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Undecidability, Uncomputability, and Unpredictability Essay Contest
December 24, 2019 - April 24, 2020
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What Is “Fundamental”
October 28, 2017 to January 22, 2018
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Wandering Towards a Goal
How can mindless mathematical laws give rise to aims and intention?
December 2, 2016 to March 3, 2017
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Trick or Truth: The Mysterious Connection Between Physics and Mathematics
Contest Partners: Nanotronics Imaging, The Peter and Patricia Gruber Foundation, and The John Templeton Foundation
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How Should Humanity Steer the Future?
January 9, 2014 - August 31, 2014
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It From Bit or Bit From It
March 25 - June 28, 2013
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Questioning the Foundations
Which of Our Basic Physical Assumptions Are Wrong?
May 24 - August 31, 2012
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Is Reality Digital or Analog?
November 2010 - February 2011
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What's Ultimately Possible in Physics?
May - October 2009
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Marius Buliga: on 4/2/11 at 19:11pm UTC, wrote There is this new paper, with detailed, but hopefully not too heavy math. ...

basudeba: on 3/20/11 at 6:17am UTC, wrote Sub: Possibility of manipulation in judging criteria – suggestions for...

James Hoover: on 2/22/11 at 21:16pm UTC, wrote "But the race of birds was created out of innocent light-minded men, who, ...

Marius Buliga: on 2/16/11 at 12:16pm UTC, wrote Hi Tom, Thanks! For a mathematician: one should think larger than...

T H Ray: on 2/15/11 at 16:11pm UTC, wrote Dear Marius, Nice! You've precisely nailed the essential question of...

Marius Buliga: on 2/13/11 at 17:49pm UTC, wrote Dear Georgina, Thanks for the interesting comment. Concerning the...

Georgina Woodward: on 2/13/11 at 11:00am UTC, wrote Dear Marius, Just wanted to let you know that I have read your essay. It...

basudeba: on 2/11/11 at 9:29am UTC, wrote Dear Sir, Homunculus argument is a wrong description of the mechanism of...


Georgina Woodward: "Observation products formed from received EMr aren't evidence of material..." in Anatomy of spacetime and...

Georgina Woodward: "Cf. Lion Location Probability Field and lion entity trapped- with QFT type..." in Anatomy of spacetime and...

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Georgina Woodward: "Thank you. Good luck." in The Nature of Time

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September 18, 2021

CATEGORY: Is Reality Digital or Analog? Essay Contest (2010-2011) [back]
TOPIC: More Than Discrete or Continuous: A Bird's View by Marius Buliga [refresh]
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Author Marius Buliga wrote on Dec. 17, 2010 @ 14:47 GMT
Essay Abstract

I try to give mathematical evidence to the following equivalence, which is based on ideas from Plato (Timaeus): reality emerges from a more primitive, non-geometrical, reality in the same way as the brain construct (understands, simulates, transforms, encodes or decodes) the image of reality, starting from intensive properties (like a bunch of spiking signals sent by receptors in the retina), without any use of extensive (i.e. spatial or geometric) properties.

Author Bio

I am a researcher working in several fields, from pure mathematics, to applied mathematics, to rational mechanics. Graduated from Bucharest University, with an MsC from Ecole Polytechnique, Paris and a Habilitation thesis from USTL, Lille, I mainly moved between Romania, France and Swiss (EPFL). Currently I am visiting Universidade do Brazil in Rio de Janeiro.

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Author Marius Buliga wrote on Dec. 18, 2010 @ 15:10 GMT
This is part of a research program, the first (technically accesible) paper is this one:

What is a space? Computations in emergent algebras and the front end visual system

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Author Marius Buliga replied on Jan. 5, 2011 @ 17:41 GMT
Trying to understand more about this project of simulating spaces, I have found a circle of vague but intriguing notions, centered around "choros" (khora, khoros, horos, hora, chorus).

