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:
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).
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.
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
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.
The property P is always part of some environment ENV which interacts with the problem P.
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.
Such a process can be described by an actor story AS.
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).
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.
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.
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.
For the analysis of a possible solution one can distinguish at least two overall strategies:
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.
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.
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
Generally it is assumed that the AAI theory is embedded in a general systems engineering approach starting with the clarification of a problem.
Two cases will be distinguished:
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.
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.
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.
Change: 6.February 2019 (Reformulating the ‘CONTEXT’ paragraph)
Change: 27.February 2019 (changing the order of the table of contents)
Change: 20.April 2019 (New section ‘The Big Picture…’)
Change: 3.-4.May 2019 (New section ‘Engineering and Society…’ and ‘Simulation and Gaming…)
Change: 5.May 2019 (Bringing the ‘bottom-up’ case in the background; it is now included in the normal AAI analysis)
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 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
Generally it is assumed that the AAI theory is embedded in a general systems engineering approach starting with the clarification of a problem.
Two cases will be distinguished:
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.
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.
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
The definition of a problem P presupposes a domain of affairs which has to be characterized in at least two respects:
A minimal description of an environment ENV of the problem P and
a list of so-called non-functional requirements (NFRs).
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.
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.
For the following analysis of a possible solution one can distinguish two strategies:
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.
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)
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.
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.
Changes from one state q to another successor state q’ are described by the object whose action deletes previous facts or creates new facts.
In this approach at least three different modes of an actor story will be distinguished:
A 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).
A textual mode generating a Textual Actor Story (TAS): In a textual mode a text in some everyday language (e.g. in English) describes the states and changes in plain English. Because in the case of a written text the meaning of the symbols is hidden in the heads of the writers it can be of help to parallelize the written text with the pictorial mode.
A 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.
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 .
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
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
##################################
# 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
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 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
LEARNING ENVIRONMENT
For an overview of all posts in this block about programming with python 3 see HERE.
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
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)
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.
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)
As a consequence of these considerations Griffiths develops the fundamental principles in the chapters 2-16 without making any reference to measurement.
PRE-KNOWLEDGE
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
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)
“A quantum property … corresponds to a subspace of the quantum Hilbert space or the projector onto this subspace.” (p.2)
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)
Quantum sample spaces can be mutually incompatible. (cf. p.3)
“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)
“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)
“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
“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
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)
“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)
“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
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
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.
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
This is a continuation from the post BACKGROUND INFORMATION 27.Dec.2018: The AAI-paradigm and Quantum Logic. The Limits of Classic Probability. 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 one is called CPT (classical probability theory), see the before mentioned post, and the other QLPT (quantum logic probability theory), which will be discussed now.
SUMMARY
First description of what Quantum Theory QT) is which is implying quantum logic.
QT AND REALITY
To approach the topic of QLTP we will start from a philosophy of science point of view beginning with the general question of the relation between ‘quantum theory (QT)’ and ‘reality’ (here we follow Griffiths (2003) in his final reflections about QT in chapter 27 of his book).
Griffiths makes the clear distinction between QT as a theory (T) and something we call real world (W) or physical reality which is clearly distinctfrom the theory.
A theory is realized as a set of symbolic expressions which are assumed to have a relation to the presupposed real world. The symbolic matter as such is not the theory but those structures in the mind of the scientists which are comprehended. In our mind – something ‘inside’ our body; usually located in the brain – we can in an abstract way distinguish elements and relations between these elements. Furthermore we can think about these elements and relations on a meta level and define concepts like ‘is coherent’, ‘is logical’, ‘is beautiful’.
Besides the definitions ‘inside the mind’ about ‘elements already in the mind’ (like ‘consistency’ …) there exists the question of the confirmation of theoretical constructs compared to the real world as it is. As we know there exist one primary mode of relationship and some secondary mode to interact with the presupposed ‘real world’:
The primary mode is the sensory perception, which generates typical internal events in the brain, and
the secondary mode is a sensory perception in cooperation with defined measurement procedures. Thus the measurement results are as such not different to other sensory perceptions but the measurement results are generated by a certain procedure which can be repeated from everybody who wants to look to the measurement results again, and this procedure is using a before agreed measurement standard object to give a point of reference for everybody.
The possible confirmation of theoretical constructs t of some theory T by measurements requires the availability of appropriate measurements communicated to the mind through the sensory perception and some mapping between the sensory data and the theoretical constructs. Usually the sensory data are by themselves not raw data but are symbolic expressions ‘representing the data in a symbolic format’. Thus the mapping in the mind has to connect the perceptions of the symbolic measurement with parts of the theory.
