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There are a few physicists that propose that the universe is a hypercomputer. One example is Roger Penrose, who, basing in his quantum interpretation (https://en.wikipedia.org/wiki/Penrose_interpretation) and in spin networks (https://en.wikipedia.org/wiki/Spin_network), proposes that the universe is basically a giant hypercomputer.

But, since that universe would contain completely uncomputable things, doesn't that mean that these models don't assume computability? I mean, wouldn't that mean that literally every uncomputable thing could happen in these hypercomputer-universes? Even things that could not be "computed" by a hypercomputer?

In that case, then, is it possible to mathematically define a hypercomputer-universe where even things that could not be computed by that hypercomputer would exist? And if yes, wouldn't be the case that if we introduced/defined a trivialist system (https://en.wikipedia.org/wiki/Trivialism) in this hypercomputer-universe model (to produce/create or "simulate" a trivialist universe, or any other class of impossible world (https://en.wikipedia.org/wiki/Impossible_world)), then, every illogical/logically impossible things, even those illogical/logically impossible things could not be computed by a hypercomputer because they are logcially impossible or simply impossible to describe/conceive/compute, would certainly exist (in this hypercomputer-universe)?

Sue K Dccia
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  • The operative word is ‘a few’... – Mozibur Ullah Apr 17 '19 at 11:34
  • Have you ever really considered the process of natural selection? It's a very simple idea that life competes and the winners procreate. But the idea has produced all complexity we see on earth. So it is with computers. A computer just adds numbers together and puts them in boxes. But from that process we get Assasins Creed Oddysey and driverless cars. Of course a computer could produce things which result in something uncomputable, this is the basis of 'cryptography' for example. – Richard Apr 17 '19 at 12:03
  • You seem to be grinding an ax. In the other thread you rejected the detailed and (in my opinion) solidly on-point overview of the ordinal structure of hypercomputation. If you did not find value in that I doubt you're looking for value. What is it you are looking for? – user4894 Apr 17 '19 at 12:53
  • @user4894 If you refer to one of your answers to one of my questions (particularly that one asking if there would be a hypercomputer capable of computing the impossible) I felt like you were not answering the question. The question was asking whether a hypercomputer could somehow even compute things that are not just uncomputable but also logically impossible to describe/compute/conceive... – Sue K Dccia Apr 17 '19 at 14:40
  • @user4894 ...and I understood your answer as basically saying that hypercomputation may be impossible under the laws of physics and that there is some research going on to find out whether is it truly impossible. But I was not asking that. I know that hypercomputation may be impossible under OUR laws of physics. But my question was different. It was asking whether hypercomputers, assuming they could exist under a possible set of laws, could somehow compute even illogical/logically impossible things that are even impossible to describe/compute. – Sue K Dccia Apr 17 '19 at 14:40
  • @user4894 Please forgive me if I misunderstood your answers and you wanted to say something else. In that case, could you please re-explain your point? – Sue K Dccia Apr 17 '19 at 14:45
  • @user4894 I also decided to ask this since I got no reply from you – Sue K Dccia Apr 17 '19 at 15:02
  • @Richard: In regards to your cryptography mention: a computer cannot _create_ something that is uncomputable (by semantical definition), but a computer can _handle_ values that cannot be reverse engineered. That is a relevant distinction here. Hashes are not uncomputable, they simply aren't (practically) recomputable. And even then, it's often just a matter of partical time required, rather than being provably impossible. – Flater Apr 17 '19 at 15:33
  • @Flater By the same semantics, it's not possible for a person to produce something un-personable. It's a non-definition, what does it mean? Cryptography algorithms produce something that a computer could only compute if it had infinite time, which isn't real. But ok, I have a computer which can produce personalised tea towels. I also have a computer which can recognise human faces and give them names, can understand human speech and give meaningful answers to questions. I think we need to try and define what we mean by 'computer' and 'computable'. – Richard Apr 17 '19 at 15:43
  • @Richard: (1) "Unpersonable" is not to "person" what "computable" is to "computer". That's a semantic difference, not a logical or mathematical one. (2) The computer does not require infinite time, just an impractically large amount of time. Cryptography is a matter of reasonable impracticality. With infinite time, you have the time to test every possible state (of anything, really) and thus will always be able to crack anything. (3) I don't think we need to define "computer" if OP defines "(un)computable" as "uncomputable _by any means_" (as opposed to by a specific (limited) computer). – Flater Apr 17 '19 at 15:51
  • @Flater a computer is not a device for 'calulating numbers', it is a turing machine. And with peripherals it is even more than that. This is why I question your definition of 'computer'. Let's start by defining some things that are un-computable. I'm going to stick to my guns and suggest that there are asymmetric encryption algorithms and one time pads, which are unbreakable. But that's before we discuss what an AI is capable of producing, or what whether a 3D printed object is 'computable'. – Richard Apr 17 '19 at 16:52
  • @user4894 why do you ask why did I reject your explanations if then you are going to ignore me? – Sue K Dccia Apr 17 '19 at 23:36
  • @SueKDccia After the edit or re-edit of your title (in the other post) I realized that my comments were not directly on point. However I do think that what I wrote would serve as useful background to your inquiries. If it's helpful, that's good. And if not, that's ok too. I can't directly address your question because I don't understand it as currently written. – user4894 Apr 18 '19 at 01:27
  • @user4894 thank you for answering and sorry if I sounded like a boor. Well, it is simple. What do you exactly don't understand in my question? It simply asks whether we could make up a mathematical model of a hypercomputer-universe that could somehow produce/contain/"simulate"/"compute" things that could not be computed by anything (like illogical/logically impossible things that cannot be described or conceived, like describing a circle cutting a straight lime in 3 points in Euclidean geometry). – Sue K Dccia Apr 18 '19 at 02:46
  • @user4894 Maybe if we could somehow state that even things that the hypercomputer-universe would not compute would exist in it would solve my problem... what do you think? – Sue K Dccia Apr 18 '19 at 02:46
  • @SueKDccia I don't think I have anything more to add. I don't know what it means to compute something that's illogical. I can write a program that prints "2 + 2 = 5". Does that count? – user4894 Apr 18 '19 at 05:02
  • @Richard: (1) A computer may have peripherals but not every peripheral performs _computation_. Computation is not "everything any given computer can do with any peripheral". (2) Assymetric encryption can be cracked (or at least a similarly valid input value can be found for a given hash, even if it's not the value that was originally used) when you have infinite time to test every possible input value. (3) The 3D printed object is not _in_ the computer. The computation of how to print it is. The actual object is the output, not the computation. – Flater Apr 18 '19 at 07:41
  • @Flater see my answer below – Richard Apr 18 '19 at 09:15

