Category Archives: Poetry

On Chapman’s Homer’s Iliad, Book XIV

Index to this series | Text of Chapman’s Homer’s Iliad

When Neptune was helping the Greeks stave off certain defeat, I tried to suggest that divine intervention in the course of events might be understood as human resolve to change that course. This was in Book XIII of the Iliad, where Neptune took the form of one of the Greeks—Calchas—in order to exhort the others. They would have listened to Calchas anyway; he was a prophet. Ajax Oileus said he could tell Calchas was “really” a god; we can read this to mean Calchas was inspiring. We can say this of somebody today, without meaning to suggest any supernatural influence.

Continue reading

On Chapman’s Homer’s Iliad, Book XIII

Index to this series | Text of Chapman’s Homer’s Iliad

Usually when your defenses are breached, you are lost. Thus when the Ottoman Turks under Mehmet I found a way through the Theodosian Walls on Tuesday morning, May 29, 1453, the city of Constantinople was theirs.

Now the Trojans under Hector have breached the wall around the Greek ships, and—the ships are not theirs. How does Homer explain this?

Continue reading

NL XXVIII: The Forms of Political Action

Index to this series

Executive summary (added September 12, 2018), To condemn political discussion is to wish for tyranny: this continues a thought from the previous chapter. The ruling class need not share their deliberations with the ruled class, but it is better if they do. As our understanding of the reason for an action evolves—at first the action is merely useful, but later it conforms to a rule—, so ruling, originally by decree, has evolved to include legislation. However, to be enforced, law does not require a formal structure; international law is an example. The best reason for an action is duty. Though the German Treitschke says our highest duty is to the state, he gives the state no duty, and so his politics are entirely utilitarian.

In Plato’s Republic, Socrates seeks understanding of the just human being through examination of the just state. In Collingwood’s New Leviathan, the order is reversed. What we first considered in somebody, we now look at in the “body politic.”

Narthex of the former Taksiyarhis Church (now museum), Ayvalık, Balıkesir, Turkey, August 30, 2018

Continue reading

On Chapman’s Homer’s Iliad, Book XII

Index to this series | Text of Chapman’s Homer’s Iliad

Both first and last place may be prominent in a narrative. Occurring three-quarters of the way into Book XII of the Iliad, but presented last below, Sarpedon’s great speech on leadership ought to be known by everybody with authority and power.

Continue reading

On Chapman’s Homer’s Iliad, Book XI

Index to this series | Text of Chapman’s Homer’s Iliad

After the active night of Book X comes the dawn of a thrilling day.

  1. AVrora, out of restfull bed, did from bright Tython rise,
  2. To bring each deathlesse essence light, and vse, to mortall eyes.

The deathless essence called Jove sends Discord to the Greeks. She lights on the ship of Ulysses, in the middle of the fleet, so all can hear as she belts out her “Orthian song.”

  1. And presently was bitter warre, more sweet a thousand times
  2. Then any choice in hollow keeles, to greet their natiu climes.

The sweetness of war is the theme of the book. Continue reading

On Chapman’s Homer’s Iliad, Book X

Index to this series | Text of Chapman’s Homer’s Iliad

In Book X of the Iliad, Diomedes and Ulysses go to spy on the Trojan camp at night. When they return to the Greek camp,

  1. Then entred they the meere maine sea, to cleanse their honord sweate
  2. From off their feet, their thighes and neckes…

I can enter the same sea now. After more than ten months, I return to my reading of Homer, and Chapman’s Homer, as I have returned to the place where I was doing it last year, on the Aegean coast opposite Lesbos, after the sweat-soaked struggle of—teaching in the Nesin Mathematics Village, south of here, in the hills above Ephesus.

Continue reading


Executive summary (added October 6, 2018). Historian Niall Ferguson praises Collingwood as a philosopher of history, while showing no sign of understanding Collingwood’s actual philosophy. This provokes me. My comments are in the following sections.

By Collingwood’s account, there is a science of our absolute presuppositions, be these in natural science or in politics. The science of absolute presuppositions is metaphysics, and it is an historical science, because absolute presuppositions do change with time.
The historian’s job is to know the thoughts of the past. Leo Strauss disagrees with Collingwood over how one goes about this; but he would seem to agree with Collingwood that what is to be known is thought, as distinct from feeling.
I know of three examples of failures to understand Collingwood (Niall Ferguson provides a fourth).
Ferguson reviews a book in which twenty historians try to recover the feeling of certain historical events. By saying that for Collingwood, “the historian was limited to reconstructing recorded thoughts,” Ferguson errs in two ways.

  1. Those thoughts need not be “recorded,” but anything can be used as evidence for a thought, if one knows how to use it.
  2. Feelings from the past can come down to us, only if they have been converted to thoughts.

See also “The Ambiguity of Feeling.”

To know whether “an individual act altered the course of history,” Ferguson does recognize that we need to know more than past feelings. For him, “We need to imagine what would’ve happened if the act in question had not happened.” However, we cannot say where any particular thought is going to go, until we see where it does go, by thinking it. In this sense, every thought alters the course of history. Neither then can we say where a thought would have gone. In this way, history is different from natural science.


A theme of my last two articles here (namely “What It Takes” and, before that, “Effectiveness”) is the value of metaphysics, as being concerned with such problems as the following:

  • Physics has not been able to reconcile its theories of the infinitesimally small and the infinitely large.
  • America has not been able, in the words of Martin Luther King, to live out the true meaning of its creed, that all of us are created equal.

