An information representation (or string) s is very compressible if the size of it's smallest possible compression K(s) is very small compared with it's observed size(s). The smallest compression size K(s) is the Kolmogorov complexity. We can define the compress-ibility C(s) of a string s to be the smallest compression K(s) divided by the size of the original representation size(s):
C(s) = K(s) / Size(s) - lower is better
The smallest compressed size" for any given string is a function that cannot be calculated in general, however you can always find an upper bound to it as soon as you find a compression of that size. A compression of s is basically a program along with it's input that can generate s as output. If is always possible to find a program slightly bigger than s (think: print "s"), therefore it is only interesting to find compression with size that is lower than size(s).
For example for the string "1 2 3 4 5 6 ..... 99999999999" you can write a short program with a "for loop" that prints all these numbers, generating this long sequence of characters. As you might realize, this example is not very compressible using usual compression algorithms (think "zip"). On the other side, any self extract archive is an accepted compression with the above this definition.
Therefore, this definition is more general than the compressed size using any compression program you might imagine. Of course, there might be small variations based on the language you are using, however for big strings this should be negligible as long as you don't hide very big strings in the language itself.
A theorem proved that K(s) only differ by a constant between different Turing machines, so a small C(s) can be similarly small on any Turing machine, for a big enough s.
Life
DNA code is such kind of super compression for the great complexity of morphology and physiology that life exhibits. If we represent all the specifics of a certain animal - that we consider a characteristic of it, a book on this would be far longer than the DNA representation of the animal.
For example, human DNA only has like 1GB of information, it seems incredible that this can encode all that is human specific, like all the body organs schematics, let along the complex human innate behaviors.
Therefore, we are forced to conclude that LIFE is very compressible.
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