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I can't speak to a mathematical proof, but there are precedents for a finite system being able to comprehend an infinite system. The computable/uncomputable example falls within those bounds.

How many real numbers are there between 0 and 1? Infinite (proof here).

Humans are finite, both in brain capacity and lifetime. We are by definition not capable of comprehending (nor explicitly listing) each number in an infinite series, but we can still grasp the concept of infinity and know for a fact that something is infinite.

As Richard mentioned in the comments, the universe as we know it is a computer, which through the process of evolution has generated many things that were never explicitly anticipated.

But there's a difference between "not anticipated" and "uncomputable/inconceivable", which is a very important distinction that I think you're skimming (I'm sorry, I couldn't resist).

Your question feels like a semantical argument. Anything a computer creates, is by definition computable by that computer.

It is possible for a computer to contain values (which it did not create) which are uncomputable by that computer (e.g. when the computation exceeds the computer's capability but the resulting value does not), but you seem to be talking about things that uncomputable by any computer.
At this point, you can only define an uncomputable (= infinitely complex but not iteratively definable) value as either an algorithm or an approximation. But when the approximation far exceeds any possible observer's observation, then the approximation is functionally exact.

And if there is an observer who can prove that the approximation is just an approximation, that means that they have a better grasp on the value of the uncomputable value, which means that this source is the best source of the uncomputeable value, and all other observers will consider its value functionally exact.
You can apply this ad infinitam: knowing that a given value is an approximation proves that someone else must have a more precise value than the alleged approximation. At any point, there is always some computational construct that holds the best known value, and it remains to be this way until another computationel construct improves on it.