These threads are so varied that I would appreciate any help in understanding more. That is why I decided to give here some links and comments, waiting for any relevant and helpful...

view entire post

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narsep replied on Jan. 22, 2011 @ 07:59 GMT
Dear Marius,

see attachment


narsep (ioannis hadjidakis)

attachments: Dear_Marius.doc

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Author Marius Buliga replied on Jan. 22, 2011 @ 20:52 GMT
Thanks Ioannis!

Yes, choragraphy was in use as the ancient name of cartography,

at least according to wikipedia (see link in previous message),

where it is written

"Chorography is a term deriving from the writings of the ancient geographer Ptolemy. In his text of the Geographia (2nd century CE), Ptolemy writes that geography is the study of the entire world or large sections or countries of it, while chorography is the study of its smaller parts—provinces, regions, cities, or ports. Ptolemy implicitly would include the making of views (not simply maps of small regions) in this category, since he claims that chorography requires the skills of a draftsman or artist rather than those of a scientist, which are needed for the practice of geography."

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Cristi Stoica wrote on Dec. 23, 2010 @ 05:53 GMT
Dear Marius,

If I understand well, your essay proposes an isomorphism between reality and our brain constructs, and you complement this view by arguing that there is a bias in how we understand physics, due to the way brain works. I find interesting your hypothesis of the "dilation gate", due to our binocular view and determining the way we understand calculus and differential geometry.

In the parallel between orwellian, stalinesque and multiple drafts, and theories in physics, you said at (b) "I am not aware of physical theories supposing that a discrete reality conspires to give (to any observer) the appearance of being continuous.". My impression is that (if I understand well your statement) there are such discrete theories - which introduce length cutoff for various reasons, mainly in order to avoid the problems due to non-renormalizability of gravity. For example, the lattice models, the causal sets of Sorkin, the spin networks of Penrose and their application to loop quantum gravity, loop quantum gravity, approaches based on Schild's ladder and Regge calculus, 't Hooft's discrete theory, GFQT approaches etc. These theories are based on discrete reality, their experimental test is out of our present capabilities, and it turned out to be difficult to make them "quack" like a continuous spacetime, with 3 spatial dimensions and one temporal, Lorentz invariance and so on.

I find very convincing your argument based on Rademacher's theorem.

I would be interested in learning more about the parallel you made:

"Under Plato's hypothesis, it follows that:

(A) reality emerges from a more primitive, non-geometrical, reality

in the same way as

(B) the brain construct (understands, simulates, transforms, encodes or decodes) the image of reality, starting from intensive properties (like a bunch of spiking signals sent by receptors in the retina), without any use of extensive (i.e. spatial or geometric) properties."

I mean, I agree with you that the brain introduces a bias. Therefore, to what extent the parallel between the brain constructs and the emergence of reality still holds?

Best regards,


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Author Marius Buliga replied on Dec. 23, 2010 @ 23:16 GMT
Dear Cristi,

Thank you for the comments. A short answer to the question: I suppose that this emergence, either (a) of reality or (b) of the "image" of reality constructed by the brain, is the result of the same type of computation. I am interested in understanding this type of unknown computation, which I call "simulating space" (see the link from previous post). I believe, presently, that such computations should involve dilation gates and some form of braids formalism.

Historically there is a host of related ideas, from Leibniz, to Toffoli (conservative logic), Kauffman (knot logic, topological quantum computation), but also in neuroscience - Koenderink (Brain a geometry engine) - or in architecture (who is more apt to understand space than an architect) Hillier (Space is the machine). This is to mention just a few.

Maybe I should prepare an explanatory paper, the subject is rather surprising, it is amazing for me to fall into a form of platonism without being initially aware of this.

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Cristi Stoica replied on Dec. 24, 2010 @ 13:56 GMT
Dear Marius,

maybe another connection between (A) and (B) is given by Jean Piaget's theory, inspired by the Erlangen program. His view is that child's mind first develops topological concepts, then projective, and then Euclidean.

If our world is a mathematical structure, it can be described by adding one kind of mathematical relation on top of another. For example, if it is a continuum, we start with the topological structure, then we add the differential one, then perhaps the Lorentz metric. The metric can emerge in two steps: first, only up to a conformal factor (the causal structure), then the affine structure, which gives the volume element. Or maybe it splits into space distance and time duration. Then there are the spin structure and the principal bundles providing the standard model forces. Of course, all this needs to be quantized.

