New Evidence for The Geometry of Thought

http://nautil.us/blog/new-evidence-for-the-geometry-of-thought >“It has long been a common prejudice in cognitive science that the brain is either a Turing machine working with symbols or a connectionist system using neural networks.” In Krakow, Gärdenfors pushed against that prejudice. In his talk, “The Geometry of Thinking,” he suggested that humans are able to do things that today’s powerful computers can’t do—like learn language quickly and generalize from particulars with ease (to see, in other words, without much training, that lions and tigers are four-legged felines)—because we, unlike our computers, represent information in geometrical space. >...He argued that the brain represents concepts in the same way that it represents space and your location, by using the same neural circuitry for the brain’s “inner GPS.” Basically, Gärdenfors says that the brain stores a mental map between the "dimensions" of our thoughts/memories. He gives the example: >This kind of mental processing might also apply to how we think about our family and friends. We might picture them “on the basis of their height, humor, or income, coding them as tall or short, humorous or humorless, or more or less wealthy,” Doeller said. And, depending on whichever of these dimensions matters in the moment, the brain would store one friend mentally closer to, or farther from, another friend. Thought some of you might find it interesting. I highly recommend reading the entire article.

geometrical space = 3-dimensional? Seems it's just more limited. ML works with n-dim.

> We might picture them “on the basis of their height, humor, or income, coding them as tall or short, humorous or humorless, or more or less wealthy,” Doeller said. And, depending on whichever of these dimensions matters in the moment, the brain would store one friend mentally closer to, or farther from, another friend. So basically a multi-dimensional vector space. Which is exactly the same thing that neural networks do. https://youtu.be/NTlXEJjfsQU

>>12685 I dont think they mean 3d space, I think it"s closer to n-dimensional phase spaces.

>>12685 i havent read the article but i think that geometrical might imply that there is a metric, (a distance between concepts) which makes sense if you think about it. red is closer to apple than it is to nilihism

>>12687 well neural nets are simplified models of brains, so yeh

>>12864 >geometrical might imply that there is a metric pretty much. technically you're talking about a more general concept called, conveniently, a "metric space". however the three "geometries" (euclidean, hyperbolic, and elliptical) all correspond to metric spaces. metrics don't have much to do with geometry though beyond that. it's more of a topological concept.

To veer away from the ''physical'' aspect a bit - thinking, phenomenologically speaking, seems geometrical. I think it's impossible for living things to *not* see structure - which i conflate with the term ''geometry'' here. It is a very pillar of all consciousness. The fact that we see material ''evidence'' that ostensibly points to ''geometry'' of thought reflects this principle.

>>12866 >>12864 >topological concept. I put my money on this The thing is that it's very difficult to test because we don't have a decent "topological representation of meaning". I'm a math student and I would love to make that my life's work. But there is one particular thing where we can test it: Spacial awareness. Paper related studies how the neurons that codify spatial awareness are spacially distributed and connected in the brain so as to reflect the homology of real world space.

I think this is a good visualization or conceptualization of it but still isnt actually how it works.

>without much training it took these parts of humanity much training, after many trials of sciencial principles, to get to where each member can easily (rightly?) class lions as cats. i know intelligent humans from nonempiricorational societies who cannot easily class lions as cats. some can, but only after years of dense guided training, and still require recurrent emphasis of the empiricorational principles.

>>13012 >i know intelligent humans from nonempiricorational societies Could you tell us more about this, please? I'm intrigued.

I only have a limited grasp of the complexity of thought, but I would argue that humans are spacial creatures, since they define themselves as an individual in a state of being (not perceiving oneself creates a number of psychological abnormalities). It would therefore be reasonable to assume that geometric thought is a more carefully assessed theory than the observation of an individual who defines itself within the context of its own spacial (both physical, spiritual, and cultural) existence. At least my two cents...

>>13012 wondering: if they're intelligent, but unable to distinguish between certain concepts, what can they properly do?

>>12683 Geometry of thought sure is reminding of something....

>>13027 He is just saying in the most pretentious way that uneducated people don't think of Lions as cats. Which is ironic, because lions aren't cats by the everyday definition of "cats".

>>13730 hmmm