Dear Dr. Akinbo. Hello, and apologies if this does not apply to you or your patients. I have read and rated your essay and about 50 others. If you have not read, or did not rate my essay The Cloud of Unknowing please consider doing so.

With best wishes from Vladimir

Hi Akinbo,

You have offered an excellent presentation examining a fundamental question, and I am pleased that you defended the side of the monad! However, I think there may be different ways in which monads can be understood and would like to get your take on this.

One way to understand monads is as cells of a cellular automata, the kind of model for physics that Edward Fredkin has developed in his digital philosophy. In this case physics consists of determining the (local) rules that operate to change the state of the cells. An example of this kind of model is described by essayist Franklin Hu. Over the years Fredkin has been able to address several issues (such as circular propagation) that bedevil naive attempts at this kind of digital physics.

A second kind of monadic model associates them with particles and views particle interactions as a kind of computational network. This type is described by essayist Deepak Vaid.

And a third way to understand monads is as voxels (volumetric pixels). In this case the computational hardware is not observable; we can only see the display screen. Physics in this case can be any finite calculation that offers a discretized output. It need not be a local computation.

My own essay Software Cosmos takes a look at the third kind of computational model from the top down, considering what we can determine about the universe if we assume it is a kind of virtual reality. In fact, I am able to construct (and carry out) an observational test to determine if we currently live in a simulated world.

Hugh

    Great Akinbo,

    This essay 'On the Road Not Taken' brings to fore some questions which have been kept under the carpet by science as no single answer is viable in all situations. Many of us have pondered over these questions. Some such questions that have baffled us include relativity, wave particle duality, pre-dominance of analogue or digital world etc.

    PicoPhysics has no such paradox. Both concepts are embedded in UNARY law. Discrete is embedded in Knergy and Analogous behaviour in Space of Unary law "Space contains Knergy".

    I do decipher the term monad. so went along the Wikipedia and see it is based on abstractions that prevailed before and around Newtonian era.

    I see you have some original questions to answer similar to mine.

    It was great, reading your article and find solace in knowing there are some people besides me, who have un-answered, un-asked questions.

    Vijay Gupta

    Proponent Unary Law - Space Contains Knergy

    Hello Akinbo

    Speaking as an author of two books, I found it to be a beautiful piece of writing.

    Your argument is fabulous, and I will be rating it as such (8) because it is foundational, and uses philosophical principles very well. In many ways your attributes of monads from i to vii align well to the fundamental interactions between boundary omnets in my model. I went very carefully through your essay, and am going to show my thoughts as I went through. They are not at any time intended to pull your ideas down, but to suggest how the argument needs to be generalized beyond geometry, and that there are several background assumptions that can't really be ignored in a foundational argument. I think that if one sees these in the spirit in which they are offered that your redevelopment will gradually or quickly converge on my own essay's foundations.

    There are several aspects within the first seven clauses about attributes of monads that are presumptive. For example, the idea of compressibility is a human-centered concept, and presumes a background space without showing how it comes to be, or indeed what space is (except as an argument subject to infinite regress). I can guess various arguments in response to this, and there is no need to point them out, but each seems to lead to further arguments, so ought to be left. The items after that assume several aspects that presume pre-existing time, with no causal mechanism shown, and would become unnecessary in terms of the GPE causal model of my essay. For example, emergence and annihilation was introduced to make the monadic concept work, but the Harmony Set evolves and brings time with it, and change in higher dimensional interpretations of the Harmony Set are likely to imply change of position of peaks of the vector strengths as the interactions between null elements superpose, which is likely given that regularity of events (regularity of change in similar situations) is guaranteed by the GPE itself. So by Occam's razor, your work can be simplified, and the endpoint of simplification would be to simply accept the GPE (as a matter of skeptical commitment) and see where it leads.

    Accepting Euclid's fundamentals is O.K. although all of mathematics is initially degenerate under the General Principle of Equivalence and the problem of bundling.

    The definitions themselves are fine, but make assumptions that there are such things, and that they are in themselves as we define them to be based on experience. But this is why the FQXi website exists, because under Kant and others we can't really do so with confidence.

    'Information' - is dark energy information? Not according to the definition.

    'Have no part' - there is probably no need to refer to geometric objects. Why not just 'objects'? Then an object can be generalized to an 'omnet' and then the idea becomes global, which is necessary for a secure argument, I think.

