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FQXi FORUM
October 24, 2019

CATEGORY: Questioning the Foundations Essay Contest (2012) [back]
TOPIC: The Place of Geometry in Physics by Patrick Alan Hutchinson [refresh]
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Author Patrick Alan Hutchinson wrote on Aug. 8, 2012 @ 12:16 GMT
Essay Abstract

Much modern theory tries to unify quantum theory with general relativity by making the model of space-time quantized. Perhaps instead the linear function model underlying quantum theory might be replaced with a nonlinear function theory based on geometry and variational calculus.

Author Bio

Name: Alan Hutchinson Birth: 1948 Nationality: British Education: MA, MMath (Cambridge); MSc, MPhil (Warwick) Employment: Programmer (1976-83) Lecturer, Computer Science (1983-85 at UMIST; 1985-2010 at KCL) Married with three children Interests include family, bell ringing, cycle touring, Alpine walking, Go, psychology

Download Essay PDF File

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Frank Makinson wrote on Aug. 8, 2012 @ 20:59 GMT
Alan,

Congratulations, this is the first essay where the term soliton is used. I had made a statement about the lack of recognition of solitons in a comment to Peter Jackson's essay, topic 1330.

"Einstein developed his theories with 'incomplete information', because he, his generation, and all those preceding, did not recognize that the system we live in provides mechanisms for the efficient transfer of energy, and the soliton is one manifestation of the mechanism."

Even though solitons are being found in all types of processes, the cherished fundamental assumptions have not been updated to account for that "not unusual" wave phenomenon. Solitons easily mesh with an electromagnetic theory of gravity if the EM field has the proper configuration.

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Author Patrick Alan Hutchinson replied on Aug. 8, 2012 @ 22:02 GMT
Frank

Thanks. I have been to meetings where authorities talked about solitons, and have read just a bit about them, but please don't regard me as an expert. They are undoubtedly pretty. Lots of good maths has emerged from the study of differential equations, and I expect there is more to be had from solitons, so it is a bit surprising that they have not excited more enthusiasm. Of course, I am not at all sure that the variational approach suggested in the essay will produce any solitons, but it is a possibility.

Alan.

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Edwin Eugene Klingman wrote on Aug. 9, 2012 @ 03:32 GMT
Dear Patrick Alan Hutchinson,

Absolutely delightful! It's hard to imagine one can pack so much into 9 pages and still be fun to read.

I was intrigued by your non-linear quantum model, which has similarities to my own, based on a non-linear field, but linearized to allow Schrodinger equation. There are also geometric particle creation aspects of the model that I don't touch on in my current essay, The Nature of the Wave Function. Thus my physical waves cannot be added, but of course the probability amplitudes can. I invite you to read my essay and comment.

Thank you for a very powerful essay -- Excellent!

I agree with your conclusion and vote for the "or else" clause. I hope you enjoy my naive approach to this.

Edwin Eugene Klingman

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Anonymous wrote on Aug. 9, 2012 @ 19:08 GMT
Dear Edwin

Thanks for your kind comments. There is a lot in your essay too, and before I shall be up to grasping it all I must read Bell and Christian, which I have never attempted. Christian's algebra looks like a combination of exterior algebra and Clifford algebra, so that much should be straightforward, but Bell's work sounds deep. You have clearly put much thought into it.

Best wishes

Alan.

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Jayakar Johnson Joseph wrote on Aug. 9, 2012 @ 20:47 GMT
Dear Patrick Alan Hutchinson,

Perhaps, the mutual distortion of two interacting particles from their point like description is indicative of the probability of string like existence of particles, in that Functional analysis in calculus of variations is applicable for the transformation and thus the gravity may be expressional.

With best wishes,

Jayaker

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Author Patrick Alan Hutchinson wrote on Aug. 10, 2012 @ 00:10 GMT
Dear Jayaker

Sorry. I don't understand this.

Any "point like description" is not an aspect of the model. If ever a particle is perceived as point like, then this would be just what we fallible human beings sometimes perceive, no more. I think psychologists and neurophysiologists sometimes agree that our perceptions are just reflections of flawed representations in our limited brains of incomplete observations of selected aspects of reality. We sometimes perceive "points" when there are no point-like objects. If my proposed model has any similarity to reality then there will be no point-like features in any particles.

I don't doubt that string theory is wonderful. I have heard a great man whom I admire talk about it more than once. Despite that, nothing has yet convinced me that it has any bearing on reality. If you like, you can look on my essay in part as my excuse for not spending time trying to understand it.

