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Wandering Towards a Goal Essay Contest (2016-2017)
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TOPIC: Putting the Elephants to Work by Jonathan J. Dickau [refresh]

TOPIC: Putting the Elephants to Work by Jonathan J. Dickau [refresh]

A conversation with Tevian Dray, on the last day of GR21, brought to light some of the ‘elephants in the room’ with quantum gravity researchers and highlighted the essential part played by non-associative Maths – in any robust formulation attempting to address those looming concerns. While this is seen as a complication by most researchers; I assert that it is instead a clear road to a solution or family of solutions to long-standing problems in Physics. This lends support to the author’s idea that nature employs the totality of all Mathematics – discovered and undiscovered – in its handiwork, such that invariant realities in Math spell out their own importance to Physics, and give rise to the universe we see today. As those same mathematical invariants unfold in the universe over time, they also give rise to processes that make the appearance and evolution of life inevitable.

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

I have not even opened your essay yet. I just noticed you were here. I was a reviewer for a paper you wrote on the cosmological implications of the Mandelbrot set. The idea was intriguing, and I have worked a variation of this up with anti-de Sitter spacetime. I attach what the projection of that is on the spatial part of AdS_3, which is a Poincare disk. So your idea was food for thought, which was one reason I accepted it.

I will read your paper probably later today or tomorrow. I have one up here as well http://fqxi.org/community/forum/topic/2737

LC

attachments: Mandelbrot_set_on_AdS.png

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I will read your paper probably later today or tomorrow. I have one up here as well http://fqxi.org/community/forum/topic/2737

LC

attachments: Mandelbrot_set_on_AdS.png

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Thanks greatly Lawrence!

I got to hear several talks on AdS/CFT and holography in the breakout sessions at GR21, and there was quite a lot of food for thought. I am eager to read your paper as well, though I am working through some of the earlier submissions first. I find the AdS Mandelbrot image very intriguing. Presently; I'm working on a follow-up to my GR21 presentation, exploring how a certain Misiurewicz point represents Bose-Einstein condensation and Schwarzschild horizons - a connection recently explored extensively by Gia Dvali and colleagues.

All the Best,

Jonathan

I got to hear several talks on AdS/CFT and holography in the breakout sessions at GR21, and there was quite a lot of food for thought. I am eager to read your paper as well, though I am working through some of the earlier submissions first. I find the AdS Mandelbrot image very intriguing. Presently; I'm working on a follow-up to my GR21 presentation, exploring how a certain Misiurewicz point represents Bose-Einstein condensation and Schwarzschild horizons - a connection recently explored extensively by Gia Dvali and colleagues.

All the Best,

Jonathan

I read your paper. Clearly you have gotten bitten by the octonion issue. Take a look at Baez' paper "The Octonions". This will give you the basic preliminaries on the structure of octonions, the Fano plane, tables, Hopf fibration and group theoretic realizations. There is area to explore here, and in particular how this leads to a general eigenvalued system with the Freudenthal triplet, or J^3(O)

Cheers LC

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Cheers LC

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Yes I agree, and Thank You Lawrence!

I wanted to avoid giving people Math overload, while teaching them about the benefits of higher-order Maths. I am a real fan of the octonions, where the more I learn about them, the more useful applications I find. I have attached the Baez paper to a comment further down, in reply to Anonymous - who is actually Karl Coryat.

I started reading your marvelous paper, but I'm also trying to work through the whole stack in chronological order - at least 3 or 4 papers a day. I will make sure I give you a review right away, and I'll likely boost your score a bit with my rating since you merit it.

All the Best,

Jonathan

I wanted to avoid giving people Math overload, while teaching them about the benefits of higher-order Maths. I am a real fan of the octonions, where the more I learn about them, the more useful applications I find. I have attached the Baez paper to a comment further down, in reply to Anonymous - who is actually Karl Coryat.

I started reading your marvelous paper, but I'm also trying to work through the whole stack in chronological order - at least 3 or 4 papers a day. I will make sure I give you a review right away, and I'll likely boost your score a bit with my rating since you merit it.

All the Best,

Jonathan

Dear Dickau,

Good essay on Number Systems....

Your words …..1.” Nature is not limited by our views about what in Math is relevant to physical law, nor is it partial to any specific patterning our Math conventions have introduced. Whether we calculate in Roman or binary is not relevant to how nature generates what we know as Physics.”…..

2. ………… ‘Octonionic Inflation avoids some of the problems with conventional Inflation cited by Steinhardt and colleagues [4], and it is a subject of my current research’…………..

But still you are considering inflation models only. That means you are neglecting 60 percent of Galaxies in the universe…. I request you to please revise your model…

Have look at my essay also…

Best wishes…………….

=snp. gupta

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Good essay on Number Systems....

Your words …..1.” Nature is not limited by our views about what in Math is relevant to physical law, nor is it partial to any specific patterning our Math conventions have introduced. Whether we calculate in Roman or binary is not relevant to how nature generates what we know as Physics.”…..

2. ………… ‘Octonionic Inflation avoids some of the problems with conventional Inflation cited by Steinhardt and colleagues [4], and it is a subject of my current research’…………..

But still you are considering inflation models only. That means you are neglecting 60 percent of Galaxies in the universe…. I request you to please revise your model…

Have look at my essay also…

Best wishes…………….

=snp. gupta

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Thank you Satyavarapu,

This is decidedly a work in progress, and there will be many revisions made, or variations tried - before the ideas are forged into a finely-tuned theory. I am pleased that some portion of my thesis resonates with you.

All the Best,

Jonathan

This is decidedly a work in progress, and there will be many revisions made, or variations tried - before the ideas are forged into a finely-tuned theory. I am pleased that some portion of my thesis resonates with you.

All the Best,

Jonathan

Jonathan,

I too am an advocate for the division algebras. I do not doubt that nature employs these structures in ways that we have yet to even imagine.

You present several things from a perspective that I had not considered. For example, the problem of non-associativity ... I have been trying to get around this but you essentially argue that it should be embraced as a powerful tool.

As another example, I was not aware that it was possible to arrive at the same result via different sets of intermediate rules ... but doesn't that basically say that associativity is still true, but you just have to view the whole problem as a single entity?

I have been wondering how to view SR & GR in terms of quaternions and octonions. Perhaps you have thoughts on this? I understand that the Maxwell Equations can be neatly expressed with quaternions. Therefore, extension to SR should be straight-forward.

I think we may have a very difficult challenge ahead. I can envision that quaternions and perhaps octonions can revolutionize how math, physics, and engineering are taught and practiced. But, it takes roughly 11 years in the public school system to have the prerequisites just for the Calculus of Real Numbers. With attitudes and constraints being what they are, how can we ever get to the point where these things are widely taught to those who can benefit from them?

Best Regards and Good Luck,

Gary Simpson

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I too am an advocate for the division algebras. I do not doubt that nature employs these structures in ways that we have yet to even imagine.

You present several things from a perspective that I had not considered. For example, the problem of non-associativity ... I have been trying to get around this but you essentially argue that it should be embraced as a powerful tool.

As another example, I was not aware that it was possible to arrive at the same result via different sets of intermediate rules ... but doesn't that basically say that associativity is still true, but you just have to view the whole problem as a single entity?

I have been wondering how to view SR & GR in terms of quaternions and octonions. Perhaps you have thoughts on this? I understand that the Maxwell Equations can be neatly expressed with quaternions. Therefore, extension to SR should be straight-forward.

I think we may have a very difficult challenge ahead. I can envision that quaternions and perhaps octonions can revolutionize how math, physics, and engineering are taught and practiced. But, it takes roughly 11 years in the public school system to have the prerequisites just for the Calculus of Real Numbers. With attitudes and constraints being what they are, how can we ever get to the point where these things are widely taught to those who can benefit from them?

Best Regards and Good Luck,

Gary Simpson

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Thanks Gary,

You are right about associativity still working for the system as a whole. The octonions, for example, are alternative (where associative and anti-associative terms alternate), so they obey a weaker form of the associative rule. The next periodicity is 8, so things get more complicated there. Rick Lockyer points to 16 flavors of octonion multiplication, which he and I think pertains to different areas of physics, much as the individual flavors of String Theory have their greatest utility for a certain portion of the energetic and interaction landscape, but become intractable in other regimes.

I think the problem is starting with the real numbers, to a degree. My nephew had trouble in Math because he had a hard time taking the concept of numbers that just sit there on faith. But in more advanced Maths, numerical quantities are more chimeric. So he could have been seeing something his teachers didn't, but was forced to conform anyway. Recent papers by Hyun Seok Yang on Emergent Spacetime claim to show that if spacetime is non-commutative at the microscale, then spacetime must also be emergent. If his proof is true, then my premise for this essay also holds water.

Warm Regards,

Jonathan

You are right about associativity still working for the system as a whole. The octonions, for example, are alternative (where associative and anti-associative terms alternate), so they obey a weaker form of the associative rule. The next periodicity is 8, so things get more complicated there. Rick Lockyer points to 16 flavors of octonion multiplication, which he and I think pertains to different areas of physics, much as the individual flavors of String Theory have their greatest utility for a certain portion of the energetic and interaction landscape, but become intractable in other regimes.

I think the problem is starting with the real numbers, to a degree. My nephew had trouble in Math because he had a hard time taking the concept of numbers that just sit there on faith. But in more advanced Maths, numerical quantities are more chimeric. So he could have been seeing something his teachers didn't, but was forced to conform anyway. Recent papers by Hyun Seok Yang on Emergent Spacetime claim to show that if spacetime is non-commutative at the microscale, then spacetime must also be emergent. If his proof is true, then my premise for this essay also holds water.

Warm Regards,

Jonathan

Hello Jonatha,;

Happy to see you on this essay's contest.Always relevant to read your works about maths and physics.

all the best,and Good luck from Belgium.:)

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Happy to see you on this essay's contest.Always relevant to read your works about maths and physics.

all the best,and Good luck from Belgium.:)

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Happy to hear you chime in Steve..

I'm glad too, that I can help inform people that the properties of higher-order spheres matters to Physics in the real world - even if that connection might not be apparent on the surface.

All the Best,

Jonathan

I'm glad too, that I can help inform people that the properties of higher-order spheres matters to Physics in the real world - even if that connection might not be apparent on the surface.

All the Best,

Jonathan

You are welcome Jonathan,

I am less parano lol ,I like now these geometreical algenbras.I beleive strongly Jonathan that my 3D quant and cosm sphères could be superimposed with an infinite higher oder considering thisn uniquenss.If max tegmark is right about multiverse that I consider like multispheres.So we have an interesting superimposing.Now if my theory of spherisation is correct, and...

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I am less parano lol ,I like now these geometreical algenbras.I beleive strongly Jonathan that my 3D quant and cosm sphères could be superimposed with an infinite higher oder considering thisn uniquenss.If max tegmark is right about multiverse that I consider like multispheres.So we have an interesting superimposing.Now if my theory of spherisation is correct, and...

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Dr Spock Jonathan, we must create this united states of the SPHERE USS ENTERPRISE ....liberation of funds......evolution spherisation......We are travellers from Stars....We are Jedis of the SPHERE lol let's spherisize this solar system .....

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Having also not yet downloaded your essay, I fear it might not be as intriguing as your earlier one where you addressed the evolution of children, something that I consider on topic this time.

Instead you are using teleological language: "nature employs the totality of all Mathematics – discovered and undiscovered – in its handiwork". My view is different. I see mathematics in Cantor's sense endlessly open even to pure phantasm that might not even be always selfconsistent. Cantor agued: "The essence of mathematics is its freedom".

I nonetheless agree: It is doesn't matter whether or not something is already discovered. Where is the borderline in physics between fabricated Platonism and discovered strictly logical common sense? My criterion is non-arbitrariness.

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Instead you are using teleological language: "nature employs the totality of all Mathematics – discovered and undiscovered – in its handiwork". My view is different. I see mathematics in Cantor's sense endlessly open even to pure phantasm that might not even be always selfconsistent. Cantor agued: "The essence of mathematics is its freedom".

I nonetheless agree: It is doesn't matter whether or not something is already discovered. Where is the borderline in physics between fabricated Platonism and discovered strictly logical common sense? My criterion is non-arbitrariness.

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Thank you Eckard,

From where I sit, there is very little difference between the Platonist's view and the discovered strict logic of common sense - if they are bumping into the same hidden structure. Most of what Maths describe arises from an exploratory testing of what is strictly logical. It makes sense to me that certain patterns emerge, where what is logical in the real world and what is logical in some purely abstract frameworks agree perfectly.

