Tommaso,
Remembering your entry last time, I looked forward to reading your essay, rather your fetching drama. The boss (your voice), erudite and "Sherlockian," unravels a spoofy mystery that is yet mathematically and scientifically emblematic. Though chickens are not spherical, I found the etchings of them attractive. Considering the size and intricacies of the universe and the universe in our bodies, we do need a "gigantic computer"
Esoteric and entertaining at the same time.
Jim
Dear George,
if the Priss-Goedel-Priss theorem is right, then the mathematical structure that corresponds to the physical universe is made up of sets and functions (as in Tegmark's MUH), and the latter are total and computable, hence they can be implemented by Turing machines (conputable) that are guaranteed to terminate on each output (total). Now, I am not completely sure about what you mean when you write "do you worry about the halting problem?". I see two possible interpretations of your words.
1. You allude, perhaps humorously, to our own existence, or life span, which, according to this view, should also terminate, without hope for some eternal existence. If this is what you intended, I just observe that there is of course no direct connection between the guaranteed termination of the computations of those defining functions and the presumed termination of our lives. The implied gap is indeed as large and obscure as the gap that separates the static universal mathematical structure envisaged by the MUH and the accidents of the history of the universe that have led to, say, the evolutionary biosphere. This is, in my opinion, one of the weak points of the MUH.
2. Alternatively, you might have intended that the 'existence' of undecidable problems/functions is undeniable (e.g. the halting problem), and it would be unwise to 'rule out' them from our 'real' universe. Well, Priss would question the above terms 'existence' and 'real': he thinks that these functions do not 'exist' in the 'real' universe - the one where SAS arise - and do not contribute to its definition.
In any case, the boss of the agency clarifies, later in the story, that a model of computation that is Turing-universal must include partial computable functions, that are undefined/divergent for some input. Priss's universe, then, would not be based on Turing-universality, which is probably one of the reasons why the agency boss disagrees with him...
Thanks for your comments. Ciao!
Tommaso
PS
I'll read your essay a second time before commenting.
Hello Tommaso,
I always love your essays! You have a rare talent of both being able to make readers laugh out loud while tackling difficult subjects at the same time. Wish my own essay was half as clever as yours- though I tried. I would greatly appreciate if you would check it out and give me your vote.
http://fqxi.org/community/forum/topic/2391
Best of luck in the contest!
Rick Searle
Tommaso -
Thanks. While I was thinking about #2 (which I now see your essay did answer), I suppose #1 is actually the more pressing concern, and I am much relieved with your reply!
The MUH does become much more understandable when we discard all assumptions of continuity. If we are indeed in a finite universe (planck units - finite number of states) then everything becomes computable (although some computations may take a long time.....). No infinities to worry about! Of course, that's not quite what Tegmark seems to say ...
If this is the case, what is the ontological status of mathematics, its theoretical continua and infinities? Mere symbols without content? Epiphenomenal finite brain states? And (this may be a dumb question) what is the hardware on which the computing algorithms are being run, and where did that hardware and those rules come from?
With many thanks, and sincere respect - George
Hi Tommaso,
I was the first to post in your thread, and agree with your point of view. Now you can check out my essay which has the links to the programs that confirms my claims(at the of the sections "program link"). Now, whether my theory is the right one or not that is another matter, although it looks like it. however, is it possible for you to at least confirms some of the results.
Thanks and good luck.
Hi Tommaso,
I think you should win an award for the best writing, and the best title! I found your essay to be a very entertaining read. But who (or what) wrote this algorithm that you say runs the universe, and why did they write it?
I quote from your article "Do Particles Evolve?" in my essay "Reality is MORE than what maths can represent".
Cheers.
Lorraine Ford
Lorraine,
who wrote the code? This is a question that I carefully avoid :-} But I am in good company with many people who refuse to answer the similar question 'Who wrote wrote the Einstein equations, or the Schroedinger equation'. ('Einstein and Shroedinger'? Sure, but that is not the point.) The question you pose is of course about who decided that the physical universe should obey those laws. Many people do not feel too frustrated for not being able to answer this question, about the origin of laws expressed in continuous mathematics, but feel just happy when they discover those laws. Switching to another form of math, algorithms and maybe discrete math, should not change that attitude...
Regards
Tommaso
Caro Tommaso,
I read and re-read your brilliant essay, finding in it a lor of precious suggestions, concerning e. g. the discrete vs continuous or the teterminismus vs indeterminismus relationship and concerning, in particular, the problem of computability, in which I am very interested from the time when I developed the ideas that I partially sketched in my contest essay.
Although I find the "Priss-Goedel-Priss theorem" (that you place significantly in 2031) not easy to be accepted, I am inclined to believe (maybe agreeing with you) that all existing facts or empirical objects of the universe (no matter if they exist in the past, the present or the future), are in principle representable by computable functions.
