Search FQXi


If you are aware of an interesting new academic paper (that has been published in a peer-reviewed journal or has appeared on the arXiv), a conference talk (at an official professional scientific meeting), an external blog post (by a professional scientist) or a news item (in the mainstream news media), which you think might make an interesting topic for an FQXi blog post, then please contact us at forums@fqxi.org with a link to the original source and a sentence about why you think that the work is worthy of discussion. Please note that we receive many such suggestions and while we endeavour to respond to them, we may not be able to reply to all suggestions.

Please also note that we do not accept unsolicited posts and we cannot review, or open new threads for, unsolicited articles or papers. Requests to review or post such materials will not be answered. If you have your own novel physics theory or model, which you would like to post for further discussion among then FQXi community, then please add them directly to the "Alternative Models of Reality" thread, or to the "Alternative Models of Cosmology" thread. Thank you.

Contests Home


Previous Contests

Trick or Truth: the Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
Media Partner: Scientific American

read/discusswinners

How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
Contest Partners: Jaan Tallinn, The Peter and Patricia Gruber Foundation, The John Templeton Foundation, and Scientific American
read/discusswinners

It From Bit or Bit From It
March 25 - June 28, 2013
Contest Partners: The Gruber Foundation, J. Templeton Foundation, and Scientific American
read/discusswinners

Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
Contest Partners: The Peter and Patricia Gruber Foundation, SubMeta, and Scientific American
read/discusswinners

Is Reality Digital or Analog?
November 2010 - February 2011
Contest Partners: The Peter and Patricia Gruber Foundation and Scientific American
read/discusswinners

What's Ultimately Possible in Physics?
May - October 2009
Contest Partners: Astrid and Bruce McWilliams
read/discusswinners

The Nature of Time
August - December 2008
read/discusswinners

Forum Home
Introduction
Terms of Use

Order posts by:
 chronological order
 most recent first

Posts by the author are highlighted in orange; posts by FQXi Members are highlighted in blue.

By using the FQXi Forum, you acknowledge reading and agree to abide by the Terms of Use

 RSS feed | RSS help
RECENT POSTS IN THIS TOPIC

Lev Goldfarb: on 2/24/10 at 18:03pm UTC, wrote The previous post is mine.

Anonymous: on 2/24/10 at 17:59pm UTC, wrote One more (probably the most) important point, which should actually be...

Lev Goldfarb: on 11/29/09 at 21:30pm UTC, wrote Hello Frank, So, you finally reached me. ;-) I must apologize: for a...

Frank DiMeglio: on 11/29/09 at 19:27pm UTC, wrote Hi Lev. The following cuts to the fundamental core of reality and physics,...

Eckard Blumschein: on 11/27/09 at 22:58pm UTC, wrote Dear Lev, Schroedinger and Einstein preferred the traditional point of...

Lev Goldfarb: on 11/27/09 at 20:49pm UTC, wrote Eckard, One more thing: natural numbers are not discrete entities any...

Lev Goldfarb: on 11/27/09 at 16:24pm UTC, wrote Eckard, I guess even Schrödinger’s observations (p. 2 of my essay)...

Eckard Blumschein: on 11/27/09 at 12:59pm UTC, wrote Dear Lev Goldfarb, Maybe it is difficult to convey the urgent need you are...


RECENT FORUM POSTS

Robert McEachern: "“Spookiness” Confirmed as a Misunderstood Classical Phenomenon Rob..." in “Spookiness”...

Steve Dufourny: ":) Doc is in you Tom :)" in Dirty Secrets...

amrit: "Quantum space-time is pure illusion. Space in not made out of Quanta, but..." in In Search of a Quantum...

Robert McEachern: "Hi Tom. I don't know if you are familiar with MATLAB, but you can purchase..." in Dirty Secrets...

Robert McEachern: "The Uncertainty Principle is fundamental, because it is the limiting case..." in Uncertainty Relations -...

Joe Fisher: "At 9:00 PM EST, on August 29, 1966, I stepped off a Pan American 707..." in Untangling Quantum...

Pentcho Valev: "Einstein's General Relativity: Deductive Theory or Empirical Concoction? ..." in What Happens Inside the...

kurt stocklmeir: "Georgina - all forces get more strong as they travel for the same reasons..." in Alternative Models of...


RECENT ARTICLES
click titles to read articles

Untangling Quantum Causation
Figuring out if A causes B should help to write the rulebook for quantum physics.

In Search of a Quantum Spacetime
Finding the universe's wavefunction could be the key to understanding the emergence of reality.

Collapsing Physics: Q&A with Catalina Oana Curceanu
Tests of a rival to quantum theory, taking place in the belly of the Gran Sasso d'Italia mountain, could reveal how the fuzzy subatomic realm of possibilities comes into sharp macroscopic focus.

Dropping Schrödinger's Cat Into a Black Hole
Combining gravity with the process that transforms the fuzzy uncertainty of the quantum realm into the definite classical world we see around us could lead to a theory of quantum gravity.

Does Quantum Weirdness Arise When Parallel Classical Worlds Repel?
Quantum mechanics could derive from subtle interactions among unseen neighboring universes


FQXi FORUM
August 30, 2016

CATEGORY: What's Ultimately Possible in Physics? Essay Contest [back]
TOPIC: What is possible in physics depends on the chosen representational formalism by Lev Goldfarb [refresh]
Bookmark and Share
Login or create account to post reply or comment.

Author Lev Goldfarb wrote on Aug. 7, 2009 @ 05:28 GMT
Essay Abstract

All of science is built on the foundation of the millennia-old numeric forms of representation and the associated measurement processes. Hence, the most promising way to approach physical reality (and physics) afresh is to shift to a non-numeric representational formalism. I discuss here one such formalism for structural/relational representation—evolving transformations system (ETS)—developed by our group. In particular, the adoption of ETS obviates the introduction of consciousness into physics, since under the formalism, the two forms of object representation—by an agent (subjective) and in Nature (objective)—agree. Moreover, ETS suggests the primacy of the new temporal representation over conventional spatial representation, and it is not difficult to envisage that the latter is actually instantiated on the basis of the former, as has also been suggested by some quantum gravity researchers.

