Integrating Engineering and the Human Factor (info@uffmm.org) eJournal uffmm.org ISSN 2567-6458, Nov 23-26, 2020
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

Applying the original P-V-Pref Document structure to real cases it became clear that the everyday logic behind the classification of facts into problems [P] or visions [V] follows a kind of logic hidden in the semantic space of the used expressions. This text explains this hidden logic and what this means for our application.

In this section several case studies will be presented. It will be shown, how the DAAI paradigm can be mapped into a concept of Generative Cultural Anthropology [GCA] or Sociology. Then it will be shown how it is possible to implement the GCA concept or a Sociology concept in real world processes subsumed under the general concept of daily life. One popular perspective is that which deals with city planning and the participation of citizens in this process. The working title of the software project related to this is komega (later we will go back to an older concept already used in the past called OKSIMO (Open Knowledge Simulation Modeling)). 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 which will partially be translated in software which can be used within experimental settings.

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)

This suggests that a symbiosis between creative humans and computing algorithms is an attractive pairing. For this we have to re-invent our official learning processes in schools and universities to train the next generation of humans in a more inspired and creative usage of algorithms in a game-like learning processes.

CONTEXT

The overall context is given by the description of the Actor-Actor Interaction (AAI) paradigm as a whole. In this text the special relationship between engineering and the surrounding society is in the focus. And within this very broad and rich relationship the main interest lies in the ethical dimension here understood as those preferences of a society which are more supported than others. It is assumed that such preferences manifesting themselves in real actions within a space of many other options are pointing to hidden values which guide the decisions of the members of a society. Thus values are hypothetical constructs based on observable actions within a cognitively assumed space of possible alternatives. These cognitively represented possibilities are usually only given in a mixture of explicitly stated symbolic statements and different unconscious factors which are influencing the decisions which are causing the observable actions.

These assumptions represent until today not a common opinion and are not condensed in some theoretical text. Nevertheless I am using these assumptions here because they help to shed some light on the rather complex process of finding a real solution to a stated problem which is rooted in the cognitive space of the participants of the engineering process. To work with these assumptions in concrete development processes can support a further clarification of all these concepts.

ENGINEERING AND SOCIETY

DUAL: REAL AND COGNITIVE

As assumed in the AAI paradigm the engineering process is that process which connects the event of stating aproblem combined with a first vision of a solution with a final concrete working solution.

The main characteristic of such an engineering process is the dual character of a continuous interaction between the cognitive space of all participants of the process with real world objects, actions, and processes. The real world as such is a lose collection of real things, to some extend connected by regularities inherent in natural things, but the visions of possible states, possible different connections, possible new processes is bound to the cognitive space of biological actors, especially to humans as exemplars of the homo sapiens species.

Thus it is a major factor of training, learning, and education in general to see how the real world can be mappedinto some cognitive structures, how the cognitive structures can be transformed by cognitive operations into new structures and how these new cognitive structures can be re-mapped into the real world of bodies.

Within the cognitive dimension exists nearly infinite sets of possible alternatives, which all indicate possible states of a world, whose feasibility is more or less convincing. Limited by time and resources it is usually not possible to explore all these cognitively tapped spaces whether and how they work, what are possible side effects etc.

PREFERENCES

Somehow by nature, somehow by past experience biological system — like the home sapiens — have developed cultural procedures to induce preferences how one selects possible options, which one should be selected, under which circumstances and with even more constraints. In some situations these preferences can be helpful, in others they can hide possibilities which afterwards can be re-detected as being very valuable.

Thus every engineering process which starts a transformation process from some cognitively given point of view to a new cognitively point of view with a following up translation into some real thing is sharing its cognitive spacewith possible preferences of the cognitive space of the surrounding society.

It is an open case whether the engineers as the experts have an experimental, creative attitude to explore without dogmatic constraints the possible cognitive spaces to find new solutions which can improve life or not. If one assumes that there exist no absolute preferences on account of the substantially limit knowledge of mankind at every point of time and inferring from this fact the necessity to extend an actual knowledge further to enable the mastering of an open unknown future then the engineers will try to explore seriously all possibilities without constraints to extend the power of engineering deeper into the heart of the known as well as unknown universe.

EXPLORING COGNITIVE POSSIBILITIES

At the start one has only a rough description of the problem and a rough vision of a wanted solution which gives some direction for the search of an optimal solution. This direction represents also a kind of a preference what is wanted as the outcome of the process.

