## 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.