For a while now, I have long since wondered if it were possible to prove once and for all if we are living in a vast simulation.
On the surface it seems impossible to prove whether we are inside some kind of matrix-type simulation, however I believe that I have come up with a hypothesis that may prove once and for all if we are or not . .
Before we come to that, let us examine the components that lead up to the proposed theory.
P Versus NP
For several decades there has been a raging debate in mathematics and computer science whether P = NP or not.
P stands for polynomial, which refers to the amount of time it takes to solve a problem, and NP stands for nondeterministic polynomial time.
A classic example of an NP problem is the travelling salesman problem (TSP).
The Travelling Salesman Problem describes a salesman who must travel between N cities. The order in which he does so is something he does not care about, as long as he visits each once during his trip, and finishes where he was at first.
Each city is connected to other close by cities, or nodes, by air, road or rail. Each of those links between the cities has one or more cost attached to it.
So the problem is what is the most optimum route for the salesman to take; whereby he travels for the least amount of time, for the smallest amount of money.
In mathematics we use algorithms as a means of a shortcut to finding answers.
If we were to set the most powerful computer on earth the task of coming up with an algorithm that could be applied to any group of cities in any country, and still come up with the correct answer, it would take that machine several times the age of the universe to work it out.
In other words the problem can not be solved in polynomial time, therefore it is called an NP problem.
It is worth mentioning that most mathematicians working in the field believe that P = NP, in other words there is no such thing as NP problems, and it is just a matter of discovery.
A Case For NP
The French scientist Pierre Laplace opined that if we were to know every position and velocity of every particle in the universe, along with the complete laws of physics, we would be able to predict the future.
Whilst that statement might have been true in a universe governed by Newtonian physics, alas the same cannot be said for one where quantum mechanics is apparent.
Quantum uncertainty states that we can never know the position and velocity of a particle before we actually measure it. It goes on to state that the measurement of one state, destroys the other.
So for example if we observe a particle moving through a vacuum, by measuring its speed we affect its location, and vice versa.
So in a rather oblique way, the uncertainty principle can be said to invoke NP mathematics, as there is no way for a computer to come up with an algorithm that can determine at once speed and velocity of a given particle.
Various experiments we have done with entangled photons have proved once and for all that the quantum uncertainty principle is real, and not just a matter of us getting better observational equipment.
So perhaps then this is the biggest clue that NP is real and in fact P is not equal to NP (P ≠ NP)
A Case For P
In 1972 mathematician Richard Karp solved 21 NP problems, and thus relegated them from NP to NP Hard, which meant that an answer to these set of problems, could be checked in P time.
This offers the question then; if NP can be reduced to NP-Hard, then surely NP-Hard can be one day boiled down to P? In other words, P = NP.
If that is the case, then all NP problems will one day be reduced to P and as far as mathematics is concerned, there will be no mysteries left in the universe.
P and NP As A Function In Simulation Theory
So all that being said; let us now look at how P = NP or indeed P ≠ NP has any bearing on whether we're living in a simulation or not.
My hypothesis states that if P does indeed equal NP, then we cannot rule out the assertion that we may indeed be living in a simulation.
However if P ≠ NP, and NP problems truly exist regardless of what computational heights a computer may achieve, then the chances of us living in a sim are vanishingly small.
The reason being that it is difficult to conceive a computer, alien or otherwise, creating a universe in which there are problems which it itself cannot solve.
This would be the equivalent of a locksmith creating a lock that he couldn't make a key for and open.
So, let's hear it for P ≠ NP, because in my humble opinion, that would prove once and for all that we are not living in a simulation.
Whether we'll prove it is another question, and in a wonderful logical loop, the proving of such, may turn out to be NP in itself!
WHAT DO YOU THINK OF MY LOGICAL REASONING? EVEN IF I AM CORRECT, WILL WE EVER BE ABLE TO PROVE THAT P ≠ NP, OR ARE WE DOOMED TO SEARCH FOR THE ANSWER FOR ALL OF HUMAN HISTORY? AS EVER, LET ME KNOW BELOW!
Extra Reading
Karp's 21 NP-complete problems
NP-completeness
MIT News P = NP?
P versus NP problem
Travelling salesman problem
@iceshaft07 just wrote a post about living in a simulation... you guys should connect & discuss!
https://steemit.com/simulation/@iceshaft07/do-we-live-in-a-simulation
Nice, thanks for the tipoff! :-)
Cryptogee
Not quite the travelling salesman, but shortest route...
can be solved an an analog way.
Where you have a bunch of strings as the roads and knots as the intersections. (and some rubber bands to keep them in place above the map.
To find the shortest route between two points, just grab the points with your finger and tug apart, and the strings will show the shortest route.
While the computer has to work out all of the routes and then sort for shortest. An NP problem.
I believe we will find many more solutions to NP problems.
However, I also believe in chaos and in synchronicity as actual foundational elements of our universe (before space and time) and thus P ≠ NP.
If you could express that as an algorithm you would win the million dollar prize attached to the problem :-)
Me too! I hope we're right.
Cryptogee
As a simple kitten, I would claim that P cannot be NP unless N = 1.
