Sorry my friend..

Marni was a participant in the very first FQXi contest and said; never again. I met her at FFP10, the same conference where I talked to Gerard. Let me just say that she is a brilliant physicist, and her PhD advisor was John Baez, but Kea has not found her niche, and no Physics related positions appear to be available to her right now. This is very sad, and a loss for the community, in my opinion. You can find some of her papers on viXra, if you are interested.

I have answers to the questions you left for me, and I'll try to enter them on my page tonight or in the AM.

All the Best,

Jonathan

Dear Akinbo,

Very good realistic argument on the topic.

I think monads have extensive applicability to integrate discrete with continuum. For example, natural transformation of strong monads may express the gravitation as a tensor product in string-matter continuum scenario, while three-dimensional structures of tetrahedral-branes emerge on eigen-rotations of string-matter segments. In that, to define the unit of mass we have to adapt Planck length as the length of fundamental string-segment that may be a monad in this continuum scenario that ascribes an eternal universe.

With best wishes

Jayakar

Dear Akinbo

I'm sorry I couldn't comment on your essay before. My duties at work demand considerable time. I found the topics of your work very interesting, I'm glad you had called my attention to your work. The notion of space is still one of the most debated in both physics and the philosophy of physics. From the ontological point of view, there are many conceptions of space. There is more less a wide consensus that space is either a substance or a mesh of relationships of objects. One can spend a lot of time discussing this two apparently irreconcilable viewpoints but at the end what matters for theoretical physics is to give a mathematical and consistent formulation of space.

I don't follow the current view of space represented by non-Euclidean geometry. Rather I upheld the view that space is a substance, a material field. In order to make this view consistent, the key is reconceptualize the notion of particle in terms of the notion of quasiparticle or solitons. In my view space is like an ocean and particles are only excitations of the ocean. This ocean is the medium for the quasiparticles and electromagnetic fields to move and interact. From this ocean quasiparticles are created and so on. The theory assumes that space is a continuous fluid in the sense of Descartes aether.

You may wish to see this video so you have an idea of what a particle is in my view.

http://www.youtube.com/watch?v=PyjwZ39EDmw

I wish you good luck in the contest

Best Regards

Israel

Dear Akimbo,

First thank you for your kind interest. This post is a tentative response to your question having in mind your very pedagogical essay about monads.

You: Monad - a fundamental unit of geometry; that of which there is no part;...

i. extended objects, not further extensible or compressible.

ii. they are fundamental and not a composite of other 'its'.

iii. they are the fundamental units of geometry, both body and space.

Me: The points of the geometries I am dealing with could perhaps be seen as monads. (e.g. the 7 points of the Fano plane in Fig. 1a. Then in Fig 1b the same points are extended as edges).

You: monads are 'it' and their change between two alternate states is the 'bit'.

Me: Agree. One edge in Fig. 2b is either black (bit 1) or white (bit 0).

You: the two-valued attribute

denoted by 0 and 1 must really occupy the deepest part of the basement!

Me: Agree, but as two elements of a triple {0,1, \infty}.

Stephen Anastasi: (above) "not only does the universe collapse to a single minimally simple omnet, all of mathematics went down the tube with it.",

Me: The translation of this sentence would be the Belyi theorem (see the step 3 in my Sec. 2 giving the definition of a child's drawing) and the property that the child's drawing D itself is the preimage of the segment [0,1], that is D=f^-1([0,1]), where the Belyi function f corresponding to D is a rational function. All black vertices of D are the roots of the equation f(x)=0, the multiplicity of each root being equal to the degree of the corresponding vertex. Similarly, all white vertices are the roots of the quation f(x)=1. Inside each face, there exits a single pole, that is a root of the equation f(x)=\infty. Besides 0, 1 and \infty, there are no other critical value of f.

Sorry about the technicalities.

You: But what about the space then?

Me: Although the model of dessins d'enfants may be applied differently, practically, in my essay, it corresponds to the (Heisenberg) space of quantum observables such as the Pauli spin matrices, or tensorial agregates of them. You would say that they cannot be monads in such a case! But they cannot be divided in the sense that the parties (let's say Alice, Bob and Charlie for the three-partite case, I used the Fano plane for this case) are linked once for all, whatever state they share, entangled or not. I don't know about Mach, I have to think more.

