Beauty

MrAl

Joined Jun 17, 2014
13,704
Hi,

A man of few words :)

Yes, it is interesting that maybe we are just seeing the shadow of reality in everyday life.

The actual physical reality of the peg has only incidental relationship to the shadow. It can be on top, all the way through, only partway through, or even riding on a thin surface of light oil ... we'd never know from a limited viewpoint, but in all cases we see the shadow unless of course there was a drastic change such as the entire removal of the peg.
If for some reason we could not see the peg, we'd have to try to infer its presence from the shadow. That's all we would have to go on.
 

cmartinez

Joined Jan 17, 2007
8,762
Having solid experimental data is what's needed to find reality
I agree, but then again, what's one to do when experimental data
Hi,

A man of few words :)

Yes, it is interesting that maybe we are just seeing the shadow of reality in everyday life.

The actual physical reality of the peg has only incidental relationship to the shadow. It can be on top, all the way through, only partway through, or even riding on a thin surface of light oil ... we'd never know from a limited viewpoint, but in all cases we see the shadow unless of course there was a drastic change such as the entire removal of the peg.
If for some reason we could not see the peg, we'd have to try to infer its presence from the shadow. That's all we would have to go on.
And so our minds create a rather impressive representation of reality, with the very little actual (and possibly unreliable) information that it's given. Most of the time this representation is useful, if somewhat inaccurate.

For me, the most important question is: will this process ever end? ... that is, will we, as humans (or whatever we eventually evolve to be) ever have a complete representation of reality?
 

atferrari

Joined Jan 6, 2004
5,012
I agree, but then again, what's one to do when experimental data

And so our minds create a rather impressive representation of reality, with the very little actual (and possibly unreliable) information that it's given. Most of the time this representation is useful, if somewhat inaccurate.

For me, the most important question is: will this process ever end? ... that is, will we, as humans (or whatever we eventually evolve to be) ever have a complete representation of reality?
Most probably we won't, lacking always minute bits of arcane data still to be known.

A word that certain lawyers seem to love a lot, suit this: illusory.
 

MrAl

Joined Jun 17, 2014
13,704
I agree, but then again, what's one to do when experimental data

And so our minds create a rather impressive representation of reality, with the very little actual (and possibly unreliable) information that it's given. Most of the time this representation is useful, if somewhat inaccurate.

For me, the most important question is: will this process ever end? ... that is, will we, as humans (or whatever we eventually evolve to be) ever have a complete representation of reality?
Hi,

Well i can only guess, but as the peg, shadow, and checker board example show, there could be more than one actual physical reality that we interpret as the same. This brings into mind the famous two slit experiment where one particle can appear to travel though two slits at the same time even though the particle appears to be smaller than the space between the two slits. It's obvious the particle is not behaving in the way we normally think a single object can behave and therefore our interpretation of reality is flawed.

The way i like to think of it sometimes is what we see, feel, and measure in common experience is a statistical average of what is actually happening. We dont interpret two particles close together as such in common experience, we interpret them as one object. In fact, even particle measurements we can only see indirectly through abstract measurements, just like the shadow tells us there is 'probably' a peg there.
Will we ever be able to show absolutely that there is such a thing as a peg and that it really exists just going by the shadow? I would think that we could only do that if the object we call the peg was a unique object otherwise we might come up with different objects that could cast the same shadow. So then i guess we would have to go on to decide if there is such a thing as a unique object at the tiny tiny scale. Then we have to also consider motion because everything is in motion, and the effect it has on the existence of the object. If the peg was moving the shadow MIGHT move, but then again if we move the peg in a different way we might not even be able to see any shadow movement and thus conclude that the peg was static in nature and then of course we would never be able to discover the dynamics of pegs. That would imply that nature does not want to reveal itself completely to us. The question then becomes, can we still gather enough information from what we DO see to be able to predict the outcome of every single possible experiment we see happening naturally in the universe? That would be sufficient for a lot of scientists but maybe not for all, and we see more curious scientists coming out of the theoretical closet every year now, where they want to dig deeper to gain more insight.

So we see this is not a question for one man alone or maybe not even for one group alone, but still very interesting to ponder. Take note that there is a theory in mathematics that says that sometimes we cant even predict if a given equation has a solution before we find one. Imagine how much more this might apply to the universe, we cant even imagine yet if there is such a solution for even a single function much less the entire universe.
 
