AAI THEORY V2 – AS –VIRTUAL MEANING AND AS

eJournal: uffmm.org,
ISSN 2567-6458, 29.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last Change: 1.February 2019 (Corrections)

— Outdated —

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the special topic of the virtual meaning and the actor story.

VIRTUAL MEANING AND ACTOR STORY

  1. In a textual actor story (TAS) using the symbolic expressions L0 of some everyday language one can describe a state with a finite set of facts which should be decidable ‘in principle’ when related to the supposed external empirical environment of the problem P. Thus the constraint of ‘operational decidability‘ with regard to an empirical external environment imposes some constraint of the kinds of symbolic expressions which can be used. If there is more than only one state (which is the usual case) then one has to provide a list of ‘possible changes‘. Each change is described with  a symbolic expression L0x. The content of a change is at least one fact which will change between the ‘given’ state and the ‘succeeding’ state. Thus the virtual meaning of an actor must enable the actor to distinguish between a ‘given state’ q_now  and a possible ‘succeeding state’ q_next. There can be more than one possible change with regard to a given state q_now. Thus a textual actor story (TAS) is a set of states connected by changes, all represented as finite collections of symbolic expressions.
  2. In a pictorial actor story (PAS) using the graphical  expressions Lg of some everyday pictorial langue one can describe a state with a finite set of facts realized as pictures of objects, properties as well as relations between these objects.  The graphs of the objects can be enhanced by graphs including symbolic expressions L0  of some everyday language.  Again it should be   decidable ‘in principle’ whether these pictorial facts can be  related to the suppose external empirical environment of the problem P. Thus the constraint of ‘operational decidability’ with regard to an empirical external environment imposes some constraint of the kinds of symbolic expressions which can be used. If there is more than only one state (which is the usual case) then one has to provide a list of ‘possible changes’. Each change is described with  an   expression Lgx. The content of a change is at least one fact which will change between the ‘given’ state and an ‘succeeding’ state. Thus the virtual meaning of an actor must enable the actor to distinguish between a ‘given state’ q_now  and a possible ‘succeeding state’ q_next. There can be more than one possible change with regard to a given state q_now. Thus a pictorial actor story (TAS) is a set of states connected by changes, all represented as finite collections of graphical  expressions.
  3. In the case of a mathematical actor story (MAS) one has to distinguish two cases: (i) a complete formal description or (ii) a graphical presentation enhanced with symbolic expressions.
  4. In case (i) it is similar to the textual mode but replacing the symbolic expressions L0 of  some everyday   langue with the symbolic expressions Lm of some mathematical language. In this book we are using predicate logic syntax with a new semantics. In case (ii) one describes the  actor story as a mathematical directed graph. The nodes (vertices) of the graph are understood as ‘states’ and the arrows connecting the nodes are  understood as changes. A node representing a state can be attached to a finite set   of facts, where a fact is a symbolic expression Lm  representing  objects, properties as well as relations between these objects.   Again it should be   decidable ‘in principle’ whether these facts  can be  related to the suppose external empirical environment of the problem P. Thus the constraint of ‘operational decidability’ with regard to an empirical external environment imposes some constraint of the kinds of symbolic expressions which can be used. If there is more than only one state (which is the usual case) then one has to use arrows which are labeled by symbolic change expressions Lmx.    The content of a change is at least one fact which will change between the ‘given’ state and an ‘succeeding’ state. Thus the virtual meaning of an actor must enable the actor to distinguish between a ‘given state’ q_now  and a possible ‘succeeding state’ q_next. There can be more than one possible change with regard to a given state q_now.
  5. If the complete actor story is given, then there is no need for the additional change expressions LX because one can infer the changes from the  pairs of the succeeding states directly. But if one wants to ‘generate’ an actor story beginning with the start state then one needs the list of change expressions.

AAI THEORY V2 – AS – MEANING: REAL AND VIRTUAL

eJournal: uffmm.org,
ISSN 2567-6458, 29.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

— Outdated —

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about  the special topic of the meaning of (symbolic) expressions.

MEANING: REAL AND VIRTUAL

  1. In semiotic terminology  the ‘meaning‘ of a symbolic expression corresponds to the image of the mapping from symbolic expressions (L) into something else (non-L). This mapping is located in that system which is using this mapping. We can call this system a ‘semiotic system‘.
  2. For the generation of an actor story we assume that the AAI experts as well as all the other actors collaborating with the AAI actors are input-output systems with changeable internal states (IS) as well as a behavior function (phi), written as phi: I x IS —> IS x O.
  3. These actors are embedded in an empirical environment (ENV) which is continuously changing.
  4. Parts of the environment can interact with the actors by inducing physical state-changes in parts of the actors (Stimuli (S), Input, (I)) as well as receiving physical responses from the actors (Responses (R), output (O)) which change parts of the environmental states.
  5. Interpreting these actors as ‘semiotic systems’ implies that the actors can receive as input symbolic expressions (L) as well as non-symbolic events and they can output symbolic expressions (L) as well as some non-symbolic events (non-L). Furthermore the mapping from symbolic expressions into something else is assumed to happen ‘inside‘ the system.
  6. From a 3rd-person view one can distinguish the empirical environment external to the actor as well as the empirical states ‘inside’ the system (typically investigated by Physiology with many sub-disciplines).
  7. The internal states on the cellular level have a small subset called ‘brain’ (less than 1% of all cellular elements).  A  subset of the brain cells is enabling what in a 1st person view is called ‘consciousness‘.  The ‘content’ of the consciousness consists of ‘phenomena‘ which are not ’empirical’ in the usual sense of ’empirical’.  Using the consciousness as point of reference everything else of the actor which is not part of the conscious is ‘not conscious‘ or ‘unconscious‘. The ‘unconsciousness‘ is then the set of all non-conscious states of the actor (which means in the biological case of human sapiens more than 99% of all body states).
  8. As empirical sciences have revealed there exist functional relations between empirical states of the external environment (S_emp) and the set of externally caused internal  unconscious input states of the actor (IS_emp_uc).
  9. The internally caused unconscious input states (IS_emp_uc) are further processed and mapped in a variety of internal unconscious states (IS_emp_uc_abstr), which are more ‘general’ as the original input states. Thus subsets of internally cause unconscious  internal states IS_emp_uc  can be elements of the more abstract internal states IS_emp_uc_abstr.
  10. These internal unconscious states are part of ‘networks‘ and parts of different kinds of ‘hierarchies‘.
  11. There are many different kinds of internal operations working on these internal structures including the input states.
  12. Parts of the internal structures can function as ‘meaning‘ (M) for other parts of internal structures which function as ‘symbolic expressions‘ (L). Symbolic expressions together with the meaning constituting elements can be used from an actor (seen as a semiotic system) as a ‘symbolic language‘ whose observable part are the ‘symbols’ (written, spoken, gestures, …) and whose non-observable part is the mapping relation (encoding) from symbols into the internal meaning elements.
  13. The primary meaning of a language is therefore a ‘virtual world of states inside the actor‘ compared to the ‘external empirical world‘. Parts of the virtual meaning world can correspond to parts of the empirical world outside. To control such an important relationship one needs commonly defined empirical measurement procedures (MP) which are producing external empirical events which can be repeatedly perceived by a population of actors, which can compare these processes and events with their 1st person conscious phenomena (PH). If it is possible for an actor (an observer) to identify those phenomena which correspond to the external measurement events than it is possible (in principle) to define that subset of Phenomena (PH_emp) which are phenomena but are correlated with events in the external empirical world.  Usually those phenomena which correspond to empirical events external PH_emp are a true subset of the set of all possible Phenomena, written as PH_emp ⊂ PH.
  14. While the empirical phenomena PH_emp are ‘concrete‘ phenomena are the non-empirical phenomena PH_abs = PH-PH_emp ‘abstract‘ in the sense that an empirical phenomenon p_emp can be an element of a non-empirical phenomenon p_abs if p_emp is not new.
  15. While the virtual meaning of a symbolic language is realized by abstract structures which can be ‘cited’ in the consciousness as p_abs,  the empirical meaning   instead occurs as concrete structures which can be ‘cited’ by the consciousness.
  16. All meaning elements can occur as part of a virtual spatial structure (VR) and as part of a virtual timely structure (VT).
  17. There is no 1-to-1 mapping from the spatial and timely structures of the external empirical world into the virtual internal world of meanings.
  18. If it is possible to correlate virtual meaning structures with external empirical structures we call this ’empirical soundness’ or ’empirical truth’.

