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**Jonathan Dickau**: *on* 6/12/15 at 6:35am UTC, wrote Thanks very much Georgina! I'll have to check out the link when I am...

**Georgina Woodward**: *on* 6/12/15 at 5:54am UTC, wrote Hi Jonathan, Thank you for sharing your essay, in particular for...

**Jonathan Dickau**: *on* 4/23/15 at 2:04am UTC, wrote Thank you my friend.. I have just had the pleasure to read and rate your...

**Jonathan Dickau**: *on* 4/23/15 at 2:03am UTC, wrote Thanks greatly Alma, Your comments were gracious. I hope I can return the...

**Akinbo Ojo**: *on* 4/22/15 at 19:02pm UTC, wrote Good to rate those who write good essays and also remain here after the...

**Alma Ionescu**: *on* 4/22/15 at 9:18am UTC, wrote Dear Jonathan, It is very interesting to read an essay where the dynamical...

**Jonathan Dickau**: *on* 4/22/15 at 4:17am UTC, wrote Your thoughtful remarks are most appreciated Cristi.. I try to go to the...

**Jonathan Dickau**: *on* 4/22/15 at 4:13am UTC, wrote Thanks very much Marc.. I am happy that my essay so resonated with you. ...

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Philosophers, physicists and neuroscientists discuss how our sense of time’s flow might arise through our interactions with external stimuli—despite suggestions from Einstein's relativity that our perception of the passage of time is an illusion.

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Objective reality, and the laws of physics themselves, emerge from our observations, according to a new framework that turns what we think of as fundamental on its head.

FQXi FORUM

October 22, 2019

CATEGORY:
Trick or Truth Essay Contest (2015)
[back]

TOPIC: How the Totality of Mathematics Shapes Physics by Jonathan J. Dickau [refresh]

TOPIC: How the Totality of Mathematics Shapes Physics by Jonathan J. Dickau [refresh]

I explore the idea that the Cosmos and the Physics that rules it are a product of the totality of Mathematics. Mathematical objects like E8 and the Mandelbrot Set are important landmarks of Math’s internal structure – and we are fortunate to have mapped them – but there is much more to discover. There may be other constructions of pure Math, yet to be revealed, which like these examples exist as timeless ideals or archetypes of form that shape natural law by their very existence. If nature is ruled by Mathematics in some measure, it has been shaped by all of the applicable Maths since the beginning of time – and nature therefore already honors mathematical rules we have yet to learn. This gives Mathematics, and its study, profound relevance to progress in Physics. Some of the Maths we already know about may play a greater role in Physics than we realize, but the subject of pure Mathematics is also worthy to develop further – because it is likely to reveal many elements of structure and form that are utilized by nature in its laws.

Jonathan Dickau is a multi-faceted individual, with skills that span academic, artistic, and technical endeavors. He has had an inquisitive mind, since an early age, and he has never quite grown up. Since winning a Grammy award for recording Pete Seeger's album "At 89," Jonathan has explored ways he can help the human race to better harmonize with Mother Earth and heal humanity's insults to the planetary biosphere. He lives in upstate New York and works in Audio and Video production, while devoting increasing amounts of time to both writing and academic studies - especially Physics and Mathematics.

Greetings to everyone,

I'd like to thank FQXi for giving me the chance to participate in the essay contest, once again, and to welcome the comments and opinions of my fellow authors, FQXi members, and anyone else who has something to say. While I would enjoy your high regard, I acknowledge that this entry is a bit deficient, instead of the thorough and polished work I had hoped to submit (and have in the past). After starting the writing process early, and with great enthusiasm, I was sidelined most of the last two months - and I hastily finished up at the last minute. I hope this paper meets your approval.

I look forward to some engaging discussions, on this fascinating topic, over the course of the contest.

Have Fun!

Jonathan

I'd like to thank FQXi for giving me the chance to participate in the essay contest, once again, and to welcome the comments and opinions of my fellow authors, FQXi members, and anyone else who has something to say. While I would enjoy your high regard, I acknowledge that this entry is a bit deficient, instead of the thorough and polished work I had hoped to submit (and have in the past). After starting the writing process early, and with great enthusiasm, I was sidelined most of the last two months - and I hastily finished up at the last minute. I hope this paper meets your approval.

I look forward to some engaging discussions, on this fascinating topic, over the course of the contest.

Have Fun!

Jonathan

Hi Jonathan ,

no worries, it certainly does meet with approval. Your enthusiasm shines through even if you don't feel your presentation is as polished as you would like.I enjoyed your descriptions of mathematics in the universe itself. I have been thinking of it as mathematics 'in the wild' controlling what can and does happen, being the relationships at the heart of everything. I also like the idea that you mentioned of lots of kinds of mathematics co-operating. Bringing an ecosystem to my mind- Organisms doing different things but somehow all working together as an entirety.

I'm not sure it is necessary for the mathematics, the relationships, to be distilled from reality and placed in an abstract theoretical space or to assume that the mathematics precedes the concrete universe. It can be distilled into pure maths but that seems to me a bit like distilling the psychology of a man and speculating that it somehow exists separately from the body of the man and the environment in which the man finds himself. (Sensory experiences, thoughts and knowledge can be considered a different facet of reality but they are still within the minds within the concrete reality influenced and shaped by it.)

Thank you for sharing your work with us, I do appreciate it. Kind regards, Georgina

report post as inappropriate

no worries, it certainly does meet with approval. Your enthusiasm shines through even if you don't feel your presentation is as polished as you would like.I enjoyed your descriptions of mathematics in the universe itself. I have been thinking of it as mathematics 'in the wild' controlling what can and does happen, being the relationships at the heart of everything. I also like the idea that you mentioned of lots of kinds of mathematics co-operating. Bringing an ecosystem to my mind- Organisms doing different things but somehow all working together as an entirety.

I'm not sure it is necessary for the mathematics, the relationships, to be distilled from reality and placed in an abstract theoretical space or to assume that the mathematics precedes the concrete universe. It can be distilled into pure maths but that seems to me a bit like distilling the psychology of a man and speculating that it somehow exists separately from the body of the man and the environment in which the man finds himself. (Sensory experiences, thoughts and knowledge can be considered a different facet of reality but they are still within the minds within the concrete reality influenced and shaped by it.)

Thank you for sharing your work with us, I do appreciate it. Kind regards, Georgina

report post as inappropriate

Thanks very much Georgina..

I am happy that my offering meets your approval, even if it was a bit rushed, or feels incomplete to me. The idea of an ecosystem for various activities is one that resonates with me, as well, and I find it is an important consideration for all kinds of endeavor. But as to the core message; I feel like only the messenger, where my discovery forced me to accept something akin to the mathematical universe hypothesis - and I am only now coming to grips with the implications of what I have learned.

All the Best,

Jonathan

I am happy that my offering meets your approval, even if it was a bit rushed, or feels incomplete to me. The idea of an ecosystem for various activities is one that resonates with me, as well, and I find it is an important consideration for all kinds of endeavor. But as to the core message; I feel like only the messenger, where my discovery forced me to accept something akin to the mathematical universe hypothesis - and I am only now coming to grips with the implications of what I have learned.

All the Best,

Jonathan

Dear Jonathan,

I was waiting for an essay from you on this topic. I fully agree with Linas Vepstas that Mandelbrot's set has to be investigated from the point of view of the the modular group SL(2,Z) and modular fonctions

http://www.linas.org/math/sl2z.html

The Monster Group is the topic of my essay where the j-function is the hero.

