Given:

(a) properTime = (nonstdMonad, properTime) where

nonstdMonad = (nonstdFuture, stdPresent, nonstdPast)

(b) particle = (physicalExtension, particle)

Now zipper (a) and (b) together so as to produce:

(c) properTime =

(

(nonstdFuture,

(stdPresent, physicalExtension),

nonstdPast),

properTime)

or–

where:

(nonstdFuture, (stdPresent, physicalExtension), nonstdPast) = (nF, (sP, pE), nP)

then

(d)

properTime =

((nF, (sP, pE), nP), ((nF, (sP, pE), nP), (((nF, (sP, pE), nP)…

…properTime)…)

Notice how ‘physicalExtension,’ ‘pE’ got injected into properTime.

In the zippering process, ‘physicalExtension’ became paired, in the language,

to the stream of properTime,

specifically at the deepest level inside properTime,

right at the nucleus of properTime,

thence paired– ‘(sP, pE)’ —

and married to its very own standardPresent

deep inside the shelter of properTime.

Thus properTime is prior

to the stream of physicalExtensions

that streams from the existence of a particle.

If one says that the Standard Models are all involved with physicalExtension,

then all of them seem to have missed, left unaccounted,

this architecture of information into which

particle = (physicalExtension, particle) may be injected,

this architecture that is seen above in equation (d),

surrounding the nucleus of existence in each element of the stream,

modeled above as (sP, pE)

the pairs of processes being emitted as pairs

…each of those pairs…

would stream in a stream, like this–

[physicalExtension, standardNow], [physicalExtension, standardNow], [physicalExtension, standardNow]…

Not some of that other stuff about this in the top half of the previous note.

Out of kindness I will leave the identities of the equations un-known.

But they know who they are.

Sorry I was insane

particle = (physicalExtension, particle).

I would need to be quite solid to get to–

monad = (nonstdMonad, standardNow)

{from ‘standardNow’ as in previous post]

As well as to the stream of such pairs.

Barwise fell under the spell of Robinson’s nonstandard analysis when they were colleagues together at Yale, both of them through logic and language. For me it goes all the way back to Euler. C. Tuckey in ‘Nonstandard methods in the calculus of variations’ shows how Euler came up the Euler-Lagrange equations by doing his mathematical experiments microscopically rather than macroscopically– thus he managed to avoid all that mind-bending stuff about finding the extremum for an integral. But Euler didn’t have Robinson’s nonstandard analysis. So he did his experiments by instead, using words like ‘infinitely close.’ Of course, in standard analysis there is no such technical term as ‘infinitely close.’ It’s a term from a different language. Robinson found that language, then wrote about Leibniz in his introduction to his book on Nonstandard Analysis; Liebniz who had first coined the term ‘monad’, and from whom Robinson was now re-habilitating the term in a new, formally rigourous, model-theoretic number language. Barwise knew that stuff backwards and forwards, and became inspired to generalize it to every mathematical language, every computer language, every diagram, every human language, every animal language, and every language of a every story in literature– spoken as well as written. With all this in front of him, Barwise after decades finally found the key Identity (think ‘equation’) in logical language about what’s between languages, and he called it ‘the infomorphism.’ Robinson had created an infomorphism from the language of standard analysis to the language of nonstandard analysis. The key to calculus is that only at the last syntactical step do you have to translate back into standard analysis from nonstandard analysis. Think of integrating something. Before, you have terms like ‘dx’ in the logical language. After integrating, you drop that language and find yourself back speaking to people in the language of real numbers, and ‘standard analysis.’ It was this magical transition that captivated Barwise. Just as the nonstandard numbers support the meaning of terms like ‘dx’; so do the nonstandardFutures in the stream support the meaning of terms like ‘possibility.’ The Born infomorphism, which is additional information theoretic structure added to the Born Rule, supports logical language translated into ‘information from the nonStandardFuture is repeatedly transmitted into the nonStandardPast;’ as much as every choice among possibilities in a game is transmitted via an information channel onto the scoreboard. The Born infomorphism involves an information channel from the nonStandardFuture into the nonStandardPast. I tried to write as best I could about this in those papers I posted on FQXI. Clear as mud probably…

]]>properTime = (nonstdMonad, properTime)

where

nonstdMonad = (nonStandardFuture, standardNow, nonStandardPast)

Substituting–

properTime = (nonstdMonad, (nonstdMonad, (nonstdMonad… properTime)…)

Which in computer science they call “a stream.” It’s just a different model of time. nonStandardFuture and nonStandardPast are ‘halos’ of nonstandard points infinitely close to standardNow, behind and in front.

