College Mathematics: The Unteachable, Or Untaught?

by Ron Penner

I obtained a degree in Mathematics, so became somewhat familiar with the way it was taught and of the difficulties it seemed to engender in many others. These experiences prompted a series of problems which I later attempted to unravel, along with other related issues, which I now propose to explore.

I was often appalled and somewhat amazed at the manner in which these courses were taught, especially at the 100 and 200 level. There was so much verbage written on a blackboard or overhead projector which appeared to me to be pointless, albeit somewhat conventional. But later I began to muse, 'how can these subjects effectively be taught' and I began to appreciate the difficulties the professors experienced. I hypothesized that they had learnt and experienced Mathematics in a way far different from most of their students and that the gap was far too wide to be bridged by any conventional pedagogical methodology

What was this exprience of learning that they and many Math majors had and others did not seem to possess? The most basic was to regard this level of Mathematics, in most of its enormous diversity, as a language, a symbolic language that needed to be learnt and used. But it was much more sensitive to how much one took in at a glance, or alternatively how quickly one read that language, than learning to read one's native language, for this is much more akin to pattern recognition of an ungerlying logic, than to reading as it is usually understood. There seemed to me to be a minimum speed of assimilation that was requisite to fully grasp these concepts and courses, and that that was an aptitude that could hardly be taught. Another was an appreciation for the elegance of the reasoning entailed, and even the elegance of the notation. And finally, there was the ability and need, to generalize, to not be content with a theorem or lemma or definition until you had expanded these, until you had discovered as many of their extensions and further implications as possible. All of this was a mind-set that one either possessed or did not possess, although these are always matters of degree, but how does one teach a mind-set that is innate in some and absent in others? This is a very difficult question, and I am not sure that there really is an adequate answer to it.

I also found that I was very sensitive to the way such subjects were set forth on the page, and rummaged through the library until I found the most elegant text---seldom the one that was prescribed for the course. For if Bertrand Russell stated 'that there is no such thing as ugly Mathematics,' that did not preclude many ugly or less than elegant textbooks. And in the Physical Sciences, in particular, the ratio between written text or explanation and mathematical formulae was important to me, so that if one could follow the text simply by following the logical development of the mathematics, that always seemed something that was desirable. These I take to possibly be limited strategems to bridge the chasm I previously adumbrated. Of course, this dictum applies to any study, but particularly to Mathematics and to a slightly lesser extent the Physical Sciences, 'Never be content, initially, with the text that is assigned.' Then there is the appreciation of rigour of analysis. In an introductory course on Differential Equations, there was a text I always will value and esteem because it was so beautifully written and rigorous, which equated to greater simplicity and ease of comprehension. But one day I heard an acquaintance refer to this text as "the yellow peril"---it had a yellow cover---and that all of the students in his class detested it, and I was amazed and at a loss for words. Rigour of analysis, I mournfully concluded must not be an easily acquired taste. There is also the width of generalization of a particular approach which gives joy to that phenomena when it occurs. In trigonometry, the double and multiple angle formulae seem to bear no intimate relationship to one another. Then one discovers complex numbers and their utility, i.e. e to the i-theta power and the whole subject opens up and much greater vistas appear. I will always remember discovering, quite on my own, the Gamma and Beta Integrals. and the joy in discovering how many integrals could be fitted into these two basic structures simply through simple changes of variables.

But there are deep differences of aptitude and approach even among math majors themselves, perhaps greater than in any other discipline. There are those who excel in reading and comprehending and using the symbolisms, of which Algebra would be the prototype, and those who are far more spacially oriented, of which the Geometries serves as the prototype. I once heard of an experiment in teaching beginning college Mathematics at a private school for the gifted in Seattle. The material had been presented from an essentially algebraic prespective, when suddenly, in the middle of the course, it was taught from an essentially geometric perspective. And suddenly the class standing tipped over, becoming almost the exact opposite of what it had been. The geometric approach can greatly simplify many areas, but there are vast stretches of Mathematics for which there is no effective substitute for symbolic tranformations and manipulations. There is one further division which is the least recognized, but has increasingly become vital in more recent years. This involves a gift for, and love of, abstraction, for its own sake. This can also involve a love of getting at the fundaments of a subject. For lack of a better term, this might be called the Axiomatic Approach. Abstract Algebra can serve as its prototype and an n-dimensional cohomology group could serve as an example. Those gifted with this approach or aptitude will tend to have a better grasp of the whole of Mathematics, at least in outline form, and be the ones most likely to achieve some of the syntheses modern Mathematics desperately needs.

