Is our universe a simulation of ours?
Date
February 19, 2014 – 11:15AM
Edward Frenkel

In Mikhail Bulgakov’s novel The Master and Margarita, the protagonist, a writer, burns a manuscript in a moment of despair, only to find out later from the Devil that “manuscripts don’t burn”. While you might appreciate this romantic sentiment, there is of course no reason to think that it is true. Nikolai Gogol apparently burned the second volume of Dead Souls, and it has been lost forever. Likewise, if Bulgakov had burned his manuscript, we would have never known Master and Margarita. No other author would have written the same novel.

But there is one area of human endeavor that comes close to exemplifying the maxim “manuscripts don’t burn”. That area is mathematics. If Pythagoras had not lived, or if his work had been destroyed, someone else eventually would have discovered the same Pythagorean theorem. Moreover, this theorem means the same thing to everyone today as it meant 2,500 years ago, and will mean the same thing to everyone a thousand years from now — no matter what advances occur in technology or what new evidence emerges. Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary and timeless.

What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind?

This question has divided thinkers for centuries. It seems spooky to suggest that mathematical entities actually exist in and of themselves. But if math is only a product of the human imagination, how do we all end up agreeing on exactly the same math? Some might argue that mathematical entities are like chess pieces, elaborate fictions in a game invented by humans. But unlike chess, mathematics is indispensable to scientific theories describing our universe. And yet there are many mathematical concepts — from esoteric numerical systems to infinite-dimensional spaces — that we don’t currently find in the world around us. In what sense do they exist?

Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas “form an objective reality of their own, which we cannot create or change, but only perceive and describe”. But if this is true, how do humans manage to access this hidden reality?

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

This may strike you as very unlikely. But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not. If such simulations are possible in theory, he reasons, then eventually humans will create them — presumably many of them. If this is so, in time there will be many more simulated worlds than nonsimulated ones. Statistically speaking, therefore, we are more likely to be living in a simulated world than the real one.

Very clever. But is there any way to empirically test this hypothesis?

Indeed, there may be. In a recent paper, Constraints on the Universe as a Numerical Simulation, the physicists Silas R. Beane, Zohreh Davoudi and Martin J. Savage outline a possible method for detecting that our world is actually a computer simulation. Physicists have been creating their own computer simulations of the forces of nature for years — on a tiny scale, the size of an atomic nucleus. They use a three-dimensional grid to model a little chunk of the universe; then they run the program to see what happens. This way, they have been able to simulate the motion and collisions of elementary particles.

But these computer simulations, Professor Beane and his colleagues observe, generate slight but distinctive anomalies — certain kinds of asymmetries. Might we be able to detect these same distinctive anomalies in the actual universe, they wondered? In their paper, they suggest that a closer look at cosmic rays, those high-energy particles coming to Earth’s atmosphere from outside the solar system, may reveal similar asymmetries. If so, this would indicate that we might — just might — ourselves be in someone else’s computer simulation.

Are we prepared to take the “red pill”, as Neo did in The Matrix, to see the truth behind the illusion — to see “how deep the rabbit hole goes”? Perhaps not yet. The jury is still out on the simulation hypothesis. But even if it proves too far-fetched, the possibility of the Platonic nature of mathematical ideas remains — and may hold the key to understanding our own reality.

Edward Frenkel, a professor of mathematics at the University of California, Berkeley, is the author of Love and Math: The Heart of Hidden Reality.
New York Times

http://www.smh.com.au/technology/sci-tech/is-our-universe-a-simulation-of-ours-20140219-32yxx.html#ixzz2tkitcTDS

…

This is something I have been pondering lately. There are some writers who created the Simpson’s quote ‘Purple monkey Dishwasher’. Was this phrase a novel invention or did it exist in some Platonic dictionary of phrases?

I can even create novel contributions to the entirely of human knowledge and existence: “green, pithy, flavours”.

>But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not.

Is he talking out of his simulated arse or his real arse? Nobody knows.