    'Point' - Here is the concept that forced me to build the Harmony Set, for if there is a point, how can a point, which can have no part, have any property that can be connected to any other point, for there is always difference between two points (assuming that points are actual objects, or actual omnets within the actual ontology (referring to my essay) and there is nothing that can connect them to make either a line or extension, unless there is some overarching principle that bring such points and their connections (see my essay). That is, the whole concept of point has a problem, which I initially could not identify. From the endpoint rationalist perspective, one finds that the idea of something being of zero dimension (not possible) is not the same as it being dimensionless. The null elements of the Harmony Set are dimensionless, in that they exist without dimension having any meaning. Rather, they bring dimensionality into existence through difference between each null element (even if this is just ontological dependence and priority - see my essay). Then these null elements, if monads, have no extension, whereas the difference between them might be monad-like in that they have extension brought about by the implied dimensionality that pops out in the structure. Of course, I have only generated the 1-space solution, and so it would not be correct to say that these 'monadic' omnets properly correspond to the equivalent forms in higher spaces, at least in the sense Leibniz meant. This is cognitively challenging, I know, but then, once one gets it, it frees up one's thinking on foundational issues (and trades it for harder problems, unfortunately).

    The bundling problem applies, and so implies a unique origin for a world of points, or lines, or fluffy animals (meaning anything else - the problem is global). Moreover, how does a world of points that experiences evolution, achieve such evolution, for the points themselves must undergo an infinity of change, and each change would experience an infinity of changes, unless it is instantaneous (the method of such change occurs through the GPE as constructor in my essay).

    'Monad' - Yes! But drop the idea of it being geometrical, for one can't trust a pre-existing spacetime or Euclidean (or anything else) background. There is no need for the geometrical for it should develop from the foundational aspects.

    'Motion' - as change of place, this could be generalized to include Aristotle's idea of place, so that geometry is irrelevant. Consider living in a two dimensional world where the x-axis is measure in degree of redness (no red, to fully red, say) and the y-axis is measured in degree of temperature. Motion is then simply a change in redness and temperature. Same result, and the human mind would likely come to interpret it similarly to that of change of position (but it would be less interesting) in the same way that the brain can images upside down if wearing glasses that invert the image.

    'Variable lifetime of monads': assumes that a monad is aware of, or affected by time in some way. But if a monad is windowless, then this would be a challenge to make consistent, for, unless the system is driven by a universal principle that acts on all at once, how does the world pick out a certain monad for existence or non-existence.

    Note: your boundary is not my boundary. Yours is a geometric object. Mine only gains a geometric property by it relations to other boundaries. This is not a point of conflict, just a point of difference.

    Whence time in your world model? What is the foundational cause of change?

    The Weyl tile argument: Yes! But this argument is founded around the expectation that the real number line is valid. In the Harmony Set interpretation, geometry contains values that are slightly fuzzy - what I call 'block numbers'. In another post I show that the Pythagorean theorem implies that mathematics is cataclysmically inconsistent (view attachment). Block numbers fix the problem, and in doing so imply Heisenberg uncertainty, in that there is a minimum fineness of scale in a Harmony Set universe. Does this imply that your monads have a minimum extension? Depends what you mean by a monad.

    In (c) 'Use for writing programs' the bother is that the shifting of an 0 from one place to another, requires that something act, already 'knowing' where the 0 has to be. But what caused the change within the mechanism that made it shift from one place to the next? This leads to an infinite regress, I believe. This is similar to Parmenides argument, and that of Zeno.

    Best wishes

    Stephen AnastasiAttachment #1: 1_A_problem_for_geometry.pdf

    Very brilliant arguments Stephen! I will have to re-read your paper. I also read the attachment and it is a very powerful counter-argument to Weyl's. Your argument may even provide a proof that the Planck limit (or some limit at least) exists at some scale and lines cannot be infinitely bisected. Will copy this on your blog and comment more later.

    On "compressibility is a human-centered concept, and presumes a background space without showing how it comes to be". My response is that monads have extension but cannot be compressed or further extended. They have no shape. The only change they can undergo is annihilation in an instant, unlike composite things that can be compressed gradually. I will however be looking deeper into the Harmony set.

    On "Whence time in your world model? What is the foundational cause of change?" I suspect that if monads can change spontaneously and can also be induced to do so, this may be the origin of determinism and uncertainty in our dynamics on the classical and quantum scale.

