Oooh. This looks clearer than what I’d read on Wikipedia. Though don’t we have another module isomorphism where we just treat ∧ in the same way? Why wouldn’t that work? Or if it would then I’ll be less surprised in the end (if there is no unique isomorphism). Thinking on it, classical factor-of-the-tensor-algebra constructions do also give some evidence of having vA from Clifford algebra and v∧A from exterior algebra corresponding better to each other than if there are any other ways.
The quest for knowledge would seem to produce minds that can come to the same conclusion independently. A bit like quantum entanglement with an underlying scheme that makes two entangled particles seem connected. All points towards a psychological field that is relevant at
I think it is more like when people try to solve different variations of the same problem, and design similar tools to solve them. Do you need to hammer nails? Invent a hammer. Do you need to hammer blocks, invent a mallet. Do you need to hammer rocks? Invent a sledge hammer.
@@umbraemilitos paradigms are also mental tools in one interpretation. In this case the notion that quantum entanglement is a fiction similar to telepathically produced independent solutions is one derived from a Bohm perspective in what, to me was a new example of the time honoured method of inventing analogies. So, the elements involved are a cultural diffusion of a paradym from one sphere of knowledge to another. Likely somebody else thought of it too, independently.
Is this abstract algebra?
yup
modules over what ring?
Any commutative ring!
whats the backwards L thing
That's the left contraction. I go over it in more detail in this video: th-cam.com/video/2AKt6adG_OI/w-d-xo.html
Oooh. This looks clearer than what I’d read on Wikipedia. Though don’t we have another module isomorphism where we just treat ∧ in the same way? Why wouldn’t that work? Or if it would then I’ll be less surprised in the end (if there is no unique isomorphism).
Thinking on it, classical factor-of-the-tensor-algebra constructions do also give some evidence of having vA from Clifford algebra and v∧A from exterior algebra corresponding better to each other than if there are any other ways.
That doesn't work because v^2 can be nonzero while v∧v is always zero.
The quest for knowledge would seem to produce minds that can come to the same conclusion independently. A bit like quantum entanglement with an underlying scheme that makes two entangled particles seem connected. All points towards a psychological field that is relevant at
I think it is more like when people try to solve different variations of the same problem, and design similar tools to solve them. Do you need to hammer nails? Invent a hammer. Do you need to hammer blocks, invent a mallet. Do you need to hammer rocks? Invent a sledge hammer.
@@umbraemilitos your example of what I was trying to say where you cite the invention of tools is splendid. I do, though wonder if
@@umbraemilitos paradigms are also mental tools in one interpretation. In this case the notion that quantum entanglement is a fiction similar to telepathically produced independent solutions is one derived from a Bohm perspective in what, to me was a new example of the time honoured method of inventing analogies. So, the elements involved are a cultural diffusion of a paradym from one sphere of knowledge to another. Likely somebody else thought of it too, independently.