But I cannot leave this article so bleak and not attempt some remedies to the difficulties posed, some way of bridging these gaps for those not disposed to Mathematics in general. There are certain moments in the life of learning where one enters, in something approaching a Piagetian sense, a totally new domain. I believe one should, in many cases, pause and survey what lies ahead, emphasizing the great power and utility of the new approach, as well as some of the anticipated difficulties and how they may be overcome, rather than proceeding linearly to cover a prescribed curricula. One such branching point would surely be the point at which variables are first introduced to stand for any number within a specified domain. Also it might help if this introduction was combined with a sense that one was entering upon a new phase of mental maturity and growth. Then there are spectacular spurts in intellectual growth which can change and redirect one's whole life, and these need to be recognized and provided for. In his book, "Disturbing The Universe," Freeman Dyson briefly described an incident that occurred when he was ten years old. He purchased a book on the Differential and Integral Calculus about 700 pages in length, and when the family went for a winter retreat at Christmas break on the east coast of England just prior to World War II, he studied the work and did all of the problems for about ten hours a day, ten days to two weeks. I have always assumed since I read this, that if this or a similar experience had not occurred at about this stage, we would never have heard of Freeman Dyson. I had a similar experience, much later in life with the Calculus in an October retreat in Moclips---also on the ocean---after a summer as a forest lookout. The only way these experiences can be accomodated in colleges and universities, for those who need and are prone to them, in my opinion, is through a liberal, tutorial approach where one can design when and how to study a specific topic or field within a discipline. Someday psychometric tests may be devised to identify these individuals before they begin to enter college. But there are many instances in which courses tailored to specific disciplines such as Physics, Chemistry, the Life Siences and the Social Sciences are specially designed for the needs of these majors. This essentially involves applied Mathematics, in which a major aspect is to understand why certain formulae give a correct description of the phenomena they model, as well as how they can most effectively be used. This is far more than simply providing a list of relevant formulae and gives 'value added' rather than a 'cookbook approach.' And especially in the Social Sciences, Statistics must be taught to clearly delineate both the strenghs and limitations or various approaches. There is perhaps a great need for mathematicians to act as a kind of academic policeman and interfere in any department of the University when they feel that their subject is being misused or trivialized. But they must also, in such courses, teach others to---and demand that they--- think for themselves. They are not meant---and do not see themselves---as a service agency for the solution of problems in Mathematics, others in the university and society as a whole, find difficult to solve on their own. Finally, the Computer Sciences have taken over part of the former function of Mathematics in providing algorithms which encompass in their generality, almost all disciplines, and, in some sense, have replaced Mathematics, as the premier discipline for all of the other sciences---and this is wellcome.

My Senecan ramble must come to a close, hoping that it has not been too disjointed or too obvious.

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"As I Walked Out One Evening"

A Walk

by Ron Penner

W. H. Auden

This poem, by Wystan Hugh Auden I have known for years and always considered it to be one of the most remarkable of poems, written in the English language in the twentieth century. There were always images in it that eluded me as to their origin, and still do, but the magic, the word magic of the poem was such that this did not matter. They all seemed right, even as I could not say why and this made the poem even more magical and wondrous. Then one insomniac night in January, I determined to wrestle with this poem, to analyze it as far as possible and extract its deeper meaning and the source of its unforgettable appeal. But I misremembered much of it, so I reread it the next morning and began refining a coherent interpretation that could do some measure of justice to this great work. The interpretation lies not on the surface and would not be evident, I believe, to a casual reader of the poem, and I thought that perhaps this type of analysis might be of some interest. I recall a television program on Auden long ago in which he walked out of his house into his Bentley and drove off, all the while nonchalantly reciting this poem. I thought, he could have chosen from among scores of his poems for this charade, but he chose this one. Ergo, one of the greatest poets of the century chose this poem as possibly his best work. For future reference, the poem is included in full on the next page.

