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- 1.
It is not important here if the artificial systems “really” understand or if they are “only” simulating understanding. We shall deal with the discussion about “strong” versus “weak” AI in Section 1.4.
- 2.
Actually the basic idea of such a formal calculus is much older. Already in the thirteenth and fourteenth century the scholastic philosopher Raimundus Lullus developed the program of an ars combinatoria, i.e. a formal method for combining different concepts in order to solve philosophical problems. Yet the idea of Lullus, naturally, found not much interest. Nowadays it reminds of certain modern computer programs that operate in a similar manner.
- 3.
In contrast to the possibility of the natural sciences Vico accepted the possibility of a science of mathematics because the objects of mathematics are also our own products (Vico 1947).
- 4.
That what is true and what has been made converge (our translation).
- 5.
The program of a “real” Artificial Intelligence , realized by the construction of sophisticated expert systems , failed too and probably for the same reasons: This program also simply denied the fact that human thinking is indeed partly only understandable in terms of hermeneutics. It must be noted, however, that expert systems are nowadays widely applied to all kinds of problems, e.g. in medical, technical, and economical domains.
- 6.
We are certainly by far not the only scholars in the social and cognitive sciences, who use the concepts and methodical approaches of “complexity science”. For a detailed and systematic overview of the influence of complexity science on the social sciences cf. Castellani and Hafferty (2009); an impression of the merging of complexity science and cognitive ones gives the collection of Polk and Seifert (2002).
- 7.
Examples for such cases are given, for example, in Epstein (1997).
- 8.
Already at the beginning of modern (natural) science one of its founders, namely Galileo Galilei, postulated this thought when he declared, “the book of nature is written in mathematical letters”. More than a century later Immanuel Kant, the probably greatest mind of the Enlightenment, remarked that each theory of nature is only so far science as it contains mathematics (Metaphysical Foundations of the Natural Sciences).
- 9.
“Simple” is, of curse, to be understood only in a relative manner. Many of the greatest minds of the human species have demonstrated how difficult it is even to understand these “simple” systems.
- 10.
Several social theorists rather early saw the possibilities the new mathematical ways could offer to the social-cognitive sciences. For example, Kurt Lewin, one of the founders of gestalt theory, spoke of a “topological psychology” and postulated the introduction of vector algebra into the social-cognitive sciences (Lewin 1969). Bourbaki, by the way, was the pseudonym of a group of French mathematicians.
- 11.
Actually von Neumann got the basic idea for cellular automata from Stanislav Ulam, the mathematical father of the hydrogen bomb.
- 12.
Conway did his first experiments with the Game of Life without using computers. He instead used little black and white plates like those known from the game of Go. Records tell us that soon his working room and other rooms were full of these plates and that it was literally impossible to capture different developments of his cellular automaton in dependency of different initial states (cf. Levy 1993).
- 13.
Holland, Rechenberg, and other pioneers in the field of evolutionary algorithms based their models on the famous “modern synthesis” in evolutionary biology (Huxley 1942). In the meantime, though, recent developments in evolutionary biology demonstrate that the modern synthesis is too simple to capture the complexity of biological evolution . In particular it is apparently necessary not only to consider simple genes as the fundamentals of evolution but also to differentiate between “toolkit” genes – the sort of genes functionally known since Mendel – and so-called regulator genes (cf. Carroll 2006).
- 14.
Basically of course a computer itself is nothing else than a huge ensemble of logical circuits, i.e. a technical application of mathematical logic.
- 15.
Reversible cellular automata are t-invariant systems, i.e. they allow computing their states in the future and the past. An Abelian group is one with commutative operations.
- 16.
Recently the former planet Pluto is not considered as a planet anymore.
- 17.
In the natural sciences frequently the term “phase state” is used instead of state space.
- 18.
The picture was drawn by Magdalena Stoica. By the way, after having made many didactical experiences with this terminology we learned that the tem “basin of attraction ” is a rather unfortunate one. Frequently students thought that the lake in the picture is the basin and not the set of different springs. A better term would be, e.g., “set of attractor springs” or “set of attractor initial states”. But because the term “basin of attraction” has been established for rather a long time we also use this term.
- 19.
The general rules characterize the algebraic properties of the respective system, the topological rules its topology – hence the name.
- 20.
The Greek word meta means exactly that, namely “above”, “beyond” or “upon” like in “metaphysics” or in “meta mathematics”.
- 21.
We borrow the term of “would-be worlds” from Casti 1997.
