London is a walkable city. From time to time I have meetings at the London Mathematical Society’s headquarters, De Morgan House in Russell Square, Bloomsbury. I can walk there from my office in an hour and a few minutes.
An advantage of walking is that I know fairly exactly how long it is going to take. If I go by public transport, I have to allow for delays, and so usually arrive well ahead of time. But, even walking, I tend to allow plenty of time. So I usually arrive a few minutes early, and go into the gardens in the square to wait.
Just inside the gate nearest to De Morgan House is a young Irish yew, with a little plaque saying that it commemorates T. S. Eliot, and was placed there by the Indian High Commissioner in the United Kingdom, in the presence of the mayor of Camden and Eliot’s widow.
If you once read “The Waste Land”, this might seem an unlikely conjunction. But as it happens, Eliot’s Four Quartets has been one of my favourite works of poetry since I was a student. The poems contain several references to yew, and a section which is a meditation on Krishna’s words to Arjuna in the Bhagavad Gita.
Of course, a poem doesn’t have a single meaning, especially one as long and complex as Four Quartets. But to me the primary meaning of the poem is about the relationship between time and eternity, which is something maybe of interest to mathematicians as well as to mystics.
Curiously, the clearest explanation of what Eliot is saying that I have found is in a completely different work, Pilgrimage of Dreams by the artist Thetis Blacker, in which she describes a series of dreams she had which stood out as being completely different from the confusion of normal dreaming. In one of these dreams, “Mr Goad and the Cathedral”, we find the statements
“Eternity isn’t a long time”
“Eternity is always now, but …”
“Now isn’t always eternity”.
In other words, eternity is not the same as infinity; it is not the time line stretched out to infinity. Rather, it is an intimation of a different dimension, which we obtain only because we are aware of the point at which that dimension intersects the familiar dimension of time. In a recurring motif in the first Quartet, “Burnt Norton”, Eliot says,
Time present and time past
Are both somehow contained in time future
And time future contained in time past.
and, in “The Dry Salvages”,
… to apprehend
The point of intersection of the timeless
With time, is an occupation for the saint
I read this, as a student, at about the time that I was becoming aware that there were other world views than the Christian one I had been raised in; what Eliot said seemed closer to the Hindu and Buddhist views. And in the meditation on the Bhagavad Gita, he summarises Krishna’s message to Arjuna in similar terms:
Not farewell, but fare forward
In other words, our job is to deal with the present situation, not to regret the past or to agonise over what might come.
In England, although there are fine stands of yew trees on the North Downs and in other places, the tree is associated with graveyards; in this setting it lives to an enormous age and grows and spreads to an impressive size. Since it is evergreen, it has been assumed by many commentators that its presence in graveyards is as a symbol of immortality. But this is not quite what Eliot is saying when he refers to “chill fingers of yew”; it seems to symbolise death, not immortality. However, the knowledge that our destination is the churchyard under the yew-tree has been recognised as one of the best reminders to live in the present. Buddhist monks meditate in graveyards, and Carlos Castaneda’s Don Juan said “Use death as an adviser”.
Here to finish are two other interpretations of this theme: William Blake’s “Eternity”:
He who binds to himself a joy
Does the winged life destroy
But he who kisses the joy as it flies
Lives in eternity’s sun rise.
and Philip Larkin’s “Days”:
What are days for?
Days are where we live.
They come, they wake us
Time and time over.
They are to be happy in:
Where can we live but days?
Ah, solving that question
Brings the priest and the doctor
In their long coats
Running over the fields.
You can almost hear Krishna asking Arjuna, “Where can we live but days?”
Is it entirely far-fetched to suggest that the relation between a theorem and the discovery of its proof is similar to that between eternity and time?