December  4, 2023

March 14-18, 2011
Workshop on Semiotics, Cognitive Science and Mathematics

to be held at the Fields Institute

Organizing Committee
Chair: Marcel Danesi (Semiotics and Linguistic Anthropology), University of Toronto
Co-Chair: Mariana Bockarova (Semiotics and Linguistic Anthropology), Harvard University
Campus Organizers: Spencer De Corneille & Alison Kathleen Inez Mann


James C. Alexander
(Case Western Reserve)
Cognitive structures and semiotics of mathematics

We explore how mathematics--higher mathematics--has incorporated cognitive mechanisms into its formal structure, a fact that is relevant to the continuing fecundity of the discipline. From this, we segue to (preliminary) questions of how the structres are implemented, and in particular, what of the semiotics of mathematics? That is, what does the formalism of mathematical notation tell us about mathematical cognition?

Myrdene Anderson, Purdue (Anthropology and Semiotics)
Qualification of Quantification across the Curriculum

At least in the social and behavioral sciences-so delineated respecting the preference from psychology-practitioners and students alike have subscribed to another distinction, that between qualification and quantification. In fact, one might easily get the impression that the latter distinction amounts to a debate, if not outright warfare.

Students arrive to their disciplines largely ignorant of the semiosic underpinnings of their own intellectual experiences and of the semiotic foundations for their elected fields of study. In addition, typically without a broad background in the history and philosophy of the disciplines, students fail to perceive how all of them interlock in a myriad of ways. Being so undisciplined about their disciplines, it is not surprising how students can be so easily recruited. The majority subscribe to a contrast between qualification and quantification, and usually in so doing they privilege the latter, assuming it to be the more "scientific" approach for meaning-making. At the same time, though, the condition of relative innumeracy of young and old, within and beyond any but the most technical fields, has been conceded without a struggle. As a consequence an unhealthy hierarchy is fractured by feelings of inadequacy and/or resentment.

Perhaps with greater engagement in public education in the future, affording younger students trickling up through the ranks a more inquiring interest in the qualia and quanta across the cultural curricula, higher education may enjoy a new lease on intellectual work and play. Meanwhile, the position taken in this paper asserts that both qualification and quantification are cultural practices, and further that "etic" quantification is predicated on prior "emic" qualification (drawing on Kenneth L. Pike). The "cultural" may at the social level include the linguistic and at the individual level include both bodily and cognitive processes.

At the same time, higher education may be able to benefit from considering approaches aimed at younger audiences. These include the "Singapore method"; the "Private Eye" approach to looking and thinking by analogy; the foregrounding of abduction larding the more recognized induction and deduction; and building on awareness through movement.

Joachim De Beule, Free University of Brussels
Agent-Based and Mathematical modeling in Semiotic Dynamics

Semiotic dynamics is the field that studies the dynamics associated with the formation, the usage and the evolution of semiotic systems. It grew out of research in artificial intelligence and evolutionary linguistics, and originally was mainly concerned with human (and human- like) languages [6, 4]. However, there is a growing body of evidence that coding and semiosis are fundamental ingredients of all life. This recently lead to a new scientific field called biosemiotics, defined as the study of signs, of communication, and of information in livingorganisms, and claimed to provide a new understanding of life [1]. If semiosis is fundamental to life, then a proper understanding of semiotic dynamics will be crucial in order to fully understand all aspects of macro-evolution, in particular the appearance of new codes and new levels of selection during major transitions [5, 2].

In this talk, I will review some of the basic notions in (coding) biosemiotics and semiotic dynamics and show how, in recent years, researchers from a variety of fields were able to, make significant progress through a combination of multi-agent simulations and mathematical (formal) modeling. I will focus on the notion of language games [7]. These are used in semiotic dynamics as vehicles for the study of evolution through conventionalization, much in the same way as games are used in evolutionary game theory to study evolution through natural selection. In particular, I will focus on the naming game, one of the simplest and currently best understood language games [3]. It will be shown how the naming game dynamics can be analyzed mathematically and can give rise to phase transitions in the coding behavior of individual code users corresponding to an increased state of global coordination. Some possible applications and extensions of the naming game will be discussed and a number of open problems will be identified.

