Symbolism vs. number of neurons in the brain

Christoph Koch writes in Biophysics of Computation (Oxford University Press, 1999, p. 87):

Given an approximate density of 100,000 cells by mm³ in the primate, a synaptic density of 6 x 10⁸ per mm³, a total surface area of about 100,000 mm² for one hemisphere, and an average thickness of about 2 mm, the average human cortex contains on the order of 20 billion neurons and 240 trillion synapses (2.4 x 10¹⁴) [...]

This reasoning is not yet complete as while the number of synapses falls from the argument, the number of neurons doesn't. However, in The Quest for Consciousness (Roberts & Company Publishers, 2004, p. 71 note 5), the same Christoph Koch says:

Given a packing density of 50,000 cells per mm³, a total surface area of 2 x 100,000 mm², and a thickness of about 2 mm, the average human cortex contains on the order of 20 billion neurons and 200 trillion synapses (2 x 10¹⁴).

Also in The Quest for Consciousness (Roberts & Company Publishers, 2004, p. 26), Koch says:

All the visual information that the brain can access is implicitly encoded by the membrane potentials of the more than 200 million photoreceptors in the two eyes.

Since photoreceptors are neurons, those facts combined provide a formal proof (we insist on the terms "formal proof" here) of the elaboration of symbols by the brain. The proof is that if each image is using 200 million neurons, only 100 images (100 x 200 million = 20 billion) can be stored by the entire brain, obviously insufficient. Information needs to be reduced (which we actually know it is, but that's besides the argument here).

This sets the scene for a formal study of symbol construction, starting with a very small number of photoreceptors and going up from there.

Bertrand du Castel

Cloud Computing Definition

Computer Theology's definition: Cloud Computing is the global optimization of computer resources.

Bertrand du Castel

Christof Koch and Roger Penrose

In Computer Theology (2008, Midori Press) we wrote (page 40):

There is indeed a tendency to observe a reducing perspective on computers, and particularly on computer systems. For example, Roger Penrose seems to suggest as much when he bases his analysis on an equation of computing with Turing machines in The Emperor’s New Mind, even considering the extreme example of a Turing machine with infinite memory, infinite state variables and unlimited computing time; there is more to computing than theoretical equivalence.

In The Quest for Consciousness (2004, Roberts & Company), Christof Kock writes (page 8, note 12):

Penrose's books (Penrose, 1989, 1994) are among the most lucid and best-written accounts of Turing Machines, Gödel theorems, computing, and modern physics I have read. However, given that both monographs nominally deal with the human mind and brain, they are equally remarkable for the almost complete absence of any serious discussion of psychology and neuroscience.

This is most remarkable in that, as we observed in Computer Theology, we should extend Koch's mention of a lack of serious discussion ... to computer science. Turing machines, as important as they are, are a minuscule part of any cursus in computer science, or, for that matter, of theoretical computer science. But that's all that Roger Penrose and Christof Koch speak about when they think of computers. In the case of Roger Penrose, it's just sad. In the case of Christof Kock, it's also surprising, as his most wonderful book of neuroscience is entitled Biophysics of Computation (1999, Oxford University Press) and is so exquisite in its description of neural computation. But again, all he seems to know about computer is Turing machines (he also make some references to computer hardware, but they are even more of a case of ignoring mainstream computer science). See for example page 469:

The brain has frequently been compared to a universal Turing machine (for a very lucid account of this, see Hofstadter, 1979). A Turing machine [...]

and then Koch explains differences between Turing machines and the brain's operations. What's remarkable is that it's obvious to a computer scientist like me that Turing machines are the wrong metaphor. I'd rather think of the theory of exceptions when considering consciousness, or of object-oriented concepts when examining miror neurons, or more generally, in mapping the brain, of ontologies, of Bayesian networks, of stochastic grammars, and many other computer science constructs. That neither Roger Penrose nor Kristof Koch, great scientists in their fields and purporting to address computer questions, would stop at computer science 101 reflects the dire state of interdisciplinary studies. If this note encourages them to dig into a science that would indeed benefit so much from these most important scientists' insights if they were more informed, I'll be happy.

Bertrand du Castel

A neurological source of spatial metaphors?

Computer Theology discusses at length the role of spatial metaphors in language and cognition (p. 281; see also Generics and Metaphors Unified under a Four-Layer Semantic Theory of Concepts).

In A Right Perisylvian Neural Network for Human Spatial Orienting (chapter 17 of The Cognitive Neurosciences, MIT Press 2009), Hans-Otto Karnath presents the symmetry between the right and left perisylvian networks:

"I appears as if this lateralization of spatial orientation to the right hemisphere network parallels the emergence of an elaborate representation for language in the left-sided perisylvian network."

In non-human primates, both the right and left perisylvian networks lead to spatial disturbance when they are damaged. In humans however, right network damage leads to spatial disturbance while with the left one there are only traces of such spatial disturbance. In a major difference with non-human primates, the human left perisylvian network is rather totally associated with language and praxis, with damage leading overwhelmingly to aphasia and apraxia, instead of spatial disturbance. (I need to point out here that I have expressed that carefully to leave the question open of the rudiments of language found in monkeys and chimpanzees -- and I would suspect more to come, since we are still on the discovery path).

If the language and spatial systems are then in fact symmetrical, this is no wonder that spatial metaphors ("I am staying on that table" vs. "I am working on this topic") are fundamental to language?

Bertrand du Castel