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TRADUZIR |  |
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1) Philosophy (i.e. Language). A clear thinking genius - Ludwig Wittgenstein of Austria - finally resolved the most intractable problems of philosophy by proving that they couldn't be solved, or even expressed.
Philosophers had tied themselves in knots trying to put into words the things they felt to be important, but, no matter which languages they used, they couldn't do it.
Ludwig realized that, as human languages are constructs, they cannot have an `essence' of their own. Therefore all `essential' truths are inexpressible in any human language.
Well, if any of us had thought about it, that seems fairly obvious - here's an everyday example:
An author's `great thought' has to be cramped and mangled merely to get it into words. Then, when those words are heard or read by another - with a uniquely different brain, and a different personal background, maybe even a different cultural history - the received impression, the end result, must differ from the original thought - which never quite made it into words anyway.
[Peter Watts has nicely doubly-extremed the analogy in "Blindsight" - quote - "Like trying to describe dreams with smoke signals" ]
Also - the same applies to "logic" which is only manipulation of a system of human-constructed symbols; the system suffers from same lack of `essential' truths. It's therefore incomplete - incapable of final proofs.
2) Science (i.e. Mathematics). Folk like Turing and Russell (an early mentor of Wittgenstein's) had tried to analyse the failure of attempts to systematize Mathematics - once thought to be `logical and therefore universal'.
1931, the Czech-born mathematician Kurt Gödel eventually proved that Mathematics is `incomplete' and must always remain so. That is, math is a human construct attempting to logically describe the Universe but its terms are merely imposed on parts of reality, they cannot describe - in a provable way - reality itself.
As he said, in Gödel's Paradox, there will be mathematical statements (about physical reality) which may or may not be true, but which are unprovable by any mathematical means.
Well, here we go again, if anybody had really thought about it, that was staring us in the face.
Shake a charm bracelet and watch one charm swing on its chain - that's a pendulum, which science can accurately describe; but when you hold the bracelet by one charm and shake the whole thing - that's at least two pendulums, one hanging from another, which science hasn't got a hope of describing accurately.
Or, look at the sun and the moon. The Moon orbits the Earth, but science can describe that only by ignoring the Sun; similarly science can only describe Earth's orbit around the Sun by ignoring the Moon.
They can't calculate the real orbits. A mere "three body problem" is out-of-reach of human science.
So scientists have to get a `pretend' description of just a simple part of the Universe.
When a human scientist (or anybody else) says anything about the real, physical universe, it will be only partly "true"; wide, complex systems are `indescribable', i.e. not able to be truthfully expressed at all.
Like Einstein said:
"When mathematics tries to talk about reality - it's inaccurate, when mathematics is accurate - it's not talking about reality"
and
"Not everything that can be counted counts, and not everything that counts can be counted."
Another example is the experts' dictum on "rogue waves". For years they'd calculated and flatly decreed that one would arise only once in a thousand years or so.
Finally however, the reports of actual sailors were confirmed by latest satellite recordings of wave-heights. They happen, around the world, every week or so!
What went wrong? First - the experts hadn't bothered to gather _all_ available facts. Second - they'd chosen the wrong mathematics.
3) Seems no-ones's addressed the same problem in Music.
Received opinions about music are mostly from posers and music snobs - no `provable' statements.
Why?
As before, let's take a look at reality:
An emotional concept of a composer - if s/he has one - is changed merely by attempting to write it down in musical notation: it's limited by the `language'.
Then the artists & their conductor / producer put their gloss on it. Finally the piece will be interpreted by each listener, almost wholly dependent on their mood, culture and background, and so uniquely for each individual.
I.e. personally quite like and am even moved by a wide range, from blue-grass to sentimental folk-song to thoughtful Mahler - which is also `sentimental'. However, have come to realize that there can be no `truth' in music, and its `beauty' is internal and unique to each listener.
Those `music snobs' are actually quite sad people - to spend time learning the technicalities & `buzz-words' of music is to lose appreciation of its emotional content - the composer's prime intention.
In fact much music seems to become associated with the happy or sad circumstances in which it was first heard, as Noel Coward probably meant when he referred to "the power of cheap music". Then the composer's intention (if not technical ability) is irrelevant.
Gödel's Paradox
He wrote it in mathematical symbols but it can be said as a simple English sentence:-
"This statement cannot be proved to be true by an all-embracing system of logic."
then :-
- if the statement is true, the logical system cannot be all-embracing;
and
- if the statement is false, an all-embracing logical system could prove it to be true;
- which are both paradoxical.
Reason why Kurt Gödel investigated mathematics as a logical system
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