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                Subject: Re: Brief Roadmarks                 Date: 01/22/97 

'Math, Philosophy .. need to be fundmentally re-built'

 
"Lawrence B. Crowell"  wrote  01/21/97 :

>(JNR)
> 1. On my abrupt statement that "topology has no firm definition of   *between*" - something we take for granted as experienced and definitionally "known", would you agree that is accurate or not? (The issue arises in closed domains like the perimeter of a circle or the surface of a sphere.)

(LC)
The concept of betweeness requires a boundary on the set. The simplest example is the midpoint on a line segment. A cocycle has no middle point.

By which answer I assume you mean: "Yes, you're right, "between" is a relationship that we can recognize as there in open or cocyclic systems but which is contingent, based on designating local or internal boundary factors. That's a rather obscure topological situation, it doesn't affect any other relationships or calculations, so what makes you think it's so significant?"

Thanks for "asking" LC. I know it is important because it gives us an insight into something fundamentally problematic with our current mathematics. It draws attention to the fact that on the one hand "between" (and similar relationships) constitute the Stapp "thought-like" things aka the Platonic "Ideal" aspect of existence, yet, once we designate two bounds or parameter sets or the like, even where the limits are transcendental numbers [ ---( rather than ----. ] , we can assign a fixed value to "between" corresponding to "length", "duration" or some other "extent" measurement with a physical meaning. IE, in our mathematical manipulations, we interchange terms having the same intrinsic values quite freely, even though in some configurations we mean to use the transcendental quality rather than the physical one (and vice versa) or both at the same time.

EG, consider a simple 2D wave function. Its organization is variable in 2 dimensions, always changing. Internally there is nothing Euclideanly "linear".  Any internal linearity is educed by the random choice of any two independent loci along the wave. A wave has a net direction of propogation, *somehow induced by its internal organization* (this being the other premiere issue: if the best description we have is disjointed QM then what "binds" the quantum components into smooth contiguous self-coherent "waves"? ...leading to quite other discussions.), and symmetry makes it convenient to use that propogation line for mathematical and geometric evaluations. And, because we approach this inner-relationship of a wave from the historical standpoint of linear geometry - where "distances" and "extents" have a physical reality: measurement - we take for granted that the loci where a wave crosses the imaginary x-axis, eg, has a physical reality ... and the distance from a to b is a rocklike thing.

I am not saying that is not valid. I am saying that in addition, the concept "distance" is not perfectly isomorphic with the measurement *of* that distance. So that is some mathematical models, the terms refer to states or conditions - static relationships, *not* to numerical variables, such as the length-of-the-relationship. Picture an equilateral triangle embedded in a
circle. Call this state (1). Ostensibly the diagram shows 3 line segments and 3 arc segments intersecting at 3 loci. I'm going to call this a "locked-state".   Generically, you can switch this figure through several symmetries: bilateral, rotational, temporal, etc and still have the "same" figure, same relationships.

Suppose, however, that I fixidly identified each individual line or arc segment, plus the 3 unique bilateral symmetries, and, apply the condition that the basic locked-state is the assembled-form of these distinguishably separate components put together, and apparently is the only assembly possible where they fit together with no empty arcs or unconnected endpoints of the segments. So far so good. Now rotate the figure until it becomes isotopic on itself again...a 1/3 lock-step. What rotational values "restore" the basic locked-state, where the individual components are in their original configurations? Ans: 1/3 and 2/3. We can tumble and jumble different arrangements of the +/- values in several different ways formulaicly, and derived a set of equations to deal with the several "symmetry" states and expressions. We can even take them into 3D space or higher, and we will still be talking combinants of 'thirds' (which indicates that something special is enacted in the topical domain where linear and curvilinear values intersect)... a very special site where information codes or translates with special qualities.

But, for practical purposes (like normalization techniques), we can say that for base-state S0, it is also "re-establishable" by combinations of +/-S1 with +/-S2. We can give the "states" cute names like "luck", we can give the segments cute names like "voice", and we can talk about all the symmetries with their own names like "happy". Some are bi-lateral, some are tri-lateral, etc.,  but y'know what? We can physically manipulate these triangle/circle structures in our laboratories ... they have a wave/matter physical presence ... but we're having the *damndest* time teasing out just one of those "voice" segments, so
that we could examine it all by itself.

Sorry LC (and friends) ... very long story short: it is my perception that quark architecture is just such a structure. We can designate "color" or "charm" or "quark", but they are probably evanescent intangible heterotelic *relationships* .... just like "between". Distinguishable, notable, useful in formulae to clarify where all the components are under different symmetries, and
how they transpose from one state-set to another ... but "vanish" or otherwise have no existence when the overall structure is dismantled. Blast away with all the terra-mega-wattage you want, you can't get right-angles to observably exist without orthogonal extants.

