The Need for Compression Transformational Methods

I think it is quite unlikely that a simple data compression system will do very much to advance software development at this time. Effective Compression Transformational Methods would.

The n-ary mathematical representation (power base) form of numbers (like binary, trinary, decimal, hexadecimal and so on) may be the most efficient representational system for the counting numbers *in general* but its real speed comes from the fact that addition and multiplication can be done so efficiently in these systems and because these methods can be applied to a range of mathematical methods that can be derived using basic computational arithmetic. So, understanding that the n-ary representational system is truly a compression of the representation of individual counting numbers, it becomes clear that the real speed-ups come from the ability to do addition, multiplication and other mathematical computations without needing to decompress the numbers into unary form (like counting collections of marks.)

Because the n-ary (power-base) form of representing numbers is not perfect for all representations of systems of numbers (to use in what I am calling 'transformational' calculations) it now becomes clear that the power to operate on compressed data and to do calculations without needing to decompress and recompress the operands would be greatly advantageous.

Other kinds of effective compression transformational methods could be developed as well.

I originally argued for Cross-Compression Transformational Functions that could operate on data objects which were compressed with different compression methods, but it would be more feasible to develop functions for compressed data that was expressed with some consistency and regularity (like n-ary numbers). So at this stage I would say that the development of compression systems (and other forms of encryption) that include transformation functions that can operate on the objects without needing to convert them back into their original form will advance computer science significantly.

This is an abstract theory, one which has not been proven but which will be pursued.