[1] Marcello Barbieri. Biosemiotics: a new understanding of life. Naturwissenschaften 95(7), pages 577–599, July 2008.
[2] Marcello Barbieri. The mechanisms of evolution. natural selection and natural conventions. In Marcello Barbieri, editor, The Codes of Life, chapter Dordrecht, pages 15–35. Springer, 2008.
[3] Andrea Baronchelli, Vittorio Loreto, and Luc Steels. In-depth analysis of the naming game dynamics: The homogeneous mixing case. International Journal of Modern Physics C, 19(5):785–812, May 2008.
[4] Ciro Cattuto, Vittorio Loreto, and Luciano Pietronero. Semiotic dynamics and collaborative tagging. Proceedings of the National Acadamy of Sciences, 104(5):1461–1464, January 2007.
[5] J. Maynard-Smith and E. Szathm´ary. The major transitions in evolution. Morgan-Freeman, 1995.
[6] Luc Steels and Frederic Kaplan. Collective learning and semiotic dynamics. In Floreano, Nicoud, and Mondada, editors, Advances in artificial life, Proceedings of ECAL’99, volume 1674 of Lecture Notes in Computer Science, 1999.
[7] Luc Steels and Paul Vogt. Grounding adaptive language games in robotic agents. In Phil Husbands and Inman Harvey, editors, Proceedings of the Fourth European Conference on Artificial Life (ECAL’97), Complex Adaptive Systems, Cambridge, MA, 1997. The MIT Press.

John Deely, St. Thomas University
The Semiosis of Mathematical Thinking

This paper discusses mathematical thinking only insofar as that thinking provides an unmistakable prime example of anthroposemiosis in its species-specific difference from all the varieties of zoösemiosis. Thus, recurring to Euclid’s triangle as a central example, my aim is to outline how relation as a mode of being exhibits a singularity that proves to be the basis for the prior possibility of semiosis in general, a singularity that mathematical objectivity makes particularly recognizable even though the feature in question extends to the full range of semiosis as an action transcending the contrast between mind-dependent and mind-independent being.

Keith Devlin, Stanford (Mathematics)
Using a video game as a medium to represent mathematics for children learning basic mathematics

To date, almost all video games designed to help students learn mathematics do little more than present traditional mathematics, represented by standard symbolic expressions, into a video game wrapper. In essence, they regard video games as a new medium on which to pour symbols. But video games provide an entirely new way to represent mathematics. I have spent the past five years investigating how to make use of the natural affordances in video games to do just that.

Vitaly Kiryushchenko, St. Petersburg State School of Economics
In May 1879 (the year Peirce's careers as a scientist and academic philosopher first overlapped, as he started teaching at the Johns Hopkins while continuing his research for the US Coast Survey), Peirce published a short paper in the American Journal of Mathematics describing his new map projection, which he called "quincuncial". The quincuncial map was a variation of conformal stereographic projection and, besides, one of the first diagrammatic pictures created with the application of complex analysis.
The present paper, by using an example of Peirce's quincuncial map, is aimed at showing how some of Peirce's late pragmatist and semiotic ideas were developed from his early practice as a scientist and a mathematician, thus providing an intriguing example of the intersection of scientific practice and philosophical speculation.

Kalevi Kull, University of Tartu, Estonia (Biology and Semiotics)
What mathematical structure is semiosis (if any at all)?

1. Semiotics and mathematics are highly incompatible - likewise poetry and logic, or life and automaton.

2. There exists a long and rich tradition of modelling of some semiosic objects, as well as a search for proper mathematical tools for thier modelling, e.g., of organisms and languages. Yet, mathematical biology and mathematical linguistics (also mathematical sociology, mathematical psychology, etc.) have challenged the problem of limitedness of mathematization of their theoretical core. In its general form, this is the problem of mathematical description (modelling) of semiosis. It will be instructive to review some examples about the searches for mathematical description (formalization) of semiosis (e.g., of Robert Rosen, of computational semiotics, of algebraic semiotics, etc.).

3. A feature that is in the focus of modelling of semiosis has to be the feature that natural languages possess and the formal languages (and formal logic) do not. If this feature resists formalization, then how is it possible that mathematics can describe the physical world, whereas it (as if) cannot describe the non-mathematical or natural language from which it is a derivative?

4. Modelling of semiosis appears to be particularly a problem for biosemiotics. Because if to accept Sebeok's thesis that semiosis is the criterion of life, then a model of sign is simultaneously a model of life. Thus the problem of distinction between natural and formal languages goes beyond languages. If languages are defined as systems that use symbols, then there exist many semiosic systems that are not languages, i.e. which include merely non-symbolic semiosis (usually called non-human life forms). This is, in other words, an old question whether it is possible to distinguish between living and non-living system, i.e. between informal (or natural) and formal sign systems on the basis of their formal (mathematical) descriptions.