Several assumptions need to be made. There may be several levels of interpretation of a poem; to seek the deepest one is, I would argue, to also seek the most internally consistent, and this latter has been my aim. I take it for granted that the poem means what its author intended. Deconstructing a poem or any work of literature is akin to an attempt to cure a patient by an operation to rearrange bodily organs. The patient dies! And if the creators take this seriously, nothing but trivia remains. I assume that all imagery in the poem ultimately relates to evolving mental and spiritual states that progress from a wild, headless Romanticism to a deep understanding and acceptance of Reality with Time serving metaphorically as a mediator. And if this poem is about changing inner realities, the lover and lovers of the poem must arise from that inner reality and not be independent of it. Whether this poem is autobiographical in nature or an Everyman poem, I do not know. I suspect that it is neither, but refers to the Artistic Age in which Auden fully participated, ending with the sobering and somber realities and realizations of World War II. In support of this as addressing his own between-the-wars' generation one can quote a famous, earlier concluding stanza from "September 1, 1939." (See previous page.) These lines suggest, not so much a refusal to accept reality as an isolation from reality, although both I believe are present, and thus make the "lover's song"---the poem is actually titled "Song: As I Walked Out One Evening"---more understandable. For lovers, in the deepest moments of their romance, can be almost oblivious to all else the is going on around them. This should then be considered, I believe, as transferred to the generation between the wars, the generation which slept through history, with all the tragedy that that ultimately entailed. Just as Romeo and Juliet seemed perfectly oblivious to the problems that they were causing their respective families and the entire city of Verona.

As I Walked One Evening

by W. H. Auden

As I walked out one evening,
     Walking down Bristol Street,
The crowds upon the pavement
     Were fields of harvest wheat.

And down by the brimming river
     I heard a lover sing
Under the arch of the railway
     "Love has no ending.

I'll love you, dear, I'll love you
     Till China and Africa meet
And the river jumps over the mountain
     And salmon sing in the street.

I'll love you till the ocean
     Is folded and hung up to dry
And the seven stars go squawking
     Like geese about the sky.

The years shall run like rabbits
     For in my arms I hold
The Flower of the Ages
     And the first love of the World."

But all the clocks in the city
     Began to whirr and chime:
"O let not Time deceive you,
     You cannot conquer Time."

In the burrows of the Nightmare
     Where Justice naked is,
Time watches from the shadow
     And coughs when you would kiss.

In headaches and in worry
     Vaguely life leaks away,
And Time will have his fancy
     To-morrow or today.

Into many a green valley
     Drifts the appalling snow;
Time breaks the threaded dances
     And the diver's brilliant bow.

The glacier knocks in the cupboard,
     The desert sighs in the bed,
And the crack in the tea-cup opens
     A lane to the land of the dead.

Where the beggars raffle the banknotes
     And the Giant is enchanting to Jack,
And the Lily-white boy is a Roarer
     And Jill goes down on her back.

O plunge your hands in water,
     Plunge them in up to the wrist;
Stare, stare in the basin
     And wonder what you've missed.

O look, look in the mirror,
     O look in your distress;
Life remains a blessing
     Although you cannot bless.

O stand, stand at the window
     As the tears scald and start;
You shall love your crooked neighbour
     With your crooked heart."

It was late, late in the evening,
     The lovers they were gone;
The clocks had ceased their chiming
     And the deep river ran on.

---

September 1, 1939

by W. H. Auden

Faces along the bar
     Cling to the average day:
The lights must never go out,
     The music must always play,
All the conventions conspire
     To make this fort assume
The furniture of home;
     Lest we should see where we are,
Lost in a haunted wood,
     Children afraid of the night
Who have never been happy or good.

There are two long quotations in the poem of about equal length, but they are totally different. The first, with a headlong romanticism, treats Reality as whatever you choose or want it to be; the second is a painful coming to terms with Reality and with the wisdom that is thereby gained. The first is symbolized by the brimming river, about to overflow its banks and leave havoc and destruction in its wake and the deep river, no longer a threat but useful to all Mankind. And the second quotation not only delineates painful aspects of Reality which must be accepted, but delineates three stages of spiritual regeneration necessary for the deep wisdom of the deep river to "flow on." Finally, that the poem seems to encapsulate the experiences of a lifetime, yet only a few moments had passed - "the clocks had ceased their chiming" - and that this sense, does or should add an element of depth to the poem which lifts it far beyond the ordinary. Auden was a meteor of his generation, a satirical and despairing poet of his Age who yet wrote the conclusion of "In Memory of W. B. Yeats."