Author Bio

Lev Goldfarb obtained Diploma in Mathematics (St.-Petersburg University) and Ph.D. in Systems Design Engineering (University of Waterloo). For twenty five years he worked as an Assistant and Associate Professor in the Faculty of Computer Science, University of New Brunswick, Canada. Now he conducts research and consulting through his company IIS. He has served on the editorial boards of Pattern Recognition, Pattern Recognition Letters, and now Cognitive Neurodynamics. Trained as a mathematician, he realized quite early the inadequacy of the conventional numeric models and has been working on the development of fundamentally new formalisms for structural representation.

Download Essay PDF File




J.C.N. Smith wrote on Aug. 7, 2009 @ 13:46 GMT
A fascinating essay! I certainly agree with your suggestion that if the road we currently are on is not taking us where we want to go we should considering taking a different road. Having never previously thought in the terms you present, however, I must admit to needing much more time and thought even to begin to absorb what you are saying. Your comment that " . . . we should consider the possibility of replacing the ubiquitous form of numeric representation by its structural, or relational, generalization" seems as though it might echo the concept of a "Machian" way of viewing the universe in purely relational terms, which strikes me as being a constructive way to proceed.

I was intrigued, too, by your observation that in your way of looking at things the conventional view of time is, as you say, "simply obviated." This happens to be the underlying theme of my own essay, 'On the Impossibility of Time Travel,' which also appears among these essays. There is a saying that when a person has just purchased or been given a shiny new hammer, everything begins to look like a nail. Consequently, I can't help wondering whether our two apparently different perspectives might have some sort of symbiotic hammer/nail relationship. Perhaps a possibility at least worth considering.

Thank you for a thought provoking essay.

report post as inappropriate


Stefan Weckbach wrote on Aug. 7, 2009 @ 16:30 GMT
Working with similarities was a long time suspicious in physics and science, because similarities had a strange flavour like alchemism and other esoteric issues.

For me it seems that similarities are somewhat necessary in our universe, because with their "counterpart", namely differences, they built a structural unity. So i am not surprised that someone has worked out these dynamics in detail, because for me it's at least natural that form and content go hand in hand, as well as quality and quantity.

As far as i have understood your main concerns in your paper, i think that it hits some profound, universal facts and therefore it's no wonder that your "Hammer" could hit many nails at once. Maybe there are many philosophical questions open to ask about your concept, but i think, at first blush, you stand on solid and promising ground with your framework and i started to like it. So thanks for the contribution!

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 7, 2009 @ 20:30 GMT
To J.C.N Smith:

Thanks for sharing your first (kind) impressions with us!

As to your essay, indeed, I am basically in agreement with you. In light of the ETS formalism it becomes relatively clear why time travel is usually not possible: the new events can typically be attached to the ‘present’ events, so that the past events are normally not ‘available’ for that purpose (unless their terminal processes have not yet been attached to some other events).

To Stefan:

Thank you for sharing your initial (kind) impressions!

Today, similarities continue to dominate almost all psychological—and now computer science (i.e. search engines, data mining)—considerations. The problem with them has been that they simply cannot be properly addressed within the conventional mathematical formalisms: the concept of ‘similarity’ cannot be adequately dealt with when ‘objects’ are represented as points in some space, i.e. you need the structural object representation.




Author Lev Goldfarb wrote on Aug. 8, 2009 @ 01:13 GMT
Stefan Weckbach wrote on Aug.7, 2009 @ 16:30 GMT

“Maybe there are many philosophical questions open to ask about your concept, …”

Stefan, one point might be worth mentioning. The formalism originated when I was fully preoccupied with induction and pattern recognition, but gradually I began to see that such powerful capabilities couldn’t have been evolutionary acquired by biological species *unless* they were guided by 'similar' informational ‘mechanisms’ permeating the nature.




Stefan Weckbach wrote on Aug. 8, 2009 @ 05:03 GMT
Dear Lev,

"but gradually I began to see that such powerful capabilities couldn’t have been evolutionary acquired by biological species *unless* they were guided by 'similar' informational ‘mechanisms’ permeating the nature."

Yes. And your *unless* reads for me as a *must*, so you probably must have been brave enough to follow your intuition, which seems to me to be in good...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Aug. 8, 2009 @ 12:40 GMT
Stefan Weckbach wrote on Aug. 8, 2009 @ 05:03 GMT

“One question that is of interest for me is, if in your concept there is a way to represent properly the qualia of one's conscious contents (for example the human's impression of the colours that seem to be equal to almost all human observers).”

Stefan, here is my (informational) view in a nutshell. As my Postulate 1 suggests, the ‘reality’ is a family of evolving and interactive classes of processes, where each process/object is an organized stream of events. An agent is endowed with the ability to represent some of the events and hence some of the processes and *their classes*. As evolution progresses, an agent might be able to enlarge the number, and the quality, of the classes perceived. Thus, all qualia are also classes or their attributes, and all we need to represent (and organize) are various classes of processes. The reason “the human's impression of the colours . . . seem to be equal” is that genetically we are endowed with almost identical mechanisms for representing events and processes.




Stefan Weckbach wrote on Aug. 8, 2009 @ 15:01 GMT
Dear Lev,

thanks for your comments. I am impressed by your framework and its rigorousity.

By contemplating the meaning of the term "information", it became clear, at least for me, that it has a very close relation to the term "definition". Information in my view is a *specific*, well-*defined* perspective of at least "interaction" (and maybe also of evaluation [and therefore...

view entire post


report post as inappropriate


Florin Moldoveanu wrote on Aug. 9, 2009 @ 02:27 GMT
Dear Lev,

Can you please answer a couple of questions about your approach?

1. How is the evolving transformations system similar or different from the modular programming paradigm?

2. Can the evolving transformations system provide a true representation of quantum mechanics, or only of a hidden variable approach to quantum mechanics?

Thank you.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 9, 2009 @ 03:34 GMT
Florin Moldoveanu wrote on Aug. 9, 2009 @ 02:27 GMT

"1. How is the evolving transformations system similar or different from the modular programming paradigm?

2. Can the evolving transformations system provide a true representation of quantum mechanics, or only of a hidden variable approach to quantum mechanics?"

