To sum up, the existence of irrational numbers that aren't formula-based proves that the reality we're living in isn't a simulation because the program required to encode for them would have to be infinite. — TheMadFool
Pegasus exists only in fiction; as do, according to some, noncomputable numbers. — fishfry
That doesn't refute my argument for everything, including fiction, has to be coded if reality is a simulation and if noncomputable irrational numbers exist in fiction, that too requires to be coded and we run into the same problem of a program that's got to be infinite in size and that means it'll never be finished/completed and so can't be compiled/translated into an executable file. Reality can't be a simulation. — TheMadFool
As far as I'm aware, the idea that reality could be an illusion has been around since Descartes' deus deceptor. In the modern computer age, this theory has morphed into what we call simulated reality, the gist of this being that what we experience as reality could be generated by a sufficiently complex program, similar to, although more advanced than, the ones we use on a daily basis, run on a powerful enough computer.
The fact that the mathematical existence of noncomputable numbers follows from the rules of standard math, doesn't imply that any noncomputable process is instantiated in the real world. — fishfry
How can you even say "reality could be simulated by a sufficiently complex program". How can that sentence make any sense? — Semiotic
What is being assumed here? That a physical computer can generate a "universe" within the computer system itself? And that from within that universe (the computer) a universe could be created that looks like our universe? That is an extravagantly loaded set of assumptions to make about the world. Think about that means in terms of the potential infinity of it. If the universe is a computer simulation, then that means within the universe that the computer exists is itself caught up in its own simulation, ad infinitum. At which point does someone finally admit, "this is too stupid a claim to take seriously because it fails to evoke the sort of feelings that normally make someone take existence as a serious subject." — Semiotic
Feeling wise, nothing in me is released or produced by the slipshod idea that I'm in a computer program, because the philosophical dead end it creates (infinity) necessitates a being in another world controlling the program. It fails to accept that there is an unknown metaphysical principle which exceeds all human contemplation, and that whatever humans can known about this Other, all we have to rely upon are the the forms of the world itself. This is the typical and anthropologically common way human beings experience Nature: as a metaphor of some vaster Being. The computer idea fails to evoke the sense of magical "participation mystique" that the normal human relationship between self and world evokes. — Semiotic
What you seem to be underemphasizing is the possibility that the idea of a computer simulated reality is really your bodies need to make sense of this existential awareness of self and being but within the terms of what you presently value as a self i.e. according to the logic of computers and programming. In this situation, you have naively failed to realize the deeper reality of metaphor, itself reflecting the ontological situation of a superior Being communicating Itself to a being within itself. Why is this idea typically spurned? Because the traumas and pains - particularly the myriad times you've felt shame in your social existence as a self - that have occurred within your development as a person prevents you from experiencing the connection i.e. the feeling, that ordinarily exists between the self aware organism and the universe itself. — Semiotic
For this theory of reality being a simulation to fly, it's necessary that the program that codes the simulation be finite for if not the program can't be completed/finished let alone executed on a computer. — TheMadFool
the idea that reality could be an illusion has been around since Descartes' deus deceptor. In the modern computer age, this theory has morphed into what we call simulated reality — TheMadFool
Why? You seem to assume that whatever meta-reality "programs" our reality is subject to the same laws and processes that occur in our world. Perhaps our notion of time does not exist there, nor the physical laws of our universe. In that case your argument concerning the irrationals is meaningless. Just a thought. — jgill
Why? You seem to assume that whatever meta-reality "programs" our reality is subject to the same laws and processes that occur in our world. Perhaps our notion of time does not exist there, nor the physical laws of our universe. In that case your argument concerning the irrationals is meaningless. Just a thought. — jgill
But what your post is completely missing, is that this has a meta-cognitive and meta-ethical dimension — Wayfarer
what truly is — Wayfarer
The first is Cipher's response. To me it doesn't much matter if my everyday reality is called a simulation or not. Pleasure and pain as I know them, the things I value, 'real' or not, just are what they are. I'm not offended by the idea that it's a simulation, but the question (as always?) is what does that really mean? — f64
The second response is more technical. The so-called 'existence' of non-computable numbers seems to be a kind of fictional/conventional existence within a particular domain. What do we mean by 'existence' and 'infinite'? Within the game the players know well enough to keep the game going, but what are we to make of these tokens removed from that semi-controlled original context? — f64
If say x, an non-computable irrational number, exists, I mean, limiting myself to the current domain of discourse, that it has the same ontolological status as, say, the number 2 or the square root of 2 or pi or e. — TheMadFool
If given a full-option offer, people will chose the real over a simulation provided that in both cases the same level of happiness is guaranteed. If the first choice is taken away, people will happily choose a simulated reality [this is what I suspect Cypher/Cipher is going through]. Neo, Morpheus, and the rest of the human underground resistance chose 4 only because their victory is a gateway to 1. Had, option 1 been precluded for whatever reason, almost everyone would go for option 2 and ask to be reconnected to The Matrix. — TheMadFool
If say x, an non-computable irrational number, exists, I mean, limiting myself to the current domain of discourse, that it has the same ontolological status as, say, the number 2 or the square root of 2 or pi or e. — TheMadFool
If you claim noncomputatlble numbers exist, name one. — fishfry
It's much simpler to show that there are uncomputable numbers in [e,pi] — f64
In other words there exists a non-computable irrational number between e and pi, existing in the same sense as e or pi. — TheMadFool
Display v [a number, any number] — TheMadFool
Note: After the first display operation for v, subsequent v's are attached to the previous v. So if the first v = 2, the second v = 23, the third v = 2345 or 2325, the fourth v = 23451267 or v = 23251246, ad infinitum.
