Category Archives: experimental psychology

REVIEW: Keith E.Stanovich, Richard F.West, Maggie E.Toplak, “The Rational Quotient. Towards a Test of Rational Thinking”, MIT Press, 2016

(Last change: Nov 1, 2023)

CONTEXT

This text belongs to the overall theme REVIEWS.

In the last months I was engaged with the topic of text-generating algorithms and the possible impact for a scientific discourse (some first notices to this discussion you can find here (https://www.uffmm.org/2023/08/24/homo-sapiens-empirical-and-sustained-empirical-theories-emotions-and-machines-a-sketch/)). In this context it is important to clarify the role and structure of human actors as well as the concept of Intelligence. Meanwhile I have abandoned the word Intelligence completely because the inflationary use in today mainstream pulverises any meaning. Even in one discipline — like psychology — you can find many different concepts. In this context I have read the book of Stanovich et.al to have a prominent example of using the concept of intelligence, there combined with the concept of rationality, which is no less vague.

Introduction

The book “The Rationality Quotient” from 2016 represents not the beginning of a discourse but is a kind of summary of a long lasting discourse with many publications before. This makes this book interesting, but also difficult to read in the beginning, because the book is using nearly on every page theoretical terms, which are assumed to be known to the reader and cites other publications without giving sufficient explanations why exactly these cited publications are important. This is no argument against this book but sheds some light on the reader, who has to learn a lot to understand the text.

A text with the character of summing up its subject is good, because it has a confirmed meaning about the subject which enables a kind of clarity which is typical for that state of elaborated point of view.

In the following review it is not the goal to give a complete account of every detail of this book but only to present the main thesis and then to analyze the used methods and the applied epistemological framework.

Main Thesis of the Book

The reviewing starts with the basic assumptions and the main thesis.

FIGURE 1 : The beginning. Note: the number ‘2015’ has to be corrected to ‘2016’.

FIGURE 2 : First outline of cognition. Note: the number ‘2015’ has to be corrected to ‘2016’.

As mentioned in the introduction you will in the book not find a real overview about the history of psychological research dealing with the concept of Intelligence and also no overview about the historical discourse to the concept of Rationality, whereby the last concept has also a rich tradition in Philosophy. Thus, somehow you have to know it.

There are some clear warnings with regard to the fuzziness of the concept rationality (p.3) as well as to the concept of intelligence (p.15). From a point of view of Philosophy of Science it could be interesting to know what the circumstances are which are causing such a fuzziness, but this is not a topic of the book. The book talks within its own selected conceptual paradigm. Being in the dilemma, of what kind of intelligence paradigm one wants to use, the book has decided to work with the Cattell-Horn-Carroll (CTC) paradigm, which some call a theory. [1]

Directly from the beginning it is explained that the discussion of Intelligence is missing a clear explanation of the full human model of cognition (p.15) and that intelligence tests therefore are mostly measuring only parts of human cognitive functions. (p.21)

Thus let us have a more detailed look to the scenario.

[1] For a first look to the Cattell–Horn–Carroll theory see: https://en.wikipedia.org/wiki/Cattell%E2%80%93Horn%E2%80%93Carroll_theory, a first overview.

Which point of View?

The book starts with a first characterization of the concept of Rationality within a point of view which is not really clear. From different remarks one gets some hints to modern Cognitive Science (4,6), to Decision Theory (4) and Probability Calculus (9), but a clear description is missing.

And it is declared right from the beginning, that the main aim of the book is the Construction of a rational Thinking Test (4), because for the authors the used Intelligence Tests — later reduced to the Carroll-Horn-Carroll (CHC) type of intelligence test (16) — are too narrow in what they are measuring (15, 16, 21).

Related to the term Rationality the book characterizes some requirements which the term rationality should fulfill (e.g. ‘Rationality as a continuum’ (4), ’empirically based’ (4), ‘operationally grounded’ (4), a ‘strong definition’ (5), a ‘normative one’ (5), ‘normative model of optimum judgment’ (5)), but it is more or less open, what these requirements imply and what tacit assumptions have to be fulfilled, that this will work.