Best wishes

Alan.

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Author Patrick Alan Hutchinson wrote on Aug. 10, 2012 @ 06:16 GMT
Hello again Jayaker

Please forget most of the long paragraph in my last mail. It was written around midnight and I wasn't thinking straight.

We do perceive particles as points, and in the essay I went to some lengths to conjecture why, and suggested that perhaps they really are small. If any of those conjectures are right, it will be because the partial differential equations for the connection and metric have such solutions.

Best wishes

Alan.

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Ted Erikson wrote on Aug. 13, 2012 @ 15:13 GMT
Having just completed, but not yet submitted, I am in process of reviewing similar approaches.

I am a simple aged educated swimmer from the "slide rule era", knowing only add, subtract, multiply, and divide with a reasonable understanding of geometry, ala Fuller's Synergetics and Physics.

The fact that an inscribed sphere, tangent to the faces of a regular tetrahedron have exactly the same surface-to-volume ratio, i.e. boundary to different content content imply equivalent "activity" as free energy. This is a simple model to apply from particle sizes (unbounded) to massive (elephants and the cosmos) to many problems. All things have a frequency of existence for equal activities of matter and energy!

Comment?

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Author Patrick Alan Hutchinson replied on Aug. 13, 2012 @ 19:32 GMT
Ted Erikson

I too used a slide rule.

The geometry in my submission is Riemannian geometry, the sort occurring in general relativity. Maybe I should have made that clear.

Your remark about the sphere inscribed in a regular tetrahedron sounds quite subtle.

Best wishes

Alan H.

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Peter Jackson wrote on Aug. 22, 2012 @ 17:29 GMT
Alan

Frank cited my essay above in context with the soliton. But I find greater consistency with yours as the only other essay so far (I've read) to recognise and explain the importance of the detector as part of the process.

I go on to explore a real ontological construction, with exciting results, but find only a simple mathematical description (see my end notes) of various relative kinetic cases.

Long ago I found issues with maths and geometry. Motion is an invalid concept in geometry and I particularly challenged it's validity in algebraic vector space, where the word 'frame' is assumed as a 'wire frame' which can overlap with other in Cartesian systems. Using non point particles interacting, including with just waves, over non zero time resolves this. Space-time is indeed then 'granular'.

In constructing the ontology with logic I can't express it mathematically, but am sure you can. In particular the nested mutually exclusive structure of truth propositional logic applies, along with an interpretation of the 'interleaved' modes of Propositional Dynamic Logic. (Each representing a discrete and equivalent 'Space time geometry'). Enough of mine but please do read, analyse (beneath the theatrical metaphors) and comment.

I find the heart of yours in the paragraphs;

"If the solution were known exactly at some instant before the interaction then a numerical calculation could reveal the free space states which the detectors would converge to afterwards. However, uncertainty is inevitable because we, our memories, and any possible measuring apparatus are part of the solution. No solution is capable of discovering and internally representing what it itself is.

...In every free space solution for a detector, either the detector has detected the quantum or it has not. After diffraction, the solution almost certainly converges to just one such set of overlapping free space solution because any other solution would be unstable."

Please expect a top score from me if only for that. You should find my real local nature equivalent, and I'm quite convinced by the vast evidence I have beyond the essay that we have the key to the toe. (Many others here are also consistent).

Very best wishes.

Peter

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Author Patrick Alan Hutchinson replied on Aug. 30, 2012 @ 08:09 GMT
Hello Peter

Thanks for your kind comment. I have been away, and only just found it. Hope to read yours soon.

Regards

Alan (the name I usually use).

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Peter Jackson wrote on Aug. 22, 2012 @ 17:34 GMT
Patrick

Too much excitement. Sorry for the middle name above.

And just when I'd got head round slide rules calculators and computers arrived. I never did quite get my head round those!

Peter

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Gurcharn Singh Sandhu wrote on Sep. 11, 2012 @ 13:10 GMT
Dear Alan,

I like your excellent essay and appreciate your viewpoint. I wish you good luck in the contest.

As you know, our community ratings will be used for selecting top 35 essays as 'Finalists' for further evaluation by a select panel of experts. There is a possibility of existence of a biased group which promotes the essays of that group by rating them all 'High' and jointly demotes some other essays by rating them all 'Low'. Therefore, any biased group should not be permitted to corner all top 'Finalists' positions for their select group.