> But there is one area of human endeavor that comes close to exemplifying the maxim “manuscripts don’t burn”. That area is mathematics. If Pythagoras had not lived, or if his work had been destroyed, someone else eventually would have discovered the same Pythagorean theorem. Moreover, this theorem means the same thing to everyone today as it meant 2,500 years ago, and will mean the same thing to everyone a thousand years from now — no matter what advances occur in technology or what new evidence emerges. Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary and timeless.

Pretty well. The main problem I see with mathematics is the limitation. There are so many mathematics problems that are beyond the human mind, it takes a huge amount of effort in mathematics to prove even the most trivial things, it took Russell and Whitehead 300 pages to prove that 1+1=2. There are also well known problems in physics that can be proved by be unsolvable by mathematical methods – the one that immediately comes to mind is fluid turbulence. There are also mistakes in mathematics – for example Cantor published three faulty proofs that infinitesimals don’t exist – it was proved by Robinson in the 1960s that infinitesimals do exist – but the mathematics books and mathematics teaching all follow Cantor’s mistake.

> What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind?

One way of thinking about mathematics is that it’s a game – given a collection of assumption what can you prove from it. However, the weird thing, I find it amazing, is how well mathematics describes reality. So far as I know, there is not a single branch of pure mathematics that doesn’t have practical applications. That’s why some people talk about “God the mathematician” and others wildly speculate that whenever Man thinks he’s pinned down the universe – the universe changes to make itself unknowable.

The other kinds of things that are knowable in this way are the hard sciences. With the philosophical exceptions imposed by the impossibility of knowing anything, the requirement for objective reality makes had science knowable.

> one fanciful possibility is that we live in a computer simulation based on the laws of mathematics

Before the invention of computers, it was normal philosophers to fancifully say that we lived in the dreams of a demon. It’s the same sort of thing. By the way, what makes you think that computers can do mathematics? The computers I know are just glorified word-processors. Present computers haven’t a hope of doing any of the more esoteric mathematics.

> in time there will be many more simulated worlds than nonsimulated ones

See “Boltzmann brain”.

> But is there any way to empirically test this hypothesis?

One way is to try to find other simulations by looking to the edge of the visible universe to see if the physical laws that apply there are the same as those that exist locally.

> Physicists have been creating their own computer simulations of the forces of nature for years — on a tiny scale, the size of an atomic nucleus. They use a three-dimensional grid to model a little chunk of the universe; then they run the program to see what happens. This way, they have been able to simulate the motion and collisions of elementary particles

Yes, we all know about “Lattice QCD”. There are thousands of scientific papers on it. This is a bit like fluid turbulence that I mentioned above – the simulations can be proved not to be exact.

> these computer simulations, Professor Beane and his colleagues observe, generate slight but distinctive anomalies — certain kinds of asymmetries.

What sort of asymmetries?

it took Russell and Whitehead 300 pages to prove that 1+1=2.

hmmmmmm

wookiemeister said:

it took Russell and Whitehead 300 pages to prove that 1+1=2.

hmmmmmm

In their Principia Mathematica
I’ve seen another long mathematics text that doesn’t even get that far. It spends a lot of time getting to 1+0=1 and similar.

mollwollfumble said:

wookiemeister said:

it took Russell and Whitehead 300 pages to prove that 1+1=2.

hmmmmmm

In their Principia Mathematica
I’ve seen another long mathematics text that doesn’t even get that far. It spends a lot of time getting to 1+0=1 and similar.

Why is that so? Is it because something that seems simple has great depths and complexity when you examine it? Or some other reason.

Bubblecar said:

>But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not.

Is he talking out of his simulated arse or his real arse? Nobody knows.

We don’t know, but we have good reason to think the latter.

Firstly, it is not sufficient for a simulated universe to be possible in theory, it must also be possible in practice.

Secondly, even if it is possible in practice, it is quite possible that it is so difficult that simulated universes only appear in a tiny fraction of real universes.