I think some folks do dwell on invented abstractions too much. Sure the Kac-Moody algebras capture many of the salient properties of the natural hyper-complex types Quaternion and Octonion, but I think the latter are fundamental - in terms of non-arbitrariness - since they arise in a simple construction from the spheres. One can fabricate spaces of the Calabi-Yau type which fit well the requirements of String Theory, but I question whether nature works like that, and therefore the naturalness of such fabrication. I like better the idea of Baez and Huerta; that Stings inherit their power from the strength of the natural algebras.

All the Best,

Jonathan

From where I sit, there is very little difference between the Platonist's view and the discovered strict logic of common sense - if they are bumping into the same hidden structure. Most of what Maths describe arises from an exploratory testing of what is strictly logical. It makes sense to me that certain patterns emerge, where what is logical in the real world and what is logical in some purely abstract frameworks agree perfectly.

I think some folks do dwell on invented abstractions too much. Sure the Kac-Moody algebras capture many of the salient properties of the natural hyper-complex types Quaternion and Octonion, but I think the latter are fundamental - in terms of non-arbitrariness - since they arise in a simple construction from the spheres. One can fabricate spaces of the Calabi-Yau type which fit well the requirements of String Theory, but I question whether nature works like that, and therefore the naturalness of such fabrication. I like better the idea of Baez and Huerta; that Stings inherit their power from the strength of the natural algebras.

All the Best,

Jonathan

That was meant to be..

As Baez and Huerta suggest; "Strings inherit their power from the strength of the natural algebras."

Sorry for the misspelling. But maybe Sting Theory makes as much sense; yes?

Regards,

Jonathan

As Baez and Huerta suggest; "Strings inherit their power from the strength of the natural algebras."

Sorry for the misspelling. But maybe Sting Theory makes as much sense; yes?

Regards,

Jonathan

Dear Jonathan.

Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that “Everything should be made as simple as possible, but not simpler. Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.”

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

Joe Fisher, Realist

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Please excuse me for I have no intention of disparaging in any way any part of your essay.

I merely wish to point out that “Everything should be made as simple as possible, but not simpler. Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.”

Only nature could produce a reality so simple, a single cell amoeba could deal with it.

The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

Joe Fisher, Realist

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Thanks Joe,

It is good to have a realist among us, and I agree that we should keep things simple - but only as simple as things really are.

All the Best,

Jonathan

It is good to have a realist among us, and I agree that we should keep things simple - but only as simple as things really are.

All the Best,

Jonathan

Von Neumann d tell us that the ponts of equilibrium are possible when the respect is mutual and sincereand when we eat all at the same table.We must save this planet Jonathan with this liberation of funds of this world bank for our solar system and the well of all.

I am not crazy it is God who said me this lol let's reach these points of equilibrium ,after all the sphere is the perfect equilibrium between forces :)they turn so they are.I am not difficult you know Jonathan I have nothing, two small dogs,alone without familly,without money,without nothing.Just a simple theory of spherisation with quant and cosm 3D sphères Inside this sphere.I am jus a simple nursery man for plants and flowers even if people have killed 12000 fuchsias aged of 3 years in belgium iomplyin,g a bankrupcy.I have said me that I will stop the horticulture and production due to this evil act of these bad persons of belgium.But In fact after some years of disaters,I have not said my last words if God permits me ....Nothing Jonathan,I will go at new York if I must.I am almready reincarnated on an other planet, I am already died you know.So this explains that.Take my friend Jedi of The Sphere and don't forget ,we fight the unconsciousness :) universally, altruistically and spherically yours

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I am not crazy it is God who said me this lol let's reach these points of equilibrium ,after all the sphere is the perfect equilibrium between forces :)they turn so they are.I am not difficult you know Jonathan I have nothing, two small dogs,alone without familly,without money,without nothing.Just a simple theory of spherisation with quant and cosm 3D sphères Inside this sphere.I am jus a simple nursery man for plants and flowers even if people have killed 12000 fuchsias aged of 3 years in belgium iomplyin,g a bankrupcy.I have said me that I will stop the horticulture and production due to this evil act of these bad persons of belgium.But In fact after some years of disaters,I have not said my last words if God permits me ....Nothing Jonathan,I will go at new York if I must.I am almready reincarnated on an other planet, I am already died you know.So this explains that.Take my friend Jedi of The Sphere and don't forget ,we fight the unconsciousness :) universally, altruistically and spherically yours

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Always a pleasure to hear from you Steve..

This time, I do feature spheres of various dimensions, in my essay. I think it is a very useful construction that nature views as fundamental.

All the Best,

Jonathan

This time, I do feature spheres of various dimensions, in my essay. I think it is a very useful construction that nature views as fundamental.

All the Best,

Jonathan

Jonathan, thank you for an enjoyable and enlightening read. I'd like to take your provocative opening sentence seriously and see where it leads. If we had to formalize the operations of arithmetic for Roman numerals, we might develop a set of rules and conditions for letter incrementing/decrementing, substitution, and so on. Even something as basic as multiplication might be so onerous it could...

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Thanks greatly Karl..

You write "Perhaps we're in a version of this Roman mathematical nightmare today." and I think it is sadly true. Too many people treat lessons in Math and Physics as concepts etched in stone, rather than something dynamic that becomes more clearly defined as we learn more about things and how they work. I agree that what we are looking for is a deeper Math, but it would appear that we have to be willing to go higher in order to see farther.

It's rather like Rick says in his comment below, that once you arrive at the octonions - they tell you what to do (so long as you follow the road signs). Michael Goodband illustrated that concept in a comment during a previous contest, showing how the information in John Baez article "The Octonions" could be used to derive the Standard Model particles - in simple and direct steps. What we don't know is how nature did it, but we do know the mathematical infrastructure is already there.

Thanks again for your comment.

Regards,

Jonathan

You write "Perhaps we're in a version of this Roman mathematical nightmare today." and I think it is sadly true. Too many people treat lessons in Math and Physics as concepts etched in stone, rather than something dynamic that becomes more clearly defined as we learn more about things and how they work. I agree that what we are looking for is a deeper Math, but it would appear that we have to be willing to go higher in order to see farther.

It's rather like Rick says in his comment below, that once you arrive at the octonions - they tell you what to do (so long as you follow the road signs). Michael Goodband illustrated that concept in a comment during a previous contest, showing how the information in John Baez article "The Octonions" could be used to derive the Standard Model particles - in simple and direct steps. What we don't know is how nature did it, but we do know the mathematical infrastructure is already there.

Thanks again for your comment.

Regards,

Jonathan

I here append Michael's comment..

Author Michael James Goodband replied on Dec. 7, 2012 @ 16:44 GMT

I just want to point out that a (S0, S1, S3, S7) universe is not just a proposal. I claim that it is the conclusion when we follow the spirit of Rick's standard of letting the algebras do the talking. However, Rick's choice of listening to the octonions violates the meta-principle of...

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Author Michael James Goodband replied on Dec. 7, 2012 @ 16:44 GMT

I just want to point out that a (S0, S1, S3, S7) universe is not just a proposal. I claim that it is the conclusion when we follow the spirit of Rick's standard of letting the algebras do the talking. However, Rick's choice of listening to the octonions violates the meta-principle of...

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attachments: baezocto.pdf

A cogent argument, Jonathan, but somehow I can't see that Math makes the emergence of the universe and life inevitable. Math certainly helps the dynamics of life be more understandable through modelling and such (which I have done), especially if you are conversant in math, and maybe that's my problem. I can see that nature, for example, wings, flower petals and leave, are mathematically expressed origami-style in their patterns of development. I too worked in an octal system of computers years ago, the Univac 1100, but I can't see that math tells the universe what to create beyond certain mathematical laws of entropy and Dr. England's theory, which I use as an example.

I am impressed with your presentation, though.

Jim Hoover

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I am impressed with your presentation, though.

Jim Hoover

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Thanks a lot Jim!

Intriguing comments. I have imagined that origami artists could assist the folks working in Causal Dynamical Triangulations to crack certain standing problems in quantum gravity. But I also read recently that some folks are using Julia sets to create 3-d forms origami style, guided by the mathematical symmetries and scaling rules inherent in such forms. So I think there is a connection.

My model for entropy is the Mandelbrot Set, which reproduces the Verhulst dynamic along the real axis - when the Real-valued Mandelbrot formula is iterated with a random seed. But each place where the Set folds back on itself becomes a bifurcation point on the adjoining diagram. I first saw this in Peitgen and Richter "The Beauty of Fractals" after it was pointed out by Michel Planat.

Thanks again!

All the Best,

Jonathan

Intriguing comments. I have imagined that origami artists could assist the folks working in Causal Dynamical Triangulations to crack certain standing problems in quantum gravity. But I also read recently that some folks are using Julia sets to create 3-d forms origami style, guided by the mathematical symmetries and scaling rules inherent in such forms. So I think there is a connection.

My model for entropy is the Mandelbrot Set, which reproduces the Verhulst dynamic along the real axis - when the Real-valued Mandelbrot formula is iterated with a random seed. But each place where the Set folds back on itself becomes a bifurcation point on the adjoining diagram. I first saw this in Peitgen and Richter "The Beauty of Fractals" after it was pointed out by Michel Planat.

Thanks again!

All the Best,

Jonathan

I can see the relevance of the mathematical model, referencing the Mandelbrot Set, Jonathan. I do mention the repeating patterns displayed at every scale of the universe and can see that math is a compact expression of a symmetry hard to visualize otherwise. It makes England's idea of replication at every scale easier to imagine, imagining something like the Menger sponge.

In the realm of aesthetics, I have a clearer appreciation of your piece.

Jim Hoover

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In the realm of aesthetics, I have a clearer appreciation of your piece.

Jim Hoover

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Thanks for this follow-up Jim..

The Mandelbrot formula is very compact, compared to the complexity of the object. And it elegantly displays the replication of similar forms at different levels of scale. I think it is the progression of form, which is the most relevant, but the regularity of its repetitive form is impressive.

I am glad I gave you something to chew on.

All the Best,

Jonathan

The Mandelbrot formula is very compact, compared to the complexity of the object. And it elegantly displays the replication of similar forms at different levels of scale. I think it is the progression of form, which is the most relevant, but the regularity of its repetitive form is impressive.

I am glad I gave you something to chew on.

All the Best,

Jonathan

Johnathan,

Liked your essay very much. Was wondering how you were going to fit octonions into the mindless, wandering theme the essay subject seemed to imply is how things are, happy to read your rejection of such a notion. It certainly alienated me from participating.

One does not have to throw out multiplicative commutation and associative laws with octonion algebra. Within its rules are real number math, associative and commutative math in any of the complex subalgebras, generally non-commutative but associative math of the quaternion subalgebras, and generally non-commutative non-associative math of the full octonion algebra. If something described by octonion algebra needs commutative math and/or associative math it is available, if not then this is also available. Octonion algebra tells us where each fits in, and more importantly how these disparate characteristics play well together in the greater whole of physics.

Back on the IMHO strange notion of wandering towards a goal, or emergence for that matter, to me Octonion Algebra is a well lit highway with numerous road signs that too few people have learned the language used such that they can appreciate their directive nature. I did not title my 2012 fqxi essay "The Algebra of Everything" just because it was a catchy title. It is no accident all of the differential forms in the Octonion equivalent of the stress-energy-momentum tensor are the full complement of my so called "Octonion Algebraic Invariants", nor that Electrodynamics is just a subset of the presentation. Nor is it a coincidence the Lorentz transformation form Electrodynamics requires falls out from the requirement both differentials of any field component transform in kind. The only ones doing aimless wondering towards a goal are the people that can't or refuse to read the road signs.

Rick

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Liked your essay very much. Was wondering how you were going to fit octonions into the mindless, wandering theme the essay subject seemed to imply is how things are, happy to read your rejection of such a notion. It certainly alienated me from participating.

One does not have to throw out multiplicative commutation and associative laws with octonion algebra. Within its rules are real number math, associative and commutative math in any of the complex subalgebras, generally non-commutative but associative math of the quaternion subalgebras, and generally non-commutative non-associative math of the full octonion algebra. If something described by octonion algebra needs commutative math and/or associative math it is available, if not then this is also available. Octonion algebra tells us where each fits in, and more importantly how these disparate characteristics play well together in the greater whole of physics.

