Peter Gärdenfors | Conceptual Spaces and the Geometry of Word Meanings

[@kodfkdleepd2876]

Some researchers at Uni of Mich. Have used Linear algebra to extract dynamics of systems in to actual equations. This allows one to recover the equations of the system and it works quite well. It is known as SINDY - Sparse identification of Non-Linear Dynamics. It is similar to NN in that linear algebra is used and NN's like systems can be used to down-sample data in to an appropriate domain. I wonder if the brain has a similar system(maybe more naturally framed so it is much more efficient) and this is how we can extract physical information from the system. E.g., we essentially determine the approximate equations of the system to use both as predictors and descriptors of that system. That is, maybe it is more than just linearly predicting at each instance but we can determine more about non-linear systems which even helps us predict non-linear dynamics. It is more like pattern matching than SINDY but similar machinery might go on. I don't think this is what is happening but who knows. That is, SINDY is specifically to recover the "dynamical equations" that generated that system but the brain does not need those equations but it might have a different representation that it uses to understand the various systems and so might approach it in a parallel way. E.g., we learn "gestures" which can be thought of as "kinematic templates" and then just compare these templates with observations to determine or predict outcomes. It should also be noted that mathematics relies on the idea of action(function) as a fundamental unit and pervades everything mathematical. Category theory, the latest mathematical theory essentially puts functions/maps on a pedal stool. and has had great success at unifying virtually all areas of mathematics(it essentially provides a common framework with maps being at the center and building up more and more complex structures of maps). I would also say that I think it is obvious from first principles that our brain will encode the world around us in terms of what the world is composed of(as this will be the direct and efficient route). Our language then will simply a map to those things in the world which, generally, will also be relatively direct. The question this is not so much as if things such as force, time, distance, kinematics, etc lay behind our words but, in fact, are there words that do not have these things behind them and are actually meaningful and/or common. Certain words and phrases clearly deal with certain non-tangible things and are likely higher level language constructs but are they just displacing these "physical" constructs in time(such future or past) or metaphorical(a sort of predicate(logic) like structure) or is there some things that are truly disjoint from our innate connection with space-time? Essentially, can we learn meanings of things and have words for them that have no basis in physical reality? E.g., love might be used but, in fact, it is heavily based in physical reality and is just a word for certain types of physical kinematics. One can claim it conjures up non-physical things such as emotions and such but those will still be tied to their physical counterpart(which set the foundation). It seems as we age our ideas and meanings of words grow too. What is love to a child is not the same as love to an adult that was that child. Love becomes far more complex with more interpretations... but the heart is what the child developed and that was what the baby developed. E.g., the parent telling the infant "I love you" while smiling or caressing. The infant is "forming" that meaning of the word through the physical connection and over time more and more things get piled on/in to it. It is very likely all language is based on kinematics(and all that goes with it including forces, sensory information, etc) and as we age and "mature" our words just become more complex dynamical systems(no less than we do ourselves and does our society, family, etc). In group theory one studies transformations with are used both in physics(physical systems are suppose to be invariant to certain transformations) there is some evidence that our brains have some group like structures for similar reasons. E.g., rotations, mirror symmetry, etc. E.g., we can recognize a picture even if it has been mirrored, we can read upside down or in a mirror, etc.

[@SEMF]

That sounds like super interesting research! Why don't you share some links and info with our community. You can join the SEMF online community at no cost other than filling a quick form here: semf.org.es/participate/join.html

[@invictus327]

Brilliant, thank you.

[@SEMF]

Thank you for your kind words, we are glad you liked our content!

[@eswyatt]

This seems consistent with what I've heard from neural net skeptics link Pinker and Gary Marcus. Pinker talks a lot about stuff like "The meeting *ran from* 4 to 6 PM", etc. Obviously, the meeting is not a *thing that can move.

[@SEMF]

Yes, there are nice resonances with those sorts of ideas.

[@projectmalus]

Very nice, thank you. Is there a major perceptual shift at around 2 years old when a baby is allowed to sleep on their side? Up to then it's a choice of being held upright - triangulating objects of value, aided by the triangles of the face of the parent perhaps - or laying on their back, with color and smell in blobby shapes with (I guess) the hippocampalentorhinal processing mechanism hard at work. Now, laying on their side seeing a connection they can find comforting to relate to, between two massive forces of gravity and light, could be a crib bar.

[@SEMF]

We are glad you enjoyed our talk. Those are really interesting thoughts; I am sure others in the community will have something to say! You can join our community platform for free and discuss with other SEMF followers: semf.org.es/participate/join.html

[@frilansspion]

You dont have children, I guess?