On account of the inherent duality of human thinking and communication embracing the cognitive space as well as the realm of real things which both are connected by complex mappings realized by the brain which operates nearly completely unconscious a long process of concrete real and cognitive actions is necessary to materialize cognitive realities within a communication process. Main modes of materialization are the usage of symbolic languages, paintings (diagrams), physical models, algorithms for computation and simulations, and especially gaming (in several different modes).

As everybody can know these communication processes are not simple, can be a source of confusions, and the coordination of different brains with different cognitive spaces as well as different layouts of unconscious factors is a difficult and very demanding endeavor.

The communication mode gaming is of a special interest here because it is one of the oldest and most natural modes to learn but in the official education processes in schools and universities (and in companies) it was until recently not part of the official curricula. But it is the only mode where one can exercise the dimensions of preferences explicitly in combination with an exploring process and — if one wants — with the explicit social dimension of having more than one brain involved.

In the last about 50 – 100 years the term project has gained more and more acceptance and indeed the organization of projects resembles a game but it is usually handled as a hierarchical, constraints-driven process where creativity and concurrent developing (= gaming) is not a main topic. Even if companies allow concurrent development teams these teams are cognitively separated and the implicit cognitive structures are black boxes which can not be evaluated as such.

In the presupposed AAI paradigm here the open creative space has a high priority to increase the chance for innovation. Innovation is the most valuable property in face of an unknown future!

While the open space for a real creativity has to be executed in all the mentioned modes of communication the final gaming mode is of special importance. To enable a gaming process one has explicitly to define explicit win-lose states. This objectifies values/ preferences hidden in the cognitive space before. Such an objectification makes things transparent, enables more rationality and allows the explicit testing of these defined win-lose states as feasible or not. Only tested hypothesis represent tested empirical knowledge. And because in a gaming mode whole groups or even all members of a social network can participate in a learning process of the functioning and possible outcome of a presented solution everybody can be included. This implies a common sharing of experience and knowledge which simplifies the communication and therefore the coordination of the different brains with their unconsciousness a lot.

TESTING AND EVALUATION

Testing a proposed solution is another expression for measuring the solution. Measuring is understood here as a basic comparison between the target to be measured (here the proposed solution) and the before agreednorm which shall be used as point of reference for the comparison.

But what can be a before agreed norm?

Some aspects can be mentioned here:

First of all there is the proposed solution as such, which is here a proposal for a possible assistive actor in an assumed environment for some intended executive actors which has to fulfill some job (task).

Part of this proposed solution are given constraints and non-functional requirements.

Part of this proposed solution are some preferences as win-lose states which have to be reached.

Another difficult to define factor are the executive actors if they are biological systems. Biological systems with their basic built in ability to act free, to be learning systems, and this associated with a not-definable large unconscious realm.

Given the explicit preferences constrained by many assumptions one can test only, whether the invited test persons understood as possible instances of the intended executive actors are able to fulfill the defined task(s) in some predefined amount of time within an allowed threshold of making errors with an expected percentage of solved sub-tasks together with a sufficient subjective satisfaction with the whole process.

But because biological executive actors are learning systems they will behave in different repeated tests differently, they can furthermore change their motivations and their interests, they can change their emotional commitment, and because of their built-in basic freedom to act there can be no 100% probability that they will act at time t as they have acted all the time before.

Thus for all kinds of jobs where the process is more or less fixed, where nothing new will happen, the participation of biological executive actors in such a process is questionable. It seems (hypothesis), that biological executing actors are better placed in jobs where there is some minimal rate of curiosity, of innovation, and of creativity combined with learning.

If this hypothesis is empirically sound (as it seems), then all jobs where human persons are involved should have more the character of games then something else.

It is an interesting side note that the actual research in robotics under the label of developmental robotics is struck by the problem how one can make robots continuously learning following interesting preferences. Given a preference an algorithm can work — under certain circumstances — often better than a human person to find an optimal solution, but lacking such a preference the algorithm is lost. And actually there exists not the faintest idea how algorithms should acquire that kind of preferences which are interesting and important for an unknown future.

On the contrary, humans are known to be creative, innovative, detecting new preferences etc. but they have only limited capacities to explore these creative findings until some telling endpoint.

This suggests that a symbiosis between creative humans and computing algorithms is an attractive pairing. For this we have to re-invent our official learning processes in schools and universities to train the next generation of humans in a more inspired and creative usage of algorithms in a game-like learning processes.

