Matism
From Atariology
Contents |
Mathematical Atariology
The strictly mathematical interpretation of Atariology. The group is heavily influenced by developments in physics and cellular automata, and generally regard Stephan Wolfram as a messiah.
Some of the beliefs of followers of Matism:
- All meaning can be encoded into a mathematical statement.
- The Universe is a 'Pixelated Universe'
- A Perfect Simulation is not possible.
The Pixelated Universe
Matism views space time as composed of pixels. This means that, according to Matism, space is composed of boxes in 3 dimensional space, and a unit of time which is discrete. Of primary concern to the Matists is the question of how a pixelated universe would behave. How would this behavior differ from that of an infinitely divisible Universe?
The Irrational Universe - The presumed existence of irrational numbers such as √2 provides the most common argument against the Pixelated Universe idea. The measurement of the hypotenuse of a triangle with side length equal to 1 is given by Pythagorus Theorem: c2 = a2 + b2. Thus c2 = 12 + 12, so c=√2. Unfortunately, in the decimal system, √2 can only be represented as an infinite sequence of integers right of the decimal. Euclidean geometry assumes that an idealized triangle could exist in space; therefore an irrational number such as √2 is a quantity that should exist. In order for a distance like √2 to exist, the Universe would need to be infinitely divisible.
Another version of this argument rests on the idea of rotational symmetry. If the Universe is composed of pixels then there would be only a limited number of rotational position measurements. For example, imagine if the Universe was only 2 dimensions and composed of 9 pixels in a 3x3 arrangement; and the only object was a straight line composed of 3 pixels centered at the origin. There would only be 4 distinct rotational states, in other words, by rotating the line in a clockwise direction, there would only be 4 distinct measurements of angle. So, if the Pixelated Universe existed, there would only be a limited number of angle measurements in a fixed frame.
The search for a limit on the number of angle measurements in space is an interesting experimental problem. By definition, any measuring apparatus will also have a limited number of possible measurements. Therefore it is not clear how to go about creating an apparatus that could exclude an indefinitely divisible Universe.
Quantum mechanics might seem to provide justification for the Pixelated Universe. This is a false belief; quantum mechanics uses complex wave functions which are continuous in space time. However, the behavior of an electron as it orbits a nucleon, emitting a photon as it jumps from a higher to a lower energy level, is behavior that might be properly modeled assuming a Pixelated Universe.
The idea of a Pixelated Universe is known in modern physics as Holographic theory. See, for example, this 2009 New Scientist article.
Problems with a Perfect Simulation
Followers of Matism believe in the Pixelated Universe. Since the belief in a Pixelated Universe implies that there is a limit to how finitely space can be divided, this view implies that there might be a limit to the fidelity of a simulation of this life. In Holographic theory, space is divisible up to a precision of 10-35 meters. The existence of a limit on the divisibility of space places a limit on the capability of any computer to create a simulation of this life. Another way to think about this, is that there is a limit to the amount of resources available in this Universe. A computer that contains a simulation of this Universe would necessarily be limited to fewer resources. A hierarchy of simulations created inside that simulation would only be able to use fewer and fewer resources with each successive simulation. Eventually there would be no resources to create any simulation deeper in the hierarchy.
The fact that the Universe is not infinitely divisible does not exclude the fact that the Universe might be a simulation. It is possible that, upon death, a person discovers that they had been playing a video-game the entire time. This is true because although there is a limit to how deep a hierarchy of simulations might reach from a computer constructed in this Universe , there is no limit to how many levels deep we might already be in upper hierarchal simulations.
Near-Perfect Simulation
Since, according to Matism, it is not possible to create an infinite hierarchy of simulations, there is no such thing as a Perfect Simulation. It is possible, however, to create a limited simulation of this Universe, that is correct enough to perfectly simulate the life experience of a single person. In other words, it is not necessary to simulate the entire Universe perfectly since a person only experiences a small portion of the total Universe. A simulation of this life that perfectly recreates the experience of one or more people is called a Near-Perfect Simulation.