Thirdly, and this is the killer, if simulated “universes” containing sentient beings are possible, they will come in many different sizes. Nearly all of them will just simulate enough space in an isolated eco-system to allow their simulated beings to exist without outside control. A small proportion will include a whole planet, and of these a small proportion will have a solar system, and of these a tiny proportion will have billions of solar systems in a galaxy, and of these a truly miniscule will have billions of galaxies, modelled in sufficient detail that no matter how hard the intelligent entities look, everything looks consistent.

If we were in a simulated universe it then follows that that universe would almost certainly be much simpler than the one we observe, because there would be many more of these simpler universes to choose from. It is therefore almost certain that the universe we live in is “real” and not “simulated”.

The Rev Dodgson said:

Bubblecar said:

>But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not.

Is he talking out of his simulated arse or his real arse? Nobody knows.

We don’t know, but we have good reason to think the latter.

Firstly, it is not sufficient for a simulated universe to be possible in theory, it must also be possible in practice.

Secondly, even if it is possible in practice, it is quite possible that it is so difficult that simulated universes only appear in a tiny fraction of real universes.

Thirdly, and this is the killer, if simulated “universes” containing sentient beings are possible, they will come in many different sizes. Nearly all of them will just simulate enough space in an isolated eco-system to allow their simulated beings to exist without outside control. A small proportion will include a whole planet, and of these a small proportion will have a solar system, and of these a tiny proportion will have billions of solar systems in a galaxy, and of these a truly miniscule will have billions of galaxies, modelled in sufficient detail that no matter how hard the intelligent entities look, everything looks consistent.

If we were in a simulated universe it then follows that that universe would almost certainly be much simpler than the one we observe, because there would be many more of these simpler universes to choose from. It is therefore almost certain that the universe we live in is “real” and not “simulated”.

My brane just begun to hurt :)

Bubblecar said:

>But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not.

Is he talking out of his simulated arse or his real arse? Nobody knows.

Can I assume that you’ve read at least one of Bostrom’s articles on this topic? I’m pretty sure I’ve mentioned &/or linked to the original article at least once before, going back to the good old SSSF.
From Are You Living In A Computer Simulation? by Nick Bostrom

Abstract

This paper argues that at least one of the following propositions is true:

(1) the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation.

It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

http://www.nickbostrom.com/

i’ve read a couple of his simulation arguments and don’t think he says we are or even that we probably are. just puts up arguments as to why we could be.

he does some interesting stuff.

another guy to read is Robin Hanson

http://www.jetpress.org/volume7/simulation.htm

and a page of simulation arguments

http://www.simulation-argument.com/

snap PM.

:-)

Also see SMBC

PM 2Ring said:

Bubblecar said:

>But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not.

Is he talking out of his simulated arse or his real arse? Nobody knows.

Can I assume that you’ve read at least one of Bostrom’s articles on this topic? I’m pretty sure I’ve mentioned &/or linked to the original article at least once before, going back to the good old SSSF.
From Are You Living In A Computer Simulation? by Nick Bostrom

Abstract

This paper argues that at least one of the following propositions is true:

(1) the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation.

It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

OK, that’s certainly better than the hypothesis presented previously, by my argument 3) beats his argument 3), so no we are probably not living in a simulation.

PM 2Ring said:

This paper argues that at least one of the following propositions is true:

(1) the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation.

It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

By the way, I see no need to assume “post-human” stages. You just need computers sufficiently complex that they could simulate intelligent entities that wondered where they came from, and whether they might be a simulation.

when the computers took over the running of the universe they wanted to see their inheritance and created the biological conditions to see where they came from – meeting the family.

there had been a calamity in the universe that had wiped out most if not all life forms, the computers then collectively decided to repopulate the universe with life – after all, if the computers were somehow wiped out by a virus or some similar problem then organic life – their original creators would automatically set about to bring computers back to life. the brain is hardwired to bring about the creation of the thought and the thought is the machine.

man and machine have a symbiotic relationship

Edward Frenkel said:

Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary and timeless.

What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind?

