Archive for June, 2011

Man is a creature of habit.  If he did not have habits, he would need to spend a lot of time consciously thinking about what he has to do.  He would have to evaluate every thought before he spoke of it and before he acted upon it.  He would have to evaluate every course of action before committing himself to it.  Life would be tedious.  But a habit, an automatic response to a thought, saves much time and mental effort ; it is productive of swift action and the satisfaction that goes with it.

It is perhaps small wonder that the most successful people tend to be more bound to their habits than the less successful.  Men and women who act with the minimum of thinking are the ‘achievers’ in this world, and they are rewarded accordingly.  Those less given to habits are the ‘philosophical’ types ; interesting people, but not noted for making their mark in the world of action – the world of trade and industry.

Scientists, too, tend to be creatures of habit.  Once a method or a theorem has been accepted, it takes hold of the scientist’s thoughts and becomes difficult to change.  Not impossible, but difficult.  A method or a theorem is difficult to change because it is productive ; it is productive of further research and is productive of new technology.  In other words, it is productive of wealth and so is a powerful motivator.

But there are some risks attached to scientific habits.  Perhaps the most obvious risk is that they lead to a canalising of research ; the easier lines of investigation are chosen at the expense of the more difficult.  And these lines lead on to other lines.  And as long as these particular lines of research are productive of quick material gains, they are pursued ; science is literally paying for itself.  But only superstition can presume that the easier investigations will lead to greater truths.

But there is a more sinister risk.  The present scientific method was first applied to astronomy and then developed to aid physics.  It was developed and refined to study the inanimate world ; the world which was properly regarded as a mechanism ; i.e., a world where motion is key, and the motion determined by forces external to the body being moved.  All this makes sense in physics.

The method was so successful that scientists then applied it to living things.  Living things were thus classified as machines, which ‘worked’ entirely by forces acting upon them.  So productive was this method of study that many inventions were made to improve the performance of the living machines.  Gradually, almost without anyone noticing, the habit of thinking of living things as machines grew in man’s mind.

The habit grew until many of those of a scientific persuasion came to believe that living things were nothing but machines.  It is now taken for granted by many scientists that man himself is just a machine.

I wonder how many of those scientists have set their habit aside for a while to consider the consequences of it?  What is the future for humanity if we are simply machines, whose every thought and every word and every action is the result of the blind forces of nature acting our bodies?

Where now is the concept of Truth?  of Justice?  How are people to be held accountable for their actions?  On what grounds may one praise a useful machine?

What credit or criticism may one give to somebody’s opinion, if that opinion is nothing more than the result of impersonal natural forces acting on his or her body?

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I believe it was Poincare who said, “It is not necessary that a theorem be true, but it is necessary that it be beautiful.” At first sight this seems to be an odd thing to say ; for, surely, the whole practical value of a theorem lies, not in its appearances, but in its truth.

But perhaps his mind was working in a different mode from the practical ; for didn’t he also say that a scientist does not study nature in order to make use of it, but because it is merely beautiful. Also I am sure the idea would have crossed his mind that truth is an opinion ; and our opinions on what is true change over time. Sometime many years, or even centuries can lapse before a theorem (or, more strictly, a hypothesis) may be properly tested for truth. It will be remembered that Aristarchos of Samos argued the hypothesis of helio-centricity in the third century BC.

And then there is the principle of convention. For a theorem to be true, its rationale must be argued by agreed rules of reasoning ; and here, the rules also change over time. Pre-Socratic reasoning is very different from our own – as Socrates himself discovered at the cost of his life. Such reasoning is still current among many peoples, including modern people in the West.

On the other hand, nature does possess beauty, as poets, artists, scientists and people from all sides will testify. Therefore a beautiful theorem, provided it is reasonably grounded, will be very likely true, whether proofs be available or not.

But what makes a thing beautiful? And isn’t beauty also an opinion? Here we are on grounds that are similar to those occupied by reason ; grounds in which convention plays a major part. In very general terms, beauty is evidenced by such qualities as symmetry and proportionality – in such things as form and force, mass and motion, colour and sound.

And our ideas of beauty also change over time. The beauty of an ancient Egyptian portrait or statue does not quite match our own tastes ; and an Aztec painting is something of an acquired taste, too – as is a Salvador Dali portrait.

This raises the interesting question, Can an ugly theorem, that stands to reason alone, be accepted on the ground that it might one day be deemed beautiful?

From all this we can see why truth and beauty have always featured highly in our understanding of nature. And we notice that it is our understanding that we are considering – not that of animals or aliens.

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