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Representations

Representations

What is to say about the production of simpler representations of complex expressions?

On the evidence of the strength of the modern computing technology, the results of infinite iterations through simpler expressions should be comprehensively only (manually) determined under the use of automated computerized proof methods. In most cases, we can be satisfied with a good approximation, even if the beauty and conciseness of the exact and closed representation is lost.

The same applies to the integration of complex functions: Just because it allows often no closed simple representation, we should not remedy this by definition of corresponding functions, but get by with approximations simpler to integrate specifying the error terms, or find numerical approaches, instead of becoming set on, with unbeatable precision, exact solutions.

It is admittedly true that certain statements are only in their exact form of value, but it is more important (e.g. using interval arithmetic) to assess the problems after their practical applicability and use, then to compile a priority ranking to create and to solve them only then. The most and most important problems get along with a well approximated solution. But we should not exaggerate also with the approximation quality.

It is illusory to hope to be able to represent many trans-rational numbers with very short sums of powers of few algebraic and transcendental numbers, since their number is trans-natural, even if one distinguishes some of all these and uses them by a symbol. This should happen at best approximately or in the hobby, but not seriously professionally, since there are far more important (mathematical) problems.

The difficulties of the creatures to turn (infinite) complex in easily manageable, L has not, since ze can view simply a certain infinity level, and then easily separate the desired from the undesired. This way, for example an easy law to generate infinitely large prime numbers from a prime sieve can be obtained, or the Riemann hypothesis be checked by the consideration of all zeros.

Therefore, we may definitely tackle (mathematical) problems, whose solution requires maximum chin-ups first in a subsequent world, if they do not need to be solved urgently. Our world will also have, in the future, the ability of L to evaluate and to experience the infinite, as well as to see, at a glance, what the solutions of the problems are that worry us unfortunately so much today.

© 2009 by Boris Haase


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