Because it is assumed that the theory is also encoded in symbolic expressions for communication one has to assume that one has to distinguish between the symbolic representation of the theory and their domain of application consisting of elements and relations generated in the mind. In modern formal theories the relationship between measurement expressions and theoretical expressions is defined in an appropriate logic describing possible inferences which deliver within a logical proof either a formal confirmation or not.
As Griffiths remarks the different confirmations of individual measurements do not guarantee the truth of the theory saying that the assumed theory is an adequate description of the presupposed real world. This results from the fact that every experimental confirmation can only give very partial confirmations compared to the nearly infinite space of possible statements which are entailed by a modern theory. Therefore it is finally a question of faith whether some proposed empirical theory is gaining acceptance and is used ‘as if it is true’. This means the theory can be refuted at any time point in the future.
For the QT Griffiths claims that nearly everybody today accepts QT as the best available theory about the real world.(cf. p.361)
Within QT the dynamical laws are inherently stochastic/ probabilistic, this means that the future behavior of a quantum system cannot be predicted with certainty. (cf. Griffiths (2003):p.362)
The reason for this unpredictability is that the elementary objects of the QT, the ‘quantum particles‘, have no precise position or momentum. A precise description of these particles is limited by the Heisenberg uncertainty principle. (cf. Griffiths (2003):p.361)
This inherent property of QT of having objects with no clear position and momentum allows the further fact that there can be different formalism logically incompatible with each other but nevertheless describing a certain aspect of the QT domain in a ‘sound’ manner. (cf. Griffiths (2003):pp.262-265)
While the interaction of a quantum system can be described, the ‘decoherence‘ of a macroscopic quantum superposition (MQS) state can directly not be measured. To enable a theoretic description for this properties requires concepts and a language which deviates from everyday experiences, concepts, and languages. (cf. Griffiths (2003):pp.265-268)
Summing up one gets the following list of important properties looking to an presupposed ‘independent real world’ (cf. Griffiths (2003):p.268f):
Physical objects never possess a completely precise position or momentum.
The fundamental dynamical laws of physics are stochastic and not deterministic.
There is not a unique exhaustive description of a physical system or a physical process.
Quantum measurements can be understood as revealing properties of a measured system before the measurement took place, in a manner which was taken for granted in classical physics.
Quantum mechanics is a local theory in the sense that the world can be understood without supposing that there are mysterious influences which propagate over long distances more rapidly than the speed of light.
Quantum mechanics is consistent with the notion of an independent reality, a real world whose properties and fundamental laws do not depend upon what human beings happen to believe, desire, or think.
Taking these assumptions for granted one has to analyze now what this implies for the description and computation of the behavior of states of properties generated by biological systems.
This post is part of the online book project for the AAI-paradigm. As mentioned in the text of the book the AAI paradigm will need for its practical usage appropriate software. Some preliminary (experimentally) programming is already underway. The programming language used for this programming is python. Here some bits of information how one can install a simple python environment to share these activities.
WINPYTHON OR ANACONDA WITH SPYDER (Windows as well as Linux (ubuntu))
To work with the python programming language — here python 3 — one needs some tools interacting with each other. For this different integrated development packages have been prepared. In this uffmm-software project I am using the spyder development environment either as part of the winpython distribution or as part of the anaconda distribution.
WINPYTHON DISTRIBUTION
The winpython package can be found here. See also the picture below.
Website of winpython distribution
If one has downloaded the winpython distribution in some local folder then you will see the following files and folders (see picture below):
winpython distribution folder after installation
SPYDER INTEGRATED ENVIRONMENT
To use the integrated spyder environment one can also look to the spyder website directly (see picture below).
spyder working environment for python – website
The spyder team recomments to download the spyder software as part of the bigger anaconda distribution with lots of additional options (see picture below).
spyder working environment embedded in the anaconda distribution
Downloading the anaconda distribution needs much more time then the winpython distribution. But one gets a lot of stuff and the software is fairly good integrated into the windows 10 operating system. I personally recomment for the beginners not to beginn with the complex anaconda environment but to stay with the spyder integrated environment only. This can be done by activating with the windows-button the list of apps, looking to the anaconda icon, and there one can find the spyder icon (an idealized spyder web). One can click with the right mouse button on this icon and then select to ‘add to the task bar’. After this operation you can observe the spyder icon as attached to the task bar like in the picture below.
