This weeks blog is based on the book in the title: "The Lifebox, The Seashell, and the Soul" by Rudy Rucker.
1) In the book, Rucker talks about Wolfram's Four classes of computation:
Simple Computations - Class 1: Uniform and consistent
Class 2: Periodic, alternating patterns, repetitive
Complex Computations - Class 3: Chaotic, seemingly random, messy
Class 4: "purposeful" seeming, complex with
unpredictable patterns
Examples of Class 1 and 2 computations in the real world include things such as the pattern in which bricks are laid to form a wall, a simple Class 2 computation, in which the pattern continuously repeats, and if carried on forever, would not change.
For class 3 and 4 computations, we can look to the veins of a single leaf, where there is no symmetrical pattern, yet observation shows that there is a semblance of a pattern in the way that the veins branch out to make a system within the leaf, making it a complex Class 4 computation.
2) As I am in a Statistics class this semester (ISTA 116), a simple computation that we can do using a statistics program such as RStudio (programming in the "R" language), is random number sampling in data sets. Taking milliseconds to compute by the computer and program, the process is feasible, and it is also unpredictable, as for example, in a data set with 10 points in it, each point may have a 10% chance of being displayed if sampling the data set for 1 data point out of the 10 present, though there is no way to guarentee or accurately determine which data point would be selected. This can also be as simple as a coin flip, where there are 2 possible outcomes, the flip itself takes little time, and the outcome is a supposed 50-50 chance between head or tails.
3) Based on the excerpt from Rucker, the difference between class 3 and 4 computations seems to be that where class 3 computations are characterized by complete randomness and utter lack of pattern in the results of the computation, class 4 computations are more closely related to class 2 relations, in that they produce patterns, though limited before changing over to a different pattern, and patterns in this sense are still relatively unpredictable unlike in class 2 computations. Also, class 4 computations give a sense of purpose, as if patterns were meant to be made as in class 2 computations, but run the computation further and it will stop the pattern. This makes class 4 computations far more intriguing than the jumbled mess that is seen as class 3 computations. Still, it can be difficult to tell between the two, as the difference is based on opinion of whether or not someone sees a partial pattern in what a mess computation, so there is difficulty in distinguishing the two with the fairly vague definitions they hold.
4) Continuous-valued Cellular Automata are computations in which cells like those used in other cellular automata are not limited to simple interger values such as 0 and 1, but can hold any number of values of real numbers, increasing the complexity tremendously. Where the Game of Life CA allowed for a simple CA with only 2 possible states for each cell, according to Rucker (direct quote), "a continuous-valued CA might have four billion possible states per cell", based on the idea that computer programs commonly allow for that many values in a real number.
Compared to Elementary cellular automata as well, continuous-valued CAs can be far more complex, where ECAs are the simplest forms of cellular automata, cvCAs can be seen as systems which may be more related to real life than the 256 different versions of ECAs studied by Stephen Wolfram. Rucker sees ECAs as to simple to model real life, where the shear number of possiblities in continuous value CAs is more valuable for real life application or study of the complex world we live in.
----Nathaniel Hendrix
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