The two requirements ’empirically based’ as well as ‘operationally grounded’ point in the direction of an tacitly assumed concept of an empirical theory, but exactly this concept — and especially in association with the term cognitive science — isn’t really clear today.

Because the authors make in the next pages a lot of statements which claim to be serious, it seems to be important for the discussion in this review text to clarify the conditions of the ‘meaning of language expressions’ and of being classified as ‘being true’.

If we assume — tentatively — that the authors assume a scientific theory to be primarily a text whose expressions have a meaning which can transparently be associated with an empirical fact and if this is the case, then the expression will be understood as being grounded and classified as true, then we have characterized a normal text which can be used in everyday live for the communication of meanings which can become demonstrated as being true.

Is there a difference between such a ‘normal text’ and a ‘scientific theory’? And, especially here, where the context should be a scientific theory within the discipline of cognitive science: what distinguishes a normal text from a ‘scientific theory within cognitive science’?

Because the authors do not explain their conceptual framework called cognitive science we recur here to a most general characterization [2,3] which tells us, that cognitive science is not a single discipline but an interdisciplinary study which is taking from many different disciplines. It has not yet reached a state where all used methods and terms are embedded in one general coherent framework. Thus the relationship of the used conceptual frameworks is mostly fuzzy, unclear. From this follows directly, that the relationship of the different terms to each other — e.g. like ‘underlying preferences’ and ‘well ordered’ — is within such a blurred context rather unclear.

Even the simple characterization of an expression as ‘having an empirical meaning’ is unclear: what are the kinds of empirical subjects and the used terms? According to the list of involved disciplines the disciplines linguistics [4], psychology [5] or neuroscience [6] — besides others — are mentioned. But every of these disciplines is itself today a broad field of methods, not integrated, dealing with a multifaceted subject.

Using an Auxiliary Construction as a Minimal Point of Reference

Instead of becoming somehow paralyzed from these one-and-all characterizations of the individual disciplines one can try to step back and taking a look to basic assumptions about empirical perspectives.

If we take a group of Human Observers which shall investigate these subjects we could make the following assumptions:

  1. Empirical Linguistics is dealing with languages, spoken as well as written by human persons, within certain environments, and these can be observed as empirical entities.
  2. Empirical Psychology is dealing with the behavior of human persons (a kind of biological systems) within certain environments, and these can be observed.
  3. Empirical Neuroscience is dealing with the brain as part of a body which is located in some environment, and this all can be observed.

The empirical observations of certain kinds of empirical phenomena can be used to define more abstract concepts, relations, and processes. These more abstract concepts, relations, and processes have ‘as such’ no empirical meaning! They constitute a formal framework which has to become correlated with empirical facts to get some empirical meaning. As it is known from philosophy of science [7] the combination of empirical concepts within a formal framework of abstracts terms can enable ‘abstract meanings’ which by logical conclusions can produce statements which are — in the moment of stating them — not empirically true, because ‘real future’ has not yet happened. And on account of the ‘generality’ of abstract terms compared to the finiteness and concreteness of empirical facts it can happen, that the inferred statements never will become true. Therefore the mere usage of abstract terms within a text called scientific theory does not guarantee valid empirical statements.

And in general one has to state, that a coherent scientific theory including e.g. linguistics, psychology and neuroscience, is not yet in existence.

To speak of cognitive science as if this represents a clearly defined coherent discipline seems therefore to be misleading.

This raises questions about the project of a constructing a coherent rational thinking test (CART).

