One thing at a time

It’s strange how we seem to spend so much time either looking forward to the future or else remembering the past.  How often are we in the here-and-now?  Aristotle recommended that we take up the art of contemplation to remedy matters.  And who better to make that suggestion?

How to begin?  First, ensure that you will not be disturbed for the next fifteen minutes or so.  Then make yourself comfortable.  Close your eyes.

Contemplating, Aristotle said, is simply paying regard to a series of statements or ideas which are infallibly true.  They must be so, because if there is any doubt about the truth of a statement, then you will start thinking about it – and contemplation must involve no thinking.  It is just regarding, or ‘looking’ at ideas that come to mind.

Sounds easy, doesn’t it?  Well, try it and see.  Aristotle himself found that there are not very many of our notions that are truly infallible.  Like his masters, Socrates and Plato, he concluded that, while we have lots of opinions about the world, not much of what we know is truly true.

He began his exploration of contemplating something like this.

“I am a man.”  (Well, that’s not a bad start.)
“My name is Aristotle.”  (No!  The name my creator gave me is unknown to me.)
“People call me Aristotle.”  (That’s sort of OK)
“I live in Athens.”  (No.  Has this place always been known as Athens?  Will it for ever be called Athens?)
“I live in a city people now call Athens”  (OK)
“I am fifty years of age.”  (No.  I have no proof of my exact age ; I have only the opinions of others.)

…. and so on ….

And so he indeed went on.  And, as he went, he had to amend almost all his ideas about himself and the world ; he had to compromise on the exact truth ; he had to admit opinions under the guise of truths.

It’s awfully hard to live fully in the here-and-now.  Maybe that’s why my own thoughts turned back to school-days while I have been writing.  I remembered a puzzle that Mr Fryer set us all those years ago.  “You think that one plus one equals two, do you?”

“Of course!”  we replied.
“Well, arithmetic is a language,” he said, “And its meanings all depend on how you use it.”

To the blackboard ….. (and I hope I remember this right!) :

a = b
a+a = a+b
2a = a+b
2a-2b = a+b-2b
2(a-b) = a-b
2 = 1

Well, it took us a bit to work that one out (we were young and thought we knew everything).

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Enduring truths

It’s  interesting how marriage can change a young man’s mind for the better, and sometimes to his complete surprise.  It is as if a thousand thoughts, neglected and unspoken in the careless days of bachelorhood, silently combine in wonderful ways to produce new understandings of the world ; which then make themselves known step by step.

This process, of unconscious thinking, has a name given by psychologists : they call it latent learning.  Of course, psychologists, being of a cautious disposition, presume that all the unconscious knowledge we have has been previously learned at a younger age, from the time of birth ; there are few now who are so bold as to presume that individuals might have knowledge that they brought with them into this world, or knowledge that they might have acquired directly mind from mind.

These thoughts were going through my mind recently as I was re-reading Tolkien’s The Lord of the Rings, a book I first read when our first daughter was on her way into the world.  For reasons I could not have been fully aware of, I began to take an interest in what was to me a somewhat alien world – the world of myth and legend, of allegory and fable.  And, to my surprise, through that master story-teller I discovered the importance of these genres ; and their essential truths.  Much more was to follow in the coming years.

Most people now know, I think, that Tolkien wrote his great book in order to fill a gap ; a gap so obvious that no-one seemed to have noticed it ; or, if they had noticed it, they felt unable or unwilling to fill it.  What was missing was a truly Anglo-Saxon grand myth.  True, there was Beowulf, but however fine that was, it made but a small contribution to our heritage and was of limited scope.

On my first reading these aims of Tolkien quickly drifted far from my mind.  That was because I was so enchanted by the story, so drawn in to the adventure, that I forgot completely the wider aims of the author.  And that was just it ought to have been ; for no successful story was ever written merely to be an exemplar of a  genre ; a mere literary exercise.

And who can doubt the success of The Lord of the Rings?  And who can doubt the essential and eternal truths it first embodies and then expresses?  Who does not, at some point and to some extent, identify with each and every character in the tale?  Whether you be woman or man, you will sympathise with Eowyn in her dilemmas.  Also with Aragorn in his dangers and toils ; with Gandalf in his mighty hopes and fears.  And we can even identify with Sauron in his striving for mastery over all things both living and unliving.  And who needs reminding of hobbits?

In myth there is a hidden power.  It is the power to stir those obscured thoughts that come to the light of consciousness only when stimulated by some mysterious power that is latent in the very words we use.  If myth were mere fantasy then our rational minds would dismiss it on first sight, and by this stage of our evolution, myth would simply not exist.  But, although a myth may contain elements of fantasy, it is not those elements which stick in our minds and touch our hearts.  And that is why true myths are ageless and enduring.  That is why they adhere to our language.  That is why all successful novels are based on traditional myths.  That is why myths appear and reappear in all our arts and sciences.

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Truth, beauty and necessity

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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The Truth is out there … really

Man is a truth-seeking creature.  How’s that for a statement of belief?  And it is a statement of belief ; for there is no proof of it.  And yet I have come across very few people who do not believe it, either explicitly or implicitly.  But what is Truth?  How often do we seriously consider that question?  For doesn’t it so often lead to a debate which has all the appearances of a mere fog of words?

