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

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

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

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

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

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?

    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

      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

      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

        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

        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

        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

        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

        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!

          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

          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

          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

          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