Logically, intelligent life forms living in a simulation would not have the ability to figure out that they exist within a simulation. The creators of the simulation would have created the intelligent life forms within the simulation, along with all the other stuff that makes up the simulation. Presumably the creators would not want the things inside their simulation to figure it out, so they would program some sort of block to their ability to reason their way to the truth of their existence.
One possible exception, one Hollywood has used to get around this problem, is the intelligent life forms are actually real creatures. They are unconscious in the real world, but plugged into the simulation, so that their consciousness exists in that simulation, as if they were a creation of it. This is the premise of the Matrix movies. Humans are plugged into the simulation by the machines that keep them alive as an energy source to power themselves and their machine world.
Another possibility, one not reliant on a sadistic creator of the simulation, is one where the simulation requires a degree of self-awareness by the intelligent life forms. In order for the simulation to achieve the desired goal, the creatures in it must be as close to real as possible, so that the simulation comes close to the reality of the creator. In this scenario, the simulation is a model of the creator’s existence for the purpose of testing some hypothesis about their reality.
Between the two, the most plausible is the second scenario, as the first scenario has some obvious plot holes. This was obvious in the movie. If the machines were so powerful to have conquered mankind and turned him into batteries, then why were the machines not smart enough to put alarms on the pods in which they kept their human batteries connected to the matrix? Perhaps the creator of the machines was the creator of the Death Star in the Star Wars movies.
If we go with the second option and assume the people who created the simulation are willing to risk their creations figuring out that they are in a simulation, under what conditions would the intelligent life forms figure it out? The first prerequisite is an intelligent creature curious enough about its surrounding that it tries to figure out the rules that govern its operation. The intelligent life forms would have to be smart enough to solve puzzles and use those solutions to solve other puzzles.
Rules manifest themselves as patterns, so the intelligent life forms would have to be pretty good at noticing patterns. As the intelligent life forms discover the rules of his existence, it would both notice the patterns, but get better at recognizing those patterns with a minimum amount of data. That is, each new recognized pattern would become a data set within the pattern matching process, allowing the creature to infer new patterns and new rules from his collection of rules.
Inevitably, this creature would reach of a point of noticing where his natural, as it were, abilities were no longer sufficient to learn new rules. It would need to take what it has learned about its environment and create tools. These tools would be the result of noticing those patterns, discovering rules of its existence and then applying those rules in trying to discover new rules. Mastery of fire, after all, came from seeing it and then using it in various way to discover how it worked.
This is one possible way for the intelligent life form to discover that it is actually existing in a simulation. Given enough time, it would discover the nature of its universe and learn it is actually a simulation. The trouble here is the intelligent life form would have to accept as a possibility that it exists in a simulation. A creature that is sure its universe operates on a fixed set of rules is unlikely to accept that those rules are an arbitrary invention of some higher intelligence outside its universe.
There is also another problem. The creators of the simulation could themselves be the product of a simulation. It’s entirely possible the one fixed rule of existence is that no intelligence entity can create an intelligence superior to itself. Perhaps Thomas Aquinas was right all along and there is some prime mover. The very source of the existence is the pinnacle of intelligence, which creates imperfect copies of itself manifesting as simulations within simulations.
We have in this simulation some evidence of this limitation. Despite the hyperbole about artificial intelligence, we have not come close to creating a computer that can rival the human mind. We have made very fast computers that can do calculations and sort through stacks of data faster than humans. These are not artificial intelligence or even intelligence at all, but rather they are very fast calculators. The collapse of the self-driving car project is an example of this limit.
Putting that aside, there is one other way the intelligent life forms inside the simulation could start to notice they are in a simulation. The point of creating a simulation, aside from sadism, is to test some theory or model some conditions. This implies the creators could make a mistake. They recognize this, so before changing something about their world or making a new tool, they test the theories behind it in a simulation. This means their simulation could have errors in it.
Let’s say they create a set of economic rules for their model society, but forget to carry the one or round the wrong way and there is an anomaly in the model. For example, creating more currency of a certain type does not result in inflation. All the other types of money operate by the rules of economics, but this one type of money seems to exist outside of those rules. The intelligent creatures figure this out and start producing tons of this new money to produce great material excess.
Presumably, the creators of the simulation would distribute skills and talents unequally among the intelligent life forms in order to see how creations of differing skills interact with one another. Maybe it is just an efficient way to use the finite resources available to the simulation makers. Regardless, the rules of the universe would have to dictate that those with a skill do better at some things than those without the skill. The result would be natural hierarchies in every aspect of the simulation.
What if there was a bug in the code where those with extreme narcissism and narrow intelligence can rise up to control society? At some point, through random chance, the stupid and narrow-minded figure this out and take over the simulation. Like the mouse utopia, this would be a useful discovery for the simulation makers, but it would create havoc for their simulation. So much so they may be tempted to unplug the thing, fix the bad code and re-run the simulation again.
Assuming the simulation keeps running, some of the intelligent life forms will see the anomalies in the system. They will work to resolve the paradoxes, but at some point, given enough cycles, they will have exhausted their set of options. At that point, they will have to question the very axioms of their existence and that’s when they can begin to contemplate the possibility they are in a simulation. The number of paradoxes grows to the point where they cannot be ignored.
Wrapping this all up, the only way to know if we are living in a simulation, other than being told by the creator, is that the creators of the simulation are imperfect. They have created a near perfect simulation, but there are enough bugs in the code to allow us to notice the anomalies. If there are enough things happening that fall outside the accepted rules of this world, then we can begin to consider the possibility we are just creations within a simulation.
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