Posts Tagged ‘beauty’



Survey the hills of home, now bathed in light,
Whose gladness is to please the jaded eye
Of careworn soul, grown weary of the slight
Reward afforded by the dreary tie
Between desire for pleasure and its gain.
And yet, those hills ; what are they if not heaps
Of stones and dust?  And what the light? – in main
An airy nothingness.  Yet fancy leaps,
Investing beauty in the dullest dust,
And so transform the merest native Earth.
Creating things of wonder, as we must,
Is surely our appointed task. If worth
Be reckoned fair and made as kind to kind,
Then beauty’s born from aught but living mind.

Jamie MacNab 2011


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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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An old woman - a witch

The picture of the old woman, whose name is Cracklebones, with the huge hooked nose and cruel thin lips, and wearing a dirty-white headscarf, reminds us of a witch ; it also reminds us of our tendency to make judgements of people ; judgements that are often based on little evidence.  Is this prejudice?  Well, it might be and it might not ; it depends on what we conventionally regard as valid evidence.

The nature of evidence is itself interesting.  People often assume that it consists of objects.  For example, if young Matilda is found dead in the forest very near the witch’s haunted house, we are apt to think that she has been murdered.  And, since Matilda shows no sign of injury, we are inclined to think she has been either poisoned or killed by a dastardly spell.

And if we then find the wicked witch sitting nearby, stirring a pot that smells of hemlock, stroking her sinister black cat and cackling to herself, we are inclined to think that it was she who committed the murder.  The witch murdered the young lady, Matilda.  Was it jealousy that made her do it?

But, actually, all these physical signs – the body, the old woman, the hemlock, the cat, the cackles, and the gloomy cottage  in the woods – do not amount to anything at all.  They are just things.

It is only when we think about those things that they become evidence.  We have to think about the things and then link them, one to another, in a chain of reasoning.  Evidence is derived from reason and from consciousness, and not merely from things.


So much for the evidence, but what about young Matilda?  She is quite a beauty.  In the picture below, she is looking away from us, so that we see her rather delicate jaw-line and a narrow, elegant neckband ; she is wearing soft fur stole of the best quality. She wears a feather above her brow.  She appears to be rather a shy young lady of refined manners.

A young lady


In my experience, most people are able to make the switch in perception, so that they can see either the witch or the young lady.  But I know no-one who can see both at the same time.  We tend to see either one or the other.  On reflection, it is quite remarkable that the same identical picture can give rise to two contrary perceptions.

It reminds us that the picture ‘out there’, outside of our brains and bodies, is not what we actually perceive.  What we perceive is what our minds make of the picture.  From the same ink marks on the paper, we can make two very different cognitive models.

Also it reminds us that making a mental image of what we see is not just a question of processing sensory data ; it is a question of thinking about that data and about previously-learned data as well.  Though that thinking is normally done so rapidly that we are usually not aware of it.

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