Alex and Doug, There are areas of the language regions that are specialized for different languages. There was a French speaker who suffered a stroke that left him unable to speak his native language. But he was able to speak German, which he had studied in school. The therapist used German to teach him how to speak French. After a relatively short time, he was able to reconnect the region for German to surviving parts of his French and recover his previous ability to speak French fluently.
As another example, there was a 19th c. Russian musician (I forgot his name) who had a stroke that left him unable to speak. But he was still able to teach students by using gestures and playing examples on his violin. He also continued to compose music, and his last symphony (composed after his stroke) was considered his best work. And there are completely different areas for speech and writing. (By the way, I made a typo in my previous note by saying that the Japanese Kanji (Chinese characters) are recognized in the left hemisphere. As images, they are recognized in the right hemisphere.) As for mathematics, there are many different kinds -- some that are more language-like and some that are more spatial or motion-like. There are many other researchers who are studying the neural implications. There is also strong evidence that the cerebellum does a lot of the computation in mathematics. The huge cerebral cortex has only 14 billion neurons, but the much smaller cerebellum has about 72 billion neurons. Those neurons are much smaller and more tightly compacted, but they do a huge amount of computation in recognizing and controlling motion. It's significant that the same neurons also do formal logic and mathematics. For slides that discuss these issues (with many URLs to articles that go into much more detail) see https://jfsowa.com/talks/bionlp.pdf I presented that article at a conference. For the publication, see https://jfsowa.com/pubs/ bionlp.pdf The article has more explanation, but the slides have more recent references and many more pictures. Some people have complained that "wetware" in the brain is not relevant to computer implementations. But the structure of the brain and the division of operations are highly relevant to the organization of any computer system that has to process the same kids of information. In particular, it's highly significant that the cerebellum (with many more short neurons than the cerebrum) is involved in mathematics. Even in questions about simple arithmetic, the cerebellum of mathematicians is active, but the cerebellum of non-mathematicians is quiet. And by the way, this is significant for discussions about GPT, which does not do any kinds of reasoning or mathematics. It just processes LLMs (Large Language Models). That is a strong reason why people like Wolfram are connecting GPT to their own systems (the Alpha English-like notation, which connects to the Mathematica system for computation). In effect, Wolfram used the software developed by his company to do the work of the cerebellum. This is an important point for all the branches of cognitive science: philosophy, psychology, linguistics, AI, neuroscience, and anthropology. John ---------------------------------------- From: "Alex Shkotin" <alex.shko...@gmail.com> Doug, Just an idea on your "It's curious that a "mental representation" is temporal. My personal mental represenation of geometric shapes is static." Think that there is an internal screen on which there are two ways of painting: by eyes and by thoughts. The idea of a triangle is stored using the language we discussed but when you decide to imagine a triangle it would be pictured on this screen. And pictured so quickly that you see it static. Alex пн, 15 мая 2023 г. в 18:35, doug foxvog <d...@foxvog.org>: On Mon, May 15, 2023 06:16, Alex Shkotin wrote: > John and All, > > I am happy to report that on page 167 of [1] I have found the syntax [2] > which is simple as a piece of cake. All, This syntax has Control, Drawing, and Arithmetic sections, the Drawing section being: It's curious that a "mental representation" is temporal. My personal mental representation of geometric shapes is static. According to the above, Int is a natural number. I presume they meant for Int to start at zero instead of one. That way, the default acceleration and turning speeds would actually be Nums. I'm presuming the blue t represents a step in time. With the instruction Move having solely a temporal parameter, for the logical location to change, the previous location, heading and speed must be maintained; but it isn't clear that such motion would have the prior acceleration and turning speed. The Turn instruction instantaneously changes the current heading without affecting the current position, but this doesn't make clear if the logically moving pen's speed, acceleration, and/or turning speed are affected. This mental representation of shapes allows for negative speeds. Does that mean the logical pen travels for the presented duration at 180 degrees from the heading direction at the absolute value of the speed? This representation should be able to draw (and therefore represent) some curves, but i'm not sure how it could express, say, an ellipse. Is someone's mental representation of a circle really a point with a constant speed and turning speed for at least a certain amount of time? It seems to me that an atemporal mental representation would be simpler: [Point]=PointWithCoordinates([Num],[Num]) [Curve] =LineSegment([Point],[Point]) [Curve] =CurveWithEquation([Equation]) [Curve]=CurveSegmentViaXRange([Curve],[Num],[Num]) [Curve]=CurveSegmentViaYRange([Curve],[Num],[Num]) As in the presented system, subprograms would allow for models of standard shapes (circles, triangles, quadralaterals, ...) which could be pieced together for more complex geometric represenations. Equations would be restricted to being in X and Y for mental represenatons of purely planar geometrical shapes. Allowing for other parameters would allow for 3D (and higher) shapes. -- doug f > Alex > > [1] https://s-m.ac/documents/phd_thesis_mathias_sable-meyer.pdf > [2] > [image: image.png]
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