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@@ -13,7 +13,7 @@ Let's say we want to build a computer system which perfectly simulates the unive
Our computer system will be located on earth. Picture an imaginary sphere around our galaxy. Outside of this sphere is what our computer simulates. It ignores the inside. The simulation gets inaccurate over time because the part which it isn't simulating (our galaxy) propagates light out at the speed of light away from us, affecting the simulation. But, since we are good system designers, we account for this. We program it so that the imaginary sphere automatically expands at the speed of light (the fastest information can travel in our universe). This means that the system does not try to simulate the slowly, ever-expanding sphere (our galaxy) in which it resides. We now have a perfectly accurate simulation of the universe, minus a relatively small expanding sphere.
-This is working fine, so let's upgrade the system. Now, it simulates the whole universe minus earth. We use the same solution as before, making an expanding sphere around the earth which it ignores. It will only take 8 minutes until that sphere touches the sun and we can no longer simulate the sun. Soon enough, we won't be able to simulate the solar system either, and it just gets worse from there. So, we upgrade the system again. Now, it simulates a sphere outside the building in which it sits. In no time flat, we already can't simulate the earth any more.
+This is working fine, so let's upgrade the system. Now, it simulates the whole universe minus earth. We use the same solution as before, making an expanding sphere around the earth which it ignores. It will only take 8 minutes until that sphere touches the sun and we can no longer simulate the sun. Soon enough, we won't be able to simulate the solar system either, and it just gets worse from there. So, we upgrade the system again. Now, it simulates a sphere outside the building in which it sits. In no time flat, we already can't simulate the earth anymore.
How small can we shrink this sphere? The smallest we can make it is if our initial non-simulated volume is coterminous with the outline of our computer system. Perhaps we can even shrink it smaller if our system is very large and some parts don't come online immediately. But we can never create a perfect simulation with this strategy because we can't shrink the non-simulated area to zero. If we try to simulate the inside of our imaginary volume, then we get an infinite regression. If a system simulates itself, then it has to simulate the simulation of itself. And so on to infinity. Maybe this is somehow possible, but it doesn't seem so.