In a technical sense, these problems may not belong to natural science or political science as such. Considered as diseases, whether of the body politic or of the “body scientific,” the problems may not be curable, either by the body’s own immune system, or by remedies from outside. What is needed may be something resembling psychoanalysis, so to speak, or what Collingwood actually calls metaphysical analysis. This is an examination of absolute presuppositions, or the fundamental assumptions that have heretofore been left unquestioned. The analyst—the metaphysician—may suspect what those assumptions are; but the patient must confirm the suspicion, or else discover the assumptions independently. In any case, the patient will not be cured without agreeing that there is a disease.

Cures do happen, because absolute presuppositions change. Continue reading



First published May 17, 2018, this essay concerns Eugene Wigner’s 1960 article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.” I wrote a lot, which I now propose to summarize by section. (The meditations also continue in the next article.)

  • Some things are miraculous. Among Wigner’s examples are
    • that mathematics is possible at all, and
    • that “regularities” in the physical world can be discovered, as by Galileo and Newton.

    For Wigner, we should be grateful for the undeserved gift of a mathematial formulation of the laws of physics. This makes no sense theologically—and here I agree with the character Larry Darrell in Somerset Maugham’s novel The Razor’s Edge. Wigner’s idea that our mathematical reasoning power has been brought to perfection makes no sense to me either.

  • Everything is miraculous. Here I agree with Collingwood in Religion and Philosophy. A miracle cannot be the breaking of a natural law, since such a thing cannot be broken. A great artist like Beethoven follows no rules in the first place, or makes them up as he goes along; and he is like God in this way.
  • Natural law. That it cannot be broken is part of the very concept of natural law. Quantum phenomena and the theory of relativity have not in fact been brought under a single law; for Wigner, it may not be possible.
  • Mystery. Not only can we not define miracles, but (as we should have observed in the first place) we cannot even say when they happen. If like Wigner we call something miraculous, this means it cleanses our own doors of perception, in the sense of William Blake.
  • Definitions. In his treatment of miracle in Religion and Philosophy, Collingwood shows the futility of trying to define a term when you are not sure how to use it. He makes this futility explicit in The Principles of Art. If we are going to think about the use of mathematics in natural science, this means we ought to be mathematician, natural scientist, and philosopher; and not just “natural scientist,” but physicist and biologist, since if mathematics is effective in physics, it would seem to be ineffective in biology.
  • Being a philosopher. We are all philosophers, in the sense that Maugham describes in the story “Appearance and Reality,” if only we think. All thought is for the sake of action. This does not mean that thought occurs separately from an action and is to be judged by the action. We may value “pure” thought, such as doing mathematics or making music or living the contemplative life of a monk. This however moves me to a give a thought to the disaster of contemporary politics.
  • Philosophizing about science. For present purposes, compart­ment­al­ization of knowledge is a problem. So is the dominance of analytic philosophy, for suggesting (as one cited person seems to think) that big problems can be broken into little ones and solved independently. In mathematics, students should learn their right to question somebody else’s solutions to problems. In philosophy, the problems themselves will be our own. Philosophy as such cannot decide what the problems of physics or biology are, though it may help to understand the “absolute presuppositions” that underlie the problems. Philosophers quâ metaphysicians cannot determine once for all what the general structure of the universe is. This does not mean they should do “experimental philosophy,” taking opinion polls about supposedly philosophical questions. What matters is not what people say, but what they mean and are trying to mean. As Collingwood observes, metaphysics is an historical science.

For more on the last points, see a more recent article, “Re-enactment.” (This Preface added June 3, 2018.)

I am writing from the Math Village, and here I happen to have read that Abraham Lincoln kept no known diary as such, but noted his thoughts on loose slips of paper. Admired because he “could simply sit down and write another of his eloquent public letters,”

Lincoln demurred. “I had it nearly all in there,” he said, pointing to an open desk drawer. “It was in disconnected thoughts, which I had jotted down from time to time on separate scraps of paper.” This was how he worked, the president explained. It was on such scraps of paper, accumulating over the years into a diaristic density, that Lincoln saved and assembled what he described to the visitor as his “best thoughts on the subject.”

Thus Ronald C. White, “Notes to Self,” Harper’s, February 2018. My own notes to self are normally in bound notebooks, and perhaps later in blog articles such as the present one, which is inspired by the 1960 article called “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” by Eugene Wigner.
Continue reading

The Tree of Life

My two recent courses at the Nesin Mathematics Village had a common theme. I want to describe the theme here, as simply as I can—I mean, by using as little technical knowledge of mathematics as I can. But I shall talk also about related poetry and philosophy, of T. S. Eliot and R. G. Collingwood respectively.

An elaborate binary tree, with spirals

Continue reading

Some Say Poetry

Potted palms with plaster farm animals on hillside behind

Kuzguncuk, 2017.11.05

I originally set out to preserve here, for future reference, a poetry review that I liked. A remark on being a student had drawn my attention:

In My Poets, a work of autobiographical criticism with occasional ventriloquial interludes, McLane recalls two “early impasses in reading,” freshman-year encounters with Charles Olson and Frank O’Hara. She writes about not “getting it” but wanting to get it, about a desire to get it that was left wanting by code-breaking and analysis and satisfied by hearing and feeling.

I shall try to say more about learning and creating, in poetry and also in mathematics, after quoting the review in its entirety. It constitutes the second half of a “New Books” column by Christine Smallwood, in the Reviews section of Harper’s, July 2017.

Continue reading