In order to ensure fair play in this selection, each participants in this contest should select about 50 essays for entry in the finalists list and RATE them 'High'. Next they should select bottom 50 essays and rate them 'Low'. Remaining essays may be rated as usual, if time permits. If all the participants rate at least 100 essays this way then the negative influence of any bias group will certainly get mitigated.

You are requested to read and rate my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space".

Finally I wish to see your excellent essay reach the list of finalists.

Best Regards

G S Sandhu

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Yuri Danoyan wrote on Sep. 14, 2012 @ 11:59 GMT
Patrick

I don't grabbed the essence of your essay .. maybe you'll understand my work.?

http://fqxi.org/community/forum/topic/1413

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Author Patrick Alan Hutchinson wrote on Sep. 14, 2012 @ 21:21 GMT
Hello Yuri

Thanks for your note.

I have looked at your essay, and you seem to be trying to do something rather different from what I tried to do. Your aim seems to be to fit all the phenomena which experimental physicists observe into patterns such as the ratio "3:1". If you can do this neatly, and in such a way that it lets people make predictions which can be tested, that will be an important approach.

In broad outline, maybe I am trying to do something similar, but the details are very different. Where you try to fit numerical patterns, I am trying to fit patterns from Riemannian geometry and partial differential equations.

I once studied in a department led by a lovely man called Jim Eels. When people asked him what he studied, he (I think) sometimes replied "Soap bubbles". The point about a soap bubble is that it is a solution to a problem which can be expressed by a partial differential equation, and in the set of all such solutions it has least energy. This is an example of a "VARIATIONAL PROBLEM". Variational problems and their solutions have been very successful in past attempts to describe physics.

In this case, I am trying to guess what the right variational problem might be. The lovely aspect which gives me courage to submit this essay is that there are the two features called
and
which emerge easily out of algebra which other people have already discovered from the Riemannian geometry. With them, one can easily invent a variational problem which seems to have all the subtlety necessary to construct a unified field theory.

That is the essence of my essay. Of course, it will all be useless unless someone can show that this variational problem really does lead to a solution which resembles what experimental physicists observe. I am a long way from checking that.

Regards, Alan H.

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Ed Unverricht wrote on Sep. 18, 2012 @ 17:55 GMT
Alan,

I have read and greatly enjoyed your essay. I have spent time attempting to construct computer models of Dirac's version of the electron. Computer models can attempt to show properties of the underlying algebra's. I was struck by your goal:

"The objective of this essay is to try to shift the emphasis from SM and algebra to GR and geometry." and "How to make geometric models"

based on

"The only justification for the algebra in SM is that it fits observed patterns among particles. The algebra in D was invented out of geometry half a century before Dirac's work. GR contains no such algebra. It is essentially pure geometry."

I would be interested in your comments on my model of a Dirac Spinor at essay 1306 (pg 6), it also includes a link to a video animation to better display its properties.

I became interested in this model (a blue electrical loop surrounded by a perpendicular torus of red magnetic lines) where one turn of the blue loop only represents 1/2 a turn of the red loop, producing an object with 720 degrees of freedom (it looks upside down after turning 360 degrees).

Would you consider these types of models legitimate geometric models of your algebras?

Many Regards.

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Author Patrick Alan Hutchinson replied on Sep. 19, 2012 @ 21:41 GMT
Hello Ed

Thanks for your note. It is nice to hear you enjoyed it. I looked at yours. I was not able to get the full sense of it because some of your very careful pretty graphics use "flash" which is not open source software, so I have not installed it on my PC.

Parts of the accompanying text read much like the Bohr model of atomic structure (see Wikipedia for an outline). Since Bohr published it, I think quantum mechanics has gone through two substantial revisions. In the first revision, electrons (and all other particles too) were represented by waves, rather than as small points. In the second, the nature of the kind of measurement which can be made on the force fields between particles was changed. In the Bohr model and its first revision, all measurements of properties of the field just provided a numeric value. After the second revision, any such measurement might cause a change in the field.

Anyone who can write a program which faithfully models this kind of idea is doing the rest of us a service. I think you are undertaking an ambitions poject.

Best wishes

Alan H.

