Hi Tom,
nice essay. I particularly like "physical measurement--which is based on local events whose causality is known, in measuring interactions bounded by arbitrarily chosen coordinate frames--has a constant relation to a metaphysical coordinate-free causality." However I disagree abut many worlds.
Best wishes
George
Dear Tom,
This is an interesting essay, and particularly timely from my perspective because gives me some new ideas about a subject I recently encountered. A few thoughts come to mind.
1. The notion of "an infinite number of questions in an infinite length of time" (page 1 of your essay) also arises in pure mathematics in relation to Godel's incompleteness theorem (without the time factor, of course). The reason is that "proof" is taken to involve only a finite number of statements in terms of the axioms of the system (e.g. natural numbers), and one must be very lucky for this to suffice to prove a true general statement which may be true for different reasons for each of an infinite number of subsets of elements. One can always test the statement for particular choices of elements, or perhaps prove the statement for certain subsets, but in most cases one cannot decide the truth in a finite number of steps. This seems very analogous to the unbounded game of 20 questions.
2. You have an interesting perspective on locality, and one I will have to think more deeply about. I like the Poincare disk analogy. For some time, I have wondered about the meaning of locality because of the assumptions it involves; ordinarily some sort of metric concept comes into play (in order to define "close" and "far away"). But quantum gravity considerations cast doubt on the notion that spacetime is a metric manifold. Perhaps locality should be defined in terms of interaction: if two systems directly interact, they are considered local. Entanglement makes this definition completely incompatible with the manifold assumption.
More to say, but a student is pestering me. I enjoyed your essay, and wish you the best of luck in the contest! Take care,
Ben Dribus
Hi Geroge,
Thanks! Yes, I know you disagree with the many worlds hypothesis. My view is that until we have a suitable alternative to collapse of the wave function, we need a place-holder for the middle value -- a coordinate-free system can never allow such a collapse because there is no particular point in the continuous range of measurement values into which it can collapse; i.e. the wave function is not probabilistic. So if Hawking ever actually said that the Everett hypothesis is "trivially true," I think that's what he meant. It's certainly what I mean.
OTOH, Joy Christian's topological structure of S^7 physical space solves the problem. Physical measures default to the non-trivial topology of S^3, with no collapse of the wave function.
All best,
Tom
Thanks, Ben ...
Interesting that your teaching duties interrupted you. My own work responsibilities interrupted my reading of your essay this morning (I'm traveling on business). Actually, I was re-reading since I read and rated your essay with a high score days ago. Still organizing my comments.
What is often called the "surprise version" of 20 questions (because the questioner is not aware until the end that there is no predetermined "right" answer) has the advantage of self-organizing its own constraints. Godel would say that those constraints were written in "The Book" even if one were incapable of calculating them. IOW, even given that not every infinite series has a finite answer, every answer requiring infinite time has a uniquely corresponding series of "questions." This stuff gets very abstract, and domain-dependent, as, e.g., Dedekind proves that there exists a pair of numbers in Dedekind cuts whose product is sqrt2, though one could never actually write those numbers.
The bottom line is that we really know very little about the continuum. Neither in terms of the number continuum, nor of spacetime.
What we *do* know, is that correspondence of boundary conditions to measurement values in any physical sense requires a bounded length of time. So a coordinate free measure of functions continuous from the initial condition is bounded in space and unbounded in time (and nevertheless consistent with the conventional general relativity interpretation of a universe bounded in time at the singularity and unbounded in space).
"Perhaps locality should be defined in terms of interaction: if two systems directly interact, they are considered local." Right on brother; that's the way Einstein saw it, too. Further, though, it is of deep consideration that Einstein noted " ... if two ideal clocks are going at the same rate at any time and at any place (being then in immediate proximity to each other), they will always go at the same rate, no matter where and when they are again compared with each other at one place." In other words, the clocks do not lose their local rate of change; no matter how spacelike separated, they are always timelike correlated -- which gets into your metric question. I won't try to answer it, because it's already been answered by Joy Christian's topological framework. Indeed, Joy obviates quantum entanglement, and takes full advantage of a topological idea of distance that ordinary geometry cannot accommodate.
Thanks for your thoughtful comments. I'll get around to commenting in your forum as soon as I can.