The context for this text is the whole block dedicated to the AAI (Actor-Actor Interaction) paradigm. The aim of this text is to give the big picture of all dimensions and components of this subject as it shows up during April 2019.

The first dimension introduced is the historical dimension, because this allows a first orientation in the course of events which lead to the actual situation. It starts with the early days of real computers in the thirties and forties of the 20 century.

The second dimension is the engineering dimension which describes the special view within which we are looking onto the overall topic of interactions between human persons and computers (or machines or technology or society). We are interested how to transform a given problem into a valuable solution in a methodological sound way called engineering.

The third dimension is the whole of society because engineering happens always as some process within a society. Society provides the resources which can be used and spends the preferences (values) what is understood as ‘valuable’, as ‘good’.

The fourth dimension is Philosophy as that kind of thinking which takes everything into account which can be thought and within thinking Philosophy clarifies conditions of thinking, possible tools of thinking and has to clarify when some symbolic expression becomes true.

HISTORY

In history we are looking back in the course of events. And this looking back is in a first step guided by the concepts of HCI (Human-Computer Interface) and HMI (Human-Machine Interaction).

It is an interesting phenomenon how the original focus of the interface between human persons and the early computers shifted to the more general picture of interaction because the computer as machine developed rapidly on account of the rapid development of the enabling hardware (HW) the enabling software (SW).

Within the general framework of hardware and software the so-called artificial intelligence (AI) developed first as a sub-topic on its own. Since the last 10 – 20 years it became in a way productive that it now seems to become a normal part of every kind of software. Software and smart software seem to be interchangeable. Thus the new wording of augmented or collective intelligence is emerging intending to bridge the possible gap between humans with their human intelligence and machine intelligence. There is some motivation from the side of society not to allow the impression that the smart (intelligent) machines will replace some day the humans. Instead one is propagating the vision of a new collective shape of intelligence where human and machine intelligence allows a symbiosis where each side gives hist best and receives a maximum in a win-win situation.

What is revealing about the actual situation is the fact that the mainstream is always talking about intelligence but not seriously about learning! Intelligence is by its roots a static concept representing some capabilities at a certain point of time, while learning is the more general dynamic concept that a system can change its behavior depending from actual external stimuli as well as internal states. And such a change includes real changes of some of its internal states. Intelligence does not communicate this dynamics! The most demanding aspect of learning is the need for preferences. Without preferences learning is impossible. Today machine learning is a very weak example of learning because the question of preferences is not a real topic there. One assumes that some reward is available, but one does not really investigate this topic. The rare research trying to do this job is stating that there is not the faintest idea around how a general continuous learning could happen. Human society is of no help for this problem while human societies have a clash of many, often opposite, values, and they have no commonly accepted view how to improve this situation.

ENGINEERING

Engineering is the art and the science to transform a given problem into a valuable and working solution. What is valuable decides the surrounding enabling society and this judgment can change during the course of time. Whether some solution is judged to be working can change during the course of time too but the criteria used for this judgment are more stable because of their adherence to concrete capabilities of technical solutions.

While engineering was and is always a kind of an art and needs such aspects like creativity, innovation, intuition etc. it is also and as far as possible a procedure driven by defined methods how to do things, and these methods are as far as possible backed up by scientific theories. The real engineer therefore synthesizes art, technology and science in a unique way which can not completely be learned in the schools.

In the past as well as in the present engineering has to happen in teams of many, often many thousands or even more, people which coordinate their brains by communication which enables in the individual brains some kind of understanding, of emerging world pictures, which in turn guide the perception, the decisions, and the concrete behavior of everybody. And these cognitive processes are embedded — in every individual team member — in mixtures of desires, emotions, as well as motivations, which can support the cognitive processes or obstruct them. Therefore an optimal result can only be reached if the communication serves all necessary cognitive processes and the interactions between the team members enable the necessary constructive desires, emotions, and motivations.

If an engineering process is done by a small group of dedicated experts — usually triggered by the given problem of an individual stakeholder — this can work well for many situations. It has the flavor of a so-called top-down approach. If the engineering deals with states of affairs where different kinds of people, citizens of some town etc. are affected by the results of such a process, the restriction to a small group of experts can become highly counterproductive. In those cases of a widespread interest it seems promising to include representatives of all the involved persons into the executing team to recognize their experiences and their kinds of preferences. This has to be done in a way which is understandable and appreciative, showing esteem for the others. This manner of extending the team of usual experts by situative experts can be termed bottom-up approach. In this usage of the term bottom-up this is not the opposite to top-down but is reflecting the extend in which members of a society are included insofar they are affected by the results of a process.

