Thursday, December 31, 2009

A Sequence of Sequences

This research was supported in part by a grant from the Universal Walloons and by a grant from the Ants of America. We thank them for their help.

Neither this infinite sequence of sequences nor any of the component sequences (which are all finite) is an unfolding sequence, but you will notice reminiscent properties. How is this generated? For component S(n), consider all words composed of "1" and "2" of length 0-n. Left justify. Sort. S(n) is the lengths of the words in sorted order. Thus S(2): Possible words are -,1,2,11,12,21,22. In sorted order, they are -,1,11,12,2,21,22. Their lengths comprising S(2) are 0,1,2,2,1,2,2.


0....................................................................0- 0

011..................................................................0- 2

0122122..............................................................0- 6

012332331233233......................................................0- 14

0123443442344344123443442344344......................................0- 30

012345545534554552345545534554551234554553455455234554553455455......0- 62

0123456656645665663456656645665662345665664566566345665664566566.....0- 63
123456656645665663456656645665662345665664566566345665664566566.....64-126

0123456776775677677456776775677677345677677567767745677677567767.....0- 63
7234567767756776774567767756776773456776775677677456776775677677....64-127
1234567767756776774567767756776773456776775677677456776775677677...128-191
234567767756776774567767756776773456776775677677456776775677677....192-254

0123456788788678878856788788678878845678878867887885678878867887.....0- 63
8834567887886788788567887886788788456788788678878856788788678878....64-127
8234567887886788788567887886788788456788788678878856788788678878...128-191
8345678878867887885678878867887884567887886788788567887886788788...192-255
1234567887886788788567887886788788456788788678878856788788678878...256-319
8345678878867887885678878867887884567887886788788567887886788788...320-383
2345678878867887885678878867887884567887886788788567887886788788...384-447
345678878867887885678878867887884567887886788788567887886788788....448-510

etc.

Doo-doo-doo Lookin Out My Backdoor





Wednesday, December 23, 2009

Nagel Mildly Questions Orthodoxy, Causes Leiter to Shit a Water Buffalo

Just because you've spent half a century as one of the greatest philosophers in the world doesn't mean Brian Leiter won't trash you should you deviate from his religious dogmas!

Vegans Beware!

It turns out that plants do things like calling over parasitic insects to kill off the eggs of insects that eat the plants. So, all you vegans who have been cruelly preying upon the plant kingdom: next time you eat a carrot, watch your back!

What?! You're Not in Favor...

of a 2400-page health-care bill written by insurance companies to line their own pockets?! Why then, the "non-partisan" people at Rock the Vote declare you are a "creep" who must never be allowed to have sex again:



(Hat tip to Nick Gillespie.)

Sunday, December 20, 2009

Callahan Responds to Doherty Responding to Callahan

Brian Doherty, in what is at least partially a response to one of my earlier posts here at Crash Landing, writes: "This aspect of Rothbard is sometimes used to attack him as an unserious thinker, but it isn’t fair to the purpose of this sort of polemic. While, for example, he is not capturing the full nuances of Karl Polanyi’s history or analysis in his The Great Transformation, Rothbard is doing what he was asked to do—sniffing out a detectable set of beliefs about modern civilization, currency, and markets that make Polanyi an ineffective ally for radical libertarians."

Doherty also notes:

"His critiques often have language along the lines of this comment on his beloved economist mentor Mises: 'Mises’ utilitarian, relativist approach to ethics is not nearly enough to establish a full case for liberty.'”

In "defending" Rothbard against my critique, Doherty, in fact, makes the very point I have been trying to make: in what are supposedly works on the "history of thought," Rothbard, in fact, has no interest in the "nuances" of the thinkers he is addressing, which is precisely what a real historian of thought ought to be interested in. Instead, he is rummaging through the history of thought and chucking thinkers into bins labeled "favorable to libertarianism" and "unfavorable to libertarianism," then trashing anyone who winds up in the first bin, while writing hagiography of anyone who winds up in the second.

I've just been reading the new isue of The Review of Austrian Economics, where D.J. Den Uyl writes: "It is, both to my way of thinking and others, the definition of 'ideology' in the pejorative sense to begin with one's political conclusions and then search for arguments to support it. The way it is supposed to work is that the arguments lead one to the conclusions." But look at Rothbard's quote concerning Mises: he makes no case that Mises was wrong, only that Mises' position should be rejected because it did not sufficiently support the conclusion Rothbard had already reached! Is there a clearer self-confession to being an ideologue "in the pejorative sense" that could be made?

