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Is Reality Digital or Analog? Essay Contest (2010-2011)
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The Distinct Nature of Physics and Cosmos by Thomas J. McFarlane
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Author Thomas J. McFarlane wrote on Feb. 8, 2011 @ 12:34 GMT
Essay AbstractThe question of whether reality is necessarily continuous or discrete (i.e., analog or digital) is investigated by examining the nature of physics. It is argued that the view of physics as describing substance--common since ancient Greece--is today obsolete, and that modern physics is better understood as a way of describing reality as mathematical order. The question of whether reality is discrete or continuous is then reframed as a question of the nature of theories and the mathematics that they use. Because both measurement and theory are fundamentally grounded in discrete mathematical concepts based on distinctions, it is concluded that any description of reality by physics is necessarily discrete at its foundations. This conclusion points to a more fundamental insight into the nature of reality beyond the scope of physics.
Author BioAfter graduating with distinction from Stanford University in physics, Thomas McFarlane earned a graduate degree in mathematics from the University of Washington, specializing in algebraic invariants of knots. He is currently a patent agent and partner at a Silicon Valley patent firm and an independent scholar with interests in the philosophy of physics. In addition to his background in science, he also has a graduate degree in philosophy and religion, and is author of Einstein and Buddha: The Parallel Sayings.
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nikman wrote on Feb. 8, 2011 @ 19:14 GMT
Excellent paper. And of course, Bohr:
"...[In] our description of nature the purpose is not to disclose the real essence of the phenomena but only to track down, so far as it is possible, relations between the manifold aspects of our experience."
and:
"Strictly speaking, the mathematical formalism of quantum mechanics and electrodynamics merely offers rules of calculation for the deduction of expectations about observations obtained under well defined experimental conditions specified by classical physical concepts."
Which some people still don't get.
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nikman wrote on Feb. 8, 2011 @ 20:22 GMT
Knew your coda was reminiscent of something:
6.41 The sense of the world must lie outside the world. In the world everything is as it is and happens as it does happen. In it there is no value -- and if there were, it would be of no value.
If there is a value which is of value, it must lie outside all happening and being-so. For all happening and being-so is accidental.
What makes it non-accidental cannot lie in the world, for otherwise this would again be accidental.
It must lie outside the world.
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Author Thomas J. McFarlane replied on Feb. 13, 2011 @ 22:09 GMT
Thanks for your feedback. Those quotes from Bohr and Wittgenstein are good ones!
Edwin Eugene Klingman wrote on Feb. 13, 2011 @ 00:06 GMT
Thomas,
I don't know if you've had a chance to check out Joy Christian's article
here. It claims that all of the so-called violations of Bell's inequality are based on an erroneous calculation. If so, the current interpretations of non-locality and non-reality are incorrect. I believe this to be the case, but only time will tell.
You quote Weyl to the effect that: "objectivity means invariance with respect to a group of automorphisms."
I would see this world as a perpetual motion machine, 'auto-morphing' endlessly into itself in meaningless fashion. Definitely compatible with nikman's "In it there is no value...". There clearly would be no room for either free will or randomness, but I see that you covered this at the end with "chaos", although it's unclear how order and chaos are coupled into one reality.
It is also unclear to me how 'scale' plays into a purely mathematical world, but perhaps it can.
I also wonder, from a theoretical viewpoint how one can reconcile such a reality with different coordinate systems. I have worked in Cartesian, spherical, cylindrical and other systems, but one of my physics books describes eleven different coordinate systems used in physics. Let us consider any problem, say the hydrogen atom, solved in each of these coordinate systems. Surely we will not obtain the exact same answer for all of these systems, so which one is "right"? If the universe is only mathematical, one of them must surely describe "reality".
There seem to me to be other problems in this perspective, but I'm curious as to your response to the above.
Finally, you state:
"Reality in its totality, then, encompasses both the cosmos(order) and its complement(chaos)."
This dualism appears to me schizophrenic, with an unbridgeable gap between the order and chaos of our universe. At this point it becomes meta-physics, not physics.