[2] See ‘cognitive science’ in wikipedia: https://en.wikipedia.org/wiki/Cognitive_science

[3] See too ‘cognitive science’ in the Stanford Encyclopedia of Philosophy: https://plato.stanford.edu/entries/cognitive-science/

[4] See ‘linguistics’ in wikipedia: https://en.wikipedia.org/wiki/Linguistics

[5] See ‘psychology’ in wikipedia: https://en.wikipedia.org/wiki/Psychology

[6] See ‘neuroscience’ in wikipedia: https://en.wikipedia.org/wiki/Neuroscience

[7] See ‘philosophy of science’ in wikipedia: https://en.wikipedia.org/wiki/Philosophy_of_science

‘CART’ TEST FRAMEWORK – A Reconstruction from the point of View of Philosophy of Science

Before I will dig deeper into the theory I try to understand the intended outcome of this theory as some point of reference. The following figure 3 gives some hints.

FIGURE 3 : Outline of the Test Framework based on the Appendix in Stanovich et.al 2016. This Outline is a Reconstruction by the author of this review.

It seems to be important to distinguish at least three main parts of the whole scientific endeavor:

  1. The group of scientists which has decided to process a certain problem.
  2. The generated scientific theory as a text.
  3. The description of a CART Test, which describes a procedure, how the abstract terms of the theory can be associated with real facts.

From the group of scientists (Stanovich et al.) we know that they understand themselves as cognitive scientists (without having a clear characterization, what this means concretely).

The intended scientific theory as a text is here assumed to be realized in the book, which is here the subject of a review.

The description of a CART Test is here taken from the appendix of the book.

To understand the theory it is interesting to see, that in the real test the test system (assumed here as a human person) has to read (and hear?) a instruction, how to proceed with a task form, and then the test system (a human person) has to process the test form in the way it has understood the instructions and the test form as it is.

The result is a completed test form.

And it is then this completed test form which will be rated according to the assumed CART theory.

This complete paradigm raises a whole bunch of questions which to answer here in full is somehow out of range.

Mix-Up of Abstract Terms

Because the Test Scenario presupposes a CART theory and within this theory some kind of a model of intended test users it can be helpful to have a more closer look to this assumed CART model, which is located in a person.

FIGURE 4 : General outline of the logic behind CART according to Stanovich et al. (2016).

The presented cognitive architecture shall present a framework for the CART (Comprehensive Assessment of Rational Thinking), whereby this framework is including a model. The model is not only assumed to contextualize and classify heuristics and tasks, but it also presents Rationality in a way that one can deduce mental characteristics included in rationality.(cf. 37)

Because the term Rationality is not an individual empirical fact but an abstract term of a conceptual framework, this term has as such no meaning. The meaning of this abstract term has to be arranged by relations to other abstract terms which themselves are sufficiently related to concrete empirical statements. And these relations between abstract terms and empirical facts (represented as language expressions) have to be represented in a manner, that it is transparent how the the measured facts are related to the abstract terms.

Here Stanovich et al. is using another abstract term Mind, which is associated with characteristics called mental characteristics: Reflective mind, Algorithmic Level, and Mindware.

And then the text tells that Rationality is presenting mental characteristics. What does this mean? Is rationality different from the mind, who has some characteristics, which can be presented from rationality using somehow the mind, or is rationality nevertheless part of the mind and manifests themself in these mental characteristics? But what kind of the meaning could this be for an abstract term like rationality to be part of the mind? Without an explicit model associated with the term Mind which arranges the other abstract term Rationality within this model there exists no meaning which can be used here.

These considerations are the effect of a text, which uses different abstract terms in a way, which is rather unclear. In a scientific theory this should not be the case.

Measuring Degrees of Rationality

In the beginning of chapter 4 Stanovich et al. are looking back to chapter 1. Here they built up a chain of arguments which illustrate some general perspective (cf. 63):

  1. Rationality has degrees.
  2. These degrees of rationality can be measured.
  3. Measurement is realized by experimental methods of cognitive science.
  4. The measuring is based on the observable behavior of people.
  5. The observable behavior can manifest whether the individual actor (a human person) follows assumed preferences related to an assumed axiom of choice.
  6. Observable behavior which is classified as manifesting assumed internal preferences according to an assumed internal axiom of choice can show descriptive and procedural invariance.
  7. Based on these deduced descriptive and procedural invariance, it can be inferred further, that these actors are behaving as if they are maximizing utility.
  8. It is difficult to assess utility maximization directly.
  9. It is much easier to assess whether one of the axioms of rational choice is being violated.