AAI THEORY V2 – Actor Story (AS)

eJournal: uffmm.org,
ISSN 2567-6458, 28.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

— Outdated —

CONTEXT

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.

  1. 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.
  2. 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.
  3. Changes from one state q to another successor state q’ are described by the object whose action deletes previous facts or creates new facts.
  4. In this approach at least three different modes of an actor story will be distinguished:
    1. 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.
    2. 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.
    3. 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.
    4. 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.

 

AAI THEORY V2 –EPISTEMOLOGY OF THE AAI-EXPERTS

eJournal: uffmm.org,
ISSN 2567-6458, 26.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the fourth chapter dealing with the epistemology of actors within an AAI analysis process.

EPISTEMOLOGY AND THE EMPIRICAL SCIENCES

Epistemology is a sub-discipline of general philosophy. While a special discipline in empirical science is defined by a certain sub-set of the real world RW  by empirical measurement methods generating empirical data which can be interpreted by a formalized theory,  philosophy  is not restricted to a sub-field of the real world. This is important because an empirical discipline has no methods to define itself.  Chemistry e.g. can define by which kinds of measurement it is gaining empirical data   and it can offer different kinds of formal theories to interpret these data including inferences to forecast certain reactions given certain configurations of matters, but chemistry is not able  to explain the way how a chemist is thinking, how the language works which a chemist is using etc. Thus empirical science presupposes a general framework of bodies, sensors, brains, languages etc. to be able to do a very specialized  — but as such highly important — job. One can define ‘philosophy’ then as that kind of activity which tries to clarify all these  conditions which are necessary to do science as well as how cognition works in the general case.

Given this one can imagine that philosophy is in principle a nearly ‘infinite’ task. To get not lost in this conceptual infinity it is recommended to start with concrete processes of communications which are oriented to generate those kinds of texts which can be shown as ‘related to parts of the empirical world’ in a decidable way. This kind of texts   is here called ’empirically sound’ or ’empirically true’. It is to suppose that there will be texts for which it seems to be clear that they are empirically sound, others will appear ‘fuzzy’ for such a criterion, others even will appear without any direct relation to empirical soundness.

In empirical sciences one is using so-called empirical measurement procedures as benchmarks to decided whether one has empirical data or not, and it is commonly assumed that every ‘normal observer’ can use these data as every other ‘normal observer’. But because individual, single data have nearly no meaning on their own one needs relations, sets of relations (models) and even more complete theories, to integrate the data in a context, which allows some interpretation and some inferences for forecasting. But these relations, models, or theories can not directly be inferred from the real world. They have to be created by the observers as ‘working hypotheses’ which can fit with the data or not. And these constructions are grounded in  highly complex cognitive processes which follow their own built-in rules and which are mostly not conscious. ‘Cognitive processes’ in biological systems, especially in human person, are completely generated by a brain and constitute therefore a ‘virtual world’ on their own.  This cognitive virtual world  is not the result of a 1-to-1 mapping from the real world into the brain states.  This becomes important in that moment where the brain is mapping this virtual cognitive world into some symbolic language L. While the symbols of a language (sounds or written signs or …) as such have no meaning the brain enables a ‘coding’, a ‘mapping’ from symbolic expressions into different states of the brain. In the light’ of such encodings the symbolic expressions have some meaning.  Besides the fact that different observers can have different encodings it is always an open question whether the encoded meaning of the virtual cognitive space has something to do with some part of the empirical reality. Empirical data generated by empirical measurement procedures can help to coordinate the virtual cognitive states of different observers with each other, but this coordination is not an automatic process. Empirically sound language expressions are difficult to get and therefore of a high value for the survival of mankind. To generate empirically sound formal theories is even more demanding and until today there exists no commonly accepted concept of the right format of an empirically sound theory. In an era which calls itself  ‘scientific’ this is a very strange fact.

EPISTEMOLOGY OF THE AAI-EXPERTS

Applying these general considerations to the AAI experts trying to construct an actor story to describe at least one possible path from a start state to a goal state, one can pick up the different languages the AAI experts are using and asking back under which conditions these languages have some ‘meaning’ and under which   conditions these meanings can be called ’empirically sound’?

In this book three different ‘modes’ of an actor story will be distinguished:

  1. A textual mode using some ordinary everyday language, thus using spoken language (stored in an audio file) or written language as a text.
  2. A pictorial mode using a ‘language of pictures’, possibly enhanced by fragments of texts.
  3. A mathematical mode using graphical presentations of ‘graphs’ enhanced by symbolic expressions (text) and symbolic expressions only.

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 decided the empirical soundness of the actor story.

