has a rather complex meaning which to understand and to check, whether everything is ‘true’, isn’t easy. The author of this post is living in the MKK and he would not be able to tell all the details of the complete meaning of the name ‘MKK’.
First Lessons Learned
Thus one can learn from these first considerations, that we as citizens are living in a natural environment where we are using observation statements which are using words with potentially rather complex meanings, which to ‘check’ deserves some serious amount of clarification.
Conjectures – Hypotheses
Changes
The above text shows that ‘observations as such’ show nothing of interest. Different numbers of citizens in different years have no ‘message’. But as soon as one arranges the years in a ‘time line’ according to some ‘time model’ the scene is changing: if the numbers of two consecutive years are ‘different’ then this ‘difference in numbers’ can be interpreted as a ‘change’ in the environment, but only if one ‘assumes’ that the observed phenomena (the number of counted citizens) are associated with some real entities (the citizens) whose ‘quantity’ is ‘represented’ in these numbers.[5]
And again, the ‘difference between consecutive numbers’ in a time line cannot be observed or measured directly. It is a ‘second order property’ derived from given measurements in time. Such a 2nd order property presupposes a relationship between different observations: they ‘show up’ in the expressions (here numbers), but they are connected back in the light of the agreed ‘meaning’ to some ‘real entities’ with the property ‘overall quantity’ which can change in the ‘real setting’ of these real entities called ‘citizens’.
In the example of the MKK the statistical office of the state of Hessen computed a difference between two consecutive years which has been represented as a ‘growth factor’ of 0,4%. This means that the number of citizens in the year 2018 will increase until the year 2019 as follows: number-citizens(2019) = number-citizens(2018) + (number of citizens(2018) * growth-factor). This means number-citizens(2019) =418.950 + (418.950 * 0.004) = 418.950 + 1.675,8 = 420.625,8
Applying change repeatedly
If one could assume that the ‘growth rate’ would stay constant through the time then one could apply the growth rate again and again onto the actual number of citizens in the MKK every year. This would yield the following simple table:
Year
Number
Growth Rate
2018
418.950,00
,0040
2019
420.625,80
2020
422.308,30
2021
423.997,54
2022
425.693,53
2023
427.396,30
Table: Simplified description of the increase of the number of citizens in the Main-Kinzig county in Germany with an assumed growth rate of 0,4% per year.
As we know from reality an assumption of a fixed growth rate for complex dynamic systems is not very probable.
Theory
Continuing the previous considerations one has to ask the question, how the layout of a ‘complete empirical theory’ would look like?
As I commented in the preceding post about Popper’s 1971 article about ‘objective knowledge’ there exists today no one single accepted framework for a formalized empirical theory. Therefore I will stay here with a ‘bottom-up’ approach using elements taken from everyday reasoning.
What we have until now is the following:
Before the beginning of a theory building process one needs a group of experts being part of a natural environment using the samelanguage which share a common goal which they want to enable.
The assumed natural environment is assumed from the experts as being a ‘process’ of consecutive states in time. The ‘granularity’ of the process depends from the used ‘time model’.
As a starting point they collect a set of statements talking about those aspects of a ‘selected state’ at some time t which they are interested in.
This set of statements describes a set of ‘observable properties’ of the selected state which is understood as a ‘subset’ of the properties of the natural environment.
Every statement is understood by the experts as being ‘true’ in the sense, that the ‘known meaning’ of a statement has an ‘observable counterpart’ in the situation, which can be ‘confirmed’ by each expert.
For each pair of consecutive states it holds that the set of statements of each state can be ‘equal’ or ‘can show ‘differences’.
A ‘difference’ between sets of statements can be interpreted as pointing to a ‘change in the real environment’.[5]
Observed differences can be described by special statements called ‘change statements’ or simply ‘rules’.
A change statement has the format ‘IF a set of statements ST* is a subset of the statements ST of a given state S, THEN with probability p, a set of statements ST+ will be added to the actual state S and a set of statements ST- will be removed from the statements ST of a given state S. This will result in a new succeeding state S* with the representing statements ST – (ST-) + (ST+) depending from the assumed probability p.
The list of change statements is an ‘open set’ according to the assumption, that an actual state is only a ‘subset’ of the real environment.
Until now we have an assumed state S, an assumed goal V, and an open set of change statements X.
Applying change statements to a given state S will generate a new state S*. Thus the application of a subset X’ of the open set of change statements X onto a given state S will here be called ‘generating a new state by a procedure’. Such a state-generating-procedure can be understood as an ‘inference’ (like in logic) oder as a ‘simulation’ (like in engineering).[6]
To write this in a more condensed format we can introduce some signs —– S,V ⊩ ∑ X S‘ —– saying: If I have some state S and a goal V then the simulator ∑ will according to the change statements X generate a new state S’. In such a setting the newly generated state S’ can be understood as a ‘theorem’ which has been derived from the set of statements in the state S which are assumed to be ‘true’. And because the derived new state is assumed to happen in some ‘future’ ‘after’ the ‘actual state S’ this derived state can also be understood as a ‘forecast’.
Because the experts can change all the time all parts ‘at will’ such a ‘natural empirical theory’ is an ‘open entity’ living in an ongoing ‘communication process’.