These statements characterize the Logic of the CART according to Stanovich et al. (cf.64)

A major point in this argumentation is the assumption, that observable behavior is such, that one can deduce from the properties of this behavior those attributes/ properties, which point (i) to an internal model of an axiom of choice, (ii) to internal processes, which manifest the effects of this internal model, (iii) to certain characteristics of these internal processes which allow the deduction of the property of maximizing utility or not.

These are very strong assumptions.

If one takes further into account the explanations from the pages 7f about the required properties for an abstract term axiom of choice (cf. figure 1) then these assumptions appear to be very demanding.

Can it be possible to extract the necessary meaning out of observable behavior in a way, which is clear enough by empirical standards, that this behavior shows property A and not property B ?

As we know from the description of the CART in the appendix of the book (cf. figure 3) the real behavior assumed for an CART is the (i) reading (or hearing?) of an instruction communicated by ordinary English, and then (ii) a behavior deduced from the understanding of the instruction, which (iii) manifests themself in the reading of a form with a text and filling out this form in predefined positions in a required language.

This described procedure is quite common throughout psychology and similar disciplines. But it is well known, that the understanding of language instructions is very error-prone. Furthermore, the presentation of a task as a text is inevitably highly biased and additionally too very error-prone with regard to the understanding (this is a reason why in usability testing purely text-based tests are rather useless).

The point is, that the empirical basis is not given as a protocol of observations of language free behavior but of a behavior which is nearly completely embedded in the understanding and handling of texts. This points to the underlying processes of text understanding which are completely internal to the actor. There exists no prewired connection between the observable strings of signs constituting a text and the possible meaning which can be organized by the individual processes of text understanding.

Stopping Here

Having reached this point of reading and trying to understand I decided to stop here: to many questions on all levels of a scientific discourse and the relationships between main concepts and terms appear in the book of Stanovich et al. to be not clear enough. I feel therefore confirmed in my working hypothesis from the beginning, that the concept of intelligence today is far too vague, too ambiguous to contain any useful kernel of meaning any more. And concepts like Rationality, Mind (and many others) seem to do not better.

Chatting with chatGPT4

Since April 2023 I have started to check the ability of chatGPT4 to contribute to a philosophical and scientific discourse. The working hypothesis is, that chatGPT4 is good in summarizing the common concepts, which are used in public texts, but chatGPT is not able for critical evaluations, not for really new creative ideas and in no case for systematic analysis of used methods, used frameworks, their interrelations, their truth-conditons and much more, what it cannot. Nevertheless, it is a good ‘common sense check’. Until now I couldn’t learn anything new from these chats.

If you have read this review with all the details and open questions you will be perhaps a little bit disappointed about the answers from chatGPT4. But keep calm: it is a bit helpful.

Protocol with chatGPT4

ACTOR-ACTOR INTERACTION [AAI] WITHIN A SYSTEMS ENGINEERING PROCESS (SEP). An Actor Centered Approach to Problem Solving

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

ATTENTION: The actual Version  you will find HERE.

Draft version 22.June 2018

Update 26.June 2018 (Chapter AS-AM Summary)

Update 4.July 2018 (Chapter 4 Actor Model; improving the terminology of environments with actors, actors as input-output systems, basic and real interface, a first typology of input-output systems…)

Update 17.July 2018 (Preface, Introduction new)

Update 19.July 2018 (Introduction final paragraph!, new chapters!)

Update 20.July 2018 (Disentanglement of chapter ‘Simulation & Verification’ into two independent chapters; corrections in the chapter ‘Introduction’; corrections in chapter ‘AAI Analysis’; extracting ‘Simulation’ from chapter ‘Actor Story’ to new chapter ‘Simulation’; New chapter ‘Simulation’; Rewriting of chapter ‘Looking Forward’)

Update 22.July 2018 (Rewriting the beginning of the chapter ‘Actor Story (AS)’, not completed; converting chapter ‘AS+AM Summary’ to ‘AS and AM Philosophy’, not completed)

Update 23.July 2018 (Attaching a new chapter with a Case Study illustrating an actor story (AS). This case study is still unfinished. It is a case study of  a real project!)