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bogosort

Joined Sep 24, 2011
696
Well i can only guess, but as the peg, shadow, and checker board example show, there could be more than one actual physical reality that we interpret as the same.
I'm curious if you get that the illusion in that particular image is that the colors of the squares labeled 'A' and 'B' look different, yet are exactly the same RGB color. I ask because you seem to be focusing on the peg. If indeed this is the case, then you've inadvertently added another layer to this science-doesn't-describe-reality discussion: we don't even know what makes our illusion an illusion. :)

Take note that there is a theory in mathematics that says that sometimes we cant even predict if a given equation has a solution before we find one. Imagine how much more this might apply to the universe, we cant even imagine yet if there is such a solution for even a single function much less the entire universe.
The space of all possible mathematical equations is much, much larger than the space of all possible configurations of the universe, so this isn't saying much. Also, note that there is a big difference between an equation or function not having a closed-form solution and not having any solution at all. If indeed we can model the entire universe with a finite set of differential equations, almost certainly it will not have a closed-form solution -- but it's guaranteed to have at least one solution, otherwise we wouldn't be here!
 

MrAl

Joined Jun 17, 2014
13,704
I'm curious if you get that the illusion in that particular image is that the colors of the squares labeled 'A' and 'B' look different, yet are exactly the same RGB color. I ask because you seem to be focusing on the peg. If indeed this is the case, then you've inadvertently added another layer to this science-doesn't-describe-reality discussion: we don't even know what makes our illusion an illusion. :)


The space of all possible mathematical equations is much, much larger than the space of all possible configurations of the universe, so this isn't saying much. Also, note that there is a big difference between an equation or function not having a closed-form solution and not having any solution at all. If indeed we can model the entire universe with a finite set of differential equations, almost certainly it will not have a closed-form solution -- but it's guaranteed to have at least one solution, otherwise we wouldn't be here!
Hi,

Yes i was expanding on the graphic not intending to comply with the original intent.

But see in your second statement you are still assuming you know something you dont. Granted that is probably right, but you really dont know for sure. Given that you are right however, some of the functions we encounter are MUCH simpler than the universe itself and we cant always predict if they have a solution before we find one. So given the class of simpler functions as the comparison set this should hold and i could give examples.
Alternately, a simpler view is that when something is complicated enough we dont always know how to predict what kind of behavior we will get out of it.
To put it another way i always like so say something like, "We have not yet begun to imagine that which we have not yet imagined because we have not yet imagined all that we need to imagine in order to imagine what we have not yet begun to imagine yet".
Without that future imagination session it is hard to predict anything about the present imagination session because we still need to form more advanced theories so we have the tools to work with that present session precisely.
 

bogosort

Joined Sep 24, 2011
696
But see in your second statement you are still assuming you know something you dont. Granted that is probably right, but you really dont know for sure. Given that you are right however, some of the functions we encounter are MUCH simpler than the universe itself and we cant always predict if they have a solution before we find one. So given the class of simpler functions as the comparison set this should hold and i could give examples.
I'm still not following your point. First, simplicity is a relative concept. For example, the equation f'(x) = f(x) is considered trivially simple by modern mathematicians, not because there's anything inherently simple about it, but because generations of mathematicians have grown up with the tools and concepts of differential calculus as part of their mindset. The equation -- and most of the machinery behind it -- would have been considered extremely complicated by the best mathematicians prior to the 16th century, and complete gobbledygook to mathematical novices. Yet today, thousands of mathematically illiterate college freshmen can solve that equation without blinking an eye.

Second, whether an equation is considered "simple" or not has no bearing on its solvability (or how easy it is for us to determine whether a solution exists). Number theory is rife with simple-looking things that are really hard -- perhaps impossible -- to answer. This may be surprising to the uninitiated, as the natural numbers seem as simple and well-behaved as numbers get. But there's a good reason for this: equations are really equivalence relations on sets, and so equations in number theory are really statements about arbitrary subsets of the natural numbers, ℕ. But the cardinality of the set of all subsets of ℕ is exponential in the cardinality of ℕ: |P(ℕ)| = 2^|ℕ|. In other words, there are as many subsets of ℕ as there are real numbers! And given that vast majority of real numbers aren't even describable, it's no surprise that we know almost nothing about the subsets of ℕ, and, hence, most number theoretic equations.