I am sure that it does not dissolve your question, at least it gives you a hint, hopefully, of what this kind of maths may do.

Please rate my essay if you like it.

Best wishes,

Michel

Dear Akinbo

Richard Feynman in his Nobel Acceptance Speech

(http://www.nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html)

said: "It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but with a little mathematical fiddling you can show the relationship. And example of this is the Schrodinger equation and the Heisenberg formulation of quantum mechanics. I don't know why that is - it remains a mystery, but it was something I learned from experience. There is always another way to say the same thing that doesn't look at all like the way you said it before. I don't know what the reason for this is. I think it is somehow a representation of the simplicity of nature."

I too believe in the simplicity of nature, and I am glad that Richard Feynman, a Nobel-winning famous physicist, also believe in the same thing I do, but I had come to my belief long before I knew about that particular statement.

The belief that "Nature is simple" is however being expressed differently in my essay "Analogical Engine" linked to http://fqxi.org/community/forum/topic/1865 .

Specifically though, I said "Planck constant is the Mother of All Dualities" and I put it schematically as: wave-particle ~ quantum-classical ~ gene-protein ~ analogy- reasoning ~ linear-nonlinear ~ connected-notconnected ~ computable-notcomputable ~ mind-body ~ Bit-It ~ variation-selection ~ freedom-determinism ... and so on.

Taken two at a time, it can be read as "what quantum is to classical" is similar to (~) "what wave is to particle." You can choose any two from among the multitudes that can be found in our discourses.

I could have put Schrodinger wave ontology-Heisenberg particle ontology duality in the list had it comes to my mind!

Since "Nature is Analogical", we are free to probe nature in so many different ways. And each of us surely must have touched some corners of it.

Good luck and good cheers!

Than Tin

Greetings my friend,

In relation to the Scientific American article by Meinard Kuhlmann cited above, and the existence or non-existence of particles; look up the Unruh effect.

Also; in relation to your comments left on my blog, about questioning the need to have a proliferation of names (like a 0-brane) or constructions for what is basically the same thing - a monad - please see the comment by Than Tin above, with the sentiments of Richard Feynman on that subject.

Back with essay comments soon.

Jonathan

    My friend,

    You make a most excellent case for revisiting the monad concept, and some wonderful things about the primal or foundational aspect of geometry. I concur whole heartedly with the assessment that it is a determine of how form in nature unfolds; ultimately the higher- and lower-dimensional aspects of geometry both enter the picture - in terms of framing what is possible. My approach to this research involves examining object/observer relations through elements of constructive geometry evolving into projective geometry (which studies perspective). It turns out there are some interesting connections with the octonions and other expected features, if you follow the thread out from minimal rules of constructivism through the projective doorway.

    Fun stuff!

    But on the downside; physicists have not observed any clear signs of graininess to the fabric of space, although there have been some attempts to elicit such information from astrophysical data and elsewhere. Lots more on that. And you should also know that your model has aspects of a Cellular Automaton or CA, which might lead to problems. The main subject of my conversation with Gerard 't Hooft was whether his CA based QG theory was or could be made Lorentz invariant. In our conversation at FFP10 he said this was very difficult. Then in his lecture at FFP11 in Paris, he devoted 4 or 5 slides to the subject and why Lorentz invariance is a difficult matter for CA based theories.

    More later,

    Jonathan

      Gee whiz..

      that should be 'and other unexpected features' in the 1st paragraph above.

      Jonathan

      I also want to mention..

      In Twistor theory, points are NOT the most fundamental piece of geometry. Instead it is the ray. I imagine the shortest that a ray of light can be is the Planck length, you might want to check out the Twistors program for some interesting insights to explore.

      Have Fun!

      Jonathan

      I'll recap a more detailed statement left on my page..

      I see no problem with multiple constructions that yield something like a monad. I mentioned the 0-brane as it is a minimal figure - infinitesimal or Planck scaled at rest. The construction Greene used in Elegant Universe was that branes could be seen as something that wraps around another geometric structure, like a balloon (a 2-brane) around a ball or sphere, or a string (a 1-brane) around a circle or disc. The idea is that is contains what is inside, perhaps renders it invisible or prevents direct observation, or covers the object contained. And of course the surface can oscillate or vibrate while doing so.

