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Math and reality
dream_weaver reacted to StrictlyLogical for a topic
Language, concept, number, these we are possessed of and are all part of our grasping of and our relating ourselves to entities. Entities themselves, however, are not in any way possessed of any of language, concept, or number. That we "find" them poetic or majestic, of a kind or a phenotype, or multitudinous or stochastic, although somethings of them, something about their identity, is touchable and accessible by our various abstraction apparatuses, those somethings of them are not themselves linguistic, conceptual, or mathematical. For those, are only us, as they only ever could and should be.1 point -
Math and reality
dream_weaver reacted to Boydstun for a topic
Oops, I got the terms mixed up. Geroch's term was "appropriate," not "adequate." It's his meaning of his term I have in mind: everything in the mathematics has physical meaning and all of the physics one wishes to talk about is describable in terms of the mathematics. Such is an appropriate mathematics for the physics. Some of our mathematics used in physics, I say, hopefully uncontroversially, is clearly a matter of chosen tool, not the mathematical character of the physical reality. Such would be using base 10 in arithmetic calculations and using various coordinate systems. As fruitful as it was to realize that curves can be described by algebraic equations written with reference to a coordinate system, when it comes to geometric facts of curves in the Euclidean plane, which we may take for planes of the physical geometry around us, the method of Euclid we learn in high school for bisecting a line segment is perfect location and physical; no coordinates lain over things by us and used to describe the curves and their intersections add something physical, which we get directly by synthetic geometry (Euclid's way being an example of synthetic geometry, as distinct from analytic geometry).1 point -
Math and reality
Boydstun reacted to StrictlyLogical for a topic
Given the specific formalization of QM as accepted I would suspect other kinds of numbers as operators or coefficients to the so-called “states” would be improper somehow. I played around with quaternions, more specifically a sort of Mandelbrot generalization to render fractals on a … believe it or not… Amiga computer back in the day. I believe there are multiple imaginary bases i j and k, each squared is -1 but the product of any two is the other (positive or negative depending on the order of multiplication)1 point