FUZZY THINKING AND OCKHAM’S RAZOR

Fuzzy thinking is far worse than fallacious thinking for whereas the latter may be spotted, or overturned by new evidence, the fuzzy variety may linger for millenia, causing endless harm, as we shall see.

There is a remedy against fuzzy thinking called “Ockham’s Razor (OR)” named after a mediaeval monk, though its roots stretch back into the classical world where it was labelled ‘lex parsimoniae‘ or ‘The Law of Parsimony’.

Ockham’s Razor states: “ALWAYS PREFER SIMPLE HYPOTHESES OVER COMPLEX ONES” which is easy enough to write down but damnably hard to justify. For instance both Newton and Einstein utterly relied upon it but both gave unsound reasons for doing so. Newton averred: “….for Nature is pleased with simplicity, and affects not the pomp of superfluous causes.” while Einstein waffled about God. He said, with regard to his Law of Gravitation “God would not have passed up the opportunity to make nature this simple.” [As it happens she had.]

SOME TRIUMPHS OF OCKHAM’S RAZOR:

1) Heliocentrism (A Sun-centred planetary system) was first advocated in modern times by Copernicus(1543) in De Revolutionibus. He didn’t have any new observations to justify his claim (the telescope wasn’t invented for another 30 years) but it was evidently much simpler than the traditional Earth -centred scheme, which needed twice as many arbitrary parameters to square it with the facts. [Confirmation only came in 1609 when Galileo with his spyglass spotted that Venus exhibited changing crescent- phases as it orbited the Sun.]

2) Newton recognised that the theory of Gravitation he proposed to explain the dynamics of the Solar System was ridiculous. He wrote: “That Gravity should be innate, inherent and essential to Matter so that one body should act upon another at a distance through a Vacuum, without the Mediation of anything else, by and which through their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe that no Man who in philosophical matters has a competent Faculty of thinking can ever fall into it.” Nevertheless that one simple law explained so many things about the heavens and about he Earth that it was quickly and universally accepted…. because it was so parsimonious.

3) In his Origin of Species (1859) Darwin acknowledged that there were so many difficulties with his hypothesis of Evolution that he wrote in his conclusions: “That many and grave objections may be raised against the theory of descent with modification through natural selection, I do not deny. And I endeavour to give them full force.” And he did. Nevertheless many readers came to accept it rather than ascribing every peculiarity of Nature as due to a special intercession by God. Again because it was so much more parsimonious. And in the fullness of time ( a century) the various objections to Natural Selection melted away as Radioactivity and Continental Drift came to light.

4) It was Henri Poincare’ (1904) who first realised that the grave difficulties which then faced Physics could be resolved by accepting the Lorenz Transformations and modifying Newton’s Laws of Motion to agree with them. This is called ‘The Theory of Special Relativity’. However Einstein got the credit for it a year later by making a single outrageous assumption: “The speed of light is constant for all observers”, which was much less satisfactory from a philosophical point of view– but oh so much simpler algebraically. As in Newton’s case one outrageous assumption explained and predicted a thousand surprising observations: parsimony again.

5) And Parsimony isn’t just about science. Not at all. Take for example Military Intelligence. R.V.Jones who was head of Air Ministry Intelligence during the SWW, and who was responsible for the threats to the UK of Nazi bombing, radar, the V1 and the V2 missiles , later wrote a very fascinating book about his experiences ‘Most Secret War‘. In his summary at the end he calls Ockham’s Razor : “The Cardinal Principle of Military Intelligence.”

SOME FUZZY TRAGEDIES

1) The Four Elements was an idea promulgated by Aristotle around 300 BC in which all substances were supposed to be composed of a mixture of Earth, Water, Air and Fire. By adjusting this hypothetical mixture, and a deal of plausible sophistry, the old thinkers could explain everything – and therefore nothing. So long as it was widely believed, serious chemistry was unnecessary and therefore unpursued. This monster was a many headed gorgon bristling with free parameters. Whenever something didn’t fit you ascribed further properties (parameters) to your 4 imaginary elements and lo everything could be made to fit once again. Thus it couldn’t be overturned; because it was too fuzzy.