Sure, Florin, let me try (and thanks for your...

view entire post





Florin Moldoveanu wrote on Aug. 9, 2009 @ 04:20 GMT
Dear Lev,

Thank you for your answers. In my first question I was simply referring to the pre object oriented way of writing software and it looked to me you can implement any concrete ETS process naturally as a C program for example. (Of course I understand that ETS is more sophisticated than that in its aims.)

For the second question, I was wandering how an event based mechanism can...

view entire post


report post as inappropriate


Stefan Weckbach wrote on Aug. 9, 2009 @ 07:35 GMT
If there is somebody interested in: There exists an event-based model to simulate QM-experiments, and those simulations have already been done successfully. Look here for further information and for the flash-applications and Java-codes.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 9, 2009 @ 14:36 GMT
Florin Moldoveanu wrote on Aug. 9, 2009 @ 04:20 GMT

"I was wandering how an event based mechanism can manage to model quantum mechanics predictions? For example, we can do a computer simulations of the Schrödinger equation, but in there we impose quantum mechanics from the outside. The strangeness of quantum mechanics is due to its use of complex numbers. Going outside the number road,...

view entire post





Florin Moldoveanu wrote on Aug. 9, 2009 @ 20:48 GMT
Dear Lev and Stefan,

Thank you for your answers. I am not sure event based systems can recover all predictions of QM, In Stefan’s link the state of the system was given by 2 consecutive states (n) and (n+1) and this resulted in oscillations after the equilibrium state was achieved. In other words, it was only an approximate modeling of QM. My expectation is that any event based description of QM will lead uniquely to a hidden variable theory, but if anybody manages to prove it otherwise, I will be very interested to read about it. The closest result I am aware of is Joy Christian’s claim of disproving Bell’s theorem, but his argument had a conceptual flaw correctly pointed by one of his critics.

Anyway, although I am skeptical, I find the ETS idea worth of consideration and exploration and I wish you both luck in this contest.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 9, 2009 @ 20:52 GMT
Florin Moldoveanu wrote on Aug. 9, 2009 @ 04:20 GMT

"The strangeness of quantum mechanics is due to its use of complex numbers. Going outside the number road, are you relaxing the inherent quantum mechanical properties stemming from its use of complex numbers?"

Florin, I wouldn’t worry about the complex numbers: they are our invention, and are not part of the "inherent quantum mechanical properties".




Florin Moldoveanu wrote on Aug. 9, 2009 @ 20:53 GMT
Sorry I had typo (missing a word). The last line should read:

I wish you both good luck in this contest.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 9, 2009 @ 20:59 GMT
Thanks, Florin!

Best wishes to you too!




Peter Morgan wrote on Aug. 9, 2009 @ 21:43 GMT
You seem to me to be doing something similar enough to category theory that you have to take account, in future, of what is being done in that approach. You need, at least, to differentiate your approach from the category-theoretic approach, if you wish to place yourself in an academic context. Try, for example, A prehistory of n-categorical physics. There's a lot there, and it's hard math, but I think you can only benefit from looking at category theory at whatever level you can make contact with it.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 10, 2009 @ 00:33 GMT
Thanks, Peter!

We have been looking at category theory from the very beginning (a postdoc of mine, from Moscow, was a specialist in it). However, I found category theory to be still too ‘close’ (for comfort) to the ‘conventional’ math.: it deals with various relationships between the classical math. structures, both algebraic and topological. The intuition has been telling me that to get to the *structural* representation we need to have a more complete break with the points-sets-mappings mindset, at least at the beginning. If you read carefully the essay (and the main paper) you might be able to see why the structs are not the familiar math. objects, yet they have to replace the ‘points’. Moreover, a struct can *naturally* represent any finite math object (not a math. structure), but not the other way around: a typical finite math object (e.g. polynomial) can be viewed as being generatively structured (in the ETS sense).




Stefan Weckbach wrote on Aug. 10, 2009 @ 04:52 GMT
Thank you Florin, my best wishes too for your own concept presented here at FQXi!

report post as inappropriate


Brian Beverly wrote on Aug. 10, 2009 @ 12:02 GMT
Amazing essay!

report post as inappropriate


T H Ray wrote on Aug. 10, 2009 @ 14:36 GMT
Lev Goldfarb,

A magnificent essay. I sincerely hope you don't abandon your mathematical roots, because I see that cutting edge research--particularly in complex systems, computer science and topology--supports your thesis of fundamental change in how we do mathematics in the future. For example:

-- Classes.

Now that the class division of all manifolds has been completed by...

view entire post


report post as inappropriate


T H Ray wrote on Aug. 10, 2009 @ 14:42 GMT
Let me see if I can get the link right.

report post as inappropriate


T H Ray wrote on Aug. 10, 2009 @ 14:46 GMT
Sorry. I am just not proficient at this. necsi.org

Tom

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 10, 2009 @ 15:34 GMT
Thank you Brian!

Thank you Tom! And don't worry about the link: I'll get your paper.

To my own amazement, as the work on the new representation progressed, it became clear that the representational issue (that have not come to the fore in mathematics and physics) have, in fact, the widest possible scientific implications. And, if you think about it, it should not have come as a surprise. ;-)




Joe Fisher wrote on Aug. 10, 2009 @ 23:04 GMT
Dr. Goldfarb:

This is a brilliant essay. The only comment I can make is that I believe that the universe is infinite in size, perpetual in motion, and eternal in duration. All human measuring assessments are finite in amount, limited in scope, and temporary in age. As such, human scientific theory and practice have no more validity than human clairvoyance has in unearthing the true nature of the universe.

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 10, 2009 @ 23:53 GMT
Joe Fisher wrote on Aug. 10, 2009 @ 23:04 GMT

"As such, human scientific theory and practice have no more validity than human clairvoyance has in unearthing the true nature of the universe."

Thank you, Joe!

But don’t you think, whether we like it or not, we are bound with Nature by a sacred covenant, which we simply cannot break and remain HUMANS, that we, as a sign of our eternal gratitude, will never end our quest to understand the Nature?




T H Ray wrote on Aug. 11, 2009 @ 10:29 GMT
Lev Goldfarb wrote:

"But don’t you think, whether we like it or not, we are bound with Nature by a sacred covenant, which we simply cannot break and remain HUMANS, that we, as a sign of our eternal gratitude, will never end our quest to understand the Nature?"