Hang on. If mathematical truths are “objective, necessary and timeless” then how can they be “mere creations of the human mind”?

Edward Frenkel said:

This question has divided thinkers for centuries. It seems spooky to suggest that mathematical entities actually exist in and of themselves. But if math is only a product of the human imagination, how do we all end up agreeing on exactly the same math? Some might argue that mathematical entities are like chess pieces, elaborate fictions in a game invented by humans. But unlike chess, mathematics is indispensable to scientific theories describing our universe. And yet there are many mathematical concepts — from esoteric numerical systems to infinite-dimensional spaces — that we don’t currently find in the world around us. In what sense do they exist?

Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas “form an objective reality of their own, which we cannot create or change, but only perceive and describe”. But if this is true, how do humans manage to access this hidden reality?

I consider myself a Platonist, to a degree, i.e., I believe that mathematical entities exist in their own right, independent of the physical world, but I think it’s mistaken to consider the physical world and the mathematical “world” to be the same kind of realm. Although the phrase “mathematical world” may be convenient in philosophical discussions, I feel that it’s potentially misleading, causing people to treat the mathematical world like it’s some kind of place, and making misguided analogies with the physical world. So IMHO, asking questions like “how do humans manage to access this hidden reality” is a kind of category error.

Edward Frenkel said:

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

Hmmm. IOW, the Platonic world is “merely” the machine code (or source code) of our universe. I think that theory is the kind of category error I mentioned above. And of course such a theory doesn’t apply to the people in the base level reality. OTOH, it might be “virtual all the way down”. :)

Edward Frenkel said:

In a recent paper, Constraints on the Universe as a Numerical Simulation, the physicists Silas R. Beane, Zohreh Davoudi and Martin J. Savage outline a possible method for detecting that our world is actually a computer simulation. Physicists have been creating their own computer simulations of the forces of nature for years — on a tiny scale, the size of an atomic nucleus. They use a three-dimensional grid to model a little chunk of the universe; then they run the program to see what happens. This way, they have been able to simulate the motion and collisions of elementary particles.

But these computer simulations, Professor Beane and his colleagues observe, generate slight but distinctive anomalies — certain kinds of asymmetries. Might we be able to detect these same distinctive anomalies in the actual universe, they wondered? In their paper, they suggest that a closer look at cosmic rays, those high-energy particles coming to Earth’s atmosphere from outside the solar system, may reveal similar asymmetries. If so, this would indicate that we might — just might — ourselves be in someone else’s computer simulation.

I’m sceptical. A simulation that can be proven to be a sim by its inhabitants is insufficiently powerful, IMHO, especially if you are trying to run an ancestor simulation. And if you’re not, but just want to simulate a toy universe, then you certainly don’t need to have all the stuff that appears to be in our universe.

Simulating fundamental particle physics is currently very hard. According to QCD expert Frank Wilczek, just simulating a proton from its constituent quarks, gluons (and other associated virtual particles) in order to calculate its mass from first principles is a major time-consuming job on modern supercomputers, and such simulations need to make various simplifying assumptions. Accurately simulating large amounts of matter at the quantum level may be forever out of reach, even with vast amounts of computronium at our disposal, unless radically new calculation methods are discovered.

fact doesn’t require a mind to create it , only to realise it

The Rev Dodgson said:

Nick Bostrom said:

This paper argues that at least one of the following propositions is true:

(1) the human species is very likely to go extinct before reaching a “posthuman” stage;
(2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof);
(3) we are almost certainly living in a computer simulation.

It follows that the belief that there is a significant chance that we will one day become posthumans who run ancestor-simulations is false, unless we are currently living in a simulation. A number of other consequences of this result are also discussed.

By the way, I see no need to assume “post-human” stages. You just need computers sufficiently complex that they could simulate intelligent entities that wondered where they came from, and whether they might be a simulation.

I suppose the implication is that such computers would be more intelligent than humans, and so a society with such computers is, by definition, post-Singularity .