No one has any special authority to criticize anothers meta-physics, but we do have a right to our own preferences, and my preference for decades has been a unitary metaphysics that I believe is best represented by an objective substantial reality that connects order and chaos into one whole universe.
My brief introduction to this approach is
here.
Edwin Eugene Klingman
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Author Thomas J. McFarlane replied on Feb. 13, 2011 @ 23:58 GMT
Edwin,
I have not studied Joy Christian's article. However, while my essay mentions violations of Bell's inequality, its argument does not hinge on them.
Your point about different coordinate systems is not clear to me. Solving the Schrödinger equation for the hydrogen atom will give the same orbitals, irrespective of whether one uses rectangular or spherical coordinates to describe them. It's just that the latter has a simpler expression due to the spherical symmetry of the problem.
The way physics is defined in the essay, the complement of the cosmos is indeed outside of physics. However, the distinction between the cosmos and its complement is not necessarily "an unbridgeable gap." On the contrary, insofar as they are aspects of a single reality, there is not an absolute distinction between them.
Regards,
Tom
Edwin Eugene Klingman replied on Feb. 14, 2011 @ 00:29 GMT
Tom,
Thanks for reply. I'm confused by your idea of a single reality and how order and chaos are connected, but that's a difficult problem for anyone to answer.
I sincerely doubt that solving the hydrogen atom in eleven different coordinate systems will provide exactly the same orbitals. Eons ago I had to solve such a problem by expanding an analytic integral as a series expansion. Being young and gung-ho, and faced with three indices, I expanded the series in all eight possible ways. To my surprise I found that seven of these expressions were 'infinite' but one of the expressions truncated with a finite number of terms, implying, I suppose, an exact answer.
I am not convinced that all coordinate systems will produce exactly the same answers, and if they do not, then the issue arises of 'which' math is real, whereas in a substantial universe there *is* a reality, and the fact that some mathematical maps get only so close to reality is not a problem.
If you are correct, that all math solutions in all possible frameworks give the exact same answer, then this supports your theory.
Good luck in the essay contest,
Edwin Eugene Klingman
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Author Thomas J. McFarlane replied on Feb. 19, 2011 @ 08:15 GMT
Edwin,
The notion of a single reality is simple. Perhaps what is confusing is the relationship between its two aspects: 1) cosmos or order and 2) its complement, which could be called chaos or formlessness. The connection between these two inheres in their nature as complementary aspects of the one reality. In other words, they exist in mutual interdependence and therefore are not absolutely independent or separable from each other. Or, to explain it in terms of a graphical metaphor, the distinction between them joins them as much as divides them. Rather than being separated by an unbridgeable gap, they are connected by an infinitesimally thin distinction.
I hope this helps clarify it.
Regards,
Tom
Edwin Eugene Klingman replied on Feb. 19, 2011 @ 22:33 GMT
Tom,
I note your second degrees in philosophy and religion, so I assume this influences your perspective. [I considered such a switch from physics, but didn't.]
My essay in the previous fqxi contest was
Fundamental Physics of Consciousness wherein I propose that the essence of one reality is 'awareness and volition' [=consciousness].
To interact with itself, a distributed field must somehow 'be aware of' itself, and any 'action' can imply 'volition'. We can of course ignore these aspects of reality and simply formulate 'potentials' and 'forces', but that doesn't change the facts.
From this perspective 'volition' is 'free will' and the implication is that consciousness has been here 'from the beginning'. Since over half a century of experiencing and thinking about awareness has convinced me that it could never arise locally from simply arranging the Lego blocks in the 'proper' order, this is compatible with my theory.
I mention this because you seem to want to break the world into 'Order' and 'Chaos', where chaos implies random to me. I prefer the concept of free will, and distinguish free will from random as follows:
free will = action by reason of awareness,
random = action for no reason at all.
This may or may not fit into your scheme of thinking, but it works well for me.