Second Lessons Learned
It is interestingly to know that from the set of statements in state S, which are assumed to be empirically true, together with some change statements X, whose proposed changes are also assumed to be ‘true’, and which have some probability P in the domain [0,1], one can forecast a set of statements in the state S* which shall be true, with a certainty being dependent from the preceding probability P and the overall uncertainty of the whole natural environment.
Confirmation – Non-Confirmation
A Theory with Forecasts
Having reached the formulation of an ordinary empirical theory T with the ingredients <S,V,X,⊩ ∑> and the derivation conceptS,V ⊩ ∑ X S‘ it is possible to generate theorems as forecasts. A forecast here is not a single statement st* but a whole state S* consisting of a finite set of statements ST* which ‘designate’ according to the ‘agreed meaning’ a set of ‘intended properties’ which need a set of ‘occurring empirical properties’ which can be observed by the experts. These observations are usually associated with ‘agreed procedures of measurement’, which generate as results ‘observation statements’/ ‘measurement statements’.
Within Time
Experts which are cooperating by ‘building’ an ordinary empirical theory are themselves part of a process in time. Thus making observations in the time-window (t1,t2) they have a state S describing some aspects of the world at ‘that time’ (t1,t2). When they then derive a forecast S* with their theory this forecast describes — with some probability P — a ‘possible state of the natural environment’ which is assumed to happen in the ‘future’. The precision of the predicted time when the forecasted statements in S* should happen depends from the assumptions in S.
To ‘check’ the ‘validity’ of such a forecast it is necessary that the overall natural process reaches a ‘point in time’ — or a time window — indicated by the used ‘time model’, where the ‘actual point in time’ is measured by an agreed time machine (mechanical clock). Because there is no observable time without a time machine the classification of a certain situation S* being ‘now’ at the predicted point of time depends completely from the used time machine.[7]
Given this the following can happen: According to the used theory a certain set of statements ST* is predicted to be ‘true’ — with some probability — either ‘at some time in the future’ or in the time-window (t1,t2) or at a certain point in time t*.
Validating Forecasts
If one of these cases would ‘happen’ then the experts would have the statements ST* of their forecast and a real situation in their natural environment which enables observations ‘Obs’ which are ‘translated’ into appropriate ‘observation statements’ STObs. The experts with their predicted statements ST* know a learned agreed meaning M* of their predicted statements ST* as intended-properties M* of ST*. The experts have also learned how they relate the intended meaning M* to the meaning MObs from the observation statements STobs. If the observed meaning MObs ‘agrees sufficiently well’ with the intended meaning M* then the experts would agree in a statement, that the intended meaning M* is ‘fulfilled’/ ‘satisfied’/ ‘confirmed’ by the observed meaning MObs. If not then it would stated that it is ‘not fulfilled’/ ‘not satisfied’/ ‘not confirmed’.
The ‘sufficient fulfillment’ of the intended meaning M* of a set of statements ST* is usually translated in a statement like “The statements ST* are ‘true'”. In the case of ‘no fulfillment’ it is unclear: this can be interpreted as ‘being false’ or as ‘being unclear’: No clear case of ‘being true’ and no clear case of ‘being false’.
Forecasting the Number of Citizens
In the used simple example we have the MKK county with an observed number of citizens in 2018 with 418950. The simple theory used a change statement with a growth factor of 0.4% per year. This resulted in the forecast with the number 420.625 citizens for the year 2019.
If the newly counting of the number of citizens in the years 2019 would yield 420.625, then there would be a perfect match, which could be interpreted as a ‘confirmation’ saying that the forecasted statement and the observed statement are ‘equal’ and therefore the theory seems to match the natural environment through the time. One could even say that the theory is ‘true for the observed time’. Nothing would follow from this for the unknown future. Thus the ‘truth’ of the theory is not an ‘absolute’ truth but a truth ‘within defined limits’.
We know from experience that in the case of forecasting numbers of citizens for some region — here a county — it is usually not so clear as it has been shown in this example.
This begins with the process of counting. Because it is very expensive to count the citizens of all cities of a county this happens only about every 20 years. In between the statistical office is applying the method of ‘forecasting projection’.[9] The state statistical office collects every year ‘electronically’ the numbers of ‘birth’, ‘death’, ‘outflow’, and ‘inflow’ from the individual cities and modifies with these numbers the last real census. In the case of the state of Hessen this was the year 2011. The next census in Germany will happen May 2022.[10] For such a census the data will be collected directly from the registration offices from the cities supported by a control survey of 10% of the population.
Because there are data from the statistical office of the state of Hessen for June 2021 [8:p.9] with saying that the MKK county had 421 936 citizens at 30. June 2021 we can compare this number with the theory forecast for the year 2021 with 423 997. This shows a difference in the numbers. The theory forecast is ‘higher’ than the observed forecast. What does this mean?
Purely arithmetically the forecast is ‘wrong’. The responsible growth factor is too large. If one would ‘adjust’ it in a simplified linear way to ‘0.24%’ then the theory could get a forecast for 2021 with 421 973 (observed: 421 936), but then the forecast for 2019 would be 419 955 (instead of 420 625).