And this entirely relates to a two-permutation group, a (modular) 'dessin d'enfant'.

Finally, I understand your feeling that the Mandelbrot set is as interesting as Moonshine for doing progress in the understanding of physics, and for shaping physics.

My best regards,

Michel

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I was waiting for an essay from you on this topic. I fully agree with Linas Vepstas that Mandelbrot's set has to be investigated from the point of view of the the modular group SL(2,Z) and modular fonctions

http://www.linas.org/math/sl2z.html

The Monster Group is the topic of my essay where the j-function is the hero.

And this entirely relates to a two-permutation group, a (modular) 'dessin d'enfant'.

Finally, I understand your feeling that the Mandelbrot set is as interesting as Moonshine for doing progress in the understanding of physics, and for shaping physics.

My best regards,

Michel

report post as inappropriate

Thank you my friend..

I appreciate your reference to Linas Vepstas, and his work with modular groups and the Mandelbrot Set. This is a significant thread to follow. As I mentioned on your essay page, this connection is expanded in recent work by Giulio Tiozzo and somewhat in the earlier work by Tao Li.

I also find the Monster fascinating, and I am certain that it plays a part in Physics, as it is one of those archetypal structures shaping whole broad areas of Math. If the totality of Math concept is more than a theory, the Monster group must be essential to understanding some areas of Physics.

All the Best,

Jonathan

I appreciate your reference to Linas Vepstas, and his work with modular groups and the Mandelbrot Set. This is a significant thread to follow. As I mentioned on your essay page, this connection is expanded in recent work by Giulio Tiozzo and somewhat in the earlier work by Tao Li.

I also find the Monster fascinating, and I am certain that it plays a part in Physics, as it is one of those archetypal structures shaping whole broad areas of Math. If the totality of Math concept is more than a theory, the Monster group must be essential to understanding some areas of Physics.

All the Best,

Jonathan

Dear Jonathan,

A nice read. I too share your sense of “oddness” about the 4 normed division algebras and that “one could equally well assert that sums of squares and properties of spheres are what defines the limit on the number of valid algebras”. But I am further surprised by their central importance in physics. In my essay I note in passing that the conditions of causation for continuous fields with a size imposes on any maths theory the very conditions that define the normed division algebras. General Relativity and the Standard Model are in terms of NDA valued fields, but the NDAs seem to lie behind most theories trying to unify them as well. In physics, you can’t seem to escape them … because of their position in maths?

Many thanks for pointing me to this essay contest.

Michael Goodband

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A nice read. I too share your sense of “oddness” about the 4 normed division algebras and that “one could equally well assert that sums of squares and properties of spheres are what defines the limit on the number of valid algebras”. But I am further surprised by their central importance in physics. In my essay I note in passing that the conditions of causation for continuous fields with a size imposes on any maths theory the very conditions that define the normed division algebras. General Relativity and the Standard Model are in terms of NDA valued fields, but the NDAs seem to lie behind most theories trying to unify them as well. In physics, you can’t seem to escape them … because of their position in maths?

Many thanks for pointing me to this essay contest.

Michael Goodband

report post as inappropriate

Gracious thanks Sir,

I appreciate your good regard Michael, especially after reading your excellent essay. I know you are one of the people participating who truly understands why certain fundaments of Math*must* find their expression in Physics. Just as with some of the most basic concepts in geometry and topology, the application of the normed division algebras in Physics is merely an expression of the natural order, and their universality reflects that order.

All the Best,

Jonathan

I appreciate your good regard Michael, especially after reading your excellent essay. I know you are one of the people participating who truly understands why certain fundaments of Math

All the Best,

Jonathan

Jonathan -

A lovely essay and beautiful graphics. I appreciate your faith in mathematics as the form of nature and the eventual pathway for solving the current problems in physics, but wonder if you see any downsides. How do you explain, and/or avoid, the difficulties of self-referential systems and the Godel theorems?

I'd appreciate your thoughts on my essay when you have a chance.

Sincerely - George Gantz

report post as inappropriate

A lovely essay and beautiful graphics. I appreciate your faith in mathematics as the form of nature and the eventual pathway for solving the current problems in physics, but wonder if you see any downsides. How do you explain, and/or avoid, the difficulties of self-referential systems and the Godel theorems?

I'd appreciate your thoughts on my essay when you have a chance.

Sincerely - George Gantz

report post as inappropriate

Thanks George,

I appreciate your comments and have read your wonderful essay. I have no problems with certain varieties of self-referential systems, and I think on some level they are essential to life, but Gödel is another matter; his contribution was brilliant, but only limits a subset of the available options, or is somewhat over-applied as a general limiter on what can be known. Sometimes a priori knowledge, in combination with what can be ascertained through reasoning, provides insights that greatly exceed what formal systems alone can reveal.

All the Best,

Jonathan

I appreciate your comments and have read your wonderful essay. I have no problems with certain varieties of self-referential systems, and I think on some level they are essential to life, but Gödel is another matter; his contribution was brilliant, but only limits a subset of the available options, or is somewhat over-applied as a general limiter on what can be known. Sometimes a priori knowledge, in combination with what can be ascertained through reasoning, provides insights that greatly exceed what formal systems alone can reveal.

All the Best,

Jonathan

Jonathan,

I'm glad you were able to get your essay in on time. You begin by stating "the totality of Math inspires Physics, but this does not exclude or deny the validity of views that math is primarily based on relations arising in physical systems, or change the fact that we could not be here to elucidate Math apart from the physical reality for us to inhabit."

So we're standing on...

view entire post

I'm glad you were able to get your essay in on time. You begin by stating "the totality of Math inspires Physics, but this does not exclude or deny the validity of views that math is primarily based on relations arising in physical systems, or change the fact that we could not be here to elucidate Math apart from the physical reality for us to inhabit."

So we're standing on...

view entire post

report post as inappropriate

Thanks Ed,

You give me quite a lot to think about. I think the biggest determiner of what fundaments find expression in Physics is that structures must be consistent both internally or externally, both globally and locally. That is; a form must agree with itself, and also with the space or universe it inhabits, including any fields the space or its forms might contain.

I see self-agreement of this type and the self-similarity in fractals to be harmonious concepts. There is an internal symmetry to the star-like sunburst shapes, for example, but they conform at the periphery to the surrounding space. This reflects a similar sensibility to your comments, as what is observed from the macro scale is always an inexact symmetry, but asymptotic to an exact and ideal symmetry at the core.

All the Best,

Jonathan

You give me quite a lot to think about. I think the biggest determiner of what fundaments find expression in Physics is that structures must be consistent both internally or externally, both globally and locally. That is; a form must agree with itself, and also with the space or universe it inhabits, including any fields the space or its forms might contain.

I see self-agreement of this type and the self-similarity in fractals to be harmonious concepts. There is an internal symmetry to the star-like sunburst shapes, for example, but they conform at the periphery to the surrounding space. This reflects a similar sensibility to your comments, as what is observed from the macro scale is always an inexact symmetry, but asymptotic to an exact and ideal symmetry at the core.

All the Best,

Jonathan

Dear Jonathan,

Whatever else might be said about Mandelbrot figures, their amazing intricacy is compelling. I watched your youtube video of the "Mandelbrot Butterfly Safari" late last night and it was a real treat - hypnotic and relaxing.