Edwin Eugene Klingman
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Steve Dufourny replied on Feb. 28, 2011 @ 15:45 GMT
Hi,
Christian is right TH, really ! But your are strong, we know your skillings, that said ,the formless is without real sense...if we take the chaos and disorders as justy foto of our motions.It's important you know that....
Steve
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Steve Dufourny replied on Apr. 1, 2011 @ 10:55 GMT
oops sorry for the confusion about your name.
Steve
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Member Ian Durham wrote on Feb. 19, 2011 @ 20:50 GMT
Thomas,
Interesting essay. Your write, "The cosmos described by physics, however, is a characterization of only that aspect of reality which is revealed when we look through the lens of discrete mathematical concepts which are all traced back to the primordial act of making a distinction." This resonates fairly well with
my own conclusion, except that I'm more of an empiricist and, while I argue for the discreteness of our knowledge of the universe, I am opposed to equating the universe itself with its mathematical model(s).
As Dean Rickles noted when discussing his own essay, you might enjoy Eddington. I wrote my PhD thesis on Eddington's Fundamental Theory (which was wrong in many ways, but still quite enlightening). I dusted it off recently (actually after Dean and his co-authors cited it in the book he mentioned in that same discussion) and have been talking to CUP about turning it into a book, but haven't gotten around to it. It's on the arXiv, but the first few chapters (which are just background material anyway) aren't that great.
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Author Thomas J. McFarlane replied on Feb. 20, 2011 @ 06:01 GMT
Ian,
Thanks for the reference to your dissertation on Eddington. I've just downloaded it from the arxiv and look forward to studying it.
Regarding the relationship of reality to the manner in which it is empirically known, I agree that they are distinct (see the conclusion of my essay). Perhaps your definition of 'universe' has a different meaning, though.
Regards,
Tom
Member Ian Durham replied on Mar. 1, 2011 @ 20:02 GMT
Tom,
I think we agree, actually. I gave your essay a more in-depth study and it has the same basic fundamental idea behind it as mine does. It's actually an excellent essay, the more I think about it.
Ian
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Author Thomas J. McFarlane replied on Mar. 9, 2011 @ 18:36 GMT
Ian,
Thanks! I appreciate the feedback.
Cheers,
Tom
Stefan Weckbach wrote on Feb. 20, 2011 @ 07:57 GMT
Dear Tom,
i read your essay and enjoyed it very much. Very clearly and consequently argued lines of reasoning.
"Insofar as the distinctions we use to describe order are free imaginative constructs, they are not so much properties inherent in reality itself, but the basic elements that make it possible to characterize and describe a cosmos at all. We may then redefine objectivity in purely mathematical terms, without any implication of an independently existing substance."
Yes, that's my line of thinking too. George Spencer-Brown has outlined the universal basement of distinctions in his famous book "laws of form".
All physical processes, be them human beings or just physical facts, must obey these laws of distinction as long as they are coupled to "duality". A fact is a provable distinction, means a 1 bit decision. If one cannot decide a thing, there's no information and hence there are no "facts".
There may be a metaphysical realm where the duality of mutually exclusive alternatives is transcendental, and i think QM is a hint in that direction.
"Because the cosmos is discrete, this suggests that its complement is a continuum—not the mathematical continuum which has definite structure, but an indefinite continuum, a formless void (i.e., the original meaning of the Greek word chaos) that lacks any order and is thus beyond comprehension in terms of concepts or distinction."
Yes again. One can think about "infinity" as "undefined" - it has no borders that could make a distinction. Hence it is "un-definite", "undefined".
My standpoint is that maths can never capture the whole ultimate reality. denumerability and non-denumerability are concepts intimately related to determinism. But no exclusively mathematical and therefore deterministic proof can prove the exclusiveness of determinism/mathematics. This does not necessarily mean that ultimate reality couldn't be exclusively deterministic/mathematic, but i strongly assume that it underlines that mathematics is limited for the same reasons why distinctions are possible in this world: namely because limits (distinctions) are the operational basement to produce facts and hence information in a dualistic world.