With the farming of a verse
     Make a vineyard of the curse,
Sing of human unsuccess
     In a rapture of distress;

In the deserts of the heart
     Let the healing fountain start,
In the prison of his days
     Teach the free man how to praise."

If this poem is, to some extent, autobiographical, it traces that evolution. Now to a brief review and comment upon some of the lines of the poem. The poem begins with the most arresting and extraordinary image; the prosaic Bristol Street upon which were a crowd that was "a field of harvest wheat." How does that opening image serve the poem as a whole? First, it serves to signal to the reader that this is no ordinary poem. But the image stands alone, and it is the only one that can definitely be ascribed to the one who is experiencing this journey of the spirit, everything else could be ascribed to the lover and "all the clocks in the city" or to Time itself. So what does it portend? This is a hallucination of a kind that might be induced by a rare and benign LSD trip. This is intended to herald that the first quote deals with Unreality and the effort of the mind to create its own Reality and the destructive consequences of that, no matter how lovely they may appear. The lover's 'song' knows no limits and creates an impossible Universe and Time thunders its rebuke, despite the nobility of his intentions. Those two lines: "But all the clocks in the city began to whirr and chime:" First, prosaically, one cannot possibly hear "all the clocks in the city" and this poem is experiential. This indicates both an illusory state of mind and a heightened sense of perception. "Whirr and chime?" Whirr signifying disorder, chime signifying order in three words and one perception seems to presage a divided Mind which perceives opposites as a whole, but without synthesis.

Suddenly everything changes, very abruptly. That thundering proclamation: "O let not Time deceive you, You cannot conquer Time." intervenes and severs the poem into two parts. I remember a Shakespearean scholar once saying that whenever you see, in reading, time capitalized by Shakespeare, you should pause and reflect, for he always then has something profound to impart. I imagine Auden remembering that when he wrote these lines. Yet here time is capitalized not once, but four times in the short space of a few lines. Is this an excess of profundity? profundity running amok? profundity on holiday? I think not, for Time itself has its lessons to teach and part of coming to terms with Reality, in the first part of the second quotation is coming to terms with time. And when you capitalize time, you are not referring to quotidian time, but to eternal time or something akin to it. Thus in this very subtle way he introduces questions of the Ultimate, for I imagine that the last thing Auden wanted to be considered was another Eliot.

Then follow three stanzas of negative aspects of Reality that this life must come to terms with. The first is disillusionment, the second dissipation, and lastly sorrow and loss. Consider the second and its second line, "Vaguely life leaks away."

"The sound must echo of the sense" wrote Pope, and this line magnificently fulfills that dictum through the velocity of language, i. e., 'vaguely life leeeeaks awway.' The line slows to an appropriate crawl. And, "You cannot conquer Time." and "Time will have its fancy..." There are many realities, many events you cannot control, unlike your attempts to control it through you own recreation of it. I must pause to note those marvelously evocative two lines:

"Into many a green valley drifts the appalling snow."(Let them stand without comment.) And Time even brings to an end Siva's many dances. The next two stanzas introduce real Evil and dread. The second stanza is curious but very effective, for it introduces evil from English nursery rhymes, thus evil hiding under a thin veneer of innocence, a sugarcoated evil which makes it all the more nightmarish.

After all of these negative aspects of reality that must be accepted for growth to occur comes tasks for spiritual regeneration. In three brief stanzas, three stages of such a regenerative process are limned. The first involves cleansing, the second unflinching self-examination, the third a deep measure of regret. Consider how strongly the second line of both the first and second stanzas reinforces the first lines. "O plunge your hands in water, Plunge them up to the wrist." "O look, look in the mirror, O look in your distress."