While I would not be surprised to find something like a Mandelbrot mechanism at a fundamental level, we seem to be in the same situation as the creators of the cosmic computer in "Hitchhiker's Guide to the Galaxy". Having used that computer to find the ultimate answer (the number 42) the creators found themselves having to create another computer to find the ultimate question, which had long been forgotten. If quantum mechanics corresponds to the incomprehensible answer, the question might be "where does quantum mechanics come from?" The answer to that question must surely involve the concepts from mathematics you discuss.

Best regards,

Colin

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Whatever else might be said about Mandelbrot figures, their amazing intricacy is compelling. I watched your youtube video of the "Mandelbrot Butterfly Safari" late last night and it was a real treat - hypnotic and relaxing.

While I would not be surprised to find something like a Mandelbrot mechanism at a fundamental level, we seem to be in the same situation as the creators of the cosmic computer in "Hitchhiker's Guide to the Galaxy". Having used that computer to find the ultimate answer (the number 42) the creators found themselves having to create another computer to find the ultimate question, which had long been forgotten. If quantum mechanics corresponds to the incomprehensible answer, the question might be "where does quantum mechanics come from?" The answer to that question must surely involve the concepts from mathematics you discuss.

Best regards,

Colin

report post as inappropriate

Thanks greatly Colin,

I'm glad you enjoyed my essay, and also that you found my Mandelbrot Butterfly video. I figured that since I've already outed myself in the YouTube videos, I might as well engage this topic with my research into this topic highlighted. The 'Hitchhiker's Guide' is a story I love too, and I'm glad to hear you make that connection plain.

Who knows? It may turn out that we live in a neighborhood of the Mandelbrot Set where there are precisely 42 spokes on the wheel of the nearest spiral.

All the Best,

Jonathan

I'm glad you enjoyed my essay, and also that you found my Mandelbrot Butterfly video. I figured that since I've already outed myself in the YouTube videos, I might as well engage this topic with my research into this topic highlighted. The 'Hitchhiker's Guide' is a story I love too, and I'm glad to hear you make that connection plain.

Who knows? It may turn out that we live in a neighborhood of the Mandelbrot Set where there are precisely 42 spokes on the wheel of the nearest spiral.

All the Best,

Jonathan

Dear Jonathan,

I am glad you were able to finish your fine piece. I totally agree with you especially on Hooft's explaination. I totally agree with him except I do think Qbit is the smallest possible and the largest possible Multiverse. Qbit is the atomic unit that describes its bigger self. To quote your quotation from the great physicist Hooft: “What does the calculating? Do we need Planck-sized atoms of space?” And he said “We don’t need atoms of space or whatever, because the laws of nature do the calculating for us.” I do believe infirmation is everything and information is describing information. Alternatively, math describes math universe. It is a self referential system of information that is bootstrapping itself into what we feel and see as our Existence. You have been the last 30 years as an independent researcher to view this new paradigm of math.

I invite you to review mine and as usual you wrote a great essay and I rate it accordingly.

Best wishes,

Leo KoGuan

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I am glad you were able to finish your fine piece. I totally agree with you especially on Hooft's explaination. I totally agree with him except I do think Qbit is the smallest possible and the largest possible Multiverse. Qbit is the atomic unit that describes its bigger self. To quote your quotation from the great physicist Hooft: “What does the calculating? Do we need Planck-sized atoms of space?” And he said “We don’t need atoms of space or whatever, because the laws of nature do the calculating for us.” I do believe infirmation is everything and information is describing information. Alternatively, math describes math universe. It is a self referential system of information that is bootstrapping itself into what we feel and see as our Existence. You have been the last 30 years as an independent researcher to view this new paradigm of math.

I invite you to review mine and as usual you wrote a great essay and I rate it accordingly.

Best wishes,

Leo KoGuan

report post as inappropriate

You are generous Leo KoGuan,

A unit that describes its bigger self can explain how the smallest possible and largest possible systems are alike. And this decidedly is true of the self-similarity seen in fractal forms. In nature; there are ferns whose 'leaves' resemble the fronds, and whose fronds resemble the whole fern - to such a degree that we have exquisite self-similarity there too.

Perhaps; it's not information itself, but the thing we can call knowledge, and is obtained by awareness or observation, that connects the levels of scale, or the abstract and objective universe. The utilization and processing of information is what makes it matter, and so the entity that makes this happen is the key - or explains why we are here. If the Qbit is that kind of unit, as your work would suggest, it is significant.

All the Best,

Jonathan

A unit that describes its bigger self can explain how the smallest possible and largest possible systems are alike. And this decidedly is true of the self-similarity seen in fractal forms. In nature; there are ferns whose 'leaves' resemble the fronds, and whose fronds resemble the whole fern - to such a degree that we have exquisite self-similarity there too.

Perhaps; it's not information itself, but the thing we can call knowledge, and is obtained by awareness or observation, that connects the levels of scale, or the abstract and objective universe. The utilization and processing of information is what makes it matter, and so the entity that makes this happen is the key - or explains why we are here. If the Qbit is that kind of unit, as your work would suggest, it is significant.

All the Best,

Jonathan

Dear Jonathan,

Thank you for the reference to Tiozzo's thesis.

It is interesting that what he defines as a quadratic interval looks the same as what we measure in the "superheterodyne calendar" of my paper [see Fig. 2 and eq. (17)] from continued fractions

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zet

a/planat6.pdf

At least the starting point and the connection to Thurston's "quadratic minor lamination" is encouraging. I would also like to recognize a possible link to the f Farey fractions of hyperbolic polygons (tesselations of the upper-half plane, or of the conformally equivalent unit disk) that I mention in Sec. 3 of my essay.

We know what we have to work on. Thanks.

Michel

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Thank you for the reference to Tiozzo's thesis.

It is interesting that what he defines as a quadratic interval looks the same as what we measure in the "superheterodyne calendar" of my paper [see Fig. 2 and eq. (17)] from continued fractions

http://empslocal.ex.ac.uk/people/staff/mrwatkin/zet

a/planat6.pdf

At least the starting point and the connection to Thurston's "quadratic minor lamination" is encouraging. I would also like to recognize a possible link to the f Farey fractions of hyperbolic polygons (tesselations of the upper-half plane, or of the conformally equivalent unit disk) that I mention in Sec. 3 of my essay.

We know what we have to work on. Thanks.

Michel

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It is my pleasure Michel,

I find it exciting, that some of these connections between different areas of Math are being seen at this time. I am glad this is happening in my lifetime, and I hope to contribute to this process, as I learn more about those connections myself. I also see that Tiozzo has some papers in the pipeline, which offer additional information on some of the relevant topics we have touched on. So the process continues, and the subject evolves.

All the Best,

Jonathan

I find it exciting, that some of these connections between different areas of Math are being seen at this time. I am glad this is happening in my lifetime, and I hope to contribute to this process, as I learn more about those connections myself. I also see that Tiozzo has some papers in the pipeline, which offer additional information on some of the relevant topics we have touched on. So the process continues, and the subject evolves.

All the Best,

Jonathan

Jonathan,

Perhaps I don't understand what you mean by "pure Mathematics." I think math does reveal many elements of structure and form utilized by nature because scientists model them that way. I agree that using math to model physical systems is a very effective way to do physics.

