So now I am in wonderland following the rabbit again. These concepts are not unfamiliar, however I have made my own names or more often have no names whatsoever for the concepts as they seem to follow logically and simply from the facts.
Quote from Wikipedia:
Quaternion algebra was introduced by Hamilton in 1843. Important precursors to this work included Euler's four-square identity (1748) and Olinde Rodrigues' parameterization of general rotations by four parameters (1840), but neither of these writers treated the four-parameter rotations as an algebra. Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published
I am approaching this from the B cross A direction. Having solved the relationships, I am now required to apply them and be able to make them usable by machine or person. I am guessing that this will never be a normal human endeavor. The teaching of necessary requisites exceed the individual lifetime if they are not devised independently by the operator. It is obvious that Gauss and Euler and others could look at a problem and devise the appropriate methods without being educated to an algorithm. Without the "instinctual" ability, the understanding is absolutely impossible and even with that skill, the time frame is so great that implementation must be done at an advanced age. If one is required to attribute each thought to a name like Euler, then it simply slows the process and makes it intractable.
And on a completely unrelated note, I wonder if destroying something that is considered patently evil in a biosphere is actually rational. The use of antibiotics has created super bugs and that isn't what I mean. I suggest that it is not possible to know if any given random biological organism ( however benign or harmful ) will mutate to be an absolutely necessary symbiotic organism. If junk DNA had been removed as useless before Mir-941 was putatively mutated to the basis of human difference, then there would be no humans at all. The complex process of biological evolution is not a deterministic process without complete knowledge of the universe. If it were discovered that certain people have a gene that makes them genius, would then everybody choose to be gene doped in that way like some sort of cosmetic neurosurgery?
You have to wonder and I thought "Brave New World" and I never read that book so I will look now. While I am going out ever more random and deeper in the rabbit hole, WTF, does "xyzzy" from Zork originate in QUATERNIONS??
And again from Wikipedia:
Brave New World's title derives from Miranda's speech in William Shakespeare's The Tempest, Act V, Scene I:I get the point, but how could I read, study, watch, analyze and absorb all these things and still have time to live a real life?
How many goodly creatures are there here!
How beauteous mankind is! O brave new world,
That has such people in't.
I think I will be happy when I can apply gravity technology and be away some where that I can read a good old Shakespeare work in peace without worrying that a drone strike will be commanded by Skynet to once and for all stop the human pest from escaping the wrath of the god machine he created.
Well the rabbit is late and i see nobody is at the door and they never ring the doorbell so you have to just go let them in when they arrive.
from numpy import *
from numpy.linalg import *
([[ 2, 1, -1, -1, 0],
[ 1, 2, 1, 0, -1],
[-1, 1, 2, 1, -1],
[-1, 0, 1, 2, 1],
[ 0, -1, -1, 1, 2]])
([[ 2, -1, -1, 0],
[-1, 3, -1, -1],
[-1, -1, 3, -1],
[ 0, -1, -1, 2]])
Node1 -> Node2[label="I1"]
Node1 -> Node3[label="I2"]
Node2 -> Node3[label="I3"]
Node2 -> Node4[label="I4"]
Node3 -> Node4[label="I5"]
Even with all these tools, the engine of the universe is difficult to mod.
What light through yon window breaks, it is the East and and that is NOT the light from my home star.
And an even more remote fact: WebM has very little meta data defined and that might be considered a shortcoming or I say a blessing as simplicity can help in a world driven by purposefully convoluted specifications to produce monopoly controls of information.
The strangest thing is that many of theses things were derived 100's of years ago and had they the context and tools that I have, they would have realized what I know. There is much more going on than is even suggested by Hamilton, Cantor, Leibniz, Gauss, Tesla, Maxwell, Feynman, and Euler.
Strange new worlds are only around the corner and that is without a trip down the rabbit hole, though I begin to wonder whether it is a hole or a manifold.