BUT, in the same breath, I suggest that "relationships" are information that is codifiable and retrievable. When a wave collapses, certain "between-ness" relationships are codified to point-like structures of dimensional compression - like viewing a disc on edge. In somecases, the info is inconsequential, in others *very* consequential: as the transformation of wavelength squared to pointlike energy value. Bilateral compression/condensation/coding (dropping down a dimension value). Translation of equivalent information, expressed in terms of different numbers of orthogonal dimension values.

The various metric-formulations - Kac-Moody, etc - where they have divined out patterns of relationships which are applicable among surfaces, spaces, points, densities, etc are dealing with groups and embedded groups of these heterotelic (contingent) artifacts. Which come and go depending upon the number of dimensions used.

Additionally, all tensor/metric explorations are primarily spatial mappings. These transformations/translations of information are never subjected to information transfer-rate limitations, the way the physical world is subject to.  This ommission is pivotal to the issue of contextuality, and a requisite correction if a blended theory is to be attained.

{yehhh, I know, everybody's happy with all the current mathematical interpretations and usages so why change things. As a philosopher, looking at the plethora of physics relationships tagged with each mathematician's name, I gotta tell you that the impression is one of a group of people each immortalized for finding things like - Hey, here's a formula to describe "up" , I'll name it after myself, the Goober Relation. Say, here's a group of changes that happen if you take a sheet and "turn it over", I'll call it the Smyth-Rabinsky Correspondence. The names may be very clear to the initiated - the short hand is very convenient - but they say bupkiss the rest of the world struggling to understand, let alone accept, the perceptions, conceptions, and observations.   No one is asking any of you to go over and over interpretations as each new person comes along, to explain things, it's just that the more complicated the mathematics becomes, the more incorrect it seems to be ...that's a reactive
statement, not a qualifying judgement of accuracy. 75 steps and requisite conditions may seem "elegant" to some of you, just for the mere fact that some problem finally gets resolved, but I can tell you that it still appears attrociously cumbersome to the rest of the world.

"Making handles" or "drilling holes" in topological spaces - for arbitrary reasons - doesn't epitomize the scientific method the rest of us are subjected to for our work criteria, either. Modern math/physics seems pure wildcatting-for-oil then. And the high-jacked terminology is potentially just as confusing to non-mathematicians as our groping for words-to-correspond- with-our-valid-(real)-observations are for mathematicians.   I may think that someone else's "system" is a crok, but I have to remember that they-SAW-something there, and are trying to communicate it. Something happened, something was perceived, and that perception has some core validity that it's worthwhile for ME to consider too. Communication is a several-way street. Everyone is obliged to consider the rest of the traffic there. OK, I'm of my soapbox. :->)

(JNR)
> 2. Was my observation incorrect or not when I discussed the cytochrome transport mechanism that raises electron energy levels and helps produce  ATP from ADP - where I noted that, depending on the parameters and factors considered, the process can be rendered as several independent yet interfunctional local entropy gradients, simultaneously enacted?

> (LC)  It is all Gibb's free energy
>
> &G = &E - T&S
>
>G = Gibb's free energy
>E = internal energy
>T = temperature
>S = entropy

(JNR) OK, here's a case in point. Where are the boundaries for the system in question? Entropy is a single monolithic term again. I can't assert strongly enough how wrong that is. If you don't mind, I'm going to talk  Maxwell's Demon scenario here - just commenting that what you wrote below about it was a "standard litany" that points out "old problems" with the "old
interpretations", but doesn't help us here and now. I couldn't care less about the energy/information evaluation of the Demon. He's superfluous. The issue is nested-sets, nested frames-of-reference.

In my version there are *3* chambers. Two small ones, with one moving particle in one of them. The 2 chambers are themselves "particles" free moving inside the larger Chamber. The little chambers are constructed in such a way that they
are hemispherically sound and whole in 3D ... except that when they near each other, their facing-surfaces weaken, and an access window opens between them. This window stays intact as long as there is the slightest quantum mechanical (statistical) probability that the one inner-particle is transiting the window between them. And since, that value for the bound c-c system is *always* greater than zero (barring any *extraneous* energy sufficient to break the bond and bring the probability to zero again), the c-c system holds.

It's seems that the formula you gave would take into consideration *all* the entropies involved? Is that right? If not, is should, because the predominant membership (c,c) is not the sole membership (c,c,p) nor are the internal bounds *in*significant. The particle p has an entropy relative to the chambers c,c - both when they are bound and when they aren't, and the chambers c,c have a separate entropy relative to Chamber C.

