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Friday, May 29, 2009

The Man from Ravena

There once was a man from Ravena
Who cut his teeth on Avicenna
He said, "My hair's essence
"Is starting to lessens
"Best I renew it with henna."

The Gardens at Naumkeag

In Stockbridge, Massachussets. Click for a larger image.

















Wednesday, May 27, 2009

My Favourite Song

From the great Stan Kelly-Bootle:

CHORUS Lemma three, very pretty,
and the converse pretty too;
But only God and Fermat
know which of them is true.

VERSE 1 When I studied number theory,
I was happy in me prime,
And all them wild conjectures,
I knocked them two at a time, but...

CHORUS

VERSE 2 Last week, at supervision,
Ken Ribet said to me:
"Did you discover
the deliberate mistake in lemma numberthree?"

CHORUS

VERSE 3 Lemma three it has puzzled
mathematicians by the score,
But Max Newman has engulfed it,
and it won't be seen no more.

CHORUS

VERSE 4 Well, the axiom of choice,
it is very clear to me:
If you wanna choose a lemma, boys,
then don't choose lemma three, for...

CHORUS

VERSE 5 And it's black and white together,
we shall not be moved,
But the four-color theorem,
it hasn't yet been proved

CHORUS Lemma three, very pretty,
and the converse pretty too;
But only God and Andrew
know which of them is true.

(Yes, both myself and the author know the four-colour theorem HAS been proved.)

Tuesday, May 26, 2009

Big, Big Formula!

1) What does the following formula generate?
2) What does the answer to 1) have to do with the "analyticity" of mathematical knowledge?

(k+2){1 – [wz+h+j–q]2 – [(gk+2g+k+1)(h+j)+h–z]2 – [2n+p+q+z–e]2 – [16(k+1)3(k+2)(n+1)2+1–f2]2 – [e3(e+2)(a+1)2+1–o2]2 – [(a2–1)y2+1–x2]2 – [16r2y4(a2–1)+1–u2]2 – [((a+u2(u2–a))2 –1)(n+4dy)2 + 1 – (x+cu)2]2 – [n+l+v–y]2 – [(a2–1)l2+1–m2]2 – [ai+k+1–l–i]2 – [p+l(a–n–1)+b(2an+2a–n2–2n–2)–m]2 – [q+y(a–p–1)+s(2ap+2a–p2–2p–2)–x]2 – [z+pl(a–p)+t(2ap–p2–1)–pm]2}

Was Hael

I'm here, after a long absence spent digging myself out from under piles of email. I'm sorry to have missed the action, particularly some question of probability to which I had been invited to contribute (Gene, "You Have Been Summoned," 090313).

In honor of probability, I shall offer here a delightful shortcut when calculating odds due to John Scarne. Suppose you repeatedly try for an unlikely outcome--let us say, the same birthday as mine (for simplicity, we'll ignore leap year, Scarne did). How many independent tries suffice to lower the odds of at least one success to 1-1 (even odds)? Here the odds are 364-1 against, and the exact calculation is tedious. For the only time that I noticed in his monumental work On Gambling, Scarne appealed to mathematics beyond (exceedingly elaborate) arithmetic and came up with a delightful shortcut: Take the 364 and multiply by 0.693 (the natural logarithm of two). In general, for odds of (n-1) to 1 out of n, (n-1) log2 repetitions will bring the odds of at least one success to even. But Scarne is very slightly wrong! Comparing the approximations (n-1) log2 and n log2, the proportional errors are second order, and the third order difference between them is minutely in favor of n log2. (n-1) log2 is low; n log2 is high; the correct value is about halfway between; n log2 is slightly closer; for large n, (n-1/2) log2 is very, very close.

Saturday, May 23, 2009

The "Immorality" of Fractional Reserve Banking Revisited

Over at the Mises blog, there has been a heated discussion on the merits of free banking, meaning a system without a central bank where banks can (if they wish) lend out some portion of their demand deposits.

At several points in the thread, someone has said, in effect, "Fractional reserve demand deposits are inherently fraudulent, because there are circumstances (e.g., all depositors show up at once) in which the bank cannot fulfill its promise to pay on demand."

Let's accept this argument for a moment and see where it leads us.

First of all, life insurance can easily be seen as equally fraudulent. There are clearly circumstances (e.g., a nuclear war) in which too many people would die at one time for an insurance company to pay all of the claims coming in. In fact, after a little more thought, it seems all insurance is fraudulent, since the same is true of any insurance policy.

But, wait, as I follow this a little further, it strikes me that all financial futures contracts are fraudulent: you know, there's always the possibility that, say, the government might nationalize the oil supply, and the person who sold oil forward won't be able to deliver.