Update 7.August 2018 (Modifying chapter Actor Story, the introduction)

Update 8.August 2018 (Modifying chapter  AS as Text, Comic, Graph; especially section about the textual mode and the pictorial mode; first sketch for a mapping from the textual mode into the pictorial mode)

Update 9.August 2018 (Modification of the section ‘Mathematical Actor Story (MAS) in chapter 4).

Update 11.August 2018 (Improving chapter 3 ‘Actor Story; nearly complete rewriting of chapter 4 ‘AS as text, comic, graph’.)

Update 12.August 2018 (Minor corrections in the chapters 3+4)

Update 13.August 2018 (I am still catched by the chapters 3+4. In chapter  the cognitive structure of the actors has been further enhanced; in chapter 4 a complete example of a mathematical actor story could now been attached.)

Update 14.August 2018 (minor corrections to chapter 4 + 5; change-statements define for each state individual combinatorial spaces (a little bit like a quantum state); whether and how these spaces will be concretized/ realized depends completely from the participating actors)

Update 15.August 2018 (Canceled the appendix with the case study stub and replaced it with an overview for  a supporting software tool which is needed for the real usage of this theory. At the moment it is open who will write the software.)

Update 2.October 2018 (Configuring the whole book now with 3 parts: I. Theory, II. Application, III. Software. Gerd has his focus on part I, Zeynep will focus on part II and ‘somebody’ will focus on part III (in the worst case we will — nevertheless — have a minimal version :-)). For a first quick overview about everything read the ‘Preface’ and the ‘Introduction’.

Update 4.November 2018 (Rewriting the Introduction (and some minor corrections in the Preface). The idea of the rewriting was to address all the topics which will be discussed in the book and pointing out to the logical connections between them. This induces some wrong links in the following chapters, which are not yet updated. Some chapters are yet completely missing. But to improve the clearness of the focus and the logical inter-dependencies helps to elaborate the missing texts a lot. Another change is the wording of the title. Until now it is difficult to find a title which is exactly matching the content. The new proposal shows the focus ‘AAI’ but lists the keywords of the main topics within AAA analysis because these topics are usually not necessarily associated with AAI.)

ACTOR-ACTOR INTERACTION [AAI]. An Actor Centered Approach to Problem Solving. Combining Engineering and Philosophy

by

GERD DOEBEN-HENISCH in cooperation with  LOUWRENCE ERASMUS, ZEYNEP TUNCER

LATEST  VERSION AS PDF

BACKGROUND INFORMATION 19.Dec.2018: Application domain ‘Communal Planning and e-Gaming’

BACKGROUND INFORMATION 24.Dec.2018: The AAI-paradigm and Quantum Logic

PRE-VIEW: NEW EXPANDED AAI THEORY 23.January 2019: Outline of the new expanded  AAI Paradigm. Before re-writing the main text with these ideas the new advanced AAI theory will first be tested during the summer 2019 within a lecture with student teams as well as in  several workshops outside the Frankfurt University of Applied Sciences with members of different institutions.

ACTOR-ACTOR INTERACTION. Philosophy of the Actor

eJournal: uffmm.org, ISSN 2567-6458
16.March 2018
Email: info@uffmm.org
Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de
Frankfurt University of Applied Sciences (FRA-UAS)
Institut for New Media (INM, Frankfurt)

PDF

CONTENTS

I   A Vision as a Problem to be Solved … 1
II   Language, Meaning & Ontology …  2
     II-A   Language Levels . . . . . . . . .  . . 2
     II-B  Common Empirical Matter .  . . . . . 2
     II-C   Perceptual Levels . . . . . . .  . . . . 3
     II-D   Space & Time . . . . . . . .  . . . . . 4
     II-E    Different Language Modes . . . 4
     II-F    Meaning of Expressions & Ontology … 4
     II-G   True Expressions . . . . . . .  . . . .  5
     II-H   The Congruence of Meaning  . . . .  5
III   Actor Algebra … 6
IV   World Algebra  … 7
V    How to continue … 8
VI References … 8