    On "the shifting of an 0 from one place to another", I hope I understand you. The O in the diagram stands for object. It does not shift from one place to another. The object remains in its own place, which place property is intrinsic to it as Zeno's Arrow paradox envisages. Motion therefore occurs because space itself participates in it, with the monad in the direction of motion changing from 1 to 0 simultaneously as the "one (since this was non-existent)" opposite changes from 0 to 1. Such action and reaction between a moving object and space being equal and opposite.

    We still have to continue this dialogue because the issues you raise are quite fundamentally important. This reply cannot exhaust all the concerns.

    Many thanks indeed.

    Akinbo

    Dear Hugh,

    Many thanks for your comments. I share the philosophy of digital physics with monads acting as cellular automata. However, it might be premature to say I am biased towards monads. As a matter of fact judgement will be delivered soon in the case of Atomistic Enterprises vs. Plato & Ors (probably August).

    I will comment more on your blog.

    Regards,

    Akinbo

    Dear Akinbo,

    You must have had a hard time in your youth deciding whether to be a philosopher, lawyer, physicist or physician. :-) I hope you agree by now that the world is most in need of caring physicians.

    Your intellectual journey down the fork less traveled (Frost is my favorite poet; "The Road not Taken" may have been the first poem I learned by heart many years ago) is rich with promise. One doesn't hear of Leibniz's monads that often anymore -- I do recall Hermann Weyl's agreement with Leibniz that nature can only be truly understood in the behavior of the very small, so you're in good company.

    I would make a note that the mathematical point at infinity is actually realized in the compactification of the complex plane, which shifts the discrete and probabilistic measure functions of the complex Hilbert space to the continuous and deterministic functions of a topological model. You might want to look into that to help further strengthen your argument.

    Something else that caught my eye in regard to Newton's idea of spatial translation: " ... unless we postulate that there are two spaces that everywhere coincide, a moving one and one that is at rest, so that the movement of a part of the moving one involves a translation of that item from the corresponding part of the resting one to a different part of the resting space ... That is crazy (translator's inclusion) ... " I have to disagree with the translator's editorializing -- Newton's conception is not crazy; it follows directly from his belief in absolute space and absolute time. The duality is necessary -- which Einstein fixed, with Minkowski's model of continuous spacetime, in which neither space nor time are independently real, but rather preserve physical reality in a union of the two.

    Thanks for your comments in my forum, and expect an appropriately high score from me.

    All best,

    Tom

    Greetings Akinbo,

    I want to take a moment in this e-mail to address the key question you left me in a general way, here rather than on my forum. I've still not made it through your essay, but your intriguing and delightful questions bear some attention, and have been unavoidably a part of my contemplations of late. I'll talk here about learning how to count and measure. This is a key part of the cognitive science research I've been engaged in the last 8 years or so. As I point out in my essay, an early cognitive landmark is grasping object constancy, but children up to a certain age have an endless appetite for games of peek-a-boo, where you hide and then appear to the child's delight. So there is a transitional period for learning to distinguish clearly between none and one, and to understand the persistence of objects (and people).

    Just so we are clear (addressing the topic of your essay); I've never quite bought into the point-particle concept, and have always thought things had to have an extent and/or underlying structure - to exist in spacetime. In order to exist, particles and composite objects must possess duration or extent in time, as well as being extended in space - in my view. So I don't adhere to that part of Plato's reasoning. So to continue...

    Distinguishing none from one, while it is a prelude to counting, also evokes a different but related skill - the ability to distinguish none from one, or a few, or from many, and from a very large number - magnitude range estimation. During this same developmental stage, however, children are also learning distance range estimation - through triangulation. There is a natural connection in this to principles of constructive and projective geometry, getting a sense of whether various things have size or thickness or depth. Children must learn the rules of dimensionality. In a lecture I attended by Alfie Kohn; I heard a wonderful story about how a group of children learned by being guided to playfully discover for themselves about standard units of measurement. At first; the teacher didn't provide rulers or tell the kids how to measure, but instead they posed a challenge - the boat had to be big enough to fit everybody in the class - and let them figure out how to do it.