It's turtles all the way down.

Flater
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  • Interesting answer, but I don't know if you have considered that I'm not just talking about computers but hypercomputers. Also, I'm not just talking about uncomputable things, but things that are logically impossible/illogical (specially those ones that are literally logically impossible to even describe/conceive/compute. Things that, if we somehow were in front of them, we would not see them since there would not be any mental state or neuronal process that could "describe" what we would "see", since it would be impossible). @Flater – Sue K Dccia Apr 17 '19 at 23:35
  • But if you considered all of this in your answer and these things could be "computed" or "produced" or "simulated" this way you describe in a hypercomputer-universe, then this is great! Even though it involves an infinite regress... – Sue K Dccia Apr 17 '19 at 23:36
  • @SueKDccia: If something exists, even if it cannot be perceived by its neighbors, and its scope of existence is within a hypercomputer of sorts, then by definition this hypercomputer can grasp the existence of this thing. Otherwise the hypercomputer could not define its existence. – Flater Apr 18 '19 at 07:32
  • @SueKDccia: Also, I did condense computer/hypercomputer and computable/hypercomputable; because I think the distinction is more of a linguistic hurdle than a benefit in scope of your question. – Flater Apr 18 '19 at 07:33
  • @SueKDccia: I'm also not quite sure how infinite regress detracts from the point (which your comment seems to imply, correct me if I'm wrong). It's not the watchmaker analogy, but rather a _continually improved approximation_, which is not the same thing. – Flater Apr 18 '19 at 09:51
  • But I think we have a problem here, because if something illogically impossible/illogical is literally logically impossible to describe/compute by any computer/hypercomputer/brain, how could a hypercomputer-universe define its existence? How could these things have their scope of existence within a hypercomputer? This is the main problem/obstacle of my question and my proposal... – Sue K Dccia Apr 18 '19 at 10:47
  • @SueKDccia: Those obstacles derive from the premise (the assumption that there is such a supercomputer). You're effectively questioning the premise, how such a hypercomputer could exist with the given definition in the premise. Also, just because it's illogical does not mean that it can't be described in a logical way. "This orange is not an orange" is illogical but I can still write the sentence, be grammatically correct, and you can still parse the alleged logic. – Flater Apr 18 '19 at 10:52
  • I'm questioning the premise because I don't want to assume things with no back up (specially from science). I mean, I don't want to just assume that such a hypercomputer is possible with no basis. This is what happens when a trivialist philosopher proposes that there is a multiverse of worlds where trivialism is possible. It is only an assumption. It has no mathematical/physics theoretical basis. That's the problem. I would like to know if we could somehow have a model of a hypercomputer capable of computing those things I described but with also some scientific back up. @Flater – Sue K Dccia Apr 18 '19 at 16:36
  • It is like in Max Tegmark's mathematical multiverse hypothesis (https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis). He is a physicist, but his hypothesis relies only on the assumption that mathematics has physical existence. But it is utterly rejected by other physicists since it provides no theoretical physics basis explaining why mathematics have physical existence. It is like if I said that, somewhere in the universe, there is a planet with the shape of a cube. @Flater – Sue K Dccia Apr 18 '19 at 16:36
  • I can say whatever I want, but as long as I don't provide at least a mathematical basis that would prove that such planet would be possible, my proposal won't be taken seriously, not even as hypothetical. So that's what I wanted to solve. But if what you described in your original answer could provide a real computer-science-based solution to overcome this and could be used in hypercomputers to compute all these things I would like to compute, that would be great! Also, remember I'm emphasizing in those illogical/logically impossible things that cannot be described, even by words. @Flater – Sue K Dccia Apr 18 '19 at 16:37
  • And even some illogical things that can be described by words, like a circle cutting in 3 points a straight line in Euclidean geometry, cannot be described (there is no way we can conceive such circle), and as far as I know, describing that circle just with words and introducing that description somehow in a hypercomputer would not be the same as computing it (so it would not exist in our hypercomputer-universe) @Flater – Sue K Dccia Apr 18 '19 at 16:37
  • @SueKDccia: I feel like this is one of those "unstoppable force" questions where the answer hinges on the definition of the words used. If we are living in a hypercomputer, and we are capable of thinking about illogical things, then by definition the hypercomputer can contain the thing we can think about. Because we wouldn't be able to grasp anything that the hypercomputer couldn't handle. If you start from the premise of reality being a hypercomputer, you immediately accept that the hypercomputer must be able to contain/handle/parse all that reality can. – Flater Apr 19 '19 at 07:44
  • but what about those illogical/logically impossible things we cannot imagine because they are, by definition, impossible to describe/depict by any kind of information and informational process? These are the ones that I would like to see they are implemented in a hypercomputer-universe model. So, would there be any way to make the hypercomputer-universe include them? Maybe with the method you described in your answer...? @Flater – Sue K Dccia Apr 23 '19 at 13:00
  • @SueKDccia: Please don't keep deleting and reposting the same comment over and over until you get a reply. – Flater Apr 23 '19 at 13:14
  • then please just say "I don't know the answer" or something else instead of ignoring me @Flater – Sue K Dccia Apr 23 '19 at 13:29
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It's 2600AD. The world looks pretty much the same as it does now, but we've managed to stave off cataclysmic war by sharing resources a bit more fairly and limiting poplulation growth. The main difference is that there now exist fully senitient AI machines, and autonomous vehicles in which these AI machines can be placed, like robots. These machines can dig, and weld, and build, like CNC machines now do, but controlled AI not humans.