Perhaps my view is simplistic in seeing a integral connection between math, the mind, and physics. What are your thoughts here?

Jim

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Perhaps I don't understand what you mean by "pure Mathematics." I think math does reveal many elements of structure and form utilized by nature because scientists model them that way. I agree that using math to model physical systems is a very effective way to do physics.

Perhaps my view is simplistic in seeing a integral connection between math, the mind, and physics. What are your thoughts here?

Jim

report post as inappropriate

Thanks Jim,

I think that where we agree is that Math and Physics resemble each other because they both partake of the same nature of the process by which things arise. I think that developing a universal measurement protocol is a good way to generate the entire body of Math, for example. And the specific form of the Mandelbrot algorithm speaks to that ideal, where something of great complexity arises from core principles that are very simple - and relate to measurement.

All the Best,

Jonathan

I think that where we agree is that Math and Physics resemble each other because they both partake of the same nature of the process by which things arise. I think that developing a universal measurement protocol is a good way to generate the entire body of Math, for example. And the specific form of the Mandelbrot algorithm speaks to that ideal, where something of great complexity arises from core principles that are very simple - and relate to measurement.

All the Best,

Jonathan

Jonathan,

Time grows short, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I had questions which leads me to your Mandelbrot algorithm: http://www.fractaldesign.net/FractalAlgorithm.aspxrated. I find that the imaginary number discussion and orbits represented on a Cartesian plane are similar to machinations of Euler's Identity that I use. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim

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Time grows short, so I am revisiting essays I’ve read to assure I’ve rated them. I find that I had questions which leads me to your Mandelbrot algorithm: http://www.fractaldesign.net/FractalAlgorithm.aspxrated. I find that the imaginary number discussion and orbits represented on a Cartesian plane are similar to machinations of Euler's Identity that I use. I hope you get a chance to look at mine: http://fqxi.org/community/forum/topic/2345.

Jim

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Jonathan, the mandelbrot set arises in chaotic systems as a natural and universal structure so it is related nicely to my work too. It seems to be a common feature of universal structures that they have a fractal self similar structure as the mandelbrot set does when you zoom in. This is close to what I see happening when iterated quantisation is used to form a universal structure emerging in mathematics. Quantisation itself is then the transformation under which the laws are self similar like a fractal structure. It would not surprise me if the Mandelbrot set turns up in physics at the deepest level in this way just as you suggest.

Your butterfly idea adds an extra level of originality to the use of fractals. Thanks for the mention too.

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Your butterfly idea adds an extra level of originality to the use of fractals. Thanks for the mention too.

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Excellent thoughts Phil!

The universality of the Mandelbrot Set is definitely worthy of note. To see that it shows up in other settings - apart from the familiar algorithmic generator or equation - is surprising but relevant. I should go back to Peitgen and Richter, and include some examples of this in my upcoming paper.

If nothing else, the Mandelbrot Set is full of delightful examples showing self-similar structures that can also be seen elsewhere. And by training eyes and minds to discern such features, we are more likely to see the principles of universality at work in nature's laws.

All the Best,

JOnathan

The universality of the Mandelbrot Set is definitely worthy of note. To see that it shows up in other settings - apart from the familiar algorithmic generator or equation - is surprising but relevant. I should go back to Peitgen and Richter, and include some examples of this in my upcoming paper.

If nothing else, the Mandelbrot Set is full of delightful examples showing self-similar structures that can also be seen elsewhere. And by training eyes and minds to discern such features, we are more likely to see the principles of universality at work in nature's laws.

All the Best,

JOnathan

Jonathan,

I am a little late reading your essay, though I had been anticipating it. I was not surprised that you addressed the Contest Topic in terms of the Topic! While many entrants in any FQXi Essay Contest quite naturally piggy-back their own special interest on any given topic, the harness generally needs an "evener", which is a common accoutrement in Amish Country where I come from. A team of horses is seldom matched in all proportions so a clever piece is built to couple the harnesses and even the load, and spare the less powerful animal being subjected to a greater part of the pull. No such devise is necessary for your superb essay, it IS your specialty!

"The question of whether ideal forms predate their physical representations, and to what extent all physical forms are a representation of their mathematical ideal, remains open." And well it should.

Perhaps there is some thing we might call geometry where the finite value obtainable for rectilinear space is also obtainable for curvilinear space, and we only lack a better way of trying to compute 'pi' that returns a finite ratio. But what we observe physically argues well that we can trust our foundational maths as being inherent to reality. The only difference between space and time might be in that dichotomy of finite vs. infinite geometries. and the origin of energy in a continuum of creation. If 'pi' reaches a finite limit, would energy cease to exist? Is it physically possible to devise a mathematic form that finds easement to directly equate flat geometry with curved geometry? If it were, wouldn't all be symmetric and the universe a singularity?

Your fascination with fractals and the asymmetry at scales is communicated well in your essay, and it should be appreciated by all that you invite the totality of mathematics to the party. Well done, Jonathan! Best wishes, jrc

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I am a little late reading your essay, though I had been anticipating it. I was not surprised that you addressed the Contest Topic in terms of the Topic! While many entrants in any FQXi Essay Contest quite naturally piggy-back their own special interest on any given topic, the harness generally needs an "evener", which is a common accoutrement in Amish Country where I come from. A team of horses is seldom matched in all proportions so a clever piece is built to couple the harnesses and even the load, and spare the less powerful animal being subjected to a greater part of the pull. No such devise is necessary for your superb essay, it IS your specialty!

"The question of whether ideal forms predate their physical representations, and to what extent all physical forms are a representation of their mathematical ideal, remains open." And well it should.

Perhaps there is some thing we might call geometry where the finite value obtainable for rectilinear space is also obtainable for curvilinear space, and we only lack a better way of trying to compute 'pi' that returns a finite ratio. But what we observe physically argues well that we can trust our foundational maths as being inherent to reality. The only difference between space and time might be in that dichotomy of finite vs. infinite geometries. and the origin of energy in a continuum of creation. If 'pi' reaches a finite limit, would energy cease to exist? Is it physically possible to devise a mathematic form that finds easement to directly equate flat geometry with curved geometry? If it were, wouldn't all be symmetric and the universe a singularity?

Your fascination with fractals and the asymmetry at scales is communicated well in your essay, and it should be appreciated by all that you invite the totality of mathematics to the party. Well done, Jonathan! Best wishes, jrc

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Thanks for coming by John,

No apology is needed, because with the sheer number of essays there is plenty to read before you get to mine. I agree though; this topic is tailor-made as a forum for me to introduce ideas I've nurtured for quite some time, to the FQXi community. Honestly; I've spent most of my time in these contests being on the fence, because I had my reservations about both choice A and B. But in this contest; they have given me an incentive to focus on something I am emphatic about, so no fence sitting this time.

Still, I realize that without decisive proof air-tight arguments, I need to be humble and leave room for other possibilities. But after considering the pros and cons for years now; I think I've found a fair number of reasons why the universe must borrow some structures found in Math, as they are the right tool to get the job of creating a universe done. I look forward to reading your essay in the near future.