Maybe our mind just tries to control/predict the outside world's behavior as a black box, (B) just tries to reproduce the functionality of (A) with an internal model, through evolution. In this case, how is implemented the functionality of (A) and (B) can be radically different, important is the functional similarity. Maybe (A) is a priori inside us, and we rediscover it by anamnesis, and this is how (B) emerges. Maybe, to connect with the orvellian/MWI, as J.A. Wheeler put it, it is all a game of 20 questions, and whatever (B) becomes, this establishes retroactively how (A) was. I hope your work may add some light here.

Good luck with your interesting and original research and with the contest,


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Author Marius Buliga replied on Dec. 25, 2010 @ 01:00 GMT
Dear Cristi,

Yes, something like this. One may add gestalt theories on top of this, and so on... This only shows that somehow this type of ideas are floating in the air.

But there are many things to say, like for example: how is this happening? Exactly how gestalt laws are implemented in the brain? Or, is it that simple? Let's make a tower with topology at the bottom and some rigid (or smooth) icing on top? These are surely just hints, except one, in my opinion: central notion is computation!

Indeed, from a descriptive point of view, the world of an affine space, say, is specified by all pairs and triples of points in a meaningful relation wrt the affine structure. If you want just a discretization, like a lattice in said space, then you have to give it somehow as a collection of points (pairs, triples, generators and relations...).

From a computational viewpoint you need only to specify a gate (a dilation gate) and a rule (quantum Yang-Baxter or left distributivity) for simplifying circuits made of such gates. Then you just give an unlimited supply of such gates.

If you want to walk around in this affine space then, no problem, just do steps using such gates. When you walk on the road in your city, in fact you don't need to know how every pebble in China is disposed.

So computationally it is not the same as descriptively specifying a reality. In the discrete versus continuous issue the discrete part seems more fitted to an economical computational approach, but this might be only a prejudice due to the limited way that we understand computations.

An example of a computation which does not seem to be one of the type studied in computer science is performed by the first stages of the visual system, be it the one of the human or the one of the fly. So, what I suggest is that if we suppose the equivalence of (A) and (B) then we might import good ideas from (A) to (B) or from (B) to (A). And, what do you say, the world as seen by humans (and flies?) LOOKS pretty continuous, right?

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basudeba wrote on Feb. 9, 2011 @ 04:27 GMT
Dear Sir,

Plato was a great thinker and we differ from your interpretation of his statement. What he meant by sight is ocular perception, which, in conjunction with tactile perception generates the notion of numbers. We have written a book on number theory, in which we have defined number precisely. In our essay, we have referred to this briefly. Often scientists avoid precise definition and resort to operational definitions that are flexible enough to be manipulated in various ways to suit one’s convenience. Thus, we find different interpretations of quantum physics.

Number is a property of substances by which we differentiate between similars. If there are no other objects similar to the one perceived, it is said to be one. If there are others, then we perceive each as one similar to the other. The sequences of different perceptions give rise to the perception of different numbers. All physical phenomena are nothing but accumulation and reduction of numbers – thus, mathematical. However, fundamentally, mathematics is done only in two ways. Linear accumulation and reduction is called addition and subtraction. Non-linear accumulation and reduction is called multiplication and division. Linear accumulation is possible only between similars. Non-linear accumulation is possible only between partially similars.

Perception is possible only if there is motion. It is because perception is the result of measurement, which in turn is the comparison between similars. Comparison is an action that is possible with the application of energy that leads to motion. Without motion (including radiation), no perception is possible. Lines are mobile points, which are either closed or open ended. Geometry is related to motion, because it is related to fields and volumes, which are generated out of closed lines. From this perspective, reality, as defined by Plato, is neither primitive nor non-geometrical.

