**Matti Pitkanen** (*matpitka@pcu.helsinki.fi*)

*Sat, 4 Sep 1999 07:29:42 +0300 (EET DST)*

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On Fri, 3 Sep 1999, Stephen P. King wrote:

*> Dear matti et al,
*

*>
*

*> A few questions...
*

*>
*

*> Matti Pitkanen wrote:
*

*> snip
*

*>
*

*> > [MP] In TGD closed spacetime surfaces are possible absolute minima
*

*> > of Kaehler action. They have necessarily finite extension in both
*

*> > time and spatial directions. One can imagine of constructing them
*

*> > by taking two finite pieces of Minkowski space in M^4_+xCP_2, slightly
*

*> > deforming them in CP_2 directions, gluing along their boundaries,
*

*> > smoothening resulting edges, and requiring that absolute minimum
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*> > of Kaehler action is in question. These surfaces decompose
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*> > to regions with Minkowskian signature and Euclidian signature
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*> > or have global Euclidian signature. They are not locally vacua:
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*> > globally they are: classical energies, momenta, etc are
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*> > of opposite sign on the two sheets. These surfaces are analogous
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*> > to vacuum bubbles appearing in perturbative quantum field
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*> > theories and contributing nothing to S-matrix elements.
*

*>
*

*> This is what I have been looking for! Thank you! Now, a question: You
*

*> are saying that the cognitive and material space-time sheets have
*

*> "opposite signs" of their "classical energies, momenta, etc". Would
*

*> there be a CPT symmetry violation predicted from TGD to account for the
*

*> statistics of neutral (?) kaons?
*

CPT is exact in TGD and experimentally. CP is broken. Breaking is caused

by the presence of classical Kaehler electric fields required by absolute

minimization of Kaehler action. CP breaking boils down at phenomenological

level to complex phases of Cabibbo-Kobayashi-Maskawa matrix

expressible V= UD^dagger, where U and D describe topological mixings

of quarks: quarks families correspond to different boundary component

topologies for CP_2 type extremal containing hole with boundary

which is sphere (e,nu_e) and (u,d), torus (mu,nu_mu), sphere with two

handles.... Last spring I constructed a detailed TGD based model to

explain CP breaking in K-antiK system in particular observed anomalous

behaviour: it almost made me mad. I will never, ever start making

numerical things at this age anymore!

The closed spacetime surfaces describe *'pure mind'*: enlightend

Buddhas staring at own navel. They could however

get glued to material spacetime sheets and interact with the world of

sinners. They have very nice nice properties: in particular, cognitive

fermion pairs are possible, not only cognitive neutrino pairs. It depends

on spectrum of induced Dirac equation how many of these are possible.

Finite number very probably. Right handed neutrinos are also in this case

in special position: if closed spacetime sheet is minimal surface,

covariantly constant right handed neutrino is certainly a solution if

induced Dirac. What is important is that absolute minimization of Kaehler

action almost predicts these objects: by Euclidicity they have negative

finite Kaehler action and this is favoured by absolute minimization of

Kaehjler action. Thus these enlightened Buddhas are there but are they

important for our brain functioning!?

An attractive idea is that the solutions of Dirac inside closed

spacetime surfaces interpretable as representations for logical thoughts

are identifiable as memes, pure ideas. They would hang aroud everywhere

and could also attach to our brain. [Basis of fermion Fock states<-->

Boolean algebra]

The second option for cognitive spacetime sheets is as spacetime sheets

with outer boundary and Minkowskian signature of induced metric: these

would *have time orientation which is same as that of material spacetime

sheets*. This is possible since cognitive neutrino pairs are possible in

this case too: the point is that neutrinos in condensed matter have

negative Z^0 binding energy much larger than their rest mass: creation of

cognitive neutrino pair with total energy=0 is possible. The fact, that

neutrinos are glued to spacetime sheets with size of epithelial sheets,

makes bell ringing inside me and I would bet that cognitive neutrinos are

characteristic for bio-consciousness.

To be honest, I do not know whether both of these two types of cognitive

spacetime sheets are important for understanding of brain.

