Tuesday, 16 March 2010

II. The Rules of Engagement

Before I proceed with the development of my thoughts, I find wise to set a few rules and regulations to assure that the yet to be revealed theories and postulates are logic, thoughtful and pertinent.

My favourite set of rules comes from Carl Sagan. It is extensive but also comprehensive, it gives no margin for error, it generates discussion and positive thinking. Carl Sagan is one of my youth heroes and I was an avid viewer of his TV series “Cosmos”.

I am always deeply moved with the intro of this series, a conjugation of the infinitely beautiful images of our Universe, with the music of Vangelis and the sage words of Carl Sagan. Just take a look and dare to disagree...

My favourite set of rules comes from Carl Sagan. It is extensive but also comprehensive, it gives no margin for error, it generates discussion and positive thinking. Carl Sagan is one of my youth heroes and I was an avid viewer of his TV series “Cosmos”. His narrative was straightforward and relevant and in the same way is his...
Baloney Detection Kit
Based on the book by Carl Sagan “The Demon Haunted World”.
Warning signs that suggest deception. The following are suggested as tools for testing arguments and detecting fallacious or fraudulent arguments:
  • Wherever possible there must be independent confirmation of the facts. 
  • Encourage substantive debate on the evidence by knowledgeable proponents of all points of view. 
  • Arguments from authority carry little weight (in science there are no "authorities"). 
  • Spin more than one hypothesis - don't simply run with the first idea that caught your fancy. 
  • Try not to get overly attached to a hypothesis just because it's yours. 
  • Quantify, wherever possible. 
  • If there is a chain of argument every link in the chain must work. 
  • Occam's razor - if there are two hypotheses that explain the data equally well choose the simpler. 
  • Ask whether the hypothesis can, at least in principle, be falsified (shown to be false by some unambiguous test). In other words, it is testable? Can others duplicate the experiment and get the same result? 
Additional issues are:
  • Conduct control experiments - especially "double blind" experiments where the person taking measurements is not aware of the test and control subjects. 
  • Check for confounding factors - separate the variables. 
Common fallacies of logic and rhetoric
  • Ad hominem - attacking the arguer and not the argument. 
  • Argument from "authority". 
  • Argument from adverse consequences (putting pressure on the decision maker by pointing out dire consequences of an "unfavourable" decision). 
  • Appeal to ignorance (absence of evidence is not evidence of absence). 
  • Special pleading (typically referring to god's will). 
  • Begging the question (assuming an answer in the way the question is phrased). 
  • Observational selection (counting the hits and forgetting the misses). 
  • Statistics of small numbers (such as drawing conclusions from inadequate sample sizes). 
  • Misunderstanding the nature of statistics (President Eisenhower expressing astonishment and alarm on discovering that fully half of all Americans have below average intelligence!) 
  • Inconsistency (e.g. military expenditures based on worst case scenarios but scientific projections on environmental dangers thriftily ignored because they are not "proved"). 
  • Non sequitur - "it does not follow" - the logic falls down. 
  • Post hoc, ergo propter hoc - "it happened after so it was caused by" - confusion of cause and effect. 
  • Meaningless question ("what happens when an irresistible force meets an immovable object?). 
  • Excluded middle - considering only the two extremes in a range of possibilities (making the "other side" look worse than it really is). 
  • Short-term v. long-term - a subset of excluded middle ("why pursue fundamental science when we have so huge a budget deficit?"). 
  • Slippery slope - a subset of excluded middle - unwarranted extrapolation of the effects (give an inch and they will take a mile). 
  • Confusion of correlation and causation. 
  • Caricaturing (or stereotyping) a position to make it easier to attack. 
  • Suppressed evidence or half-truths. 
  • Weasel words - for example, use of euphemisms for war such as "police action" to get around limitations on Presidential powers. "An important art of politicians is to find new names for institutions which under old names have become odious to the public" 
It is without question that mankind has amassed an enormous amount of culture, data, science (of relevance or not). However there are “discoveries” of discussable merit as we live in a society highly westernised, in permanent search of accolades, where the front page of a tabloid has more relevance than the result itself. One example that crops to my mind is the hyped proof of Fermat's Last Theorem by Andrew Wiles, a mammoth mathematical paper of more than 200 pages, using mathematical processes unknown to XVIII century France. Pierre de Fermat wrote on a corner of a page that he had found a cunning process of proofing that there are no integer numbers n that satisfy the equation:
This equation and consequent thought process is as interesting and has as many applications to human daily life as the cryptic crossword of the Sunday Times. No interest whatsoever… apart from the challenge. And these challenges are as enticing as climbing the Everest… people get sucked in, because they are there and need climbing or proofing. The beauty and confusion of Fermat’s story is that his alleged proof would have never taken 200 pages and would have never used the “mathematical vocabulary” of Andrew Wiles.

On the same note we will never know if George Mallory died before or after climbing Mount Everest; it is up to an emotional reward that some people (me included) want to believe that the first human that set foot at the Top of the World was him with simple tools and cheer guts.

This begs the question... was Wiles the first human to proof Fermat’s Last Theorem? In terms of media he has all the advantages, English speaker, English born, English teacher, a bit geeky, living in modern times, all that against a difficult French Judge, living in Toulouse in 1630, for which mathematical work was an intense hobby.

I am of the opinion that Pierre’s proof takes no more than a couple of pages and he probably put it in the rubbish totally absent–minded. That satisfies the Baloney Detection Kit a)8. if there are two hypotheses that explain the data equally well choose the simpler. By inverting this argument I have a “gut feeling” that there is a fundamental flaw somewhere in Wiles’ proof not of his fault, but on the building of the argument (for example the use and assumed isomorphism of the Tanyiama–Shimura conjecture against the above Fermat's equation).

Science is made by men, can be tricky and become tricked by men too, no malice implied. Hence, sticking to some rules is always good, keep it simple, keep it clear.

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