Only possibilities exist in the nonStandardFuture and information only exists in the nonStandardPast. In terms of game theory, possibilities in the nonStandardFuture are like squares where the player can move. The scoreboard for the game exists in the nonStandardPast. The ‘opposing player’ (wave function) gives the possibilities and assigns scores.

The player (particle, e.g. in Bohm’s theory) guesses which trajectory per nonstdMonad– for example, one of the trajectories in the two slit experiment in Bohm and Hiley’s Undivided Universe.

After the player guesses, the wave function reveals where it placed the ‘payoff.’ If it’s where the player guesses, great! The player takes it in and lives to play another day. But if the payoff occurs at some other possibility, the player regrets having chosen that possibility, say possibility X. (And has to live off stored payoff for a while).

On the other hand, say the player chooses some possibility other than X, and then on the reveal sees that the wave function placed the payoff at X. Now the player regrets NOT having chosen X.

So for each possibility (each X), there is on the scoreboard the player sees (a) regret from having chosen X, when the payoff occurred somewhere else, and (b) regret from NOT having chosen X, when the payoff did occur there but the player chose some other possibility.

When the two regrets (per possibility) balance each other, the probability of the payoff being placed at X equals the probability of the player choosing X. It’s a well-studied game called ‘probability learning.’

Complex numbers, as the wave function, model possibility. First, of all the types of numbers, one wants one of the division algebras– because a possibility can always be removed from play, which we model as division.

A numerical product of possibilities is the logical ANDing of those possibilities.

One doesn’t want real numbers to model possibility, because they relate by the greater than/less than relation. But possibilities are not like that– something either IS a possibility or IS NOT a possibility. Greater than/less than relations one may leave for probabilities.

Further, one wants the product of possibilities (the logical ANDing) to commute– we don’t care which one comes first in the statement. Of all the division algebras (real, complex, quaternion, octonion) that leaves only the complex numbers standing.

The product of the complex valued wave function at a possibility with its conjugate models ‘there is the possibility of the physical extension being at X AND the impossibility of a physical extension occurring anywhere else.’

I have to say it like that because in the nonStandardFuture, only possibilities exist– not yet the particle.

particle = (physicalExtension, particle), zipped to the above equation for proper time.

So Psi Psi* = P per possibility, the Born rule.

Now I wonder how all this might relate to your work! I will read…

]]>You know, one idea that I’ve had about the self–and I know this isn’t a perfect analogy, because there aren’t quantum fields for composite entities…but I sometimes think of the self as an ‘excitation’ in a ‘field’. I think this might be true in some sense. If so, then I am the excitation, and I would consider the Field to be God.

Ultimately, I think I’m a Christian and favor the Western views of the self and God…but that doesn’t mean the Eastern and Western views are adversarial. Rather, like religion and science, the Eastern and Western views of Divinity and Selfhood may be two sides of a single coin. You can see this in the New Testament idea of the Holy Spirit–the divinity to be found in all people–which parallels Hinduism and Buddhism. Then there is Jesus’ saying, ‘I am the vine and you are the branches.’ A very Brahman/Atman view being expressed right there in the Bible!

‘I am the vine and you are the branches’, I think, could also be rephrased, ‘I am the field and you are the quantum’. ]]>

Oh–speaking of spirituality; I thought of your William Byrd screenplay the other day (the one you sent me in 2016). I saw the film-trailer of that new Mary Queen of Scotts movie and thought to myself, ‘I wonder if Ruth and her sister finally sold part of their screenplay?’ ]]>