Image-based Intelligence (Abstraction Is Its Metaphor)
Constructivist Bayesian Syllogism by Nalimov
A Russian mathematician, philosopher and shaman Vasily Nalimov for more than ten years worked on the problems of probability and complexity with Andrei Kolmogorov, one of the greatest mathematicians of the twentieth century.
Nalimov proposed that Bayesian inference can act as a syllogism. From two premises: universal meaning derived from semantic field as a prior and the real life experience as a filter, a posterior conclusion with new semantics invariantly follows.
“In Bayesian syllogism, in contrast to the categorical syllogism by Aristotle, both the premises and the conclusion are not atomic but probabilistically fuzzy, and at least the second premise is a conditional (conditioned by the situation), not a categorical one,” Nalimov wrote.
Source: Constructivist Aspects of a Mathematical Model of Nalimov
Metaphor as Imaginative Syllogism by Avicenna
According to Ibn Cina (Avicenna), the medieval Islamic follower of Aristotle, metaphor is also a form of Aristotelian syllogism. Ibn Sina named metaphor an imaginative syllogism. He described metaphor as a synthesised syllogism with a stated conclusion and two premises omitted.
In the same way as in Bayesian syllogism the imaginative syllogism by Ibn Cina manifests itself in the probabilistic fuzziness and the contingency of one of the premises to the situation.
While in a categorical syllogism an invariant semantics relation between conclusion and its two premises exists, in the case of metaphor as an imaginative syllogism “a wide and 'open' measure of semantic oscillation exists, because there’s a definite subjective and psychological ingredient in metaphorical synthesis.”
Source: Avicenna’s Commentary on the Poetics of Aristotle
Fresh and Lively Metaphors by Aristotle
Aristotle excluded the use of metaphors from logical reasoning. Only unambiguous definitions were accepted. But definition, according to Aristotle, was always preceded by metaphor that allowed people to understand unknown things through their resemblance with things which they understood.
“New strange words simply puzzle us; ordinary words convey only what we know already; it is from metaphor that we can best get ahold of something fresh,” he wrote in Rethorics.
Metaphor, according to Aristotle, conveys the liveliness of things by making people see things. Under making people see things he meant using metaphorical “expressions which represent things as in a state of activity.”
Source: Rhetoric
Once again, as in the case of Nalimov and Ibn Cina, we see in the words of Aristotle the reference to a specific dynamical way in which metaphor (an imaginative syllogism or a Bayesian syllogism) presents things.
Mental Structures of Conceptual Metaphors by Lakoff
An idea is an object (a thing). An object can be placed into a bounded space (a container) of concept. Mind is a global space containing locations - bounded spaces of concepts. Thoughts are moving across mind-space from one location to another. This is a conceptual metaphor: mind is space.
Mind is a target domain and space is a source domain in this metaphor. We use a source domain to imagine a target domain.
George Lakoff, an American linguist and cognitive scientist, introduced the theory of conceptual metaphor together with Mark Johnson in 1980 in a book Metaphors We Live By. Lakoff also coined the invariance principle of metaphor. It states that “metaphorical mappings preserve the cognitive topology (that is, the image-schema structure) of the source domain, in a way consistent with the inherent structure of the target domain.”
Here we can see that the invariance of metaphor as a Bayesian or imaginative syllogism is topological by nature unlike the categorical invariance of an Aristotelian syllogism.
Source: The Contemporary Theory of Metaphor
“What is more interesting, and I think more exciting, is the realization that many of the most basic concepts in our conceptual systems are also comprehended normally via metaphor-concepts like time, quantity, state, change, action, cause, purpose, means, modality and even the concept of a category,” Lakoff specifies.
“Abstract reasoning is a special case of image-based reasoning. Image-based reasoning is fundamental and abstract reasoning is image-based reasoning under metaphorical projections to abstract domains”, he states.
Complex abstract concepts, according to him, are understood “via multiple conceptual metaphors that provide different understandings of the concepts”.
He and Mark Johnson discovered that conceptual metaphor was made up of primitive metaphors that were acquired in ordinary daily life when two basic embodied experiences regularly occurred together.
Source: Mapping the brain’s metaphor circuitry: metaphorical thought in everyday reason
Lakoff thinks that domains can be supported in the brain by hierarchically organized mental structures that organize knowledge. Such structures, which he calls frames, make use of primitive concepts and may make use of other conceptual metaphors as well.