What a wonderful statement. I find it every bit as profound as Jacob Bronowski's reflections on the relationship between science and human values. At the end of the day, how does an enduring sense of gratitude, toward one's gift of freedom in mind and body, differ from love?

Tom

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 11, 2009 @ 11:27 GMT
T H Ray wrote on Aug. 11, 2009 @ 10:29 GMT

"At the end of the day, how does an enduring sense of gratitude, toward one's gift of freedom in mind and body, differ from love?"

Tom,

I believe it is not just a matter of love, it also a matter of our obligation.




T H Ray wrote on Aug. 11, 2009 @ 22:22 GMT
Lev,

The obligation of giving back is actually my context for love. Martin Buber wrote of an I-Thou relationship (Ich und Du)in which reciprocity characterized the highest relationship a person could have, with anyone or anything.

Obligation is a choice, is it not?

Well, I didn't mean to get too far off topic--you struck a chord.

Tom

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 11, 2009 @ 22:48 GMT
T H Ray wrote on Aug. 11, 2009 @ 22:22 GMT

"The obligation of giving back is actually my context for love. Martin Buber wrote of an I-Thou relationship (Ich und Du)in which reciprocity characterized the highest relationship a person could have, with anyone or anything.

Obligation is a choice, is it not?"

Tom,

My be you are right, but I'm not sure.

What I'm actually talking about is this. Why is it that the majority of 'scientists' do not approach their work in the spirit we are discussing? Are they incapable of 'loving' in your sense or are they incapable of 'devotion' in my sense? Love has this 'flesh and blood' connotation, while devotion has a more spiritual one. What do you think?




T H Ray wrote on Aug. 12, 2009 @ 07:26 GMT
Lev wrote:

"What I'm actually talking about is this. Why is it that the majority of 'scientists' do not approach their work in the spirit we are discussing? Are they incapable of 'loving' in your sense or are they incapable of 'devotion' in my sense? Love has this 'flesh and blood' connotation, while devotion has a more spiritual one. What do you think?"

Most certainly, Einstein...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Aug. 13, 2009 @ 00:22 GMT
Well, Tom, this isn't really the best place for such discussion, but . . . ;-) again, I remain skeptical: I suspect that love emanates from 'flesh and blood' and always involves more 'flesh and blood' feelings , albeit at the subconscious level, than *spiritual* devotion. And so it is quite possible that the *proportion* of people capable of love is much larger than the proportion of those capable of spiritual devotion.

This could be the main reason for the situation I described in the very first paragraph (in section 1) of my essay.

It appears that many people prefer to erase the above difference.




T H Ray wrote on Aug. 13, 2009 @ 11:16 GMT
Lev,

Let me try and steer this back around to the content of your essay. It does relate in a very straightforward way. You quoted Schrodinger, Von Neumann ... and Einstein. Of these three, it was Einstein who supported, in a practical way, Von Neumann's concept of logic and mathematics residing in the central nervous system. I don't have a reference at my elbow, but Einstein spoke of a...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Aug. 13, 2009 @ 12:57 GMT
Tom,

Talking about Einstein, he is a prime example of what we are discussing. I am convinced he has been absolutely misunderstood regarding his views of quantum mechanics, precisely because he was simply applying higher standards to the physical theory that most of the physicists, who I’m sure *love* their subject.

Why? Because if you ‘simply’ love something/someone, you...

view entire post





T H Ray wrote on Aug. 13, 2009 @ 14:29 GMT
Lev,

That's an interesting point of view. Einstein was certainly instrumental in opening the door to QM (with his groundbreaking paper on the photoelectric effect), and right, he didn't love it ("... doesn't play dice ..."). He always felt that a complete theory could be neither quantum nor continuum, and worked toward an alternative until he died.

But "worship?" I never got the...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Aug. 13, 2009 @ 16:31 GMT
Thank you Tom!

But I certainly hope it was not me who we were discussing.

And though you say:

"Both quantum mechanics and general relativity are mathematically complete theories, with correspondence to physical phenomena. In that sense, they are perfect."

they are not perfect at all. They give us quite *incomplete* and one sided pictures of reality, and that's why they are not directly unifiable. By the way, that is why, in particular, we also have FQXi contests and all that talking that we are doing here. ;-)




T H Ray wrote on Aug. 13, 2009 @ 18:04 GMT
Oh come on, Lev ... you know that a mathematical theory is not required to explain everything, just what its domain encompasses. The world really is continuous in some way, and it really is discontinuous in another way.

Yes, the mystery of it all! :-)

Tom

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 15, 2009 @ 19:17 GMT
T H Ray wrote on Aug. 13, 2009 @ 18:04 GMT

"... you know that a mathematical theory is not required to explain everything, just what its domain encompasses. The world really is continuous in some way, and it really is discontinuous in another way."

Yes, the mystery of it all! :-)

---------------------------------------------------------
--

"Mathematical theory" is all we've got!

And as you can see, we've come to the point where it is clear to the majority of theoretical physicists that the two theories (QM & GR) must be unified. In fact that is where all (fundamental) efforts of theoretical physicists are directed.

Also Tom, when I hear that "the world really is continuous in some way, and it really is discontinuous in another way" I immediately want to vehemently object that it is only according to our *current* concepts "the world is continuous in one way and discontinuous in another way. As far as the reality is concerned, there simply can nor be "two ways". I am *absolutely* convinced that it is our present task to get rid of such, using Einstein's characterization, "the Heisenberg-Bohr tranquilizing philosophy" and to look for the new fundamental formal structures which would replace that dichotomy and capture more adequately the presently quite hazy, dichotomous 'reality'. ;-)




T H Ray wrote on Aug. 16, 2009 @ 12:50 GMT
Lev writes,

"Mathematical theory" is all we've got!

And as you can see, we've come to the point where it is clear to the majority of theoretical physicists that the two theories (QM & GR) must be unified. In fact that is where all (fundamental) efforts of theoretical physicists are directed.