Abstract

As preparation for this text one should read the chapter about the basic layout of an Actor-Actor Analysis (AAA) as part of an systems engineering process (SEP). In this text it will be described which internal conditions one has to assume for an actor who uses a language to talk about his observations oft he world to someone else in a verifiable way. Topics which are explained in this text are e.g. ’language’,’meaning’, ’ontology’, ’consciousness’, ’true utterance’, ’synonymous expression.

INTELLIGENT MACHINES – INTRODUCTION

eJournal: uffmm.org,
ISSN 2567-6458, 09.Oct 2017 – April 9, 2022, 13:30 h
Email: info@uffmm.org
Author: Gerd Doeben-Henisch
Email: gerd@doeben-henisch.de

 Remark April 2022

This post from Oct 2017 will be reviewed in the new conceptual framework of an Applied Empirical Theory [AET] with an additional Dynamic Format [DF]. For more details see HERE.

OVERVIEW

A short story telling You, (i) how we interface the intelligent machines (IM) part with the actor-actor interaction (AAI) part, (ii) a first working definition of intelligent machines (IM) in this text, and (iii) defining intelligence and how one can this measure.

IM WITHIN AAI

In this blog we see IM not isolated, as a stand alone endeavor, but as embedded in a discipline called actor-actor interaction (AAI)(later called DAAI := Distributed Actor Actor Interaction).  AAI investigates complex tasks and looks how different kinds of actors are interacting in these contexts with technical systems. As far as the participating systems have been technical systems one speaks here of a system interface (SI) as that part of a technical system, which is interacting with the human actor. In the case of biological systems (mostly humans, but it could be animals as well), one speaks of the user interface (UI). In this text we generalize both cases by the general concept of an actor — biological and non-biological –, which has some actor interface (ActI), and this actor interface embraces all properties which are relevant for the interactions of the actor.

For the analysis of the behavior of actors in such task-environments one can distinguish two important concepts: the actor story (AS) describing the context as an observable process, as well as different actor models (AM). Actor models are special extensions of an actor story because an actor model describes the observable behavior of actors as a behavior function (BF) with a set of assumptions about possible internal states of the actors. The assumptions about possible internal states (IS) are either completely arbitrary or empirically motivated.

The embedding of IM within AAI can be realized through the concept of an actor model (UM) and the actor story (AS). Whatever is important for something which is called an intelligent machine application (IMA) can be defined as an actor model within an actor story. This embedding of IM within AAI offers many advantages.

This has to be explained with some more details.

An Intelligent Machine (IM) in an Actor Story

Let us assume that there exists a mathematical-graph representation of an actor story written as AS_{L_{ε}}. Such a graph has nodes which represent situations. Formally these are sets of properties, probably more fine-grained by subsets which represent different kinds of actors embedded in this situation as well as different kinds of non-actors.

Actors can be classified (as introduced above) as either biological actors (BA) or non-biological actors (NBA). Both kinds of actors can — in another reading — be subsumed under the general term of input-output-systems (IO-SYS). An input-output system can be a learning system or non-learning. Another basic property is that of being intelligent or non-intelligent. Being a learning system and being an intelligent system is usually strongly connected, but this must not necessarily be so. Being a learning system can be associated with being non-intelligent and being intelligent can be connected with being non-learning.(cf. Figure 1)

Classification of input-output systems according to learning, intelligence and beeing biological or not biological
Classification of input-output systems according to learning, intelligence and being biological or non-biological

While biological systems are always learning and intelligent, one can find non-biological systems of all types: non-learning and non-intelligent, non-intelligent and learning, non-learning and intelligent, and learning and intelligent.

