Am trying to solve a puzzle:
A great deal of modern physics is represented by the book: "QED. The Strange Theory Of Light And Matter" by Richard Feynman.
(I recommend getting hold of a copy from a library or somewhere).
It is written for the general reader, and not very long.
The crunch is: QED (quantum electrodynamics) largely revolves around "the adding of probability amplitudes" (whatever they are).
Whatever they are, they are represented by so-called "complex numbers".
"Complex numbers" are 2-dimensional numbers, as far as I know.
They apparently can be represented by ordered pairs of numbers (which seems sensible to me).
But people often represent a complex number in the form "a + ib", where "i" is the square root of minus 1.
Now that looks very dodgy (there's a good book about sq. rt. -1 called "Sqare root -1 AN Imaginary Tale" or something. A cartoon suggests imaginary numbers might be numbers like "eleventy-twelve" or something. But no, they actually work in practical use for electrical engineers.
According to the history of sq. rt. -1; people tended to treat this weird "impossible" number as rather suspect. But "imaginary" is apparently unfortunate wording and the whole thing a misunderstanding, suggests the book.
The two vectors that multiply to give a unit vector in a negative direction, is if I recall, all it is. Each of those two vectors is a sq. rt. - 1.
So what is vector multiplication?
I vaguely recall it involves rotating a vector 90 degrees about the origin.
It all sounds like befuddlement though.
However, as "complex numbers" are, according to www.emmy.noether.com, how the book of nature is read; then figuring out EXACTLY what this is all about should clear up a lot of confusion.
Well; I think, how about it is: man who reads the book of nature by comparing and matching patterns?
And two comparisons gives you two new patterns, to be compared and matched.
Since the basic structure is 1, 2, 3 (pattern A, pattern B, comparison C); then the complex number must be the representitive of the two patterns compared?
And you are right about a 3rd dimension in the comparison of the other two views of a square from a practical point of view; this is implicit.
What Dr. Dick may have discovered is that 3-D space is constructed by implication in this way, sort of projected holographically, from the self-referential comparison of two patterns.
In exposing the implicit 3-D-ness you have illustrated a theory of how space may be constructed holographically from 2-D pattern matching.
Dr. Dick says that events have dimensions. Interaction of two patterns may holographically generate the 3-D space? In your example, my view required a 3rd dimension to compare the two views. But: could the two views be unconnected squares that, on seeing each other, formed a mutual 3-D space?
When you look at how words are defined, it involves the intersection of two categories. When I say "telephone" partially contains "communication"; and "communication" partially contains "telephone"; you know from experience that these words do partially define each other in that region they have in common.
What Dr. Dick has done is found a partial differential equation that maps this in principle.
What Chris Langan has done is note the mutual self-containment I guess in his CTMU (Cognitive Theoretic Model Of The Universe).
If instead I wrote 5278483 partially contains 64738920, which partially contains 5278483; where the numbers represent words of unknown meaning; it starts to look more like what Dr. Dick did.
It also looks like 5278483 self-referred and projected out 64738920 in the process. So everything contains everything else in self-reference, in consciousness? 64738920 exists and to exist is to be different, so is separate by definition from 5278483; but they see each other in "self-reference 'space' "; they find each other are projected out of Consciousness itself?
So by being fully conscious, you can see other things created by consciousness. The door opens on telepathy and teleportation as natural abilities for fully conscious humans?
Dr. Dick does appear to have found a simple in principle way to obtain major physics laws; and allow paradoxes to be unravelled.
Two dimensional numbers just represent two ways of looking at something, in one view, it seems.
One view of a 2-D object, a square, is the view from one edge.
I thought (but may be wrong) that how about: from the perspective of the square seen from one edge, that one edge is just "a" amount of edge.
The other edge is represented as sq. rt. -1 square(i) x b amount of that edge
So a + ib can mean edge 'a' + (edge 'b' represented as sq.rt. of missing square)?