5. Formal sign systems are derivatives from natural sign systems - similarly to artefacts and dead languages. What makes them formal is the lack of the very feature the modelling of semiosis is addressing - the semiosity, the life itself. The existence of codes is a necessary but not a sufficient condition for semiosis, because constructions of non-living machines (i.e., certain artefacts) also include codes.

6. The sciences that are dealing with everything that can be described in an unambiguous (formal) way can be called phi-sciences (physical sciences), whereas the sciences that can deal with equivocal (polysemous, like natural language, poetry and life itself) descriptions can be called sigma-sciences (semiotic sciences).

Solomon Marcus, Mathematical Section of the Romanian Academy (Mathematics)
Mathematics, Between Semiosis and Cognition

1. The nature of mathematical cognition is controversial.
2. The invention-discovery interplay in mathematics raises delicate questions.
3. Is Mathematics, like Music, predominantly syntactic?
4. Mathematical rigor is frequently obtained at the expense of meaning.
5. Mathematical concepts emerge from diaphoric self-referential metaphors.
6. Mathematics of the macroscopic universe is associated with human language and semiosis, relatively sharp distinction between subject and object, Euclidean paradigm and Galileo-Newtonian paradigm.
7. The mathematics of the infinitely small and of the infinitely large adopts the strategy of Plato's allegory of the cave.
8. Cognitive mathematical models and metaphors are by their nature conflictual.

Yair Neuman, Ben-Gurion University of the Negev
Semiotics, Mathematics & Information Technology: The Future is already here ...

Semiotics is considered as an anachronistic academic field the same as Philology and Egyptology. In this presentation, I would like to refute this dogma and to show how the synergy of Semiotics, as a meta-perspective for cognition, Category Theory as a meta-perspective for mathematics, and Information Technology as a meta-tool for computation, may introduce breakthroughs in the study of cognition.
Based on our latest research and algorithms, I would like to review some of these breakthroughs: How we may automatically screen for depression through the use of metaphors, an algorithm that differentiates between denotation and connotation (wet hair vs. wet dream) and identifies the meaning of an abstract connotation (wet dream = erotic dream), how "Hypostatic Abstraction" proposed by Peirce explains the way "language" enables the abstraction of "thought", and how semiotic ideas may be used for semi-automatically excavating hidden and unconscious themes in group-dynamics.

Frank Nuessel, University of Louisville (Semiotics and Linguistics)
The Representation of Mathematics in the Media

Mathematics and mathematical concepts appear in the print(books, newspapers, magazines, other publications, text-based objects) andnon-print (television and cinema) media with some frequency. This paperexamines selectively these popular cultural manifestations of mathematics withspecial attention to those exemplars that incorporate reasonably accurateversions of mathematics. A limited number of copies of the text of the paperwill be available for the audience.

Rafael Nunez, University of California, San Diego
What is the nature of mathematics? A view from the Cognitive Science of the number line

Mapping numbers to space is fundamental to mathematics. The number line is arguable one the simplest but richest examples of the power of such mappings. But, what are its cognitive origins? Are the intuitions underlying the number line "hard-wired"? Is the number line a cultural construct? Contemporary research in the psychology and neuroscience of number cognition has largely assumed that the representation of number is inherently spatial and that the number-to-space mapping is a universal intuition rooted directly in brain evolution. I'll review material from the history of mathematics as well as empirical results from two of our recent studies to defend a radically different picture: the representation of number is not inherently spatial and the intuition of mapping numbers to space is not universal. In one study we show that there are non-spatial representations of numbers that co-exist with spatial ones, as indexed by instrumental manual actions, such as squeezing and bell-hitting, and non-instrumental actions, such as vocalizing. Moreover, the results suggest that the number-to-line mapping—a *spatial* mapping— is not a product of the human biological endowment but that it has been culturally privileged and enhanced. The other study, which we carried out in the remote mountains of Papua New Guinea, shows experimentally that individuals from a culture that has a precise counting system (and lexicon) for numbers greater than twenty lack the intuition of a number-to-line mapping, suggesting that this intuition is not universally spontaneous, and therefore, unlikely to be rooted directly in brain evolution. The number-to-line mapping appears to be learned through— and continually reinforced by— specific cultural practices, such as measurement tools, writing systems, and elementary mathematics education. It is over the course of exposure to these cultural practices that well-known brain areas such as the parietal lobes are recruited to support number representation and processing, which in turn, allow the learning of more elaborated mathematical concepts.

