A computer does not have the ability to solve problems which involve concepts of
continuity and
infinitesimals. It has been proven that the proper sequence of tranfers between
registers can solve any problem that has a
convergent solution, given enough
time. This means that a computer can solve any problem that has a definite solution and can be achieved in a finite number of steps.
Numerical analysis is a branch of the science of
Mathematics, which studies methods for solving or approximating solutions of problems in a finite number of steps. Most of the mathematic statements and functions of
BASIC are actually routines of this type.
Each
register is made up of
bits. One bit of information can have a status ON or OFF, thus, 1 or 0 numerically, or a YES or NO
logically. Since bits can have exactly two distinct values it is easy to see that the register can represent a number in the range from 0 to 2
n-1, where
n is the size of the register in bits.
So, a register's value is a collection of 0's and 1's. Now we are talking about
binary arithmetic. And if any mathematic problem with a convergent solution can be solved using binary arithmetic, the computer can solve any solvable problem, and state when the problem isn't. Now, since mathematical problems are of algorithmic nature, and their solutions are also, we can conclude that any mathematical
algorithm can be constructed in
binary arithmetic and solved, or performed for algorithm's sake.
Pythagoras' theory that the world is made up and can be interpreted using mathematics probably fits in here somewhere, seeing as, if any problem can be constructed using maths, and the capabilities of the computer are getting more and more
humanlike, and already on our screens we have realistic depictions of human and material world representations, we might conclude that the material world is made up of
mathematical algorithms. The intangible, a priori,
cosmic constituent could be a form of numerical values, all processed by some huge computer to give us senses, and the
material world. Sort of like
The Matrix, except a using natural computer system that could only be labelled as
God which processes
very advanced mathematic algorithms.
So once again, we're led to question whether our
senses are receiving correct
information,
Descartes and his goddamn universal doubt all over again... *sob*, I don't think I can take this any more. It's just so hard to bear, I feel lost in a world which I don't understand. *whail*