 

 

AAI THEORY V2 –TOP-DOWN OR BOTTOM-UP?

eJournal: uffmm.org,
ISSN 2567-6458, 26.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last Change: 27.February 2019

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about  two different strategies how to proceed in the AAI analysis.

TOP-DOWN OR BOTTOM-UP?

The elaboration of an actor story AS   happens generally during a process driven by some actors, which communicate with each other and the environment. This can be done in various ways. Here we consider two main cases:

  1. Top-down: There exists a group of experts EXPs which will analyze a possible solution, will test these, and then will propose these as a solution for others. During this process they mainly communicate only with the  stakeholder of the problem (and probably with experts from other departments).
  2. Bottom-up: There exists a group of experts EXPs too but additionally there exists a group of customers CTMs which are also the stakeholder of the process and which will be guided by the experts to use their own experience to find a possible solution.

In reality  there can be many forms of collaboration which are mixing these two idealized cases. The top-down paradigm is very common although it produces many problems, especially in communal projects. A bottom-up process including the topic of ‘participation’ in communities and cities is today highly demanded, but not well specified and not a common practice.

In this book  the  bottom-up paradigm will be discussed explicitly.  This requires that the AAI experts collaborate from the beginning with a group of common users from the application domain. To do this they will (i) extract the knowledge which is distributed in the different users, then (ii) they will start some modeling from these different facts to (iii) enable some basic simulations. These simple simulations (iv) will be enhanced to   interactive simulations which allow serious gaming either (iv.a) to test the model or to enable the users (iv.b) to learn the space of possible states. The test case will (v) generate some data which can be used to evaluate the model with regard to pre-defined goals. Depending from these findings (vi) one can try to improve the model further.

EXAMPLE

The mayor of a city has the identified problem P that there exists a certain road which has a to high load of traffic. He wants to find a new configuration S which minimizes this problem without creating a new problem P’.

He decides to attack this problem not by delegating it to a group of experts only but to a group of experts collaborating with all the citizens which think to be affected by this problem and a possible solution. Thus the mayor opts for a bottom-up approach. This poses the challenge to find a procedure which enables the inclusion of the citizens in the overall process.

 

 

AAI THEORY V2 – DEFINING THE CONTEXT

eJournal: uffmm.org,
ISSN 2567-6458, 24.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the second chapter where you have to define the context of the problem, which should be analyzed.

DEFINING THE CONTEXT OF PROBLEM P

  1. A defined problem P identifies at least one property associated with  a configuration which has a lower level x than a value y inferred by an accepted standard E.
  2. The property P is always part of some environment ENV which interacts with the problem P.
  3. To approach an improved configuration S measured by  some standard E starting with a  problem P one  needs a process characterized by a set of necessary states Q which are connected by necessary changes X.
  4. Such a process can be described by an actor story AS.
  5. All properties which belong to the whole actor story and therefore have to be satisfied by every state q of the actor story  are called  non-functional process requirements (NFPRs). If required properties are are associate with only one state but for the whole state, then these requirements are called non-functional state requirements (NFSRs).
  6. An actor story can include many different sequences, where every sequence is called a path PTH.  A finite set of paths can represent a task T which has to be fulfilled. Within the environment of the defined problem P it mus be possible to identify at least one task T to be realized from some start state to some goal state. The realization of a task T is assumed to be ‘driven’ by input-output-systems which are called actors A.
  7. Additionally it mus be possible to identify at least one executing actor A_exec doing a  task and at least one actor assisting A_ass the executing actor to fulfill the task.
  8. A state q represents all needed actors as part of the associated environment ENV. Therefore a  state q can be analyzed as a network of elements interacting with each other. But this is only one possible structure for an analysis besides others.
  9. For the   analysis of a possible solution one can distinguish at least two overall strategies:
    1. Top-down: There exists a group of experts EXPs which will analyze a possible solution, will test these, and then will propose these as a solution for others.
    2. Bottom-up: There exists a group of experts EXPs too but additionally there exists a group of customers CTMs which will be guided by the experts to use their own experience to find a possible solution.

EXAMPLE

The mayor of a city has identified as a  problem the relationship between the actual population number POP,    the amount of actual available  living space LSP0, and the  amount of recommended living space LSPr by some standard E.  The population of his city is steadily interacting with populations in the environment: citizens are moving into the environment MIGR- and citizens from the environment are arriving MIGR+. The population,  the city as well as the environment can be characterized by a set of parameters <P1, …, Pn> called a configuration which represents a certain state q at a certain point of time t. To convert the actual configuration called a start state q0 to a new configuration S called a goal state q+ with better values requires the application of a defined set of changes Xs which change the start state q0 stepwise into a sequence of states qi which finally will end up in the desired goal state q+. A description of all these states necessary for the conversion of the start state q0 into the goal state q+ is called here an actor story AS. Because a democratic elected  mayor of the city wants to be ‘liked’ by his citizens he will require that this conversion process should end up in a goal state which is ‘not harmful’ for his citizens, which should support a ‘secure’ and ‘safety’ environment, ‘good transportation’ and things like that. This illustrates non-functional state requirements (NFSRs). Because the mayor wants also not to much trouble during the conversion process he will also require some limits for the whole conversion process, this is for the whole actor story. This illustrates non-functional process requirements (NFPRs). To realize the intended conversion process the mayor needs several executing actors which are doing the job and several other assistive actors helping the executing actors. To be able to use the available time and resources ‘effectively’ the executing actors need defined tasks which have to be realized to come from one state to the next. Often there are more than one sequences of states possible either alternatively or in parallel. A certain state at a certain point of time t can be viewed as a network where all participating actors are in many ways connected with each other, interacting in several ways and thereby influencing each other. This realizes different kinds of communications with different kinds of contents and allows the exchange of material and can imply the change of the environment. Until today the mayors of cities use as their preferred strategy to realize conversion processes selected small teams of experts doing their job in a top-down manner leaving the citizens more or less untouched, at least without a serious participation in the whole process. From now on it is possible and desirable to twist the strategy from top-down to bottom up. This implies that the selected experts enable a broad communication with potentially all citizens which are touched by a conversion and including  the knowledge, experience, skills, visions etc. of these citizens  by applying new methods possible in the new digital age.

 

 

AAI THEORY V2 – DEFINING THE PROBLEM

eJournal: uffmm.org,
ISSN 2567-6458, 23.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de 

CONTEXT

An overview to the enhanced AAI theory  version 2 you can find here.  In this post we talk about the first chapter where you have to define the problem, which should be analyzed.