Thanks for visiting my site,
all the best
Stefan
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Author Thomas J. McFarlane replied on Feb. 24, 2011 @ 20:42 GMT
Stefan,
Thanks for your comments, with which I'm in agreement. I'm familiar with Laws of Form.
Lou Kauffman has done some interesting related work.
Best regards,
Tom
Armin Nikkhah Shirazi wrote on Feb. 20, 2011 @ 17:15 GMT
Thomas,
I found your essay to be insightful and very well written. Until I got to the last two paragraphs, I thought that the essay was intended to make a case for the discrete nature of reality, and it argues this rather effectively.
The last two paragraphs confused me a bit. Was the intent to suggest that reality may be both discrete and continuous, after all? Or that this question is unanswerable? If so, it did not balance the first part at all in terms of depth of treatment given to defend that position. In fact, the concept of the 'complement of the cosmos', based on the sparse description offered, strikes me as a bit mystical. Does it have a place in science? It seems to me that you take the position that it doesn't ('beyond the scope of mathematics, physics ...'). There clearly are subjects which are outside the scope of these fields, but how can the boundaries of physics and mathematics with these subjects be mapped onto the boundary between the discrete and continuous aspects of reality? I wished that this argument would have been fleshed out a bit more.
Nonetheless, I did enjoy reading your essay and wish you the best.
Armin
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Author Thomas J. McFarlane replied on Feb. 24, 2011 @ 21:03 GMT
Armin,
Thanks for your comments. I'm glad you enjoyed the essay.
Regarding the last couple paragraphs of the essay, you are correct that they touch upon a topic that is outside the scope of the fields of mathematics and physics. That was the primary reason why I did not develop those ideas further in the essay, despite the fact that fleshing them out more (as you suggest) could be interesting.
The kind of 'continuity' associated with the complement to the cosmos is perhaps more appropriately termed 'formlessness' in order to avoid confusion with the continuity associated with the mathematical continuum, which actually has a definite structure to it. So the mathematical continuum would then be a kind of order that is comprehensible using our discrete concepts, while the formlessness that is the complement to what is comprehensible by discrete concepts would be ineffable.
Physics and mathematics, as particular ways of viewing reality, would not have boundaries that correspond to the limit of comprehensibility per se since there are various other possible ways of viewing reality.
I hope this addresses your questions.
Regards,
Tom
Member Dean Rickles wrote on Mar. 7, 2011 @ 15:15 GMT
Hi Tom,
Finally got around to reading your essay properly. It's very impressive. You, Ian, and I have somehow developed a very similar worldview: it's uncanny. My guess is a love of Symmetry and Kant (Weyl and Eddington shared this too, of course!). Hopefully my rating will boost you up the rankings, as is deserved.
Best,
Dean
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Author Thomas J. McFarlane replied on Mar. 9, 2011 @ 18:32 GMT
Hi Dean,
Thank you for your feedback. I appreciate it! I've also been very impressed by your essays and look forward to following your work (and Ian's) since your perspective resonates with mine.
Cheers,
Tom
Author Yuri Danoyan+ wrote on Mar. 9, 2011 @ 20:02 GMT
Not to be arrogant to this essay
http://www.fqxi.org/community/forum/topic/946
My dаughter Danoyan Tamara, administrative associate in Stanford University
http://www.stanford.edu/dept/psychology/node/93
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John Merryman wrote on Mar. 13, 2011 @ 01:31 GMT
Thomas,
You make a good argument for why reality can only be understood in terms of its discrete relationships, but it's wrong. With your last paragraph, it's clear you understand your point has its limits, but relegate the wholistic view to mystery. It isn't mysterious at all. It's overlooked because it's so basic. Math says that if you add two things together, they equal two. Well, if...
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Thomas,
You make a good argument for why reality can only be understood in terms of its discrete relationships, but it's wrong. With your last paragraph, it's clear you understand your point has its limits, but relegate the wholistic view to mystery. It isn't mysterious at all. It's overlooked because it's so basic. Math says that if you add two things together, they equal two. Well, if that's the case, you haven't actually added them together. Necessarily actually adding things together means you have one of something larger. In basic terms, it's like adding two piles of sand together and having one larger pile, but in reality it's more like components combining to create a larger whole. Whether physics, or biology, we like to take things apart to see how they work, but the fact is that they work together. Much like all the parts of your body add up to a larger whole, or all the components of an atom add up to an atom, not to mention all the various levels between, above and below the atom and the person.
