Editing Kolmogorov Complexity (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Kolmogorov complexity is understood through '''Description Length''' and '''Patterns'''.

'''1. The Shortest Program''':
Imagine two strings of 100 characters:
* '''String A''': "ABABAB... (repeating 50 times)"
* '''String B''': "q8zP2m... (completely random characters)"
Which is more complex?
* '''String A''' has low complexity because the program `print "AB"*50` is very short.
* '''String B''' has high complexity because the only way to "Describe" it is to write the whole string out. The program is `print "q8zP2m..."`.

'''2. Randomness as "Lack of Patterns"''':
In this field, "Random" means "Patternless."
* If a string has a pattern (like the digits of Pi), it is NOT random, even if it looks random.
* Because a short program can calculate Pi to a billion digits, the "Complexity" of a billion digits of Pi is actually quite low.

'''3. The Uncomputability Problem''':
Here is the catch: we can never write a program that calculates the *exact* Kolmogorov complexity of any other string.
* This is related to the '''Halting Problem'''. We can't know for sure if a shorter program exists that we just haven't found yet.
* Kolmogorov complexity is a "Theoretical Limit" that we can get close to, but never reach perfectly.

'''Minimalism''': Kolmogorov complexity is the mathematical definition of minimalism. It asks: "What is the absolute bare minimum amount of data I need to recreate this thing?"
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