Your statement B) has a different explanation. Perception may be of two types: those that are directly perceptible – like matter and those that are perceptible only because of their effect on matter – like energy. Space and time belong to the second category. They do not have physical existence. We note the order of arrangement of objects and designate the interval between these as space through alternative symbolism. Same way, we designate the order of arrangement of events as time. While matter particles having mass confined around a central point are linearly accumulative, energy without such confinement behaves differently. Different forces co-exist, but are not linearly accumulative. Reality is a combination of both. We have taken these into account in our essay and discussed the issue without any exotic “mathematics”. In fact from various posts under different eddays, you may see that we have explained motion without any exotic manipulation in the name of mathematics.



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basudeba wrote on Feb. 11, 2011 @ 09:29 GMT
Dear Sir,

Homunculus argument is a wrong description of the mechanism of ocular perception. We have discussed the mechanism of ocular perception briefly in our essay. When the field set up by the radiation from an objects travels through the intervening space between the object and our eyes, and interacts with the field set up by our eyes, it is measured (compared) with the later. The picture looks somewhat similar to the Earth’s magnetosphere when it interacts with solar wind. This explains the shape of the eye. When these impressions are carried by the neurons, they carry an opposite (mirror image) impression. This opposite impression, when interacts with the specific regions of the brain, becomes the true image, just like a casting is prepared with mirror image gives rise to the true object. There no “homunculus” other than the conscious mechanism. This wrong description of facts cannot be used to build a theory of reality.

Beta movement is related to the perception of indiscernible. Since two indiscernible light sources appear in quick succession at short intervals, it gives the illusion of jumping of the light source.

Multiple Drafts Model of Consciousness, as proposed by Dennett, claims that conventional explanations of the color change boil down to either Orwellian or Stalinesque hypotheses, which he says are the result of Descartes’ continued influence on our vision of the mind. The Orwellian hypothesis is fictional, and the Stalinesque hypotheses’ depicts dictatorial perversion. Hence these cannot be used to build a theory of reality.

Multiple drafts hypothesis – “there are a variety of sensory inputs from a given event and also a variety of interpretations of these inputs” – is again a wrong description of the mechanism of perception. We receive different sensory inputs which are processed differently (some have been described briefly in our essay). These perceptions are centrally processed in our brain to give the final out put. For example, when we see a flower, we also smell its fragrance and without touching, perceive its softness.

These wrong interpretations led Everett to propose his misguided theory known as Many-Worlds Interpretation of Quantum Mechanics. We believe in Multiverses which we derive from fundamental principles, but not in Everett’s theory.



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Georgina Woodward wrote on Feb. 13, 2011 @ 11:00 GMT
Dear Marius,

Just wanted to let you know that I have read your essay. It was in fact the first that I read because I was curious to see if there was overlap in our ideas and the content submitted for this contest. Although we are both looking at the appearance of reality,( which when produced by a human being is an experience of reality generated in part through binocular vision, as you discuss), you are looking at the human experience and I am dealing more with external reality.

I do not have a mathematical background so your mathematical explanations and terminology soon became too much for me.It is obvious from your high rating that others have not found it so and I seen no reason for you not to communicate your ideas as you think best and in the way most suited to your thinking style and education.I have had to use plain English which I suppose may seem a little naive to physics specialists or mathematicians such as yourself.

I do think that the gulf between the experience of reality and external reality that can be supposed and is modeled by physics and mathematics is a very important one. I do not know if neuroscience or physics will be the first to claim this territory or whether it will generate a dynamic area of interdisciplinary research.

Most of all I loved your explanation of the title at the very end. I had not heard that before and thought it was lovely. It was nice that it tied the end of the essay in with the philosophical introduction. Good luck to you.

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Author Marius Buliga replied on Feb. 13, 2011 @ 17:49 GMT
Dear Georgina,

Thanks for the interesting comment. Concerning the mathematical explanations, Alice's exploration program is in fact very simple, if you just do what is described there, transforming it into a some kind of film, then I think all the math lingo will become clear (one exception maybe: just forget about the probability "kernel" and replace it instead with the rule "Alice then jumps randomly to a nearby point").