Back on the IMHO strange notion of wandering towards a goal, or emergence for that matter, to me Octonion Algebra is a well lit highway with numerous road signs that too few people have learned the language used such that they can appreciate their directive nature. I did not title my 2012 fqxi essay "The Algebra of Everything" just because it was a catchy title. It is no accident all of the differential forms in the Octonion equivalent of the stress-energy-momentum tensor are the full complement of my so called "Octonion Algebraic Invariants", nor that Electrodynamics is just a subset of the presentation. Nor is it a coincidence the Lorentz transformation form Electrodynamics requires falls out from the requirement both differentials of any field component transform in kind. The only ones doing aimless wondering towards a goal are the people that can't or refuse to read the road signs.

Rick

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I really appreciate this comment Rick..

Since I wholeheartedly agree with almost every point you make verbatim, I shall let your words stand as evidence that I backed the right horse (or elephant as the case might be). I see the octonions as doing all of the heavy lifting that gets the ball rolling in the early universe. Since all of the exceptional Lie groups are of the octonion lineage (according to the Cartan-Killing classification), it would be hard for nature to create the array of forms we observe without them.

So indeed; I'm with you brother. The octonions are a well-lit road and the only ones who see them as aimless are those who have not taken the time to learn enough about them. My conversation with Tevian was a reality check, because I could hardly believe so many really smart people could ignore the need to employ non-associative Maths to crack the deeper problems, or the loud and clear message of the octonions. When he said "I agree with everything you've said up to this point; what's your question?" I knew for sure that I'm not just imagining things.

All the Best,

Jonathan

Since I wholeheartedly agree with almost every point you make verbatim, I shall let your words stand as evidence that I backed the right horse (or elephant as the case might be). I see the octonions as doing all of the heavy lifting that gets the ball rolling in the early universe. Since all of the exceptional Lie groups are of the octonion lineage (according to the Cartan-Killing classification), it would be hard for nature to create the array of forms we observe without them.

So indeed; I'm with you brother. The octonions are a well-lit road and the only ones who see them as aimless are those who have not taken the time to learn enough about them. My conversation with Tevian was a reality check, because I could hardly believe so many really smart people could ignore the need to employ non-associative Maths to crack the deeper problems, or the loud and clear message of the octonions. When he said "I agree with everything you've said up to this point; what's your question?" I knew for sure that I'm not just imagining things.

All the Best,

Jonathan

Dear Jonathan,

Very interesting, in-depth essay and important findings to research ways to overcome the total crisis of understanding in the fundamental science:

"Roman numerals carved in stone represent unchanging quantities well, but viewing Mathematics in that way is a mistake, because Math is about how unchanging attributes and quantities come to be that way through a process. Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution comes from will disappear when we realize what Math is at its root, a systematic exploration of features characterizing the laws by which form evolves.

The unchanging quantities of Math itself include figures like the Mandelbrot Set, E8 and the other exceptional groups, as well as other mathematical invariants. While one could argue that humans constructed these things; it can also be said they were only discovered or always existed – even before the universe had its birth. So it is with even higher orders and levels of Mathematics we have not discovered yet, which the universe is already putting to use. But we are fortunate, at this juncture, to be equipped to learn how Math gives rise to life, in order to foster the evolution of consciousness."

I believe that the solution to the "hard problem of consciousness" is possible after solving the super hard problem of the foundations of mathematics (knowledge). Mathematicians, physicists and poets should have a single, full of life's meaning, picture of the world. I invite you to read and evaluate my ideas.

Yours faithfully,

Vladimir

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Very interesting, in-depth essay and important findings to research ways to overcome the total crisis of understanding in the fundamental science:

"Roman numerals carved in stone represent unchanging quantities well, but viewing Mathematics in that way is a mistake, because Math is about how unchanging attributes and quantities come to be that way through a process. Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution comes from will disappear when we realize what Math is at its root, a systematic exploration of features characterizing the laws by which form evolves.

The unchanging quantities of Math itself include figures like the Mandelbrot Set, E8 and the other exceptional groups, as well as other mathematical invariants. While one could argue that humans constructed these things; it can also be said they were only discovered or always existed – even before the universe had its birth. So it is with even higher orders and levels of Mathematics we have not discovered yet, which the universe is already putting to use. But we are fortunate, at this juncture, to be equipped to learn how Math gives rise to life, in order to foster the evolution of consciousness."

I believe that the solution to the "hard problem of consciousness" is possible after solving the super hard problem of the foundations of mathematics (knowledge). Mathematicians, physicists and poets should have a single, full of life's meaning, picture of the world. I invite you to read and evaluate my ideas.

Yours faithfully,

Vladimir

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Many thanks Vladimir,

I agree with your assessment. The 'hard problem' of consciousness is more easily solved when we do understand the evolutive properties in Math that provide a clear basis for such things. As you implied; Math is about knowledge, or how we can know things, so the two go hand in hand.

All the Best,

Jonathan

I agree with your assessment. The 'hard problem' of consciousness is more easily solved when we do understand the evolutive properties in Math that provide a clear basis for such things. As you implied; Math is about knowledge, or how we can know things, so the two go hand in hand.

All the Best,

Jonathan

Hi Jonathan,

You present an excellent portrayal of the dynamism of mathematics. I found the emphasis on non-associativity particularly engaging since I bump into that in my unfinished essay about a quaternion derivative. For me, your essay is kind of inspirational, in that there seems to be growing interest in understanding the origin of the non-associative Elephants.

Colin

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You present an excellent portrayal of the dynamism of mathematics. I found the emphasis on non-associativity particularly engaging since I bump into that in my unfinished essay about a quaternion derivative. For me, your essay is kind of inspirational, in that there seems to be growing interest in understanding the origin of the non-associative Elephants.

Colin

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This is most appreciated!

I greatly respect your work Colin, and given your areas of expertise I really value the compliment. To learn that I have inspired someone like yourself is about the best reward I can have. I think there is indeed growing interest in non-associative Maths, and I hope my shining a light on the elephants will wake a few people up, or speed up the process of our collective awakening.

Who knows? Maybe my curiosity at GR21 got Tevian thinking and he has something really fun cooking. I asked some pointed questions of Gerard 't Hooft at FFP10 and then found a few extra slides in his presentation at FFP11 - addressing the concerns I raised about Lorentz invariance. To a degree; what's needed is for enough of the right questions to be asked, so the experts are forced to think more deeply about certain things that would otherwise escape notice.

All the Best,

Jonathan

I greatly respect your work Colin, and given your areas of expertise I really value the compliment. To learn that I have inspired someone like yourself is about the best reward I can have. I think there is indeed growing interest in non-associative Maths, and I hope my shining a light on the elephants will wake a few people up, or speed up the process of our collective awakening.

Who knows? Maybe my curiosity at GR21 got Tevian thinking and he has something really fun cooking. I asked some pointed questions of Gerard 't Hooft at FFP10 and then found a few extra slides in his presentation at FFP11 - addressing the concerns I raised about Lorentz invariance. To a degree; what's needed is for enough of the right questions to be asked, so the experts are forced to think more deeply about certain things that would otherwise escape notice.

All the Best,

Jonathan

Jonathan,

It looks like we have both been one-bombed ... any idea who?

Good Luck,

Gary Simpson

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It looks like we have both been one-bombed ... any idea who?

Good Luck,

Gary Simpson

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Invisible trolls would be my guess..

It appears that some people accord points only to those who agree with their premise, and we are among the ones who do not. I hope you have good luck otherwise, or anyway.

All the Best,

Jonathan

It appears that some people accord points only to those who agree with their premise, and we are among the ones who do not. I hope you have good luck otherwise, or anyway.

All the Best,

Jonathan

The person who did this has to be an essay author. I would suspect they are somebody who wrote an essay that appeared in the group Feb 21.

LC

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LC

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This is not my concern..

JJD

JJD

Your notion of maths guiding reality rings true. The octonion algebra is new to me, but seems really complex. It would seem that one can always explain reality by adding hidden dimensions and multiverses and octonions.

But a simpler reality of just two complex dimensions seems to have all the complexity needed to explain the universe. Isn't simpler better?

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But a simpler reality of just two complex dimensions seems to have all the complexity needed to explain the universe. Isn't simpler better?

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The correct answer is always the best one Steve...

Effective theories need only consider the parameters they incorporate, or attempt to explain. But this is why GR and QM don't agree at the fringes. Explaining the whole universe at once requires one to work in the area of fundamental theories - which is fundamentally more difficult.

All the Best,

Jonathan

Effective theories need only consider the parameters they incorporate, or attempt to explain. But this is why GR and QM don't agree at the fringes. Explaining the whole universe at once requires one to work in the area of fundamental theories - which is fundamentally more difficult.

All the Best,

Jonathan

I am putting my response you wrote in my area here. I noticed you had not gotten to it or responded yet. I have have been getting caught up with work after having spent the week down with the flu.

Thanks for the positive response. I will comment more tomorrow. It is getting a bit late for a long writing session. This is in line with the approach with Raamsdonk that spacetime is built from entanglements. I wrote an answer on stack exchange that connects with this perspective with regards to Hawking radiation.

The open world emerges from the existence of gauge hair and BPS charge. The hair of the black hole is entangled with particles in a vast number of other black holes in the universe. In the unique situation where there are two black holes maximally entangled one would have a complete Einstein-Rosen bridge connection to the interior of the other black hole in this other world. The openness comes from the fact the spatial surface in region I has an ambiguity with respect to being connected to other cosmology or the black hole interior region. For maximal entangled Bhs one in principle can avoid the singularity and travel around to other worlds.

I will write more tomorrow. I have been recovering from influenza, and today it the first day I feel not utterly horrible. I am not that familiar with DGP model, but I will see what I can make of it.

Cheers LC

PS --- I also noticed something bizarre happened. I was ranked around 17 or so from the top, but a lot of people were I think tanked with a vote of one. Now I am #4. It looks like you went down with that; too bad. I was not me who did that. I would not give a lot of papers the lowest score like that.

LC

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Thanks for the positive response. I will comment more tomorrow. It is getting a bit late for a long writing session. This is in line with the approach with Raamsdonk that spacetime is built from entanglements. I wrote an answer on stack exchange that connects with this perspective with regards to Hawking radiation.

The open world emerges from the existence of gauge hair and BPS charge. The hair of the black hole is entangled with particles in a vast number of other black holes in the universe. In the unique situation where there are two black holes maximally entangled one would have a complete Einstein-Rosen bridge connection to the interior of the other black hole in this other world. The openness comes from the fact the spatial surface in region I has an ambiguity with respect to being connected to other cosmology or the black hole interior region. For maximal entangled Bhs one in principle can avoid the singularity and travel around to other worlds.

I will write more tomorrow. I have been recovering from influenza, and today it the first day I feel not utterly horrible. I am not that familiar with DGP model, but I will see what I can make of it.

Cheers LC

PS --- I also noticed something bizarre happened. I was ranked around 17 or so from the top, but a lot of people were I think tanked with a vote of one. Now I am #4. It looks like you went down with that; too bad. I was not me who did that. I would not give a lot of papers the lowest score like that.

LC

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I thank you Lawrence,

I am not worried about you being a vote rigger. It does appear there must be folks who enter the contest on a pretense, then vote for their friends, while casting down those who might be serious competition. It is discouraging to see such childish behavior.

Sorry to hear about the flu. I have had lingering cold symptoms myself. I think it might be worth elaborating on the hairy ball theorem, as an explanation of the above. The conventional sphere S2 has hair that can't all flow one way, so is non-trivial, while S3 can be combed all the way around - because it is parallelizable.

More later,

Jonathan

I am not worried about you being a vote rigger. It does appear there must be folks who enter the contest on a pretense, then vote for their friends, while casting down those who might be serious competition. It is discouraging to see such childish behavior.

Sorry to hear about the flu. I have had lingering cold symptoms myself. I think it might be worth elaborating on the hairy ball theorem, as an explanation of the above. The conventional sphere S2 has hair that can't all flow one way, so is non-trivial, while S3 can be combed all the way around - because it is parallelizable.

More later,

Jonathan

Jonathan,

Is it possible for there to be a non-integer value for the number of dimensions associated with a space? If so, how?

Trolls? The trolls in "Frozen" were amusing. The trolls in "Trolls" are amusing. These trolls are just small. That makes it easy to hide.

Best Regards and Good Luck,

Gary Simpson

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Is it possible for there to be a non-integer value for the number of dimensions associated with a space? If so, how?