This dichotomy is basic to the difference between eastern and western philosophy. In that we in the west tend to focus on objects and view their actions as emergent. While in the east, there is the contextual view and the particulars within the context are as much a part of the larger whole as your nose is part of you.
One aspect of this that I raise quite frequently and was the subject of my entry in the Nature of Time contest, is that we are looking at time backward. The basis of our rationality and from that, language, culture, history, etc, is the concept of time as the present moving from past to future. So it is natural to include this into our physical theories of how reality functions, but the fact is that it is the changing configuration of what is, the present, which turns the future into the past. We don't travel the fourth dimension from yesterday to tomorrow. Tomorrow becomes yesterday because the earth rotates. It is not that we move from a decided past into a probabilistic future, but that the continuous collapse of probabilities which turns the future into the past. Time is an effect of motion, not the basis for it.
In fact, in eastern cultures, the past is considered to be in front of the observer and the future behind, because both the past and what is seen are known, while what is behind one and the future cannot be seen. Physically we do understand what is in front of us and can be seen is of past events, be they across the room, or across the universe, but we consider ourselves to be moving through our environment, rather than part of it, so we think of ourselves moving from past situations to future ones, as a function of our own spatial action. The irony is that this creates a deterministic view of time, since we only exist at the moment of the present and cannot change the past, or affect the future. On the other hand, when we understand ourselves as fully integrated into our own context, then our actions are part of the process creating these situations and we affect our context, as it affects us.
You do conclude your essay with a nod toward Complexity Theory, with its dichotomy of order and chaos, but I think this relationship can better be described as a dichotomy of information and energy. Energy manifests information, while information defines energy. The information is the top down view of the details, while the energy is bottom up process. They are like two sides of the same coin, such that there cannot be one without the other. They are still opposites though, as energy is fundamentally dynamic, while information is necessarily static.
Think in terms of how you perceive the distinctions you use to define your view of reality: Necessarily you must move from one to the next, otherwise it is that frozen featureless void. So there are the distinctions and there is your movement from one to the next. That is time. Remember the clock has two features; the hands and the face. We think of the hands as moving clockwise, but from the context of the hands, it is the face which moves counterclockwise. The hands represent the present, as it moves from one unit of time to the next.
As I pointed out though, it is the energy of the present which forms and dissolves these units of time. The future becoming the past.
So it is the wholistic present which is creating these discrete units which come into being, grow as long as they absorb more energy then they lose, eventually to lose all energy and fade into the past.
One way to think of this is as a factory: The products go from initiation to completion, but the production line faces the other direction, consuming raw material and expelling finished product.
The mind functions in a similar fashion, as it consumes masses of information, turns it into discrete thoughts, which are then replaced by the next. The brain is physically real, thus it exists in the present. Thoughts coalesce out of the future and fade into the past.
I could go on, but this makes the basic point.
Regards, John
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Sreenath B N wrote on Mar. 13, 2011 @ 11:07 GMT
Dear Thomas J. McFarlane,
Your historical background of the essay is excellent;but it is partial because you have concentrated only in explaining digital aspect of reality but not its analog nature.Yet in the ending you are not sure whether reality is digital or analog although you side with the former.You have not mentioned in your essay GR which is purely classical (analog) theory.
Inorder to have a balanced view,please, read my essay and make your comments.
Thanks for your thoroughly enjoyable essay.
Best regards and good luck.
Sreenath B N.
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Alan Lowey wrote on Mar. 19, 2011 @ 11:17 GMT
Dear Thomas,
Congratulations on your dedication to the competition and your much deserved top 35 placing. I have a bugging question for you, which I've also posed to all the potential prize winners btw:
Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?