*>
*

*> > Physical considerations pose no restrictions on the density of these
*

*> > purely 'mindlike' objects (using the terminology of TGD inspired
*

*> > theory of consciousness): they represent pure thought.
*

*> > I have told about amusing structural isomorphism between the properties of
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*> > asymptotic selves (selves for which all subsystems have vanishing p-adic
*

*> > entanglement) and between the closed Euclidian 4-surfaces.
*

*> > I would identify them as liberated Buddhas! (Ontogeny recapitules
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*> > phylogeny.)
*

*> > *****************
*

*>
*

*> But, Matti, these are mere geometric objects and do not follow the
*

*> requirements of minds (e.g. boolean lattice-like structures).
*

[MP]

They are geometric objects which correspond to certain selves: they form

cognitive representations by interacting with material spacetime sheets.

They contain cognitive fermion pairs (counterparts closed fermionic

bubbles) and fermionic Fock states provide physical representation for

Boolean algebra. And they correspond to conscious: even more,

ORP suggests that they correspond to asymptotic selves: end points of

evolution by quantum jump which cannot anymore reduce

their entanglement entropy by quantum jumps and are therefore

entanglement entropy=0 enligthened beings!

[ORP= Ontogeny ....]

*> I see the
*

*> "vacuum bubbles" are the objects of observation by other LSs. You see,
*

*> all geometry, is cast as the content of an observation with the Chu
*

*> space duality paradigm.
*

[MP]

These vacuum bubbles glued to material background could be objects

of observation also. Gluing could transfer tiny energy inside bubble.

*> The mind that does the observations is modeled
*

*> in terms of the boolean (for 2-nary relations) structures that act as
*

*> the "labels" of the geometries. This results from a consideration that
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*> the class of labels (or meanings) that can be attached to any given
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*> geometric object can not be trivially mapped to a geometry itself,
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*> unless one is considering the singleton case (it is self-dual, e.g. MIND
*

*> = BODY for the Universe as a whole).
*

[MP]

Have you considered possibility of representing Boolean algebra by

fermions? Cognitive fermion pairs inside these Buddhas are solutions of

induced Dirac and form representations for geometry. Each statement

about spacetime geometry would be represented by many fermion state.

These statements are certainly very abstract.

*> One the other hand, the phylogenic hierarchical ordering of the sheets
*

*> is very important! I see it as the "vertical" organization of a self,
*

*> just as you think of it. But, it is a mistake to assume that the mind is
*

*> geometries or fields of matter/energy. (Bohm has pointes out that they
*

*> are the same thing really!)
*

*>
*

[MP]

No, I would never claim this: cognitive spacetime sheets only contribute

dominantly to the constents of experiences of selves and

this makes practical to identity self with cognitive spacetime sheet!

ORP suggests very strongly that the closed spacetime

surfaces are geometric counterparts of S=0 selves. The correspondences are

rather impressive.

a) S=0 self as asymptotic of subjective time evolution<-->closed absolute

minimum as asymptotic of Kahler evolution (perhaps very much like

blackhole). [BTW, elementary particles reprsented by CP_2 type extremals

are closed vacua with hole drilled in them to carry elementary particle

vacuum numbers.] S=0 selves could be the blackholes of TGD.

b) S=0 self <--> closed vacuum.

Closedness is the geometric counterpart for the trait of Buddhas

to stare in their navels!

c) Extended free will of S=0 selves<--> extended classical nondeterminism

of closed spacetime surfaces. One can take discrete sequence of 3-surfaces

with arbitary short timelike separations belonging to closed

local vacuum extremal and find absolute minimum

going through them. There is this kind of absolute minimum since there

is vacuum extremal with vanishing action going through them.

d) S=0 selves must be stable against generation of entanglement which

means falling asleep and snoring Buddhas! Join along

boundaries bonds with external world make generation of entanglment

probable (to form join along boundaries bond is to touch). But if there

are no boundaries, there can be no join along

boundary bonds and hence no entanglement is generated.

