The adoption of terminology to describe the universe is troublesome when it implies more than it is represents. If I look at the universe as a whole, there is no negative sign to be seen. I would guess that my way of looking at things is confusing to some people. Less than nothing. What exactly does that imply? In the case of vectors it is left and right , up and down, fore and back, future and past. There is no real negative there except by convention. Left is negative or positive and the rotation of vectors changes positive to negative, left to right.
I have an equation which works for dimensional space as a transform of these axis conventions and I do not think that it can be done any other way and be intelligible or useful. It is quite a bit easier to describe and demonstrate principles with programs, as the type of complex relationships are inherent.
find -L ~/ -maxdepth 4 -type f -size 0 -print0 | xargs -0 -r ls -la | grep antfarm | grep x
This is an example of command line programming that involves sets and characteristics of objects and methods(functions) applied to sets. It is my opinion that a competent programmer has intuitive knowledge of mathematical relationships beyond the bounds of institutional math. I could do f(z=f(y=f(x))) as a normal , everyday thing. I would write it with more clarity in the naming conventions ( one would hope), but in the end it describes the interaction of multiple variables.
I can get out my oiler[sic] or more properly Euler or Naperian to lubricate the process, but in the end there is only XUL.
In order to remove the imaginary and increase the clarity of the product, it is necessary to introduce properties of numbers in a dimensional system that have relationships defined by functions ( methods) in the same way that + - / * are defined for quantity. In vector math and matrices, these are already inherent and it is merely the terminology applied that suffers. The root relationships , literally , have additional properties that must be expressed to exclude the ambiguous. A process does require interpretation as to its context unless context is excluded in the process of its analysis. In dimensional space, the relationship in space of 1, 2, 3, 4, or 5 objects has unique combinatorial significance.
An example of what I am implying is as follows:
state_of_bouncing_ball=(sin(t))/(t^2) // where t is time from 1 to n
// a decaying oscillation.
t can be negative here and it could be said that it describes something in the past, but honestly there is no sense in applying some mystical significance to my choice of axis center about t. In this particular case it is wrong to conclude that -t describe a past state of the system. It mirrors on t ( -1 to -n). If it were predicting the past of such a function, it would be the inverse in logic, or sin(-t)*t^2 and in this case the -t becomes a direction vector of CCW or CW ( Meaning Clockwise or Counterclockwise). And even that is ambiguous without defining a plane surface normal (N). Thus it would better be written as sin((N)CW*t)*f(t) or sin((N)CCW*t)*f(t).
It seems that defining a function which is the infinite extension of the concept of slope (1/n), automatically makes it infinitely differentiable and integrable. It is like Hilbert's Hotel with a Schroedinger's cat in every other room. An infinite series shifted left or right is still a recursive to infinity and equal when all the terms are continuous products.
I could be off base here, but this seems less mystical a relationship and more of a circular definition ( no pun intended ) , all hail Leibniz and Euler. Another thing is bothering me, When I have two equations describing a line like:
2x + 5y = 0
and
58x + 145y = 0
145*2=290 and 58*5=290 because they are the same line and to call that some super special method is being way to serious about the elegant complexity of that relationship. I won't bore people with the detail,, but if the slope of A and slope of B are the same then inverting one and multiplying is hardly more than junior high level geometry foo. I could be wrong, but I could also be right. The next videos will be the inclusion of various periodic functions in factorial combination. Fibonacci and fractals with sines and exponential loops should be something interesting to see in 3D.
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