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I had never understood how imaginary numbers had any bearing on physics (probably because I'd never been taught). But lately I've thinking about how all mathema
by cmollis 10y ago
I had never understood how imaginary numbers had any bearing on physics (probably because I'd never been taught). But lately I've thinking about how all mathematics must have some natural physical equivalent or relation. E.g. how does multiplication happen in nature.. what does it mean really to multiply something?...how does this happen in nature? For the most part, we take these things as facts and learn the mechanics, but in physics, it seems to me, you really need to understand how these algebraic interpretations translate into physical realities (also, perhaps sort of obvious for everyone reads HN). For someone who enjoys discovering these perhaps obvious things later in life, it's clear how mathematicians and physicists could clearly come to the same mathematical conclusions from completely opposite vectors.. I guess this probably happens all the time.
- tim333 10y agoIt's an interesting and unresolved question whether imaginary numbers are fundamental to the nature of physics or just a handy tool to calculate stuff. They are certainly handy for calculating - they are an easy way to represent oscillations.
- digler999 10y agoMaybe it's a mistake to allow imaginary to ever be separate from real numbers ? Another post here brought up how easily it is to work with imaginaries if you just treat them as the vector [re im]. Maybe (philosophically speaking), there are no purely real numbers. Could it be that all quantities in nature must contain a (sometimes zero) Im component ? That might be a more satisfying interpretation than just allowing them to creep in when they are absolutely required, such as polynomial equations.
- logfromblammo 10y agoYou should read about Maxwell's original equations for electromagnetism in component form (1865), then in quaternion form (1873), and Heaviside's vector-based rewrite (1888), then look at how they can be rewritten in geometric algebra. If you invent enough crazy new mathematical constructs, eventually one of them will mirror a natural physical phenomenon. And then a pile of equations collapses into something incredibly simple.