[@paulhaube]

It borrows from Deleuze”s Logic Of Sense with the convexity concept (i.e., intensity & extension). To redefine the English rules of language may not be applicable to others languages; not universal enough for me.

[@SEMF]

What part of the talk are you referring to specifically?

[@frilansspion]

Thanks for sharing. Sounds a little shaky for being touted a "3rd paradigm" of how the brain encodes information? Its pretty vague what the "topology" and polar coordinates actually explains that neurons firing for red/green etc doesnt. And if someone could paraphrase the "Why convexity?" part for me, I would be grateful. A lot of this just feels like word-salad at the moment Im afraid

[@SEMF]

What we got from Peter is that there are ways to systematically assign topology and geometry to perceptual spaces rather than simple assign numerical quantities. This may sound vague to a general audience but it can be made operational with the proper treatment of the mathematical formalism and the experimental design.

[@frilansspion]

@@SEMF Youre not too sure either then :) Thanks for the reply!

[@kodfkdleepd2876]

There is no proofs that prove the brain encodes information in specific structures. What we do know is that logic functions are encoded by the neurons and the collective is effectively EQ to a large NN. The math essentially works out to all be the same(it is general enough to do whatever). Now neurons process electrical signals and neurons also divide and grow. This alone gives some type of topological structure out of necessity(essentially a metric space must exist although it doesn't necessarily have a direct relationship to how information is encoded). Others have conjectured that memories are actually electrical signals that persist in the brain in loops(there is some experiments for this). It is very likely the brain is just a large efficient and plastic NN. It is likely that as sensory information enters the brain(in the form of electricity) that it modifies the structure simply due to the nature of electricity. The way it does this then structures the brain according to how the sensory information is comes in through the "boundary". Essentially the electrical patterns will modify the topological structure of the brain much like, say, sound waves will modify small light particles(nodes will be attractors) or magnets modify small iron filings. That is, it is really the sensory "forces" that shape the brain(and obviously there is a feedback loop) forcing neurons to develop/grow/whatever according to such information. E.g., we know, I believe, that learning causes "neural growth". What is learning? Just experience. All experiences do this more or less and one can think of the brain as just an extremely complex neural highway or switchboard. Experiences modify the pathways in the brain either solidifying old paths(repetition of experiences) or creating new ones. Of course no experiences are disjoint. Learning to skydive still uses the same senses and will have many similar sensory input((such as smells, feelings, etc). This then alone will dictate a sort of differential structure. One would expect this differential structure to be laid out spatially due to electrical characteristics. Precisely how it works and such may never be known but the abstract structure is relatively simple(well, for someone that learns the bases of science). I think he means by the color analogy is not that it is encoded in the brain but it is a conceptual encoding that we as humans use to understand color(it is a model) and you are taking it too literally. After all, it literally says conceptual space. What it does do though is give a model that would, in some mappable structure, exist in some way in the brain((since we can obviously move through color space(such as using swatches) and our brains can understand the movement. That is, it's not embedded in the brain but there is at least an equivalence in some way. The kind of point, at least from my own experiences(I haven't finished watching the vid) and self-education is this: The brain is clearly a spatial structure. The brain is clearly an electrical structure. The brain is clearly a logical structure. These three things, individually, have implications. As a whole they have more implications(and limits the actual structure of the brain further). That is, since electricity works in certain ways(transmission lines, ohms law, etc) this has an effect on the brain's structure(and body of course). Since the neurons function like switches this has implications on how the signals move through the system. Allt his then allows us to use similar systems to help understand the brain. E.g., you can use human construction/maps as a way to understand spatial activity and topology. You can use computers and NN's to understand the logical side. You can use electronics to understand the electrical(and topological and logical). It's really not something that can easily be taught. One has to experience all those things. E.g., if you've never done much in electricity such as design your own circuits you are unlikely to have much of a clue what it really means. If you've never learned about how computers work it is unlikely you can have a clue and apply it to the brain. In some sense the brain is very simple(assuming neurologists haven't made any fundamental mistakes about it's composition). It's just a mass of neurons. It's the "mass" part that really makes the brain powerful. I also do not think it is coincidence that there are many parallels between the brain and other things such as NN's, human society, etc.

[@SEMF]

@@kodfkdleepd2876 This is a great comment! I would suggest you share your thoughts in our online community over here: semf.org.es/participate/join.html

[@frilansspion]

@@kodfkdleepd2876 He obviously doesnt mean spatial in that trivial sense, but of the representation. "...I do not think its coincidence that there are parallels between the brain and neural networks..."... jesus christ dude