State Aggression

Brian Doherty writes:

"States, after all, cannot function without first aggressing against someone, if only to get tax money to fund their activities."

It's amazing to me that libertarians can make such statements as if they were obviously true or uncontroversial, and something with which their opponents already agree. "So, you see," they will continue, "you are in favor of some forms of aggression!"

But this argument is entirely circular as it is typically formed: The State is illegitimate because it engages in aggression, and we can say it must engage in aggression because its collection of taxes is illegitimate -- but, of course, since the collection of taxes is how the State survives, to say their collection is illegitimate is to just re-state that the State is illegitimate. Thus, the argument runs, "The State is illegitimate because the State is illegitimate."

Or, to put it differently, if the State is legitimate, then so is its collection of taxes, and therefore collecting them is not an act of aggression. (In that case, in fact, it would be withholding of taxes due that would be theft!)

A Sandy Interview by the Beach

Wednesday, December 16, 2009

Rothbard on Karl Polanyi

I have previously noted that Rothbard presents us with a cartoon version of Rousseau. I am now reading K. Polanyi's The Great Transformation for a class I am teaching with the same name, and I just noticed Rothbard gets Rousseau wrong in a review of that very book. So what did he have to say about Polanyi?

Shockingly (although I really shouldn't be shocked by this anymore!) Rothbard gets Polanyi even more wrong than he gets Rousseau. With Rousseau I figured that he had the excuse that he had never read him, but only read about him, but here he's actually reviewing Polanyi's book! And he attributes to it a "Worship of the Primitive" that "permeates the book."

Well, I was already halfway through Polanyi's book, and I can assure you, the thought had not once occurred to me anywhere in my readings that I was in the presence of the least bit of "worship of the primitive." Yes, occasionally Polanyi will mention this or that aspect of some primitive tribe he thinks is/was admirable, but there just is nothing even resembling "worship" present at all, let alone permeating the book.

A couple of other quick notes:

"Polanyi seems to think that he has scored a great coup on free market economists when he says that trade first developed in international and interregional channels, and not from first local and then international. So what? This is certainly not in any sense a refutation of free market economics."

But Polanyi certainly doesn't present this as any sort of "refutation of free market economics"! He presents it as a refutation of the ideas that markets began locally and spontaneously spread out from their local origens.

"Polanyi angrily criticizes those, like Mises..."

So, I looked through all of the pages mentioning Mises. Here's the kind of fierce anger I encountered: "And a century later Mises was still reiterating tthat labor and money were no more of a concern of the government than any other commodity on the market."

In short, Rothbard appears to have been so flummoxed by Polanyi's book that he basically could not read it at all. I picture him reading two sentences, throwing the book across the room in anger, picking it up a few minutes and ten pages later, reading another sentence, hurling the book, etc., then sitting down to write a review of what he imagined Polanyi was writing about.

UPDATE: Alasdair MacIntyre on Polanyi: "see Karl Polanyi The Great Transformation... still the single most illuminating account of the inception of institutionalized modernity..."

But all Rothbard could find in this single most illuminating account was "a farrago of confusions, absurdities, fallacies, and distorted attacks on the free market." Sigh.

Nothing to Undo!

Ever since I upgraded to the new iPhone OS, that message pops up on my screen from time to time. Underneath is a button reading 'Cancel'.

OK, if there is nothing to undo, what the heck does 'cancelling' it mean? And what if I don't cancel it? Will the phone go ahead and undo nothing?

Tuesday, December 08, 2009

Brett Favre Has Learned

The upshot of this column, which contains lines like, "Favre also understands this offense can't afford to be dominated like it was against Arizon," is this:

Last year, Favre did not understand that you're not supposed to suck at the end of the season and blow a chance to make the playoffs. This year, he has learned that for all those millions, he's supposed to not suck. Therefore, he won't.

Whew.

Thursday, December 03, 2009

The World's Great Sandwiches

OK, my research has advanced to the point that I can forward two candidates. Now, when I say "sandwiches," I mean something you could eat everyday for lunch, and not "Sloth tongue with Antibean bee's jelly butter and a lacy crust of fried morel tarts" or anything like that -- some restaurant may make such a dish, and it may be fantastic, but you aren't going to be making it for your lunch. No, I mean sandwiches with readily available ingredients that cost a couple of dollars and that you can make in under 20 minutes. Also, I am looking at when the "sandwichness" itself is what is so good about them -- of course, if you take a fantastic piece of steak and place it between two decent slices of bread, it will taste good -- but not as a sandwich, but as a fantastic piece of steak that happens to be between some bread.