Also Tom, when I hear that "the world really is continuous in some way, and it really...

view entire post


report post as inappropriate


amrit wrote on Aug. 16, 2009 @ 15:35 GMT
Dear Lev

I deeply agree with your essay. ETS is something will give an immense vision in physics. My essay is about how to experience physical phenomena consciously without mind interfering.

Yours amrit

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 17, 2009 @ 14:37 GMT
T H Ray wrote on Aug. 16, 2009 @ 12:50 GMT

To echo your response, Lev, our current concepts are all we've got! :-)

. . .

I just don't think we can abandon mathematics in our quest. We have to do what physicists have always done with mathematical models -- extend. It was quite fruitful for Einstein to employ Riemannian geometry to extend Newton. So long as we continue to support mathematics research, I think we are guaranteed a sufficient variety of models to pull off the shelf in order to serve our physical theories.

------------------------------------

Tom, I'm a mathematician by education and the whole point of my essay is that most likely we cannot "extend" the existing math to fit the needs. So, the 'good time' is over: we don't have the 'right' model on the shelf ;-)




T H Ray wrote on Aug. 17, 2009 @ 17:51 GMT
Lev writes,

Tom, I'm a mathematician by education and the whole point of my essay is that most likely we cannot "extend" the existing math to fit the needs. So, the 'good time' is over: we don't have the 'right' model on the shelf ;-)

--------------------------------------

Well, sure, I agree.

And then again, perhaps we don't yet have a deep enough understanding of those physical models that we have created so far. Even in the last 10 years--make that five years--the proliferation of new techniques and computing technology is breathtaking.

Tom

report post as inappropriate


Roy Johnstone wrote on Aug. 18, 2009 @ 11:53 GMT
Lev

A very thought provoking essay. This is a novel approach to achieving a generalised, consistent formalism with the potential to describe all phenomena from the fundamental "reductionist" standpoint, to the higher level, effective theoretical (chemistry/biology) standpoint in a more seamless way than what we have now.

I agree that the math representations of QM & GR, with their corollary of complex numbers, irrational real numbers with infinite decimal expansions, ideal forms that are not realised in nature, probabilistic interpretations etc, are telling us something. I think that something is that Mother Nature doesn't give two hoots about man's evolved forms of "numerically" making sense of the world!

Whilst I am still getting my head around your scheme, at first glance it seems like an extension of Feynman diagrams, but with the probabilistic "coupling strength" calculations etc replaced by some sort of "class constrained" transformation process to the next state of the representation (at micro scales)? Decoherence seems to be naturally incorporated also.

I'm not sure what your scheme does for our understanding of the "nature of time" though. For instance, could you clarify your statement in footnote (i) to figure 4... "This is the direction of precedence of temporal encoding over the spacial one in nature"? Does this imply the view that change "happens in time" rather than time "emerging from change"? I would have thought from your later claim that ETS "embodies a more general, structural form of temporality", that the latter view would be required? But I may be completely missing the essence of your scheme at this stage.

I was also wondering how in ETS you would represent a quantum superposition, such as a split photon wave function? Or indeed any coherent quantum state? This would have implications for quantum computing for instance.

Congatulations on an excellent essay & good luck withe the contest!

PS: I think if Max Tegmark reads this essay, he will fall off his chair!!!

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 18, 2009 @ 13:15 GMT
Thank you Roy for the comments!

Roy Johnstone wrote on Aug. 18, 2009 @ 11:53 GMT

“Whilst I am still getting my head around your scheme, at first glance it seems like an extension of Feynman diagrams, but with the probabilistic "coupling strength" calculations etc replaced by some sort of "class constrained" transformation process to the next state of the representation (at micro...

view entire post





Juan ramos wrote on Aug. 20, 2009 @ 10:04 GMT
Lev:

Great essay.

Lev, Tom:

greater disscussion.

Lev:

greatest tool and formalism (ETS)

report post as inappropriate


Author Lev Goldfarb wrote on Aug. 31, 2009 @ 11:57 GMT
Tom (T. H. Ray),

At the risk of sounding, again, as a preacher, but having in mind the young scientists who are supposed to benefit from such contests as this one, let me try once more to justify my point (‘love is not enough’) more clearly and relevantly to the topic of this contest.

What I was implying is that we are witnessing now a period in the history of science in which...

view entire post





Steve Dufourny wrote on Sep. 1, 2009 @ 17:34 GMT
Hi Lev ,

Interesting work about math and computing .

Sincerely

Steve

report post as inappropriate


Steve Dufourny wrote on Sep. 1, 2009 @ 17:35 GMT
Von Nieuman would be happy .

Steve

report post as inappropriate


Author Lev Goldfarb wrote on Sep. 1, 2009 @ 20:42 GMT
Steve Dufourny wrote on Sep. 1, 2009 @ 17:35 GMT

"Von Nieuman would be happy."

--------------------------------------------------

Ste
ve,

And what about your happiness? ;-)




T H Ray wrote on Sep. 2, 2009 @ 08:39 GMT
Hi Lev,

I don't disagree in general. Einstein is also a hero of mine, and I do think that the meaning and usefulness of his scientific legacy extends beyond that of Bohr. Perhaps there's a metaphor here--Einstein's universe of continuous functions against Bohr's event of the moment.

Love without wisdom? I doubt that in my context, such s thing is even possible. If one identifies...

view entire post


report post as inappropriate


Anonymous wrote on Sep. 2, 2009 @ 12:02 GMT
T H Ray wrote on Sep. 2, 2009 @ 08:39 GMT

"I think the next generation of scientists will be artists, not philosophers."

-------------------------------------

Hi Tom,

At the dawn of the new civilization, *if there is going to be one*—exactly as at the dawn of ours (I’m referring to the Greeks)—we need philosophers, since the patterns are becoming even more...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Sep. 2, 2009 @ 12:05 GMT
Tom, I'm not anonymous, I'm Lev. ;-)




Steve Dufourny wrote on Sep. 2, 2009 @ 18:13 GMT
Hi Lev ,

Heu hihihi in fact ,it's a big question what I look for since 34 years ago .

My answer in total transparence is no .Perhaps one day I hope but in fact it's not important for me .I agree what I must adapt me .

