“masturbation” as in “entertaining but fruitless”. 
Heh. With one fell swoop, you wipe out The Matrix and the Bible. I tip my virtual hat to you. 
Maybe you’re just a by-product. Whoever created this sim created billions of us, randomly, in the hopes of getting a few interesting entities like Einstein and Plato. The rest of us are just extras.
It is not so much that we have to assume we aren’t. It is that it makes no difference in the way we conduct science, our lives or anything else.
I think we have no idea how the world is structured, so anything is possible, therefore, we cannot make the blanket statement that this fact should not affect anything we do.
As an example, in The Matrix, the fact that Neo became curious led him to escape the Matrix. In general, maybe the sim is constructed such that a few entities who “figure it out” can gain some advantages, like “supernatural” powers, or even being uploaded into the upper world.
We have no idea. There are a billion ways this world can be set up, and each is equally likely.
I would say, however, that I think that, as of now, no one has “figured it out” or done anything “supernatural” (despite claims by several religions to the contrary)
Unless we discover evidence that the universe is a simulation; it might be buggy, even hackable; there might be deliberate clues left behind, or the computer cops might discover what’s going on and a voice from nowhere will announce : “Attention. This is an illegal simulation. Prepare for shutdown. Our apologies for the inconvenience.”
Re: scenario 2 - is “infinity = infinity” a valid mathematical construct? I thought I was reading only yesterday that there are many more irrational numbers than, say, natural numbers, even though there is an infinity of both of them.
I occassionaly think that we may be living in a simulation. I remember reading somewhere that a program that created a simulation has no need to simulate everything down to a microscopic level as we can’t perceive anything that small. However, if we start using a microscope to look at something small the program knows we are using a microscope and then generates the microscopic world for only that that we are looking at. As soon as we remove our eye from the microscope the need for simulating the microscopic portion of world is no longer needed and disappears. So in other words things don’t exist unless we look at them. Sounds to me a lot like how parts of quantum mechanics behave.
Also even though the computer running the simulation is obviously powerful it has its limits and just doesn’t have the capacity to simulate on a smaller and smaller scale. Once it reaches it’s limit that’s what we call the Planck Length - the smallest length we can move. It’s similar to a character in a video game who can only move in units of one pixel not in halfs or thirds of pixel. Maybe the Planck Length is the size of our pixels.
Anyhow this got me thinking to my prefered ending for The Matrix. At the end of the film the camera pans out from the land showing an ever larger area. First we see the Earth then the Solar System then nearby stars followed by our galaxy, more galaxies and finally the camera pans out far enough so that we reverse out of a window of a machine that is the computer running the simulation that is the Matrix. The camera then pans out even further and we see that machine is in the corner of a dusty room covered in something similar to cobwebs. The final shot before we fade to black is of the building the computer is housed in which is on a planet that is lifeless and long abandoned thereby showing us that our entire universe is some forgotten program and our entire existence is basically meaningless.
**Polerius ** and Der Trihs, The Matrix is very particular in that it is a simulation of the actual pre-existent universe at a recent moment and there were peers on the outside. If this were Conway’s Game of Life, or an alien high school project or the work of angels, then we couldn’t escape. We could arguably hack it to our advantage (i.e. perform magic) but not gain consciousness or understanding of the outside world. Of course, we don’t know if this is a Matrix style construct and won’t know until we try
So what your saying is that if you live your lives acording to a set of principles defined by the creator you may be elevated to a differant place, a place that would seem supernatural by our current standards?
If proof of Religious belief came from advanced technology that would be the most delicious irony.
Ratios between infinities don’t work like that. For example, the number of integers and the number of integers exactly divisible by 1000 are both infinite; however, a randomly chosen integer is not “equally likely” to be divisible or not divisible by 1000.
There are indeed different “sizes” of infinity, referred to in formal mathematics as different cardinalities. Any infinite set that’s in correspondence with the natural numbers is called countably infinite, while infinite sets with more elements than the natural numbers are called uncountable. (The irrationals numbers are uncountable.)
However, there are some unexpected results about these infinities. For instance, if you combine a countably infinite number of finite numbers, you still get a countable infinity. Hence if we have a countable set of real universes and each one produces several billion virtual universes, the total number of virtual universes is still countable. And since all countably infinite sets have the same number of elements, then the number of virtual universes would be the same as the number of real ones in this scenario.
(And if you think this sounds crazy, you’re not alone. When German mathematician Georg Cantor first proposed this stuff in the late nineteenth century, some of his colleagues seriously believed he had gone insane and wanted him institutionalized.)
Actually there cannot be a “randomly chosen integer”. In other words, you can’t randomly pick an integer from among all the integers, precisely because the integers are infinite.
Think of this way. If I ask for a randomly chosen integer between one and ten, we can put ten labeled marbles into a bag and pick one without looking; there’s our random choice. If I ask for a randomly chosen integer between one and a billion,we could (in theory) put a billion marbles in a bag and choose. But we can’t put an infinite number of marbles into a bag, even theoretically, because the probability of picking any particular marble becomes 1 / (infinity) = 0.
Hence, odd as it may seem, the argument about us being more likely to choose an integer that isn’t divisible by 1000 doesn’t work. This is highly counterintuitive, but it’s accepted by almost all modern mathematicians, and it leads to bizarre results such as the fact that there’s only one infinite random graph.