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Posts Tagged ‘**mathematical logical**’

### Ironing out a few chaotic glitches

Posted by: adonis49 on: December 9, 2009

**Ironing out a few chaotic glitches; (Dec. 5, 2009)**

Philosophers have been babbling for many thousand years whether the universe is chaotic or very structured so that rational and logical thinking can untangle its laws and comprehend nature’s behaviors and phenomena.

Plato wrote that the world is comprehensible. The world looked like a structured work of art built on mathematical logical precision. Why? Plato was found of symmetry, geometry, numbers, and he was impressed by the ordered tonality of musical cord instruments. Leibnitz in the 18^{th} century explained “In what manner God created the universe it must be in the most regular and ordered structure. Leibnitz claimed that God selected the simplest in hypotheses that generated the richest varieties of phenomena.” A strong impetus that the universe is comprehensible started with the “positivist philosophers and scientists” of the 20^{th} century who were convinced that the laws of natures can be discovered by rational mind.

Einstein followed suit and wrote “God does not play dice. To rationally comprehend a phenomenon we must reduce, by a logical process, the propositions (or axioms) to apparently known evidence that reason cannot touch.” The pronouncement of Einstein “The eternally incomprehensible universe is its comprehensibility” can be interpreted in many ways. The first interpretation is “what is most incomprehensible in the universe is that it can be comprehensible but we must refrain from revoking its sacral complexity and uncertainty”. The second interpretation is “If we are still thinking that the universe is not comprehensible then may be it is so, as much as we want to think that we may understand it; thus, the universe will remain incomprehensible (and we should not prematurely declare the “end of science”).

The mathematician Herman Weyl developed the notion: “The assertion that nature is regulated by strict laws is void unless we affirm that it is related by simple mathematical laws. The more we delve in the reduction process to the bare fundamental propositions the more facts are explained with exactitude.” It is this philosophy of an ordered and symmetrical world that drove Mendeleyev to classifying the chemical elements; Murry Gell-Mann used “group theory” to predicting the existence of quarks.

A few scientists went even further; they claimed that the universe evolved in such a way to permit the emergence of the rational thinking man. Scientists enunciated many principles such as “the principle of least time” that Fermat used to deduce the laws of refraction and reflection of light; Richard Feynman discoursed on the “principle of least actions”; we have the “principle of least energy consumed”, the “principle of computational equivalence”, the “principle of entropy” or the level of uncertainty in a chaotic environment.

Stephen Hawking popularized the idea of the “Theory of Everything TOE” a theory based on a few simple and non redundant rules that govern the universe. Stephen Wolfran thinks that the TOE can be found by a thorough systematic computer search: The universe complexity is finite and the most seemingly complex phenomena (for example cognitive functions) emerge from simple rules.

Before we offer the opposite view that universe is intrinsically chaotic let us define what is a theory. Gregory Chaitin explained that “a theory is a computer program designed to account for observed facts by computation”. (Warning to all mathematicians! If you want your theory to be published by peer reviewers then you might have to attach an “elegant” or the shortest computer program in bits that describes your theory)

Kurt Gödel and Alain Turing demonstrated what is called “incompletude” in mathematics or the ultimate uncertainty of mathematical foundations. There are innumerable “true” propositions or conjectures that can never be demonstrated. For example, it is impossible to account for the results of elementary arithmetic such as addition or multiplication by the deductive processes of its basic axioms. Thus, many more axioms and unresolved conjectures have to be added in order to explain correctly many mathematical results. Turing demonstrated mathematically that there is no algorithm that can “know” if a program will ever stop or not. The consequence in mathematics is this: no set of axioms will ever permit to deduce if a program will ever stop or not. Actually, there exist many numbers that cannot be computed. There are mathematical facts that are logically irreducible and incomprehensive.

Quantum mechanics proclaimed that, on the micro level, the universe is chaotic: there is impossibility of simultaneously locating a particle, its direction, and determining its velocity. We are computing probabilities of occurrences. John von Neumann wrote: “Theoretical physics does not explain natural phenomena: it classifies phenomena and tries to link or relate the classes.”

Acquiring knowledge was intuitively understood as a tool to improving human dignity by increasing quality of life; thus, erasing as many dangerous superstitions that bogged down spiritual and moral life of man. Ironically, the trend captured a negative life of its own in the last century. The subconscious goal for learning was to frustrate fanatic religiosity that proclaimed that God is the sole creator and controller of our life, its quality, and its destiny. With our gained power in knowledge we may thus destroy our survival by our own volition; we can commit earth suicide regardless of what God wishes. So far, we have been extremely successful beyond all expectations. We can destroy all living creatures and plants by activating a single H-Bomb or whether we act now or desist from finding resolution to the predicaments of climate changes.

I have impressions. First, what the mathematicians and scientists are doing is not discovering the truth or the real processes but to condense complexity into simple propositions so that an individual may think that he is able to comprehend the complexities of the world. Second, nature is complex; man is more complex; social interactions are far more complex. No mathematical equations or simple laws will ever help an individual to comprehend the thousands of interactions among the thousands of variability. Third, we need to focus on the rare events; it has been proven that the rare events (for example, occurrences at the tails of probability functions) are the most catastrophic simply because very few are the researchers interested in investigating them; scientists are cozy with those well structured behaviors that answer collective behaviors.

My fourth impression is that I am a genius without realizing it. Unfortunately Kurt Gödel is the prime kill joy; he would have mock me on the ground that he mathematically demonstrated that any sentence I write is a lie. How would I dare write anything?