Dear Lev,

I am a very bad computer ,it's a problem for me ,do you know a good link about a course about how architecturate a system with adapted...

view entire post


report post as inappropriate


Anonymous wrote on Sep. 2, 2009 @ 18:32 GMT
Excellent essay Lev.

I feel it demonstrates the 'new way of thinking' most of the greats in physics have postulated is needed.

My own humble offering here has firm conceptual links, but suggests multiple 'rotational' representations, becoming helical with temporality (all particle 'events' are based on 'spin') holding the evolving relational data. I really don't explain formal...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Sep. 2, 2009 @ 19:13 GMT
Thank you Peter!




T H Ray wrote on Sep. 3, 2009 @ 09:23 GMT
Lev writes

There is a difference between a philosopher and a poet in the generality and priority of patterns that each perceives.

-------------------------------------------

If there is, I think that it is a difference without distinction.

That is, a poet of the, say, William Blake variety, may see the world in a grain of sand and eternity in an hour--while a...

view entire post


report post as inappropriate


Leshan wrote on Sep. 8, 2009 @ 15:48 GMT
Dear readers,

I do not see the critique of essay. It is not a forum for cosmetics and women, it is a forum for physics! If you rate an essay, it means that you read and understand the essay. Therefore, please publish your opinion and critique of the essay. We do not write holy papers, all essays have errors.

Why all physicists are afraid of criticism? I'm sure it is the main cause of the crisis in science. Every year a lot of papers are published but a little critique appears only. The false theories will grab all the world without critique!

report post as inappropriate


Steve Dufourny wrote on Sep. 9, 2009 @ 08:25 GMT
Hi Leshan ,

Yes you are right ,but a good critic takes time too and needs reflexions .

I am goig to read yours and critic it hihi .

Cordialy

Steve

report post as inappropriate


Jayakar Johnson Joseph wrote on Sep. 15, 2009 @ 08:49 GMT
Dear Lev Goldfarb,

It’s a very good roadmap by the observables on mathematical evolution. In Universe with no void, ‘Nothing is always Something’. In this context I think the Numeric representational formalism with inclusion of ‘zero’ is a big constrain and in many representations we may have to include Non-numeric representational formalism, that is more prior and have parallel...

view entire post


report post as inappropriate


Anonymous wrote on Sep. 15, 2009 @ 13:23 GMT
Thanks, Jayakar!

report post as inappropriate


Anonymous wrote on Sep. 16, 2009 @ 21:31 GMT
Dear Lev-

Thanks for your interesting essay. It is well written and I liked the quoted text on page 2 and your suggestion for a very different approach towards unification. However, I feel that your suggestion of a different formalization will not bring us closer to a unified theory of physics. The likelihood for success ('to hit the target') is extremely small, since there are an infinite...

view entire post


report post as inappropriate


Ben Baten wrote on Sep. 16, 2009 @ 21:33 GMT
Forgot to add my name to the last submission.

report post as inappropriate


Author Lev Goldfarb wrote on Sep. 17, 2009 @ 14:22 GMT
Dear Ben,

Thank you very much for the extensive comments!

Here are my responses to only two of your comments:

“However, I feel that your suggestion of a different formalization will not bring us closer to a unified theory of physics. The likelihood for success ('to hit the target') is extremely small, since there are an infinite number of possible formalizations. The 'chosen...

view entire post





Author Lev Goldfarb wrote on Sep. 20, 2009 @ 16:17 GMT
Because of the lack of space, I omitted in my essay several points, one of which is quite important.

*In science, the term ‘discrete’ means just the negation of ‘continuous’ and no more*.

So that while all of modern science is based on the formalism that is precise elaboration of the ‘continuous’, I am convince, we have not had a precise and general elaboration of the ‘discrete’. My essay outlines a formalism addressing the latter issue.




Owen Cunningham wrote on Sep. 22, 2009 @ 10:21 GMT
Dr. Goldfarb, just wanted to add my voice to the choir here. Excellent paper. I didn't realize until I read through some of your clarifications in the comment thread here just how similar the core concepts of our papers are. I just wrote a lengthy clarification of my own paper and in the process came up with a point that I would be curious to get your opinion on:

It seems there are a great many in the physics community who, in their heart of hearts, believe that IF a genuine theory of everything is ever found, it will consist solely of equations. The philosophical essence of my paper is, what if the ToE is better expressed as _source_code_ than as a bunch of equations? That seems to be the core question from which you proceeded as well (or at least that's how I view it).

report post as inappropriate


Author Lev Goldfarb wrote on Sep. 22, 2009 @ 13:39 GMT
Owen,

Of course , I agree with you main point (except for the term “_source_code_” ;-) ).

It’s uncanny: before I saw your message, I was posting the related comment on the essay by Giovanni Amelino-Camelia. Please refer to it.

Thanks!




Owen Cunningham wrote on Sep. 22, 2009 @ 15:20 GMT
I just read your comment on Giovanni's paper. You make an insightful point by talking about the need for a universal data representation mechanism. I think our papers both attempt to construct the simplest possible system that can serve as that universal mechanism, but they are oppositely "polarized" with respect to mathematics -- you went the logical route, bleaching all the numbers out of your...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Sep. 24, 2009 @ 04:36 GMT
Owen,

I'll get back to you shortly with some comments on your essay.




Narendra Nath wrote on Sep. 28, 2009 @ 06:58 GMT
in most of the essays i notice great emphasis on tackling physics through the tool of mathemetics. Fine. However, i have a feeling that one needs to work out the concepts/precepts of the study being undertaken before applying the mathematical tools. The variables and the boundary conditions all depend on the broadest of considerations one has given to the underlying truth. The qualities of mind...

view entire post


report post as inappropriate


Emile Grgin wrote on Sep. 29, 2009 @ 03:41 GMT
Dear Lev,

I have two reactions to your essay: a very good one, and a letdown.

Beginning with the first, I enjoyed reading your paper because it enriched me with new ideas. Ideas of the type that make us say "Hey! I should have thought of this myself!" I appreciate this part. Thank you.

But I was also disappointed because, at the end, where I expected a concrete example (or...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Sep. 29, 2009 @ 11:24 GMT
Emile Grgin wrote on Sep. 29, 2009 @ 03:41 GMT

“But I was also disappointed because, at the end, where I expected a concrete example (or reference to it) of how an essentially linguistic structure produces a concrete number (let's say Weinberg's angle), you only tell us that you believe it will. Well, I'll wait for it.”