DEFINING THE PROBLEM

  1. Generally it is assumed that the AAI theory is embedded in a general systems engineering approach starting with the clarification of a problem.
  2. Two cases will be distinguished:
    1. A stakeholder is associated with a certain domain of affairs with some prominent aspect/ parameter P and the stakeholder wants to clarify whether P poses some ‘problem’ in this domain. This presupposes some explained ‘expectations’ E how it should be and some ‘findings’ x pointing to the fact that P is ‘sufficiently different’ from some y>x. If the stakeholder judges that this difference is ‘important’, than P matching x will be classified as a problem, which will be documented in a ‘problem document D_p’. One can  interpret this   analysis as a ‘measurement M’ written as M(P,E) = x and x<y.
    2. Given a problem document D_p a stakeholder organizes an analysis to find a ‘solution’ which transfers the old ‘problem P’ into a ‘configuration S’ which at least should ‘minimize the problem P’. Thus there must exist some ‘measurements’ of the given problem P with regard to certain ‘expectations E’ functioning as a ‘norm’ as M(P,E)=x and some measurements of the new configuration S with regard to the same expectations E as M(S,E)=y and a metric which allows the judgment y > x.
  3. From this follows that already in the beginning of the analysis of a possible solution one has to refer to some measurement process M with an accepted standard E, otherwise there exists no problem P and no possible solution.

EXAMPLE

The mayor of a city wants to know whether the finances of his city x are in a good state compared to some well accepted standards E. Already the definition of  a ‘good state’ of the finances can pose a problem.  Let us assume that such a standard E exists and the standard tells the mayor that a ‘good state’ for his finances would ideally equal y or all values ‘above y’. If the measurement M(x, E) would generate a result like x < y, then this would indicate in the ‘light of the standard E’ that his city has a problem P. Knowing this the mayor perhaps is interested to analyze this problem P by organizing a process which gives him as a result a configuration S which generates after a measurement M(S,E) the further result that x = y or even x > y. Thus this new configuration S would be an attractive state which should be a valuable goal state for his city.

ADVANCED AAI-THEORY – V2. A Philosophy Based Approach

eJournal: uffmm.org,
ISSN 2567-6458, 23.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Last change: 27.February 2019 (changing the order of the table of contents)

Last change: 6.February 2019 (Reformulating the ‘CONTEXT’ paragraph)

CONTEXT

In a previous post I started the re-formulation of the general framework of  the AAI theory.  I decided to organize the text now in a more flexible way: One main post for the overview of all topics and then for every topic an individual post with possibly more detailed extensions. This will generate a tree-like structure with the root-post at level 0 and from this following the links you will reach the posts of level 1, then level 2 and so forth. The posts from level 0 and level 1 will be highly informal; the posts from level 2 and higher will increasingly become more specialized and associated with references to scientific literature. This block is inspired by many hundreds of scientific papers and books.

THE NEW AAI FRAMEWORK IN A NUTSHELL

  1. A Philosophical Framework
  2. TOP-DOWN OR BOTTOM-UP?
  3. ACTOR-ACTOR INTERACTION ANALYSIS – BLUEPRINT: Top-Down
  4. ACTOR-ACTOR INTERACTION ANALYSIS – BLUEPRINT: Bottom-up
  5. USABILITY AND USEFULNESS
  6. TASK INDUCED ACTOR REQUIREMENTS (TAR)
  7. ACTOR INDUCED ACTOR REQUIREMENTS (AAR)
  8. ASSISTING ACTOR MOCKUPS
  9. MEASURING USABILITY
  10. SIMULATION AND GAMING
  11. ACTOR MODELS (AMs)
    1. MODELS USING  Machine Learning (ML)
    2. MODELS USING  Cognitive Modeling (CM)
    3. MODELS as System Tutors (ST)
    4. MODELS as Purely Personal Assistant (PPA)
  12. SIMULATION BASED  MEASURING
    1. AUTOMATIC VERIFICATION
    2. MEASURING USEFULNESS
    3. MEASURING SUSTAINABILITY (RESILIENCE)
  13. CASE STUDIES
  14. REFERENCES

ADVANCED AAI-THEORY

eJournal: uffmm.org,
ISSN 2567-6458, 21.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Here You can find a new version of this post

CONTEXT

The last official update of the AAI theory dates back to Oct-2, 2018. Since that time many new thoughts have been detected and have been configured for further extensions and improvements. Here I try to give an overview of all the actual known aspects of the expanded AAI theory as a possible guide for the further elaborations of the main text.

CLARIFYING THE PROBLEM

  1. Generally it is assumed that the AAI theory is embedded in a general systems engineering approach starting with the clarification of a problem.
  2. Two cases will be distinguished:
    1. A stakeholder is associated with a certain domain of affairs with some prominent aspect/ parameter P and the stakeholder wants to clarify whether P poses some ‘problem’ in this domain. This presupposes some explained ‘expectations’ E how it should be and some ‘findings’ x pointing to the fact that P is ‘sufficiently different’ from some y>x. If the stakeholder judges that this difference is ‘important’, than P matching x will be classified as a problem, which will be documented in a ‘problem document D_p’. One interpret this this analysis as a ‘measurement M’ written as M(P,E) = x and x<y.
    2. Given a problem document D_p a stakeholder invites some experts to find a ‘solution’ which transfers the old ‘problem P’ into a ‘configuration S’ which at least should ‘minimize the problem P’. Thus there must exist some ‘measurements’ of the given problem P with regard to certain ‘expectations E’ functioning as a ‘norm’ as M(P,E)=x and some measurements of the new configuration S with regard to the same expectations E as M(S,E)=y and a metric which allows the judgment y > x.
  3. From this follows that already in the beginning of the analysis of a possible solution one has to refer to some measurement process M, otherwise there exists no problem P.

CHECK OF FRAMING CONDITIONS

  1. The definition of a problem P presupposes a domain of affairs which has to be characterized in at least two respects:
    1. A minimal description of an environment ENV of the problem P and
    2. a list of so-called non-functional requirements (NFRs).
  2. Within the environment it mus be possible to identify at least one task T to be realized from some start state to some end state.
  3. Additionally it mus be possible to identify at least one executing actor A_exec doing this task and at least one actor assisting A_ass the executing actor to fulfill the task.
  4. For the  following analysis of a possible solution one can distinguish two strategies:
    1. Top-down: There exists a group of experts EXPs which will analyze a possible solution, will test these, and then will propose these as a solution for others.
    2. Bottom-up: There exists a group of experts EXPs too but additionally there exists a group of customers CTMs which will be guided by the experts to use their own experience to find a possible solution.

