[Fis] Limits of Formal Systems

[Carlos Gershenson]

Hi Eric,

> On 2/5/2024 4:43 PM, Carlos Gershenson wrote:
>> It is clear that models/descriptions will never be as rich as the modeled/phenomena, and that is the way it should be. As Arbib wrote, “a model that simply duplicates the brain is no more illuminating than the brain itself”. [1]
> On the one hand, you state that a model/description will never be as rich as the model/phenomena it describes. And, then in the next sentence you quote Arbib who presupposes that there could be a model that duplicates the brain.  Duplicating the brain presupposes that that model is as rich in structure and information as the thing it models, namely the brain.
> 
> Of course, Arbib is wrong. If we did have model that duplicates the brain, then given the model is something like an LLM residing on my laptop, that model would not only be as rich but richer in many ways than the brain it modeled.  It would give us unprecedented insight into the organization and function of its architecture.
> 
It seems I was not clear enough. Nobody believes that we can actually have a model as rich as a brain, the phrase is just to illustrate the necessity of simplification in models. I mean, sometimes we try to make models richer and richer:

“The best material model for a cat is another, or preferably the same cat”
—Rosenblueth A, Wiener N. The Role of Models in Science. Philos Sci. 1945;12:316–321



But of course there should be a balance between the simplicity of a model and its predictive/explanatory powers

“So we now use the country itself, as its own map, and I assure you it does nearly as well.”
— Lewis Carroll, Sylvie and Bruno Concluded (1895)



...In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province. In time, those Unconscionable Maps no longer satisfied, and the Cartographers Guilds struck a Map of the Empire whose size was that of the Empire, and which coincided point for point with it. The following Generations, who were not so fond of the Study of Cartography as their Forebears had been, saw that that vast Map was Useless, and not without some Pitilessness was it, that they delivered it up to the Inclemencies of Sun and Winters. In the Deserts of the West, still today, there are Tattered Ruins of that Map, inhabited by Animals and Beggars; in all the Land there is no other Relic of the Disciplines of Geography.

—Suarez Miranda,Viajes de varones prudentes, Libro IV,Cap. XLV, Lerida, 1658

(Jorge Luis Borges, On Exactitude in Science (1946))



“an aging double ends up being confused with the real thing”
—Jean Baudrillard, Simulacra and Simulation (1981) 


Best wishes,
Carlos

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