Thanks very much Georgina..

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

All the Best,

Jonathan

Thanks Jim,

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

All the Best,

Jonathan

Excellent thoughts Phil!

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

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

All the Best,

JOnathan

Thanks for coming by John,

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

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

Warm Regards,

Jonathan

Dear Jonathan,

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

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

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

Best of luck in the contest!

Rick Searle

    Thanks Rick,

    I appreciate your comment, and the discovery that you are a kindred spirit. I shall likely get to your essay later today, and I look forward to reading it.

    All the Best,

    Jonathan

    Jonathan,

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

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

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

    Fondly, jrc

    Good question John!

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

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

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

    Regards,

    Jonathan

    Dear Mr. Dickau,

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

    Do let me know what you think about this: This is my single unified theorem of how the real Universe is occurring: Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of abstract NOTHING. Proof exists that every real astronomer looking through a real telescope has failed to notice that each of the real galaxies he has observed is unique as to its structure and its perceived distance from all other real galaxies. Each real star is unique as to its structure and its perceived distance apart from all other real stars. Every real scientist who has peered at real snowflakes through a real microscope has concluded that each real snowflake is unique as to its structure. Real structure is unique, once. Unique, once does not consist of abstract amounts of abstract quanta. Based on one's normal observation, one must conclude that all of the stars, all of the planets, all of the asteroids, all of the comets, all of the meteors, all of the specks of astral dust and all real objects have only one real thing in common. Each real object has a real material surface that seems to be attached to a material sub-surface. All surfaces, no matter the apparent degree of separation, must travel at the same constant speed. No matter in which direction one looks, one will only ever see a plethora of real surfaces and those surfaces must all be traveling at the same constant speed or else it would be physically impossible for one to observe them instantly and simultaneously. Real surfaces are easy to spot because they are well lighted. Real light does not travel far from its source as can be confirmed by looking at the real stars, or a real lightning bolt. Reflected light needs to adhere to a surface in order for it to be observed, which means that real light cannot have a surface of its own. Real light must be the only stationary substance in the real Universe. The stars remain in place due to astral radiation. The planets orbit because of atmospheric accumulation. There is no space.

    Warm regards,

    Joe Fisher

      Thanks for writing Joe,

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

      On the other hand, there is a pattern where every quartz crystal has similar properties - though each one is certainly unique and different from all the other crystals in existence. They are not identical, but different pieces of quartz are obviously the same in many ways. Similarly; all snowflakes display a hexagonal symmetry, though none is absolutely symmetrical.

      I think Science advances, Joe, when people notice consistent patterns over time. So while we can get into trouble by trying to apply abstract principles too broadly, it is better if you are not looking into the mouth of Old Faithful geyser at the start of an eruption, and therefore it is wise to know how often eruptions come - on the average - so that one can stand back and watch it happen, rather than getting a face full of boiling hot water.

      All the Best,

      Jonathan

      Dear Jonathan,

      Always something to learn from your essays. Well done!

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

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

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

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

      Best regards,

      Akinbo

        • [deleted]

        • Post #32

        Dear Jonathan,

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

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

        Man is the only creature who does not have a natural habitat. Living near a volcano is unnatural. Birds have enough sense not to do so.

        Warm Regards,

        Joe Fisher

        Jonathan,

        It's all weird to me! As I said in an exchange with Constantinos Ragazas on Steve Sax's page, I often wonder if mathematicians realize how phenomenal their memory capabilities are. I rely on people like you to gain some insight of what the myriad maths are about, and often find myself completely out of my depth.

        Intuitively though, it seems that if the addition operation is short-cutted, a moderating value would be lost, and the butterfly comes out of chrysalis in the round, as one direction lengthens without restraint. I still can't grasp the morphology of quarternions and division algebras that project a 4-D shape, and lost track of where I read a post of yours about 3-D imagining being an approximation. Like many I suppose, I find the images beautiful and can only wonder how that fills space over time.

        And of course there is the ever present counter-intuitiveness of QM that over-shadows just how counter-intuitive Relativistic spacetime is itself! I for one greatly appreciate that yours is a genuine kindness in patient explanations of the rudiments of mathematical physics, thank-you. jrc

        Thanks for sharing Joe,

        I think I am starting to get the gist of what you are saying.

        All the Best,

        Jonathan

        I have considered these questions, Akinbo...

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

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

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

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

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

        All the Best,

        Jonathan

        Hi Jonathan,

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

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

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

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

        All best,

        Tom

          Thanks Tom,

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

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

          All the Best,

          Jonathan

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

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

          Best,

          Tom

          4 days later

          Dear Jonathan,

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

          Best.

          Michel

          6 days later

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