Trolls? The trolls in "Frozen" were amusing. The trolls in "Trolls" are amusing. These trolls are just small. That makes it easy to hide.

Best Regards and Good Luck,

Gary Simpson

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Interesting question. I have this idea cooking up about Hausdorff dimensions with Ising chains. This might be a way of working a renormalization scaling for estimating the 3-dim Ising problem.

LC

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LC

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Hi Gary,

Non-integer dimension arises in causal structure theories of quantum gravity, which is referred to simply as a running D - compared to the case where D = n, where n = 0,1,2,3... Of course; this gives space a fractional dimension, and makes it a fractal - along the way - which is simply how surface roughness evolves into a new (whole) dimension or extent. So briefly; fractional dimension arises because of folding of space in the microscale. As Lawrence alludes, the Hausdorff dimension evolves.

One can also think of this as relating to emergent spacetime, because if the observed properties of space and time, this means that intermediate values are accessible between the onset of geometrogenesis and the current era. One can also see this as connected with a different root dimension for the microscale and macroscale, as with Rainbow Gravity (which was explored by Magueijo, Amelino-Camelia, and others). If space is 2-d at the Planck scale and 3-d at the common scale; what is it in between?

Lastly; this is a broad feature of what is called bi-metric gravity. There are many formulations in that family. There's too much to say simply, but as the name implies there are two co-existent descriptions of space - to deal with the weak-field and strong-field, low-energy and high-energy regime, or common scale and microscale, and so on.

All the Best,

Jonathan

Non-integer dimension arises in causal structure theories of quantum gravity, which is referred to simply as a running D - compared to the case where D = n, where n = 0,1,2,3... Of course; this gives space a fractional dimension, and makes it a fractal - along the way - which is simply how surface roughness evolves into a new (whole) dimension or extent. So briefly; fractional dimension arises because of folding of space in the microscale. As Lawrence alludes, the Hausdorff dimension evolves.

One can also think of this as relating to emergent spacetime, because if the observed properties of space and time, this means that intermediate values are accessible between the onset of geometrogenesis and the current era. One can also see this as connected with a different root dimension for the microscale and macroscale, as with Rainbow Gravity (which was explored by Magueijo, Amelino-Camelia, and others). If space is 2-d at the Planck scale and 3-d at the common scale; what is it in between?

Lastly; this is a broad feature of what is called bi-metric gravity. There are many formulations in that family. There's too much to say simply, but as the name implies there are two co-existent descriptions of space - to deal with the weak-field and strong-field, low-energy and high-energy regime, or common scale and microscale, and so on.

All the Best,

Jonathan

I can tell that your essay is very well written. I wish I could follow along on all the details, but I think it would require of me a serious commitment to read up quite a lot on the relevant mathematics. At this stage, I can only point out that the essays by Yanofsky and Simpson are also talking a lot about the mathematical terms that are mentioned in your essay. All the best and thanks for your help. Cheers!

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I am happy you enjoyed it Willy..

Even some hardcore Math folks shy away from the octonions, but they are worth the effort for those with the skills. My main point is that if you go high enough up the chain, evolutive properties in Math are easy to observe.

All the Best,

Jonathan

Even some hardcore Math folks shy away from the octonions, but they are worth the effort for those with the skills. My main point is that if you go high enough up the chain, evolutive properties in Math are easy to observe.

All the Best,

Jonathan

For those visiting here..

I thank you for your interest in my work and I'll try to reply to all comments eventually, to most as soon as there is time. I will also attempt to read as many as possible of the other essays in the time allotted.

I will be systematically working from the earlier submissions to the present, while trying to honor those who visit my essay with an earlier reading and feedback. I'll be trying to also look for topics of my own special interest and authors whose work I respect. Lastly; I will look to the community and public ratings to find essays to read, during the final run up.

While I don't often give out a rating of 10, I have not given a score lower than 5 so far this contest. I will give out a decent rating if an essay is either well-written or makes a powerful point, with extra points for essays that do both. Mostly; I will be looking for quality of writing, strength of premises, and compelling logic. Essay that have all of that will be rated highly.

Good Luck to Everyone!

Jonathan

I thank you for your interest in my work and I'll try to reply to all comments eventually, to most as soon as there is time. I will also attempt to read as many as possible of the other essays in the time allotted.

I will be systematically working from the earlier submissions to the present, while trying to honor those who visit my essay with an earlier reading and feedback. I'll be trying to also look for topics of my own special interest and authors whose work I respect. Lastly; I will look to the community and public ratings to find essays to read, during the final run up.

While I don't often give out a rating of 10, I have not given a score lower than 5 so far this contest. I will give out a decent rating if an essay is either well-written or makes a powerful point, with extra points for essays that do both. Mostly; I will be looking for quality of writing, strength of premises, and compelling logic. Essay that have all of that will be rated highly.

Good Luck to Everyone!

Jonathan

Hi, Jonathan. This is a great essay and I agree on the role of the octonions etc. It's good that you concentrated on that theme.

You mentioned consciousness a few times but did not go into much detail. What is your view on consciousness? Is it an illusion, some new physics or what?

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You mentioned consciousness a few times but did not go into much detail. What is your view on consciousness? Is it an illusion, some new physics or what?

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Thanks greatly Phil,

I could have written a very different essay, emphasizing the progression of consciousness angle. But I wanted to show that those Maths shape Physics in a definite way. The octonions generate a hierarchy in levels of abstraction, though, such that a pattern like what Young describes can be spelled out in many different ways to form sentences. I've written out several dozen at this point.

One, open, as multiplicity and formless nothingness, finds peace in true relation, and knows all as self. Oneness, leads to openness, as-ifness, multiplicity, and so on. The rest reflect the theme of a book by Briggs and Peat 'Turbulent Mirror' that there is a far shore to chaos where order re-emerges, and life exploits that border region greatly. This one is a sort of personal credo. But you could also put it in religious terms.

One being, Goddess and God, begat manyness, then complexity beyond reckoning, to find the missing pieces of themselves, and become as one again. So then it becomes a love story featuring the male and female persona of the divine, arising from the order found in the octonions. But it's a bit controversial that the divine feminine emerges first; don't you think?

I know that sounds pretty wild, but I think the stages in the progression within octonion algebra have moods, so that the octonions could be used to craft a fully subjective and qualitative relational database, as a counterpart to the powerful objective and quantitative data classification systems we have today. But this only works because it is also something emergent in the properties of non-associative Maths.

All the Best,

Jonathan

I could have written a very different essay, emphasizing the progression of consciousness angle. But I wanted to show that those Maths shape Physics in a definite way. The octonions generate a hierarchy in levels of abstraction, though, such that a pattern like what Young describes can be spelled out in many different ways to form sentences. I've written out several dozen at this point.

One, open, as multiplicity and formless nothingness, finds peace in true relation, and knows all as self. Oneness, leads to openness, as-ifness, multiplicity, and so on. The rest reflect the theme of a book by Briggs and Peat 'Turbulent Mirror' that there is a far shore to chaos where order re-emerges, and life exploits that border region greatly. This one is a sort of personal credo. But you could also put it in religious terms.

One being, Goddess and God, begat manyness, then complexity beyond reckoning, to find the missing pieces of themselves, and become as one again. So then it becomes a love story featuring the male and female persona of the divine, arising from the order found in the octonions. But it's a bit controversial that the divine feminine emerges first; don't you think?

I know that sounds pretty wild, but I think the stages in the progression within octonion algebra have moods, so that the octonions could be used to craft a fully subjective and qualitative relational database, as a counterpart to the powerful objective and quantitative data classification systems we have today. But this only works because it is also something emergent in the properties of non-associative Maths.

All the Best,

Jonathan

I wanted to add this..

If viewed as a generator of conceptual hierarchy; the octonions appear to spell out the entire arc of learning - from knowing only that you exist, to knowing everything about the universe and seeing it all as a part of yourself. This last stage is sort of like the experience described in T.S. Eliot's classic poem "Little Gidding" to return back home and see it anew, as if for the first time, but now in fullness with the perspective gained from exploring the world.

For the record; I don't think I am making this up, but re-discovering an ancient truth. The same message appears again and again in Mythology, where the Zen Ox fables and the Hero's Journey tell the same tale. Arthur Young expounds somewhat on this Math-Mythology connection, but I think that he never got to make the explicit connection with the octonions - which is what jumps out for me.

All the Best,

Jonathan

If viewed as a generator of conceptual hierarchy; the octonions appear to spell out the entire arc of learning - from knowing only that you exist, to knowing everything about the universe and seeing it all as a part of yourself. This last stage is sort of like the experience described in T.S. Eliot's classic poem "Little Gidding" to return back home and see it anew, as if for the first time, but now in fullness with the perspective gained from exploring the world.

For the record; I don't think I am making this up, but re-discovering an ancient truth. The same message appears again and again in Mythology, where the Zen Ox fables and the Hero's Journey tell the same tale. Arthur Young expounds somewhat on this Math-Mythology connection, but I think that he never got to make the explicit connection with the octonions - which is what jumps out for me.

All the Best,

Jonathan

Jonathan,

You write: " ... evolution of consciousness or intelligence will be seen as a natural outgrowth of higher-order Math."

I think it's rather the other way around. Math is an artificial language. Whether invented or discovered, it remains an artifice.

You spend a lot of time on dimensionality. This, you also treat as artifice, as if spacetime is not physically real and thus not interactive.

Do you think that?

Best,

Tom

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You write: " ... evolution of consciousness or intelligence will be seen as a natural outgrowth of higher-order Math."

I think it's rather the other way around. Math is an artificial language. Whether invented or discovered, it remains an artifice.

You spend a lot of time on dimensionality. This, you also treat as artifice, as if spacetime is not physically real and thus not interactive.

Do you think that?

Best,

Tom

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And Jonathan, please let me remind you of the productive dialogue you launched between you, me and Steven Kenneth Kauffmann in 2013.

http://fqxi.org/community/forum/topic/1586

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http://fqxi.org/community/forum/topic/1586

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Thanks for your interest Tom..

While it may be true that Math as we know it is an invented language; it is also a fact that certain regularities arising in mathematics display the same form, regardless the area of interest or line of reasoning that brings one to them. In the realm of pure abstraction; I can observe that the power of observation is supreme, in that the awakening of...

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While it may be true that Math as we know it is an invented language; it is also a fact that certain regularities arising in mathematics display the same form, regardless the area of interest or line of reasoning that brings one to them. In the realm of pure abstraction; I can observe that the power of observation is supreme, in that the awakening of...

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If spacetime is not * physically * real, Jonathan, special relativity is false.

I did not say math is invented. I said no matter whether it is invented or discovered, it is artifice.

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I did not say math is invented. I said no matter whether it is invented or discovered, it is artifice.

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Dear Jonathan,

To say like "It seems silly to ask how aimless Math can give life and the universe a sense of

direction, when Mathematics is anything but aimless......" is quite wrong within itself because, the mathematical terms as we derive in circular motion, v^2/r is actually mindless terms but see my essay 'Newtonian Dynamics: An explict diversion...' how big scientific breakthrough could it posses when a bit sense is applied on it. And saying like "Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution..........." is always not to be true as our mathematical framing are based on mostly in virtual or imaginary tendency whose real applicants are only observed indirectly through a different path way than it directly refers..and to observe its real presence we need to create the 'sixth sense'.

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To say like "It seems silly to ask how aimless Math can give life and the universe a sense of

direction, when Mathematics is anything but aimless......" is quite wrong within itself because, the mathematical terms as we derive in circular motion, v^2/r is actually mindless terms but see my essay 'Newtonian Dynamics: An explict diversion...' how big scientific breakthrough could it posses when a bit sense is applied on it. And saying like "Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution..........." is always not to be true as our mathematical framing are based on mostly in virtual or imaginary tendency whose real applicants are only observed indirectly through a different path way than it directly refers..and to observe its real presence we need to create the 'sixth sense'.

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Thanks for weighing in Bishal..

You mention circular motion, and I am sure that you can appreciate how a wheel without friction continues spinning endlessly. A point on the wheel will move up and down, or left and right, alternately. One can model this using the imaginary unit*i* to generate sines and cosines using Euler's famous equation (which does not render correctly here). I guess I did not explain adequately that the quaternions and octonions are merely an extension of this principle into 3 or 7 dimensions of rotation.