Then comes that lofty yet down to earth denouement, all so unexpected: "You shall love your crooked neighbour with your crooked heart." By twice using the adjective 'crooked' Auden escapes from any charge of didacticism or pious moralizing and ends the second quotation on Reality with an uncompromising adjective, twice given. But as with any such valid moral injunction, it extends beyond itself to alter whatever it touches, thus these two denouement lines can be read as branching out to all of the ethical life of Man.

The final stanza says more, I believe, than any of the others. Each line has a significant message to tell and each integrates with the rest of the poem. "It was late, late in the evening."

It was late in life when this evolution or series of transformations began and ultimately were realized. Perhaps it is always late, or seems so. "The lovers they were gone:"

This is the most complex line to interpret, and I do not want the interpretation to seem forced, so I would only ask that it be considered only in the light of all the rest. I wrote at the beginning that this was a poem of only a unitary consciousness, that the images were ultimately intended to indicate mental and spiritual states and stages of growth and evolution. If this be so, then there can be no outside voices, they all come from within one consciousness. Then, the lover who speaks the first quote is part of that unitary consciousness. But lovers?! Yes, for this symbolizes or indicates a divided self, the divided self of the first part of the poem. The reception of that speech is divided from the speech itself. That self was badly fractured and a significant part of the growth and healing of the second part of the poem, though unstated, was the unification of that self. But the "lovers... were gone." 'Gone' has a finality to it meant to imply that that aspect of the self had not just been transformed, it had died. "The clocks had ceases their chiming." How long does it take clocks to chime? What seemed like half a lifetime had passed in only a few moments. "And the deep river ran on." The river of life which this represents, was now a very different river from the brimming river of the first part of the poem. Now it was on an altogether different plane, secure within its banks, its depth signifying all the hard won wisdom that had been gained, a benefit and no longer a threat to the plain, flowing securely on to eventually join the ocean. But all that the ocean implies lies beyond the scope of this poem, for it is not spoken of, therefore neither shall I speak of it.

Thus the central problem of this poem is how to account for the sudden need for repentance and atonement, for regeneration and reform which so dramatically and suddenly divides this poem into two parts. Some might say that I have been grasping at straws. I would reply that I have been grasping, but only for any clues and interpretations from the poem that might provide a holistic and well-rounded rationale for those needs.

The author and his friend Bob Seitz converse

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The Senecan Ramble

by Ron Penner

Let us, for a moment, seriously consider the Senecan ramble; it flourished for a period in English literature, especially in essays, so it must have much to recommend itself. I have guessed -- merely guessed -- that some may not write because they feel that they ought to write about only one subject at a time with internal consistency throughout. I would hope to be among the last to denigrate this, but why should not a Senecan ramble -- a series of loosely connected insights and/or observations with no central theme be equally valued if the quality of thought therein were of equal value with more tightly organized writing? As one would go for a walk in the country and comment upon what one saw with no predetermined plan in mind, so one could gather together the treasured insights of a month into a ramble for the edification of us all. And as this is about the Senecan ramble, I intend herein to ramble. (One will notice little connection between the first paragraph and the second.)

One poem that I have always remembered and ever shall is "The Soul and Body of John Brown" by Muriel Rukeyser, subtitled, "Multitudes, multitudes in the valley of decision!" from the book of Joel. The poem, in a most profound way, attempts to recapture to experience of a nation in the summer of 1940, still dazed by the Depression and bewilderingly trying to face a future of awesome responsibilities and global effort, of massive deaths and sufferings. The poem, which I highly recommend, is a highly complex interweaving of strands and a magnificent ramble! I will quote one stanza which, in its own way, sums up the entire poem and which I have always regarded as one of the most evocative and memorable in all of the English literature encountered in a lifetime.

"White landscapes emphasize his nakedness
reflected in countries of naked who shiver and stare at fires,
their backs to the face that unrolls new worlds around them.
--They go down the valleys. They shamble in the streets.
Blind to the sun-storming image echoed in their eyes.
--They dread the surface of their victim life,
lying helpless and savage in shade parks,
asking the towers only what beggars dare:
food, fire, water, and air."

We need not shamble, but we can ramble.