ACTOR STORY (AS)

  1. The goal 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 between the different states M.
  2. 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’, ‘u1’, …) 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.
  3. Changes from one state q to another successor state q’ are described by the object whose action deletes previous facts or creates new facts.
  4. In this approach at least three different modes of an actor story will be distinguished:
    1. 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).
    2. 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.
    3. A mathematical mode generating a Mathematical Actor Story (MAS): n the mathematical mode the pictorial and the textual modes are translated into sets of formal expressions forming a graph whose nodes are sets of facts and whose edges are labeled with change-expressions.

TASK INDUCED ACTOR-REQUIREMENTS (TAR)

If an actor story AS is completed, then one can infer from this story all the requirements which are directed at the executing as well as the assistive actors of the story. These requirements are targeting the needed input- as well as output-behavior of the actors from a 3rd person point of view (e.g. what kinds of perception are required, what kinds of motor reactions, etc.).

ACTOR INDUCED ACTOR-REQUIREMENTS (AAR)

Depending from the kinds of actors planned for the real work (biological systems, animals or humans; machines, different kinds of robots), one has to analyze the required internal structures of the actors needed to enable the required perceptions and responses. This has to be done in a 1st person point of view.

ACTOR MODELS (AMs)

Based on the AARs one has to construct explicit actor models which are fulfilling the requirements.

USABILITY TESTING (UTST)

Using the actor as a ‘norm’ for the measurement one has to organized an ‘usability test’ in he way, that a real executing test actor having the required profiles has to use a real assisting actor in the context of the specified actor story. Place in a start state of the actor story the executing test actor has to show that and how he will reach the defined goal state of the actor story. For this he has to use a real assistive actor which usually is an experimental device (a mock-up), which allows the test of the story.

Because an executive actor is usually a ‘learning actor’ one has to repeat the usability test n-times to see, whether the learning curve approaches a minimum. Additionally to such objective tests one should also organize an interview to get some judgments about the subjective states of the test persons.

SIMULATION

With an increasing complexity of an actor story AS it becomes important to built a simulator (SIM) which can take as input the start state of the actor story together with all possible changes. Then the simulator can compute — beginning with the start state — all possible successor states. In the interactive mode participating actors will explicitly be asked to interact with the simulator.

Having a simulator one can use a simulator as part of an usability test to mimic the behavior of an assistive actor. This mode can also be used for training new executive actors.

A TOP-DOWN ACTOR STORY

The elaboration of an actor story will usually be realized in a top-down style: some AAI experts will develop the actor story based on their experience and will only ask for some test persons if they have elaborated everything so far that they can define some tests.

A BOTTOM-UP ACTOR STORY

In a bottom-up style the AAI experts collaborate from the beginning with a group of common users from the application domain. To do this they will (i) extract the knowledge which is distributed in the different users, then (ii) they will start some modeling from these different facts to (iii) enable some basic simulations. This simple simulation (iv) will be enhanced to an interactive simulation which allows serious gaming either (iv.a) to test the model or to enable the users (iv.b) to learn the space of possible states. The test case will (v) generate some data which can be used to evaluate the model with regard to pre-defined goals. Depending from these findings (vi) one can try to improve the model further.

THE COGNITIVE SPACE

To be able to construct executive as well as assistive actors which are close to the way how human persons do communicate one has to set up actor models which are as close as possible with the human style of cognition. This requires the analysis of phenomenal experience as well as the psychological behavior as well as the analysis of a needed neuron-physiological structures.

STATE DYNAMICS

To model in an actor story the possible changes from one given state to another one (or to many successor states) one needs eventually besides explicit deterministic changes different kinds of random rules together with adaptive ones or decision-based behavior depending from a whole network of changing parameters.

LIBRARIES AS ACTORS. WHAT ABOUT THE CITIZENS?

eJournal: uffmm.org, ISSN 2567-6458, 19.Januar 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

In this blog a new approach to the old topic of ‘Human-Machine Interaction (HMI)’ is developed turning the old Human-Machine dyad into the many-to-many relation of ‘Actor-Actor Interaction (AAI)’. And, moreover, in this new AAI approach the classical ‘top-down’ approach of engineering is expanded with a truly ‘bottom-up’ approach locating the center of development in the distributed knowledge of a population of users assisted by the AAI experts.

PROBLEM

From this perspective it is interesting to see how on an international level the citizens of a community/ city are not at the center of research, but again the city and its substructures – here public libraries – are called ‘actors’ while the citizens as such are only an anonymous matter of driving these structures to serve the international ‘buzz word’ of a ‘smart city’ empowered by the ‘Internet of Things (IoT)’.

This perspective is published in a paper from Shannon Mersand et al. (2019) which reviews all the main papers available focusing on the role of public libraries in cities. It seems – I could not check by myself the search space — that the paper gives a good overview of this topic in 48 cited papers.

The main idea underlined by the authors is that public libraries are already so-called ‘anchor institutions’ in a community which either already include or could be extended as “spaces for innovation, collaboration and hands on learning that are open to adults and younger children as well”. (p.3312) Or, another formulation “that libraries are consciously working to become a third space; a place for learning in multiple domains and that provides resources in the form of both materials and active learning opportunities”. (p.3312)

The paper is rich on details but for the context of the AAI paradigm I am interested only on the general perspective how the roles of the actors are described which are identified as responsible for the process of problem solving.

The in-official problem of cities is how to organize the city to respond to the needs of its citizens. There are some ‘official institutions’ which ‘officially’ have to fulfill this job. In democratic societies these institutions are ‘elected’. Ideally these official institutions are the experts which try to solve the problem for the citizens, which are the main stakeholder! To help in this job of organizing the ‘best fitting city-layout’ there exists usually at any point of time a bunch of infrastructures. The modern ‘Internet of Things (IoT)’ is only one of many possible infrastructures.

To proceed in doing the job of organizing the ‘best fitting city-layout’ there are generally two main strategies: ‘top-down’ as usual in most cities or ‘bottom-‘ in nearly no cities.

In the top-down approach the experts organize the processes of the cities more or less on their own. They do not really include the expertise of their citizens, not their knowledge, not their desires and visions. The infrastructures are provided from a birds perspective and an abstract systems thinking.

The case of the public libraries is matching this top-down paradigm. At the end of their paper the authors classify public libraries not only as some ‘infrastructure’ but “… recognize the potential of public libraries … and to consider them as a key actor in the governance of the smart community”. (p.3312) The term ‘actor’ is very strong. This turns an institution into an actor with some autonomy of deciding what to do. The users of the library, the citizens, the primary stakeholder of the city, are not seen as actors, they are – here – the material to ‘feed’ – to use a picture — the actor library which in turn has to serve the governance of the ‘smart community’.