Dear Emile,

I can appreciate this, but the whole...

view entire post





Lawrence B. Crowell wrote on Sep. 29, 2009 @ 17:02 GMT
In reading your article I was struck by the prospect this could lead to a view of physics as a system of processors. Each of the little elements you propose as similar to C-NOT or Hadamard gates. I think that Emile is right that at the end some number does need to be computed. It would then seem to me that these elements need to be connected in ways which emulate or compose symmetries in nature from a computational perspective.

Cheers LC

report post as inappropriate


Author Lev Goldfarb wrote on Sep. 29, 2009 @ 18:00 GMT
Lawrence,

Thanks for your comments!

However, I believe you are missing the whole point: you are looking at the figures and thinking about the conventional ‘hardware’, while I’m talking about new abstract entities ‘structs’. As I mentioned in the essay, they are supposed to replace numbers and ‘play their role’ and, of course, they are a far-reaching (non-numeric) generalization of numbers.




Lawrence B. Crowell wrote on Sep. 30, 2009 @ 12:21 GMT
Of course physics is an expterimental subject, which means at the end of the line measurements are taken. Measurements involve numbers and quantities. So somewhere in the pipeline here there must be a connection made there.

Cheers LC

report post as inappropriate


Author Lev Goldfarb wrote on Sep. 30, 2009 @ 12:44 GMT
Well, again, the proposal is that we should generalize the measurement process, where the outcomes of the measurements are structs (which may sometime 'degenerate' to numbers).




Author Lev Goldfarb wrote on Oct. 5, 2009 @ 01:39 GMT
A further clarification of the important point mentioned in my post of Sept. 20 might be useful.

As suggested by Schrödinger (see p. 2 of my essay), when the idea of ‘discrete’ entered physics at the beginning of the 20th century, it “has been forced upon us very much against our will”. Now, more than a century later, despite the popularity the term ‘discrete’ has gained, our understanding of the ‘discrete’—as it is present in nature—has not really advanced.

As I mentioned in the above post, the reason this situation persists has to do with the lack of any adequate conception of ‘discrete’. We still talk of the ‘discretizations of space and time’ in spite of the fact that such concepts are not formally meaningful: ‘discretization’ of the continuous model does not produce a ‘discrete’ model.




Terry Padden wrote on Oct. 6, 2009 @ 10:46 GMT
Lev

I found your essay very interesting in relation to mine. I found your Von Neumann quote very relevant. We share the view that the problem for physics is due to limitations of the mathematical representation. I try to show why. For my essay it is the conclusion.

You are taking it as your starting point, and attempting to fix the problem. I applaud your effort.

I...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Oct. 8, 2009 @ 12:43 GMT
Terry,

Please read my posts of Sept. 20 and Oct. 5.




Terry Padden wrote on Oct. 9, 2009 @ 23:05 GMT
Lev

I had read those posts and the others several times. Not to do so before posting would be discourteous. I don't think they cover my point; but I was only expressing an opinion. So no response is really required.

report post as inappropriate


Eckard Blumschein wrote on Oct. 12, 2009 @ 14:54 GMT
Dear Lev Goldfarb,

Your essay and most of the belonging discussions are largely in unison with my attitude.

I just managed to fix problems of providing access[/unlink].

I recall Thomas Ray making good points at the previous contest and would appreciate his response too.

Please do not hesitate to tell me in what you absolutely disagree.

Regards,

Eckard

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Oct. 12, 2009 @ 23:49 GMT
Dear Eckard,

Thanks! I'll post my comment on your essay's web page tomorrow.




Steven Oostdijk wrote on Oct. 16, 2009 @ 20:49 GMT
This essay is an attempt at what I would call the "powerpointerization" of physics, equivalent to the same "powerpointerization" of computer programming languages by making them "object oriented". The author comes from "Inductive Information Systems" and that shows.

The physical world operates in a discrete continuum, not by boxes and arrows with fuzzy meanings.

Good luck with the...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Oct. 16, 2009 @ 21:21 GMT
Dear Steven,

By the way, the "physical world" cannot operate "in a discrete continuum", simply because *no such entity exists*.




Aaron P wrote on Oct. 23, 2009 @ 01:33 GMT
Brilliant essay Lev. I truly beleive a new formalism is the only way for the future. But have you read the essay a few above yours, 'Perfect Symmetry' Somebody mentions 'fruits', which refers to it growinbg the fruits of a system like yours. You have to look hard for it, but I'm sure you'll find it as the methodology he used to get there is so akin to your own.

Aaron

report post as inappropriate


Peter Jackson wrote on Oct. 26, 2009 @ 14:13 GMT
Hi Lev

I noticed your ref to the definition of 'discrete', and criticism of your essay for not arriving at an example. It is a weakness, but;

I use the same method, the word, and do the latter in my own offering. You may not have noticed if you 'skipped over' the essay as it was deliberate test. But a bit too difficult I fear, see the posts! (Perfect Symmetry)

I use the...

view entire post


report post as inappropriate


Narendra Nath wrote on Oct. 27, 2009 @ 09:37 GMT
Dear Lev,

although my comments of Sept 28 have remained unresponded, it may not interest the author to read some further comments that i may make.

We are viewing the universe from within and are thus conditioned by its infinite dominance. Such distractions may well result in limited understanding.

In order to free ourselves we can make use of the capability of our mind when it...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Oct. 27, 2009 @ 20:35 GMT
Hi Peter,

I'll get back to you on your essay's web page a little late: I'm in the middle of a massive house renovation. ;-)

Thanks,

--Lev




Author Lev Goldfarb wrote on Oct. 27, 2009 @ 20:59 GMT
Dear Narendra,

I thought that your comment of Sept. 28 didn’t really need any response, since it is stated as your views.

However, since apparently you do want to see my response here it is.

I may not be quite competent to comment on all the issue you raised, but my essay suggests (my) answers to some of your principle concerns: the connections between the mind and the...

view entire post





Jeffrey Nicholls wrote on Oct. 28, 2009 @ 20:42 GMT
Hi Lev,

I liked your essay. I particularly like the idea of generasting the universe from very simple primitives, consistent with the idea that it started as an initial unstructured singularity.