I fail to see how the unsolvability of a "simple" equation relates to the solvability of the universe. As I see it, there are two possible cases: either the universe can be mathematically modeled or it cannot. If the former is true, then we know that its equations must have some solution, otherwise we wouldn't be here to ponder the question. And if the latter is true, if the universe is fundamentally incomputable, then the best we can do is devise approximations, which -- obviously -- must have solutions (otherwise they would be useless).

Alternately, a simpler view is that when something is complicated enough we dont always know how to predict what kind of behavior we will get out of it. To put it another way i always like so say something like, "We have not yet begun to imagine that which we have not yet imagined because we have not yet imagined all that we need to imagine in order to imagine what we have not yet begun to imagine yet".
Without that future imagination session it is hard to predict anything about the present imagination session because we still need to form more advanced theories so we have the tools to work with that present session precisely.
More to the point: we don't know what we don't know. But so what? How does that inform our next step along the decision tree? It's easy to see that we haven't figured it all out yet. On the other hand, over the history of humanity, it sure seems that science has been progressing. Whether we're on the right track or we've been completely wrong about every single thing, there's no good reason to change the paradigm. Our universe could be a computer simulation, or the dream of some demigod, or something entirely beyond our comprehension. What difference does it make? We plod along as best we can, searching for subtle clues for how this crazy place works.
 

MrAl

Joined Jun 17, 2014
13,704
I'm still not following your point. First, simplicity is a relative concept. For example, the equation f'(x) = f(x) is considered trivially simple by modern mathematicians, not because there's anything inherently simple about it, but because generations of mathematicians have grown up with the tools and concepts of differential calculus as part of their mindset. The equation -- and most of the machinery behind it -- would have been considered extremely complicated by the best mathematicians prior to the 16th century, and complete gobbledygook to mathematical novices. Yet today, thousands of mathematically illiterate college freshmen can solve that equation without blinking an eye.

Second, whether an equation is considered "simple" or not has no bearing on its solvability (or how easy it is for us to determine whether a solution exists). Number theory is rife with simple-looking things that are really hard -- perhaps impossible -- to answer. This may be surprising to the uninitiated, as the natural numbers seem as simple and well-behaved as numbers get. But there's a good reason for this: equations are really equivalence relations on sets, and so equations in number theory are really statements about arbitrary subsets of the natural numbers, ℕ. But the cardinality of the set of all subsets of ℕ is exponential in the cardinality of ℕ: |P(ℕ)| = 2^|ℕ|. In other words, there are as many subsets of ℕ as there are real numbers! And given that vast majority of real numbers aren't even describable, it's no surprise that we know almost nothing about the subsets of ℕ, and, hence, most number theoretic equations.

I fail to see how the unsolvability of a "simple" equation relates to the solvability of the universe. As I see it, there are two possible cases: either the universe can be mathematically modeled or it cannot. If the former is true, then we know that its equations must have some solution, otherwise we wouldn't be here to ponder the question. And if the latter is true, if the universe is fundamentally incomputable, then the best we can do is devise approximations, which -- obviously -- must have solutions (otherwise they would be useless).


More to the point: we don't know what we don't know. But so what? How does that inform our next step along the decision tree? It's easy to see that we haven't figured it all out yet. On the other hand, over the history of humanity, it sure seems that science has been progressing. Whether we're on the right track or we've been completely wrong about every single thing, there's no good reason to change the paradigm. Our universe could be a computer simulation, or the dream of some demigod, or something entirely beyond our comprehension. What difference does it make? We plod along as best we can, searching for subtle clues for how this crazy place works.
Hello,

The point is so simply but you are complicating it so much that it begins to seem not plausible. In fact, i am not even sure it deserves this much attention.