This shows at least the following aspects:
The empirical observations as such can vary ‘a little bit’. One had to clarify which degree of ‘variance’ is due to the method of measurement and therefore this variance should be taken into account for the evaluation of a theoretical forecast.
As mentioned by the statistical office [9] there are four ‘factors’ which influence the final number of citizens in a region: ‘birth’, ‘death’, ‘outflow’, and ‘inflow’. These factors can change in time. Under ‘normal conditions’ the birth-rate and the death-rate are rather ‘stable’, but in case of an epidemic situation or even war this can change a lot. Outflow and inflow are very dynamic depending from many factors. Thus this can influence the growth factor a lot and these factors are difficult to forecast.
Third lessons Learned
Evaluating the ‘relatedness’ of some forecast F of an empirical theory T to the observations O in a given real natural environment is not a ‘clear-cut’ case. The ‘precision’ of such a relatedness depends from many factors where each of these factors has some ‘fuzziness’. Nevertheless as experience shows it can work in a limited way. And, this ‘limited way’ is the maximum we can get. The most helpful contribution of an ‘ordinary empirical theory’ seems to be the forecast of ‘What will happen if we have a certain set of assumptions’. Using such a forecast in the process of the experts this can help to improve to get some ‘informed guesses’ for planning.
Forecast
The next post will show, how this concept of an ordinary empirical theory can be used by applying the oksimo paradigm to a concrete case. See HERE.
Comments
[1] Cities of the MKK-county: 24, see: https://www.wegweiser-kommune.de/kommunen/main-kinzig-kreis-lk
[3] Karl Popper, „A World of Propensities“,(1988) and „Towards an Evolutionary Theory of Knowledge“, (1989) in: Karl Popper, „A World of Propensities“, Thoemmes Press, Bristol, (1990, repr. 1995)
[4] Karl Popper, „All Life is Problem Solving“, original a lecture 1991 in German, the first tome published (in German) „Alles Leben ist Problemlösen“ (1994), then in the book „All Life is Problem Solving“, 1999, Routledge, Taylor & Francis Group, London – New York
[5] This points to the concept of ‘propensity’ which the late Popper has discussed in the papers [3] and [4].
[6] This concept of a ‘generator’ or an ‘inference’ reminds to the general concept of Popper and the main stream philosophy of a logical derivation concept where a ‘set of logical rules’ defines a ‘derivation concept’ which allows the ‘derivation/ inference’ of a statement s* as a ‘theorem’ from an assumed set of statements S assumed to be true.
[7] The clock-based time is in the real world correlated with certain constellations of the real universe, but this — as a whole — is ‘changing’!
[8] Hessisches Statistisches Landesamt, “Die Bevölkerung der hessischen Gemeinden am 30. Juni 2021. Fortschreibungsergebnisse Basis Zensus 09. Mai 2011″, Okt. 2021, Wiesbaden, URL: https://statistik.hessen.de/sites/statistik.hessen.de/files/AI2_AII_AIII_AV_21-1hj.pdf
[9] Method of the forward projection of the statistical office of the State of Hessen: “Bevölkerung: Die Bevölkerungszahlen sind Fortschreibungsergebnisse, die auf den bei der Zensuszählung 2011 ermittelten Bevölkerungszahlen basieren. Durch Auswertung von elektronisch übermittelten Daten für Geburten und Sterbefälle durch die Standesämter, sowie der Zu- und Fortzüge der Meldebehörden, werden diese nach einer bundeseinheitlichen Fortschreibungsmethode festgestellt. Die Zuordnung der Personen zur Bevölkerung einer Gemeinde erfolgt nach dem Hauptwohnungsprinzip (Bevölkerung am Ort der alleinigen oder der Hauptwohnung).”([8:p.2]
[10] Statistical Office state of Hessen, Next census 2022: https://statistik.hessen.de/zahlen-fakten/zensus/zensus-2022/zensus-2022-kurz-erklaert
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 assumeautomatically 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 Δextmust 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.
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 externalenvironment [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 comparepast (stored) states Spast with an actual state Snow. If 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 describeobjects 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 speakeris 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 — representationENVint 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 instanceinterprets 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 */
In this section several case studies will be presented. It will be shown, how the DAAI paradigm can be applied to many different contexts . Since the original version of the DAAI-Theory in Jan 18, 2020 the concept has been further developed centering around the concept of a Collective Man-Machine Intelligence [CM:MI] to address now any kinds of experts for any kind of simulation-based development, testing and gaming. Additionally the concept now can be associated with any kind of embedded algorithmic intelligence [EAI] (different to the mainstream concept ‘artificial intelligence’). The new concept can be used with every normal language; no need for any special programming language! Go back to the overall framework.
COLLECTION OF PAPERS
There exists only a loosely order between the different papers due to the character of this elaboration process: generally this is an experimental philosophical process. HMI Analysis applied for the CM:MI paradigm.