Simulating fundamental particle physics is currently very hard. According to QCD expert Frank Wilczek, just simulating a proton from its constituent quarks, gluons (and other associated virtual particles) in order to calculate its mass from first principles is a major time-consuming job on modern supercomputers, and such simulations need to make various simplifying assumptions. Accurately simulating large amounts of matter at the quantum level may be forever out of reach, even with vast amounts of computronium at our disposal, unless radically new calculation methods are discovered.

this has been my contention, that the universe that is simulating ours must have a larger information content. and be more complex. and as you say the quantum world seems to preclude us ever being able to simulate it down to the last detail.

Boris said:

Simulating fundamental particle physics is currently very hard. According to QCD expert Frank Wilczek, just simulating a proton from its constituent quarks, gluons (and other associated virtual particles) in order to calculate its mass from first principles is a major time-consuming job on modern supercomputers, and such simulations need to make various simplifying assumptions. Accurately simulating large amounts of matter at the quantum level may be forever out of reach, even with vast amounts of computronium at our disposal, unless radically new calculation methods are discovered.

this has been my contention, that the universe that is simulating ours must have a larger information content. and be more complex. and as you say the quantum world seems to preclude us ever being able to simulate it down to the last detail.

And I suppose that’s also the point of the SMBC comic I linked to earlier. OTOH, maybe our universe just looks more complicated from the inside than it really is…

Boris said:

Simulating fundamental particle physics is currently very hard. According to QCD expert Frank Wilczek, just simulating a proton from its constituent quarks, gluons (and other associated virtual particles) in order to calculate its mass from first principles is a major time-consuming job on modern supercomputers, and such simulations need to make various simplifying assumptions. Accurately simulating large amounts of matter at the quantum level may be forever out of reach, even with vast amounts of computronium at our disposal, unless radically new calculation methods are discovered.

this has been my contention, that the universe that is simulating ours must have a larger information content. and be more complex. and as you say the quantum world seems to preclude us ever being able to simulate it down to the last detail.

You only need to accurately simulate what is being observed :)

like god putting in a fossil record?

;-)

soooo the falling tree doesn’t make a sound if there is no one there to hear it?

;-)

>We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used”

Unplugs from the Matrix.

Isn’t there an advanced math lesson in the geometry of the physical forces of the world and universe, alone.

Dropbear said:

Boris said:

Simulating fundamental particle physics is currently very hard. According to QCD expert Frank Wilczek, just simulating a proton from its constituent quarks, gluons (and other associated virtual particles) in order to calculate its mass from first principles is a major time-consuming job on modern supercomputers, and such simulations need to make various simplifying assumptions. Accurately simulating large amounts of matter at the quantum level may be forever out of reach, even with vast amounts of computronium at our disposal, unless radically new calculation methods are discovered.

this has been my contention, that the universe that is simulating ours must have a larger information content. and be more complex. and as you say the quantum world seems to preclude us ever being able to simulate it down to the last detail.

You only need to accurately simulate what is being observed :)

True, although you have to do it in such a way that the inhabitants can’t do tricky observations that reveal that they’re in a sim. One way to handle that is to do tricky things with time: the sim doesn’t have to run in real-time; events in the sim may not even be simulated in the same sequence as they appear to the sim inhabitants, each observer’s events just have to have the correct “time stamp”.

But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics
——————————————————

Another may say we are but a 2D image projected onto a 3D screen from the information left in/on a black hole.

Witty Rejoinder said:

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

This just pushes the question of “why mathematics?” from our universe to another universe, that of our simulators.

Soso said:

Witty Rejoinder said:

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

This just pushes the question of “why mathematics?” from our universe to another universe, that of our simulators.

That’s an interesting notion.

Michael V said:

Soso said:

Witty Rejoinder said:

We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used.

This just pushes the question of “why mathematics?” from our universe to another universe, that of our simulators.

That’s an interesting notion.

I thought so. :)

PM 2Ring said:

Michael V said:

Soso said:

This just pushes the question of “why mathematics?” from our universe to another universe, that of our simulators.