Wolf-Michael Roth, University of Victoria (Semiotics and Mathematics)
Tracking the Origin of Signs in Mathematical Activity: A Material Phenomenological Approach

The semiotic literature tends to take signs as given. Even in constructivist and embodiment accounts of cognition, the sign, such as a gesture that exhibits some linear relation or trend, is merely the enactment of a pre-existing schema the enactment of which results in the production of a sign. Yet empirical evidence shows that the human sign form, as thing that stands for another thing, does not constitute the beginning – children do not make a distinction between the thing and its name. To understand signs, we therefore need to take a genetic perspective. In this paper, I present a material phenomenological account of how signs and thoughts emerge in ongoing activity. I provide a very detailed description of a lecture excerpt, essential features of which cannot be explained by presupposing signs, thoughts, or mental schema. The approach I offer provides explanations for some of the difficult problems in education, psychology, and cognitive science.

Fernando Soto
Lewis Carroll's Name-Number Nexus: Snarky Wonderland Games.

In this paper I first set out to demonstrate how the etymologically-trained mathematician Charles Lutwidge Dodgson (better known as Lewis Carroll) uses ambiguity as he confuses and abuses words and their meanings in his "Nonsense" works. I then trace the etymological links between the words "name," "number," and "numismatic," and how Carroll creatively used and confused them. I then go on to provide several example of name/number/coining word-play in Alice's Adventures in Wonderland, The Hunting of the Snark, and Through the Looking-Glass. I finish off the talk by presenting a partial etymological answer to Carroll's famous "Why is a raven like a writing-desk" riddle.

Kumiko Tanaka-Ishii, University of Tokyo, Japan (Computer Science)
Dyadic vs. Triadic Sign Models Through Computer Programs

The theme of this talk is the relation between the dyadic and triadic sign models in the context of computer programs as the semiotic target. The content of the talk appeared in my recent book "Semiotics of Programming," published by Cambridge University Press in 2010. Since computer programs are mechanically interpreted on machines and are therefore rigorous, semiotic analysis of programs enables formal reconsideration of the sign models proposed so far.

Among various dyadic and triadic models, the discussion here centers on the correspondence between the triadic sign model proposed by Peirce and the dyadic sign model proposed by Saussure. Traditionally, it has been thought that Peirce's interpretant corresponds to Saussure's signified, and that Saussure's model lacks Peirce's object. Analysis of the two most widely used computer programming paradigms, however, suggests that Peirce's object formally corresponds to Saussure's signified, and that Saussure's sign model is obtained when Peirce's interpretant is located outside his model in the programming language system. Further, I suggest how this distinction may dissolve when signs are introduced through self-reference.

Mark Turner, Case Western (Cognitive Science)
Mental Packing and Unpacking in Mathematics

Recently, it has been hypothesized that human working memory greatly increased during the Upper Paleolithic, and that this evolutionary change caused, or at least sparked, the cognitively modern human mind, with its outstanding creative capacities, including mathematical insight and scientific discovery. According to this “working memory” explanation of our unusual abilities, capacious working memory made it possible to activate large ranges of ideas and connect them creatively; it produced conceptual networks much more complicated than anything that had previously been possible (Wynn 2002, Wynn & Coolidge 2003 & 2004, Wynn, Coolidge, & Bright 2009, Balter 2010). Be that as it may, the management of complex conceptual networks requires quite different powers of conceptual packing and unpacking. Packing and unpacking make working memory useful. Packing and unpacking are provided by the basic mental operation of conceptual integration, otherwise known as blending. Blending provides packed mental structures congenial to human cognition. These packed mental structures can be carried without the assistance of working memory, and later unpacked creatively to create large conceptual networks involving new information. In this way, the packed blend provides something that can travel with us mentally for future service. The packed blend is additionally indispensable in providing a congenial basis, suited to human cognition, from which to grasp and manipulate conceptual networks that would otherwise lie far beyond our ability to maintain, manage, and manipulate. Mathematics as we know it is in large part made possible by this feature of conceptual integration. Mathematics specializes in providing instruments of packing and unpacking.