Hi GFR!
It is on a gut feeling level +mathematics must explain processes possible . I think that 1/2 is a true dynamic constant, while i is continuously variable and pi most likely discrete (but may be not).
I think +i and -i are different, but the difference is dynamic, sorry to say that, so that there is space where they mean rotation in diffferent directions and are not interchangeable.
The fact that angle can truly equal pi is by itself amazing since pi is a limit of discrete approximation of circle via polygons, from both sides, geometrically - in plane. if You try to find out pi by measuring the lenght of circle in 3D You end up with the fact that pi definitely may vary from 1/2 pi to 3/2 pi depending on the angle in 3D between the measurable and measuring disc, size of measuring circle etc. When the measuring circle gets infinitely small, than value of pi is achieved, but the cost is that You do not know anymore the angle at which You measure since all give the same result. When you know the angle, measuring disc is of finite sizes, and pi varies depending on that angle.
See the very interesting link, please: http://cvt.com.sapo.pt/tp/tp.htm
That thinking I have does not come from mathematics, its more like .... coming from thinking that things should be simpler, but probably, little unorthodox.
Any dynamic balance could divide any 2 processes in 1/2 - even if we now nothing about the quantity involved nor about the scale it is happening in. e.g if we would like to weigh the whole Universe and assume it is infinitely divisible , than only way would be to balance one half of it against another (do not ask me how) . Despite the fact that Universe might be infinite, might consist of things we can not define, we could imagine that such balance can be achieved. Then , if we take half we have balanced,we again can balance it ...etc. Zeno paradox. In that sense we can balance anything in any scale with the same and always achieve 1/2, if that what we balance is infinitely divisible. So 1/2 in each (hyperdimensional) scale is , means the same, so it is a true constant. If quantum world is not infinitely divisible, we can not do it if we do not add subquantum part- but that is nothing special since as we can not directly measure it, only via interactions with quantum world, we may add it as well- for a sake of symbol.
I was wandering why complex plane and real axis are looked upon as something separeate- in my opinion, real axis has imaginary rotating ( so that left is not right) extension perpendicular to it and every function just crosses real axis on it rotating way via infinite hyperdimenions . So basically You have kind of a cylinder, but each projection of functions on real axis may contain 3 parts- 2 rotation in opposite directions in that hyperspace , 1 truly real - like 3 parts of h odd, h even and x^1/x of h(x) when x< e^-e. That is probably the only place where they separate so obvously, the other being h(x) where x> e^(1/e).
It is on a gut feeling level +mathematics must explain processes possible . I think that 1/2 is a true dynamic constant, while i is continuously variable and pi most likely discrete (but may be not).
I think +i and -i are different, but the difference is dynamic, sorry to say that, so that there is space where they mean rotation in diffferent directions and are not interchangeable.
The fact that angle can truly equal pi is by itself amazing since pi is a limit of discrete approximation of circle via polygons, from both sides, geometrically - in plane. if You try to find out pi by measuring the lenght of circle in 3D You end up with the fact that pi definitely may vary from 1/2 pi to 3/2 pi depending on the angle in 3D between the measurable and measuring disc, size of measuring circle etc. When the measuring circle gets infinitely small, than value of pi is achieved, but the cost is that You do not know anymore the angle at which You measure since all give the same result. When you know the angle, measuring disc is of finite sizes, and pi varies depending on that angle.
See the very interesting link, please: http://cvt.com.sapo.pt/tp/tp.htm
That thinking I have does not come from mathematics, its more like .... coming from thinking that things should be simpler, but probably, little unorthodox.
Any dynamic balance could divide any 2 processes in 1/2 - even if we now nothing about the quantity involved nor about the scale it is happening in. e.g if we would like to weigh the whole Universe and assume it is infinitely divisible , than only way would be to balance one half of it against another (do not ask me how) . Despite the fact that Universe might be infinite, might consist of things we can not define, we could imagine that such balance can be achieved. Then , if we take half we have balanced,we again can balance it ...etc. Zeno paradox. In that sense we can balance anything in any scale with the same and always achieve 1/2, if that what we balance is infinitely divisible. So 1/2 in each (hyperdimensional) scale is , means the same, so it is a true constant. If quantum world is not infinitely divisible, we can not do it if we do not add subquantum part- but that is nothing special since as we can not directly measure it, only via interactions with quantum world, we may add it as well- for a sake of symbol.
I was wandering why complex plane and real axis are looked upon as something separeate- in my opinion, real axis has imaginary rotating ( so that left is not right) extension perpendicular to it and every function just crosses real axis on it rotating way via infinite hyperdimenions . So basically You have kind of a cylinder, but each projection of functions on real axis may contain 3 parts- 2 rotation in opposite directions in that hyperspace , 1 truly real - like 3 parts of h odd, h even and x^1/x of h(x) when x< e^-e. That is probably the only place where they separate so obvously, the other being h(x) where x> e^(1/e).