But if you believe the wheel keeps spinning, so long as there is no impeding force to slow it, then you implicitly understand the evolutive properties of Math. Higher order numbers are like wheels within wheels, in that they encode multiple axes of rotation in layers. This is why they can behave like an evolving system. I am sorry if the natural beauty of the Mathematics does not speak to you, as it does for me. However; it would appear that some of the Math you invoke in your own paper depends upon what I am saying to be true.

All the Best,

Jonathan

You mention circular motion, and I am sure that you can appreciate how a wheel without friction continues spinning endlessly. A point on the wheel will move up and down, or left and right, alternately. One can model this using the imaginary unit

But if you believe the wheel keeps spinning, so long as there is no impeding force to slow it, then you implicitly understand the evolutive properties of Math. Higher order numbers are like wheels within wheels, in that they encode multiple axes of rotation in layers. This is why they can behave like an evolving system. I am sorry if the natural beauty of the Mathematics does not speak to you, as it does for me. However; it would appear that some of the Math you invoke in your own paper depends upon what I am saying to be true.

All the Best,

Jonathan

Dear Jonathan,

".........and I am sure that you can appreciate how a wheel without friction continues spinning endlessly"- please note that this term directly reflect the conservation of angular-momentum which is impossible in none of frame or place in reality because, to move endlessly requires setting no friction but in real practical world it is impossible...whether you perform in empty space or here on earth surface....most of time we refer the perfect empty-space as a possible test of different thought experiments but we all forget that the extrinsic-effect interactions on any body is almost impossible there.. and so, the impeding force you say is never effective to any body extrinsically there in one aspect and in other way in gravitating surface we could not reduced the friction zero.....

best regards from Nepal

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".........and I am sure that you can appreciate how a wheel without friction continues spinning endlessly"- please note that this term directly reflect the conservation of angular-momentum which is impossible in none of frame or place in reality because, to move endlessly requires setting no friction but in real practical world it is impossible...whether you perform in empty space or here on earth surface....most of time we refer the perfect empty-space as a possible test of different thought experiments but we all forget that the extrinsic-effect interactions on any body is almost impossible there.. and so, the impeding force you say is never effective to any body extrinsically there in one aspect and in other way in gravitating surface we could not reduced the friction zero.....

best regards from Nepal

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Hi Jonathan,

Good to be in another contest with you and to read your excellent paper.

I am reluctant to put a crown on language or mathematics. I consider mathematics as an evolution of language. And mathematics itself is a forever evolving ring of power. And as a ring of power it is a false god. The ring of power caused Frodo no end of trouble!

Nevertheless this essay is one of the best.

Put on your never ending list of things to do (it's important) to read my two papers on gravity and dark energy. These are listed in my about the author section.

Will mathematics grow up (evolve) and solve its own problems :)

Don Limuti

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Good to be in another contest with you and to read your excellent paper.

I am reluctant to put a crown on language or mathematics. I consider mathematics as an evolution of language. And mathematics itself is a forever evolving ring of power. And as a ring of power it is a false god. The ring of power caused Frodo no end of trouble!

Nevertheless this essay is one of the best.

Put on your never ending list of things to do (it's important) to read my two papers on gravity and dark energy. These are listed in my about the author section.

Will mathematics grow up (evolve) and solve its own problems :)

Don Limuti

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Thanks greatly Don!

It is good to be in community with you as well. I think there is plenty of confusion in the Math and Physics community, where a lot of people put the symbolic reality ahead of the real world. But when I talk about Mathematics in the context of this essay; it is rather about the unchanging patterns that make Math what it is. Projective geometry is the mathematical study of perspective. I can't tell you why some of its root postulates bring us straight to the octonions, but I know it is true.

Math is much abused by those who try to make it bend to their will. A good example of Math forged into a ring of power would be the Gaussian Copula Function, which was the basis for financial derivatives, and was itself based on formulas used in risk and failure analysis. But it was used fictitiously (as though predictable risk equals zero risk), and its broad mis-usage was one of the contributing factors of the market crash in 2008. Mandelbrot had warned us before then, but the finance gurus did not listen.

So pure Math had the answers, but nobody wanted to hear.

All the Best,

Jonathan

It is good to be in community with you as well. I think there is plenty of confusion in the Math and Physics community, where a lot of people put the symbolic reality ahead of the real world. But when I talk about Mathematics in the context of this essay; it is rather about the unchanging patterns that make Math what it is. Projective geometry is the mathematical study of perspective. I can't tell you why some of its root postulates bring us straight to the octonions, but I know it is true.

Math is much abused by those who try to make it bend to their will. A good example of Math forged into a ring of power would be the Gaussian Copula Function, which was the basis for financial derivatives, and was itself based on formulas used in risk and failure analysis. But it was used fictitiously (as though predictable risk equals zero risk), and its broad mis-usage was one of the contributing factors of the market crash in 2008. Mandelbrot had warned us before then, but the finance gurus did not listen.

So pure Math had the answers, but nobody wanted to hear.

All the Best,

Jonathan

Hi dear Jonathan,

It is a pleasure to re-meet you here in FQXi Essay Contest.

I have just read your nice Essay. As usual, you released a remarkable contribution. In this case, your Essay seems also a bit provocative, but I strongly appreciate people "thinking outside the box". Hence, your Essay deserves the highest score that I am going to give you. Good luck in the Contest!

Cheers, Ch.

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It is a pleasure to re-meet you here in FQXi Essay Contest.

I have just read your nice Essay. As usual, you released a remarkable contribution. In this case, your Essay seems also a bit provocative, but I strongly appreciate people "thinking outside the box". Hence, your Essay deserves the highest score that I am going to give you. Good luck in the Contest!

Cheers, Ch.

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Thank You greatly Christian!

It is my pleasure to again encounter you here. As you know; I hold your work in high regard, and your praise is much valued. I think that we need to look 'outside the box' to a degree, since Physics will paint itself into a corner otherwise, but I was trying to awaken people also to part of what we have inside of the box with us.

So many in Physics make use of the mechanisms of Math in a utilitarian way, but I think to an extent our tools have a life of their own, which deserves to be brought to light. While people in some parts of the world are eager to make elephants into beasts of burden, they are marvelous creatures in their own right, and they deserve as much appreciation as the mahout who skillfully prods them along - to do our bidding.

All the Best,

Jonathan

It is my pleasure to again encounter you here. As you know; I hold your work in high regard, and your praise is much valued. I think that we need to look 'outside the box' to a degree, since Physics will paint itself into a corner otherwise, but I was trying to awaken people also to part of what we have inside of the box with us.

So many in Physics make use of the mechanisms of Math in a utilitarian way, but I think to an extent our tools have a life of their own, which deserves to be brought to light. While people in some parts of the world are eager to make elephants into beasts of burden, they are marvelous creatures in their own right, and they deserve as much appreciation as the mahout who skillfully prods them along - to do our bidding.

All the Best,

Jonathan

Thanks Jonathan.

Yes, I completely agree with you that awakening people to part of what we have inside of the box with us is important in the same way that thinking outside the box. What is important in both of the cases is starting from plausible hypotheses and proceeding with mathematical rigor. Your aphorism on elephants is very nice.

I hope that you will have a chance to read our Essay.

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Yes, I completely agree with you that awakening people to part of what we have inside of the box with us is important in the same way that thinking outside the box. What is important in both of the cases is starting from plausible hypotheses and proceeding with mathematical rigor. Your aphorism on elephants is very nice.

I hope that you will have a chance to read our Essay.

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Jonathan,

I've been looking forward to reading an essay arguing the more minority view and I found you did an excellent job, though I can't say you reversed my support of physical 'causality' in the universe, which at times your language seemed to challenge; i.e. mathematics*'giving rise to processes'* and *'telling the universe what to create'.*

I assume you really haven't abandoned cause and effect, i.e. an action producing an effect not the mathematics that describes it, but if that's true then appearing to do so did seem to need a little more explanation.

I have a rudimentary understanding of non-commutativity and non-associative geometry but both seemed in need of your definition before invoking them so heavily. Similarly I never did see or fully understand your own view of what the elephant in the room actually was. I've long understood and rationalised octonians, fractals and perturbation theory (to higher orders), loved the amplituhedron, and know those in QG see it as the only way ahead, but do you felt you introduced any new argument to win over those less sold on the concepts?

I was interested in your comments on the '2D' higher order case that some math posits, (which seems rather at odds with 10D!). What I first saw I tended to dismiss as 'unreal' understanding but for me such responses are always provisional so can you provide any good links on that?

Nicely written and argued as usual and I think should certainly be a finalist.

I hope you may also offer a mathematical perspective on classical momentum transfer distributions I describe in my own essay appearing to reproduce QM's predictions.

Best wishes

Peter

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I've been looking forward to reading an essay arguing the more minority view and I found you did an excellent job, though I can't say you reversed my support of physical 'causality' in the universe, which at times your language seemed to challenge; i.e. mathematics

I assume you really haven't abandoned cause and effect, i.e. an action producing an effect not the mathematics that describes it, but if that's true then appearing to do so did seem to need a little more explanation.

I have a rudimentary understanding of non-commutativity and non-associative geometry but both seemed in need of your definition before invoking them so heavily. Similarly I never did see or fully understand your own view of what the elephant in the room actually was. I've long understood and rationalised octonians, fractals and perturbation theory (to higher orders), loved the amplituhedron, and know those in QG see it as the only way ahead, but do you felt you introduced any new argument to win over those less sold on the concepts?

I was interested in your comments on the '2D' higher order case that some math posits, (which seems rather at odds with 10D!). What I first saw I tended to dismiss as 'unreal' understanding but for me such responses are always provisional so can you provide any good links on that?

Nicely written and argued as usual and I think should certainly be a finalist.

I hope you may also offer a mathematical perspective on classical momentum transfer distributions I describe in my own essay appearing to reproduce QM's predictions.

Best wishes

Peter

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Thank you Peter,

I appreciate the time taken to read the essay, and also your comments. I should indeed have defined my terms better, and failing that I needed to include some endnotes with appropriate definitions and a descriptive summary of important concepts my point hinges on. I will cue you in to other works in the queue, which will explain the 2-d relevance. Suffice it for now, to say that the Mandelbrot Set is maximally asymmetric, and so serves as a counterpart to highly symmetric objects like E8. It serves as a window into how higher-dimensional trends drive evolution - but it is a cross-section in 2-d.

All the Best,

Jonathan

I appreciate the time taken to read the essay, and also your comments. I should indeed have defined my terms better, and failing that I needed to include some endnotes with appropriate definitions and a descriptive summary of important concepts my point hinges on. I will cue you in to other works in the queue, which will explain the 2-d relevance. Suffice it for now, to say that the Mandelbrot Set is maximally asymmetric, and so serves as a counterpart to highly symmetric objects like E8. It serves as a window into how higher-dimensional trends drive evolution - but it is a cross-section in 2-d.

All the Best,

Jonathan

Hi Jonathan,

I read your submission and I am glad that you are one of the many people in this contest that choose the math aspect of the contest question to answer instead of the the mind aspect. Reading your article I find out you are a fan of string theory. That does not make me happy, but I can't count it against your article. What I do count against your article is the fault in your...

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I read your submission and I am glad that you are one of the many people in this contest that choose the math aspect of the contest question to answer instead of the the mind aspect. Reading your article I find out you are a fan of string theory. That does not make me happy, but I can't count it against your article. What I do count against your article is the fault in your...

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I am compelled to respond to this..

While I am not a great fan of String Theory; I admit its value and I think it's part of the total picture we must examine, but it is a smaller piece of the puzzle than some believe. I am a friend of Brian Greene and I have met Ed Witten, but I am more in the camp of Abhay Ashtekar, in regards to how the Strings program fits into the overall spectrum of...

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While I am not a great fan of String Theory; I admit its value and I think it's part of the total picture we must examine, but it is a smaller piece of the puzzle than some believe. I am a friend of Brian Greene and I have met Ed Witten, but I am more in the camp of Abhay Ashtekar, in regards to how the Strings program fits into the overall spectrum of...

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Jonathan J. Dickau,

Evolution starts from biological virus.

Knowledge of virology, linguistic, memes, contagion and mechanics of computer virus can help us solve this problem.

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Evolution starts from biological virus.

Knowledge of virology, linguistic, memes, contagion and mechanics of computer virus can help us solve this problem.

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I appreciate the insight Shaikh Raisuddin..

It is true, as you say, that simple organisms like the virus begin the upward spiral on the ladder of evolution - forming early branches on the tree of life, while not yet living in the sense of what evolved organisms have achieved. Indeed; we are a symbiosis of co-opted pieces from earlier organisms, where bits of code have been merged to form our human genome.