Best wishes,
Alan
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Marcel-Marie LeBel wrote on Jun. 7, 2011 @ 00:02 GMT
Thomas,
Congratulation for your essay! It reads well and is very interesting. But..
What one sees depends on the lens he chooses. At the focus of all these different lenses is one and the same subject; the substance. And, built into it, the cause.
You could have made your point without attacking the substance. Sure, physics is not about the substance. The original question was about what substance makes the universe and what cause accounts for it spontaneous evolution.
Physics cannot (and will not) answer these questions. They are nevertheless the ultimate question before which we cannot quit in the face of easier answers.
The questions remain and you cannot wave them away. Ignorance can't be a wish. Never.
Thanks,
Marcel,
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Sridattadev wrote on Aug. 10, 2011 @ 17:16 GMT
Dear Thomas,
Physics at best is relative explanation and hence can never describe singularity or
absolute truth in words or expressions or symbols. Truth can only be experienced in silence in one self that is the ultimate reality and true nature of universe.
Love,
Sridattadev.
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Artur wrote on Aug. 25, 2011 @ 23:41 GMT
Dear Thomas,
your essay interested me very much because I had similar ideas recently, some of them inspired by a notion of entropic gravity presented in Erik Verlinde's paper. Below I share my thoughts. I hope that despite many similarities you will find something interesting.
Firstly - what is the reason for the existence of material objects as opposed to abstract ideas? This...
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Dear Thomas,
your essay interested me very much because I had similar ideas recently, some of them inspired by a notion of entropic gravity presented in Erik Verlinde's paper. Below I share my thoughts. I hope that despite many similarities you will find something interesting.
Firstly - what is the reason for the existence of material objects as opposed to abstract ideas? This question is not necessary if we assume that the material world does not exist, or, equivalently, it is not different from abstract ideas. And there seems to be no necessity to explain why abstract ideas (like 'empty set') exist or whether they exist or not. The fact that we actually experience material world may be just our own representation of what is accessible to us.
Second thing is the nature of laws of physics. The entropic explanation of gravity is an example of the phenomena that a law of physics that we experience may be just a consequence of lack of laws or chaos. The entropic force of gravity is described by Verlinde as a consequence of some set of information (bits) changing randomly over time to less organized state. So what if we assume that there are no laws? This assumption is appealing for some reasons:
- laws operate on something. If there is no objective existence only abstracts, everything is allowed
- physics seeks for the ultimate theory which has a minimal set of assumptions which explain everything. Theory without assumptions would be truly ultimate. It would not be possible to explain it in terms of a simpler theory.
So if there were no laws, why should we experience the laws? After all, in real life most things are predictable and if I am sitting in my room, I will not find myself on the moon the next second. Again I tried to avoid this question - we do not experience chaos not because there is no chaos but because of what we are. We may be that part of 'universe' that is based on aspects of order (on the other hand it is interesting to note that not everything is predictable and ordered; although I will not be on moon the next second, I do not know many things that will happen the next second to me, like what I will see on my TV. This degree of randomness seems to be conncted with the concept of time).
I was also thinking about our inability to understand infinity 'natively'. In science we think by operating on finite information. For example we cannot operate on infinite sequences of natural numbers. We can only use finite descriptions of such sequences. This implies that there are sequences we are not able to describe accurately at all (set of all infinite sequences is uncountable and set of finite descriptions of countable set of letters is countable). Such and other limitations may be the reason why we cannot experience 'everything' that 'exists' in the 'universe', only things which contain some order. Perhaps even our consciousness as we know it (do we?) is based on (or is some aspect of) order, in which case to experience chaos fully would be less possible to us than it is possible for 2-dimensional creature to fit 3rd dimension somewhere in its world. We are only exposed to aspects that exhibit some laws.
It seems far fetched to try to explain the universe using the assumption that the universe does not exist and there are no laws in it. Perhaps one day we will derive Einstein's equations from these assumptions. My feeling is that to do that we need to understand some more fundamental things - like what we are and how it is related to our experience of time and space.
Thanks for the essay,
Artur
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