FROM DAAI to GCA. Turning Engineering into Generative Cultural Anthropology. This paper gives an outline how one can map the DAAI paradigm directly into the GCA paradigm (April-19,2020): case1-daai-gca-v1
A first GCA open research project [GCA-OR No.1]. This paper outlines a first open research project using the GCA. This will be the framework for the first implementations (May-5, 2020): GCAOR-v0-1
Engineering and Society. A Case Study for the DAAI Paradigm – Introduction. This paper illustrates important aspects of a cultural process looking to the acting actors where certain groups of people (experts of different kinds) can realize the generation, the exploration, and the testing of dynamical models as part of a surrounding society. Engineering is clearly not separated from society (April-9, 2020): case1-population-start-part0-v1
Bootstrapping some Citizens. This paper clarifies the set of general assumptions which can and which should be presupposed for every kind of a real world dynamical model (April-4, 2020): case1-population-start-v1-1
Hybrid Simulation Game Environment [HSGE]. This paper outlines the simulation environment by combing a usual web-conference tool with an interactive web-page by our own (23.May 2020): HSGE-v2 (May-5, 2020): HSGE-v0-1
The Observer-World Framework. This paper describes the foundations of any kind of observer-based modeling or theory construction.(July 16, 2020)
Last change: 23.February 2019 (continued the text)
Last change: 24.February 2019 (extended the text)
CONTEXT
In the overview of the AAI paradigm version 2 you can find this section dealing with the philosophical perspective of the AAI paradigm. Enjoy reading (or not, then send a comment :-)).
THE DAILY LIFE PERSPECTIVE
The perspective of Philosophy is rooted in the everyday life perspective. With our body we occur in a space with other bodies and objects; different features, properties are associated with the objects, different kinds of relations an changes from one state to another.
From the empirical sciences we have learned to see more details of the everyday life with regard to detailed structures of matter and biological life, with regard to the long history of the actual world, with regard to many interesting dynamics within the objects, within biological systems, as part of earth, the solar system and much more.
A certain aspect of the empirical view of the world is the fact, that some biological systems called ‘homo sapiens’, which emerged only some 300.000 years ago in Africa, show a special property usually called ‘consciousness’ combined with the ability to ‘communicate by symbolic languages’.
As we know today the consciousness is associated with the brain, which in turn is embedded in the body, which is further embedded in an environment.
Thus those ‘things’ about which we are ‘conscious’ are not ‘directly’ the objects and events of the surrounding real world but the ‘constructions of the brain’ based on actual external and internal sensor inputs as well as already collected ‘knowledge’. To qualify the ‘conscious things’ as ‘different’ from the assumed ‘real things’ ‘outside there’ it is common to speak of these brain-generated virtual things either as ‘qualia’ or — more often — as ‘phenomena’ which are different to the assumed possible real things somewhere ‘out there’.
PHILOSOPHY AS FIRST PERSON VIEW
‘Philosophy’ has many facets. One enters the scene if we are taking the insight into the general virtual character of our primary knowledge to be the primary and irreducible perspective of knowledge. Every other more special kind of knowledge is necessarily a subspace of this primary phenomenological knowledge.
There is already from the beginning a fundamental distinction possible in the realm of conscious phenomena (PH): there are phenomena which can be ‘generated’ by the consciousness ‘itself’ — mostly called ‘by will’ — and those which are occurring and disappearing without a direct influence of the consciousness, which are in a certain basic sense ‘given’ and ‘independent’, which are appearing and disappearing according to ‘their own’. It is common to call these independent phenomena ’empirical phenomena’ which represent a true subset of all phenomena: PH_emp ⊂ PH. Attention: These empirical phenomena’ are still ‘phenomena’, virtual entities generated by the brain inside the brain, not directly controllable ‘by will’.
There is a further basic distinction which differentiates the empirical phenomena into those PH_emp_bdy which are controlled by some processes in the body (being tired, being hungry, having pain, …) and those PH_emp_ext which are controlled by objects and events in the environment beyond the body (light, sounds, temperature, surfaces of objects, …). Both subsets of empirical phenomena are different: PH_emp_bdy ∩ PH_emp_ext = 0. Because phenomena usually are occurring associated with typical other phenomena there are ‘clusters’/ ‘pattern’ of phenomena which ‘represent’ possible events or states.
Modern empirical science has ‘refined’ the concept of an empirical phenomenon by introducing ‘standard objects’ which can be used to ‘compare’ some empirical phenomenon with such an empirical standard object. Thus even when the perception of two different observers possibly differs somehow with regard to a certain empirical phenomenon, the additional comparison with an ’empirical standard object’ which is the ‘same’ for both observers, enhances the quality, improves the precision of the perception of the empirical phenomena.
From these considerations we can derive the following informal definitions:
Something is ‘empirical‘ if it is the ‘real counterpart’ of a phenomenon which can be observed by other persons in my environment too.
Something is ‘standardized empirical‘ if it is empirical and can additionally be associated with a before introduced empirical standard object.
Something is ‘weak empirical‘ if it is the ‘real counterpart’ of a phenomenon which can potentially be observed by other persons in my body as causally correlated with the phenomenon.
Something is ‘cognitive‘ if it is the counterpart of a phenomenon which is not empirical in one of the meanings (1) – (3).
It is a common task within philosophy to analyze the space of the phenomena with regard to its structure as well as to its dynamics. Until today there exists not yet a complete accepted theory for this subject. This indicates that this seems to be some ‘hard’ task to do.
