[deleted]
Amazing essay!
Amazing essay!
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 Perelman's proof of the Thurston Geometrization Conjecture, we have a bit more inkling of how n-dimensional extensions, n > 3, may create feedback effects to our familiar world of Lebesgue measure. Connectedness is nearer than we used to think.
-- Structs.
Nice coinage. Consider that the primary characteristics of a self organizing system are self similarity and self limitation. I think that a mathematical model awaits this concept of structs--and I think that the complex system idea of multi-scale variety (Y. Bar-Yam, New England Complex Systems Institute, necsi) will drive it.
--Time
Your idea of time as information (2.3.3) is precisely echoed in my ICCS 2007
paper, "Time, Change & Self-Organization." (1.3.0) [www.necsi.org].
I wish you the best of fortune. Thanks for a great paper.
Tom
Let me see if I can get the link right. [link:necsi.org]
Sorry. I am just not proficient at this. necsi.org
Tom
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. ;-)
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.
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?
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
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.
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
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?
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 combined love and devotion--in the same sense that Spinoza meant: "amor dei intellectualis." That is a rational love. I.e.,the same emotion that attends love for understanding nature attends love of another person, whether a relationship is physical or not. Physical intimacy that often passes for love is only one expression of devotion. A sexual relationship is not necessarily intimate nor devotional.
I don't really know how most scientists approsch their work. I rarely discuss it with them. Sometimes, it is a delight to surprise oneself. :-)
Tom
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.
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 _kinesthetic_ sensation toward his theories; he felt it in his bone and muscle in a literal, not metaphorical, sense. When you speak of flesh and blood sensations as characterizing physical love--I am saying that some people really do have the demonstrable capacity to experience love as rational spirituality (Spinoza, Buber, et al) that is accompanied by physical sensation. (Schrodinger was notorious for his romantic liaisons; one wonders about a connection between his intellectual output and his physical appetites.) Perhaps all of us have a latent capacity to combine devotion toward intellectual pursuits with physical sense:
Keith Devlin, the renowned mathematics poularizer with a grandly universalist view, argues that there is no "math gene" that endows one with talent to do mathematics; he even goes further, to point out the mathematical patterns that animals exhibit without apparently conscious effort.
Back to Einstein, I had occasion recently to respond to another participant in this forum rgarding Einstein's doubts (as you mention in your essay) about the ability of continuous functions to describe how the world really works. In the final paragraph to Appendix II, "Relativistic Theory of the Non-Symmetric Field," from [Einstein, 1956, The Meaning of Relativity] Einstein wrote "One can give good reasons why reality cannot at all be represented by a continuous field. From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum numbers). This does not seem to be in accordance with a continuum theory, and must lead to an attempt to find a purely algebraic description of reality. But nobody knows how to obtain the basis of such a theory."
As for me, I am in full accord with your thesis as it regards the independence of language and meaning, a subject I have also adressed in several papers since 2002. I am aware that mathematics is what I do, not what I am. Loving what one does, however, is also a sensual, consuming experience.
All best,
Tom
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 *forgive* all kinds of blemishes, and this is why in spite of the general agreement that, as Feynman put it, "nobody understands quantum mechanics", practically all physicists *love* it. On the other hand, if you *worship* the Nature--remember Einstein's relatively frequent use of "Lord" for "Nature"-- you will not be satisfied with your 'offering' unless it is without any serious imperfections.
Of course, all of this is particularly applicable to our time, to what we do to even a greater extent, since we are facing an unprecedented scientific transition, and what is at stake is, again, the *quality* of our visions.
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 impression that Einstein's love of nature (The Old One, The Good Lord, etc.) was anything more than what he professed it to be, deference to Spinoza's God for which amor dei intellectualis is the highest expression of one's devotion to truth and understanding in a universalist, pantheistic context. I don't think one can charcterize that as worship in a conventional sense.
And what does "imperfection" mean, in the context of a physical theory? Both quantum mechanics and general relativity are mathematically complete theories, with correspondence to physical phenomena. In that sense, they are perfect. But again, given the independence of language and meaning--not perfectly meaningful, against the magnificence of creation that we experience.
Well anyway, I appreciate the high quality of _your_ vision.
Tom
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. ;-)
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
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'. ;-)
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 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 philoTsophy" and to look for the new fundamental formal structures which would replace that dichotomy and capture more adequately the presently quite hazy, dichotomous 'reality'. ;-)"
-------------------------------------
To echo your response, Lev, our current concepts are all we've got! :-)
As I quoted, Einstein also believed that new mathematical methods are necessary to reconcile the discrete with the continuous. (That's my aim, with an extradimensional model that compels, for lack of better terminology, an algebra of continuous functions.)
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