And that's as far as I managed to get...comments?! — TheMadFool
Fine, name one. All you have is an existence proof; and an existence proof is a weaker class of metaphysical existence than a constructive proof like showing that 2/3 or pi exists. — fishfry
I'm afraid I didn't follow your algorithm at all — fishfry
But if you are generating a number from an algorithm, you haven't generated a noncomputable. — fishfry
There is an enumeration of the computable numbers; but there is no computable enumeration of the computable numbers! — fishfry
While the set of real numbers is uncountable, the set of computable numbers is classically countable and thus almost all real numbers are not computable — wikipedia
And either way, mathematical existence is not physical existence, A computer could put in our minds the idea of a flying horse, Captain Ahab, Captain Kirk, and noncomputable numbers. But since those things don't exist in the physical world, they are not evidence that the world is not a computer. — fishfry
Penrose's bad ideas are better than most people's good ones. — fishfry
To sum up, the existence of irrational numbers that aren't formula-based proves that the reality we're living in isn't a simulation because the program required to encode for them would have to be infinite. — TheMadFool
You gave an existence proof without naming any specific noncomputable number. And in order to do so you needed a cardinality or a measure theoretic argument, neither of which are physically meaningful. — fishfry
Of course his post is finite so it's not likely that he's specified any particular noncomputable real. But the larger point is that a number that encodes an infinite amount of information has a lesser claim to mathematical existence than one that encodes only a finite amount of information. — fishfry
And either way, mathematical existence is not physical existence, A computer could put in our minds the idea of a flying horse, Captain Ahab, Captain Kirk, and noncomputable numbers. But since those things don't exist in the physical world, they are not evidence that the world is not a computer. — fishfry
All that out of the way, I'd like to run something by you. I have this notion of infinite randomness in my mind. To me it means the existence of an infinity that is completely devoid of all patterns. If such infinite randomness were discovered to exist (I don't care as to where) can we infer the impossibility of reality being an illusion based on the premise that to code infinite randomness would require an infinite set of instructions, a task that can't be completed, and if so, such a code can't ever be actually executed? — TheMadFool
Now that I think of it, humans have struggled greatly with the concept of infinity. Basically, infinity DOESN'T COMPUTE! for humans. Last I checked, it all "started making sense" in the 1870's with Georg Cantor's work. — TheMadFool
This, at some level, suggests that the universe doesn't contain actual infinities and that our brains can't handle what is essentially infinite information. — TheMadFool
The other side of this story is that non-computable irrationals (Chaitin's constant for example) exist. In other words, the universe does contain instances of infinite randomness and these can't be reduced to finite algorithms. Ergo, the universe isn't a simulation. — TheMadFool
infinite does compute — f64
What does infinity even mean? — f64
finally get that magical rational number that finally squares to 2 — f64
computer checkable proof — f64
Chaitin gently suggesting that maybe real numbers aren't real — f64
understand infinity — f64
So, what's infinity + 1? How does your answer, which must be infinity, square with the answer to 2 + 1? — TheMadFool
A proof of the existence of noncomputables is not the same as an algorithm that can generate noncomputables. — TheMadFool
Insofar as the universe being a simulation is the issue, the distinction real-unreal is irrelevant. The real numbers can be accessed through our minds and that means they have to be encoded in the simulation unless the universe is a partial simulation like a cyborg or thereabouts. — TheMadFool
Thanks for the stimulating discussion. I'm out of my depth here so thanks for indulging me and my bizarre ideas. — TheMadFool
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