Learning System

To classify a system as a learning system this requires the general ability to change the behavior of this system in time thus that there exists a time-span (t1,t2) after which the behavior as response to  certain critical stimuli has changed compared to the time before. [1] From this requirement it follows, that a learning system is an input-output system with at least one internal state which can change. Thus we have the general assumption:

Def: Learning System (LS)

  1. LS(x) iff
  2. x=<I, O, IS, phi >
  3. φ : I x IS —> IS x O
  4. I := Input
  5. O := Output
  6. IS := Internal states

Some x is a learning system (LS) if it is a structure containing sets for input (I), Output (O), as well as internal states (IS). These sets are operated by a behavior function φ which maps inputs and actual internal states to output as well as back to internal states. The set of possible learning functions is infinite.

Intelligent System

The term ‘intelligent’ and ‘intelligence’ is until now not standardized. This means that everybody is using it at little bit arbitrarily.

In this text we take the basic idea of a scientific usage of the term ‘intelligence’ from experimental psychology, which has developed clearly defined operational concepts since the end of the 19. Century which have been proved as quite stable in their empirical applications. [2a,b,c] 

The central idea of the psychological concept of the usage of the term ‘intelligence’ is to associate the usage of the term ‘intelligence’ with observable behavior of those actors, which shall be classified according defined methods of measurement.

In the case of experimental psychology the actors have been biological systems, mainly humans, in the first years of the research school children of certain ages. Because nobody did know what ‘intelligence’ means ‘as such’ one agreed to accept the observable behavior of children in certain task environments as ‘manifestations’ of a ‘presupposed unknown intelligence’. Thus the ability of children to solve defined tasks in a certain defined manner became a norm for what is called ‘intelligence’. Solving the tasks in a certain time with less than a certain amount of errors was used as a ‘baseline’ and all behavior deviating from the baseline was ‘better’ or ‘poorer’.

Thus the ‘content’ of the ‘meaning’ of the term ‘intelligence’ has been delegated to historical patterns of behavior which were common in a certain time-span in a certain geographical and cultural region.

While these behavior patterns can change during the course of time the general method of measurement is invariant.

In the time since then experimental psychology has modified and elaborated this first concept in some directions.

One direction is the modification of the kind of tasks which are used for the tests. With regard to the cultural context one has modified the content, thereby looking to find such kinds of task which seem to be ‘invariant’ with regard to the presupposed intelligence factor. This is an ongoing process.

The other direction is the focus on the actors as such. Because biological systems like humans change the development of their intelligence with age one has tried to find out ‘typical tasks for every age’. This too is an ongoing process.

This history of experimental psychology gives very interesting examples how one can approach the problem of the usage and the measurement of some X which we call ‘intelligence’.

In the context of an AAI-approach we have not only biological systems, but also non-biological systems. Thus most of the elaborated parameters of psychology for human actors are not general enough.

One possible strategy to generalize the intelligence-paradigm of experimental psychology could be to ‘free’ the selection of task sets from the narrow human cultures of the past and require only ‘clearly defined task sets with defined interfaces and defined contexts’. All these tasks sets can be arranged either in one super-set or in a parameterized field of sets. The sum of all these sets defines then a space of possible behavior and associated with this a space of possible measurable intelligence.

A task has then to be given as an actor story according to the AAI-paradigm. Such a specified actor story allows the formal definition of a complexity measure which can be used to measure the ‘amount of intelligence necessary to solve such a task’.

With such a more general and extendable approach to the measurement of observable intelligence one can compare all kinds of systems with each other. With such an approach one can further show objectively, where biological and non-biological systems differ generally, where they are similar, and to which extend they differ with regard to concrete circumstances.

Measuring Intelligence by Actor Stories

Presupposing actor stories (AS) (ideally formalized as mathematical graphs) on can define a first operational general measurement of intelligence.