So I agree that what you suggest can be helpful.

All the Best,

Jonathan

It is true, as you say, that simple organisms like the virus begin the upward spiral on the ladder of evolution - forming early branches on the tree of life, while not yet living in the sense of what evolved organisms have achieved. Indeed; we are a symbiosis of co-opted pieces from earlier organisms, where bits of code have been merged to form our human genome.

So I agree that what you suggest can be helpful.

All the Best,

Jonathan

Johnathan, I am pleasantly surprised by how accessible and enjoyable your essay was considering it was primarily about mathematics.Well done. I think the point you make about complex algebras being non commutative and naturally related to geometry and sequential change very important as that is what a description of the material universe requires. Quaternions have that non commutative characteristic. They are sufficient or modelling evolving 3 dimensional objects and fractals too. I 'm not sure that higher (than 4) dimensional algebras are needed for modelling the material universe we inhabit, though I'm sure they do produce interesting models. Isn't it just that the 3 spatial dimensions unobserved don't have an orientation? we could say they are in all orientations, any orientation or no orientation as orientation is relative and without the observer viewpoint orientation doesn't apply.Could 248 dimensional E8 be an approximation of that? What is it about the higher (than 4) dimensional algebras that makes them particularly relevant. You mentioned hidden variables, and sphere packing -is there something else that in your opinion make them necessary, rather than just appealing? Kind regards Georgina

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Thanks for your kind remarks Georgina..

I am happy you grasp my main point. Some folks learn a lot of Math, but don't have the sense of such things, possibly because they are stuck on manipulating symbols or finding equations that are easy to work with, while nature ignores our boundaries of convenience. One knowledgeable friend asserts that many scientists simply don't go far enough with the Math to do the job correctly, or stop short of a rigorous treatment with the solution in sight. Borrowing an idealized equation from a textbook, without considering its limitations, won't always allow you to capture nature as it is.

But I agree that it is a waste of time to invoke the octonions for everyday Physics, while the quaternions have great utility - and do capture the needed dynamism to model evolutive properties. However; when one gets to some of the tough problems at the crux of fundamental Physics, as with quantum gravity where one is dealing with the extreme regions where both gravity and QM have a strong effect, is where knowing about the octonions and non-associativity becomes important. And the 8-d octonions are adequate to hold E8, even though its largest regular extent is in 248-d. One can also make a beautiful Zome model in 3-d, which is a projection of the 8-d figure. Pretty cool, huh?

All the Best,

Jonathan

I am happy you grasp my main point. Some folks learn a lot of Math, but don't have the sense of such things, possibly because they are stuck on manipulating symbols or finding equations that are easy to work with, while nature ignores our boundaries of convenience. One knowledgeable friend asserts that many scientists simply don't go far enough with the Math to do the job correctly, or stop short of a rigorous treatment with the solution in sight. Borrowing an idealized equation from a textbook, without considering its limitations, won't always allow you to capture nature as it is.

But I agree that it is a waste of time to invoke the octonions for everyday Physics, while the quaternions have great utility - and do capture the needed dynamism to model evolutive properties. However; when one gets to some of the tough problems at the crux of fundamental Physics, as with quantum gravity where one is dealing with the extreme regions where both gravity and QM have a strong effect, is where knowing about the octonions and non-associativity becomes important. And the 8-d octonions are adequate to hold E8, even though its largest regular extent is in 248-d. One can also make a beautiful Zome model in 3-d, which is a projection of the 8-d figure. Pretty cool, huh?

All the Best,

Jonathan

I don't know yet, where still higher dimensions will fit in..

But I think there is a place for them on the spectrum of possibilities, that nature will employ and project down to three dimensions if that's where it's needed. I mainly imagine that there are important things to know about what happens in the higher heavens of Math, but I don't claim to be able to explain their import. There appears to be a telescoping property that I think is inherited from Bott periodicity, where higher order quantities are extensible, but can be reflected down to lower order forms. So some of what happens there can be shown relevant to what happens here.

All the Best,

Jonathan

But I think there is a place for them on the spectrum of possibilities, that nature will employ and project down to three dimensions if that's where it's needed. I mainly imagine that there are important things to know about what happens in the higher heavens of Math, but I don't claim to be able to explain their import. There appears to be a telescoping property that I think is inherited from Bott periodicity, where higher order quantities are extensible, but can be reflected down to lower order forms. So some of what happens there can be shown relevant to what happens here.

All the Best,

Jonathan

Dear Jonathan Dickau

I saw your comments on the essay of K. Willy and I become curious about both essays.

There are different ways of “decoding” the universe; yours and mine are quite different. I read your essay, which is very well written, and you present well your point. I think that you have a promising approach but it is not my line of reasoning, I can only be a curious spectator of your work.

I read that you are part of viXra team; well, I want to congratulate and thank you. I have a paper in viXra with more then 900 downloads in spite of my almost null divulgation of it (vixra.org/abs/1107.0016) ; I receive emails from cosmologists confirming that I found the solution to the cosmological problem, some urging me to publish it in whatever “citable” place. However, as I am not “affiliated” and that solution implies a change of paradigm, hardly could I ever publish it in a relevant scientific journal. I hope that one day you will see viXra entering the history of science because of that paper that could not be published anywhere else.

From the above, you may assume that I am an “amateur”. If you are so kind to take a look at my essay, you will understand that I am something else - in spite of our different approaches. And I have something to ask you: a piece of advice.

All the best

Alfredo Gouveia de Oliveira

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I saw your comments on the essay of K. Willy and I become curious about both essays.

There are different ways of “decoding” the universe; yours and mine are quite different. I read your essay, which is very well written, and you present well your point. I think that you have a promising approach but it is not my line of reasoning, I can only be a curious spectator of your work.

I read that you are part of viXra team; well, I want to congratulate and thank you. I have a paper in viXra with more then 900 downloads in spite of my almost null divulgation of it (vixra.org/abs/1107.0016) ; I receive emails from cosmologists confirming that I found the solution to the cosmological problem, some urging me to publish it in whatever “citable” place. However, as I am not “affiliated” and that solution implies a change of paradigm, hardly could I ever publish it in a relevant scientific journal. I hope that one day you will see viXra entering the history of science because of that paper that could not be published anywhere else.

From the above, you may assume that I am an “amateur”. If you are so kind to take a look at my essay, you will understand that I am something else - in spite of our different approaches. And I have something to ask you: a piece of advice.

All the best

Alfredo Gouveia de Oliveira

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Your comments are most appreciated Alfredo..

Differences in perspective often bring clarity to a subject, because people tend to get tunnel-vision over time. Something called the Einstellung effect sets in, where people try to adapt their prior assumptions as little as possible, rather than adopting a superior model when it comes along - even if there is a great leap in predictive capability. Sometimes the compelling utility of existing understanding, or even the great investment in effort required to master a subject (as with String Theory), will blur our vision on better alternatives.

I am also unaffiliated with any academic institution. But I make an effort to appear at conferences and submit my papers for publication. At this point; I get invitations from time to time, some of my prior publications got me on somebody's list of authors in a certain field. But once that happens; you need to keep yourself in the game by participating - submissions to journals, abstracts to conference organizers, proposals for grants, entries to contests, and so on. Only when the right people know who you are can they advance your cause.

All the Best,

Jonathan

Differences in perspective often bring clarity to a subject, because people tend to get tunnel-vision over time. Something called the Einstellung effect sets in, where people try to adapt their prior assumptions as little as possible, rather than adopting a superior model when it comes along - even if there is a great leap in predictive capability. Sometimes the compelling utility of existing understanding, or even the great investment in effort required to master a subject (as with String Theory), will blur our vision on better alternatives.

I am also unaffiliated with any academic institution. But I make an effort to appear at conferences and submit my papers for publication. At this point; I get invitations from time to time, some of my prior publications got me on somebody's list of authors in a certain field. But once that happens; you need to keep yourself in the game by participating - submissions to journals, abstracts to conference organizers, proposals for grants, entries to contests, and so on. Only when the right people know who you are can they advance your cause.

All the Best,

Jonathan

Dear Jonathan,

thanks for the very interesting essay (with a high vote from my side). Your consideration of octonions keep me interested

again in this interesting topic. I considered the hypercomplex numbers years ago but forgot

it.

Some remarks from topology. There is a topological view on these normed algebras (C, H, O).

The unit elements are spheres: S^1, S^3 and S^7. Now there is a "topological" proof that

C,H,O are the only normed algebras. If there is a non-zero vector field on the sphere S^1,

S^3, S^7 then there is a non-zero element of the algebra which can be reversed (allowing

division). But one needs more: every element of the algebra (except zero of course) must be of this form. But then you need as much as non-zero independent vector fields like the dimension of the sphere. A deep theorem states now that only the S^1, S^3 and S^7 have this property so that the only normed algebras are C, H and O. (BTW I used this result for a no-go theorem in quantum computing, see my paper.)

Nonassociated algebras are not so special in math. A large class are the Lie algebras (with the Jacobi identity instead of the associative law). But octonions are more than that. This algebra is deeply connected to the exceptional Lie groups (like E_8, E_7 or G_2). In geometry there are special manifolds with a calibration (a linear form with special properties). There, the octonions appear as G_2 structures on 7-dimensional manifolds. M theory as part of string theory used them.

But you rather ask for low-dimensional (3D, 4D) counterparts. I'm specialized in this dimensions and here it is: a very large class of 3-dimensional manifolds (arithmetic hyperbolic 3-manifolds) is constructed by using the quaternion algebra and its properties are strongly related to (or determined by) this algbera.

4-dimensional manifolds (simply-connected i.e. where all closed curves can be contracted to a point) are classified by the intersection form: a bilinear form with the intersection number of the embedded surfaces. This bilinear form is taken over the integers. In the classification of these forms, the so-called E_8 lattice played a fundamental role. But this lattice is nothing else then the integer octonions (Kirmse integers). So, your octonions are directly related to the spacetime (seen as 4D manifold) and you don't need any extra dimensions.

If you like please have a look into my essay where I used topological methods to understand our brain.

All the best

Torsten

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thanks for the very interesting essay (with a high vote from my side). Your consideration of octonions keep me interested

again in this interesting topic. I considered the hypercomplex numbers years ago but forgot

it.

Some remarks from topology. There is a topological view on these normed algebras (C, H, O).

The unit elements are spheres: S^1, S^3 and S^7. Now there is a "topological" proof that

C,H,O are the only normed algebras. If there is a non-zero vector field on the sphere S^1,

S^3, S^7 then there is a non-zero element of the algebra which can be reversed (allowing

division). But one needs more: every element of the algebra (except zero of course) must be of this form. But then you need as much as non-zero independent vector fields like the dimension of the sphere. A deep theorem states now that only the S^1, S^3 and S^7 have this property so that the only normed algebras are C, H and O. (BTW I used this result for a no-go theorem in quantum computing, see my paper.)

Nonassociated algebras are not so special in math. A large class are the Lie algebras (with the Jacobi identity instead of the associative law). But octonions are more than that. This algebra is deeply connected to the exceptional Lie groups (like E_8, E_7 or G_2). In geometry there are special manifolds with a calibration (a linear form with special properties). There, the octonions appear as G_2 structures on 7-dimensional manifolds. M theory as part of string theory used them.

But you rather ask for low-dimensional (3D, 4D) counterparts. I'm specialized in this dimensions and here it is: a very large class of 3-dimensional manifolds (arithmetic hyperbolic 3-manifolds) is constructed by using the quaternion algebra and its properties are strongly related to (or determined by) this algbera.

4-dimensional manifolds (simply-connected i.e. where all closed curves can be contracted to a point) are classified by the intersection form: a bilinear form with the intersection number of the embedded surfaces. This bilinear form is taken over the integers. In the classification of these forms, the so-called E_8 lattice played a fundamental role. But this lattice is nothing else then the integer octonions (Kirmse integers). So, your octonions are directly related to the spacetime (seen as 4D manifold) and you don't need any extra dimensions.

If you like please have a look into my essay where I used topological methods to understand our brain.

All the best

Torsten

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This post is full of useful info Torsten!

I think you are talking about the fact that the Frobenius conjecture is proved, and is therefore a theorem, in your comment "A deep theorem states now that only the S^1, S^3 and S^7 have this property so that the only normed algebras are C, H and O." I used to freak out when I saw that name, close the book or put down the paper, and then say "that's enough for now," but I have since learned that Frobenius was a friend to my cause all along.