*> > We might imagine that a flat, closed, unbounded universe of this
*

*> > type would tend to collapse if it contained any matter, unless a
*

*> > non-zero cosmological constant is assumed. On the other hand, I'm
*

*> > not sure what "collapse" would mean in this context. It might
*

*> > mean that the R parameters would shrink, but R is not a dynamical
*

*> > parameter of the model. The 4D field equations operate only on
*

*> > x,y,z,t. Also, any "change" in R would imply some meta-time
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*> > parameter T, so that all the R coefficients in the embedding
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*> > formulas would actually be functions R(T).
*

*>
*

*> All of this applied, but to the "what" is observed by an LS. The
*

*> difference in properties between the "inside" and "outside" of an LS are
*

*> very important! Umm, the idea of mapping (or identifying) the perceived
*

*> behaviour of objects in a given observer's universe (which is a finite
*

*> subset of The Universe) with the "internal" dynamics of the quantum
*

*> propagator is what I call "clocking and gauging"...
*

*> The key notion is that we must understand that we can not ever observe
*

*> The Universe, only "our version of it"!
*

*>
*

*> > It seems that the flatness of the 4-space is independent of the
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*> > value of R(T), and if the field equations are satisfied for one
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*> > value of R they would be satisfied for any value of R.
*

*>
*

*> This, I see as the "free fall" frame of the observer. The "forces" are
*

*> given when comparisons of pairs of frames like Bill's NOW/PAST pairs!
*

*>
*

*> > But I'm not sure how the meta-time T would relate to the internal time
*

*> > t for a given observer. It might require some "meta field
*

*> > equations" to relate T to the internal parameters x,y,z,t.
*

*> > Possibly these meta-equations would allow (require?) the value
*

*> > of R to be "increasing" versus T, and therefore indirectly
*

*> > versus our internal time t = f(T), in order to achieve stability.
*

*>
*

*> How could meta-time T be observable? Why is it even necessary to
*

*> consider such an idea? Is "stability" really necessary to assume? (think
*

*> of dissipative systems!)
*

*>
*

*> > [MP] In critical Robertson-Walker cosmology one has somewhat
*

*> > similar situation. 3-space is Euclidian and could be compactified to
*

*> > 3-torus. Allowing R to on t one obtains curved 4-space as is clear from
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*> > the fact that mass density (G^tt component of Einstein tensor) is
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*> > nonvanishing. In special case one would have the
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*> >
*

*> > ds^2= t^2(dt^2 -dx^2-dy^2-dz^2)
*

*> >
*

*> > I checked from general formula for mass density in RW cosmology
*

*> > that mass density goes like 1/t^4, that is scales. This is to be expected
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*> > since line element is Weyl equivalent to flat metric. It seems
*

*> > that this is nothing but the radiation dominated critical cosmology which
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*> > is scale invariant (massless particles dominate).
*

*> > In this case R indeed increases with t linearly.
*

*>
*

*> So this is a quantification of "what can be observed" given a
*

*> particular "mass density"
*

[MP]

What I intented to say that 4-torus like line element with over-all

scaling factor depending on one of the coordinates seems to repreresent

radiation dominated critical cosmology. The criticality and high

symmetries force critical radiation ominance.

*> >
*

*> > [MP] It is often believed that quaternions and octonions are inherently
*

*> > Euclidian objects. This is actually not true as I discovered for year or
*

*> > two ago. The point is that one can define inner product as
*

*> > real part Re(z1z2) of z1z2: the resulting inner product is standard
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*> > Minkowskian inner product. If one defines inner product as Re(z1^*z2)
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*> > one obtains the usual Euclidian inner product.
*

*>
*

*> What is the relationship between Re(z1z2) and Re(z1^*z2)? Are they
*

*> orthogonal?
*

[MP] Sorry for not establishing notation. Re means real part. Consider

instead of quaterions and octonions complex numbers.

z=x+iy and Re(z1z2) = x1x2-y1y2 which is nothing but Minkowski inner

product in plane. Re(z^2)= x^2-y^2. In case of quaterions Re

can be regarded as real number or as a real quaternion: in latter

case one can speak about orthogonality but Re(z12) and

Re(z1^*z2) are not orthogonal.

*>
*

*> Later,
*

*>
*

*> Stephen
*

*>
*

**Next message:**Matti Pitkanen: "[time 670] Re: [time 664] Reply to NOW/PAST question"**Previous message:**WDEshleman@aol.com: "[time 668] Re: [time 664] Reply to NOW/PAST question"**Next in thread:**WDEshleman@aol.com: "[time 663] Re: [time 659] Cylindrical But Locally Lorentzian Universes"

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