- 22.
Perhaps the most famous story of such a simulation is the novel “Confessions of the confidence trickster Felix Krull” (Bekenntnisse des Hochstaplers Felix Krull) by Thomas Mann.
- 23.
The procedure of partitioning a set of data or samples into equivalence classes is also frequently used for testing the validity of a computer program.
- 24.
In many adventure stories the hero is able to impress the natives of a simple tribe or a pre-scientific society by correctly predicting an eclipse of the sun and by that to save his life. The scientific reason for this capability is the t-invariance of the Kepler equations.
- 25.
0, 2(0 + 1) = 2, 2(2+ 1) = 6.
- 26.
A classical example is the discipline of history where historians permanently discuss the reasons, i.e. rules, why certain historical processes went their specific way and not another. Many facts about the succession of social states are known yet there is seldom any consent about the rules that lead from one state to the next one.
- 27.
It must be noted, by the way, that even in the case of explanation some predictions are necessary: A successful theory must not only explain known facts but also predict unknown ones.
- 28.
Readers who want to know more about these subjects can look up the according definitions in more detail in Klüver and Klüver (2007).
- 29.
The concept of an “objective” meaning of, e.g., a certain word is simply due to the fact that in each social community with a common language must exist social conventions about the intersubjective usage of a sign. For example, one expects of a user of the linguistic symbol “oak” that he refers to a certain tree and not to an animal. Yet the meaning of “oak” is certainly not the same for a ranger in a national park and for a joiner.
- 30.
The association field may be significantly larger than just one additional attractor. For example, in 2007 we added a third network to the message with “Paris”, namely a network consisting of some concepts from a detective novel by Agatha Christie, where “Paris” played an important role.
- 31.
Strictly speaking Shannon and Weaver did not give a definition of information but one of the degree of information
- 32.
Shannon and Weaver called their theory “A Mathematical Theory of Communication”, which is rather unfortunate because they themselves emphasize that they do not deal with meaning.
- 33.
From this definition Shannon derived his famous concept of “bit”.
- 34.
In statistics the concept of “expectation vector” is also known. Yet the statistical expectation vector has more to do with the objective probability of the Shannon-Weaver definition than with our concept of the expectation of a certain receiving system.
- 35.
By “usual” we mean that this linear activation function is frequently used when constructing neural nets. There are other functions too, for example the sigmoid function.
- 36.
MEW 3, 5, italics in the original, our translation from the German original: “Die Frage, ob dem menschlichen Denken gegenständliche Wahrheit zukomme – ist keine Frage der Theorie sondern eine praktische Frage. In der Praxis muss der Mensch die Wahrheit… seines Denkens beweisen”. C.S. Peirce in his famous Pragmatic Maxim articulated principally the same position.
- 37.
A brief but interesting and informative overview about the field of AI can be found in Agogino (1999).
- 38.
The famous or infamous respectively experiments with the teaching of language to chimpanzees had only one result, namely that apes can learn, if at all, only a few words; whether they really “understood” the words they had learned is rather doubtful (cf. Pinker 1994).
- 39.
In his latest stories Asimov introduced robots that are able to learn and even can ignore the three laws by formulating a “zero law”. But these additional capabilities emerged within some robots by “mutation”, which Asimov did not describe either.
- 40.
We must confess that we do not know exactly what Clarke meant by the term “Hofstadter-Möbius loop”. We know of course the famous Möbius loop, namely a two-dimensional closed curve that allows changing sides without leaving the curve. We assume that Clarke simply meant that HAL was caught in an endless loop without being able to leave it. We shall come back to this problem below.
- 41.
Cf. for example episode 35 “The Measure of a Man” from “Star Trek, The Next Generation”.
- 42.
Usually the term “android” means a robot, which looks and acts like human beings.
- 43.
The web intelligence in “Coils” is a mere virtual being because it exists only as an emergent quality of the coupling of many computers; hence the web intelligence knows about the physical world only by its contact to the human hero of the story. The novel was written in 1982 when the authors obviously anticipated something like the Internet respectively a vast Intranet.
- 44.
It is not by chance that John von Neumann both developed the formal systems of CA and the concept of Von Neumann machines. A CA is basically a grid or lattice respectively consisting of artificial units, namely the cells that are in different states and change their states according to rule-governed interactions between the cells. For a detailed description of CA cf. for example Klüver (2000) and Levy (1993).
- 45.