Also, it seems to me to be implied in the definition of 'universe' that the initial state was subject to no external constraints, contrary to the common idea that somehow the whole future of...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Oct. 29, 2009 @ 21:04 GMT
Hi Jeffrey,

Thanks for the comments!

Following the logic of the propose formalism, it appears that the ‘constraints’ come from the corresponding informational structure rather than from the conventional equations. So for this and other reasons, the proposed informational structure resembles the Platonic (and Aristotelian) forms to a greater extent than the conventional...

view entire post





Eckard Blumschein wrote on Nov. 23, 2009 @ 21:59 GMT
Dear Lev,

Hopefully the reconstruction work in your home is over.

Having looked at most of the many approved contributions to the discussion on your essay, I still wonder why engineers like me seem to have no problems to attribute for instance real-valued and unilateral continuous functions of time to symmetrical complex discrete functions of frequency and vice versa.

...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Nov. 24, 2009 @ 20:55 GMT
Eckard,

It appears that you misunderstood me. The issue of the discrete model that I was talking about has nothing to do with the current use of the term discrete in mathematics/science. So do not get hang up on the term discrete since its current usage is half-hazard. I am actually using the term in a new sense to suggest the need for a completely new kind of scientific...

view entire post





Eckard Blumschein wrote on Nov. 25, 2009 @ 18:02 GMT
Dear Lev,

I looked in vain for "discrete" in your essay but found 2 results for discontinuous, 25 results for primitive, 7 for point and 40 for event.

To me, discrete is the opposite of continuous even if present mathematics deviates from Peirce's definition of a continuum.

Regards,

Eckard

report post as inappropriate


Author Lev Goldfarb wrote on Nov. 25, 2009 @ 18:19 GMT
Eckard,

Please see my posts of Sept. 20 and Oct. 5.




Eckard Blumschein wrote on Nov. 26, 2009 @ 17:40 GMT
Dear Lev,

You already asked Terry Padden to do so. Are we stupid?

Sept. 20:

*In science, the term ‘discrete’ means just the negation of ‘continuous’ and no more*.

-- Mathematics has problems with the notion continuum since Dedekind's "Stetigkeit und Irrationale Zahlen". Numbers are always considered discrete.

So that while all of modern science is based...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Nov. 27, 2009 @ 02:43 GMT
“You already asked Terry Padden to do so. Are we stupid?”

Eckard, the reason I keep pointing to these posts has to do with the fact that for some readers my point is not getting across. ;─)

And reading your last message I understood why it is so (in your case): in a sense, you don’t want to understand it, since as you yourself mentioned, “engineers [at least you] are...

view entire post





Eckard Blumschein wrote on Nov. 27, 2009 @ 12:59 GMT
Dear Lev Goldfarb,

Maybe it is difficult to convey the urgent need you are claiming. Why?

Let me ask a perhaps unexpected but possibly helpful question:

Who made Albert Einstein? It was Max Planck who fostered him.

Now my second question:

Is Planck's constant h really a quantum?

I see it a factor: Energy = h multiplied by frequency can be considered as...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Nov. 27, 2009 @ 16:24 GMT
Eckard, I guess even Schrödinger’s observations (p. 2 of my essay) didn’t help you.

Again, best wishes,

--Lev




Author Lev Goldfarb wrote on Nov. 27, 2009 @ 20:49 GMT
Eckard,

One more thing: natural numbers are not discrete entities any more—as they were originally, thousands of years ago—since they were *completely* integrated into the real number system (see even any text on number theory), so that their discreteness does not play any significant role in science.




Eckard Blumschein wrote on Nov. 27, 2009 @ 22:58 GMT
Dear Lev,

Schroedinger and Einstein preferred the traditional point of view: continuous functions of time. Neither of these physicists was aware of the equivalence between one-sided functions of time and also one-sided functions of frequency just in IR+. They assumed a time block that extends from minus infinity to plus infinity and required complex treatment. Again, nobody understood that...

view entire post


report post as inappropriate


Frank Martin DiMeglio wrote on Nov. 29, 2009 @ 19:27 GMT
Hi Lev. The following cuts to the fundamental core of reality and physics, and it directly relates to the claims/core ideas of your essay as well. I would appreciate your detailed thoughts. Thanks.

According to Jonathan Dickau, my idea of "how space manifests as electromagnetic/gravitational energy" is "right on" as a central and valuable idea/concept in physics.

Since dreams make...

view entire post


report post as inappropriate


Author Lev Goldfarb wrote on Nov. 29, 2009 @ 21:30 GMT
Hello Frank,

So, you finally reached me. ;-)

I must apologize: for a number of reasons, I cannot comment on your pronouncements on dreams, "sensory experience (including gravity and electromagnetism/light)", etc.

(As I mentioned several times, I'm in the middle of a major house renovation.)

My best wishes to you,

--Lev




Anonymous wrote on Feb. 24, 2010 @ 17:59 GMT
One more (probably the most) important point, which should actually be elaborated in a book form.

_______________________________________________________
___________________

It is a historical fact that practically all of our modern mathematics grew out and on the basis of early activities related to *spatial* measurements (of length, in particular). Thus, it is fair to speak of our mathematics/physics as the 'spatial' mathematics/physics.

____________________________________________________________
______________

However, if it will turn out that the space is actually instantiated on the bases of another, more fundamental, discrete, 'mechanism'--as has been suggested in my essay and by a number of quantum gravity researchers--the developed (continuous) mathematics is not as useful as has been implicitly assumed.

That is why we need to encourage at the very least some developments that investigate the above possibility by proposing new, non-spatial, mathematical formalisms, motivated by some reasonably clearly articulated considerations. In that case, if the modeling considerations are sufficiently compelling, one can begin to analyze both formal and modeling implications.

report post as inappropriate


Author Lev Goldfarb wrote on Feb. 24, 2010 @ 18:03 GMT
The previous post is mine.




Login or create account to post reply or comment.

Please enter your e-mail address:

And select the letter between 'C' and 'E':


Note: Joining the FQXi mailing list does not give you a login account or constitute membership in the organization.