What we  would call Chemistry was ruled for over 2000 years by Aristotle’s hypothesis. Almost no material evidence supported his scheme but it appealed to religions such as Christianity and Islam looking for a comforting order to life. It wasn’t overturned so much as left behind by crisis, the firewood crisis which struck Britain in the 18th century after it had cut down most of its forests to build houses and ships. A new source of power had to be found and the mining of coal led to a desperate search for new materials and new contrivances such as pumps to stop the mines flooding. Experiments were necessary, and from experiments came evidence that made no sense within Aristotle’s fuzzy scheme. For instance burned in air some substances became heavier not lighter. And careful balance measurements initiated by Joseph Black in Glasgow University (1750, the English universities didn’t teach science then!) showed that substances combined in precise ratios to form compounds. Out of such observations the notions of atoms and molecules grew. These in turn gave rise to materials of great strength like steel, and to new compounds of great value such as artificial dyes. Crisis, experiment, discovery, understanding, wealth: The infinitely flexible, therefore unprogressive chemistry of Aristotle was simply left behind as unprofitable.

(B) The Four Humours was another fuzzy Greek hypothesis which held up progress for 2 millenia. Modelled on the Four Elements it imagined that health was determined by a balance of four liquids: choler, melancholer, phlegm and blood. Physicians who were learned in such jiggery-pokery dosed us, leeched us and charged us, shortening our lives as they impoverished our purses. Again the hypothesis was immune to criticism because it was infinitely adaptable. In place of bones it had an infinitude of free paramaters –  and what was more could earn good money. Again it couldn’t be displaced by evidence, being infinitely flexible. It was gradually superseded by more useful notions about physiology such as the germ theory of disease, a direct result of the invention of the microscope. But Greek Medicine held up real medicine for twenty centuries

(C) The ‘Argument by Design’ opined that all things wise and wonderful, all creatures great and small, were instances of The Creator’s wonderful powers of invention. After all no other cause could be imagined for the intricacies of Nature’s architecture, from the perfect spiral of a sea shell to the extravagance of a Rainbow Lorikeet’s plumage. Science at the ancient universities, even to the end of the nineteenth century, was solely aimed at uncovering such wonderful manifestations of the Almighty. Since nothing was outside His powers everything could be explained. There was no possibility of bringing Him down, since nothing was beyond Him, even burying fossils of inexplicable design merely to challenge our faith in Him. This ‘Argument by Design’ could have been rejected by nothing else but Parsimony, by the discovery of an alternative theory which was simpler, far simpler than a Great Designer in the Sky. And so it eventually was (see Darwin above) The trouble with Him was that he had an infinite number of free parameters (fudge factors).

RELIGION AND FUZZY THINKING

To my mind the greatest obstacle to progress in Western Society was Christianity. Forced upon the Roman Empire by Constantine on his deathbed (337 AD) in return for ‘absolution’ for his sins (he’d murdered his wife and son) it brought Thinking to an abrupt end for over a thousand years for, as Saint Augustine its early theologian wrote (~400 AD) : “There is another form of temptation, even more fraught with danger. This is the disease of curiosity ……It is this which drives us to try and discover the secrets of nature, those secrets which are beyond our understanding, which can avail us nothing and which man should not wish to learn.” Shortly afterwards Christians burned down the Great Library in Alexandria and executed its head by torture.

With no good evidence for its core belief in Jesus Christ as the Son of God Christianity (and other Abrahamic religions) at least offered a very desirable and necessary explanation for “the wonders of Nature” [see ‘The Argument by Design’ above]. But when Darwin and Parsimony had punctured that, thoughtful Christians, like the Bishop of Worcester’s wife, knew that Christianity’s days were numbered. As she put it : “Dear me, let us hope it is not true. But if it is true, let us hope it does not become widely known.”

BUT WHY WAS OCKHAM RIGHT?