I would say that your value S for the Gibb's Free energy should be a convergent series of nested alternating entropy values (f1-f2+f3-f4...).   When you chose a specific set to be your calculation reference base, you can probably exclude values beyond usable significant digits for practical purposes, BUT, the alternating signs *signify the presence of a relationship of
extraordinary importance* .... the dynamics of information interaction in nested sets. THIS IS THE ROOT OF HOW COMPLEX SYSTEMS ARE BUILT. When the liaison region where the position/momentum values of an inner-set exists in a compatible range with the position/momentum values of its outer-set.

You mentioned below (snipped out) the "coupling of separate Gibb's energies in a cascade", or something to that effect. Seems to me that that is the area of critial importance. Yes? No?

And, not to be taken for granted, exactly what do we want Entropy to signify?    Is it "the ability to do work" (the measure of how much "gradient" is present, partitioned within the most outer-defined boundary), or is it "disorder" (the inability to get information/get work done)? Seems to me that if "extracting work" is the generic criteria, then it's just as difficult to get work done if the energy is sitting totally motionless in a container, or thoroughly diffused regardless of the motion present (!). So,
which condition is the "highest entropy" state?

Conclusion: Spatial diffusion is a separate entropy factor. It is "degree's of freedom" also. So it becomes a statistical property. Say, how about that!  We're not locked into temperature and thermodynamics if we want to talk "entropy". We're free to discuss it QM-ly and topologically. Isn't that terrific!?!?! (I think so.) Cause then, you can think about partial differentials as contributing independently to the mix of entropies present. And if you can do it for space, you can do it for time. And it becomes a many-entropied universe, not just a many-bodied universe.

And you can build a structure like TGD. Now ain't *that* neat.

So, you don't have to worry about normalization to get rid of troublesome infinities. You don't have to worry about the inability to calculate the meaning of the number of eigenstates involved in these nested set-states where we get intimidated by an infinite regress of super-powers, like 10~100~100~100~100~.... It's nice to imagine that the flap of a butterfly wing will generate a hurricane someday ... notions like that make everything we do special and unique. But when our star goes Red Giant, *that* will affect the angular momentum of the Milky Way, not the butterfly, or the hurricane.

Its more important the we should be cognizant of the translations and transductions of energy and information in domains having adjacent significance.  Seeing that *those processes* are in effect for all and whatever domains and assemblies exist. And that my children is why we can apply the same simple mathematical formulae to proton distrubutions, animal speciations, cosmic
distributions, and test results, et al

----snipped----

>
>(JNR)
> That concept being: that the presense of a "force" is indicative of a   "particle" to carry the force. The extreme-association- dilemma, where   the premiere example is the need for a "graviton" quantum particle to carry the force "gravity".

(LC)
HMMM!!! the existence of forces arises from local phase shifts on a wave function that must transform homogeneously. As such, with some work, it can be shown that gauge potentials are introduced.

(JNR)
So a "force" need *not* be associated with a "particle" per se?
Also, is the phsse shift restricted to quantum units? Can it be continuous?

---snip----

>(JNR)
> I have been making a point of asking this question for 30 years now:  If the gravity-well of black-holes is *so* strong that *nothing* escapes (Hawking evaporation noted as the possible exception), and, if gravity is carried by emitted gravitons that massively flood the space around black-holes, then we should be seeing (or mathematically describing) massive local  distortions as the generated/escaping gravitons *affect each other*.
>
>
(LC)The goal of quantum gravity is to show that the black hole can be "produced" by the field sources of gravitons. The gravitons that come from a black hole, an ugly way of saying this actually, are the result of a polarization of the quantum gravity vacuum. AS such these gravitons are virtual. Real quanta come when the black hole is disturbed from is equilibrium configuration. Throwing mass into a black hole will result in gravity waves. These gravity waves can be thought of as the classical limit for the graviton.

>(JNR) In the absense of such observations we have to conclude
>
> 1. that gravitons do *not* affect each other,

(LC) Absolutely not!!! Gravitons, being made of mass energy, self gravitate and thus interact with all other gravitons; including themselves. this is what makes quantum gravity so infernally tough. The photon is not self interacting.

(JNR)
Then where are the Rayleigh-Taylor type of interactions ... the dis-homogeneous fluctuations in the gravity well? The irregularities of the well?

> (JNR) or
> 2. that the affects are beneath the Plancke limit of observation,  or
> 3. that gravity is another type of force altogether not associative with a particle
>

(LC)
Don't know really: no one really does know. Planck scale, which includes subPlanck stuff, is really not well known. What we have really are just mathematical toy models.

(JNR)  THANK YOU.  Thank you for implying that the door is still open for other models, (which may focus on or bring to light quite new considerations).

---snip---

(JNR)> 4. Did you understand how and why I applied the terms "in vivo" "in  vitro" to atom formations? That an atom's electron cloud can validly be described (for thematic modeling purposes, not necessarily calculation) as the "environment" which the nucleus resides in?

Did ya'?

> Thanks, Lawrence

>> Jamie

Ditto!