    There is a connection between the developmental or learning processes above and the hierarchy of smooth, topological, and measurable objects and spaces. Smooth relations admit fields and waves, topology is for objects that have a face, surface, or hypersurface, and the property of measurability arises only when you have two or more such objects to compare sizes. So there is a natural progression from continuity to distinct and separate identity, and for the verifiability or knowability of same. In my view, the way we learn about these things parallels how nature unfolds form. And it is certain that learning the difference between none and one helps the child to then learn how to count as well as to estimate magnitude, but that is grasped in stages.

    All the Best,

    Jonathan

      Akinbo,

      Thank you for a great submission. Very well structured/readable. Interesting parallel between 1,0 and what I understood to be Monad Pairs (?). I think the idea that space substrate itself could be a giant Boolean Network of Monads is a model that may prove to be fruitful. Correct me if I'm a bit off here.

      I also responded to your questions under my submission if you care to take a look @ that as well.

      All the Best,

      John

      Akinbo My Friend,

      I want you to understand me rightly, and out of respect I am posting it here. While I acknowledge that sometimes life reduces chices down to either/or decisions, the tendency to assume this applies more generally is a harmful logical flaw prevalent in modern society, because it fails to ask "Is there a middle path?" In more detail; sometimes the middle is excluded erroneously, in other cases the fact there are multiple choices is not considered, and in some cases there is a virtually continuous range of choices - where sometimes our choice among these cases is determined by how we interact with the system. According to an article in August's Scientific American by Meinard Kuhlmann; that sometimes applies for the choice of 'particles vs vacuum' which begs the question "Is there a particle or no particle?"

      I first read about the hierarchy of objects and spaces as a point made in passing by Alain Connes, in one of his papers about non-commutative geometry. Measurable is a subset of topological, which is a subset of smooth - in relating the categories of well-defined spaces. This point has more than passing importance, however, to people who study differential geometry and topology. In some cases; one can assert that the boundary between stable conditions or well-defined regions is a fractal. That is; there are interpenetrating regions of yes and no, or black and white, as in an M.C. Escher artwork. So while sometimes a simple yes or no will suffice; sometimes a more subtle answer is called for.

      The studies begun at Tübingen, and run by the German Psychological Association for a number of years, showed a marked decline in the perceptual acuity in discerning shades of gray and other colors, for people at the end of the study vs the beginning. Early on more than 200 shades were easily distinguished, and later participants could discern half that - focusing mostly on bright colors. I would hate to imagine a world where everything had to be reduced to yes or no, black or white.

      All the Best,

      Jonathan

      Dear Akinbo,

      You have made the relationship between It and Bit quite explicit in your elegantly argued essay and finally have said that both are from each other and hence of equal importance for us. This is also what I have said in my essay while concluding. You have logically based your argument on the concept of 'monad' as fundamental indivisible entity and listed some of its attributes and also have identified it and its attributes with both It and Bit. You have historically analyzed the origin and development of the concept of monad and its current application to contemporary problems in physics and successfully explained the notion of motion with the help of diagrams. It is good to note that there are 10^180 bits of information in the universe derived from the concept of monad. I would like to rate your lucid essay with an excellent rating after you read my essay and post your comments on it in my thread. http://fqxi.org/community/forum/topic/1827.

      Best regards,

      Sreenath

      As you might imagine, ...

      That should be 'sometimes life reduces choices.' I'm sorry for any confusion.

      Jonathan

      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

          Dear Adel,

          Thanks for your comments. Also thanks for the referral to Feynman's checkerboard model. It appears to be a way to quantize spacetime. I will meet you in a few minutes on your blog.

          Regards,

          Akinbo

          Thanks Steve for your encouraging comments. I doubt if I will be able to lay my hands on Lee Smolins book soon but I have read a couple of his papers which I found very good. Like the 'Three Roads to Quantum Gravity'.

          Wheelers viewpoint that information is fundamental and that we only need to consider all the various binary possibilities underlying reality is very inspiring. Infinitessimal and the infinite may be examples of this, but I suspect that they will be mathematical 'bits', not physical. The infinitesimal could confront Planck's length in the near future.

          I will check your blog again to see if I have rated your essay.

          Regards,

          Akinbo

          TAKE NOTICE that judgement will be delivered on Sunday, July 28 at 12 O'clock in the forenoon in the case of

          Atomistic Enterprises Inc. vs. Plato & Ors.

          As you deem fit or otherwise, you are therefore invited to make your pleadings/RATINGS for or against any of both parties in the case.

          THANK YOU!!

          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