Let me try one more time.
We have two functions one is simpler than the other. We have a theory that says that we cant predict if the simple function can be solved. Now it the simpler function in theory can not be predicted to have a solution, then it makes sense that more complex functions will follow the same rule since it could be even harder to predict. By more complex i mean of course in the context of computational complexity theory.
 

killivolt

Joined Jan 10, 2010
836
Just as a thought experiment, I don't believe Homo Erectus believed when they discover smashing rocks together would produce fire, but doing so elevated hominid species while their minds expanded by neutrifing neurons to grow as well as the neural net of the other homo species encountered each other as they begin to dominate the animal kingdom.

https://en.wikipedia.org/wiki/Homo_erectus
East African sites, such as Chesowanja near Lake Baringo, Koobi Fora, and Olorgesailie in Kenya, show potential evidence that fire was utilized by early humans. At Chesowanja, archaeologists found fire-hardened clay fragments, dated to 1.42 M.Y.A.[75] Analysis showed that, in order to harden it, the clay must have been heated to about 400 °C (752 °F). At Koobi Fora, two sites show evidence of control of fire by Homo erectus at about 1.5 M.Y.A., with reddening of sediment associated with heating the material to 200–400 degrees Celsius (392–752 degrees Fahrenheit).[75] At a "hearth-like depression" at a site in Olorgesailie, Kenya, some microscopic charcoal was found—but that could have resulted from natural brush fires.[75]
Unwittingly they as ancestors did not understand how far that thought experiment went, taking thousands if not millions of years to accomplish the smashing of particles down to an N quanta. Higgs God particle really? Wether they did or didn't make fire, I feel we today are truly making history as we expand our minds neural net as we'll as we expand our neural net of conversations, this interaction after re-reading this entire Thread makes my mind growing in a thought about the universe not mathematically rather philosophically.

Not that I could contribute but, these and many conversations being hashed out makes me happy to be Homo Sapiens, Sapiens. I'm just pleased it didn't go into flame wars.

Carry on gentlemen while I smash my rocks together.

kv

Edit: As we further evolve what's going to be next.

https://en.wikipedia.org/wiki/Neil_Harbisson

Neil Harbisson

Born 27 July 1984 (age 34)[1]
Belfast, Northern Ireland, United Kingdom
Nationality
  • United Kingdom[2]
  • Ireland[3]
Education
Known for
Notable work
  • Cyborg Antenna, Transdental Communication, Solar Crown, Sound Portraits
Movement Cyborg art
Awards
  • 2018 Guinness World Record[5][6][7]
    Guinness Book of Records
  • 2016 Tribeca X Award[8]
    Tribeca Film Festival, New York
  • 2015 Futurum Award[9]
    Futurum, Monaco
  • 2014 Bram Stoker Gold Medal[10]
    Trinity College, Dublin
  • 2013 Focus Forward Grand Jury Award[11]
    Sundance Film Festival, USA
  • 2010 Cre@tic Award 2010[12]
    Tecnocampus Mataro
  • 2009 Phonos Music Grant[13]
    IUA Phonos, Spain
  • 2005 Best Performing Story[14]
    ResearchTV, UK
  • 2004 Innovation Award 2004
    Submerge (Bristol, UK)
  • 2004 Europrix Multimedia Award[15]
    Vienna, Austria
  • 2001 & 2010 Stage Creation Award[16]
    IMAC Mataro, Spain
Website Harbisson.com
Neil Harbisson (born 27 July 1984) is a Catalan-raised, Northern Irish-born[17] cyborg artist and transpecies activist based in New York City.[18] He is best known for being the first person in the world with an antenna implanted in his skull[19] and for being legally recognized as a cyborg by a government.[20][21] His antenna sends audible vibrations through his skull to report information to him. This includes measurements of electromagnetic radiation, phone calls, music as well as video or images which are translated into audible vibrations.[22]His WiFi-enabled antenna also allows him to receive signals and data from satellites.[23]

Since 2004, international media has described him as the world's first cyborg[24] or the world's first cyborg artist.[25] In 2010, he co-founded the Cyborg Foundation, an international organisation that defends cyborg rights, promotes cyborg art and supports people who want to become cyborgs.[26][27] In 2017, he co-founded the Transpecies Society, an association that gives voice to people with non-human identities, raises awareness of the challenges transpecies face, advocates for the freedom of self-design and offers the development of new senses and organs in community.
 
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bogosort

Joined Sep 24, 2011
696
Let me try one more time.
We have two functions one is simpler than the other. We have a theory that says that we cant predict if the simple function can be solved. Now it the simpler function in theory can not be predicted to have a solution, then it makes sense that more complex functions will follow the same rule since it could be even harder to predict. By more complex i mean of course in the context of computational complexity theory.
You mean equations instead of functions, yes? What criteria are you using to determine whether one equation is simpler than another? I don't think we can use complexity theory here: if we don't know whether an equation is solvable, how can we assign it to a complexity class?