But, on the other hand, I am not sure that consciousness is a fact or an empirical object. (As well as I am non sure that all merely possible state of affairs can be described by computable functions, if only because their set is probably uncountable, while the set of all computable functions is certainly denumerable.)
I wonder if these will be still issues in 2075..
Tanti cordiali saluti
Giovanni
Caro Giovanni,
what I find original in the Priss-Goedel-Priss Theorem (2031) is that it reverses the intuition that the phenomenon of consciousness is too complicated to be part of a universe constrained by discreteness and denumerability (of the computable functions). According to the Theorem, a universe in which consciousness exists - a universe that can be perceived by sentient entities - must somehow constrain its complexity within the bounds of discreteness and the denumerable, computable functions: due to the need to stick consciousness in it, the design of the universe is 'forced' to be relatively simple, and simpler than many other mathematically expressible structures.
I feel that the Theorem pushes Tegmark's views on the Mathematical Universe (more precisely, his Computable Universe Hypothesis CUH) to a most attractive consequence, placing consciousness, as everything else, under the rule of computable, total functions (in my opinion, the issue of universality and total/non-total functions is a bit confusing in Tegmark's paper).
But, as expressed in the last part of my essay, the CUH cannot account for concepts such as evolution, history, emergence. On the contrary, these features are perfectly compatible with a computational universe perspective (not to be confused with the CUH). I this respect, and coming to your point, I do not feel like excluding the possibility that consciousness itself be an emergent phenomenon that goes hands in hands with increasing complexity of matter, as suggested so effectively by Teilhard de Chardin (see my 2014 FQXi essay), possibly even measurable along the lines of Tononi's work.
So, while I agree that computable functions are probably too weak a tool for a complete description of the Universe with its unknowable evolution, I am ready to accept that a computational universe in which evolution and growing complexity derive from the emergent properties of the computation, as it unfolds, might also host phenomena such as consciousness.
Cordiali saluti
Tommaso
Dear Dr. Bolognesi,
I thought that your engrossing essay was exceptionally well written and I do hope that it fares well in the competition.
I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.
All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.
Joe Fisher
Tommaso,
My non-GMO robins are not spherical but "free-range". Have you had a chance to read about them?
Jim
Dear Tommaso Bolognesi
Last year you asked me, where I have correction to Tononi's model. Now I find that my inclusion of quantum free will is this difference. Thus, if free will is excluded, every answer given by neural network is defined in advance. Thus in principle there is not a lot of options for various qualia, but only one option. But free will must be added that many options are obtained.
You give a cue that you do not believe in quantum randomness ('t Hooft), and that you do not believe in existence of consciousness. It is oppositely at me. And, I think that consciousness does not exist without quantum randomness. (I think these two sentences agree, this means that we agree here?)
I also agree with you that consciousness can be reduced more and more. I think that at the end some primitive consciousness remain, but you think that it completely disappears at the end?
I have some questions. Platonic level 4 is often mentioned in this contest. Let us say that mathematical functions exist independent of physical world. But why it is necessary here to introduce this Tegmark's complicated anthropic principle? Namely, I think that physical world is build up from one very simple math, maybe it is so simple that it does not contain axioms. Thus what is the reason for introduction of this anthropic principle?
Why do you think that we do not live in simulation? I think that space around us is real in the same manner as web pages inside computer.
Tononi believe in panpsychism, does this means that you do not?
This is a very artistic piece of work, similarly as a year before. You also have some specific knowledge, so I hope that you will find something new.
One metaphor: ''You are Tomaso, who do not believe in consciousness, although he put fingers in it.'' :)
Best regards
Janko Kokosar
Dear Tommaso,
Once again this contest, you submitted an original, entertaining and thought provoking essay! I had read it with great interest shortly after it was posted and now realise I'd never gotten to comment on it and rate it. I like the reference to Isaac Asimov's classic story, "The Billiard Ball"!
I agree with many things that future-fictional-scientist Priss says about the fundamental nature of physical reality. In my essay, I also explore the hypothesis that "physical reality is that [mathematical] layer, and that layer is all there is". As Priss says, "What else [could it be]?". I also agree that if a mathematical structure doesn't contain conscious entities, it is not really relevant to determine what kind of existence it has: as Priss says, "the ontological status of mathematical structures involving non-computable functions, or even restricted to computable functions, but not entailing consciousness, is, in my opinion, irrelevant."
I find the Priss-Gödel-Priss Theorem of 2031 a bit surprising. It is quite possible that only total, computable functions can generate universes that contain consciousness, but why would all these universes be isomorphic to each other? Unless of course you take the totality of physical existence that can be generated by these computable functions and group it in one humongous ensemble that you call "Universe". But I think that ensemble (containing at least all the bubble universes of eternal inflation) is closer to what most people would call a multiverse... Or do you believe that the set of coherent computable total functions that can generate a physical reality is so limited that it produces a relatively small physical universe?
