Experiment # 2 (second try): Irrational numbers and files
Let’s define a numerical system that uses irrational numbers to compress computer files.
Irrational numbers are the numbers that can not be represented as the exact fraction of two whole numbers. These numbers have infinite length after the decimal point and have no period (the decimal sequence is not repeated).
Computer files are millions of ones and zeros (binary representation), a.k.a., numbers of great lengths. Each file can be part of the sequence of an irrational number (actually we could imagine them as irrational numbers with a specific length). If we could find a shorter representation of the irrational number we could minimize the file size.
The problem is that irrational numbers do not follow any logic. Sometimes they’re generated by series (seriesof sums of integers or fractions, etc.) or sometimes are the result of a root. The problem lies in finding a logical relation to create short representations of each irrational number (or even mapevery irrational number to its corresponding short series or roots).
In each irrational number we can find all different combinations of numbers. What we’d look for is to find the irrational number that has the same sequence of numbers as the file to compress. Once we find the irrational number and its generating sequence we can generate the compressed file. This method works continuously, if we have already compressed a file, we can use the compressing process over again.
Cheers,
Gorka