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The Man Who Died Twice

A Tribute

by Ron Penner

"The Man Who Died Twice" by Edwin Arlington Robinson is the most unforgettable poem I have ever read; the kind of poem which once read, remains with you for the rest of ones life. Nor, apparently, is this opinion unique to me, for it received the Pulitzer Prize for Poetry in 1925, his "Collected Works" —which in the book I have in front of me runs to 1488 pages — won the same prize in 1922.

The poem attempts what must be almost impossible, to make a character with the most improbable name of Fernando Nash come alive and be believable in a very long poem. For he was "meant" to be one of the Immortals of musical composition, to rank along with Bach, Beethoven, and Mozart, yet he never achieved this — his daimon. He destroyed his first two symphonies, and he died unknown, save for the narrator of the poem.

Robinson presaged this poem in three other poems that I am aware of. In "George Crabbe" a sonnet in honor of the 17th and 18th century English metaphysical poet he had written in the sestet:

From time to time the vigor of his name
Against us like a finger for the shame
And emptiness of what our souls reveal
In books that are as altars were we kneel
To consecrate the flicker, not the flame."

A younger E. A. Robinson

And in "Flammonde", the man who came to play the Prince of Castaways, he wrote these lines:

"Rarely at once will nature give
The power to be Flammonde and live."

And in "The Man Against the Sky" he catalogues all of the ways a man may meet an inevitable fate.

"Rarely at once will nature give
The power to be Flammonde and live."

What did Robinson mean by these lines and how do they provide a window into this poem. "The Man Who Died Twice," first to all died to the vast creative powers that were within him, and then died physically. When I was sixteen, a man whom I shall never forget came to direct the play "McBeth" and act as the character McDuff in the play for a private school I attended on Vancouver Island. The headmaster, in my opinion, used this man to publicize the school. He had taught there previously as a rest cure from alcoholism for two or three years, although I did not attend then. He would regularly scandalize much of the staff by his unorthodox behavior. I remember that I felt like shouting to them, 'Stop criticizing this man! What right have you to do so? Do you not have a conception of how difficult it is for Ian Thorne simply to be Ian Thorne?' But I must say that I never had the temerity to utter those words. For I sensed someone in whom searing fires of creativity were burning either to destruction or remarkable creativity. And although, thereafter, he wrote, directed and acted in major productions for the CBC and the BBC, the world barely knows of him, and I cannot but believe that for all of his attainments he ultimately failed to achieve his potential. And this is echoed in this poem in these lines:

"But there he shook his head
In hopeless pity — not for the doomed, I saw,
But rather for the sanguine ordinary
That has no devil and so controls itself,
Having nothing in especial to control."

How could Robinson possibly have made this character come alive and become believable, a being so remote from all the rest of humanity? Could he have faced a greater challenge? The answer is complex and various. First there is Robinson's almost flawless use of poetic diction and symbolic imagery and rhythm, although in this poem he creates a strange poetic imagery, all his own, of which you should only ask that it all coheres and attains to an integrated whole, which it does. (Robinson was never one to believe that the simplest word is best; he utilized the full diapason of the English language to remarkable effect.) To give but one tiny example:

"And he was too far sundered from his faith
And his ambition, buried somewhere together
Behind him to go stumbling back for them,
Only to find a shadowy grave that held
So little and so much."

"sundered", "stumbling back", "a shadowy grave". I would have to quote much more to really indicate why these are just the right words in the right place. Then in the middle of the poem there are a series a terrible maledictions which Fernando Nash hurls at himself until prevented from going further by sheer exhaustion. And as he lies dying, having not eaten in three weeks and barely able to move, a whole series of hallucinations and visions come over him in a titanic effort to perceive his final fate. There is no thought there, only experience from the depths of the Unconscious. And if there are hallucinations, it matters not, for they are milestones on a spiritual journey that knows the heights of ecstasy alternating with the depths of despair, the sublime and utter degradation. And they are holistic with their own internal logic. As when Mozart composed "Don Giovanni" or his "Requiem" did he pause at various stages to ask 'Now what comes next?' No! For such works would never have been written if he had not, somehow, seen them in their entirety from the beginning. Just so, Fernando Nash experiences his final hours as though a great work of Art were unfolding before him. He experiences a series of mystic visions of terrible intensity which seem natural to him but which are denied to all but the very few. Thus Robinson somehow makes this extraordinary character come alive. And I recall a televised review of the life and oeuvre of Ezra Pound in which the literary critic remarked that it was not enough to have arresting and glittering lines and phrases sparkle through his Cantos, but that he had to sustain it from the beginning to the very end, not to deviate or wander to any length from a sure path that he had set but to continually maintain the continuity of the whole. This Robinson also achieves in this poem.