BRIDGING THE GAP BETWEEN BRAINS
As one can see in figure 1 a brain in a body is completely disconnected from the brain in another body. There is a real, deep ‘gap’ which has to be overcome if the two brains want to ‘coordinate’ their ‘planned actions’.
Luckily the emergence of homo sapiens with the new extended property of ‘consciousness’ was accompanied by another exciting property, the ability to ‘talk’. This ability enabled the creation of symbolic languages which can help two disconnected brains to have some exchange.
But ‘language’ does not consist of sounds or a ‘sequence of sounds’ only; the special power of a language is the further property that sequences of sounds can be associated with ‘something else’ which serves as the ‘meaning’ of these sounds. Thus we can use sounds to ‘talk about’ other things like objects, events, properties etc.
The single brain ‘knows’ about the relationship between some sounds and ‘something else’ because the brain is able to ‘generate relations’ between brain-structures for sounds and brain-structures for something else. These relations are some real connections in the brain. Therefore sounds can be related to ‘something else’ or certain objects, and events, objects etc. can become related to certain sounds. But these ‘meaning relations’ can only ‘bridge the gap’ to another brain if both brains are using the same ‘mapping’, the same ‘encoding’. This is only possible if the two brains with their bodies share a real world situation RW_S where the perceptions of the both brains are associated with the same parts of the real world between both bodies. If this is the case the perceptions P(RW_S) can become somehow ‘synchronized’ by the shared part of the real world which in turn is transformed in the brain structures P(RW_S) —> B_S which represent in the brain the stimulating aspects of the real world. These brain structures B_S can then be associated with some sound structures B_A written as a relation MEANING(B_S, B_A). Such a relation realizes an encoding which can be used for communication. Communication is using sound sequences exchanged between brains via the body and the air of an environment as ‘expressions’ which can be recognized as part of a learned encoding which enables the receiving brain to identify a possible meaning candidate.
DIFFERENT MODES TO EXPRESS MEANING
Following the evolution of communication one can distinguish four important modes of expressing meaning, which will be used in this AAI paradigm.
VISUAL ENCODING
A direct way to express the internal meaning structures of a brain is to use a ‘visual code’ which represents by some kinds of drawing the visual shapes of objects in the space, some attributes of shapes, which are common for all people who can ‘see’. Thus a picture and then a sequence of pictures like a comic or a story board can communicate simple ideas of situations, participating objects, persons and animals, showing changes in the arrangement of the shapes in the space.
Even with a simple visual code one can generate many sequences of situations which all together can ‘tell a story’. The basic elements are a presupposed ‘space’ with possible ‘objects’ in this space with different positions, sizes, relations and properties. One can even enhance these visual shapes with written expressions of a spoken language. The sequence of the pictures represents additionally some ‘timely order’. ‘Changes’ can be encoded by ‘differences’ between consecutive pictures.
FROM SPOKEN TO WRITTEN LANGUAGE EXPRESSIONS
Later in the evolution of language, much later, the homo sapiens has learned to translate the spoken language L_s in a written format L_w using signs for parts of words or even whole words. The possible meaning of these written expressions were no longer directly ‘visible’. The meaning was now only available for those people who had learned how these written expressions are associated with intended meanings encoded in the head of all language participants. Thus only hearing or reading a language expression would tell the reader either ‘nothing’ or some ‘possible meanings’ or a ‘definite meaning’.
If one has only the written expressions then one has to ‘know’ with which ‘meaning in the brain’ the expressions have to be associated. And what is very special with the written expressions compared to the pictorial expressions is the fact that the elements of the pictorial expressions are always very ‘concrete’ visual objects while the written expressions are ‘general’ expressions allowing many different concrete interpretations. Thus the expression ‘person’ can be used to be associated with many thousands different concrete objects; the same holds for the expression ‘road’, ‘moving’, ‘before’ and so on. Thus the written expressions are like ‘manufacturing instructions’ to search for possible meanings and configure these meanings to a ‘reasonable’ complex matter. And because written expressions are in general rather ‘abstract’/ ‘general’ which allow numerous possible concrete realizations they are very ‘economic’ because they use minimal expressions to built many complex meanings. Nevertheless the daily experience with spoken and written expressions shows that they are continuously candidates for false interpretations.
FORMAL MATHEMATICAL WRITTEN EXPRESSIONS
Besides the written expressions of everyday languages one can observe later in the history of written languages the steady development of a specialized version called ‘formal languages’ L_f with many different domains of application. Here I am focusing on the formal written languages which are used in mathematics as well as some pictorial elements to ‘visualize’ the intended ‘meaning’ of these formal mathematical expressions.
One prominent concept in mathematics is the concept of a ‘graph’. In the basic version there are only some ‘nodes’ (also called vertices) and some ‘edges’ connecting the nodes. Formally one can represent these edges as ‘pairs of nodes’. If N represents the set of nodes then N x N represents the set of all pairs of these nodes.
In a more specialized version the edges are ‘directed’ (like a ‘one way road’) and also can be ‘looped back’ to a node occurring ‘earlier’ in the graph. If such back-looping arrows occur a graph is called a ‘cyclic graph’.
If one wants to use such a graph to describe some ‘states of affairs’ with their possible ‘changes’ one can ‘interpret’ a ‘node’ as a state of affairs and an arrow as a change which turns one state of affairs S in a new one S’ which is minimally different to the old one.