Warm Regards,

Jonathan

No apology is needed, because with the sheer number of essays there is plenty to read before you get to mine. I agree though; this topic is tailor-made as a forum for me to introduce ideas I've nurtured for quite some time, to the FQXi community. Honestly; I've spent most of my time in these contests being on the fence, because I had my reservations about both choice A and B. But in this contest; they have given me an incentive to focus on something I am emphatic about, so no fence sitting this time.

Still, I realize that without decisive proof air-tight arguments, I need to be humble and leave room for other possibilities. But after considering the pros and cons for years now; I think I've found a fair number of reasons why the universe must borrow some structures found in Math, as they are the right tool to get the job of creating a universe done. I look forward to reading your essay in the near future.

Warm Regards,

Jonathan

Jonathan,

I was so pleased to hear from you, don't spend too much time looking for an essay from me I can get in enough trouble just commenting.

In the post you made on the T or T page 3/22/15 @ 20:41; you explained, "The Mandelbrot formulae involves multiplying a complex number by itself, then adding the result back to the original number. That is; you square the starting value, then add the initial value."

Question; Doesn't squaring a complex value result in a real number, so that then adding the initial complex value reduces the real value of the final result? This appears suspiciously akin to the Lorentz Factor, as well as the exponential function and the inverse square law. Am I dreaming or just profoundly deficient in math tools?

Fondly, jrc

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I was so pleased to hear from you, don't spend too much time looking for an essay from me I can get in enough trouble just commenting.

In the post you made on the T or T page 3/22/15 @ 20:41; you explained, "The Mandelbrot formulae involves multiplying a complex number by itself, then adding the result back to the original number. That is; you square the starting value, then add the initial value."

Question; Doesn't squaring a complex value result in a real number, so that then adding the initial complex value reduces the real value of the final result? This appears suspiciously akin to the Lorentz Factor, as well as the exponential function and the inverse square law. Am I dreaming or just profoundly deficient in math tools?

Fondly, jrc

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Good question John!

Squaring a pure imaginary number gets you a*negative* real number, which then gets added to the original pure imaginary number, and this becomes a complex number - as it has both real and imaginary components. If we start out with a complex number, it will almost always give us a complex result, although sometimes summing makes terms cancel out - and we end up with a pure real, a pure imaginary, or a null result (0,0i).

If we take out the addition step, and just iterate the squaring function, we find that any initial value whose distance is greater than 1 from the origin will grow unendingly, and for initial values whose distance is less than 1 from the origin, the successive values approach the origin or shrink monotonically. Of course; for a value or distance in C of exactly 1, the function remains at the boundary forever, neither growing nor shrinking.

However; when I tried to use a similar shortcut for the Mandelbrot algorithm, by looking for a result that shrinks over 3 successive iterations; I didn't get the Mandelbrot Set at all, and what I found was the Mandelbrot Butterfly instead. Pretty weird, huh?

Regards,

Jonathan

Squaring a pure imaginary number gets you a

If we take out the addition step, and just iterate the squaring function, we find that any initial value whose distance is greater than 1 from the origin will grow unendingly, and for initial values whose distance is less than 1 from the origin, the successive values approach the origin or shrink monotonically. Of course; for a value or distance in C of exactly 1, the function remains at the boundary forever, neither growing nor shrinking.

However; when I tried to use a similar shortcut for the Mandelbrot algorithm, by looking for a result that shrinks over 3 successive iterations; I didn't get the Mandelbrot Set at all, and what I found was the Mandelbrot Butterfly instead. Pretty weird, huh?

Regards,

Jonathan

Dear Jonathan,

I greatly enjoyed you beautifully written essay. It gives me confidence that someone such as yourself who has spent so much time pondering the question has reached conclusions similar to my own.

Please take the time to read, comment on and vote on my essay.

http://fqxi.org/community/forum/topic/2391

Best of luck in the contest!

Rick Searle

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I greatly enjoyed you beautifully written essay. It gives me confidence that someone such as yourself who has spent so much time pondering the question has reached conclusions similar to my own.

Please take the time to read, comment on and vote on my essay.

http://fqxi.org/community/forum/topic/2391

Best of luck in the contest!

Rick Searle

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Dear Mr. Dickau,

I have no wish to be disrespectful to you or your essay, but I think abstract mathematics and abstract physics have nothing to do with how the real Universe is occurring for the following real reason:

Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was...

view entire post

I have no wish to be disrespectful to you or your essay, but I think abstract mathematics and abstract physics have nothing to do with how the real Universe is occurring for the following real reason:

Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was...

view entire post

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Thanks for writing Joe,

I find value in at least some of what you have to say, and I agree even if for very different reasons from yours, because I too think the uniqueness of individual units of form is often unappreciated or trivialized - and indeed like a snowflake each one is different. To assume otherwise is problematic, and prevents one from seeing what is real sometimes.

On...

view entire post

I find value in at least some of what you have to say, and I agree even if for very different reasons from yours, because I too think the uniqueness of individual units of form is often unappreciated or trivialized - and indeed like a snowflake each one is different. To assume otherwise is problematic, and prevents one from seeing what is real sometimes.

On...

view entire post

Dear Jonathan,

Thank you for not reporting my comment to FQXi.org as being inappropriate in order for it to be classified as Obnoxious Spam.

Each quartz crystal has a real surface, and rather than trying to arrange abstract numbers of abstract crystals in a pretty pattern the only thing one needs to know is that the surface of all quartz crystals travel at the same constant speed as...

view entire post

Thank you for not reporting my comment to FQXi.org as being inappropriate in order for it to be classified as Obnoxious Spam.

Each quartz crystal has a real surface, and rather than trying to arrange abstract numbers of abstract crystals in a pretty pattern the only thing one needs to know is that the surface of all quartz crystals travel at the same constant speed as...

view entire post

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Dear Jonathan,

Always something to learn from your essays. Well done!

I have my biased perspective just like others have theirs, hence I have partly pondered the below questions in my essay and I think you should too:

- If there is indeed a Planck lower limit to size ~10^{-35}m, how will the Mandelbrot Set pattern confront this limit?

- On "Planck-sized atoms of space", if indeed space is of such nature, what will separate one atom from another?

- Are the 'laws of nature' or 'atoms of space' eternally existing or can they perish and cease to exist?

Best regards,

Akinbo

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Always something to learn from your essays. Well done!

I have my biased perspective just like others have theirs, hence I have partly pondered the below questions in my essay and I think you should too:

- If there is indeed a Planck lower limit to size ~10

- On "Planck-sized atoms of space", if indeed space is of such nature, what will separate one atom from another?

- Are the 'laws of nature' or 'atoms of space' eternally existing or can they perish and cease to exist?

Best regards,

Akinbo

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I have considered these questions, Akinbo...

1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

All the Best,

Jonathan

1st - the Mandelbrot's cusp at (.25,0i) is the minimum extent and highest energy represented in the Mandelbrot figure. But the theory would indicate that this translates into a minimum time step. However; for anything to persist longer than the Planck time, in this theory, it must have a non-zero size.

2nd - particles act as probes of the properties of a given space, retaining and conveying information about separability and separation. I would say that once forms exist as self-contained independent units, which can move relative to each other, this defines or helps determine the dimensionality of space as well.

3rd - I think part of the meaning of Math is that it preserves some features of natural law that are persistent, from cosmological era to era, from inception to its demise or the beginning of a new cycle, or from universe to universe in a multiverse scenario (more below).