Why should anyone accept Ockham’s Razor? That’s the central point. All the explanations I have examined are either unconvincing, or go off into stratospheric mathematics — which is the same thing. The problem is that anything as fundamental as Ockham’s Razor has to be grounded on a clear understanding of Common Sense — which was lacking. Put it another way: any claim to understand Common Sense Thinking must lead to a crystal clear explanation for OR. But don’t expect it to be simple or obvious — otherwise it would have popped out of the woodwork long since.

The secret, as always, turned out to be The Detective’s Equation (DE). Whenever you are trying to understand Hypothesis Testing, which is surely the aim, the DE can be used to calculate the Odds for or against the hypothesis under test, whenever the evidence and the assumptions are changed. So you can play around and find out what adds to one’s certainties and what subtracts, and out of such calculations Ockham’s Razor gradually emerged from the shadows. The best reason to believe any hypothesis is that it fits the existing evidence better than it has any right to do by chance. A simple hypothesis has little chance of fitting more complex data unless it is actually right, whereas a complex hypothesis deliberately contrived to fit it is hardly convincing. Much the best way to understand how things work is to look at a specific example, and we shall go through one in detail below while there is a whole chapter in my book Thinking for Ourselves about OR and its multifarious implications.

Because most scientists still don’t understand CST they don’t realize just how counterproductive it is to complexify their pet theories to fit new but inconvenient facts. Thus Big Bang Cosmology has been so seriously challenged by modern observations that cosmologists have been forced to fuzzify it with strange new parameters like Dark Energy, without realising that in doing so they’ve entirely undermined its credibility.

CONCLUSIONS

Once a hypothesis conflicts with the facts it cannot be left unmodified. But fixing it by introducing arbitrary modifications one by one to remove the separate discrepancies won’t work either because each such mod. will weaken the odds on the hypothesis overall. Only if one can find a mod. which offers to clear up several discrepancies at once should it be seriously considered. Of course that will be much harder — but nevertheless that is the challenge.

Applied to Big Bang Cosmology (BBC), Inflation (to fix isotropy), Cold Dark Matter (to fix galaxy-formation) and Dark Energy (to fix acceleration) shouldn’t be considered seriously because none was ambitious enough to fix more than one serious discrepancy. It was, and is, much healthier to admit that as it stands BBC is seriously at variance with the facts (observations). Some of it might be right ( e.g. expansion) and it is certainly hard to think of a plausible alternative. But it is much healthier for now to admit that BBC has failed. Trying to keep it alive, (Like Ancient Greek medicine) is the kind of fuzzy thinking which can hold up progress for generations, millennia perhaps. BBC has failed — we’ve got to start again.

Looking at the wider picture beyond Cosmology, we can see just how fundamental Ockham’s Razor must be to clear thinking of all kinds, from Astronomy to Military Intelligence. What was lacking was a transparent explanation of just how and why it works, but now the Detective’s Equation (i.e. Common Sense) has supplied that.

Ockham’s Razor must surely be one of the Seven Pillars of Wisdom .

My detailed explanation of why Ockham’s Razor works is given at:

https://mjdisney.org/wp-content/uploads/2020/10/scamsmv5.pdf

The best reference on the history and influence of Ockham’s Razor that I know of is Chapter 8 of Hugh Gauch Jr.’s volume “Scientific Method in Practice” CUP 2003. He goes so far as to say. “…. the scientific enterprise has never produced and never will produce a single conclusion without invoking parsimony. It is absolutely essential and pervasive.”

A readable but sceptical account of Big Bang Cosmology is In Search of the True Universe, by Martin Harwit, CUP 2013

P.S. Is there a quick way to check whether some hypothesis is unhealthily fuzzy? I believe there is: find out how many Free Parameters it has. BBC has 18. But so does The Standard Model of Particle Physics. That makes one wonder. That seems to be stuck in a cul-de-sac too: no exciting developments since the 1970’s . Umm. Do Quarks really exist? No one has actually captured one.[Constructing Quarks, by Andrew Pickering, Univ. Chicago Pr. 1984, makes for provocative reading].

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