5 ms·

Knowledge doesn't "enter" us, that's the point. It's an emergent property of (many, many) memorized & networked sensations, which do enter us through our variou

Knowledge doesn't "enter" us, that's the point. It's an emergent property of (many, many) memorized & networked sensations, which do enter us through our various sensory organs. It is virtually impossible to teach an abstract concept like "cup" without a) providing real, sensory examples of what you mean by "cup" or b) relating to analogous concepts that the student has already learned through personal experience (like "bowl" with "handle") and is capable of communicating.

marginalia_nu 5y ago
There is a point where we do not have knowledge, let's say when we are born, then we have perceptions, and after that we (may) have knowledge about the world. I will say that knowledge has entered us through perceptions. If something is not in my mind, I have a perception, then it is in my mind; and if I was unable to have perceptions it could not have entered my mind, then it has entered through that perception. All physical phenomena are to some extent emergent down to subatomic particles and possibly even further. It doesn't really have much of an effect on the subjective human experience which principle is more emergent, and the subjective human experience is the only human experience. It's very hard to teach someone who has no relationship with the world, but you don't need a large set of concepts to synthesize additional concepts. You can derive most of mathematics from a few simple axioms. Democritus concluded the world was made of atoms based on observations about how the world appeared to work, on encountering problems like Zeno's paradox. Knowledge, as well as language, is all about how things relate to each other. Words to meanings, causes to effects.
- pphysch 5y ago
  > You can derive most of mathematics from a few simple axioms. Yeah, nothing is stopping you from building towers of abstractions that are N degrees from any real experience or data. But those heavily-derived concepts are prohibitively difficult to teach and communicate, because each level in the abstraction hierarchy adds semantic noise. A major reason why classical, "pure" mathematics pedagogy is infamously ineffective. Ultimately, every great mathematician learned to count with rocks or apples -- not by internalizing Peano's axioms.
  - marginalia_nu 5y ago
    That is how it is commonly taught, but can it really be argued it's the only way it can be taught? Regardless which method is easier, why is it possible to interact with negative, irrational, or complex numbers without anyone having ever seen them, but not integers? There of course needs to be a common set of ideas to communicate, but I'm not convinced you need one particular set. In many cases, having some of the ideas means you can synthesize the rest. You could for example reason about numbers by drawing upon size rather than quantity. Then you basically end up with the Euclidean method, a mathematics of proportion that goes a surprisingly long way.
    - pphysch 5y ago
      Abstract quantities, even positive integers, don't exist in reality. Heck, even "objects" don't really exist, because "boundaries between things" don't concretely exist except in our perception and imagination. If there is any primal, axiomatic concept, it is "object"/"thing". From object you can derive quantity (many objects), from quantity you can derive quality (two objects are different), and so on and so forth.
      - marginalia_nu 5y ago
        You can reason about the same reality in various different terms, and the choice in terms shapes how you see the world. I don't think it's easy to argue that one concept is the true concept from which all concepts inevitably derive. You can just as easily think of things as parts of a whole as objects in an emptiness. In some languages the name for door is the same as the name for mouth, and a door is a bit like a mouth so it makes sense to relate them. All language is metaphorical like that, except not always as explicitly. When we say a thing is an object, we say that our concept of that thing shares similarities to the concept we have for objects.
- svnt 5y ago
  > It's very hard to teach someone who has no relationship with the world It is impossible, by definition.

marginalia_nu 5y ago

There is a point where we do not have knowledge, let's say when we are born, then we have perceptions, and after that we (may) have knowledge about the world. I will say that knowledge has entered us through perceptions. If something is not in my mind, I have a perception, then it is in my mind; and if I was unable to have perceptions it could not have entered my mind, then it has entered through that perception. All physical phenomena are to some extent emergent down to subatomic particles and possibly even further. It doesn't really have much of an effect on the subjective human experience which principle is more emergent, and the subjective human experience is the only human experience. It's very hard to teach someone who has no relationship with the world, but you don't need a large set of concepts to synthesize additional concepts. You can derive most of mathematics from a few simple axioms. Democritus concluded the world was made of atoms based on observations about how the world appeared to work, on encountering problems like Zeno's paradox. Knowledge, as well as language, is all about how things relate to each other. Words to meanings, causes to effects.

pphysch 5y ago
> You can derive most of mathematics from a few simple axioms. Yeah, nothing is stopping you from building towers of abstractions that are N degrees from any real experience or data. But those heavily-derived concepts are prohibitively difficult to teach and communicate, because each level in the abstraction hierarchy adds semantic noise. A major reason why classical, "pure" mathematics pedagogy is infamously ineffective. Ultimately, every great mathematician learned to count with rocks or apples -- not by internalizing Peano's axioms.
- marginalia_nu 5y ago
  That is how it is commonly taught, but can it really be argued it's the only way it can be taught? Regardless which method is easier, why is it possible to interact with negative, irrational, or complex numbers without anyone having ever seen them, but not integers? There of course needs to be a common set of ideas to communicate, but I'm not convinced you need one particular set. In many cases, having some of the ideas means you can synthesize the rest. You could for example reason about numbers by drawing upon size rather than quantity. Then you basically end up with the Euclidean method, a mathematics of proportion that goes a surprisingly long way.
  - pphysch 5y ago
    Abstract quantities, even positive integers, don't exist in reality. Heck, even "objects" don't really exist, because "boundaries between things" don't concretely exist except in our perception and imagination. If there is any primal, axiomatic concept, it is "object"/"thing". From object you can derive quantity (many objects), from quantity you can derive quality (two objects are different), and so on and so forth.
    - marginalia_nu 5y ago
      You can reason about the same reality in various different terms, and the choice in terms shapes how you see the world. I don't think it's easy to argue that one concept is the true concept from which all concepts inevitably derive. You can just as easily think of things as parts of a whole as objects in an emptiness. In some languages the name for door is the same as the name for mouth, and a door is a bit like a mouth so it makes sense to relate them. All language is metaphorical like that, except not always as explicitly. When we say a thing is an object, we say that our concept of that thing shares similarities to the concept we have for objects.
svnt 5y ago
> It's very hard to teach someone who has no relationship with the world It is impossible, by definition.