As for atoms of space, however; that concept speaks mainly to how the fabric of spacetime emerges, and one can't discern individual unit cells after that. If space and time are relativistically indistinguishable; then there is a lower limit of around 10^-13 cm - where particle separability is possible - in which Relativity is defined. And item 2 answers this.

The Cosmology based on the Mandelbrot Set does not tell us whether a cold dark end is the universe's ultimate fate, or whether a new cycle would begin, as I can show you the graphical representation of both scenarios. Likewise; it supports the idea that the universe is singular and allows for the possibility of multiple universes. This suggests these possibilities coexist equivalently.

All the Best,

Jonathan

Hi Jonathan,

You get my high mark, even while I disagree with your view of Tegmark's view.

You and Max both approach your respective frameworks for a unifying physical theory with personal, subjective accounts of your journey through mathematics -- Max's hypothesis is not philosophy, however; he explicitly holds forth a way to refute the physical framework.

That's why I have a hard time getting my mind around a particular mathematical structure, such as the Mandelbrot set (or Julia, or Koch or ...) as fundamental to a unifying theory. (Same goes for Lisi's E_8 symmetry.)

For if we allow the fundamental reality of such structures, we lend more meaning to the calculating machinery that creates them, than to relations between and among the quantities and qualities that dominate our physical experience. The former is static and discrete; the latter is dynamic and continuous.

All best,

Tom

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You get my high mark, even while I disagree with your view of Tegmark's view.

You and Max both approach your respective frameworks for a unifying physical theory with personal, subjective accounts of your journey through mathematics -- Max's hypothesis is not philosophy, however; he explicitly holds forth a way to refute the physical framework.

That's why I have a hard time getting my mind around a particular mathematical structure, such as the Mandelbrot set (or Julia, or Koch or ...) as fundamental to a unifying theory. (Same goes for Lisi's E_8 symmetry.)

For if we allow the fundamental reality of such structures, we lend more meaning to the calculating machinery that creates them, than to relations between and among the quantities and qualities that dominate our physical experience. The former is static and discrete; the latter is dynamic and continuous.

All best,

Tom

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Thanks Tom,

This same question was raised by Lorraine on the general discussion page for the contest (Brendan's thread); she asserted that the Mandelbrot Set is 100% boring, and I presented a different view. To me; the static nature of the object belies what's going on beneath the surface (so to speak), where every point on the set is associated with a different flavor of dynamism.

In fact; we can look at the Julia Set for any one point, and study its properties as a dynamical system. This can get boring too, though it leaves room for variations. But when the entire Mandelbrot spawning these Julias is considered, the evolutive properties of the dynamism become apparent. It is this evolution of dynamism that is my primary area of research and interest in M.

All the Best,

Jonathan

This same question was raised by Lorraine on the general discussion page for the contest (Brendan's thread); she asserted that the Mandelbrot Set is 100% boring, and I presented a different view. To me; the static nature of the object belies what's going on beneath the surface (so to speak), where every point on the set is associated with a different flavor of dynamism.

In fact; we can look at the Julia Set for any one point, and study its properties as a dynamical system. This can get boring too, though it leaves room for variations. But when the entire Mandelbrot spawning these Julias is considered, the evolutive properties of the dynamism become apparent. It is this evolution of dynamism that is my primary area of research and interest in M.

All the Best,

Jonathan

Well, of course I don't think that the Mandelbrot set, or any of the variety of self similar sets are boring. The Mandelbrot set, in fact, has earned its title as the most complex object in mathematics.

What I mean, is that the initial conditions for any of these structures are arbitrarily chosen and cannot be shown to be generated from any first principle more general than the spatial assumptions that precede them.

Best,

Tom

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What I mean, is that the initial conditions for any of these structures are arbitrarily chosen and cannot be shown to be generated from any first principle more general than the spatial assumptions that precede them.

Best,

Tom

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Dear Jonathan,

Thank you for your generous comments on my blog. I did not attempt to be on the ridge, there are many snipers! For sure, we will contnue to interact and learn from each other as I experience from many authors at this contest.

Best.

Michel

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Thank you for your generous comments on my blog. I did not attempt to be on the ridge, there are many snipers! For sure, we will contnue to interact and learn from each other as I experience from many authors at this contest.

Best.

Michel

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Jonathan, Sorry I hate this essay. It is entirely too hagiographic, in that it makes mathematics into a Godlike hero. That is entirely unjustified by the facts. What I see is a human illusion that mathematics is effective in physics and a lot of propaganda to justify making mathematics take over the role of GOD. Sorry I am not buying this modern mythology of mathematics as the new GOD.

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I'm sorry too Harry..

But it appears you are judging me by what I didn't write. Perhaps if this contest had a more spiritual slant, asking how Math might shape or be shaped by the nature of the Divine, I would have written something to your liking. I did ponder some questions relating to that matter, in my writing, some years ago. I do not reject God or a belief in God, but I think that even an all-powerful deity would need some amazingly reliable and dependable tools - to create a universe like the one we observe. This is what I think Math provides.

All the Best,

Jonathan

But it appears you are judging me by what I didn't write. Perhaps if this contest had a more spiritual slant, asking how Math might shape or be shaped by the nature of the Divine, I would have written something to your liking. I did ponder some questions relating to that matter, in my writing, some years ago. I do not reject God or a belief in God, but I think that even an all-powerful deity would need some amazingly reliable and dependable tools - to create a universe like the one we observe. This is what I think Math provides.

All the Best,

Jonathan

Dear Jonathan,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Dearly Beloved Jonathan,

I am so excited about your absract,which constitutes a significant commentary on the inseparable coefficiency between Maths and Physics.I am even much more elated with your lucid explanation of the phenomenon in the body of your essay.

Keep on flourishing.

Lloyd Tamarapreye Okoko.

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I am so excited about your absract,which constitutes a significant commentary on the inseparable coefficiency between Maths and Physics.I am even much more elated with your lucid explanation of the phenomenon in the body of your essay.

Keep on flourishing.

Lloyd Tamarapreye Okoko.

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Dear Jonathan,

Thank you ever so much for the terrific you left about my essay.

All real things have a real surface. Real light does not have a real surface. Real light does not consist of abstract photons, or abstract plasmons. It is physically impossible to create a real light by means of manipulating an abstract photoelectric effect.

Proof that real light did not have a real surface was established by the slit test. When the pre-light emission struck the first surface, real light appeared on all of the area of the surface, except of course where the slit, or slits had been cut. The pre-light emission flew through the slit or slits and when they struck the surface behind the slits they had to produce a real light effect that was different than the real light showing on the first surface.

Joe Fisher

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Thank you ever so much for the terrific you left about my essay.

All real things have a real surface. Real light does not have a real surface. Real light does not consist of abstract photons, or abstract plasmons. It is physically impossible to create a real light by means of manipulating an abstract photoelectric effect.

Proof that real light did not have a real surface was established by the slit test. When the pre-light emission struck the first surface, real light appeared on all of the area of the surface, except of course where the slit, or slits had been cut. The pre-light emission flew through the slit or slits and when they struck the surface behind the slits they had to produce a real light effect that was different than the real light showing on the first surface.

Joe Fisher

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Hi Jonathan,

It is a pleasure to meet you in FQXi Essay Contest. Once again, you made an excellent work through a very interesting and enjoyable Essay. Here are some comments:

1) Your idea that Nature has been shaped by all of the applicable Maths since the beginning of time is intriguing. In this way Nature seems a unique sentient being.