DISCUSSION

Yes, this comment can be understood as a bit ‘harsh’ because one can read the text of the authors a bit different in the sense that the citizens are not only some matter to ‘feed’ the actor library but to see the public library as an ‘environment’ for the citizens which find in the libraries many possibilities to learn and empower themselves. In this different reading the citizens are clearly seen as actors too.

This different reading is possible, but within an overall ‘top-down’ approach the citizens as actors are not really included as actors but only as passive receivers of infrastructure offers; in a top-down approach the main focus are the infrastructures, and from all the infrastructures the ‘smart’ structures are most prominent, the internet of things.

If one remembers two previous papers of Mila Gascó (2016) and Mila Gascó-Hernandez (2018) then this is a bit astonishing because in these earlier papers she has analyzed that the ‘failure’ of the smart technology strategy in Barcelona was due to the fact that the city government (the experts in our framework) did not include sufficiently enough the citizens as actors!

From the point of view of the AAI paradigm this ‘hiding of the citizens as main actors’ is only due to the inadequate methodology of a top-down approach where a truly bottom-up approach is needed.

In the Oct-2, 2018 version of the AAI theory the bottom-up approach is not yet included. It has been worked out in the context of the new research project about ‘City Planning and eGaming‘  which in turn has been inspired by Mila Gascó-Hernandez!

REFERENCES

  • S.Mersand, M. Gasco-Hernandez, H. Udoh, and J.R. Gil-Garcia. “Public libraries as anchor institutions in smart communities: Current practices and future development”, Proceedings of the 52nd Hawaii International Conference on System Sciences, pages 3305 – 3314, 2019. URL https: //hdl.handle.net/10125/59766 .

  • Mila Gascó, “What makes a city smart? lessons from Barcelona”. 2016 49th Hawaii International Conference on System Sciences (HICSS), pages 2983–2989, Jan 2016. D O I : 10.1109/HICSS.2016.373.

  • Mila Gascó-Hernandez, “Building a smart city: Lessons from Barcelona.”, Commun. ACM, 61(4):50–57, March 2018. ISSN 0001-0782. D O I : 10.1145/3117800. URL http://doi.acm.org/10.1145/3117800 .

Python Program Example: Simple Population Simulation

eJournal: uffmm.org, ISSN 2567-6458, 30.Dec 2018
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

CONTEXT

In a preceding post I have described a simple way to install the python software as part of a integrated development environment. In this post I show a simple program to simulate the increase/ decrease of a population with nearly no parameters. It can be used as a starting point for further discussions and developments.

HOW TO MAKE IT

Of one has installed (in case of windows) the winpython software as described above and one has selected the ‘spyder.exe’ module from the folder of the winpython software) either directly (by double clicking) or one clicks the icon on the task bar (which one has placed there before), then one has the spyder working environment on the screen.

spyder software screen appearance
spyder software screen appearance

In the left subscreen one can now edit the program (by copy th source code below and paste it into the window) and then one can test the software by clicking on the green run button (alternatively: pressing F5).

Then the python console will be activated in the sub-window in the lower right corner. One has to enter the required values. After the input the console window will show the numbers as well as the graph.

THE PROGRAM SOURCE CODE

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
“””
Created on Wed Jan 2 19:34:43 2019

@author: gerd doeben-henisch
Email: gerd@doeben-henisch.de
“””

##################################
# pop1()
###################################
#
# IDEA
#
# Simple program to compute the increase/ decrease of a population with
# the parameters population number (p), birth-rate (br), death-rate (dr),
# mirgration Plus (migrPlus), and migration Minus (migrMinus)
#

#######################################
# Used modules

import matplotlib.pyplot as plt
import numpy as np

#########################################
# Defining a function pop1()

def pop1(p,br,dr,migrPlus,migrMinus):

p=p+(p*br)-(p*dr)+migrPlus-migrMinus

return p

###################################
# Asking for input values
#
# input() creates a strng which has to be converted into an int()

baseYear = int(input(‘Basisjahr als Zahl ? ‘))

p = int(input(‘Bevölkerung als Zahl ‘))

br = float(input(‘Geburtenrate in % ‘))

dr = float(input(‘Sterberate in % ‘))

migrPlus = int(input(‘Zuwanderung Zahl ‘))
migrMinus = int(input(‘Abwanderung Zahl ‘))

n = int(input(‘Wieviele Jahre voraus ? ‘))

############################################
# processing the data
#
# creating a range called ‘run’ for the years to compute

run = np.arange(1, n+1, 1)

####################################
# pop is a ‘list’ to collect the pop-values for every year

pop = []

########################################
# The first element of pop is the base year
pop.append(p)

######################################
# Compute the changing values for the population p and store these in pop
# Use for this computation the function pop1() defined before

for i in run:
p=pop1(p,br,dr,migrPlus,migrMinus)
pop.append(p)

##############################################
# Print the content of pop for the user to show
# the different years with their pop-values

for i in range(n+1):
print(‘Jahr %5d = Einw. %8d \n’ %(baseYear+i, pop[i]) )

##############################################
# Make the numbers visible as a graph

plt.figure(1)
plt.axis([0, len(run)+1, 1, max(pop)])

run2 = np.arange(0, n+1, 1)
plt.plot(run2, pop, ‘bo’)

plt.show()
plt.close()

EXAMPLE RUNS

EXAMPLE 1

Shows a population with a lower birth rate than death rate but a positive migration outcome. (Bevölkerung = population, Zahl = number, Gebrtenrate = biirth rate, Sterberate = death rate, Zuwanderung = migration plus, Abwanderung = migration minus, Wieviele Jahre voraus = how many years forcasting)

Bevölkerung als Zahl 1000

Geburtenrate in % 0.15

Sterberate in % 0.17

Zuwanderung Zahl 200

Abwanderung Zahl 100

Wieviele Jahre voraus ? 20

Jahr 2019 = Einw. 1000

Jahr 2020 = Einw. 1080

Jahr 2021 = Einw. 1158

Jahr 2022 = Einw. 1235

Jahr 2023 = Einw. 1310

Jahr 2024 = Einw. 1384

Jahr 2025 = Einw. 1456

Jahr 2026 = Einw. 1527

Jahr 2027 = Einw. 1596

Jahr 2028 = Einw. 1665

Jahr 2029 = Einw. 1731

Jahr 2030 = Einw. 1797

Jahr 2031 = Einw. 1861

Jahr 2032 = Einw. 1923

Jahr 2033 = Einw. 1985

Jahr 2034 = Einw. 2045

Jahr 2035 = Einw. 2104

Jahr 2036 = Einw. 2162

Jahr 2037 = Einw. 2219

Jahr 2038 = Einw. 2275

Jahr 2039 = Einw. 2329

example 1 - increasing population
example 1 – increasing population

EXAMPLE 2

Shows a population with a lower birth rate than death rate and a negative migration outcome. (Bevölkerung = population, Zahl = number, Gebrtenrate = biirth rate, Sterberate = death rate, Zuwanderung = migration plus, Abwanderung = migration minus, Wieviele Jahre voraus = how many years forcasting)

