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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)?

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  • The operative word is ‘a few’...
    – Mozibur Ullah
    Apr 17, 2019 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, 2019 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, 2019 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, 2019 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, 2019 at 14:40

2 Answers 2

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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.

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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, 2019 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, 2019 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, 2019 at 7:32
  • @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, 2019 at 7:33
  • @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, 2019 at 9:51
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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.

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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, 2019 at 9:42
  • [..] 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, 2019 at 9:43
  • @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, 2019 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, 2019 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, 2019 at 11:30

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