As a state of affairs I understand here a ‘situation’ embedded in some ‘context’ presupposing some common ‘space’. The possible ‘changes’ represented by arrows presuppose some dimension of ‘time’. Thus if a node n’ is following a node n indicated by an arrow then the state of affairs represented by the node n’ is to interpret as following the state of affairs represented in the node n with regard to the presupposed time T ‘later’, or n < n’ with ‘<‘ as a symbol for a timely ordering relation.
The space can be any kind of a space. If one assumes as an example a 2-dimensional space configured as a grid –as shown in figure 6 — with two tokens at certain positions one can introduce a language to describe the ‘facts’ which constitute the state of affairs. In this example one needs ‘names for objects’, ‘properties of objects’ as well as ‘relations between objects’. A possible finite set of facts for situation 1 could be the following:
TOKEN(T1), BLACK(T1), POSITION(T1,1,1)
TOKEN(T2), WHITE(T2), POSITION(T2,2,1)
NEIGHBOR(T1,T2)
CELL(C1), POSITION(1,2), FREE(C1)
‘T1’, ‘T2’, as well as ‘C1’ are names of objects, ‘TOKEN’, ‘BACK’ etc. are names of properties, and ‘NEIGHBOR’ is a relation between objects. This results in the equation:
These facts describe the situation S1. If it is important to describe possible objects ‘external to the situation’ as important factors which can cause some changes then one can describe these objects as a set of facts in a separated ‘context’. In this example this could be two players which can move the black and white tokens and thereby causing a change of the situation. What is the situation and what belongs to a context is somewhat arbitrary. If one describes the agriculture of some region one usually would not count the planets and the atmosphere as part of this region but one knows that e.g. the sun can severely influence the situation in combination with the atmosphere.
Let us stay with a state of affairs with only a situation without a context. The state of affairs is a ‘state’. In the example shown in figure 6 I assume a ‘change’ caused by the insertion of a new black token at position (2,2). Written in the language of facts L_fact we get:
Thus the new state S2 is generated out of the old state S1 by unifying S1 with the set of new facts: S2 = S1 ∪ {TOKEN(T3), BLACK(T3), POSITION(2,2), NEIGHBOR(T3,T2)}. All the other facts of S1 are still ‘valid’. In a more general manner one can introduce a change-expression with the following format:
This can be read as follows: The follow-up state S2 is generated out of the state S1 by adding to the state S1 the set of facts { … }.
This layout of a change expression can also be used if some facts have to be modified or removed from a state. If for instance by some reason the white token should be removed from the situation one could write:
These simple examples demonstrate another fact: while facts about objects and their properties are independent from each other do relational facts depend from the state of their object facts. The relation of neighborhood e.g. depends from the participating neighbors. If — as in the example above — the object token T2 disappears then the relation ‘NEIGHBOR(T1,T2)’ no longer holds. This points to a hierarchy of dependencies with the ‘basic facts’ at the ‘root’ of a situation and all the other facts ‘above’ basic facts or ‘higher’ depending from the basic facts. Thus ‘higher order’ facts should be added only for the actual state and have to be ‘re-computed’ for every follow-up state anew.
If one would specify a context for state S1 saying that there are two players and one allows for each player actions like ‘move’, ‘insert’ or ‘delete’ then one could make the change from state S1 to state S2 more precise. Assuming the following facts for the context:
PLAYER(PB1), PLAYER(PW1), HAS-THE-TURN(PB1)
In that case one could enhance the change statement in the following way:
This would read as follows: given state S1 the player PB1 inserts a black token at position (2,2); this yields a new state S2.
With or without a specified context but with regard to a set of possible change statements it can be — which is the usual case — that there is more than one option what can be changed. Some of the main types of changes are the following ones:
RANDOM
NOT RANDOM, which can be specified as follows:
With PROBABILITIES (classical, quantum probability, …)
DETERMINISTIC
Furthermore, if the causing object is an actor which can adapt structurally or even learn locally then this actor can appear in some time period like a deterministic system, in different collected time periods as an ‘oscillating system’ with different behavior, or even as a random system with changing probabilities. This make the forecast of systems with adaptive and/ or learning systems rather difficult.
Another aspect results from the fact that there can be states either with one actor which can cause more than one action in parallel or a state with multiple actors which can act simultaneously. In both cases the resulting total change has eventually to be ‘filtered’ through some additional rules telling what is ‘possible’ in a state and what not. Thus if in the example of figure 6 both player want to insert a token at position (2,2) simultaneously then either the rules of the game would forbid such a simultaneous action or — like in a computer game — simultaneous actions are allowed but the ‘geometry of a 2-dimensional space’ would not allow that two different tokens are at the same position.
Another aspect of change is the dimension of time. If the time dimension is not explicitly specified then a change from some state S_i to a state S_j does only mark the follow up state S_j as later. There is no specific ‘metric’ of time. If instead a certain ‘clock’ is specified then all changes have to be aligned with this ‘overall clock’. Then one can specify at what ‘point of time t’ the change will begin and at what point of time t*’ the change will be ended. If there is more than one change specified then these different changes can have different timings.