Def: Task-Intelligence of a task τ (TInt(τ))

    1. Every defined task τ represents a graph g with one shortest path pmin(τ)= π_{min} from a start node to a goal node.
    2. Every such shortest path π_{min} has a certain number of nodes path-nodes(π_{min})=ν.
    3. The number of solved nodes (ν_{solved}) can become related against the total number of nodes ν as ν_{solved}/ν. We take TInt(τ)= ν_{solved}/ν. It follows that TInt(τ) is between 0 and 1: 0 ≤ TInt(τ)≤ 1.
    4. To every task  a maximal duration Δ_{max} is attached; all nodes which are solved within this maximal duration time Δ_{max} are declared as ‘solved’, all the others as ‘un-solved’.

The usual case will require more than one task to be realized. Thus we introduce the concept of a task field (TF).

Def: Task-Field of type x (TF_{x})
Def: Task-Field Intelligence (TFInt)

A task-field TF of type x includes a finite set of individual tasks like TF_{x} = { τ{x.1}, τ{x.2}, … , τ{x.n} } with n ≥ 2. The sum of all individual task intelligence values TInt(τ{x.i}) has to be normalized to 1, i.e. (TInt(τ{x.1}) + TInt(τ{x.2}) + … + TInt(τ{x.n}))/ n (with 0 in the nominator not allowed). Thus the value of the intelligence of a task field of type x TFInt(TF_{x}) is again in the domain of [0,1].

Because the different tasks in a task field TF can be of different difficulty it should be possible to introduce some weighting for the individual task intelligence values. This should not change the general mechanism.

Def: Combined Task-Fields (TF)

In face of the huge variety of possible task fields in this world it can make sens to introduce more general layers by grouping task fields of different types together to larger combined fields, like TF_{x,…,z} = TF_{x} ∪ TF_{y} ∪ … ∪ TF_{z}. The task field intelligence TFInt of such combined task fields would be computed as before.

Def: Omega Task-Field at time t (TF_{ω}(t))

The most comprehensive assembly of such combinations shall here be called the Omega-Task-Field at time t TF_{ω}(t). This indicates the known maximum of intelligence measurements at that point of time.

Measurement Comments

With these assumptions the term intelligence will be restricted to clearly defined domains either to an individual task, to a task-field of type x, or to some grouped task-fields or being related to the actual omega task-field. In every such domain the intelligence value is in the realm of [0,1] or written as some value between 0 or 100%.

Independent of the type of an actor — biological or not — one can measure the intelligence of such an actor with the same domains of defined tasks. As a result one can easily compare all known actors with regard to such defined task domains.

Because the acting actors can be quite different by their input-output capabilities it follows that every actor has to organize some interface which enables him to use the defined task. There are no special restrictions to the format of such an interface, but there is one requirement which has to be observed strictly: the interface as such is not allowed to do any kind of computation beyond providing only the necessary input from the task domain or to provide the necessary output to the domain. Only then are the different tests able to reveal some difference between the different actors.

If the tests show differences between certain types of actors with regard to a certain task or a task-field then this is a chance to develop smart assistive interfaces which can help the actor in question to overcome his weakness compared to the other type of actor. Thus this kind of measuring intelligence can be a strong supporter for a better world in the future.

Another consequence of the differing intelligence values can be to look to the inner structure of an actor with weaker values and asking how one could improve his capabilities. This can be done e.g. by different kinds of training or by improving his system structures.

COMMENTS

[1] Sara J.Shettleworth, Biological Approaches to the Study of Learning, pp.185 – 219, in: N.J.Mackintosh (Ed.), Animal Learning and Cognition, Academic Press, San Diego, New York, London et.al., 1994

[2a] Ernest R.Hilgard, Rita L.Atkinson, Richard C.Atkinson, Introduction to Psychology, Harcourt Brace Jovanovic, Inc., Psychology, 7th ed., New York, San Diego, Chicago et.al, 1979

[2b] Detlef H.Rost, Intelligenz. Fakten und Mythen, Belz Verlag, Weinheim – Basel, 2009

[2c] Detlef H.Rost, Handbuch Intelligenz, Beltz Verlag, Weinheim – Basel, 2013