SOCIETY

Societies in the past and the present occur in a great variety of value systems, organizational structures, systems of power etc. Engineering processes within a society are depending completely on the available resources of a society and of its value systems.

The population dynamics, the needs and wishes of the people, the real territories, the climate, housing, traffic, and many different things are constantly producing demands to be solved if life shall be able and continue during the course of time.

The self-understanding and the self-management of societies is crucial for their ability to used engineering to improve life. This deserves communication and education to a sufficient extend, appropriate public rules of management, otherwise the necessary understanding and the freedom to act is lacking to use engineering in the right way.

PHILOSOPHY

Without communication no common constructive process can happen. Communication happens according to many implicit rules compressed in the formula who when can speak how about what with whom etc. Communication enables cognitive processes of for instance understanding, explanations, lines of arguments. Especially important for survival is the ability to make true descriptions and the ability to decide whether a statement is true or not. Without this basic ability communication will break down, coordination will break down, life will break down.

The basic discipline to clarify the rules and conditions of true communication, of cognition in general, is called Philosophy. All the more modern empirical disciplines are specializations of the general scope of Philosophy and it is Philosophy which integrates all the special disciplines in one, coherent framework (this is the ideal; actually we are far from this ideal).

Thus to describe the process of engineering driven by different kinds of actors which are coordinating themselves by communication is primarily the task of philosophy with all their sub-disciplines.

Thus some of the topics of Philosophy are language, text, theory, verification of a theory, functions within theories as algorithms, computation in general, inferences of true statements from given theories, and the like.

In this text I apply Philosophy as far as necessary. Especially I am introducing a new process model extending the classical systems engineering approach by including the driving actors explicitly in the formal representation of the process. Learning machines are included as standard tools to improve human thinking and communication. You can name this Augmented Social Learning Systems (ASLS). Compared to the wording Augmented Intelligence (AI) (as used for instance by the IBM marketing) the ASLS concept stresses that the primary point of reference are the biological systems which created and create machine intelligence as a new tool to enhance biological intelligence as part of biological learning systems. Compared to the wording Collective Intelligence (CI) (as propagated by the MIT, especially by Thomas W.Malone and colleagues) the spirit of the CI concept seems to be similar, but perhaps only a weak similarity.

This is a continuation from the post about QL Basics Concepts Part 1. The general topic here is the analysis of properties of human behavior, actually narrowed down to the statistical properties. From the different possible theories applicable to statistical properties of behavior here the one called CPT (classical probability theory) is selected for a short examination.

SUMMARY

An analysis of the classical probability theory shows that the empirical application of this theory is limited to static sets of events and probabilities. In the case of biological systems which are adaptive with regard to structure and cognition this does not work. This yields the question whether a quantum probability theory approach does work or not.

THE CPT IDEA

Before we are looking to the case of quantum probability theory (QLPT) let us examine the case of a classical probability theory (CPT) a little bit more.

Generally one has to distinguish the symbolic formal representation of a theory T and some domain of application D distinct from the symbolic representation.

In principle the domain of application D can be nearly anything, very often again another symbolic representation. But in the case of empirical applications we assume usually some subset of ’empirical events’ E of the ’empirical (real) world’ W.

For the following let us assume (for a while) that this is the case, that D is a subset of the empirical world W.

Talking about ‘events in an empirical real world’ presupposes that there there exists a ‘procedure of measurement‘ using a ‘previously defined standard object‘ and a ‘symbolic representation of the measurement results‘.

Furthermore one has to assume a community of ‘observers‘ which have minimal capabilities to ‘observe’, which implies ‘distinctions between different results’, some ‘ordering of successions (before – after)’, to ‘attach symbols according to some rules’ to measurement results, to ‘translate measurement results’ into more abstract concepts and relations.

Thus to speak about empirical results assumes a set of symbolic representations of those events as a finite set of symbolic representations which represent a ‘state in the real world’ which can have a ‘predecessor state before’ and – possibly — a ‘successor state after’ the ‘actual’ state. The ‘quality’ of these measurement representations depends from the quality of the measurement procedure as well as from the quality of the cognitive capabilities of the participating observers.

In the classical probability theory T_cpt as described by Kolmogorov (1932) it is assumed that there is a set E of ‘elementary events’. The set E is assumed to be ‘complete’ with regard to all possible events. The probability P is coming into play with a mapping from E into the set of positive real numbers R+ written as P: E —> R+ or P(E) = 1 with the assumption that all the individual elements e_i of E have an individual probability P(e_i) which obey the rule P(e_1) + P(e_2) + … + P(e_n) = 1.