Now a great light is dawning upon me, and I see even more revealed! In fact, all business contracts whatsoever are fraudulent: they all involve the future, don't they, and so they all contain clauses that might not be fulfilled. And work for hire is clearly fraudulent if the employer doesn't fill the worker's bank account continuously as work progresses, since otherwise there is some possibility the wage won't be paid!

This is surely the mark of a fertile principle: from what we at first thought was an argument only rejecting a very particular business practice, we have managed, using only our original logic, to shut down the world economy!

Thursday, May 21, 2009

Fancy Pants Car Week

Ben Powell was crazy enough to lend me this baby for a jaunt into town:



Man, was it hard to find an identical orange Mustang in Great Barrington after I totaled the one above.

Discussing Fractional Reserve Banking

George Selgin, Jeff Hummel, and Dan Klein:




Tuesday, May 19, 2009

Those Unassimable Muslims!

Folks, the neocons are right -- there is just no way Muslims can integrate into any contemporary Western society:

The Best Analysis of "Stimulus" Programs I Have Seen

The recent economic crisis has liberated the brilliant "inner macroeconomist" that has been locked inside my friend Mario Rizzo. See his recent Think Markets post for a devastating critique of current stimulus programs.

Sunday, May 17, 2009

Ethics Galore

By the way, Danny Shahar et al.'s discussion of ethics has now spilled onto at least its fourth blog.

Chris? Up for making it a quintet?

All for God's Glory Humiliation

2007 Master's: "I just believed it was his time, kind of like I did with Payne Stewart in 1999. I felt like God spoke to my heart that [Zach Johnson] was going to be the one to take that trophy home and use the platform for God's glory."

2009 Master's: "I felt like God spoke to my heart that [Zach Johnson] was going to be the one to totally fail to even make the cut and use the platform for God's humiliation."'

Friday, May 15, 2009

Is There a "Perennial Philosophy"?

My friend Danny Shahar, whom, I predict, will be a philosophical star very soon (lest Danny think I am buttering him up, in fact, I am like an NBA scout who hopes to get credit for being the first one to spot the high school hoopster who is going to be a first-round pick and a pro franchise player), has ignited a discussion on morality that has now spanned three blogs. (See, for instance, here and here, and, finally, this post.)

What I want to address in the present post is Danny's objection that my list of moral theorists supporting the notion that there is an objective moral reality is flawed, because "many of those thinkers held mutually incompatible positions ." Danny backs up this contention by noting that various luminaries on my list did not offer identical philosophical groundings for their moral views.

Now, Danny is no doubt right about this; but, I argue, that is beside the point. Let's say I am arguing for the existence of an objective 'natural' world, based on the fact that, for instance, when I see a tree in front of me, all other normally endowed people do so as well. But, my critic objects, I am mistaken: when I say I see a tree, the Frenchman says he sees an 'arbor', and the German a 'baum'. And, lest I suggest that simple translation software can handle that complaint, he further notes that some people regard the object I am indicating as a form of God, some as a chance product of evolution, some as a miracle of nature, and so on. However, as a Marxist might put it, these are the 'ideological superstructures' erected upon a common 'material basis'. Surely, what marks the tree as 'objectively real' is that we all agree it is woody and leafy, that running into it headfirst will hurt, that it can provide shade on a hot day, and that if we cut it down we can use it as fuel. And just so, as I see it, with morality: while various of the thinkers I cited offer different embellishments as to the metaphysical standing of morality, they all view it as on objective reality whose precepts we must heed if we wish to live a good life.

Let me illustrate what I mean by examining a few of the names from my list. Aristotle, for instance, held that there were moral principles one must follow if one wishes to achieve eudomania -- the best form of human life. Lao-Tsu contended that there is a 'way' (the 'Tao') that should be follwed to achieve peace of mind and self-fulfillment. Buddha taught there is a path (the 'Dharma') that must be followed to reach Nirvana (release from captivity to suffering). Christ preached about a pattern (the 'Logos') that, if one acted in conformance with, one could enter 'the Kingdom of Heaven'. (And whatever meaning this has in relation to an after-life, it is clear to me the he was [also?] pointing to a state one could reach right here and now -- the Kingdom of Heaven is 'at hand'.)

Certainly, all of these teachings were colored by the cultural milieu in which they arose, and so they all differ in emphasis, in metaphysical assumptions, and more. But aren't they all saying something very similar, namely, that there is an objective moral order to which anyone who wishes to achieve true happiness must pay attention? Isn't it significant that, when Buddhist missionaries traveled to China and encountered Taoism, they quickly translated 'the Dharma' as 'the Tao', and achieved success by placing Buddhist precepts in Taoist terms? And when Christian missionaries followed after, they swiftly translated 'the Logos' as 'the Tao'? Aren't all of these offerings essentially regional variations of the 'same dish'? (By arguing this, I don't mean to suggest that Taoism, Buddhism, and Christianity are really 'just the same thing' -- their differences may or may not be of some crucial importance. What I am arguing is that, in terms of how they view humanity's relationship to an objective moral order, they are quite similar. For instance, someone holding, as many Christians do, that Jesus offers the only true path to salvation, should still have no problem acknowledging that Lao-Tsu and Buddha were perceiving, even if imperfectly, the same moral order that Christ described -- and, in fact, that is exactly the attitude that many of the Church fathers took towards 'pre-Christian saints', such as Socrates.)