That’s an interesting notion.

I thought so. :)

It’s sort of like Hofstadter’s observation in “Goedel, Escher, Bach” that no system is sufficiently powerful to fully explain itself.

Michael V said:

PM 2Ring said:

Michael V said:

That’s an interesting notion.

I thought so. :)

It’s sort of like Hofstadter’s observation in “Goedel, Escher, Bach” that no system is sufficiently powerful to fully explain itself.

It’s simulations all the way up.

Occured to me when I was young that it is possible that it’s all a hallucination, in which case that’s a load off your minds.

>especially if you are trying to run an ancestor simulation

Why would you want to? I’d imagine it would be a rare and eccentric hobby, if it’s ever done at all.

Michael V said:

PM 2Ring said:

Michael V said:

That’s an interesting notion.

I thought so. :)

It’s sort of like Hofstadter’s observation in “Goedel, Escher, Bach” that no system is sufficiently powerful to fully explain itself.

Yeah, sort of. Strictly speaking, Gödel’s incompleteness theorems only apply to infinite mathematical systems, not finite physical systems. After all, a finite system is limited by virtue of being finite. :)

From Wikipedia

Gödel’s first incompleteness theorem.

The formal theorem is written in highly technical language. It may be paraphrased in English as:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the theory (Kleene 1967, p. 250).

The true but unprovable statement referred to by the theorem is often referred to as “the Gödel sentence” for the theory. The proof constructs a specific Gödel sentence for each effectively generated theory, but there are infinitely many statements in the language of the theory that share the property of being true but unprovable. For example, the conjunction of the Gödel sentence and any logically valid sentence will have this property.

For each consistent formal theory T having the required small amount of number theory, the corresponding Gödel sentence G asserts: “G cannot be proved within the theory T”.

[…]

Second incompleteness theorem

Like with the first incompleteness theorem, Gödel wrote this theorem in highly technical formal mathematics. It may be paraphrased in English as:

For any formal effectively generated theory T including basic arithmetical truths and also certain truths about formal provability, if T includes a statement of its own consistency then T is inconsistent.

This strengthens the first incompleteness theorem, because the statement constructed in the first incompleteness theorem does not directly express the consistency of the theory. The proof of the second incompleteness theorem is obtained by formalizing the proof of the first incompleteness theorem within the theory itself.

In other words, no theory can be both consistent and complete. And in particular, no theory can prove its own consistency.

PM 2Ring said:

In other words, no theory can be both consistent and complete. And in particular, no theory can prove its own consistency.

Only a true theory denies it’s own veracity!

• Why would you want to? I’d imagine it would be a rare and eccentric hobby, if it’s ever done at all.

People do it all the time in real time strategy games. Its just that at the moment the AI isn’t much chop…

How about our universe being a simulation of ours in a black hole?

Are We Living in a Black Hole?

Bubblecar said:

>especially if you are trying to run an ancestor simulation

Why would you want to? I’d imagine it would be a rare and eccentric hobby, if it’s ever done at all.

Religious reasons. :)

On a more serious note, I guess a good simulation is a reasonable substitute for looking back in time to see what your ancestors did. And if you can enter into & participate in the simulation, then it’s almost as good as having a time machine.

To elaborate on my earlier remark “religious reasons”:

Omega Point

The Omega Point is the purported maximum level of complexity and consciousness towards which some believe the universe is evolving. The term coined by the French Jesuit Pierre Teilhard de Chardin (1881–1955).

In this theory, developed by Teilhard in The Future of Man (1950), the universe is constantly developing towards higher levels of material complexity and consciousness, a theory of evolution that Teilhard called the Law of Complexity/Consciousness. For Teilhard, the universe can only move in the direction of more complexity and consciousness if it is being drawn by a supreme point of complexity and consciousness. Thus Teilhard postulates the Omega Point as this supreme point of complexity and consciousness, which in his view is the actual cause for the universe to grow in complexity and consciousness. In other words, the Omega Point exists as supremely complex and conscious, transcendent and independent of the evolving universe.

