On The Road Not Taken by Akinbo Ojo

Hi Akinbo,

Thank you for reading my essay. While it is hard to tell what you precisely have in mind( I have read yours many times), there seems to be some similarity between our theories in a specific area which is particle propagation. My theory follows standard QM which does not have easy interpretation in that regard. However, I am researching this issue in my system which seems to somehow include a concept that is called Feynman checkerboard, which has a sophisticated version of your idea.

just google " feynman checkerboard model", you will find loads of information, but you have to read a lot to see the similarity to your system.

My essay is all about how this interaction arises, please read carefully the first 3 sections. Of course, my essay was written for an academic person with extensive experience in QM in mind, so I have not spelled out everything clearly. Now, in classical physics the charge e is just a numbers assigned to a particle that enters the equation where 1/r is postulated via experiments. In QFT a similar but more sophisticated in the sense that now 1/r law is not postulated but derived (through the notorious virtual particles concept). Zee in his QFT in a nutshell book called that the greatest discovery in physics. Other theories like String and others describe charge as again a sort of abstract math like windings and such.

In my theory charge is a dynamic quantity that arises from the interaction and not the other way around. There is no positive and negative particles as such, it was forced upon standard physics because of the experiment and model strategy. It is all about the line intersection concept which is the basis of interaction and hence the rise of charge and the associated expectation value change corresponding to force.

Gravity is a bit harder because the weak force it produces making the numbers fluctuate highly. However I state my conjecture in the essay, which is when the lines meet head on at Lp. But why Lp? I leave that for the second season episode!!

Finally I have rated your essay very good for your nice try and good active participation.

Adel

Dear Dr. Ojo,

Your essay offers a very fascinating approach to information and fundamental reality. As I mentioned in reply to your interesting questions on my page, I like discussions about monads and infinities, and think these to be very fundamental. Although the infinitesimal and the infinite may seem as opposites, that in fact really links them. I also very much enjoyed the poetry and theatrical setting you provided, while still being very clear and scientific. Have you had a chance to check out Lee Smolin's new book, 'Time Reborn' ? It also offers insight into some of the concepts you mentioned, like the platonic idea of the world composed of imperfect versions of perfect models, and also Leibniz's viewpoints.

Also, I wanted to address that second question you asked about the binary possibilities in Wheeler's quote, in view of inspiration from your essay: perhaps another way of casting the binary choices, is that they represent the infinite and the infinitesimal. The choice of '1' or 'on' or 'yes' all mean the same thing - completeness. It's there and it's whole. But this is an infinite change from being 'off'. Likewise, the choice of '0' or 'off' or 'no' all mean the same thing - an absence of wholeness or there-ness. It may sound similar to non-existence except that the "acknowledgement of the absence of something" is yet something too, but only as a starting point and that's it. This is I think similar to the monad ideas you brought forward, and it relates to the infinitesimal, that is, the starting point per se.

Fundamentally, this describes why only two states are logically possible, and how they would relate to each other. It also could lead to the nature of dualism in physics which touches on so many topics.

Thanks for an inspiring essay, and I rated it highly. Also, I'm not sure if you also had a chance to rate mine after you reviewed it but I hope you get a chance if not already. Thanks again,

Steve Sax

Hello again Akinbo,

I wanted to mention a few things. First off; as with Tom, Frost's 'The Road Not Taken' is one of my favorite poems and I also like the musical arrangement by Randall Thompson, which I have performed many times. And secondly; I told a story above of attending a lecture by Alfie Kohn, where he told the story of children learning to measure through guided play.

Though that evening was the first time I ever went to the James Earl Jones theater, and I was not certain exactly where to go, but for the most part I did not travel by the road. I went through the woods (not yellow, but...). There is a road in the woods too, that once carried horse-drawn carriages. To be honest, I took the road the last part of the way, but not the whole distance.

At the same event where I met 't Hooft, there was a lecture by Marni Sheppeard about the value of Ternary logic in QM - which of course sends us down the middle path sometimes. Right now I am sad, because Marni (Kea in the blogs) is struggling - but she is brilliant! So every once and a while; I wish those was a victory for those who travel the untrammeled road, walk the middle path, or insist that it is best to consider the third option.

Regards,

Jonathan

Akinbo,

Very nice article. I read it with great interest and ranked it accordingly. For writing your program with monads, your may find the following invention of magnetic racetrack memory to be interesting, see http://en.wikipedia.org/wiki/Racetrack_memory

Best wishes,

Brian

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

Your answers are there, Akinbo.

You can find them on my essay page. Thank you for your kind interaction.

Have Fun!

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