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M. V. Vasilyeva wrote on Sep. 19, 2012 @ 01:27 GMT
Mr. Hutchinson,

I enjoyed reading your essay. I too advocate geometry as means of better understanding based on visualization of underlying processes in physics. One thing that remained unclear to me in your essay is the number of dimensions in the geometry you propose. And by the way, what do you think of Octonion Algebra? As for me, I offer a geometrical model of space and show that the addition of just one spatial dimension, the 4th, dispels most paradoxes that plague physics today. My vision is purely geometrical and my approach is top down, based on the hypothesis that 4D configuration corresponds to the lowest energy state for the dynamic structure of space. I would very much appreciate your feedback.

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Author Patrick Alan Hutchinson replied on Sep. 19, 2012 @ 22:04 GMT
Hello Ms Vasilyeva

Thanks for your kind remarks.

Throughout my essay, I stick to the traditional notion that we are in a space with 3 space dimensions and 1 time dimension. Four space dimensions are very different from three, and three suffice for all I want to write. For instance, it is not possible to tie a knot in a piece of string in 4 dimensions. Other funny things happen, e.g. there are many different versions of the notion of smoothness in 4 dimensions. All this makes good fun for mathematicians. The same goes for quaternions. They are well worth studying for their own sake, but as yet I don't know of any reason to suppose they will help to illuminate physics. I may be completely wrong about this.

Best wishes

Alan H.

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Hoang cao Hai wrote on Sep. 19, 2012 @ 14:44 GMT
Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regards !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Member Benjamin F. Dribus wrote on Sep. 25, 2012 @ 20:38 GMT
Dear Alan,

I enjoyed reading your essay, which I think is both well-motivated and well-explained. I have a couple of questions/remarks.

1. Like you, I tend to find certain aspects of quantum theory and quantum field theory less well-motivated than relativity, which is based on simple physical principles. In particular, even in ordinary quantum theory, I am not very fond of the...

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Author Patrick Alan Hutchinson replied on Sep. 27, 2012 @ 17:03 GMT
Hello Ben

Thanks for your note. Some (maybe) short responses:

1. Describing states with functions in a Hilbert space does not of itself worry me. The functions are functions on space-time, which seems to be what is wanted if particles are diffuse. The problems arise when one tries to combine this kind of account with GR.

2. Asselmeyer-Maluga's essay is not easy reading, but it is an eye opener. I have looked at a few of his papers on arXiv, and at a summary of a book cited in one of them. The idea that matter arises through exotic smooth structures appears at first outlandish, but the effect of the sort of surgery he considers on connections seems to fit rather neatly with Einstein's notion of matter in GR. I am as yet far from understanding it all properly.

3. Hopf algebras seem to pop up in lots of places.

It will take a lot to disconnect physics from manifolds, after the success of GR. I like manifolds. Have you seen John Milnor's little book: "Topology from the differentiable viewpoint"? I read that long ago, and was hooked. The only caveat is that he says nothing about differential forms. I ought to have understood them too.

bw

Alan H.

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Member Benjamin F. Dribus replied on Sep. 28, 2012 @ 03:25 GMT
Dear Alan,

I never read that one, which is funny seeing that I've read a fair bit of his other work (K-theory, etc.) But I would consider myself "hooked" as well, at a mathematical level: I like Griffiths and Harris's Algebraic Geometry (complex manifold viewpoint), and Spivak's 5-volume set on differential geometry is good. Claire Voisin has written two excellent books on Hodge theory and complex algebraic geometry. I also like Hatcher's algebraic topology and Adams' old book about spectra. I think Carroll, Wald, and Hawking and Ellis are all good for GR, though at different levels. These days it seems more and more profitable to look for material online, however.

I agree that "it will take a lot to disconnect physics from manifolds," but "disconnect" is a rather strong word. To believe that manifolds are an immensely useful and astonishingly accurate tool (given their highly idealized properties) to use for physics is not incompatible with a recognition that they also raise some serious issues, which always seem to arise precisely in regard to those properties which seem least physically relevant. In criticizing manifolds as fundamental, I probably come across as much more "anti-manifold" than I actually am.

By the way, there are some other contributions from the "pro-manifold forces" here which you might enjoy if you haven't already read them: the shape dynamics essays (Barbour, Gryb/Mercati, Alves), the "desingularization" paper by Abhijnan Rej and the "singular" one by Cristinel Stoica, and of course the one by Krol that I mentioned before.

Anyway, I am sure manifolds have a lot more to offer physics, regardless of my opinions! Take care,

Ben

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Author Patrick Alan Hutchinson replied on Sep. 28, 2012 @ 08:58 GMT
Dear Ben

Thanks for your note of this morning. In particular, thanks for all the references. Someone once offered to get a copy of the 5-volume Spivak set for me, and I didn't take him up. I should have done.