The program was implemented on the basis of a CA-shell of ours by Christian Horn; the experiments were made by Filiz Kurt and Vahdet Kirli. Readers who are interested to experiment with this system may obtain it from the authors.
- 46.
The respective probabilities can be varied, i.e. a user can choose probabilities as he wishes. In particular it is possible to let the different cells mutate with different probability values.
- 47.
We speak of “formal equivalents” because we do not wish to become identified with the position of the so-called “strong AI ”, at least not here. We shall discuss this position in the next subchapter and leave it here open if such machines develop a “real” will to survive or are only simulating it.
- 48.
In his once famous program “Tierra” the evolutionary biologist Ray already demonstrated in a much larger and more complex evolutionary artificial system similar effects of the emergence of such traits (Ray 1992).
- 49.
An exception is Penrose (loc. cit.), who not very convincingly postulates the necessity of a new physics if one wants a real AI . Because Penrose, an eminent mathematician and physicist, is not very clear on this point we do not discuss his position in detail (see next subchapter).
- 50.
The scientific literature about the Turing Test is full of anecdotes that describe this difficulty. Hofstadter, one of the early advocates of the so-called strong AI , tells about a Turing experiment with a group of his students where he himself served as the test person. When he finally selected one of his communication partners as the computer he learned that this partner was the group of his students who intentionally and successfully tried to simulate a computer program (Hofstadter 1985). The proposal of Penrose (loc. cit.) to take a female proband because women are better to put themselves into the position of other humans than men is quite amusing but hardly a solution of this problem.
- 51.
Weizenbaum was, as he remarked, inspired by Eliza, the heroine of the famous musical “My Fair Lady”, based on the theatre play “Pygmalion” by Shaw. In the play (and musical) Eliza became an artificial product by her education in language and cultural behavior and could act despite her socially humble origins as a lady of the noble society. Weizenbaum, though, claimed in 1976 that the name Eliza has its origin in the ancient Greek saga of Pygmalion; no such name existed in ancient Greek. In his original article from 1966 he correctly referred to G. B. Shaw.
- 52.
Originally Weizenbaum intended to parody the Roger method.
- 53.
The linguist Pinker (1994) explains the reactions of trained dogs the same way. The dog does of course not understand remarks like “Fido, you noisy dog, stop barking and come here”. The dog in contrast hears “Fido, blah, blah, blah…” and only reacts to the key word “Fido”. Like Eliza Fido just ignores all other words.
- 54.
We omit the fact that in different cultures the terms “father” and “parents” can be used in other ways than in the Western cultures.
- 55.
Similar neural network versions of Eliza, i.e. similar feed forward networks, can be found in the Internet.
- 56.
This usage of interactive or semantical networks is described in more detail in Klüver and Klüver (2007); cf. also below Chapters 4 and 5.
- 57.
We thank Reverend Ilie Stoica for telling us where to find this famous quotation in the Bible.
- 58.
There are slightly different versions of the thought experiment with the Chinese room. We describe the basic version (cf. also Penrose loc. cit.).
- 59.
Another critical aspect of AI is, according to Searle, the fact that programs do not act in an intentional way because they just follow the implemented algorithms or rules respectively. We do not discuss this problem here because we shall deal with the problem of AI and intentionality in the next chapter.
- 60.
Axioms can be considered as initial states of formal systems. Each analysis whether a given statement can be derived within the system starts with one or several of the axioms and carries on with logical procedures. If by applying these procedures the statement can be generated then the statement is derivable in the system. If this is not possible then the statement is not derivable and, if the system is complete with respect to a certain field of knowledge, then the statement is false. Number theory, by the way, is the theory of integers, i.e. 1, 2, 3,….
- 61.
Frequently logicians and mathematicians assume that the source of the paradoxes is the introduction or allowance of self-referentiality. That is not quite exact because mainly the paradoxes are constructed by the coupling of self-referentiality and negation, for example in the paradox by Russell “the set of all sets that do not contain themselves as elements” or our example of the statement S. It is easily possible to construct systems with self-referentiality that generate no paradoxes.
- 62.
The German poet Hans Magnus Enzensberger illustrated this consequence from Gödel’s theorem “you can describe your brain with your brain but not totally” (Hommage à Gödel). German original: “Du kannst Dein eignes Gehirn mit Deinem eignen Gehirn erforschen: aber nicht ganz.”
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Klüver, J., Klüver, C. (2011). Introduction: Historical Methodical and Conceptual Frames. In: Social Understanding. Theory and Decision Library A:, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9911-2_1
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