All best,
Tom
If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is [math]R_1 [/math] and [math]N_1 [/math] was the quantity of people which gave you ratings. Then you have [math]S_1=R_1 N_1 [/math] of points. After it anyone give you [math]dS [/math] of points so you have [math]S_2=S_1+ dS [/math] of points and [math]N_2=N_1+1 [/math] is the common quantity of the people which gave you ratings. At the same time you will have [math]S_2=R_2 N_2 [/math] of points. From here, if you want to be R2 > R1 there must be: [math]S_2/ N_2>S_1/ N_1 [/math] or [math] (S_1+ dS) / (N_1+1) >S_1/ N_1 [/math] or [math] dS >S_1/ N_1 =R_1[/math] In other words if you want to increase rating of anyone you must give him more points [math]dS [/math] then the participant`s rating [math]R_1 [/math] was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.
Sure, Peter, I'll be glad to take a look, with no guarantee that I will have the knowledge to evaluate it. Thanks for the kind comments.
Tom
I did not yet read all your essay, but I looked abstract and conclusion. There I find the first question, with which I agree: "Am I alive?"
I gave you 10 points maybe in the last minute, possible.
Please read my My essay
Best regards Janko Kokosar
Hello Tom,
Assuming there will be no more casting about; it is my pleasure to congratulate you as a finalist. I enjoyed your essay greatly, though it took a couple of readings for some ideas to sink in. I think it is especially poignant; the overlooked point that being an observer is inherently centric. Whatever information is being received, it is coming from a distance toward the observer. That's all an observer sees, and never the receding wave.
I made a similar point, once upon a time, though in a more philosophical setting or context. And I had to look through a lot of my old writings to find the references. Generally speaking; a point of view defines a frame of reference, and a sense of proximal and distal space. Toward and away are relative to the point of observation. And always it is that point at infinity which is bringing us information.
So yes; I think you deserve to be in the finals. May the judges treat you kindly.
All the Best,
Jonathan
Hi Jonathan,
Thank you so much. You know that I also hold your research in high esteem, and it is the greatest reward for any of us to have like-minded friends "get it."
I am happy to return the congratulations, and wish you the greatest success in the contest, with your journal, and in all other endeavors.
All best,
Tom
Hi Tom,
The conversation among you, Michael, and Joy was a very interesting sidebar to the contest. Your finish in the contest was deserved. In other words, you deserve to be bounced around good. :) Just kidding. Congratulations.
James
LOL! Thanks, James. It was bumpy ride, but most enjoyable. Not the least of it was your welcome contributions; your challenging questions, good humor and peacemaking! Thank you above all for being a mensch.
All best,
Tom
While browsing *The Demon and the Quantum* by Robert Scully and Marlan Scully (good book - recommended)I came across (p. 148)a marvelous quote by George Ellis. Robert Scully relates that at a conference, Ellis was asked: "Do we need quantum mechanics to ensure free will?" Ellis is reported to have answered in a Zen koan-like manner: "On Monday, Wednesday and Friday, I think not. On Tuesday, Thursday and Saturday, I think so."
Scully used the quote to support his contention that nobody knows " ... is classical chaos enough to provide freedom of choice, i.e., free will?" I think he missed the point of George's reply (which I am going to ask George himself to confirm or deny, in this forum) for the following reason:
Just a short number of pages prior (pp 130-132), Scully had noted that the quantum eraser proposed by Marlan Scully and Kai Druhl that when published in 1982 'shook the physics community' in the words of Aharonov and Zubairy " ... underscores the statement (that) information is a physical quantity. That is, information is real and the utilization of information is what the quantum eraser is all about."
In his figure 9.6, p 131, Scully shows the wavelike correlation between erased potential and detected information (which corresponds to figure 2 in my essay).
That is the single message of classical chaos, Wheeler delayed choice, and the quantum eraser: Information is real. I think that the opportunity Scully missed is in realizing that George's comment could only have come from a physicist so steeped in relativity that no other answer than "yes" is possible. We need the continuous measurement function equally with discrete quantum detection to have complete information -- and objective knowledge -- of the evolving state. What do you think, George?
Tom
Tom,
Isn't the assumption of an observer-created reality at variance with the original notion of reality as something assumed to exist objectively? For instance, a wave can be observed at effectively the same location by different observers moving relative to the medium with different velocities. It is nonetheless just one wave with one velocity re medium.
What about singularities, see Fig. 3 of my essay.
Eckard
Hi Tom,
I have put a new paper on the arXiv. I thought you might find it interesting.
I am also attaching a PDF file below for your convenience.
