Tom,

Its great to see your essay getting attention of serious and informed people, and free of those whom like to dance on the bar and start fights. That's probably because your approach of possible vs. probable is presented with math results that many people don't know enough about what they come from. I sure can't contribute much! I do have more a curio than a question that might be pertenent...

Steven Sax provided an e-address for a thesis on laser experiments with Rubidium that I've waded into and think you would find interesting, and from which he launches his discourse on decidability. Here 'tis; http://www.bgu.ac.il/atomchip/Theses/Amir_Waxman_MSc_2007.pdf

Its QM, of course, and uses the Bloch Sphere as the spin co-ordinate system. I realized that in their protocols what they specify as 'free precession' is in fact 'freely gimballed', in that the axis of precession intersects the origin at intersection of the orthogonals. To be 'free precession', the antipodal points of the axis of precession must be free to wander like the magnetic poles of the earth, the p-axis does not necessarily intersect the orthogonal. Intuitively this must fundamentally alter the landscape of co-ordinate pairs. And what seems to be already decided in QM is symmetric precession. Would that not impose an undecidable condition?

I don't get into coin tossing, I pinch pennies like to bring a tear to Lincoln's eye. So maybe this niave observation is a standard issue. Your comment would be instructive, at your leisure, I'm just now off on errands.

All the best, as always. jrc

Hey, John -- I have always thought of *you* as a serious and informed person! :-)

Give me your email address, and I'll send you something privately that addresses your question.

Thanks for the link to Steve's research -- it's on my list.

All best,

Tom

One of the advantages of being as old as I am, is that distant memories come into sharp focus with the right trigger.

The trigger to my recollection of Jim Cowan's wonderful short story was David Hestenes's discussion of modeling in his essay forum.

The Cowan story ("The Spade of Reason") and Jose Luis Borges's "Library of Babel" are two pieces of fiction that have had a deep impact on my intellectual life. Remarkably enough, Borges's story is referenced in Cowan's story.

All best,

Tom

    Thanks much Tom,

    I just posted my e-address to your 1209, sent this date 5:59pm.

    I'm getting myself a little swamped, but appreciate any help in learning 'the language'. And things just matured that are time sensitive that I have to concentrate on to finalize and make sure my ducks are in a row. I'm in for a long weekend but will acknowledge receipt of your post. If your check for receipt of my post to: 'contact' on your blog and don't find me, let me know here.

    Thanks again, I rely on the acumen of you and others whom come to converse rather than convert. Like the song goes, 'I can make my own mistakes just fine.' :-> jrc

    Tom,

    Got it! Six short pages! I gave it a quick read and its really well written. There will be questions, and once I have a list I'll try posting through my e-mail. Thanks very much and good luck with it! Later, Friend - jrc

    Dear Thomas,

    Thank for the comments on my blog and the high rate. I had your essay in my list and you write about CHSH!

    You can expect my feedback soon.

    All the best,

    Michel

      Dear Thomas,

      I just read Jim Cowan's short story "The Spade of Reason" at your suggestion. Indeed, it is great: philosophical science-fiction just the way I like it! I especially like it when the main character says that "one kind of madness is not knowing that the model is all we will ever know."

      Marc

      Dear Thomas,

      Thank you for your comments about my essay. I have left a reply on my page.

      Yours is an intriguing and very ambitious essay!!! You tackle deep fundamental issues such as probability and free will, and I have to confess that I'm having some difficulty in following all the details, since I am not familiar enough with many theoretical results that you build upon.

      I have questions about the "quadratic" relationship that you postulate between math M and physics P: M = P q^2, which becomes M = 4P because q = 2.

      1. Why does the constant have to be the square of something? I see the parallel with E = m c^2, but I don't see why it has to hold.

      2. Is your equation M = 4P dimensionless? In E = m c^2, E is in joules, m is in kilograms and c^2 is in joules per kilogram (or in meters squared by seconds squared). What are the "units" (if any) of physics P and math M?

      So far, your essay is looking good in the ratings... Good luck!

      Marc

        Tom,

        An excellent essay. Although I am not certain I fully understand your solution, but the issue of whether or not reality is objective or observer dependent is critical to understanding how math integrates with science. Might it be the case that the reality is objective but measurement is observer dependent and is that consistent with your thinking?

        thanks

        Rob

          Marc, that's my favorite line, too. :-) Thanks.

          Tom

          Rob, that's exactly right. The question -- "What determines the objective result of a measurement, hidden variables or hidden assumptions"? -- refers to metaphysical realism (measurement outcome) vs anti-realist assumptions.

          The assumption of non-locality is obviated by the time parameter (Hess-Philipp) in that every point of a 4 dimension Minkowski space is an operator.

          Because the time parameter is not real, independent of spacetime (special relativity), pairwise measurement outcomes are simultaneous with past-future local spacetime states that obviously include the observer as an element. The assumption of nonlocality is therefore superfluous, with the implication that the assumption of a nonlocal measurement value is superfluous. The observer -- whether human or point particle -- is one more degree of freedom than allowed by 3 dimension measure.

          In a continuous function classical measure, the macroscopic description of position in time as well as space is bounded only by the cosmological state. A microscopic state is therefore dependent on the cosmological state, and not discontinuous with the operator that exists at every point of local 4 dimension spacetime.