In the formal theory T_cpt it is not explained ‘how’ the probabilities are realized in the concrete case. In the ‘real world’ we have to identify some ‘generators of events’ G, otherwise we do not know whether an event e belongs to a ‘set of probability events’.

Kolmogorov (1932) speaks about a necessary generator as a ‘set of conditions’ which ‘allows of any number of repetitions’, and ‘a set of events can take place as a result of the establishment of the condition’. (cf. p.3) And he mentions explicitly the case that different variants of the a priori assumed possible events can take place as a set A. And then he speaks of this set A also of an event which has taken place! (cf. p.4)

If one looks to the case of the ‘set A’ then one has to clarify that this ‘set A’ is not an ordinary set of set theory, because in a set every member occurs only once. Instead ‘A’ represents a ‘sequence of events out of the basic set E’. A sequence is in set theory an ‘ordered set’, where some set (e.g. E) is mapped into an initial segment of the natural numbers Nat and in this case the set A contains ‘pairs from E x Nat|\n’ with a restriction of the set Nat to some n. The ‘range’ of the set A has then ‘distinguished elements’ whereby the ‘domain’ can have ‘same elements’. Kolmogorov addresses this problem with the remark, that the set A can be ‘defined in any way’. (cf. p.4) Thus to assume the set A as a set of pairs from the Cartesian product E x Nat|\n with the natural numbers taken from the initial segment of the natural numbers is compatible with the remark of Kolmogorov and the empirical situation.

For a possible observer it follows that he must be able to distinguish different states <s1, s2, …, sm> following each other in the real world, and in every state there is an event e_i from the set of a priori possible events E. The observer can ‘count’ the occurrences of a certain event e_i and thus will get after n repetitions for every event e_i a number of occurrences m_i with m_i/n giving the measured empirical probability of the event e_i.

Example 1: Tossing a coin with ‘head (H)’ or ‘tail (T)’ we have theoretically the probabilities ‘1/2’ for each event. A possible outcome could be (with ‘H’ := 0, ‘T’ := 1): <((0,1), (0,2), (0,3), (1,4), (0,5)> . Thus we have m_H = 4, m_T = 1, giving us m_H/n = 4/5 and m_T/n = 1/5. The sum yields m_H/n + m_T/n = 1, but as one can see the individual empirical probabilities are not in accordance with the theory requiring 1/2 for each. Kolmogorov remarks in his text that if the number of repetitions n is large enough then will the values of the empirically measured probability approach the theoretically defined values. In a simple experiment with a random number generator simulating the tossing of the coin I got the numbers m_Head = 4978, m_Tail = 5022, which gives the empirical probabilities m_Head/1000 = 0.4977 and m_Teil/ 1000 = 0.5021.

This example demonstrates while the theoretical term ‘probability’ is a simple number, the empirical counterpart of the theoretical term is either a simple occurrence of a certain event without any meaning as such or an empirically observed sequence of events which can reveal by counting and division a property which can be used as empirical probability of this event generated by a ‘set of conditions’ which allow the observed number of repetitions. Thus we have (i) a ‘generator‘ enabling the events out of E, we have (ii) a ‘measurement‘ giving us a measurement result as part of an observation, (iii) the symbolic encoding of the measurement result, (iv) the ‘counting‘ of the symbolic encoding as ‘occurrence‘ and (v) the counting of the overall repetitions, and (vi) a ‘mathematical division operation‘ to get the empirical probability.

Example 1 demonstrates the case of having one generator (‘tossing a coin’). We know from other examples where people using two or more coins ‘at the same time’! In this case the set of a priori possible events E is occurring ‘n-times in parallel’: E x … x E = E^n. While for every coin only one of the many possible basic events can occur in one state, there can be n-many such events in parallel, giving an assembly of n-many events each out of E. If we keeping the values of E = {‘H’, ‘T’} then we have four different basic configurations each with probability 1/4. If we define more ‘abstract’ events like ‘both the same’ (like ‘0,0’, ‘1,1’) or ‘both different’ (like ‘0,1’. ‘1,0’), then we have new types of complex events with different probabilities, each 1/2. Thus the case of n-many generators in parallel allows new types of complex events.

Following this line of thinking one could consider cases like (E^n)^n or even with repeated applications of the Cartesian product operation. Thus, in the case of (E^n)^n, one can think of different gamblers each having n-many dices in a cup and tossing these n-many dices simultaneously.