What theory are you talking about? I'm not aware of any general result on the solvability of arbitrary equations. You seem to be making this inference: if equation A is simpler (by some criterion) than equation B, and if the solvability of equation A is unknown, then the solvability of equation B -- by virtue of its greater complexity -- must also be unknown. But this is clearly not true for some obvious choices of simplicity. For example, we may say that one equation is simpler than another if it has fewer unknowns, e.g., 2a = 4 is simpler than 2a + 3b = 7. We can write Goldbach's conjecture in terms of two unknowns, prime numbers p1 and p2. Then, for any positive natural number n, we don't know if 2n = p1 + p2 is solvable. However, we can easily construct an equation with, say, a hundred unknowns that is clearly solvable: a1 + a2 + ... + a99 + a100 = 5,050. The solutions are, of course: a1 = 1, a2 = 2, ..., a100 = 100.
 

MrAl

Joined Jun 17, 2014
13,704
You mean equations instead of functions, yes? What criteria are you using to determine whether one equation is simpler than another? I don't think we can use complexity theory here: if we don't know whether an equation is solvable, how can we assign it to a complexity class?

What theory are you talking about? I'm not aware of any general result on the solvability of arbitrary equations. You seem to be making this inference: if equation A is simpler (by some criterion) than equation B, and if the solvability of equation A is unknown, then the solvability of equation B -- by virtue of its greater complexity -- must also be unknown. But this is clearly not true for some obvious choices of simplicity. For example, we may say that one equation is simpler than another if it has fewer unknowns, e.g., 2a = 4 is simpler than 2a + 3b = 7. We can write Goldbach's conjecture in terms of two unknowns, prime numbers p1 and p2. Then, for any positive natural number n, we don't know if 2n = p1 + p2 is solvable. However, we can easily construct an equation with, say, a hundred unknowns that is clearly solvable: a1 + a2 + ... + a99 + a100 = 5,050. The solutions are, of course: a1 = 1, a2 = 2, ..., a100 = 100.

Hi again,

A more complex equation is harder to solve. It does not mean we can not solve it, but that the only way to know it can be solved is to solve it as there is no other way to know. So i thought that was sort of like where we are with the equations that we think govern the universe. We dont know it if is solvable because there is no way to predict that without knowing the solution first. It's really a simple idea.
This is not quite the same as "we dont know what we dont know" (sounds like a quote from AOC ha ha) because it suggests that we cant even know if we will ever know it simply because we dont have a solution to prove we can.

Is that one of the million dollar prize theories that is yet to be proven? I'll have to look that up again i guess.

But the main point here is that BECAUSE we can not yet solve the 'universe' (if you will), we dont know if it is solvable. There is no theory that suggests that everything we encounter will have a solution, but there is a theory (if i remember right) that says that some functions can not be solved without actually having a solution first, and i thought that was exactly like what we are seeing with the possible solution(s) to the universe. Many people have tried and died, but still no agreed upon solution.

What it looks like may be that we have so much mathematics and so finite an observable universe that we should find more than one solution. But that idea has no grounds whatsoever in fact just pure conjecture even though it sounds plausible.
 

MrAl

Joined Jun 17, 2014
13,704
Hi again,

Hey here is another view.

When it comes to understanding the universe, we could be existing in the initial knowledge conditions of the Dunning Kruger Effect.
This also ties in with what i was trying to say previously and is characterized as having a limited view of the universe without even realizing it is a limited view and therefore everything we come up with will always fall short of what is really out there. It might be like seeing a leaf for the first time but not being able to see the tree, then theorizing that the leaf somehow exits on it's own without any other support structure, not knowing what a tree is yet or should i say not knowing that anything such as a tree exits yet.
 

cmartinez

Joined Jan 17, 2007
8,762
Hi again,

Hey here is another view.