Best,
Thanks, Joy! I haven't time to do more than scan it right now. I know I'm going to enjoy it, though. Years ago, I tried to follow the periodic newsletter on spinors/twistors that Roger Penrose published (perhaps still does)-- like so much of Sir Roger's work, for me, I found it tough going.
I have found your approach to classical orientation entanglement, geometry and topology much closer to my own understanding of the subjects.
Best,
Tom
I'm not ignoring you, Eckard. It's just that I don't have LaTex installed on my work computer and I want to use mathematical symbols. Time at my home computer has been very limited lately.
In the interim:
Yes, of course, I agree that reality is objective and local. I'll deal with the question of observer-wave correlation in my formal reply later. (Much of the answer is informally addressed in my essay.)
In re your figure 3: I think one has to see Dedekind's "pebble like" notion of number in the context of Dedekind Cuts. In that, for example, there do exist two numbers that when multiplied together produce sqrt2. We don't know what these numbers are, and we are unlikely to ever know what they are -- but we can know, by explicit construction, that they exist.
Dedekind's and Weyl's work on the Continuum is some of the deepest in mathematics (and something I have studied extensively), and I can't do justice to it here. I will venture to say, however, that I don't think that there is a *real* distinction between mathematical structures and physical reality, although in experimental science there is a very sharp and practical demarcation. So in this respect, I agree with Max Tegmark in the reality of mathematical continuity with physical phenomena -- though at the same time I am compelled to address all the nonsense written that identifies Tegmark's view as Platonic. True Platonism posits an ideal world independent of our physical reality (consider Plato's allegory of the cave). Tegmark's hypothesis is of a mathematical world identical to our physical reality.
If we speak simply of mathematical realism and leave Plato out of it -- we get a constructivist philosophy supported by eminent 20th century mathematicians whose work either strongly relates to, or is based in, physics. Not only Dedekind and Weyl, but Brouwer, Weierstrass, Poincare and others. Not a bad club to belong to.
Tom
Tom,
While I agree with you on that reality isn't observer-created, I would like to more elaborate Robert McEachern's view. Concerning the uncertainty relation between time and frequency I gave results of MATLAB simulations in my previous essays.
You know, my understanding of reality differs from yours. To me the reality is a belief in objective relationships including causality and the possibility to be influenced or to influence in principle. It is not necessarily a belief in something constructed that can be reduced to binary pairs.
What about your trust in mathematics as basic to anything, please look at my Fig. 4 that illustrates how modern (introduced by Weierstrass, Dedekind, and G. Cantor) mathematics differs from logic.
Eckard
"You know, my understanding of reality differs from yours. To me the reality is a belief in objective relationships including causality and the possibility to be influenced or to influence in principle. It is not necessarily a belief in something constructed that can be reduced to binary pairs."
You're right, Eckard -- objective science doesn't have anything to do with personal belief in my world. The binary relation (bit) is that which constructs, not that which is derived from a construction necessitating the axiom of choice (Zorn's lemma); it's the most fundamental relation, as Wheeler allows, in nature as well as in mathematics. As a general law, I find (as my essay instructs) that the irreducible binary relation is exactly equivalent to the relation between a pair of odd primes of any magnitude. In other words, a pair (P_1, P_2) are inequivalent in any respect except mod 2.
The whole story follows in the attachment.
TomAttachment #1: Buridans_Principle_and_the_point_at_infinity.pdf
Tom,
I see your arguments presented in a horribly confusing manner and also most likely wrong.
In your "Buridan's Principle and the point at infinity" you wrote: t goes to infinity. You introduced "(x,y) variables are either fixed or fluctuating values of a continuous range. In other words, the car (x) at time t and the tree (y) at time t..." This is not understandably explained to me.
You referred to Wheeler: "The binary relation (bit) is that which constructs, not that which is derived from a construction necessitating the axiom of choice (Zorn's lemma); it's the most fundamental relation, as Wheeler allows, in nature as well as in mathematics."
I consider this idea wrong, no matter whether or not you accepts AC. I see Euclid's abstraction to the notion unity the basis of mathematics and any repetition of this operation already belonging to the level of abstraction in my Fig. 1. Accordingly there is obviously no exact equality in reality, and trichotomy is something artificial that decouples mathematics from logics.
What about Planck's constant h, I don't see it necessarily related to the uncertainty principle which is also valid for time and frequency. Plank's constant is just a factor of proportionality that relates position to momentum.
Eckard
Fine, Eckard. Then perhaps you'll take your questions to a source that gives you answers you want to hear.
Tom