Basisjahr als Zahl ? 2019

Bevölkerung als Zahl 1000

Geburtenrate in % 0.15

Sterberate in % 0.17

Zuwanderung Zahl 100

Abwanderung Zahl 120

Wieviele Jahre voraus ? 30
Jahr 2019 = Einw. 1000

Jahr 2020 = Einw. 960

Jahr 2021 = Einw. 920

Jahr 2022 = Einw. 882

Jahr 2023 = Einw. 844

Jahr 2024 = Einw. 807

Jahr 2025 = Einw. 771

Jahr 2026 = Einw. 736

Jahr 2027 = Einw. 701

Jahr 2028 = Einw. 667

Jahr 2029 = Einw. 634

Jahr 2030 = Einw. 601

Jahr 2031 = Einw. 569

Jahr 2032 = Einw. 538

Jahr 2033 = Einw. 507

Jahr 2034 = Einw. 477

Jahr 2035 = Einw. 447

Jahr 2036 = Einw. 418

Jahr 2037 = Einw. 390

Jahr 2038 = Einw. 362

Jahr 2039 = Einw. 335

Jahr 2040 = Einw. 308

Jahr 2041 = Einw. 282

Jahr 2042 = Einw. 256

Jahr 2043 = Einw. 231

Jahr 2044 = Einw. 206

Jahr 2045 = Einw. 182

Jahr 2046 = Einw. 159

Jahr 2047 = Einw. 135

Jahr 2048 = Einw. 113

Jahr 2049 = Einw. 90

example 2 - decreasing population
example 2 – decreasing population

QUANTUM THEORY (QT). Basic elements

eJournal: uffmm.org, ISSN 2567-6458, 2.January 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email:
gerd@doeben-henisch.de

CONTEXT

This is a continuation from the post WHY QT FOR AAI? explaining the motivation why to look to quantum theory (QT) in the case of the AAI paradigm. After approaching QT from a philosophy of science perspective (see the post QUANTUM THEORY (QT). BASIC PROPERTIES) giving a ‘birds view’ of the relationship between a QT and the presupposed ‘real world’ and digging a bit into the first person view inside an observer we are here interested in the formal machinery of QT. For this we follow Grifftiths in his chapter 1.

QT BASIC ELEMENTS

MEASUREMENT

  1. The starting point of a quantum theory QT are ‘phenomena‘, which “lack any description in classical physics”, a kind of things “which human beings cannot observe directly”. To measure such phenomena one needs highly sophisticated machines, which poses the problem, that the interpretation of possible ‘measurement data’ in terms of a quantum theory depends highly on the understanding of the working of the used measurement apparatus. (cf. p.8)
  2. This problem is well known in philosophy of science: (i) one wants to built a new theory T. (ii) For this theory one needs appropriate measurement data MD. (iii) The measurement as such needs a well defined procedure including different kinds of pre-defined objects and artifacts. The description of the procedure including the artifacts (which can be machines) is a theory of its own called measurement theory T*. (iv) Thus one needs a theory T* to enable a new theory T.
  3. In the case of QT one has the special case that QT itself has to be part of the measurement theory T*, i.e. QT subset T*. But, as Griffiths points out, the measurement problem in QT is even deeper; it is not only the conceptual dependency of QT from its measurement theory T*, but in the case of QT does the measurement apparatus directly interact with the target objects of QT because the measurement apparatus is itself part of the atomic and sub-atomic world which is the target. (cf. p.8) This has led to include the measurement as ‘stochastic time development’ explicitly into the QT. (cf. p.8) In his book Griffiths follows the strategy to deal with the ‘collapse of the wave function’ within the theoretical level, because it does not take place “in the experimental physicist’s laboratory”. (cf. p.9)
  4. As a consequence of these considerations Griffiths develops the fundamental principles in the chapters 2-16 without making any reference to measurement.

PRE-KNOWLEDGE

  1. Besides the special problem of measurement in quantum mechanics there is the general problem of measurement for every kind of empirical discipline which requires a perception of the real world guided by a scientific bias called ‘scientific knowledge’! Without a theoretical pre-knowledge there is no scientific observation possible. A scientific observation needs already a pre-theory T* defining the measurement procedure as well as the pre-defined standard object as well as – eventually — an ‘appropriate’ measurement device. Furthermore, to be able to talk about some measurement data as ‘data related to an object of QT’ one needs additionally a sufficient ‘pre-knowledge’ of such an object which enables the observer to decide whether the measured data are to be classified as ‘related to the object of QT. The most convenient way to enable this is to have already a proposal for a QT as the ‘knowledge guide’ how one ‘should look’ to the measured data.

QT STATES

  1. Related to the phenomena of quantum mechanics the phenomena are in QT according to Griffiths understood as ‘particles‘ whose ‘state‘ is given by a ‘complex-valued wave function ψ(x)‘, and the collection of all possible wave functions is assumed to be a ‘complex linear vector space‘ with an ‘inner product’, known as a ‘Hilbert space‘. “Two wave functions φ(x) and ψ(x) represent ‘distinct physical states’ … if and only if they are ‘orthogonal’ in the sense that their ‘inner product is zero’. Otherwise φ(x) and ψ(x) represent incompatible states of the quantum system …” .(p.2)
  2. “A quantum property … corresponds to a subspace of the quantum Hilbert space or the projector onto this subspace.” (p.2)
  3. A sample space of mutually-exclusive possibilities is a decomposition of the identity as a sum of mutually commuting projectors. One and only one of these projectors can be a correct description of a quantum system at a given time.cf. p.3)
  4. Quantum sample spaces can be mutually incompatible. (cf. p.3)
  5. “In … quantum mechanics [a physical variable] is represented by a Hermitian operator.… a real-valued function defined on a particular sample space, or decomposition of the identity … a quantum system can be said to have a value … of a physical variable represented by the operator F if and only if the quantum wave function is in an eigenstate of F … . Two physical variables whose operators do not commute correspond to incompatible sample spaces… “.(cf. p.3)
  6. “Both classical and quantum mechanics have dynamical laws which enable one to say something about the future (or past) state of a physical system if its state is known at a particular time. … the quantum … dynamical law … is the (time-dependent) Schrödinger equation. Given some wave function ψ_0 at a time t_0 , integration of this equation leads to a unique wave function ψ_t at any other time t. At two times t and t’ these uniquely defined wave functions are related by a … time development operator T(t’ , t) on the Hilbert space. Consequently we say that integrating the Schrödinger equation leads to unitary time development.” (p.3)
  7. “Quantum mechanics also allows for a stochastic or probabilistic time development … . In order to describe this in a systematic way, one needs the concept of a quantum history … a sequence of quantum events (wave functions or sub-spaces of the Hilbert space) at successive times. A collection of mutually … exclusive histories forms a sample space or family of histories, where each history is associated with a projector on a history Hilbert space. The successive events of a history are, in general, not related to one another through the Schrödinger equation. However, the Schrödinger equation, or … the time development operators T(t’ , t), can be used to assign probabilities to the different histories belonging to a particular family.” (p.3f)

