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                Subject:   TGD & BRST quantum cohomology                 Date: 01/28/97

'Fundamental re-build ..'   (continued)

Lawrence Barr Crowell wrote on 01/28/97:

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[LBC] Now you claim that (1/sqrt2 x 1/sqrt2 = (pi)/4). Well the square root of 2 is about .707, and further (1/sqrt2 x 1/sqrt2 = 1/2. After all you just took an operation and then performed its inverse. Pi is about 3.14 and pi/4 then about .8. So your equation says that 1/2 = .8, at least approximately. Obviously this is a falsehood.

[JNR]  Falsehood under standard parameters, yes. I've been using this example so long that I was delinquent in specifying that "x" is not the standard cross-product function. Your patience please, and my extreme apology. I beg your indulgence and will *briefly* rectify the error by saying that I generally use the symbol of an x-in-a-circle. I can only justify its "meaning" by use of a diagram which you can easily draw with 5 lines.

Draw x and y axes. Scribe a simple unit circle around (0,0). Mark off 1/sqrt2   along each axis. Draw a horizontal line from (0,1y/sqrt2) to where it   intersects the circle on the right, and a vertical line likewise from (1x/sqrt2,0) upwards. The diagram is complete.

The newly defined function (x) is a transdimensional operator. It takes two Cartesian/Euclidean linear "values" and produces a single radial/conic "value" relevant to the *circumference* of the unit circle. Left side are in regard to the linear sets (x,y) (or x1,x2 if you prefer), and the right side is in regard to a combined "over-bar (xy)" otherwise called the circumference, c. The
"multiplication" intersects the circle at pi/4, going from (1,0) upwards .

The (x) is a translator-function - transforming the information expressed per one set of domains (x,y) into the information/values of quite another separate yet related domain (c). This is the core operator/equation of the Heisenberg U.P. The remaining factors are limitations imposed by the quantum constants. The U.P. is essentially an apparatus for translating information relevant to several *continuums*, one to another; much more than a delineator of quantum reality and "limitations of information extraction" {p or d, but not both}.

This is undoubtedly a totally new notion to you. Your skepticism is reasonable.

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>(JNR) The second is that modern Information Theory is effectively a tautology. Implicit-Information Theory (Calculus) was used to define Explicit-Information Theory (Shannon).

(LC) I agree with this statement, but to formulate it you need to understand the Riemann zeta function.

[JNR]  Thank God we agree on something! :->! I ain't *daft* y'know! The only foundation needed to "understand" or "formulate" that statement of mine - which I have never seen put forth explicitly anywhere except in my own writings (and which I presented at Tucson II) - is to have an accurate handle on and appreciation for the fundamental dynamics and interrelationships of how information gets-around in our universe. I have that in spades. Riemann zeta may be one way of understanding the truth of that relationship, but not the only way!

BTW, you should have seen the reactions I got at T-II when I posted that statement. You'd have thought I had Ebola. (ahh the joy of not living under a lamp-post!)

>(JNR) Continuum precedes quantum.

(LC) No, its really the other way around!

[JNR] No, it's really not! I know the standard litany of ultra-successful quantum mechanics. The 1991 Santa Fe article by Wheeler sledge-hammer's the QM-->CM point home loud and clear, as a matter of fact. But look at what you just agreed to Lawrence! Quantum values are super imposed on a foundation of Calculus formulae - continuum! - the *vanishingly* small (heh,heh - where "the boundary of a boundary is zero" - to quote dear John Archibald Wheeler) - and the resulting configuration generates QM and <bra|ket>, et al. Topology *demands* "continuum" in order to maintain any homologies and ideo-morphisms or relational morphisms.

I am *not* suggesting that QM or your work (as representative of the field) is "wrong". I *am* saying that there are more fundamental reasons why they are "right", beyond considerations now broadly held. Look at Linde's work (which you just cited today) ... even those 10~100~80 universes "smooth" into one another - potentially interact, so to speak. Look at Nanopolous and crew. Look at Pitkanen's TGD. Look at information coding in *all* hologramic transductions. Look at Cantor. Look at *my* work.

Look at Bohm. He had to go outside Hilbert space. Look at Prigogine, he too has now gone to "extra-Hilbert space, H+", and calls Time "primal", not "generated" anymore. We may be locked into quantum "experiences" of time and space, but the bed-rock of our mathematics says otherwise. Wheeler is going to be the last/best champion of QM, I dare say!

I guarantee you, no one has looked into the linguistics/etymology of mathematics before, the way I have. It's an area everybody takes for granted; assumes there is nothing of importance left to learn from its exposition. But there is.

Unless a person understand that information can be coded topologically intact into many different groups of "dimensions" because *continuum structure is fundamental*, then statements like Matti's representative one that "3 dimensional p-adic space is a point on the surface of z-space" (or something like that - this is a recollection, not a perfect quote) has absolutely NO
meaning. Ya can't get-there from here, ya can't map with any confidence.

Wheeler enjoins us to champion "it-from-bit". A quantum-minimalist formal "bit-size" comes before all else. Can't be. Tain't so. Calculus already smashes right through any formal "bit-barrier" restriction.

If I get you to recognize no other issue out of all my writings, *this* is the one I would want you to embrace. It doesn't invalidate anything you already know from your own work, expertise and training, it just puts the puzzle pieces together in a better way, much better way.