In particular, thanks for the suggested reading list of other essays. The range of contributions is enormous, from no maths to the wildest ideas, right up to topos theory. I am just looking at the one by Abhijnan Rej, which seems to touch on the theory of infinite Galois groups and, perhaps, something called the Krull topology which was the subject of the very last lecture of a course which went beyond the syllabus of the final year of my first degree. Out of a large class, only 5 or 6 of us attended it.

Much of it is wonderful stuff, but what all this might have to do with physics mystifies me. It seems that one can get a very long way with just the ideas underlying the theories of Einstein and Dirac: a 4-dimensional Riemannian manifold, and the algebra derived from its Riemannian structure, and maybe a variational principle. Anything beyond that counts as good clean fun, but not physics until there is evidence otherwise.

bw, Alan H.

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Viraj Fernando wrote on Sep. 26, 2012 @ 04:24 GMT
Dear Patrick,

I read your essay with interest. I too have taken a Geometric approach. However, unlike yours, it concerns very simple Geometric relationships leading to trignometric expressions between related phenomena. It makes relativistic phenomena quite understandable visually. I am sure you would like my essay

The gist of my essay:...

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attachments: 2_Primordial_Foundational_Problems.doc, 2_GEOMETRODYNAMICS_OF_ENERGY.doc

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Author Patrick Alan Hutchinson replied on Sep. 27, 2012 @ 17:22 GMT
Hello Viraj

Thanks for your comments. As there are so many submissions, it is hard to know where to start reading. I have been trying to understand Asselmeyer-Maluga's ideas. I don't know if his essay will be the winner, but certainly there are enough new ideas in it to keep me occupied for a few months. A lot of the fancy maths which gets talked about seems to be just that. He and the other writers he cites make it seem that the notion of exotic smooth structures could fit neatly into GR. Have you looked at his work?

As to assessment: it does seem to give each of us reason to not vote as perhaps we should. I don't know what to do about it. Maybe just live with it, and vote with one's heart. It is a bit like the prisoner's dilemma.

bw

Alan H.

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Member Tejinder Pal Singh wrote on Sep. 26, 2012 @ 13:44 GMT
Dear Peter,

Thank you for your remarks on my post. I very much enjoyed reading your essay. The idea of an asymmetric component of the metric [possibly implemented through non-commutative geometry] leading from classical to quantum dynamics has always been fascinating for me. I have played around with it in some of my simplistic papers, but without much success yet. More promising, as of now, seems to be the the theory of Trace Dynamics developed by Stephen Adler and collaborators, which seems to have strong elements whereby noncommutative classical dynamics gets connected to quantum dynamics.

Regards,

Tejinder

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Anonymous wrote on Sep. 28, 2012 @ 13:12 GMT
Dear Alan,

I agree with you about the role of geometry in physics. Indeed, bundles over manifolds, having as fiber various structures, are responsible for much of the progress attained so far, and even more is expected to come. Quantum mechanics too has much to gain from geometry, which indeed may be the connection between QM and GR. I sketched somethign about this in these slides. Congratulations for the essay and good luck with the contest.

Best regards,

Cristi Stoica

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Author Patrick Alan Hutchinson replied on Sep. 29, 2012 @ 20:13 GMT
Dear Cristi

Thanks for reading my essay, and for your kind remarks on it, and for the link to your slides which I have read. Quite apart from your discussion, they taught me some physics I didn't understand before.

My immediate reaction is that your conclusion "indeterminism exists only in the initial conditions" sounds almost right. Maybe one might add that this indeterminism will never be resolved by us poor mortals because "we, our memories, and any possible measuring apparatus are part of the solution. No solution is capable of discovering and internally representing what it itself is". One aspect of this is that, in this universe of which we are part, no computer can have more gates and memory cells than there are elementary particles. We cannot construct a computer which will extrapolate numerically from any given possible initial condition with unlimited precision.

Best wishes, and trusting your slide presentation will be well received. Alan H.

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Sergey G Fedosin wrote on Oct. 4, 2012 @ 07:27 GMT
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
and
was the quantity of people which gave you ratings. Then you have
of points. After it anyone give you
of points so you have
of points and
is the common quantity of the people which gave you ratings. At the same time you will have
of points. From here, if you want to be R2 > R1 there must be:
or
or
In other words if you want to increase rating of anyone you must give him more points
then the participant`s rating
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.

Sergey Fedosin

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