I will follow up on your essay page.

All the Best,

Jonathan

I think you are talking about the fact that the Frobenius conjecture is proved, and is therefore a theorem, in your comment "A deep theorem states now that only the S^1, S^3 and S^7 have this property so that the only normed algebras are C, H and O." I used to freak out when I saw that name, close the book or put down the paper, and then say "that's enough for now," but I have since learned that Frobenius was a friend to my cause all along.

I will follow up on your essay page.

All the Best,

Jonathan

I had a deep theorem of Adams in mind (which spheres have a trivial tangent bundle, answer only S^1, S^3 and S^7)

Frobenius conjecture is more connected with sporadic groups (with many relations to integer octonions).

More later

Torsten

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Frobenius conjecture is more connected with sporadic groups (with many relations to integer octonions).

More later

Torsten

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Hi,

Thank you for an interesting article. A central part of my essay is also about the Octonions. However I think our perspectives are different. But, again thank you for some interesting ideas.

All the best,

Noson

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Thank you for an interesting article. A central part of my essay is also about the Octonions. However I think our perspectives are different. But, again thank you for some interesting ideas.

All the best,

Noson

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Thank you Noson..

After reading your essay; I agree our perspectives are quite different, but our views complement each other well - filling in the gaps of what is left unsaid.

More later,

Jonathan

After reading your essay; I agree our perspectives are quite different, but our views complement each other well - filling in the gaps of what is left unsaid.

More later,

Jonathan

Dear Jonathan J. Dickau,

Thank you for your comment and the article of A. D. Sakharov, you sent.

And I very much appreciate that

“This is a question I addressed in my first ever Gravity Research Foundation essay, just submitted this week. I also employ the metaphor of a sink drain, though it is not my central thesis”

If it is possible, I would like to read your essay in Gravity Research Foundation.

Thank you again,

With Best Regards,

Ch.Bayarsaikhan

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Thank you for your comment and the article of A. D. Sakharov, you sent.

And I very much appreciate that

“This is a question I addressed in my first ever Gravity Research Foundation essay, just submitted this week. I also employ the metaphor of a sink drain, though it is not my central thesis”

If it is possible, I would like to read your essay in Gravity Research Foundation.

Thank you again,

With Best Regards,

Ch.Bayarsaikhan

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Thank you for your interest..

As you know, I did send the paper you requested, and you acknowledged on your own essay thread. I hope my Gravity Research Foundation essay is of some value.

Regards,

Jonathan

As you know, I did send the paper you requested, and you acknowledged on your own essay thread. I hope my Gravity Research Foundation essay is of some value.

Regards,

Jonathan

Nice to read your essay.... and your proposal about small scales...from my poit of view the String proposal of KK spaces (Universes) of 6D is very interesting and suitables... these 6D could be the floor generators of Our Scale Universe, and that could explain why String Theory is good to explain Our Scale Range... because it is composed by very small 6D branes.... Vacuum will be these 6D KK structure.... but inside these KK 6D spaces, other universes could be...

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Thanks greatly David,

As I recall, I much enjoyed your alternatively scale-relative essay.

Kind Regards,

Jonathan

As I recall, I much enjoyed your alternatively scale-relative essay.

Kind Regards,

Jonathan

Dear Jonathan,

I am going to disappoint you ! I never felt so handicapped perusing any essay as I felt while reading this. I had to consult and learn the mathematical terms afresh. Took the whole day just doing that. Even then my knowledge fell short to understanding dense / cryptic use of mathematics and their implications. So, I am not in a position to add value with my...

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I am going to disappoint you ! I never felt so handicapped perusing any essay as I felt while reading this. I had to consult and learn the mathematical terms afresh. Took the whole day just doing that. Even then my knowledge fell short to understanding dense / cryptic use of mathematics and their implications. So, I am not in a position to add value with my...

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Thanks anyway Rajiv!

In a way, you have paid me a compliment and shown me I am at a crossroads. I felt the same, the first time I read Alain Connes' paper "Noncommutative Geometry Year 2000" I would get a few pages in, get overloaded, then come back again another day until I could get a little further each time. Much of it seemed utterly incomprehensible, but I eventually grasped a few key concepts - due to sheer repetition. Later I learned that Connes advised budding mathematicians to do exactly that, adding that when his brain became full he would recline for a while and nap or lay in reverie while letting the new ideas sink in.

I am presenting an idea that is foreign to almost everyone literate in Math, which goes against the grain of some of what we are taught early on, and that only a handful of mathematicians are masterful about. The fact that I see it as a key is only that I have focused so intently on certain points of interest for years. No worries!

All the Best,

Jonathan

In a way, you have paid me a compliment and shown me I am at a crossroads. I felt the same, the first time I read Alain Connes' paper "Noncommutative Geometry Year 2000" I would get a few pages in, get overloaded, then come back again another day until I could get a little further each time. Much of it seemed utterly incomprehensible, but I eventually grasped a few key concepts - due to sheer repetition. Later I learned that Connes advised budding mathematicians to do exactly that, adding that when his brain became full he would recline for a while and nap or lay in reverie while letting the new ideas sink in.

I am presenting an idea that is foreign to almost everyone literate in Math, which goes against the grain of some of what we are taught early on, and that only a handful of mathematicians are masterful about. The fact that I see it as a key is only that I have focused so intently on certain points of interest for years. No worries!

All the Best,

Jonathan

Dear Jonathan,

Interesting and original essay! I share your interest in the strange beasts of higher mathematics, the Monster Group, the Mandelbrot Set, E8, etc., even if I am not convinced that we can recover as much fundamental physics from them that you think can be done. But what I fully agree with, having come up with the same incomprehension with my own Mathematical Universe Hypothesis related scenarios, is that most people have a completely inaccurate conception of what math is! I fully agree with you when you say that

"Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution comes from will disappear when we realize what Math is at its root, a systematic exploration of features characterizing the laws by which form evolves."

Good luck in the contest! Sincerely,

Marc

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Interesting and original essay! I share your interest in the strange beasts of higher mathematics, the Monster Group, the Mandelbrot Set, E8, etc., even if I am not convinced that we can recover as much fundamental physics from them that you think can be done. But what I fully agree with, having come up with the same incomprehension with my own Mathematical Universe Hypothesis related scenarios, is that most people have a completely inaccurate conception of what math is! I fully agree with you when you say that

"Seeing Math as dry – as though it was mindless and lifeless – is the real problem, and the mystery of where evolution comes from will disappear when we realize what Math is at its root, a systematic exploration of features characterizing the laws by which form evolves."

Good luck in the contest! Sincerely,

Marc

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Thanks greatly Marc,

I appreciate that you share my opinion about the true nature of Math, because it has become hard for me to see Math as dull and lifeless. Instead; I am continually surprised by discoveries of beauty and hidden order in structures I thought I had understood. I thank you for the thoughtful remarks and a fair rating along with. I have been looking forward to reading your essay, and I'll push it up the queue a bit, to get to it sooner.

All the Best,

Jonathan

I appreciate that you share my opinion about the true nature of Math, because it has become hard for me to see Math as dull and lifeless. Instead; I am continually surprised by discoveries of beauty and hidden order in structures I thought I had understood. I thank you for the thoughtful remarks and a fair rating along with. I have been looking forward to reading your essay, and I'll push it up the queue a bit, to get to it sooner.

All the Best,

Jonathan

Dear Jonathan

I enjoyed your essay despite the fact that it mostly refers to areas of Maths that I only heard about without learning - quaternions, octonians, E8, and the others you are thankfully comfortable with.

Because of writing my contribution to last years's fqxi contest I have thought a lot about the intimate relationship of physics and mathematics. I concluded that it is not to be wondered that the human mind, having evolved from organisms that themselves evolved evolved closely on the molecular scale with Nature itself, has the capacity to understand that Nature. Also that mathematics itself is firmly rooted in -at least - the model of the Universe I have concocted: concepts like number, dimensions, rotation, geometry all emerge from the lattice of of an evolving cellular automata.

For the above reason I felt a little uncomfortable with the autonomous almost living powers you almost give to mathematics, although you are of course right in trusting its continuing importance in physics.

Vladimir

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I enjoyed your essay despite the fact that it mostly refers to areas of Maths that I only heard about without learning - quaternions, octonians, E8, and the others you are thankfully comfortable with.

Because of writing my contribution to last years's fqxi contest I have thought a lot about the intimate relationship of physics and mathematics. I concluded that it is not to be wondered that the human mind, having evolved from organisms that themselves evolved evolved closely on the molecular scale with Nature itself, has the capacity to understand that Nature. Also that mathematics itself is firmly rooted in -at least - the model of the Universe I have concocted: concepts like number, dimensions, rotation, geometry all emerge from the lattice of of an evolving cellular automata.

For the above reason I felt a little uncomfortable with the autonomous almost living powers you almost give to mathematics, although you are of course right in trusting its continuing importance in physics.

Vladimir

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One needs to acknowledge..

The science of optical perspective is encoded in Projective Geometry, a branch of Mathematics which oddly turns out to be connected with the octonions. 'Why should this be?' I wonder, but know it is true. So there are ways the everyday and higher Maths are intertwined. However; sometimes fundamental realities really are as simple as we imagine them to be, as with your 'beautiful universe' theory. So do not lose sight of the fact you can be on to something, even if that is not the full picture or a commanding view.

My main point is that Math evolves, as you appear to agree, only I think Math moves forward under its own power.

All the Best,

Jonathan

The science of optical perspective is encoded in Projective Geometry, a branch of Mathematics which oddly turns out to be connected with the octonions. 'Why should this be?' I wonder, but know it is true. So there are ways the everyday and higher Maths are intertwined. However; sometimes fundamental realities really are as simple as we imagine them to be, as with your 'beautiful universe' theory. So do not lose sight of the fact you can be on to something, even if that is not the full picture or a commanding view.

My main point is that Math evolves, as you appear to agree, only I think Math moves forward under its own power.

All the Best,

Jonathan

How nice that optical perspective/ projective geometry are related to octonians! As a primarily visual person I fully understand the former, but the algebraic form confuses me. I have invented a mechanical device the Perspector to draw perspectives of 3D objects and in one of my fqxi essays used the example of perspective to show how an observer's point-of-view can 'distort' an object while the object is actually unchanged (to contrast Einsten's observer-based Special Relativity from one embedded in an absolute universe).

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Oh and I forgot to mention that I wrote my entire post whilst enjoying listening to Pete Seeger's "At 89" which you contributed to as "choir, chorus, engineer, mixing, vocals"- great! One wants to know more about your other talents and achievements!

V

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V

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Thank you so much Vladimir!

Your comments are most welcome, and I look forward to reading your essay. It is a busy day for me, but I expect to get back to reading later today, and I'll have a full comment then.

All the Best,

Jonathan

Your comments are most welcome, and I look forward to reading your essay. It is a busy day for me, but I expect to get back to reading later today, and I'll have a full comment then.

All the Best,

Jonathan

Jonathan Dickau,

I enjoyed your essay because it is open to the idea that math itself contains the seeds of consciousness. I am an agnostic when it comes to the existence of consciousness or volition before it emerges in physical form but do agree with you that these must be based on a mathematical structure.

Fractal structures are ubiquitous in nature; causal lattices find a home in various mappings from the most fundamental particle interactions through the most complex structures in the universe, neural nets.

Also, I think that to dismiss imaginary and complex numbers as nonphysical is shortsighted as the equations that contain them fit with physical observation in a way that classical equations (those with just real numbers) do not. You put it well when you say: “… Nor does it make sense to assert that the real world is content to function within the space of real numbers.”

Hawking's question: “what puts the fire in the equations?” becomes relevant here. It has long been the contention of philosophers that abstract objects are causally inert; and here again I am an agnostic. There is the old saw in physics, which may well be operant, that whatever is not forbidden is mandatory; so given a start, any start, to physical existence, even a probabilistic one, it opens the door for a physical emergence of consciousness.

Another of your observations, beautifully put: “… non-zero ordinary or simple numbers are the end of the process chain.”

I am being speculative here, but it seems the complex interference patterns of the eigenstates of physical being held in superposition takes place in a complex space. And, as George Ellis puts it, collapse of the wavefunction is contextual. The inner product of that interference pattern is discarded by observation (probabilistically, by decoherence or by a conscious intervention) and what remains is the real number part.