Information Patterns of Winnerless Competition by Rabinovich
Mental structures by Lakoff resemble information patterns - mathematical models of cognitive dynamics based on winnerless competition. Their hierarchical generative/inhibitory organization resembles hierarchical and topologically invariant semantic structures of conceptual metaphors.
“We analyze sequential discrete coding based on winnerless competition low-frequency dynamics. Under such dynamics, entrainment, and heteroclinic coordination leads to a large variety of coding regimes that are invariant in time”, mathematicians Mikhail Rabinovich and Pablo Varona wrote in their paper “Discrete Sequential Information Coding: Heteroclinic Cognitive Dynamics”.
They propose that dynamical switching between different information patterns represented as brain network modes may neurologically support many cognitive processes including understanding.
The dynamics of such information patterns should be flexible and sensitive to semantic oscillations within the domain of a conceptual metaphor. Yet they need to be robust to external perturbations to secure invariance of the cognitive topology of the metaphor at the same time.
In order to support required sensitivity and robustness information patterns have to follow “a set of rules: (i) winnerless competition between modes, (ii) hierarchical functional organization of the global networks and the cognitive resources, (iii) hierarchical stability of the multilevel architecture. To follow these principles in our dynamical models, it is necessary to use the concept of inhibition at all levels: cognition, emotion, metacognition, and behaviour”.
Abstract Reasoning Is a Metaphor of Image-based Reasoning
Lakoff hypothesises in The Contemporary Theory of Metaphor that, “if the Invariance Principle is correct, it has a remarkable consequence, namely that: Abstract reasoning is a special case of imaged-based reasoning. Image-based reasoning is fundamental and abstract reasoning is image-based reasoning under metaphorical projections to abstract domains.”
Interestingly, we can find a direct and solid confirmation of his idea in the way Albert Einstein described his thinking process.
In his search for the secret of scientific genius a prominent French mathematician Jacques Hadamard interviewed some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. Like Claude Levi-Strauss in his Savage Mind Hadamard didn’t recognize that the process of scientific discovery is the same process that each and every human being uses in the process of understanding of any fresh idea or concept.
I think, it’s important to read the answers of Einstein to questions of Hadamard in full:
"(A) The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be "voluntarily" reproduced and combined. There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought--before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.
(B) The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will.
(C) According to what has been said, the play with the mentioned elements is aimed to be analogous to certain logical connections one is searching for.
(D) Visual and motor. In a stage when words intervene at all, they are, in my case, purely auditive, but they interfere only in a secondary stage, as already mentioned.
(E) It seems to me that what you call full consciousness is a limit case which can never be fully accomplished. This seems to me connected with the fact called the narrowness of consciousness (Enge des Bewusstseins)"
From "A Mathematician's Mind, Testimonial for An Essay on the Psychology of Invention in the Mathematical Field by Jacques S. Hadamard, Princeton University Press, 1945." in Ideas and Opinions.
Jean Piaget, a Swiss psychologist and philosopher contributed to the field of cognitive development by introducing the theory of constructivism. According to constructivism people form meaning based upon their experiences. Understanding is a process of inventing (constructing) meaning from motorical and imagery semantics. Piaget believed that language was emerging upon “structures formed by the pre-existing sensory motor intelligence.”
Source: To Understand Is to Invent.
GUI — Graphic User Intelligence
Test version of Graphical User Interface was designed by Xerox PARC based on the ideas of Piaget. Steve Jobs saw and implemented it in the GUI of Macintosh. Bill Gates borrowed it for Microsoft Windows. Now we use sensory-motor and image based intelligence for navigating virtually any device.
Yet we still undervalue it and even doubt its existence. Why are we so ignorant? By chance only I found an answer today in an old article of John von Neumann, one of the greatest mathematicians of all times and the creator of one of the first computers.
“In all its stages the industrial revolution consisted of making available more and cheaper energy, more and easier controls of human actions and reactions, and more and faster communications. Each development increased the effectiveness of the other two,” he wrote in 1955.
Source: Can We Survive Technology?
Do We Need Intelligence?
The question remains: “Do we need intelligence if we still need “more and easier controls of human actions and reactions?” If the industrial revolution continues, the question about the need for human intelligence has a clear and invariant answer: “Humans need no intelligence, nor understanding neither creativity.”
Yet then another question arises: “What do we expect from artificial intelligence if we don’t even need the human one?”
Yet one more: “What do we mean by intelligence atop the obedience of programmed automata?”
Can human intelligence survive technology?