THIRD PERSON VIEW
Up until now the point of view describing a state and the possible changes of states is done in the so-called 3rd-person view: what can a person perceive if it is part of a situation and is looking into the situation. It is explicitly assumed that such a person can perceive only the ‘surface’ of objects, including all kinds of actors. Thus if a driver of a car stears his car in a certain direction than the ‘observing person’ can see what happens, but can not ‘look into’ the driver ‘why’ he is steering in this way or ‘what he is planning next’.
A 3rd-person view is assumed to be the ‘normal mode of observation’ and it is the normal mode of empirical science.
Nevertheless there are situations where one wants to ‘understand’ a bit more ‘what is going on in a system’. Thus a biologist can be interested to understand what mechanisms ‘inside a plant’ are responsible for the growth of a plant or for some kinds of plant-disfunctions. There are similar cases for to understand the behavior of animals and men. For instance it is an interesting question what kinds of ‘processes’ are in an animal available to ‘navigate’ in the environment across distances. Even if the biologist can look ‘into the body’, even ‘into the brain’, the cells as such do not tell a sufficient story. One has to understand the ‘functions’ which are enabled by the billions of cells, these functions are complex relations associated with certain ‘structures’ and certain ‘signals’. For this it is necessary to construct an explicit formal (mathematical) model/ theory representing all the necessary signals and relations which can be used to ‘explain’ the obsrvable behavior and which ‘explains’ the behavior of the billions of cells enabling such a behavior.
In a simpler, ‘relaxed’ kind of modeling one would not take into account the properties and behavior of the ‘real cells’ but one would limit the scope to build a formal model which suffices to explain the oservable behavior.
This kind of approach to set up models of possible ‘internal’ (as such hidden) processes of an actor can extend the 3rd-person view substantially. These models are called in this text ‘actor models (AM)’.
HIDDEN WORLD PROCESSES
In this text all reported 3rd-person observations are called ‘actor story’, independent whether they are done in a pictorial or a textual mode.
As has been pointed out such actor stories are somewhat ‘limited’ in what they can describe.
It is possible to extend such an actor story (AS) by several actor models (AM).
An actor story defines the situations in which an actor can occur. This includes all kinds of stimuli which can trigger the possible senses of the actor as well as all kinds of actions an actor can apply to a situation.
The actor model of such an actor has to enable the actor to handle all these assumed stimuli as well as all these actions in the expected way.
While the actor story can be checked whether it is describing a process in an empirical ‘sound’ way, the actor models are either ‘purely theoretical’ but ‘behavioral sound’ or they are also empirically sound with regard to the body of a biological or a technological system.
A serious challenge is the occurrence of adaptiv or/ and locally learning systems. While the actor story is a finite description of possible states and changes, adaptiv or/ and locally learning systeme can change their behavior while ‘living’ in the actor story. These changes in the behavior can not completely be ‘foreseen’!
COGNITIVE EXPERT PROCESSES
According to the preceding considerations a homo sapiens as a biological system has besides many properties at least a consciousness and the ability to talk and by this to communicate with symbolic languages.
Looking to basic modes of an actor story (AS) one can infer some basic concepts inherently present in the communication.
Without having an explicit model of the internal processes in a homo sapiens system one can infer some basic properties from the communicative acts:
Speaker and hearer presuppose a space within which objects with properties can occur.
Changes can happen which presuppose some timely ordering.
There is a disctinction between concrete things and abstract concepts which correspond to many concrete things.
There is an implicit hierarchy of concepts starting with concrete objects at the ‘root level’ given as occurence in a concrete situation. Other concepts of ‘higher levels’ refer to concepts of lower levels.
There are different kinds of relations between objects on different conceptual levels.
The usage of language expressions presupposes structures which can be associated with the expressions as their ‘meanings’. The mapping between expressions and their meaning has to be learned by each actor separately, but in cooperation with all the other actors, with which the actor wants to share his meanings.
It is assume that all the processes which enable the generation of concepts, concept hierarchies, relations, meaning relations etc. are unconscious! In the consciousness one can use parts of the unconscious structures and processes under strictly limited conditions.
To ‘learn’ dedicated matters and to be ‘critical’ about the quality of what one is learnig requires some disciplin, some learning methods, and a ‘learning-friendly’ environment. There is no guaranteed method of success.
There are lots of unconscious processes which can influence understanding, learning, planning, decisions etc. and which until today are not yet sufficiently cleared up.
An overview to the enhanced AAI theory version 2 you can find here. In this post we talk about the special topic how the actor story (AS) can be used for a modeling of the real world (RW).
AS AND REAL WORLD MODELING
In the preceding post you find a rough description how an actor story can be generated challenged by a problem P. Here I shall address the question, how this procedure can be used to model certain aspects of the real world and not some abstract ideas only.
There are two main elements of the actor story which can be related to the real world: (i) The start state of the actor story and the list of possible change expressions.
FACTS
A start state is a finite set of facts which in turn are — in the case of the mathematical language — constituted by names of objects associated with properties or relations. Primarily the possible meaning of these expressions is located in the cognitive structures of the actors. These cognitive structures are as such not empirical entities and are partially available in a state called consciousness. If some element of meaning is conscious andsimultaneously part of the inter-subjective space between different actors in a way that all participating actors can perceive these elements, then these elements are called empirical by everyday experience, if these facts can be decided between the participants of the situation. If there exist further explicit measurement procedures associating an inter-subjective property with inter-subjective measurement data then these elements are called genuineempirical data.