The rules of non-commutative and non-associative math make it a tougher slog to an understanding. In none of my science classes was this presented as a path forward. At the point where the math becomes that much more challenging, for those of us who possess more scientific curiosity than mathematical ability, it becomes very discouraging indeed to be confronted with this much homework; it becomes a barrier to entry. When the phenomenon we see in nature do not yield to the simple formulations about the mathematics we know well, and then again to the intermediate formulations and then again to the more difficult formulations, it then finally occurs to us that, yes indeed, it can be this difficult. It goes against the grain of the human tendency to look for the keys under the lamp post, where the looking is easier.

Also, I really like the idea that, on its smallest levels, the structure (quantized discrete structures?!) of space goes (go) back to being 2-D and you go on to suggest that dimensionalities should be viewed as a spectrum, and further they are not limited to integer values and change over time, which opens the idea even more. Well done, sir! That opens the problem up nicely. I don't believe we will ever be able to go back to conceiving of physical reality limited to a simple Euclidean form.

I don't think of nature or math as an orchestrator of relationships; nature does not have to resort to trying these combinations out in sequence. Mathematics holds all of the eigenstates of physical being in superposition and can solve them by the interference patterns they produce; they shimmer into existence by virtue of their holographic fruitfulness.

Some of the underlying structures are more fruitful than others, so one would intuit that evolution would occur over a spacio-temporal spectrum of emergence. As you say: “we will see that math requires it.”

Best regards,

Jim Stanfield

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I enjoyed your essay because it is open to the idea that math itself contains the seeds of consciousness. I am an agnostic when it comes to the existence of consciousness or volition before it emerges in physical form but do agree with you that these must be based on a mathematical structure.

Fractal structures are ubiquitous in nature; causal lattices find a home in various mappings from the most fundamental particle interactions through the most complex structures in the universe, neural nets.

Also, I think that to dismiss imaginary and complex numbers as nonphysical is shortsighted as the equations that contain them fit with physical observation in a way that classical equations (those with just real numbers) do not. You put it well when you say: “… Nor does it make sense to assert that the real world is content to function within the space of real numbers.”

Hawking's question: “what puts the fire in the equations?” becomes relevant here. It has long been the contention of philosophers that abstract objects are causally inert; and here again I am an agnostic. There is the old saw in physics, which may well be operant, that whatever is not forbidden is mandatory; so given a start, any start, to physical existence, even a probabilistic one, it opens the door for a physical emergence of consciousness.

Another of your observations, beautifully put: “… non-zero ordinary or simple numbers are the end of the process chain.”

I am being speculative here, but it seems the complex interference patterns of the eigenstates of physical being held in superposition takes place in a complex space. And, as George Ellis puts it, collapse of the wavefunction is contextual. The inner product of that interference pattern is discarded by observation (probabilistically, by decoherence or by a conscious intervention) and what remains is the real number part.

The rules of non-commutative and non-associative math make it a tougher slog to an understanding. In none of my science classes was this presented as a path forward. At the point where the math becomes that much more challenging, for those of us who possess more scientific curiosity than mathematical ability, it becomes very discouraging indeed to be confronted with this much homework; it becomes a barrier to entry. When the phenomenon we see in nature do not yield to the simple formulations about the mathematics we know well, and then again to the intermediate formulations and then again to the more difficult formulations, it then finally occurs to us that, yes indeed, it can be this difficult. It goes against the grain of the human tendency to look for the keys under the lamp post, where the looking is easier.

Also, I really like the idea that, on its smallest levels, the structure (quantized discrete structures?!) of space goes (go) back to being 2-D and you go on to suggest that dimensionalities should be viewed as a spectrum, and further they are not limited to integer values and change over time, which opens the idea even more. Well done, sir! That opens the problem up nicely. I don't believe we will ever be able to go back to conceiving of physical reality limited to a simple Euclidean form.

I don't think of nature or math as an orchestrator of relationships; nature does not have to resort to trying these combinations out in sequence. Mathematics holds all of the eigenstates of physical being in superposition and can solve them by the interference patterns they produce; they shimmer into existence by virtue of their holographic fruitfulness.

Some of the underlying structures are more fruitful than others, so one would intuit that evolution would occur over a spacio-temporal spectrum of emergence. As you say: “we will see that math requires it.”

Best regards,

Jim Stanfield

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Thank you very much Jim!

As I recall; I am preaching to the choir for you, because your essay strongly espoused a view that the universe is mathematical at its roots. But your detailed comments indicate that you read the essay top to bottom, which means I kept your attention throughout. Some of the complication introduced by hyper-complex terms that arise in Physics were there to start...

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As I recall; I am preaching to the choir for you, because your essay strongly espoused a view that the universe is mathematical at its roots. But your detailed comments indicate that you read the essay top to bottom, which means I kept your attention throughout. Some of the complication introduced by hyper-complex terms that arise in Physics were there to start...

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Dear Jonathan,

With great interest I read your essay, which of course is worthy of high rating.

I share your aspiration to seek the truth

**«But scientists now think space itself must have a microscopic and quantum mechanical structure, like a fabric with an amazing weave that knits space and time together.»**

I agree with you

**«I assert that nature puts the looming realities of higher Math to work automatically, because they help set nature in motion, and keep it on course toward ideal or optimal goals.» **

«So it is easy to forget that every object is the product of a process by which it came to be, and that ongoing processes maintain its form – giving it specific properties.»

«geometry enters the calculation in an organic way.»

«I see the most recent void discovery as further evidence that the universe is fractal at all scales.»

I wish you success in the contest.

Kind regards,

Vladimir

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With great interest I read your essay, which of course is worthy of high rating.

I share your aspiration to seek the truth

I agree with you

«So it is easy to forget that every object is the product of a process by which it came to be, and that ongoing processes maintain its form – giving it specific properties.»

«geometry enters the calculation in an organic way.»

«I see the most recent void discovery as further evidence that the universe is fractal at all scales.»

I wish you success in the contest.

Kind regards,

Vladimir

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Wow Thank You Vladimir,

I appreciate your good words and high regard. I don't think I've read your essay yet, so I'll wait to comment here until I do.

I wish you luck as well.

Regards,

Jonathan

I appreciate your good words and high regard. I don't think I've read your essay yet, so I'll wait to comment here until I do.

I wish you luck as well.

Regards,

Jonathan

Dear Jonathan.

We meet again :) If you Think of the elephants, how do they communicate? How is the room defined?

Maybe this has been forgotten in QG frame?

Sheers

Ulla.

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We meet again :) If you Think of the elephants, how do they communicate? How is the room defined?

Maybe this has been forgotten in QG frame?

Sheers

Ulla.

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Thanks greatly Ulla!

The elephants dance! And they talk over great distances in a low hum. The room is the entire universe. And people don't realize that primordial gravity waves are the deep low hum of the elephants. I'm glad you could come by.

I loved your essay.

All the Best,

Jonathan

The elephants dance! And they talk over great distances in a low hum. The room is the entire universe. And people don't realize that primordial gravity waves are the deep low hum of the elephants. I'm glad you could come by.

I loved your essay.

All the Best,

Jonathan

Dear Jonathan,

Good to see you again here. I thought I had written earlier on your essay, but I now see why I didn't. Our views are almost orthogonal, so it makes little sense for me to critique your essay. But it is good you present the*Platonic* view of math, as I try to present the *Realist* view of physics. Thus those who are undecided get a chance to ponder both views of reality.

There are some excellent essays (as usual) and I count yours as one of them. I particularly like the following:

"*I'm sure nature is perfectly happy with processes taking more or fewer stages to complete, but the math itself dictates that certain patterns are more stable than others*."

I think that works from both of our perspectives.

Best wishes to you, and as our mutual friend Ray Munroe used to say:

Have fun,

Edwin Eugene Klingman

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Good to see you again here. I thought I had written earlier on your essay, but I now see why I didn't. Our views are almost orthogonal, so it makes little sense for me to critique your essay. But it is good you present the

There are some excellent essays (as usual) and I count yours as one of them. I particularly like the following:

"

I think that works from both of our perspectives.

Best wishes to you, and as our mutual friend Ray Munroe used to say:

Have fun,

Edwin Eugene Klingman

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Thanks so much Ed!

I will indeed have fun. And I feel well-qualified to critique your essay, so I have done so. I could do quite a credible job of presenting the realist view, I'll have you know, but I'm much happier reading what you have to say on that view of things. I never want to be accused of being a hard nosed realist.

All the Best,

Jonathan

I will indeed have fun. And I feel well-qualified to critique your essay, so I have done so. I could do quite a credible job of presenting the realist view, I'll have you know, but I'm much happier reading what you have to say on that view of things. I never want to be accused of being a hard nosed realist.

All the Best,

Jonathan

Thanks to everyone who has come here..

I appreciate your interest in my ideas, and I am pleased that you have chosen to give me a high standing in this esteemed company. With so many distinguished professional scientists in this year's essay entrants, and with so many wonderful essays by amateurs and retired pros, I am privileged to be among you.

I will quietly read and grade a few more essays tonight, leaving brief or no comments, but I want to continue to show my support by giving my time to review your work.

Good luck to all.

Warm Regards,

Jonathan

I appreciate your interest in my ideas, and I am pleased that you have chosen to give me a high standing in this esteemed company. With so many distinguished professional scientists in this year's essay entrants, and with so many wonderful essays by amateurs and retired pros, I am privileged to be among you.

I will quietly read and grade a few more essays tonight, leaving brief or no comments, but I want to continue to show my support by giving my time to review your work.

Good luck to all.

Warm Regards,

Jonathan

Hi Jonathan,

A draft of my second paper on quantum correlations has been posted at sites.google.com/site/quantcorr. There is also a file with C functions for calculating correlations based on the "geometric probability" of crossing a threshold.

Cross posted on my blog under your thread.

Best wishes,

Colin

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A draft of my second paper on quantum correlations has been posted at sites.google.com/site/quantcorr. There is also a file with C functions for calculating correlations based on the "geometric probability" of crossing a threshold.

Cross posted on my blog under your thread.

Best wishes,

Colin

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Thanks Colin..

I'll check that out.

JJD

I'll check that out.

JJD

Jonathan,

I did start to read your essay during the contest, but I did not comment or rate your essay (I never rate without comment). Your paper seems to be all about mathematic's relationship with the universe and not about existence of life or intelligence. I felt it was off-topic. As an essay, it is well written and clear. You try to present your ideas to a general science readership and do not require reference to other papers to understand your essay. I would have given it a "6". Readable counts for a lot with me.

All the best,

Jeff

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I did start to read your essay during the contest, but I did not comment or rate your essay (I never rate without comment). Your paper seems to be all about mathematic's relationship with the universe and not about existence of life or intelligence. I felt it was off-topic. As an essay, it is well written and clear. You try to present your ideas to a general science readership and do not require reference to other papers to understand your essay. I would have given it a "6". Readable counts for a lot with me.

All the best,

Jeff

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Thanks Jeff,

I also value readability highly, in FQXi contests. Some folks seem to feel that only correct assertions or reasonable conclusions are worthy of credit, but I found quite a few essays I thought were wrong-headed or off-topic, and yet were sufficiently well-written to make me think - and thus require some acknowledgement by according them points in the rating. I didn't give out any ones this time, and I even gave Joe Fisher a 5 - though I don't agree with much he says - because his writing has continued to improve.

I will go back and read your essay, even though it won't count toward your score or my popularity, because I value your opinion.

All the Best,

Jonathan

I also value readability highly, in FQXi contests. Some folks seem to feel that only correct assertions or reasonable conclusions are worthy of credit, but I found quite a few essays I thought were wrong-headed or off-topic, and yet were sufficiently well-written to make me think - and thus require some acknowledgement by according them points in the rating. I didn't give out any ones this time, and I even gave Joe Fisher a 5 - though I don't agree with much he says - because his writing has continued to improve.

I will go back and read your essay, even though it won't count toward your score or my popularity, because I value your opinion.

All the Best,

Jonathan

Jonathan,

I don't know if I would give Joe Fisher a "5", but he does add something to the contest. He has a throw all the concepts in science into a blender and make it into art style of writing like Jackson Pulluk (sp?) did for painting.

I did see many math as a bases for the Universe essays, so maybe I was off-topic.

Jeff

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I don't know if I would give Joe Fisher a "5", but he does add something to the contest. He has a throw all the concepts in science into a blender and make it into art style of writing like Jackson Pulluk (sp?) did for painting.

I did see many math as a bases for the Universe essays, so maybe I was off-topic.

Jeff

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