When it comes to understanding the universe, we could be existing in the initial knowledge conditions of the Dunning Kruger Effect.
This also ties in with what i was trying to say previously and is characterized as having a limited view of the universe without even realizing it is a limited view and therefore everything we come up with will always fall short of what is really out there. It might be like seeing a leaf for the first time but not being able to see the tree, then theorizing that the leaf somehow exits on it's own without any other support structure, not knowing what a tree is yet or should i say not knowing that anything such as a tree exits yet.

https://en.m.wikipedia.org/wiki/Allegory_of_the_Cave

The Allegory of the Cave, or Plato's Cave, was presented by the Greek philosopher Plato in his work Republic (514a–520a) to compare "the effect of education (παιδεία) and the lack of it on our nature"
 

bogosort

Joined Sep 24, 2011
696
A more complex equation is harder to solve. It does not mean we can not solve it, but that the only way to know it can be solved is to solve it as there is no other way to know. So i thought that was sort of like where we are with the equations that we think govern the universe. We dont know it if is solvable because there is no way to predict that without knowing the solution first.
But certainly the equations that govern the universe -- if such things actually exist -- must have a solution, namely, the solution that leads to this particular universe. Even if the universe is not computable, in the sense that we can never find a finite set of equations that completely characterizes it, we can still find a set of solvable equations that approximates it to some order. Indeed, this is the current situation.

Is that one of the million dollar prize theories that is yet to be proven? I'll have to look that up again i guess.
Ah, I see, you're probably referring to Hilbert's 10th problem, for which it was shown that there is no general algorithm for deciding whether so-called Diophantine equations -- polynomials with integer coefficients -- will have integer solutions. While interesting in itself, the result doesn't really matter here, as we already know that the equations -- whatever they turn out to be -- must have solutions (and almost certainly they won't be integer solutions).

But the main point here is that BECAUSE we can not yet solve the 'universe' (if you will), we dont know if it is solvable.
The universe is the solution; what we're looking for is the equations and initial conditions that lead to this particular solution.
 

MrAl

Joined Jun 17, 2014
13,704
Hi there,

Oh thanks for bringing that up i havent read Plato or anything like that in a very long time now. I have the set called "Great Books Of The Western World" which contains quite a few hard cover books but unfortunately i dont have them with me right now as i put them in storage when i moved last time.

That shadow analogy is almost like the peg and shadow analogy ha ha. That is cool.
 

Attachments

MrAl

Joined Jun 17, 2014
13,704
But certainly the equations that govern the universe -- if such things actually exist -- must have a solution, namely, the solution that leads to this particular universe. Even if the universe is not computable, in the sense that we can never find a finite set of equations that completely characterizes it, we can still find a set of solvable equations that approximates it to some order. Indeed, this is the current situation.


Ah, I see, you're probably referring to Hilbert's 10th problem, for which it was shown that there is no general algorithm for deciding whether so-called Diophantine equations -- polynomials with integer coefficients -- will have integer solutions. While interesting in itself, the result doesn't really matter here, as we already know that the equations -- whatever they turn out to be -- must have solutions (and almost certainly they won't be integer solutions).


The universe is the solution; what we're looking for is the equations and initial conditions that lead to this particular solution.
Hi,

Yes that analogy is not exactly perfect, but you must see that if there is a solution we dont know what it is yet so to be perfectly scientific about this i think we have to say that it is only a belief that we think there is a solution. That's why i brought up that math problem.

Another way to look at this is that we might ask what if there are no *real* solutions. We dont even know what *real* is yet. From a math point of view we might say that a complex (as in complex number) solution exists, but then that brings up the question again as to what is real and what is not real, and that leads to even more dimensions and we dont know if these extra dimensions are real or just math tools that help lead to a solution that again we have to deem as real.

Also, keep in mind that it is possible to trick a machine that knows everything about everything into giving a false answer to a properly designed question.
What we know for sure is that there is a chance that we may not know everything for sure. That is also self fulfilling because we may not even know that for sure. This brings us to the question of is there a logical statement that can can not be disproved and as such be one of the founding definitions of the universe ... that is, a definition that can be used in an argument that defines the universe that can NEVER be contradicted no matter how many men look for an antithesis.
I hate to bring this up, but that in turn leads to the thought of how much time we have to do all this. If we had an infinite time we may, but if the human race is limited in time even given a colony on Mars, then the human viewpoints leave the equation anyway so it just doesnt matter anymore. A pretty grim view i know.
 
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cmartinez

Joined Jan 17, 2007
8,762
Hi,

Yeah thanks, i think it was he that devised the mechanical argument that states that a machine that knows everything can be tricked into giving a false answer.
Not sure about what you're saying. But it was he that gave mathematical proof that there are some truths that can never be proved. The reason is that to know everything about a system (in this case, the Universe) one has to be outside of the system.
 
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