Thus we have something like the following structure for an empirical theory of classical probability: CPT(T) iff T=<G,E,X,n,S,P*>, with ‘G’ as the set of generators producing out of E events according to the layout of the set X in a static (deterministic) manner. Here the set E is the set of basic events. The set X is a ‘typified set’ constructed out of the set E with t-many applications of the Cartesian operation starting with E, then E^n1, then (E^n1)^n2, …. . ‘n’ denotes the number of repetitions, which determines the length of a sequence ‘S’. ‘P*’ represents the ’empirical probability’ which approaches the theoretical probability P while n is becoming ‘big’. P* is realized as a tuple of tuples according to the layout of the set X where each element in the range of a tuple represents the ‘number of occurrences’ of a certain event out of X.

Example: If there is a set E = {0,1} with the layout X=(E^2)^2 then we have two groups with two generators each: <<G1, G2>,<G3,G4>>. Every generator G_i produces events out of E. In one state i this could look like <<0, 0>,<1,0>>. As part of a sequence S this would look like S = <….,(<<0, 0>,<1,0>>,i), … > telling that in the i-th state of S there is an occurrence of events like shown. The empirical probability function P* has a corresponding layout P* = <<m1, m2>,<m3,m4>> with the m_j as ‘counter’ which are counting the occurrences of the different types of events as m_j =<c_e1, …, c_er>. In the example there are two different types of events occurring {0,1} which requires two counters c_0 and c_1, thus we would have m_j =<c_0, c_1>, which would induce for this example the global counter structure: P* = <<<c_0, c_1>, <c_0, c_1>>,<<c_0, c_1>,<c_0, c_1>>>. If the generators are all the same then the set of basic events E is the same and in theory the theoretical probability function P: E —> R+ would induce the same global values for all generators. But in the empirical case, if the theoretical probability function P is not known, then one has to count and below the ‘magic big n’ the values of the counter of the empirical probability function can be different.

This format of the empirical classical probability theory CPT can handle the case of ‘different generators‘ which produce events out of the same basic set E but with different probabilities, which can be counted by the empirical probability function P*. A prominent case of different probabilities with the same set of events is the case of manipulations of generators (a coin, a dice, a roulette wheel, …) to deceive other people.

In the examples mentioned so far the probabilities of the basic events as well as the complex events can be different in different generators, but are nevertheless ‘static’, not changing. Looking to generators like ‘tossing a coin’, ‘tossing a dice’ this seams to be sound. But what if we look to other types of generators like ‘biological systems’ which have to ‘decide’ which possible options of acting they ‘choose’? If the set of possible actions A is static, then the probability of selecting one action a out of A will usually depend from some ‘inner states’ IS of the biological system. These inner states IS need at least the following two components:(i) an internal ‘representation of the possible actions’ IS_A as well (ii) a finite set of ‘preferences’ IS_Pref. Depending from the preferences the biological system will select an action IS_a out of IS_A and then it can generate an action a out of A.

If biological systems as generators have a ‘static’ (‘deterministic’) set of preferences IS_Pref, then they will act like fixed generators for ‘tossing a coin’, ‘tossing a dice’. In this case nothing will change. But, as we know from the empirical world, biological systems are in general ‘adaptive’ systems which enables two kinds of adaptation: (i) ‘structural‘ adaptation like in biological evolution and (ii) ‘cognitive‘ adaptation as with higher organisms having a neural system with a brain. In these systems (example: homo sapiens) the set of preferences IS_Pref can change in time as well as the internal ‘representation of the possible actions’ IS_A. These changes cause a shift in the probabilities of the events manifested in the realized actions!

If we allow possible changes in the terms ‘G’ and ‘E’ to ‘G+’ and ‘E+’ then we have no longer a ‘classical’ probability theory CPT. This new type of probability theory we can call ‘non-classic’ probability theory NCPT. A short notation could be: NCPT(T) iff T=<G+,E+,X,n,S,P*> where ‘G+’ represents an adaptive biological system with changing representations for possible Actions A* as well as changing preferences IS_Pref+. The interesting question is, whether a quantum logic approach QLPT is a possible realization of such a non-classical probability theory. While it is known that the QLPT works for physical matters, it is an open question whether it works for biological systems too.

REMARK: switching from static generators to adaptive generators induces the need for the inclusion of the environment of the adaptive generators. ‘Adaptation’ is generally a capacity to deal better with non-static environments.