It's like 26 = 26
Or 26 = N*26
N must be one, if you want to use simple multiplication algebra.
If it's one, it's meaningless, so I would conclude that this reality, until scientifically proven otherwise, is a foundation reality, rather than a simulation.
I would use science here, and demand an observation that actually hints at the idea that this reality isn't a foundation reality. Without an observation, we cannot create a testable hypothesis, and without that, there is no science being done.
We must first observe the truth, because understanding it.
And as it is, there is no reason to believe on mere math alone, that this is a simulation universe, rather than a real universe. Math will be more useful once we have an observation, of course, but before the observation, I'd rather apply Occam's Razor, and simply conclude (with the idea that we do not have perfect knowledge one way or the other yet), that this is a foundational reality.
what's that theory from cosmology now... that everything is just a projection emanating from the surface of a black hole. Holographic principle. I was on a jag watching Neil Degrasse Tyson, Michael Green, and Leonard Susskind a few years back.
Great post! I've long said a simulation implies an architect.........
My money is on P=NP..............
It does imply an architect, though that doesn't rule it out, simply throw up lots, and lots of questions.
My money is on P not being NP, or at least I'm hoping that's the case . .
Cryptogee
In the words of Zappa, " I figure the odds be fifty/fifty.........
What happens if the programs/Archons DON'T know the answer to this question?
It's possible they would believe in the architect yet not know what it is.....
This is one of my theological positions based on my experiences....But it's metaphysical speculation as I'm aware of the fallacy inherent in the proposition.....
I'm also okay if you end up being right.....
peace:)
Reminds me of a huge and heavy hard cover book I own called https://en.wikipedia.org/wiki/A_New_Kind_of_Science
If I recall, Wolfram talked about how there is no room in the universe for the size of computer needed to predict the next state of this universe. That might imply we're not simulated.
We're going to be using the TSP in the VIVAconomy to determine the best way to distribute assets. I've worked with it in the past when I was an Engineer in an AI lab. It can be approached in an analog way as builderofcastles suggests, and those analog ways can be simulated digitally much like music is via MP3s etc.
I'm rambling! Thanks for getting my brain thinking about cool things!
Please ramble away! Very interesting ramblings :-) Yes @builderofcastles did indeed identify the analogue way for shortest distance, however it doesn't take into account cost and of course one has to do it over and over again to verify the right answer.
In fact, you would probably be checking for an NP amount of time! :-D
Cryptogee
Good point! One thing we always considered in the AI lab is - it is often better to quickly get an adequate answer than take lots of time to get a perfect answer. Take some time to make sure you aren't stuck in a local energy well by jumping around a lot, but eventually produce an answer without knowing if hoping over that next mountain will land you in an even lower valley, where the lowest landscape point is the best answer.
We were doing expert systems for the military, and a good quick answer is better than a slow perfect answer that you are too dead to use.
Yes, as is often the case these questions are kind of perfect world scenarios, and are just there for the sake of sound theory. But yes, an aproximate answer is better than no answer at all.
Cryptogee
If I may, can I boil this down to non-genius level, for myself mainly?
If there are problems that exist in the universe that cannot be solved by a computer that could fit in the universe, we're not living in a simulation?
Basically if a computer can build a simulation, then any "problems" within that simulation should be solvable with the available physics.
So if we discover that there are unsolvable problems with available maths/physics then we are not living in a sim. So yeah, pretty much as you say :-)
Cryptogee
"The reason being that it is difficult to conceive a computer, alien or otherwise, creating a universe in which there are problems which it itself cannot solve.
This would be the equivalent of a locksmith creating a lock that he couldn't make a key for and open."
I don't see that this is necessarily something we can assume. I find both these scenarios plausible.
Good write up.
I think you have a flawed supposition: "The reason being that it is difficult to conceive a computer, alien or otherwise, creating a universe in which there are problems which it itself cannot solve."
...Unless the alien is creating the simulation for the purpose of solving equations they cannot otherwise solve. We do this now with computers (AI and DL being examples).
Perhaps you're right, and as you point out we do this with computers now. However the difference is these computers do not hold a complexity that is near infinite. Which is what it would require to create a simulation that included consciousness and quantum mechanics.
In my humble opinion, the thought of a computer that can work out each position of each atom in such a vast space in realtime, yet not be able to solve equations that were generated by its own generations, is not a plausible one.
Cryptogee
This was exceptionally written. I loved it. Very well laid out. Especially in lay-man's terms.
So I have two things. As far as I know:
A simulation does not require NP in order for it to be a simulation. It can still be solvable and still be a simulation. Just because an artificial or other kind of intelligence knows how to solve it does not make it not a simulation.
Also, just because Karp solved 21 NP problems does not make all NP problems solvable. I'm not saying it doesn't make them NOT solvable, but one does not mean the other.
Let me know what you think! Thanks for the stimulating read.
Hi, thanks for your comments, I'll attempt to answer them . .
I think you misunderstood me, I am actually saying a simulation can't have NP, as that would imply a computer has generated a simulation which can generate calculations it can't solve.
Agreed, in fact I hope it means that they aren't solvable, as that is where I'm leading with my theory.
Thanks again!
Cryptogee