MacDougal Alley, Greenwich Village where Robinson lived

And there is another element of his life that transcends ordinary human experience. He "knew" from boyhood that he was destined to write his Symphony Number Three, that would come down like 'choral fire from heaven to still those drums of death' and 'that thereafter all would be a toil of joy for Immortality' and the floodgates of his vast creative abilities would open and he would realize his daimon, if only he would wait. And, of course, not merely wait, but wait in a state akin to that of creative Grace. But he did not wait and the choral fire of that symphony never came until it was too late, and thus he failed himself and all Mankind for countless generations and the God who had given him this gift, for there is a religious element to this poem, but it never intrudes but only proceeds naturally from the narrative. But he does at last hear strains of that symphony in one of his last days and this is enough to reconcile himself to his fate, to know real peace, probably for the first time in his life and to die in peace after the destructive fires of his arrogance and disdain and greed for life had burnt away everything that was gross in him. For it has often been inferred that renunciation must always accompany true genius, and this he lacked or had an insufficiency of. Robinson describes that moment in only eight lines, thus:

"With blinding tears of praise and of exhaustion
Pouring out of his eyes and over his cheeks,
He groped and tottered into the dark hall,
Crying aloud to God, or man, or devil,
For paper — not for food. It may have been
The devil who heard him first and made of him.
For sport, the large and sprawling obstacle
They found there at the bottom of the stairs."

So the poem begins with Fernando Nash discovered after years of absence by the narrator:

"beating a bass drum
And shouting Hallelujah with a fervor
At which, as I remember, no man smiled."

He is, from the beginning, a ruined hulk of a man, or of a personality, seeming to be a maniac or megalomaniac, shouting "Glory to God, I had it — once!" But slowly the poem begins to surround you and to envelop you, and slowly you begin to see the vastness of the man and of the poem, and finally it overwhelms you. And a whole cathedral of images and symbols emerge — the drums of life, the drums of death, the daimon and the demon of genius, 'the grapes of heaven' which are golden grapes, 'and golden dregs which are the worst dregs of all' the choral fire, the messengers who came again and again and always found him absent, the leering symphony that seventy rats dressed in coat and tails performed for his unwilling ears, images of ruin and decay and self-immolation and finally a sublime clarity and peace.

Robinson upon Fernando Nash's demise has the narrator attempt to sum up his experience of him with these closing words:

"There was in the man,
With all his frailties and extravagances.
The caste of an inviolable distinction
That was to break and vanish only in fire
When other fires that had so long consumed him
Could find no more to burn; and there was in him
A giant's privacy of lone communion
With other giants who made a music
Whereof the world has not impossibly heard
Not the last note; and there was in him always,
Unqualified by guile and unsubdued
By failure and remorse, or by redemption,
The grim nostalgic passion of the great
For glory all but theirs. And more than these,
There was the nameless and authentic seal
Of power and of ordained accomplishment —
Which may not be infallibly forthcoming,
Yet in this instance came. So I believe,
And shall, till admonition more disastrous
Than any has yet imperiled it
Invalidates conviction. …
To be the giant of his acknowledgment.
Crippled and cursed and crucified, the giant
Was always there, and always will be there.
For reasons less concealed and more sufficient
Than words will ever make them, I believe him
Today as I believed him while he died,
And while I sank his ashes in the sea."

By now it should be clear that I have set myself an impossible task in attempting to render for you the essence of this poem. This poem may seem from what I have written, apart from being very confused, which it assuredly is not, dark and grim almost beyond endurance, yet it is a tragedy until the very end, and like all true tragedies, as Aristotle has assured us, purges with catharsis. This is a parable of the Talents told in strange and unfamiliar dress and with a terrible intensity. I fail to see how anyone who reads this poem slowly and meditatively, savoring every line, as one must, cannot fail to ask themselves, 'What was my daimon and how far have I wandered from it amidst the quotidian demands of life.

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