Descriptive differential dynamics: complex-complex numbers and defining division
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- čas přidán 11. 09. 2024
- Space-time, hologram, rest and motion, derivative-stopping and a stop-derivative, division's definition, the linear fractional equation and the identity dimension, operators and arithmetic, complex-complex numbers, mathematical attack and defense, point at infinity, contours and geometrical intuition, Jordan curve, complex topology, complex domains, Newton's laws, Newton's zero-eth laws.
I wish I had the background to understand these topics in a more comprehensive manner. I would love if you could upload a general introductory video for each of these books/playlists.
Thanks for recording all these.
What you do is explore each of the mentioned topics, you'll start to find they're all one big topic.
26:00 If you construct a complex number whose entries are complex-valued, either you need a new i that interacts with the original i differently (much like the j of the quaternions), or you just get a complex number again. That is, if A+Bi = (a+bi)+(c+di)i, then that's (a-d)+(b+c)i which is back to a standard complex number, except now you've lost the fact that complex numbers defined to have real entries are unique; for example, (4+2i) + (3+1i)i = 3+5i = (7+4i) + (1+4i)i.
If you define a new i that interacts in some way with your standard i, (let's call it j for clarity), then you get numbers of the form A+Bi = (a+bj)+(c+dj)i = a + ci + bj + dji and you have to make a choice of what ji does. Clearly though, since there's a bj term, you're not working with a system that can be called complex numbers anymore. I'd guess from that form that you'd have to be working with a system that is morphic (whether iso- or homo- or something else, I don't know) to some class of hypercomplex numbers, which have been studied since the 1850s or earlier
What you're getting at is even a recursive sort of definition, as what was introduced was a sort of left-complex and right-complex numbers, simply whether it's a + bi or ai + b, then those are only written in quadrants II and IV, because quadrant 1 is fulfilling this identity-dimension bit. Yeah, otherwise you figure all of mathematics is very well explored then that you'd wonder how it's possible at all to even have a style. That the complex numbers are just a diagram sitting on R^2, or, for example, that the definition of division of complex numbers _is a definition_ meaning _it's not a derivation_ so there are branches, of it, division in complex numbers, just like complex numbers are a branch themselves. In 1985 we knew that positive real numbers had at least two roots: the principal and any non-principal branches, and as here those are also singularities in a multiplicity theory.
Unwatchable
something something mobius thingamajig something something time travel something something, gatekeeper negotiations
brodie got pressed when i questioned him 😭😭😭 he’s just blabbing incessantly on these videos 😹
Won't shut up
is any of this even remotely correct? this whole channel is just you going on and on with mathematical jargon that seems unintelligible and illogical
I'm correct. Go away then.
maybe write some of what you’re saying down? a weird way to show off your so called knowledge in mathematics with a bunch of books and a spinning globe 😭