2) I am fascinated by fractals. I see that you were a pioneer of fractal cosmology. Is it a coincidence that your original work on this issue is dated 1987, i.e. the same year that Luciano Pietronero and his team attempted to to model the distribution of galaxies with a fractal pattern?

3) I am pleasured to know that you entertained a proposition similar to Tegmark’s MUH long before his framing of it. Congrats, this must be popularized.

4) I did not know Gibbs' statement that “the laws of physics are a universal behaviour to be found in the class of all possible mathematical systems.” I completely agree with Phil. Now, I am going to read his Essay.

5) It is not a coincidence that you have found that the concepts and entities most central or fundamental to Math also have the greatest relevance to Physics.

6) Gerard ’t Hooft's answer “We don’t need atoms of space or whatever, because the laws of nature do the calculating for us” is intriguing and I agree with your interpretation that this means the laws of nature are inherently mathematical.

Finally, I find your Essay extremely intriguing. Thus, I am going to give you a deserved highest score.

I hope you will have a chance to read my Essay.

I wish you best luck in the Contest.

Cheers, Ch.

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It is a pleasure to meet you in FQXi Essay Contest. Once again, you made an excellent work through a very interesting and enjoyable Essay. Here are some comments:

1) Your idea that Nature has been shaped by all of the applicable Maths since the beginning of time is intriguing. In this way Nature seems a unique sentient being.

2) I am fascinated by fractals. I see that you were a pioneer of fractal cosmology. Is it a coincidence that your original work on this issue is dated 1987, i.e. the same year that Luciano Pietronero and his team attempted to to model the distribution of galaxies with a fractal pattern?

3) I am pleasured to know that you entertained a proposition similar to Tegmark’s MUH long before his framing of it. Congrats, this must be popularized.

4) I did not know Gibbs' statement that “the laws of physics are a universal behaviour to be found in the class of all possible mathematical systems.” I completely agree with Phil. Now, I am going to read his Essay.

5) It is not a coincidence that you have found that the concepts and entities most central or fundamental to Math also have the greatest relevance to Physics.

6) Gerard ’t Hooft's answer “We don’t need atoms of space or whatever, because the laws of nature do the calculating for us” is intriguing and I agree with your interpretation that this means the laws of nature are inherently mathematical.

Finally, I find your Essay extremely intriguing. Thus, I am going to give you a deserved highest score.

I hope you will have a chance to read my Essay.

I wish you best luck in the Contest.

Cheers, Ch.

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Dear Jonathan,

How are you? I noticed a valuable post from you on Foster's blog about this contest

"Did you grasp (Sylvain) that Ed Klingman is using Dirac's criterion Sylvain, instead of Pauli's? If you accept Dirac's formula, it naturally follows that Pauli's criterion in QM has a restricted codomain - which is only reasonable if the Physics of the experimental setup demand it. This is what Edwin Klingman calls into question, and changes the outcome if all other logical steps are the same."

Do you mean in the context of Dirac equations?

If so my paper below may be helpful in the sense that it connects Dirac matrices (i.e. two-qubit operators) to the CPT group and the E8 Weyl group. The work was inspired by Socolovsky's paper in Ref. [1] of the paper.

http://xxx.lanl.gov/pdf/0906.1063.pdf (Int.J.Theor.Phys.49:1044-1054,2010 ).

The issue of Bell's theorem is not discussed in the paper although it is implicit through the entangled matrices generating W(E_8). This work had further ramifications as here

http://xxx.lanl.gov/abs/1002.4287 (Physica Scripta 147 (2012) 014025)

It may well be that one can gain much by putting Bell's question in a wider group theoretical frame. But this is part of my present "dessin d'enfant" frame, as you already now. Philosophically, more maths is needed than just Bell's too qualitative arguments and his reference to Bohm's classical (space-time) interpretation.

Best wishes,

Michel

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How are you? I noticed a valuable post from you on Foster's blog about this contest

"Did you grasp (Sylvain) that Ed Klingman is using Dirac's criterion Sylvain, instead of Pauli's? If you accept Dirac's formula, it naturally follows that Pauli's criterion in QM has a restricted codomain - which is only reasonable if the Physics of the experimental setup demand it. This is what Edwin Klingman calls into question, and changes the outcome if all other logical steps are the same."

Do you mean in the context of Dirac equations?

If so my paper below may be helpful in the sense that it connects Dirac matrices (i.e. two-qubit operators) to the CPT group and the E8 Weyl group. The work was inspired by Socolovsky's paper in Ref. [1] of the paper.

http://xxx.lanl.gov/pdf/0906.1063.pdf (Int.J.Theor.Phys.49:1044-1054,2010 ).

The issue of Bell's theorem is not discussed in the paper although it is implicit through the entangled matrices generating W(E_8). This work had further ramifications as here

http://xxx.lanl.gov/abs/1002.4287 (Physica Scripta 147 (2012) 014025)

It may well be that one can gain much by putting Bell's question in a wider group theoretical frame. But this is part of my present "dessin d'enfant" frame, as you already now. Philosophically, more maths is needed than just Bell's too qualitative arguments and his reference to Bohm's classical (space-time) interpretation.

Best wishes,

Michel

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Jonathan,

It was clear the subject was right up your street and you did it good justice in the space available. I'm clearly of the opinion the major 'missing pieces' you identify can be found in the hierarchical structures of fractals, Mandelbrot and also Fibonacci. We must somehow perhaps popularise the concept of phenomena below the 'EM scale' limit of the Planck length.

I've identified that even the simple rules of brackets in arithmetic form such a structure, extending and repeating indefinitely - in my essay, which I hope you get to. I'm very glad I got to yours, my score should give you a deserved boost. After the contest I hope you may also look at this recent (9min but very dense) video identifying some of the solutions which arise from fractal dynamics.

http://youtu.be/KPsCp_S4cUs.

This new paper on the 'twists within twists' of light confirms that concept.)

Accelerated rotation with orbital angular momentum modes

Very well done and best of luck in the run in.

Peter

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It was clear the subject was right up your street and you did it good justice in the space available. I'm clearly of the opinion the major 'missing pieces' you identify can be found in the hierarchical structures of fractals, Mandelbrot and also Fibonacci. We must somehow perhaps popularise the concept of phenomena below the 'EM scale' limit of the Planck length.

I've identified that even the simple rules of brackets in arithmetic form such a structure, extending and repeating indefinitely - in my essay, which I hope you get to. I'm very glad I got to yours, my score should give you a deserved boost. After the contest I hope you may also look at this recent (9min but very dense) video identifying some of the solutions which arise from fractal dynamics.

http://youtu.be/KPsCp_S4cUs.

This new paper on the 'twists within twists' of light confirms that concept.)

Accelerated rotation with orbital angular momentum modes

Very well done and best of luck in the run in.

Peter

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Thank you so much Peter!

Your comments are gracious. I have bookmarked your presentation, and viewed part of it. The linked experiment looks very interesting. People don't realize the strange power of the Bessel beam (using a conical lens). But one can attain a degree of control over the fringes conventional optics cannot offer.

All the Best,

Jonathan

Your comments are gracious. I have bookmarked your presentation, and viewed part of it. The linked experiment looks very interesting. People don't realize the strange power of the Bessel beam (using a conical lens). But one can attain a degree of control over the fringes conventional optics cannot offer.