Thus the collection of facts constituting a state of an actor story can be realized as a set of empirical facts, at least in the format of empirical by everyday experience.
CHANGES
While a state represents only static facts, one needs an additional element to be able to model the dynamic aspect of the real world. This is realized by change expressions X.
The general idea of a change is that at least one fact f of an actual state (= NOW), is changed either by complete disappearance or by changing some of its properties or by the creation of a new fact f1. An object called ‘B1’ with the property being ‘red’ — written as ‘RED(B1)’ — perhaps changes its property from being ‘red’ to become ‘blue’ — written as ‘BLUE(B1)’ –. Then the set of facts of the actual state S0= {RED(B1)} will change to a successor state S1={BLUE(B1)}. In this case the old fact ‘RED(B1)’ has been deleted and the new fact ‘BLUE(B1)’ has been created. Another example: the object ‘B1’ has also a ‘weight’ measured in kg which changes too. Then the actual state was S0={RED(B1), WEIGHT(B1,kg,2.4)} and this state changed to the successor state S1= {BLUE(B1), WEIGHT(B1,kg,3.4)}.
The possible cause of a change can be either an object or the ‘whole state‘ representing the world.
The mapping from a given state s into a successor state s’ by subtracting facts f- and joining facts f+ is here called an action: S –> S-(f-) u (f+) or action(s) = s’ = s-(f-) u (f+) with s , s’ in S
Because an action has an actor as a carrier one can write action: S x A –> S-(f-) u (f+) or action_a(s) = s’.
The defining properties of such an action are given in the sets of facts to be deleted — written as ‘d:{f-}’ — and the sets of facts to be created — written ‘c:{f+}’ –.
A full change expression amounts then to the following format: <s,s’, obj-name, action-name, d:{…}, c:{…}>.
But this is not yet the whole story. A change can be deterministic or indeterministic.
The deterministic change is cause by a deterministic actor or by a deterministic world.
The indeterministic change can have several formats:e.g. classical probability or quantum-like probability or the an actor as cause, whose behavior is not completely deterministic.
Additionally there can be interactions between different objects which can cause a change and these changes happen in parallel, simultaneously. Depending from the assumed environment (= world) and some laws describing the behavior of this world it can happen, that different local actions can hinder each other or change the effect of the changes.
Independent of the different kinds of changes it can be required that all used change-expressions should be of that kind that one can state that they are empirical by everyday experience.
TIME
And there is even more to tell. A change has in everyday life a duration measured with certain time units generated by a technical device called a clock.
To improve the empirical precision of change expressions one has to add the duration of the change between the actual state s and the final state s’ showing all the deletes (f-) and creates (f+) which are caused by this change-expression. This can only be done if a standard clock is included in the facts represented by the actual time stamp of this clock. Thus with regard to such a standard time one can realize a change with duration (t,t’) exactly in coherence with the standard time. A special case is given when a change-expression describes the effects of its actions in a distributed manner by giving more than one time point (t,t1, …, tn) and associating different deletes and creates with different points of time. Those distributed effects can make an actor story rather complex and difficult to understand by human brains.
An overview to the enhanced AAI theory version 2 you can find here. In this post we talk about the generation of the actor story (AS).
ACTOR STORY
To get from the problem P to an improved configuration S measured by some expectation E needs a process characterized by a set of necessary states Q which are connected by necessary changes X. Such a process can be described with the aid of an actor story AS.
The target of an actor story (AS) is a full specification of all identified necessary tasks T which lead from a start state q* to a goal state q+, including all possible and necessary changes X between the different states M.
A state is here considered as a finite set of facts (F) which are structured as an expression from some language L distinguishing names of objects (like ‘D1’, ‘Un1’, …) as well as properties of objects (like ‘being open’, ‘being green’, …) or relations between objects (like ‘the user stands before the door’). There can also e a ‘negation’ like ‘the door is not open’. Thus a collection of facts like ‘There is a door D1’ and ‘The door D1 is open’ can represent a state.
Changes from one state q to another successor state q’ are described by the object whose action deletes previous facts or creates new facts.
In this approach at least three different modes of an actor story will be distinguished:
A textual mode generating a Textual Actor Story (TAS): In a textual mode a text in some everyday language (e.g. in English) describes the states and changes in plain English. Because in the case of a written text the meaning of the symbols is hidden in the heads of the writers it can be of help to parallelize the written text with the pictorial mode.
A pictorial mode generating a Pictorial Actor Story (PAS). In a pictorial mode the drawings represent the main objects with their properties and relations in an explicit visual way (like a Comic Strip). The drawings can be enhanced by fragments of texts.
A mathematical mode generating a Mathematical Actor Story (MAS): this can be done either (i) by a pictorial graph with nodes and edges as arrows associated with formal expressions or (ii) by a complete formal structure without any pictorial elements.
For every mode it has to be shown how an AAI expert can generate an actor story out of the virtual cognitive world of his brain and how it is possible to decide the empirical soundness of the actor story.
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