      If we note that spheres and circles are part of the same family and share the same formula, the original point can be made clear. The equation of a unit sphere is simply r = 1, and a sphere of a given dimension is called an n-sphere, where n is 1,2,3,... The conventional sphere is called the 2-sphere, and the 1-sphere is a circle. But a brane of a given dimension is a generalization of the associated sphere. So this reveals that the 0-brane is actually a pair of points. In the 1 1 dimensional space that the 0-brane is said to inhabit or define, it is usually assigned the role of instanton, having no extent in space but holding a Planck sized instant of time.

      Of course String theorists like putting a charge on 0-branes and making them dance, but perhaps a resting 0-brane is a sort of monad.

      More soon,

      Jonathan

      And my main message is..

      I see having more than one road to the same end as powerful evidence there is something worth seeing there. I don't think the monad is any different. If it is found essential in a new setting or in a new way, that is good. I posted the whole paragraph from Feynman that Than Tin excerpted, that eloquently makes my point, back on my essay page. And you can read the comment from me I'm struggling to recap there.

      Have Fun,

      Jonathan

      Hello Than and Jonathan,

      I will posting on your blogs what I feel can throw more light on the scheme at hand. And thanks for all the information and references. I will be checking them out.

      Regards,

      Akinbo

      Hi Akinbo,

      I just upped the score on your underrated essay.

      Point particles are a problem, and physics is crippled until it gets rid of them. Standard physics responds with do not worry about point particles, calculus handles them just fine, and in fact it gets rid of the logic of that goof off Zeno. The problem as you know is that particles are not points and calculus does not get rid of Zeno paradox. We are stuck with Zeno's conclusion that nothing can move. That is the truth, but it is not a show stopper. Remember the show must go on!

      So, I started my "monad" logic with Zeno's statement that I interpret as "no quantum mechanical object can have a velocity in a space-time that is continuous". Since everything is composed of quantum mechanical particles, all quantum particles and all classical objects cannot move. How can that be?

      The answer is that Zeno left out a detail that should have been included. Zeno's statement should read: "Nothing moves, everything changes". There is no such thing as velocity outside of calculations we make on a changing space-time.

      You are not alone :)

      Best of Luck,

      Don L.

      PS thanks of the history of monads

        Dear Akinibo

        thank you for your nice essay, refreshing my high school knowledge about monads. Maybe your monads are the qubits of my quantum cellular automaton, though they have no extension literally, since space-time is emergent from them: but in this sense, they then acquire a Planck extension.

        Coming back to your problem raised in by essay thread about the Mach principle and the Newton bucket, here I report my answer from my thread.

        You are touching the apocryphal principle of Mach, which Einstein was so fond of, but, unfortunately he couldn't achieve in his GR. Its space-time metric played the role of a kind of ether. In his Lecture in Leiden he said that he believed that the rotating Newton bucket would have the water pushing up the bucket walls, even in an empty universe (see the masterpiece Einstein's biography of Walter Isaacson). Do we have the absolute inertial frame, or even the rest frame, as an ether? In practice we have an ether: it is the background radiation. It is a frame with respect to which we can check that we are moving. And, in practice, we define the inertial frame only relying on fixed stars. In an emergent space-time from an automaton Lorenz covariance is distorted, meaning that the principle of relativity does not hold in a ultra-relativistic regime.

        I will post this also on your blog, as you asked me.

        Thank you for raising the issue.

        My best regards

        Mauro

        Dear Don,

        Your comments are treasured. Yes, I agree Zeno left out a detail. What is that detail? I will post this on your blog and give my suggestion what I think that detail could be. And thanks for the rating.

        Best regards,

        Akinbo

        Dear Akinbo,

        I read your fine essay some time ago but could not think of any intelligent comment or question that would do it justice. I was hoping to do better than very well written, exceptionally clearly explained and relevant.It was interesting for me to learn about monads. Anyway for now I want to let you know I have read it and think you deserve to do well. Good luck, Georgina

        Dear Akinbo and all,

        Thank you for posting in my essay. Here is some work I am doing to achieve what you are trying to do as well.

        Simple mathematical truth of zero=I=infinity, iSphere and iSeries as described below can explain all the aspects of reality mathematically.