All the Best,

Jonathan

Dear Jonathan,

One again in this contest, you build upon your fascination with the Mandelbrot set! I have to thank you: it is through the reference in your essay that I got acquainted with Philip Gibbs' "Theory of Theories". Like you, I find fascinating the idea that something like an averaged path integral of mathematical structures could converge to yield something like our physical reality. As you put it, "things are shaped by the totality of math"... intriguing!

Let us keep exploring the mysterious interface between mathematical and physical existence! All the best,

Marc

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One again in this contest, you build upon your fascination with the Mandelbrot set! I have to thank you: it is through the reference in your essay that I got acquainted with Philip Gibbs' "Theory of Theories". Like you, I find fascinating the idea that something like an averaged path integral of mathematical structures could converge to yield something like our physical reality. As you put it, "things are shaped by the totality of math"... intriguing!

Let us keep exploring the mysterious interface between mathematical and physical existence! All the best,

Marc

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Thanks very much Marc..

I am happy that my essay so resonated with you. Over the course of the contest; I have found that many people have dabbled in some of the ideas I explore in my essay, such as the universal path integral you mention. I think it is very cool that by simply comparing notes with the other participants, there is so much to learn.

All the Best,

Jonathan

I am happy that my essay so resonated with you. Over the course of the contest; I have found that many people have dabbled in some of the ideas I explore in my essay, such as the universal path integral you mention. I think it is very cool that by simply comparing notes with the other participants, there is so much to learn.

All the Best,

Jonathan

Dear Jonathan,

Your very well composed, balanced and clear writing style only benefits your arguments. I found a few very powerful ideas in your essay, expressed in a memorable form. Allow me to quote them: “there are some structures that can be described as mathematical invariants, which arise as unchanging patterns within the core of Mathematics, or enduring features of the mathematical landscape, that are timeless and exist apart from any specific construction of that form.” and “That Mathematics is a precursor to Physics is more difficult to prove, than the utility of Math as a descriptive tool for Physics”. Even the question you are posing “Why should pure Mathematics shape Physics?” is deep and striking. Your essay does a very good job at reclaiming and shedding new light on the meaning of math. You are using well-chosen examples and you are illustrating your point with the words and thoughts of classics like Mandelbrot and ‘t Hooft. Congratulations on this great piece!

Warm regards,

Cristi

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Your very well composed, balanced and clear writing style only benefits your arguments. I found a few very powerful ideas in your essay, expressed in a memorable form. Allow me to quote them: “there are some structures that can be described as mathematical invariants, which arise as unchanging patterns within the core of Mathematics, or enduring features of the mathematical landscape, that are timeless and exist apart from any specific construction of that form.” and “That Mathematics is a precursor to Physics is more difficult to prove, than the utility of Math as a descriptive tool for Physics”. Even the question you are posing “Why should pure Mathematics shape Physics?” is deep and striking. Your essay does a very good job at reclaiming and shedding new light on the meaning of math. You are using well-chosen examples and you are illustrating your point with the words and thoughts of classics like Mandelbrot and ‘t Hooft. Congratulations on this great piece!

Warm regards,

Cristi

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Your thoughtful remarks are most appreciated Cristi..

I try to go to the heart of some of the deep concepts that shape this subject, and I am glad that you feel I have succeeded in some measure. I look forward to reading your essay, which I hope will happen before the cutoff time.

All the Best,

Jonathan

I try to go to the heart of some of the deep concepts that shape this subject, and I am glad that you feel I have succeeded in some measure. I look forward to reading your essay, which I hope will happen before the cutoff time.

All the Best,

Jonathan

Dear Jonathan,

It is very interesting to read an essay where the dynamical evolving systems that fractals are playing a key role, because they are the closest relative of symmetry breaking. I enjoyed your insightful remarks about the pattern behind patterns, the mathematical invariants and the internal consistency of theory. My main take away from your essay is the idea that we should further study the way that symmetries are conserved and broken; I think that indeed that is a key area of research, if we are aiming for a complete description of nature. You are doing a very good job presenting new arguments for supporting the mathematical universe, arguments that would have much benefited the initial proposal of this principle, I would dare say. Thank you for a very engaging read! I wish you best of luck in the contest and I accompany my wish with a well-deserved rating.

Warm regards,

Alma

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It is very interesting to read an essay where the dynamical evolving systems that fractals are playing a key role, because they are the closest relative of symmetry breaking. I enjoyed your insightful remarks about the pattern behind patterns, the mathematical invariants and the internal consistency of theory. My main take away from your essay is the idea that we should further study the way that symmetries are conserved and broken; I think that indeed that is a key area of research, if we are aiming for a complete description of nature. You are doing a very good job presenting new arguments for supporting the mathematical universe, arguments that would have much benefited the initial proposal of this principle, I would dare say. Thank you for a very engaging read! I wish you best of luck in the contest and I accompany my wish with a well-deserved rating.

Warm regards,

Alma

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Good to rate those who write good essays and also remain here after the contest to engage intellectually. My rating didn't seem to change the score but certainly will neutralize the 1-bombers.

Regards,

Akinbo

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Regards,

Akinbo

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Hi Jonathan,

Thank you for sharing your essay, in particular for reminding me about fractals, how wonderful they are, and for showing us your butterfly set. Also thanks for responding to the many comments.

I thought you might find this you tube video TED talk interesting if you haven't already come across it. Michael Hansmeyer talking about building shapes that can not be imagined because they are too complex and at a scale of folding that can't be carried out by human beings. He shows that how to produce these shapes can be thought about quite simply, even though the output itself is unimaginable. It is a very simple process likened to morphogenesis and he mentions breeding of types to produce new designs. He also mentions designing processes rather than shapes in the future. So it seems we are not limited by our imagination. Michael Hansmeyer: Building unimaginable shapes.

I also posted it on Silvia Wenmackers discussion as she wrote and talked about being unable to imagine the unimaginable. Best wishes, Georgina

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Thank you for sharing your essay, in particular for reminding me about fractals, how wonderful they are, and for showing us your butterfly set. Also thanks for responding to the many comments.

I thought you might find this you tube video TED talk interesting if you haven't already come across it. Michael Hansmeyer talking about building shapes that can not be imagined because they are too complex and at a scale of folding that can't be carried out by human beings. He shows that how to produce these shapes can be thought about quite simply, even though the output itself is unimaginable. It is a very simple process likened to morphogenesis and he mentions breeding of types to produce new designs. He also mentions designing processes rather than shapes in the future. So it seems we are not limited by our imagination. Michael Hansmeyer: Building unimaginable shapes.

I also posted it on Silvia Wenmackers discussion as she wrote and talked about being unable to imagine the unimaginable. Best wishes, Georgina

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Thanks very much Georgina!

I'll have to check out the link when I am awake. Hansmeyer's content sounds really cool. But fractals are like that; a simple seed lets one create forms of unimaginable beauty and complexity - and that's how nature works too!

My gratitude for sharing this, and for your appreciation of my contributions.

All the Best,

Jonathan

I'll have to check out the link when I am awake. Hansmeyer's content sounds really cool. But fractals are like that; a simple seed lets one create forms of unimaginable beauty and complexity - and that's how nature works too!

My gratitude for sharing this, and for your appreciation of my contributions.

All the Best,

Jonathan

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