So, one way or another, we tend to escape the fog and develop a handy argument which puts Truth into some kind of framework ; and from there we can explore further.  For me, such a handy framework came from one of my unofficial mentors, the physicist AN Whitehead.  He put it something like this:

When an individual regards an event or an object, he forms in his mind an Appearance of it.  This is how it appears to him.

If two people regard the same event, then each has his own Appearance of it.

If the two people cannot agree on what they have seen, then we have simply two Appearances to deal with.  But if they can agree, then they have reached a Truth about it.

For example, if two people see a small flock of birds fly by, they might each have the Appearance of  seven birds ; and since they agree on this figure, they are satisfied that they have discovered a Truth.

But suppose the flock is much greater in number?  One person might have the Appearance of fifty birds, and the other an Appearance of sixty.  Here, they have discovered no Truth ; each will say to the other, “My figure is true and yours is false.”

But, suppose the observers have doubts about what they have seen?  Then they might well agree on a compromise figure ; they might agree that there were fifty-five birds in the flock.  Thus, by negotiation, they have reached a Truth.

But note : this Truth of fifty-five birds is an opinion and not reality ; the truth has not told us how many birds were really there.  So, what is Reality?  Surely Reality is just itself, and not a matter of opinion ; and it is nonsense to ask whether it be true or false.

So, in this world wide and long, there are countless Appearances and many Truths.  But there is only one Reality – and we don’t know what that is.

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Just a thought

I know a nice lady, Mrs Bradshaw, who once had a real-life adventure. So my short account of her adventure begins like this : “Mrs Bradshaw pulled on her favourite green sweater, ran a comb through her hair, and stepped out of the house to go to her sister’s rather forbidding place in Reading”. This is exactly how it happened ; I was there and saw it. Indeed, I was there throughout her adventure, and recorded all of it.

But, in my desire to protect her privacy, I decide to change some details. My account now begins : “Mrs Mason pulled on her favourite black sweater, ran a comb through her hair, and stepped out of the house to go to her sister’s rather forbidding place in Bracknell“. The question now arises, Have I told lies? Will my account of Mrs Bradshaw’s adventure be accurate? Is it believable any more? Can I be regarded as a reliable reporter?

Most people would argue that no lie has been told, provided the purpose of the story is merely to relate the substance of the adventure. In this case, the names and other details do not matter. For Mrs Bradshaw, we may read Mrs Everywoman. Or even Mr Everyman. So, now I have produced a work of fiction which is also a work of truth.

But, suppose the adventure which I am relating does not have a satisfying ‘ring’ to it? Suppose it does not quite capture the spirit of Mrs Bradshaw? Suppose that, on the day of the actual adventure, she is feeling a little below par, and is not quite herself ; and, as a result, she is not acting as the mighty heroine I know her to be? Would I be justified in recalling an earlier event (which I witnessed) that showed her in her true colours – and working that event into my story? Now I have deepened the fiction ; but am I still being truthful?

What I seem to be constructing here is not lies, but an account of the nature of Mrs Bradshaw ; the focus is now on her personality as well as her adventure – but much more on her personality. And, since my memories and my reason lead me to suppose that most women could handle the adventure with the skill and heroism of Mrs Bradshaw, I am narrating not a mere lie, not a mere fiction, not a mere fantasy ; I am constructing a myth. For a myth is a narrative that is founded on disciplined observation and disciplined imagination ; it is also somewhat idealized. A myth does not necessarily tell the truth, but it reveals a truth within the mind of the reader. It opens the reader’s mind, if not to the facts, then to the possibilities.

We all love myths, so let there be more of them.

So to the anthropologist who discovers a small number of stones lying a little below the surface of the ground. By exercising a disciplined observation, he surmises that these stones somewhat resemble real bones that he has seen in a modern skeleton ; he therefore exercises a disciplined imagination to conclude that these stones were moulded to the shapes of the bones of a human-like being. Further disciplined observations and imaginings lead him to conclude that the imagined bones are one hundred thousand years old. Yet more laborious observations and imaginings lead to the proposition that the long-dead creature walked upright, had a dark skin and black hair ; also brown eyes seem appropriate to his personality. And, why not give him a name? Phillip will do.

But, surely, isn’t this mere fiction? No such person ever existed. What modern anthropologist was present to record these details one hundred thousand years ago? The anthropologist’s narrative is almost all an imaginative disciplined construction. Lies? Deceit?

No. It is much more interesting than that. What we have is a myth. And a very good one it is, too ; for it holds our imaginations captive and enlightens us, if not to the facts, then to certain principles and to certain possibilities.

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The wellspring of forgiveness

How well you knew me, faithful friend,
Before you even knew
Precisely what my conscience bore
And how my heart did flag.

No word you spoke before your eye
Had pierced my aching soul ;
The sword of truth had made its mark,
And this you knew full well.

What fool I was to make believe
My secret could be hid
From one so great with second sight ;
Who sensed the hurt I did.

As we embraced I, too, did feel,
But in a different way ;
I felt that power flow to me,
Your gift that made me graced.

Forgiveness, sure, bestowed on me,
It undeserved and kind ;
And more, much more, received I then ;
For love undoes all sin.

In silence (for no word of mine
Would you allow intrude)
We ate our meal in memory
Of Him who set me free.

And even then your heart let slip
A truth I’d never guessed :
You too had known the pain I bore ;
Your ransom, too, had been full-paid.

Jamie MacNab

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