Posted by: Alexandre Borovik | December 20, 2009

Structures, Learning and Ergosystems

A wonderful text by Michael Gromov:


  1. He has just updated the text (on 21 Dec).

    Presumably the stories you collect are of interest to him; there seemed to be an explicit quote about something like this in the latest version but i cannot find it now, and dont quite remember what was it about.

  2. Gromov mentions something about the special role of the olfactory sense and “automorphism groups of Lebesgue-Rokhlin spaces” as involved symmetry group. This may be interesting in that context: “… another radical theory that Dr. Lynch has proposed, which is the idea that the olfactory cortex formed the template for the evolution of the cortex in mammals and primates. This intriguing theory brings a new perspective to the fact that the olfactory system has unique access to important brain systems including the frontal lobes, the amygdala (which is involve in emotion), and the hippocampus (which is essential to long-term memory).” So, comes the “ergobrain” from the olfactory system? What is the meaning of the later belonging to such a symmetry group? (And what are “Lebesgue-Rohklin spaces” and their automorph.-groups?)

  3. This is interesting – thanks for giving the references.

    I suspect, however, that the privileged access of the olfactory system to other brain systems excludes it from the list of suspects: mathematics is a hack.

  4. Another thought – Gromov’s intentional neglection of “meaning” in his ergosystems makes me wonder if he gives the fascinating example of Ramanujan’s dealing with infinite series much weight. But is in contrast not most of mathematics about “patterns of meaning”?

    Gromov relates concepts of “meaning” with “Egosystems”, and therefore inheriting the later’s incompatibility with “Ergosystems”. But one could equally try to trace “meaning” back to intuitive social competences, which probably developed much earlier than modern humans and human language. Such competences include a modeling of other hominid’s mentalities, i.e. something much more complex than everything else in their surrounding, and would naturally have lead to a “mysterious” mental surplus-capacity like that which Gromov gives as reason for suposing “Ergostructures”. E.g. the emergence of intuitive social competences seems to coincide with the hominid’s independence from specific ecological niches. I would associate “Egostructures” with language, i.e. something much later. If one takes this as extreme case for an “Egosystem”, one sees that it makes sense to view that as adaption to language-based large groups, but surely not earlier.

  5. A new book on child psychology: “Children and adults are different forms of Homo sapiens,” writes Gopnik in The Philosophical Baby, a tour through the recent findings of cognitive science about the minds of young children. … Gopnik offers the captivating idea that children are more conscious than adults but also less unconscious, because they have fewer automatic behaviors… the child is a full partner, with a different brain than that of the adult, more capacious, with a greater plasticity, and a more highly attuned ability to drink in new information. The child is the auteur, the adult the producer. … Even infants are sensitive to statistical patterns. The learning of language in its earliest stages involves the statistical prediction of which sounds are most likely to follow one another—an unconscious exercise in probability theory. Gopnik argues that this ability to detect probability patterns extends beyond language—to musical tones in eight-month-olds, for instance—and isn’t limited to a specialized part of the brain as Noam Chomsky and others believe.”

  6. Wonderful!

  7. MPG news on how the brain analyses sensoric input: “An important implication of this study is that visual perception depends on an active generation of predictions. This stands in contrast to the classical view that visual perception mainly results from a more passive cascade of responses to visual signals spreading through the brain”.

  8. Here is a fascinating new article of the New Scientist on “cell intelligence”, connecting nicely to the observation with which Gromov starts.

  9. It is intriguing indeed.

  10. On a related apparent ‘paradigm change’ in linguistics: “this view, the brain of a child does not arrive pre-programmed with abstract linguistic rules. Instead, its initial setting is much simpler: the first job of the brain is to build a more complicated brain. This it does using any input that it gets, including language. “

  11. Here the link to Misha Gavrilovich ‘s thoughts on set theory, wich he relates to some of Gromov’s ideas.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s


%d bloggers like this: