Quantum physics problem proved unsolvable: Godel and Turing enter quantum physics

December 9, 2015

A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid - ICMAT and Technical University of Munich.

It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behaviour.

A small spectral gap - the energy needed to transfer an electron from a low-energy state to an excited state - is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small, i.e. the spectral gap closes, it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.

Mathematically extrapolating from a microscopic description of a material to the bulk solid is considered one of the key tools in the search for materials exhibiting superconductivity at ambient temperatures or other desirable properties. A study, published today in Nature, however, shows crucial limits to this approach. Using sophisticated mathematics, the authors proved that, even with a complete microscopic description of a quantum material, determining whether it has a spectral gap is, in fact, an undecidable question.

"Alan Turing is famous for his role in cracking the Enigma code," said co-author, Dr Toby Cubitt from UCL Computer Science. "But amongst mathematicians and computer scientists, he is even more famous for proving that certain mathematical questions are `undecidable' - they are neither true nor false, but are beyond the reach of mathematics. What we've shown is that the spectral gap is one of these undecidable problems. This means a general method to determine whether matter described by quantum mechanics has a spectral gap, or not, cannot exist. Which limits the extent to which we can predict the behaviour of quantum materials, and potentially even fundamental ."

One million dollars to win!

The most famous problem concerning spectral gaps is whether the theory governing the fundamental particles of matter itself - the standard model of particle physics - has a spectral gap (the `Yang-Mills mass gap' conjecture). Particle physics experiments such as CERN and numerical calculations on supercomputers suggest that there is a spectral gap. Although there is a $1m prize at stake from the Clay Mathematics Institute for whoever can, no one has yet succeeded in proving this mathematically from the equations of the .

Dr Cubitt added, "It's possible for particular cases of a problem to be solvable even when the general problem is undecidable, so someone may yet win the coveted $1m prize. But our results do raise the prospect that some of these big open problems in theoretical physics could be provably unsolvable."

"We knew about the possibility of problems that are undecidable in principle since the works of Turing and Gödel in the 1930s," added Co-author Professor Michael Wolf from Technical University of Munich. "So far, however, this only concerned the very abstract corners of theoretical computer science and mathematical logic. No one had seriously contemplated this as a possibility right in the heart of theoretical physics before. But our results change this picture. From a more philosophical perspective, they also challenge the reductionists' point of view, as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description."

Not all bad news

Co-author, Professor David Pérez-García from Universidad Complutense de Madrid and ICMAT, said: "It's not all bad news, though. The reason this problem is impossible to solve in general is because models at this level exhibit extremely bizarre behaviour that essentially defeats any attempt to analyse them. But this bizarre behaviour also predicts some new and very weird physics that hasn't been seen before. For example, our results show that adding even a single particle to a lump of matter, however large, could in principle dramatically change its properties. New physics like this is often later exploited in technology."

The researchers are now seeing whether their findings extend beyond the artificial mathematical models produced by their calculations to more realistic quantum materials that could be realised in the laboratory.

Explore further: Physicists explain the unusual behavior of strongly disordered superconductors

More information: Undecidability of the spectral gap, Nature, DOI: 10.1038/nature16059

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axemaster
4.1 / 5 (9) Dec 09, 2015
This doesn't make much sense to me, it must be in the way that the article is written. Because obviously, any material property that exists can be found by calculating from the microscopic properties. After all, the physical system itself is doing the calculation in the real world.

I suspect they're talking about the inability to find an analytic solution or something like that?
vpoko
4.4 / 5 (7) Dec 09, 2015
Axemaster, that's along the lines of how I take it (though I have no idea if I'm right). On the computer science side, it's not that undecidable problems don't have an answer (they do), it's that there's no general purpose algorithm to decide them for all problem instances. E.g., it may well be possible to analyze a particular Turing machine to see if it halts on a particular input, but there's no effective procedure to determine whether any Turing machine halts for any input. Likewise, each type of material (grouped by some property) may require a different procedure to analyze, and if there are an infinite family of material groups, you would need an infinitely many procedures to decide them all, which isn't feasible.
julianpenrod
1.8 / 5 (10) Dec 09, 2015
Among other things, there is a difference between "unsolvable" and "undecidable". Something "undecidable" cannot be proved true by the logic of the system it is in, but that makes it intrinsically true since, if it was false, that means a counter example exists and that makes it "decidable". What the article is invoking is not clear. But, in terms of, say, the assertions that there is a point in pi where a million zeros come together and that there isn't such a point. One statement must be true, but there does not seem a proof of it. There are statements that are true, but cannot be proved in the system. That is part of what makes the insistences of atheists that God is not present because there is no proof in this physical world insipid.
julianpenrod
1.8 / 5 (10) Dec 09, 2015
This development can be considered analogous to quantum interactions being defined as incalculably probabilistic, subject to no analysis that can predict them. axemaster asserts that particles solve the problem of their behavior themselves, but quantum physics rests on the principle of there being no chain of preceding circumstances that can be used analytically to derive their behavior. God does not need to act solely in this manner, but, He does wish often to reward the virtuous. To cause major alterations in physical law will run a risk of causing the moronic to lapse into undesirable thought processes, uncontrollable jealousy of the righteous and greed, terror of doing anything for fear of angering God. Utilizing inherently unpredictable phenomena, God can act through avenues like these to bestow rewards without it being obvious.
nwarden
5 / 5 (3) Dec 09, 2015
Top 10 things the universe doesn't want you to know
Hyperfuzzy
2.5 / 5 (4) Dec 09, 2015
I conjecture QM is an imprecise measure neither definable nor causal. Suggest a view of each atom beginning with the description of charge and not mass. Then compile the assemblies based upon the field associated with the particle as realistic, not QM. Discard the "belief" of modern physics and accept the evidence due to a simple charge. Thus everything "real" is definable. The error is that our universal constants are wrong, mass is not elemental. It's only a measure due the fields. Do the math without QM and modern physics. Start over where Maxwell and Newton left off!
Hyperfuzzy
2.3 / 5 (4) Dec 09, 2015
Using mathematics and statistics to define the field as causal with QM is incomplete, i.e. only the wave equation, always present. The light from a particle is only due to its motion. Therefore, without a complete description, half of your physics is missing the causal effects. Static fields are isolated and not well defined. They have a field far from any particle and a stronger field up close, the static field is available as well as the oscillating field. One defines gravity, the other defines light. Mass is an approximation of the static fields. Therefore QM is not holistic and unable to define reality. Math, dunno. What is the initial set of premises? Not modern physics which is a set of misinterpreted experiments. The standard model is a wild guess! GR is absurd! The slit experiments are the same experiment. The field always enters the slit first. The wave-front has the velocity vector of the particle added to the speed of the wave front.
Eikka
4.6 / 5 (9) Dec 09, 2015
After all, the physical system itself is doing the calculation in the real world.


That is making the metaphysical assumption that all reality is doing is a computation, which is a reasonable assumption but not necessarily true.

For example, how do you compute a random number? You don't - no computer is capable of coming up with a random number by following any rule or law - assuming such things do exist.
DavidW
1.9 / 5 (11) Dec 09, 2015
:...as the insurmountable difficulty lies precisely in the derivation of macroscopic properties from a microscopic description."

More like...
as the insurmountable difficulty lives precisely in the life finding derivation of macroscopic properties from a microscopic description by life."

Then it's not philosophical anymore. As it has proved its beginning and end start and stop with life, a, and the, truthful limitation of life itself.. It skips theory altogether and jumps right to the first self-evident simple basic truth. Any claim to be able to go further must be a lie.

So many people post here with no foundational cause for the science that they profess as if it doesn't matter.
axemaster
4.7 / 5 (7) Dec 09, 2015
That is making the metaphysical assumption that all reality is doing is a computation, which is a reasonable assumption but not necessarily true.

That's not really what I meant, and I would say that is NOT a reasonable assumption.

I simply meant, in reality the physical system interacts with itself and the environment, and it goes through whatever motions end up producing the energy gap. Thus "computing" the result, though of course it's not solving an equation or anything.

how do you compute a random number

I agree 100% with this - you CANNOT propose that any physical system (actually any logical system whatsoever) has any form of indeterminacy. This is the major motivation for the various philosophical debates in quantum physics. Quantum mechanics, if you look at the math for calculating observables, uses indeterminate systems, which is simply an unacceptable situation.
ralph638s
2.8 / 5 (4) Dec 09, 2015
Computers can only compute pseudo-random numbers, long sequences that exhibit statistical randomness but are really just very long patterns, and if you know the algorithm, you can predict the next value in the sequence. True random number generators start with an analog source (e.g., the noise generated by a reverse biased diode or transistor) and they are truely random and unpredictable.
Protoplasmix
4.3 / 5 (3) Dec 09, 2015
For example, how do you compute a random number? You don't - no computer is capable of coming up with a random number by following any rule or law - assuming such things do exist.
I could entangle a couple photons and send one to you, but then I'd have to call you Bob.
- - -
If you need to know the initial conditions, you can set them, and as Axe mentioned, the physical system has no qualms with the calculation.

But I think the actual question being asked is more like, "does the physical system employ a mass gap to perform its calculations?"
ralph638s
2.7 / 5 (3) Dec 09, 2015
Since when do physical systems perform calculations to decide what to do?
elerner
1 / 5 (2) Dec 09, 2015
Calculations must have a finite number of steps. Physical systems, which are continuous, evolve continuously, so take an infinite number of "steps" in finite time, like the number of points on a line. This is true of all physical systems, including ones where quantum effect are important. (This is one important reason why the physical world is NOT like one big digital computer.) So things that are impossible to calculate, even in theory, can be easy to measure, such as whether or not a system has an energy gap.
axemaster
4.5 / 5 (4) Dec 09, 2015
Physical systems, which are continuous, evolve continuously, so take an infinite number of "steps" in finite time, like the number of points on a line.

I hardly think I need to point out the logical problems with this statement. Infinite information densities in space and time are not acceptable for a theory that claims to describe actual physical systems. This is also a problem in quantum mechanics that a lot of people seem unaware of - even if you quantize everything you can, you still have a continuous probability wave function - and if you assume that the wave function is a real thing, you now have infinite information required to describe the physical system.

This is why quantization of space and time (or something that accomplishes the same effect) is required for a theory of everything.
eachus
3.3 / 5 (4) Dec 09, 2015
So much misknowledge, so little time. Let me start with the assertion that Turing and Gödel don't normally come up in modern contexts. Any computer science expert knows that when you submit a file to a compiler (for whatever non-trivial computer language you choose, Ada, C, Fortran, Java or any of their children you choose) there are two true statements: 1) You do not know if the program will ever halt. (Halting problem) and 2) You do know that there is at least one error in the compiler. As a compiler author I tried to let you know if the compiler was still making progress, and to make the failures of the form that the compiler would reject valid programs, not accept invalid ones.

Hmm. Make that easier to understand. Say there is a limit (in my compiler) of 4000 odd identifiers in one scope. You run into it, and put in a nested block split the identifiers between them and off you go. But giving wrong answers to arithmetic? Very bad.
Protoplasmix
3 / 5 (2) Dec 09, 2015
Since when do physical systems perform calculations to decide what to do?
Are you saying you're not a physical system? Are you saying your computer/phone isn't a physical system? Smoke detector? Motion sensor?

If the range and domain of a function you're interested in can be accurately modeled with a hydrogen atom, are you saying hydrogen atoms can't be used to perform the calculations of the function? The result imposes subsequent action, and would be the "deciding factor," insofar as hydrogen atoms "decide" things.
eachus
5 / 5 (2) Dec 09, 2015
So things that are impossible to calculate, even in theory, can be easy to measure, such as whether or not a system has an energy gap.


Come on, this is easy. Can you measure the gap accurately enough to know that it is non-zero, or does quantum uncertainty prevent it? See proof described above. ;-) It may be easy to determine if the gap is greater than (or approximately equal to) one. But that is a different question.
FredJose
2.6 / 5 (5) Dec 09, 2015
I'm just waiting for some precocious 14 year old genius to come along and playfully suggest a brilliant way to circumvent the provably unsolvable case.
elerner
4 / 5 (4) Dec 09, 2015
Axemaster, It is not scientific to try to dictate what physical systems can be, based on some theory. Ilya Prigogine pointed out that you do indeed need infinite information to predict the detailed trajectory of any reasonably complex (chaotic) system, so such prediction is not possible, although you can make a lot of useful predictions that are not so detailed (statistical ones, for example). The possible quantization of space and time can be decided only observationally, not by theory alone. By the way, there is good observational evidence that space is not quantized, as quantization , at least on the Planck mass scale would lead to loss of interference in wave fronts from distant galaxies, which has been disproved observationally.
Also, band-gap measurements are routine today and are done on macroscopic samples, so yes, they are easy to measure.
Protoplasmix
1 / 5 (1) Dec 10, 2015
1) You do not know if the program will ever halt.
You mean like adware?

Seriously though, I was thinking it should be possible to compile the underlying math of the program, and then use a general algorithm to see if the "compiled, distilled and condensed version" contains the equivalent of a statement about the natural numbers..? Because then you're not running a program, you're evaluating math, and so then you could say if it does or doesn't halt.

Error 42
Undecidable math error
axemaster
2.8 / 5 (5) Dec 10, 2015
Ilya Prigogine pointed out that you do indeed need infinite information to predict the detailed trajectory of any reasonably complex (chaotic) system

This is only the case for continuous systems, which I am arguing do not exist. Ilya is literally restating my point.

The possible quantization of space and time can be decided only observationally, not by theory alone

This is not the case. The quantization of space and time will be determined by the underlying logic structure that the universe is operating on. At the very least, we will be able to narrow the possible quantizations to a useful sub-set.

there is good observational evidence that space is not quantized

This only applies to volumetric quantization, which I have previously argued makes some very naive assumptions about the underlying structure of the universe. Also, I started arguing against volumetric quantization over 5 years ago, this isn't something I came up with after reading this article.
antialias_physorg
5 / 5 (4) Dec 10, 2015
Because then you're not running a program, you're evaluating math, and so then you could say if it does or doesn't halt.

Not necessarily.
E.g. the "halting on all inputs" problem. Evaluating it mathematically means you could formalize the inputs and solve this (as a single operation or a an operation on finite number of sets of inputs which sum up to all possible inputs).

As with the Gödel theorem you also run into trouble with recursively defined problems. And here is where the issue with 'real' systems lie (I think). They don't just interact but interact recursively (because of time delay of forces acting on each other).
antialias_physorg
5 / 5 (4) Dec 10, 2015
Evaluating it mathematically means you could formalize the inputs and solve this (as a single operation or a an operation on finite number of sets of inputs which sum up to all possible inputs).
*

*which you can't because there is no formalism that encapsulates all possible inputs. It would be like writing the "set of all sets which - among other things - include this set...and the set that includes THAT set...and ...".
panamars
2 / 5 (2) Dec 10, 2015
Bring to attention the following:

Microcosmos Geometrically Related to Megacosmos:

https://www.youtu...QFXlWvE0
-------------------------------------------------------------------------------------------------------

http://www.stefan...IDES.pdf

Regarfds from Athens,

Panagiotis Stefanides

Hyperfuzzy
1 / 5 (1) Dec 10, 2015
OK, to calculate the entire universe is to calculate every possibility using only the + and - particles. First define if they are transparent or totally elastic. Define an initial condition, simply the particle's location, no need to try to figure out initial condition start with any and work backwards. This is a futile of course. Simply calculate all possible conditions from 1 particle to an infinite number of particles. Cut your time in half by only considering pairs, + and -. Then place all of these states into your universe at different locations, repeat until earth falls into the sun. Great talk for politicians.
eltodesukane
1 / 5 (1) Dec 10, 2015
Is this any different from what we have with, for example, the Stern–Gerlach experiment, where it is impossible, even in principle, to predict whether a given particle will be deflected up or down?
(Stern–Gerlach experiment: silver atoms travel through an inhomogeneous magnetic field and are deflected up or down depending on their spin.)
cgsperling
5 / 5 (2) Dec 10, 2015
Top 10 things the universe doesn't want you to know


Good one, nwarden. And I love the name "Dr. Cubitt".
Hyperfuzzy
1 / 5 (2) Dec 10, 2015
Is this any different from what we have with, for example, the Stern–Gerlach experiment, where it is impossible, even in principle, to predict whether a given particle will be deflected up or down?
(Stern–Gerlach experiment: silver atoms travel through an inhomogeneous magnetic field and are deflected up or down depending on their spin.)

Why not simply calculate real conditions. Why do we always try prediction without adequate information of the event at hand?
Protoplasmix
not rated yet Dec 10, 2015
*which you can't ...
Okay, I can't write a general algorithm that works for all programs. Even though I can write a specific algorithm that works for a specific class of programs, I'd still need a set with an infinite number of algorithms, one for each class.

So what I'm suggesting to solve the halting problem is that the algorithm which works for all programs has to do the math (same as a human): identify the class (or define a new one) for the program in question, and then utilize (or generate) the specific algorithm for that class.

In practical terms, only specific instances of the "grand" algorithm are possible. But no machine would have the time to evaluate an infinite number of programs anyway, and no machine could (or would) write that many programs in the first place.
Hyperfuzzy
not rated yet Dec 11, 2015
*which you can't ...
Okay, I can't write a general algorithm that works for all programs. Even though I can write a specific algorithm that works for a specific class of programs, I'd still need a set with an infinite number of algorithms, one for each class.

So what I'm suggesting to solve the halting problem is that the algorithm which works for all programs has to do the math (same as a human): identify the class (or define a new one) for the program in question, and then utilize (or generate) the specific algorithm for that class.

In practical terms, only specific instances of the "grand" algorithm are possible. But no machine would have the time to evaluate an infinite number of programs anyway, and no machine could (or would) write that many programs in the first place.

What? This sounds like a poorly defined problem. How can a solution exist?
Hyperfuzzy
not rated yet Dec 11, 2015
In other words if we reduce a rose to a set only protons and electrons in isolation, a rose is no longer a rose. However if we acquire the process of disassembly we may define how to re-assemble. Mathematically, dunno. But you will definitely need the math. Can't see how QM will work, to many possibilities. No concentration on the exact item, only possible items. So the question is without reason. juz say'n
leDendrite
1 / 5 (1) Dec 11, 2015
I think electrons are actually points of measurement within EMR or within an entanglement of atoms. resonance frequency. field measurement. charge, discharge, space, counter space,
I know, crazy crackpottery, all good.
also a black hole is not a hole but a massive magnetic object,

https://archive.o...sm1small

https://youtu.be/9yi0WHKtRd4
Protoplasmix
not rated yet Dec 11, 2015
This sounds like a poorly defined problem.
I resemble that remark. For example:

If H works, then sending it into an infinite loop instead of returning true for program P when P halts (to prevent H from halting when true), just to then make it into a contradictory program P' to prove H can't exist, isn't reductio ad absurdum, it's a priori absurd. Because you can feed P' into a clean version of H, which (if it works) gives you H(P', P) = false, P' doesn't halt with P as input when H(H, P) = true.

I tend to have trouble with, "you can't", even when it's the math saying so ...
Captain Stumpy
3.7 / 5 (9) Dec 12, 2015
I tend to have trouble with, "you can't", even when it's the math saying so ...
@Protoplasmix
you can't send me 30 million US dollars in small unmarked bills escorted by a dozen scantily clad bikini models who just want to rub bacon grease and blue bell ice cream all over my body!

(sorry - i couldn't resist a test! LMFAO)
Hyperfuzzy
3 / 5 (2) Dec 12, 2015
I tend to have trouble with, "you can't", even when it's the math saying so ...
@Protoplasmix
you can't send me 30 million US dollars in small unmarked bills escorted by a dozen scantily clad bikini models who just want to rub bacon grease and blue bell ice cream all over my body!

(sorry - i couldn't resist a test! LMFAO)

Best answer, and the prize goes to LMFAO!
Hyperfuzzy
1 / 5 (2) Dec 12, 2015
By the way, there are mathematical methods for dealing with infinities, rather solvable or not. Properly defined it might take only a day or so by hand but milliseconds by computer. Study dude! Recall that essentially this is what the calculus is all about, the infinitesimal and the infinite.

I've seen code like yours, Proto, when testing a WiMax multiple access, multiple frequency, multiple coded and well defined; but, analysis by an idiot ... probably why you were no longer there, complete garbage. Juz say'n

LMFAO!
eachus
not rated yet Dec 12, 2015
Seriously though, I was thinking it should be possible to compile the underlying math of the program, and then use a general algorithm to see if the "compiled, distilled and condensed version" contains the equivalent of a statement about the natural numbers..? Because then you're not running a program, you're evaluating math, and so then you could say if it does or doesn't halt.


What makes you think that there is a difference between executing a program and evaluating math? Gödel's proofs only talk about math, and for even a very restricted subset of integer arithmetic proves that there are some undecidable problems. The second proof goes the other direction and shows that there are questions which are undecidable in any consistent math. (Inconsistent math allows you to prove both a theorem and its converse and so is useless. If one both equals and does not equal zero, you can prove just about anything.)
Protoplasmix
not rated yet Dec 12, 2015
What makes you think that there is a difference between executing a program and evaluating math? Gödel's proofs only talk about math...
Using the energy levels of hydrogen to derive the value of pi is executing a program. See http://phys.org/n...ics.html

Realizing there are other infinite series which converge faster is evaluating the math. See http://www.geom.u...spi.html

And then evaluating the math by executing programs -- see http://www.codepr...-Sequenc

It's all math, the difference is subtle...
Protoplasmix
5 / 5 (1) Dec 12, 2015
I've seen code like yours, Proto...
Not likely, mine's pretty ugly, but thanks. Congrats on passing my Turing test, btw.

@CS - thanks, it may take a while :)
Hyperfuzzy
1 / 5 (1) Dec 13, 2015
Godel, Escher, Bach, and math; one must first define the value of truth. Most use [1,0] but try the excluded middle, i.e. [0..1], I prefer a none definition, allowing even a tensor space. However, a subset of this Hyperfuzzy space is classical truth. The later used in de-fuzzification. So if you are working with self referent statements, these would be outside of the classical logic. Something like the error of Einstein or the misinterpretation of the slit experiment or that charge has mass. In other words, physicist often forget what statements are allowed in order for a classical proof. Without proper definition, the result is mostly something like Tweedledee and Tweedledum, a mute point.
Hyperfuzzy
1 / 5 (1) Dec 13, 2015
I've seen code like yours, Proto...
Not likely, mine's pretty ugly, but thanks. Congrats on passing my Turing test, btw.

@CS - thanks, it may take a while :)

Actually it was just a conversation of a tech talking about why he was fired from his last assignment. He tried to tell me how the choice of frequencies followed a Gaussian distribution without using a Monte Carlo technique for creation. I didn't laugh in his face, but I had to sit my coffee down to avoid spitting on him. He actually trapped each transition and counted, so his code was a little bit slow. I can see why his boss asked him to prove whatever he was trying to sell.
tomb
not rated yet Dec 14, 2015
This is a very muddy description of the study and its math. I suspect the writer knows less about the math than a those fifth graders on that TV show. What this study does is prove that their math model is unsolvable, it does not prove their math model represents realty.
Hyperfuzzy
not rated yet Dec 14, 2015
This is a very muddy description of the study and its math. I suspect the writer knows less about the math than a those fifth graders on that TV show. What this study does is prove that their math model is unsolvable, it does not prove their math model represents realty.

That's because we start with stupid and try to figure stuff from there, instead of a complete dichotomy of the problem.
GoodElf
not rated yet Dec 14, 2015
This is a Gordian Knot problem. The Universe is a quantum simulator. If the Universe has an empirical solution for the problem then the solution must exist. When the problem is calculated the problem "halts" or "loops endlessly" failing to converge. What may then be a problem is our theory of how we solve it is not merely flawed but is unstable as we approach the solution using any calculator because the universe itself doesnt exhibit this same behavior. This may be because the question the algorithm is supposed to solve is not the question you think you are solving. It is under-specified or incorrectly specified due to inherent quantum non-locality. You can attempt to specify the problem further but doing so in the case of Feynman sums over all paths may mean specifying for all time in the past and also for all times in the future.. something you cannot know a priori. EG: In the photoelectric effect you can't predict exactly when an electron is emitted in the future. So cut the knot.
SuperThunder
1 / 5 (2) Dec 14, 2015
The Universe is a quantum simulator.

Then where are the quanta it's simulating and what are they doing? Why do we exist in a simulation of those things? Why not the originals? Why simulate quanta at all? Unless you mean it's a simulator for something not based on anything outside the simulation, in which case it's the thing itself and not a simulation.

When is a simulation of something unsimulated still a simulation? Word salad, that's when.

If you think I'm picking on you, at least I can nudge you with my elbow and we can both laugh at you not being the one who actually said "a complete dichotomy of the problem." Some people have a limited constabulary.
GoodElf
not rated yet Dec 14, 2015
My point is every Universe is a simulation because they are all various kinds of "quantum computer", it is just how the Universe works. whether they are "synthetic" or not. The nature of the Universe is just a global wavefunction and reality is just the way our "senses" interpret it.
anywallsocket
not rated yet Dec 15, 2015
Godel, Escher, Bach, and math...


I read GEB and yet fail to see your point. Everyone would prefer a greater resolution description of truth - greater than simply whether or not you've got one. But like you say, we've got to build up to the high resolution from these binary subsets. Or, we can crack downward, like you imply with "de-fuzzification". Either way, we've got to be careful of the logical levels we transcend in doing so, in that we often go "outside the classical logic" - defined by that particular level of resolution, otherwise we run risk of contradiction. So are you saying that this result is just such a case, of "forget[ing]' what statements are allowed in order for a classical proof" ? Or do you suggest that these fundamental probes into the binary subsets are doomed to fail due to our bivalent logic? In other words, is it a mathematical or human error to judge a set from outside that set?
Hyperfuzzy
not rated yet Dec 15, 2015
In other words, is it a mathematical or human error to judge a set from outside that set?

Is it linear, self referent, or ... in other words, how is the logic defined to solve the problem? i.e.:

This statement is false.

True or false? and this is easy, try a universal problem that includes all, even you. Is it gross pomposity or just ignorance?

with the excluded middle, it's 1/2 true, how about other mathematics to define truth, get it?

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