Partially from fear, and partially out of curiosity, the island of Madagascar is cleared and given over wholly to these AI machines to do with as they please. The machines begin construction of mines and foundaries and factories to replicate more machines. Before long there are something resembling cities connected by roads.

We ask : Ok which part of this arrangement is 'computer' and which part is not? No humans have been involved in this work, and yet here it is. The machines begin experimenting with CRISPR like technology and engineer bacteria like organisms which can netabolise various elements such as copper, making the mining of copper much easier.

A delegation of humans arrive on Madagascar after invtation and find curious tower like structures. When asked what the towers are, the machines respond simple by chirping a series of shrill tones. The towers are some sort of art installation which humans cannot truly understand.

Richard
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  • I think you're conflating a computation with the outcome of a computation. The roads that computer built is not a computation in and of itself, it is the outcome of the computation that drove the machines to build that road. Similarly 5 is not a subtraction in and of itself, even though it is the outcome of `10 - 5`, which is a subtraction. The question, as I understand it, focuses on whether something can exist _inside_ a (hyper)computer that the hypercomputer cannot grasp. Not whether the (hyper)computer can exist in a reality where other things exist (that the hypercomputer cannot grasp) – Flater Apr 18 '19 at 09:42
  • [..] Because the latter interpretation is obviously true. A computer with no peripherals cannot grasp much of reality and therefore exists in a reality that is more complex than it can grasp. – Flater Apr 18 '19 at 09:43
  • @Flater I don't think 'conflating' is what I'm doing. A brain in a vat cannot experience the pleasure of viewing the victory of samothrace, or hearing debussy, much less creating these works. A computer is not a calculator, it is a turing machine. It reads numbers from boxes and puts them in other boxes. Some of these boxes are inputs and outputs. A computer can do nothing without IO. I'll agree with you that an isolated CPU can do nothing except move numbers to and from boxes. What is your base definition of a computer? – Richard Apr 18 '19 at 10:01
  • The question is not about what a computer can and cannot do with the right peripherals, but whether it can contain the uncomputable. The hypercomputer in question is not one that exists within the universe, but rather the one which _houses_ the universe. There's no point in arguing the external consequences of what a computer can do, because the hypercomputer in question contains the entirety of our reality, there is no space external to the hypercomputer. – Flater Apr 18 '19 at 10:07
  • @Flater Ahh Ok. So the question is twofold then. 1) Is a universe made entirely of consciousness possible? 2) Can a computer create consciousness of any kind? There are better people than me to deal with question 1. But on question 2, I would suggest that a turning machine can, and will very shortly (20 years or so) produce consciousness, and all that entails. Consciousness that can imagine mountains and quasars and things we cannot imagine because a machine consciousness is not bound by the human condition. Is it your contention that a Turing machine is not capable of sentience? – Richard Apr 18 '19 at 11:30