## Posts

Showing posts from May, 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.

### 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.)

### 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 repetit…

### 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…

### The Card Players

Dan Klein and Fred Folvary end the conference with a game of hearts.

### Next...

The hazmat people showed up to clear out our intellectual rubbish:

### Massachusetts Troopers

Hearing there are economists gathering, show up to take action:

### 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:

### Here's the Shack

Where AIER is making us stay.

### Off to the Berkshires

For a meeting at AIER (American Institute for Economic Research). Ed Stringham picks me up in his fancy pants car.

### 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.

### 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."'

### 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' worl…

### 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!'

### 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!

### 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.

### 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.

### Now Available!

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

### 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 extrapol…

### 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.