Danny, at several points, tries to separate the idea of an objective moral reality from the notion that certain courses of action will result in happiness and others in misery, e.g., 'It's surely different to say, "That action is inconsistent with the aim of integrating yourself properly into the natural flow of reality," than it is to say, "It would be morally wrong to fail to integrate yourself properly into the natural flow of reality."' But, if particular kinds of actions consistently result in unhappiness, and others in happiness, whether or not the person following those courses believes in some 'moral fiction' or not, isn't that very good evidence for an objective moral reality, rather than an argument against the existence of one?

Finally, regarding Danny's contention that Buddha may have been a 'moral fictionalist', I admit I am puzzled: I am unaware of any Buddhist sage who held, for instance, that the law of Karma (which, by the way, looks awfully similar to the Christian precept, 'as ye reap, so shall ye sow', doesn't it?) is just a 'fiction' that it will be useful to embrace. Surely Buddha believed that the law of Karma was an inescapable universal principle, operating independently of one's 'subjective' beliefs, no?

Tuesday, May 12, 2009

The Ultimate Philosophical Error

I was discussing a topic with Bob today, and he said, 'I see -- you're not saying they're wrong -- you're saying they're inconsistent'.

I responded, 'But Bob, for a philosopher, being inconsistent is the ultimate error. If you're wrong about, say, God, you might face eternal damnation, but if you're inconsistent, you won't get tenure!'

Monday, May 11, 2009

If You Liked...

my paper 'Economics and Its Modes', you'll love Chris Rolliston's commentary on it, which, judging by the length of Part I, will turn out to be longer than my paper!

Friday, May 08, 2009

Typography

A great web site for typographical tips. A couple of important items I still see violated frequently:

"You must always put exactly one space between sentences" -- putting two spaces after a period is a relic of the typewriter age.

"It would be awkward if the introductory heading ARGUMENT appeared on the last line of a page, and the actual argument started at the top of the following page."

We get papers at NYU with the second problem all the time -- the last thing on the page is the heading for what's on the next page.

Thursday, May 07, 2009

Ignorance...

gets you a job as a music writer:

'Miles Davis's Kind of Blue had come out a couple of months earlier, just a few months after John Coltrane's Giant Steps, each disdaining chord changes in favor of solemn inquiries into chords and modes. Davis's "So What" coolly navigated between a couple of minor Mixolydian modes; Coltrane's "Giant Steps" circled the circle of fifths.'

Aargh! Going around the circle of fifths is going through a sequence of chord changes, and anyway Coltrane's innovation was to go around a circle of major thirds instead of fifths.

Tuesday, May 05, 2009

Now Available!

The paper you've all been waiting for, 'Economics and Its Modes', is available at Collingwood and British Idealism Studies.

Monday, May 04, 2009

Why Is the Nanny Magical?

Did you ever wonder why, in, for instance, Mary Poppins or Nanny McPhee, the magical character is the nanny? Well, reading R.G. Collingwood's The Philosophy of Enchantment (edited, by the way, by my PhD advisor, David Boucher), I found out why. Collingwood notes, with regret, that under the influence of Enlightenment rationalism, the educated classes began to look down upon fairy tales and such "nonsense." (Collingwood feels that such tales convey important concepts to young children that they are not yet ready to grasp in another form.) So when their parents would no longer read or tell fairy tales to their young children, who would? Why, of course, it was the nanny, who being less "educated," had not yet decided these stories were worthless rubbish. And so naturally, when these children grew up and wrote stories of enchantment, the conduit of magic into the children's world was the nanny. (That last bit is not in Collingwood, but is a Callahanian extrapolation.)

Friday, May 01, 2009

Lecture at Yeshiva University

So today, I gave a lecture on capital theory at Yeshiva University. For some reason, on the subway ride uptown, all I could think of was, 'Damn, I need some almotriptan malate tablets!' I can't understand why.



When I got up to 181st Street, I discovered I was in an Hispanic neighborhood. Naturally, I assumed that my audience would be mostly Hispanic.



My lecture was at the 'WILF' campus, as the school wisely decided to keep me away from the 'MILF' campus a few blocks to the south.




Much to my surprise (see note on 'Hispanic neighborhood' above), who showed up for my lecture but a whole bunch of Jewish blokes? It must be my connection to Israel Kirzner!



I thought of stopping at Lake Como Pizza afterwards, but decided pizza from the heart of a lake would be a little soggy.