HILBERT SPACE: FINITE AND INFINITE

  1. “The wave functions for even such a simple system as a quantum particle in one dimension form an infinite-dimensional Hilbert space … [but] one does not have to learn functional analysis in order to understand the basic principles of quantum theory. The majority of the illustrations used in Chs. 2–16 are toy models with a finite-dimensional Hilbert space to which the usual rules of linear algebra apply without any qualification, and for these models there are no mathematical subtleties to add to the conceptual difficulties of quantum theory … Nevertheless, they provide many useful insights into general quantum principles.”. (p.4f)

CALCULUS AND PROBABILITY

  1. Griffiths (2003) makes considerable use of toy models with a simple discretized time dependence … To obtain … unitary time development, one only needs to solve a simple difference equation, and this can be done in closed form on the back of an envelope. (cf. p.5f)
  2. Probability theory plays an important role in discussions of the time development of quantum systems. … when using toy models the simplest version of probability theory, based on a finite discrete sample space, is perfectly adequate.” (p.6)
  3. “The basic concepts of probability theory are the same in quantum mechanics as in other branches of physics; one does not need a new “quantum probability”. What distinguishes quantum from classical physics is the issue of choosing a suitable sample space with its associated event algebra. … in any single quantum sample space the ordinary rules for probabilistic reasoning are valid. ” (p.6)

QUANTUM REASONING

  1. The important difference compared to classical mechanics is the fact that “an initial quantum state does not single out a particular framework, or sample space of stochastic histories, much less determine which history in the framework will actually occur.” (p.7) There are multiple incompatible frameworks possible and to use the ordinary rules of propositional logic presupposes to apply these to a single framework. Therefore it is important to understand how to choose an appropriate framework.(cf. p.7)

NEXT

These are the basic ingredients which Griffiths mentions in chapter 1 of his book 2013. In the following these ingredients have to be understood so far, that is becomes clear how to relate the idea of a possible history of states (cf. chapters 8ff) where the future of a successor state in a sequence of timely separated states is described by some probability.

REFERENCES

  • R.B. Griffiths. Consistent Quantum Theory. Cambridge University Press, New York, 2003

 

WHY QT FOR AAI?

eJournal: uffmm.org, ISSN 2567-6458, 2.January 2019
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email:
gerd@doeben-henisch.de

CONTEXT

This is a continuation from the post QUANTUM THEORY (QT). BASIC PROPERTIES, where basic properties of quantum theory (QT) according to ch.27 of Griffiths (2003) have been reported. Before we dig deeper into the QT matter here a remark why we should do this at all because the main topic of the uffmm.org blog is the Actor-Actor Interaction (AAI) paradigm dealing with actors including a subset of actors which have the complexity of biological systems at least as complex as exemplars of the kind of human sapiens.

WHY QT IN THE CASE OF AAI

As Griffiths (2003) points out in his chapter 1 and chapter 27 quantum theory deals with objects which are not perceivable by the normal human sensory apparatus. It needs special measurement procedures and instrumentation to measure events related to quantum objects. Therefore the level of analysis in quantum theory is quite ‘low’ compared to the complexity hierarchies of biological systems.

Baars and Edelman (2012) address the question of the relationship of QT and biological phenomena, especially those connected to the phenomenon of human consciousness, explicitly. Their conclusion is very clear: “Current quantum-level proposals do not explain the prominent empirical features of consciousness”. (Baars and Edelman (2012):p.286)

Behind this short statement we have to accept the deep insights of modern (evolutionary and micro) biology that a main characteristics of biological systems has to be seen in their ability to overcome the fluctuating and unstable quantum properties by a more and more complex machinery which posses its own logic and its own specific dynamics.

Therefore the level of analysis for the behavior of biological systems is usually ‘far above’ the level of quantum theory.

Why then at all bother with QT in the case of the AAI paradigm?

If one looks to the AAI paradigm then one detects the concept of the actor story (AS) which assumes that reality can be conceived — and then be described – as a ‘process’ which can be analyzed as a ‘sequence of states’ characterized by decidable ‘facts’ which can ‘change in time’. A ‘change’ can occur either by some changing time measured by ‘time points’ generated by a ‘time machine’ called ‘clock’ or by some ‘inherent change’ observable as a change in some ‘facts’.

Restricting the description of the transitions of such a sequence of states to properties of classical probability theory, one detects severe limits of the descriptive power of a CPT description compared to what has to be done in an AAI analysis. (see for this the post BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. The Limits of Classic Probability). The limits result from the fact that actors within the AAI paradigm are in many cases ‘not static’ and ‘not deterministic’ systems which can change their structures and behavior functions in a way that the basic assumptions of CPT are no longer valid.

It remains the question whether a probability theory PT which is based on quantum theory QT is in some sense ‘better adapted’ to the AAI paradigm than Classical PT.

This question is the main perspective guiding the further encounter with QT.

See next.

 

 

 

 

 

 

 

 

 

 

 

 

 

QUELLEN

  • Bernard J. Baars and David B. Edelman. Consciousness, biology, and quantum hypotheses. Physics of Life Review, 9(3):285 – 294, 2012. D O I: 10.1016/j.plrev.2012.07.001. Epub. URL http://www.ncbi.nlm.nih.gov/pubmed/22925839
  • R.B. Griffiths. Consistent Quantum Theory. Cambridge University Press, New York, 2003