Elliptical Affinity

April 17, 2019 – 2:21 pm

After Descartes gave geometry the power of algebra in 1637, a purely geometrical theorem of Apollonius that is both useful and beautiful was forgotten. This is what I conclude from looking at texts from the seventeenth century on.

In ellipse, colored triangles move to illustrate theorem Continue reading →

By David Pierce | Posted in Conic Sections, Descartes, Mathematics | Tagged , , , , , , , , | Comments (0)

We the Pears of the Wild Coyote Tree

April 15, 2019 – 9:12 pm

This is a preliminary report on two recent films:

  • The Wild Pear Tree, by Nuri Bilge Ceylan;
  • We the Coyotes, by Marco La Via and Hanna Ladoul.

The report is preliminary, not because there is going to be another, but because I have seen each film only once, and I may see one of them again. I remember that François Truffaut liked to see films at least twice. I would guess that I read this in The Washington Post, in an appreciation published when Truffaut died; however, he died on October 21, 1984, during the first semester of my sophomore year in Santa Fe, when I would not have been reading the Post. While in college, I did enjoy seeing some films twice, or a second time; Truffaut’s own 400 Coups was an example, a French teacher having shown it to us in high school.

The two films that I am reviewing concern young adults trying to find their own way in the world, in defiance of their elders. We all have to do this. In every generation, some will do it more defiantly than others. Heraclitus can be defiant, he of Ephesus and thus one of the Ionian philosophers, whose spirit I imagine to haunt the Nesin Mathematics Village. A further reason to bring up Heraclitus will be—gold.

Eva Brann, The Logos of Heraclitus, on Marmara Island, July, 2012

Continue reading →
By David Pierce | Posted in Uncategorized | Tagged , , , , , , , , , , | Comments (0)

Piety

March 14, 2019 – 9:33 pm

The post below is a way to record a passage in the Euthyphro where Socrates say something true and important about mathematics. The passage is on a list of Platonic passages that I recently found, having written it in a notebook on May 23, 2018. The other passages are in the Republic; Continue reading →

By David Pierce | Posted in Collingwood, Homer, Mathematics, Nesin Mathematics Village, New Leviathan, Philosophy, Plato, Strunk and White | Tagged , , , , , | Comments (1)

NL XLV: The Germans

February 21, 2019 – 9:14 am

Index to this series

At the end of Collingwood’s New Leviathan (1942), we reach a chapter whose theme is that of my more recent articles on grammar.

By August Macke – The Yorck Project (2002) 10.000 Meisterwerke der Malerei (DVD-ROM), distributed by DIRECTMEDIA Publishing GmbH. ISBN: 3936122202., Public Domain, Link

As history, Collingwood’s last chapter is difficult, for the reasons that trouble Herbert Read at the beginning of his Concise History of Modern Painting (revised 1968, augmented 1974). Read opens his first chapter with a passage from Collingwood’s Speculum Mentis (1924):

Continue reading →

By David Pierce | Posted in Education, Grammar, New Leviathan | Tagged , , | Comments (0)

NL XLIV: The Turks

February 20, 2019 – 7:47 am

Index to this series

The last part of Collingwood’s New Leviathan (Oxford, 1942) is “Barbarism.” The first chapter of the part is “What Barbarism Is”; the remaining chapters describe examples of barbarism in turn. The fourth and last example is the one that Britain is fighting as Collingwood writes.

Sun behind mosque on cover of The Ottoman Centuries (Lord Kinross, a.k.a. Patrick Balfour) Continue reading →

By David Pierce | Posted in History, New Leviathan, Turkey | Tagged , , , , | Comments (1)

A Defense

January 12, 2019 – 1:27 pm

Here is the defense (savunma) of Ayşe Berkman before the 36th Heavy Penalty Court (Ağır Ceza Mahkemesi) of Istanbul, January 10, 2019, against the charge of making propaganda for a terrorist organization (terör örgütü propagandası yapmak).

Crowd of mostly smiling people outside a courtroom

The crowd from the courtroom when the session was over.
From a tweet of the Peace Academics

Continue reading →

By David Pierce | Posted in Freedom, Turkey | Tagged | Comments (4)

Logic of Elliptic Curves

January 6, 2019 – 8:49 pm

In my 1997 doctoral dissertation, the main idea came as I was lying in bed one Sunday morning. Continue reading →

By David Pierce | Posted in Aristotle, Hitchens, Mathematics | Tagged , , , , | Comments (1)

On Gödel’s Incompleteness Theorem

December 15, 2018 – 8:43 am

This is an appreciation of Gödel’s Incompleteness Theorem of 1931. I am provoked by a depreciation of the theorem.

In the “Gödel for Dummies” version of the Theorem, there are mathematical sentences that are both true and unprovable. This requires two points of clarification. Continue reading →

By David Pierce | Posted in Categorical Thinking, Descartes, Euclid, Hitchens, Mathematics, Philosophy, Science | Tagged , , , , , , , , , , , , , , , , , , , , | Comments (6)

Antitheses

December 13, 2018 – 10:18 am

The Antitheses are the six parallel teachings, delivered by Jesus of Nazareth in the Sermon on the Mount, as recounted in Chapter 5 of the Gospel According to St Matthew, starting at verse 21. I summarize:

  1. Do not kill people; do not even get angry with them.
  2. Do not commit adultery; do not even fantasize about it.
  3. In divorce, follow the established procedure; do not even divorce.
  4. Do not forswear yourself; do not even swear.
  5. Keep retribution commensurate with the crime; do not even seek retribution.
  6. Love your neighbor; love even your enemy.

For better or worse, these are part of the cultural heritage of many of us; they are at least a commentary on the cultural heritage (the Mosaic Law) of more of us.

I write now specifically, because I think the Antitheses can illustrate or illuminate some contemporary philosophical concerns, Continue reading →

By David Pierce | Posted in Collingwood, Freedom, Galileo, New Leviathan, Philosophy, Science, Stoicism | Tagged , , , | Comments (10)

NL XLIII: The Second Barbarism: The ‘Albigensian Heresy’

October 13, 2018 – 7:01 am

Index to this series

Summary. Suppose your society has certain rites and customs, perceived as essential to its functioning. When some persons among you reject those rites and customs, what are you going to do? Persecution would be the normal response of a society that aimed to preserve itself. In the example to be considered here, the society is medieval Christendom, where

  • buildings called churches were customarily the abode of friendly spirits, and
  • the rite of swearing an oath was a sign of special commitment.

Oaths and churches were rejected by persons called Paulicians, or Bogomils, or Albigensians. Their beliefs were Manichaean. These persons were persecuted so successfully that we do not understand them very well. Therefore we must leave open the question of whether they were barbarists.

Here I am going to review, among other things,

  • what it means to fight barbarism;
  • the response to German bombardment described in Goodbye, Mr. Chips;
  • what Jesus Christ says about swearing;
  • how the United States accommodates various beliefs (as by allowing affirming instead of swearing, or allowing Muslims to swear on a Quran);
  • the threat of a lying President;
  • the threat of ignoring climate change;
  • the etymology of heresy;
  • the discussion of mythos and logos in Pirsig.

Fire temple, Yazd, Iran, September 2012. See “Duty to Nature”

Continue reading →
By David Pierce | Posted in Collingwood, Language, New Leviathan, Philosophy, Pirsig | Tagged , , , , , , , | Comments (4)