The Man, I do not use
http://en.wikipedia.org/wiki/Superposition_principle for Superposition definition if A+B = AB by this meanning:
Doron, I am certain that your assertion above, where you claim that your “
Superposition” does not “use”, well, superposition, surprises no one here.
AB is, for example, a superposition between A=dead cat + B=alive cat, which is an uncertain id, that can be collapsed into certain identity A=dead cat or certain identity B=alive cat (
http://en.wikipedia.org/wiki/Schrödinger's_cat ).
I’m quite familiar with the Schrödinger's cat thought experiment, while obviously you are not. The cat is never in “a superposition of between A=dead cat + B=alive cat…”. Again uncertainty, even about the cat’s status, is not a superposition of the cat’s status (“A=dead cat + B=alive cat”), that is the whole point of that thought experiment. A point you either missed or simply ignored.
I’m also quite familiar with Quantum Superposition, which (as I’m sure wont surprise anyone except perhaps you) is actually based on the superposition principle. So I suggest you actually read your own references.
but be aware that OM's superposition is not mrasured by complex or real numbers, which are some certain ids (like certain A or B ids if AB superposition is collapsed).
By your own assertions above “OM's superposition” doesn’t even involve superposition, so as usual your “OM” has simply “collapsed” in upon itself.
AB notation means that we do not know for certain the identification of x branch of some k-Uncertainty x k-Redundancy tree (where identity A or identity B are certain ids) because A and B are in superposition (x identity is not collapsed into certain identity A or certain identity B).
So now you’re back to “uncertainty”. Which as I said before is already established, to varying degrees, by the fact that “x” is a variable and represented by the values x can take as the set X like (A,B). Your AB “identity” is completely superfluous since it doesn’t actually represent anything (like superposition) other then the simple fact that “x” is a variable and the values it can take which is already represented by the variable x and the set X of the values it can take. Once again your OM is a poor substitute for actual mathematics
AB is a notation that defines a superposition among two possible certain identities, where the certainty is only a potential as long as AB superposition is not collapsed into one of the certain options (A or B).
No Doron it (as usual) just defines your fantasies which by your own assertion “do not use” superposition.
Indeed there is no redundant id in DS (A,B,AB), but there is an uncertain id in DS (A,B,AB) because of AB superposition.
See, now was that so hard? You could have just answered the question when I asked directly if AB was a different “identity” than A or B.
------------------------------------------
Here are the detailed example of k=0 to 2 of k-Uncertainty x k-Redundancy tree, and you can clearly see that AA or BB are not under Y-axis (that has no "," between symbols) or X-axis (that has "," between single symbols like "A" or group of symbols like "AB" ) of this tree:
So what? Just because you do not include “AA or BB” in your “tree” does not make such a superposition “impossible” as you claimed before, of course we have already established that your “OM's superposition” does not “use”, well, superposition.
Code:
0x0
(0)=()
1x1
A * .
(1) = (A)
(0) = ()
2X2
(AB,AB) (AB,A) (AB,B) (AB) (A,A) (B,B) (A,B) (A) (B) ()
A * * A * * A * . A * . A * * A . . A * . A * . A . . A . .
| | | | | | | | | | | | | | | | | | | |
B *_* B *_. B *_* B *_. B ._. B *_* B ._* B ._. B *_. B ._.
(2,2) = (AB,AB)
(2,1) = (AB,A),(AB,B)
(2,0) = (AB)
(1,1) = (A,A),(B,B),(A,B)
(1,0) = (A),(B)
(0,0) = ()
If you get k-Uncertainty x k-Redundancy tree, then plase try to define the general formula that returns the numbetr of DS of any given k-Uncertainty x k-Redundancy tree (k=0 to n, where n is some natural number).
Let’s have a look at the “uncertainty” and “redundancy” in each of your “2X2” examples, shall we.
“(2,2) = (AB,AB)”: “uncertainty” = 2, “redundancy”=1. Your “(2,2) simply replaces each element with the number of letters in that element.
“(2,1) = (AB,A),(AB,B)”: “uncertainty” = 1, “redundancy”=0. Your “(2,1) simply replaces each element with the number of letters in that element.
“(2,0) = (AB)”: “uncertainty” = 1, “redundancy”=0. Your “(2,0) simply replaces the one element with the number of letters in that element and adds a “0” representation for the letters of a single element that is simply not present.
“(1,1) = (A,A),(B,B)”,: “uncertainty” = 0, “redundancy”=1. Your “(1,1) simply replaces each element with the number of letters in that element.
“(1,1) =” “(A,B)”: “uncertainty” = 0, “redundancy”=0. Your “(1,1) simply replaces each element with the number of letters in that element.
“(1,0) = (A),(B)”: “uncertainty” = 0, “redundancy”=0. Your “(1,0) simply replaces the one element with the number of letters in that element and adds a representation for the letters of a single element that is simply not present.
“(0,0) = ()”: “uncertainty” = 0, “redundancy”=0 , hey look your “(0,0)” might actually represent your “uncertainty” and “redundancy” of the empty set. However the indication would be (like before) that you were just representing the lack letters in the two elements you were expecting, that the empty set does not have.
So out of the ten examples of your “2x2” “k-Uncertainty x k-Redundancy tree”:
Only one has an “uncertainty” of 2, none have a “redundancy” of 2.
Only 4 have any “uncertainty” and only 3 have any “redundancy”.
4 have no “uncertainty” or “redundancy”.
So beside there being very little and often no “uncertainty” and/or “redundancy” in your “2x2” “k-Uncertainty x k-Redundancy tree”, the only thing that is “2x2” in your “2x2” “k-Uncertainty x k-Redundancy tree” are your ‘connect the dots’ drawings where you simply add dots when there is just one element and even no elements in your examples just so you can pretend there is something “2x2” in each example.
Your so “called Distinction State (DS)” simply represent the number of letters in each element of your examples with you putting an indication of “0” for elements that are not in your examples just so you can pretend there are always 2 elements in each example.