Part of the task bar in windows with icons for spyder (right border) and a python environment (left from spyder)
If one activates the spyder icon a window opens showing some standard configuration of the integrated spyder development environment (see picture below).
spyder working environment with editor, console, and additional object informations
The most important sub-windows are the window left from the editor and the window right-below from the console. One can use the console to make small experiments with python commands and the editor to write larger source code. In the header bar are many helpful icons for editing, running of programs, testing, and more.
LINUX (UBUNTU)
If one is working with linux (what I am usually are doing; I use the distribution ubuntu 18.04.1 LTS) then python is part of the system in version 2 as well in version 3 and spyder can be used too.
WINPYTHON CONSOLE
Besides the integrated development editor (IDE) spyder you can find even more programming tools. One very helpful tool is the WinPython Console (see icon within the red circle). You can attach this icon on your task bar too and then you can start the Winpython Console by clicking on it.
Figure 1: Directory path after starting the WinPython Console
To apply this console to some python programm you have to navigate to that folder where you have the python program to be executed. If You do not know already the whole path then you have two options: (i) move the path upwards by using the command ‘cd ..’ (change directory one level upwards) or (ii) move the path downwards by using the command ‘cd DIR-NAME‘. If you are in a new folder you can use the command ‘dir‘ to list all the files and folders in the actual directory. Doing this You can reach the following folder with some python program files:
Figure 2: Folder with some python programs
There is one example file pop0e.py which we can start (the whole program will be described later in detail).
Figure 3: Shows an example run with the program pop0e.py, some print outs as well as a diagram.
For this last example with the Winpython Console the program can be edited by nearly any kind of a text editor. After the file has been saved with a .py ending one can use the console to start the program. In the last example (cf. figure 3) the important input was: ‘python pop0e.py‘ this states that the python interpreter shall take the program text of the file ‘pop0e.py’ and execute the program.
LEARNING ENVIRONMENT
For an overview of all posts in this block about programming with python 3 see HERE.
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.
As mentioned in a preceding post the AAI paradigm has to be reconsidered in the light of the quantum logic (QL) paradigm. Here some first concepts which have to be considered (see for the following text chapter two of the book: Jerome R. Busemeyer and Peter D. Bruza, Quantum Models of Cognition and Decision, Cambridge University Press, Cambridge (UK), 2012).
The paradigms of ‘quantum logic’ as well as ‘quantum probability theory’ arose in the field of physics, but as it became clear later these formalisms can be applied to other domains than physics too.
The basic application domain is a appears as a paradigm – real or virtual – in which one can distinguish ‘events‘ which can ‘occur‘ along a time-line as part of a bigger state. The ‘frequency‘ of the occurrences of the different events can be ‘counted’ as a function of the presupposed time-line. The frequency can be represented by a ‘number‘. The frequency can be a ‘total frequency’ for the ‘whole time-line’ or a ‘relative frequency’ with regard to some part of a ‘partition of the time-line’. Having relative frequencies these can possibly ‘change‘ from part to part.
The basic application domain can be mapped into a formalism which ‘explains’ the ‘probability’ of the occurrences of the events in the application domain. Such a formalism is an ‘abstraction’ or an ‘idealization‘ of a certain type of an application domain.
The two main types of formalisms dealt with in the mentioned book of Busemeyer and Bruza (2012) are called ‘classical probability theory’ and ‘quantum probability theory’.
The classical theory of probability (CTP)has been formalized as a theory in the book by A.N. Kolmogorov, Foundations of the Theory of Probability. Chelsea Publ. Company, New York, 2nd edition, 1956 (originally published in German 1933). The quantum logic version of the theory of probability (QLTP) has been formalized as a theory in the book John von Neumann, Mathematische Grundlagen der Quantenmechanik, published by Julius Springer, Berlin, 1932 (a later English version has been published 1956).
In the CTP the possible elementary events are members of a set E which is mapped into the set of positive real numbers R+. The probability of an event A is written as P(A)=r (with r in R*). The probability of the whole set E is assumed as P(E) = 1. The relationship between the formal theory CTP and the application domain is given by a mapping of the abstract concept of probability P(A) to the relation between the number of repetitions of some mechanism of event-generationn and the number of occurrences m of a certain event A written as n/m. If the number of repetitions is ‘big enough’, then – according to Kolmogorov — the relation ‘n/m’ will differ only slightly from the theoretical probability P(A) (cf. Kolmogorov (1956):p.4)
The expression ‘mechanism of event-generation‘ is very specific; in general we have a sequence of states along a time-line and some specific event A can occur in one of these states or not. If event A occurs then the number m of occurrences m is incremented while the number of repetitions n corresponds to the number of time points which are associated with a state of a possible occurrence counted since a time point declared as a ‘starting point‘ for the observation. Because time points in an application domain are related to machines called ‘clocks‘ the ‘duration‘ of a state is related to the ‘partition’ of a time unit like ‘second [s]’ realized by the used clock. Thus depending from the used clock can the number of repetitions become very large. Compared to the human perception can this clock-based number of repetitions be ‘misleading’ because a human observer has seen perhaps only two occurrences of the event A while the clock measured some number n* far beyond two. This short remark reveals that the relationship between an abstract term of ‘probability’ and an application domain is far from trivial. Basically it is completely unclear what theoretical probability means in the empirical world without an elaborated description of the relationship between the formal theory and the sequences of events in the real world.