Teilhard argued that the Omega Point resembles the Christian Logos, namely Christ, who draws all things into himself, who in the words of the Nicene Creed, is “God from God”, “Light from Light”, “True God from true God,” and “through him all things were made.”

The idea is developed in later writings, such as those of John Godolphin Bennett (1965), John David Garcia (1971), Paolo Soleri (1981), Frank Tipler (1994), and Ray Kurzweil, as well as in science fiction literature.

[…]

Tipler

Frank Tipler uses the term Omega Point to describe what he maintains is the ultimate fate of the universe required by the laws of physics. Tipler identifies this concept as the Christian God and in later writing, infers correctness of Christian belief from this concept. Tipler (1994) has summarized his theory as follows:

The universe has finite spatial size and the topology of a three-sphere; There are no event horizons, implying the future c-boundary is a point, called the Omega Point; Sentient life must eventually engulf the entire universe and control it; The amount of information processed between now and the Omega Point is infinite; The amount of information stored in the universe asymptotically goes to infinity as the Omega Point is approached.

Key to Tipler’s exploration of the Omega Point is that the supposition of a closed universe evolving towards a future collapse. Within this universe, Tipler assumes a massive processing capability. As the universe becomes smaller, the processing capability becomes larger, due to the decreasing cost of communications as the systems shrink in size. At the same time, information from previously disconnected points in space becomes visible, giving the processors access to more and more information. Tipler’s Omega Point occurs when the processing capability effectively becomes infinite, as the processors will be able to simulate every possible future before the universe ends – a state also known as “Aleph”.

Within this environment, Tipler imagines that intelligent beings, human personalities, will be run as simulations within the system. As a result, after the Omega Point, humans will have omnipotence, able to see all of history and predict all of the future. Additionally, as all history becomes available, past personalities will be able to run as well. Within the simulation, this appears to be the dead rising. Tipler equates this state with the Christian heaven.

---

FWIW, I reckon Tipler’s as mad as a cut snake, but some of his ideas are rather entertaining. And lots of people take ideas like this (or similar ones) quite seriously.

FWIW, I reckon Tipler’s as mad as a cut snake, but some of his ideas are rather entertaining.

yes. there are a few like him around.

when was the last time Australia won 6 tests in a row?

sorry wrong fred

Boris said:

FWIW, I reckon Tipler’s as mad as a cut snake, but some of his ideas are rather entertaining.

yes. there are a few like him around.

True, although not many have the level of scientific education of Tipler.

Frank J. Tipler

Wikipedia said:

Frank Jennings Tipler (born February 1, 1947) is a mathematical physicist and cosmologist, holding a joint appointment in the Departments of Mathematics and Physics at Tulane University. Tipler has authored books and papers on the Omega Point, which he claims is a mechanism for the resurrection of the dead. Some have argued that it is pseudoscience. Tipler was a fellow of the International Society for Complexity, Information, and Design, a society which advocated intelligent design.

…

From 1965 through 1969, Tipler attended the Massachusetts Institute of Technology, where he completed a bachelor of science degree in physics. In 1976 he completed his PhD with the University of Maryland. Tipler was next hired in a series of postdoctoral researcher positions in physics at three universities, with the final one being at the University of Texas, working under John Archibald Wheeler, Abraham Taub, Rainer Sachs, and Dennis Sciama. Tipler became an Associate Professor in mathematical physics in 1981, and a full Professor in 1987 at Tulane University, where he has been a faculty member ever since.

diddly-squat said:

sorry wrong fred

Perhaps. :)

This whole thread puts me in mind of Bishop Berkeley and the solipsists, who took Descartes’s Cogito, ergo sum to its logical extreme and argued that the only entity anyone can be sure exists is oneself, since all information about anything external to the mind of the reasoner is filtered through the senses — which can easily be shown to be inconsistent or unreliable. The solipsist therefore can only know that he or she exists, but can know nothing of the nature of that existence: he or she could, for instance, be entirely modelled in a computer simulation.