        I am attaching the iDNASeries.bmp that I have envisioned and how it shows the DNA structure in its sequence.

        I give you all a cosmological iSeries which spans the entire numerical spectrum from -infinity through 0 to +infinity and the simple principle underlying it is sum of any two consecutive numbers is the next number in the series. 0 is the base seed and i can be any seed between 0 and infinity.

        iSeries always yields two sub semi series, each of which has 0 as a base seed and 2i as the first seed.

        One of the sub series is always defined by the equation

        Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

        where S0 = 0 and S1 = 2 * i

        the second sub series is always defined by the equation

        Sn = 3 * Sn-1 -Sn-2

        where S0 = 0 and S1 = 2 * i

        Division of consecutive numbers in each of these subseries always eventually converges on 2.168 which is the Square of 1.618.

        Union of these series always yields another series which is just a new iSeries of a 2i first seed and can be defined by the universal equation

        Sn = Sn-1 + Sn-2

        where S0 = 0 and S1 = 2*i

        Division of consecutive numbers in the merged series always eventually converges on 1.618 which happens to be the golden ratio "Phi".

        Fibonacci series is just a subset of the iSeries where the first seed or S1 =1.

        Examples

        starting iSeries governed by Sn = Sn-1 + Sn-2

        where i = 0.5, S0 = 0 and S1 = 0.5

        -27.5 17 -10.5 6.5 -4 2.5 -1.5 1 -.5 .5 0 .5 .5 1 1.5 2.5 4 6.5 10.5 17 27.5

        Sub series governed by Sn = 2 * Sn-1 + Sigma (i=2 to n) Sn-i

        where S0 = 0 and S1 = 2i = 1

        0 1 2 5 13 34 ...

        Sub series governed by Sn = 3 * Sn-1 - Sn-2

        where S0 = 0 and S1 = 2i = 1

        0 1 3 8 21 55 ...

        Merged series governed by Sn = Sn-1 + Sn-2 where S0 = 0 and S1 = 2i = 1

        0 1 1 2 3 5 8 13 21 34 55 ...... (Fibonacci series is a subset of iSeries)

        The above equations hold true for any value of I.

        As per Antony Ryan's suggestion, I searched google to see how Fibonacci type series can be used to explain Quantum Mechanics and General Relativity and found an interesting article.

        http://msel-naschie.com/pdf/The-Fibonacci-code-behin

        d-super.pdf

        Now that I split the Fibonacci series in to two semi series, seems like each of the sub semi series corresponds to QM and GR and together they explain the Quantum Gravity. Seems like this duality is a commonality in nature once relativity takes effect or a series is kicked off from a basic singularity. The only commonality between the two series is at the base seed 0 (singularity) and first seed 1, which are the bits in our binary system.

        Its also interesting to see the singularity is in the base seed of zero and how it is all pervasive all through out the DNA structure in the attached image. I have been telling that I is that nothing which dwells in everything and this DNA structure seems to prove that notion. Singularity is right with in the duality. Absolute is right with in the relativity. This proves that both of these states of singularity and duality are interconnected and are the source of life.

        Love,

        Sridattadev.

          Hi Akinbo,

          I had a glance over your essay and the basic idea is that one should instead of idealized points consider "extended points" or monads. Is this correct? This idea seems to have some connection with the idea that there will be some smallest size one can probe (e.g. Planck size) and beyond this it is impossible to go to smaller distances. In some sense that there is a smallest unit of space-time. This is an idea which has received some attention. A colleague and friend of mine Piero Nicolini and co-workers have been looking at non-commutative geometry -- the postulate that just as in QM one has non-trivial commutators between x and p

          ([x, p] =/=0) so too there is some new non-trivial commutator between coordinates x, y, z for example [x, y] =/=0). The implication of this is that one can't simultaneously take x and y to zero (just as one can't simultaneously take x and p to zero in QM) or in other words one can't shrink things to a point. He has a nice review article of these ideas:

          "Noncommutative Black Holes, The Final Appeal To Quantum Gravity: A Review"

          Piero Nicolini (Trieste U. & INFN, Trieste & Fresno State),

          Int.J.Mod.Phys. A24 (2009) 1229-1308; e-Print: arXiv:0807.1939 [hep-th]

          In any case this seems to have some connection to the idea of monads.

          Best,

          Doug