          All best,

          Tom

          Thanks, Marc. Indeed, I fretted all the time I was writing it, over whether this work might be *too* ambitious. Details can run away from one, if the scope gets too big. In the end, I could not escape the conclusion that if free will exists, it cannot be a property of random observer choice. This being so:

          Only a binary decision that is square integrable can share a reciprocal relation *continuously* with a continuous range of variables in a finite interval of time (Buridan's principle is limiting). The linear relation M = 4P is not physically meaningful in the first degree, because it is not dynamic; M - 4P = 0. The second degree equivalent, M = Pq^2, q = 2, accounts for the full range of possible binary decisions in any finite interval where M = P. Tracing the relation back to the cosmological initial condition, the rest state of the universe is a "fourity" of possibilities in any locally bounded interval.

          The units of M and P are dimensionless to the extent that M = P is unitary. In the reciprocal relationship M = Pq^2, the fundamental dimensionality M = 4P (P = M/4) gives us the division algebras we know to exist (R, C, O, H) as a complete algebraically closed range of computational fields relating binary choice to a continuous range of variables limited by a finite time interval.

          Physical units are derived from empirical observations in a bounded measure space. Since four pure physical states imply the Hawking-Penrose singularity theorem, and insofar as four are the minimum necessary and sufficient for dynamic interaction between physics and mathematics (i.e., between measure and model), maybe we can move a little closer to Hawking's question of what "puts the fire in the equations" with number-theoretic arguments alone. Just thinking out loud here.

          All best to you and your essay, too!

          Tom

          Thanks, Michel! I look forward to productive dialogue and wish all the best to you and your essay in the competition.

          Tom

          Tom,

          I was just looking in and your responses to both Robert and Marc are helpful to understanding your maths and your thinking. You do speak to mathematicians, and that assumes an 'ideal reader'. I've been hoping good questions would draw you into something of tutorial discussion.

          Robert puts it succinctly that reality is objective and measurement is observer dependent. Math, like the color purple, is a figment of human imagination. The reality is that randominity is limited by necessity. 'There is no such thing as cold, cold is the absence of heat' - (Louie Ritchey). When we reach absolute Zero Kelvin, they can have pure randominity. I won't care. ;-> jrc

          Tom,

          Let me elaborate on my last comment before returning to some personal matters.

          I think your identification of escape velocity with any point in space is a profound insight. It is both physical and at the same time mathematically versatile. It is where the path of least resistance is provided to the random walk. The escape velocity at any given point in space will naturally vary with the dynamics of change in position of masses that come within relativistic proximity to that point. Conversely, the escape velocity initially observed will migrate to another (and potentially others) as the dynamic evolves.

          If I am meandering in a crowd of people, my easiest path will be toward an adjacent space that momentarily opens up, which will effectively reduce that openness. Continually. I will eventually find my way to the periphery.

          This generality was touched on in dialogue I've been having with Constatinos Ragazas and in communication with Ed Klingman in regard to Planck's solution to the violet catastrophe. The exponential increase in the possible numbers of waves per second as frequency increases across the continuous spectrum, would result in an equal chance of thermal energy in Wien's furnace, to choose an ever higher frequency over a lower one. That doesn't happen, obviously. The curve of intensity of spectroscopic frequency analysis was only matched

          when Planck introduced a finite constant energy value into his equation of probability distribution. Effectively showing that a specific quantity of energy in any given wave event results in the energy in the furnace seeking equilibrium with the ambient environment, must avail itself of lower frequencies as well as randomly chosen higher ones. The Quantum is causal of that distribution by the physical necessity that the furnace must shed thermal energy in every path available to maintain a stable temperature. Wien's furnace was a furnace, it was continuously heated. It would melt if the energy didn't take the path of least resistance in its random walk.

          Well, I've indulged in putting things off this morning long enough. Do continue to expound the elements in your math arguments. The pedagogical role is part of scientific writing, and it should not offend anyone if you present things as if rudimentary operations need explained. The explosion of mathematics in the last couple centuries actually require it. Maybe we should call it Accumulated Math Disorder. Best, jrc

          Thanks, John. So as not to confuse the reader, though -- your comments refer to something I sent you privately, and not the contents of the essay per se. I'm not quite ready for wide distribution of that Email piece.

          All best,

          Tom

          Dear Tom,

          Your essay is multivalued in the sense that

          * you clarify the relationship between physics P and mathematics M, postulating a linear (Tegmarkian) equation E = k*P,

          * you put this in perspective with Bell's (or CHSH) inequality and a establish a link to number theory (the unsoved Goldbach conjecture as revisited by Popper),

          * you question the role of probabilty in the MP correspondance (as commented by John Cox in his post),

          * you relate to Euler's identity (James Hoover has an essay on this topic as you know)...

          All this aspects are justified in technical terms sometimes in an unexpected way. You received many valuable comments, a proof of respect. I add my congratulations and my good community mark.

          Best wishes.

          Michel

          No problem, John. I've given it some limited exposure, just not prepared to take questions yet. :-)

          Best,

          Tom

          Michel, I am deeply honored. Thank you so much for your careful reading, feedback, and vote of confidence.

          All best wishes for success in the essay contest,

          Tom