Extending the main page another important idea has to be noticed: quantum logic, originally created in the realm of modern physics, has brought forward a formalism dealing with superposition states (states of substantial uncertainty for the observer). This formalism has meanwhile entered other disciplines, especially disciplines dealing with cognition and decision processes (see as an excellent example the book: Jerome R. Busemeyer and Peter D. Bruza, Quantum Models of Cognition and Decision, Cambridge University Press, Cambridge (UK), 2012).
As it turns out there is a bad and a good message for the AAI paradigm: the ‘bad’ message is, that the AAI formalism so far is written in a non-quantum logic style. Thus it seems as if the AAI paradigm is stuck with the classical pre-quantum view of the world. The ‘good’ message is, that this ‘pre-quantum’ style is only at the ‘surface’ of the AAI paradigm. If one considers the ‘actor models’ – which are a substantial component of the AAI paradigm – as ‘truly quantum-like systems‘ (what they are in the ‘normal case’), then one can think of the ‘actors’ as systems having three components at least: (i) a biological basis (or some equivalent matter) consisting of highly entangled quantum systems, which are organized as ‘biological bodies‘ with a brain; (ii) a ‘consciousness‘ interacting with (iii) an ‘unconsciousness‘. The consciousness is heavily depending from the behavior of the unconsciousness in a way which resembles a superposition state! By ‘learning‘ the system can store some ‘procedures’ for later activation in the unconsciousness, but the stored procedures (a) can not override the superposition state completely and (b) the stored procedures are not immune against changes in time. Thus from the point of ‘decisions’ and of ‘thinking’ an actor is always an inherently in-deterministic system which can better be described with a quantum-logic similar formalism than with a non-quantum-logic formalism.
In general one should abandon the term ‘quantum’ from the formalism because the domain of reference are not some physical ‘quanta’ below the atoms but complete learning systems with a stochastic unconsciousness as basis for learning.
To implement these quantum logic perspective into the AAI paradigm does not change the paradigm as a whole but primarily the descriptions of the participating actors.
As a consequence of this change the simulation process has to be seen in a new way: because every participating actor is a truly indeterministic system, the whole state at some time point t is a superposition state. Therefore every concrete simulation is a ‘selection’ of ‘one path out of many possible ones’. Thus a concrete simulation can only show one fragment of an unknown bigger space of possible other runs. And their is another point: because all actors are ‘learning’ actors in the unrestricted sense (known artificial intelligence systems today are strongly restricted learners!) the actors in the process are ‘changing’. Thus an actor at time point t+x is not the same as the actor with the same ‘name’ at an earlier time point t! To draw conclusions about possible ‘repetitions in the future’ is therefore dangerous. The future in a quantum-like world will never repeat the past.
If You are wondering why no new updates appear on the main page the reason why is, that some heavy work is going on in the background using the AAI paradigm published here so far within a German course called Mensch-Maschine Interaktion (MMI) in the Frankfurt University of Applied Sciences (FRA-UAS) as well in a growing interdisciplinary project where the AAI paradigm is applied to the topic of ‘communal planning using e-gaming’. Because both activities are in German there is time lacking to continue writing in English :-). In the context of the ‘communal planning with e-gaming’ project we are planning to do some more field-experiments in the upcoming months with ‘normal citizens’ using these methods as a ‘bottom-up strategy’ for getting shared models of their cities which can be simulated. It is highly probable that a small booklet in German will appear to support these experiments before this English version will be expanded.
During the time since Nov-4, 2018 the theory of the AAI paradigm could be improved in many points (documented in the German texts) and meanwhile I have started to program a first version of a software (in python) by myself. Doing this the experience is always the same: You think You ‘know’ the subject matter’ because You have written some texts with formulas, but if You are starting programming, You are challenged in a much more concrete way. Without theory the programming wouldn’t know what to do, but without programming you will never understand in a sufficient concrete way what You are thinking
Integrating Engineering and the Human Factor (info@uffmm.org) eJournal uffmm.org ISSN 2567-6458