I liked your essay. The overlap is related to a notion appearing in Plato' Timaeus. It is really worthy to actually read the dialogue, in particular because Plato speaks there about the "choros", the place, the space, Timaeus 48e-53c. Here is only an excerpt:

"Suppose a person to make all kinds of figures of gold and to be always transmuting one form into all the rest-somebody points to one of them and asks what it is. By far the safest and truest answer is, That is gold; and not to call the triangle or any other figures which are formed in the gold "these," as though they had existence, since they are in process of change while he is making the assertion; but if the questioner be willing to take the safe and indefinite expression, "such," we should be satisfied. And the same argument applies to the universal nature which receives all bodies-that must be always called the same; for, while receiving all things, she never departs at all from her own nature, and never in any way, or at any time, assumes a form like that of any of the things which enter into her; she is the natural recipient of all impressions, and is stirred and informed by them, and appears different from time to time by reason of them. But the forms which enter into and go out of her are the likenesses of real existences modelled after their patterns in wonderful and inexplicable manner, which we will hereafter investigate. For the present we have only to conceive of three natures: first, that which is in process of generation; secondly, that in which the generation takes place; and thirdly, that of which the thing generated is a resemblance. And we may liken the receiving principle to a mother, and the source or spring to a father, and the intermediate nature to a child; and may remark further, that if the model is to take every variety of form, then the matter in which the model is fashioned will not be duly prepared, unless it is formless, and free from the impress of any of these shapes which it is hereafter to receive from without."

I think we both try to understand "choros", the "mother of all generation", somehow.

Thanks for the final remarks of your comment, I completely agree.

Good luck, Marius

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T H Ray wrote on Feb. 15, 2011 @ 16:11 GMT
Dear Marius,


You've precisely nailed the essential question of whether external nature is different from brain mechanics. You could be right that a specific brain geometry drives perception. I expect this is going to be a very lively and interdisciplinary research area, and you've certainly got a leg up on it.

You might be interested, with your emphasis on metric spaces and random walks, that I gave a specifically physical definition to the time metric (NECSI, ICCS 2006) -- "n-dimension infinitely orientable metirc on self-avoiding random walk" -- to skirt the very problem you suggest. I.e., we don't know except as defined what we mean by a manifold. However, as we know that every Riemann surface is orientable, analytic continuation over n dimensions allows metric space properties and random walk dynamics.

As mathematcians, we know that we can't answer whether that is because of the way our brain is configured, or whether nature is so constructed, though my bet is on the latter.

Good luck with your research program and the contest.

All best,


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Author Marius Buliga replied on Feb. 16, 2011 @ 12:16 GMT
Hi Tom,

Thanks! For a mathematician: one should think larger than riemannian manifolds.

This (false) dichotomy discrete-continuous is just created by a lack of imagination. What could be more than the choice between a manifold and a discrete space?

Well, quite a lot. The spaces alluded in the essay, Heisenberg group in particular, are sub-riemannian or Carnot-Carathéodory spaces. These are infinitesimally different than riemannian manifolds, without being different topologically.

You have to see them to believe. I recommend Carnot-Carathéodory spaces seen from within and Introduction to metric spaces with dilations for starters.

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James Lee Hoover wrote on Feb. 22, 2011 @ 21:16 GMT
"But the race of birds was created out of innocent light-minded men, who,

although their minds were directed toward heaven, imagined, in their simplicity,

that the clearest demonstration of the things above was to be obtained by

sight; these were remodelled and transformed into birds, and they grew feathers

instead of hair." (source [1])


My view is that reality is independent of prescient beings who try to simulate it and gather its characteristics from those simulations. I believe the metaphor above indicates how we taint reality with simple approaches.

Jim Hoover

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basudeba wrote on Mar. 20, 2011 @ 06:17 GMT
Sub: Possibility of manipulation in judging criteria – suggestions for improvement.


We had filed a complaint to FQXi and Scienticfic American regarding Possibility of manipulation in judging criteria and giving some suggestions for improvement. Acopy of our letter is enclosed for your kind information.

“We are a non-professional and non-academic entrant to the Essay...

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