Saturday, December 10

Are scientific theories really better when they are simpler? – Elliott Sober | Aeon Essays

Given that you're doing logic, I think you will appreciate this essay. 
Generally making thing simpler is better. But then we also have to keep an eye out on complexity. Economics frequently comes up with intellectually clean theories and with major assumptions to avoid contaminating the model with the messy thing that is real life. And when you have central banks and commercial banks and governments adopting public policy because of these simplistic models, the impact felt on the people who have been assumed out is huge. For example, most models assume that people are rational. They aren't. And as we have seen, their behaviours can turn normally and commonly held opinions and perspectives upside down. That causes severe dislocations. 
So yes simple is better but sometimes simple can be dangerous as well. 

Are scientific theories really better when they are simpler? – Elliott Sober | Aeon Essays
(via Instapaper)

Two of Barcelona's architectural masterpieces are as different as different could be. The Sagrada Família, designed by Antoni Gaudí, is only a few miles from the German Pavilion, built by Mies van der Rohe. Gaudí's church is flamboyant and complex. Mies's pavilion is tranquil and simple. Mies, the apostle of minimalist architecture, used the slogan 'less is more' to express what he was after. Gaudí never said 'more is more', but his buildings suggest that this is what he had in mind.
One reaction to the contrast between Mies and Gaudí is to choose sides based on a conviction concerning what all art should be like. If all art should be simple or if all art should be complex, the choice is clear. However, both of these norms seem absurd. Isn't it obvious that some estimable art is simple and some is complex? True, there might be extremes that are beyond the pale; we are alienated by art that is far too complex and bored by art that is far too simple. However, between these two extremes there is a vast space of possibilities. Different artists have had different goals. Artists are not in the business of trying to discover the uniquely correct degree of complexity that all artworks should have. There is no such timeless ideal.
Science is different, at least according to many scientists. Albert Einstein spoke for many when he said that 'it can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience'. The search for simple theories, then, is a requirement of the scientific enterprise. When theories get too complex, scientists reach for Ockham's Razor, the principle of parsimony, to do the trimming. This principle says that a theory that postulates fewer entities, processes or causes is better than a theory that postulates more, so long as the simpler theory is compatible with what we observe. But what does 'better' mean? It is obvious that simple theories can be beautiful and easy to understand, remember and test. The hard problem is to explain why the fact that one theory is simpler than another tells you anything about the way the world is.
One of the most famous scientific endorsements of Ockham's Razor can be found in Isaac Newton's Mathematical Principles of Natural Philosophy (1687), where he states four 'Rules of Reasoning'. Here are the first two:
Rule I. No more causes of natural things should be admitted than are both true and sufficient to explain their phenomena. As the philosophers say: nature does nothing in vain, and more causes are in vain when fewer suffice. For nature is simple and does not indulge in the luxury of superfluous causes.
Rule II. Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same. Examples are the cause of respiration in man and beast, or of the falling of stones in Europe and America, or of the light of a kitchen fire and the Sun, or of the reflection of light on our Earth and the planets.
Newton doesn't do much to justify these rules, but in an unpublished commentary on the book of Revelations, he says more. Here is one of his 'Rules for methodising/construing the Apocalypse':
To choose those constructions which without straining reduce things to the greatest simplicity. The reason of this is… [that] truth is ever to be found in simplicity, and not in the multiplicity and confusion of things. It is the perfection of God's works that they are all done with the greatest simplicity. He is the God of order and not of confusion. And therefore as they that would understand the frame of the world must endeavour to reduce their knowledge to all possible simplicity, so it must be in seeking to understand these visions…

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