I found your final discussion about "deterministic chaos" and physical laws as "data compressors" quite enlightening. Overall, you submitted a strong entry, and I find it a bit disappointing that it has not generated more interest (judging by the number of comments and your average rating). At least, this time, the judges will select 10 entries at their discretion irrespective of rating, so it's not over until it's over!
Good luck in the contest, and all the best,
Marc,
thanks for your message. I have not been able to read and review as many essays as I would have wanted this year. Your title was one of the few that kept attracting my curiosity, so I'll give a try tonight - likely the last reading before the end of the voting phase.
The isomorphism conjecture is quite bold indeed; it would gratify the ego of all owners of some degree of consciousness, and could perhaps be criticized for suggesting that the phenomenon of consciousness is in some sense unique (although occurring in several blends in the only universe where it emerges). What I found attractive, however, is the idea that an understanding of this phenomenon might help in catching the ultimate theory of the physical world, somehow reversing the expected logical order of discovery...
Confusing? Maybe, but it's late.. Ciao!
Tommaso
Dear Tommaso,
Your dialogue is enjoyable to read with several layers to decipher. There is music, geography, time events, algebra, murders, the number 42 and a pizza in Pisa! You anticipated a 2031 theorem relating 'total computability' and conscious states. You write " The Universe is not a static mathematical structure ... It is the unfolding of a computation, and a relentless source of novelty; its future gifts are mathematically unknowable until they actually come into existence." You show how unexpected structures may emerge from computation. This asks the question what are those that don't emerge from an algorithm and how it relates to Tegmark's MUH. The "downgrading of quantum mechanics to the status of a mere tool" is quite surprising. I liked your essay anyway and it merits more attention.
Best wishes,
Michel
Thank you Michel. I just mention that when I wrote about the 'downgrading of Quantum mechanics', which is looked upon as a tool, not as a theory, I am almost directly quoting:
Gerard 't Hooft - The Cellular Automaton Interpretation of Quantum Mechanics - arXiv:1405.1548v2 (2014)
Not my idea (but I look forward for it to come true!)
Cheers
Tommaso
Dear Tommaso,
I was attracted to your essay because of the original title.
I was not disappointed, it is original and very interesting.
If you think that the Universe is the unfolding of a computation, you might want to take a look at my essay and if you want to find out how I got to those equations you can check out my website.
All the best,
Patrick
Ciao Tommaso,
You have spherical chicken and I have spherical cows. I propose to put them together after the end of the contest and start a farm; at least something good can come out of the contest this way. I'm sorry for dropping by so late. I just read one of your comments upper on the page and I want to say that I perfectly understand what you mean; for which reason I hope to compensate with my vote. I enjoyed your essay because it was designed to be entertaining; apparently not everyone has a stomach for humor these days. I also enjoyed your essay because it's a study in topology, symmetry, computability and randomness, which should not be discounted just because they were presented in a light-hearted manner. I like very much how you described the real value of having mathematical models. You have a very good writing style and talent for writing beyond those of a non-professional writer; it is a bit like imbuing a cyberpunk writer such as William Gibson with humor.
Warmest regards,
Alma
Hey Tommaso,
Armin directed me here, and I'm glad he did. I enjoyed your essay, even though I was a little confused trying to visualize the knot and billiards scenes.
I think you'd like my Digital Physics essay, and the actual movie. The movie was inspired by the likes of Wolfram, T'Hooft, Fredkin, Chaitin, Leibniz, Turing, Shannon, and others. I would be interested to hear your thoughts on my essay, which only briefly touches on some of the themes explored in the movie. There are also some questions at the end of the essay that might interest you, though.
Thinking towards the future... Suppose a deterministic model started to become more accepted in the physics community, and then people started to believe that we don't have free will. Do you think we'd have more empathy at that point towards people that committed crimes? Do you think we would be more concerned with rehabilitating people as opposed to punishing them? My optimistic view is that maybe we'd feel like we were all in this crazy computation together at that point:)
Are you familiar with James Gates' "Adinkras" which are visual representations of super symmetry functions? Dr. Gates says that representing the super symmetry equations in this graphical way reveals that they are isomorphic to error correction code, like the kind used to fix bit flips when information is transmitted over the internet. "Error correction" sounds so benevolent and like a real mature way to handle our human mistakes. I only mention it because I thought it sort of tied in with that optimistic view of a future I just imagined.
Feel free to sign up for the mailing list if you want to know when and where "Digital Physics" is going to be shown.
Thanks,
Jon
Best congratulations, Tommaso, for the prize you have won! Your very beatiful and creative essay surely deserved it!
Ciao, un caro saluto,
Giovanni