So, here are my two candidates (not ranked in order):

1) The Reuben
Ingredients: Pastrami (cut it out with the corned beef, already), swiss cheese, sauerkraut, Russian dressing, rye bread.

2) The Cheddar Ploughman
Ingredients: Cheddar cheese, cucumbers, lettuce, tomatoes, mayonnaise, Branston pickle, brown bread. (I've eaten lots of these, and I know the igredients can vary quite a bit -- this is just my favorite combination.)

What these sandwiches have in common is that their excellence stems from a blend of surprising ingredients that you might not think would go together at first, but that somehow merge into a single taste that seems greater than the sum of its parts.

A Note on the English Versus the American Sandwich:
The are two quite different sandwich making philosophies at work here, and like Aristotle's types of constitutions, they each have their good and their degenerate variety.

The English style is to thinly layer each ingredient in balance. When done well, the result is something that tastes more like a single food than any American sandwich does. When you encounter the degenerate variety, you have just paid £2.95 for two slices of bread.

The American style is too lay the ingredients on more thickly. When done well, it never tastes as unified as the English style can, but you get a nice hearty meal and a clear taste of your ingredients. In the degenerate version, encountered especially in rural areas where "value" means lots of calories per dollar, you are faced with eating a lump of a half pound of roast beef, upon which a few scraps of lettuce, tomato, and bread seem to have gotten stuck.

Wednesday, December 02, 2009

Climategate: The Sequel

I was asked to look at the CRU source code to see if the comments looked reasonable to me, so I've gotten myself a bit familiar with this whole "Climategate" bru-ha-ha. I've read a few (knowledgeable) people saying it's nothing, and a few saying it's terrible. If you're thinking of wading in on this, I will say, confidently, that there is little to no chance that you can figure out which camp is right unless you are a professional working in this area. (Which I'm not!)

Nevertheless, many, many amateurs will post on the web extremely strong opinions on this matter. And the funny thing is, in nearly every single case, their opinion will line up exactly with just what they thought about AGW before Climategate! What a remarkable coincidence.

Tuesday, December 01, 2009

Friday, November 27, 2009

A Simple Man

At Thanksgiving dinner several people were in a group talking. As I joined them, they were saying things like, "You know, running is my drug." "Oh, for me, food is my drug." "Oh, for me it's sex." Then they looked over at me.

"You know, I'm a very straightforward man, and for me, it's been quite enough to have drugs be my drug."

Tuesday, November 24, 2009

Why Does Only the Dow Have an Absolute Level?

I listen to CBS News Radio when driving. Every half hour they give the financial news. Over years, I've noticed that the only stock index for which an absolute index is ever given is the Dow: "The Dow was down 25 points to 10,420. The NASDQ fell 10 points, and the S&P was down 5."

I swear, you could spend a decade listening to their reports and you could make a chart of the NASDAQ and S&P moves over that period, but you'd never know what their actual level is.

Monday, November 23, 2009

Dangerous Dirt

I noticed today on my bag of garden soil a warning that reads "Keep out of reach of children." OK, let's set aside the question of why dirt needs to be kept out of the reach of children, and ask instead how, given that I'm going to be putting this stuff on the ground, am I supposed to keep it "out of children's reach"?

Tuesday, November 17, 2009

Properties of the WTS (and Addendum) III - Wohin?

Properties of the WTS (and Addendum) III -- Wohin? wb 091117

8. Generalized unfolding product.

8.1. By the generalized unfolding produce (GUP), we mean
8.1.1. φ(x) ≡ Π{0 ≤ i < ∞, 1+µ(i) x^(2^i)}
= (1+µ(0) x)(1+µ(1) x^2)(1+µ(2) x^4)(1+µ(3) x^8)...
8.1.2. φ(x) = 1 + µ(0) x + µ(1) x^2 + µ(0) µ(1) x^3
+ µ(2) x^4 + µ(0) µ(2) x^5 + µ(1) µ(2) x^6 + µ(0) µ(1) µ(2) x^7 +...

8.2. We have examined several GUPs, for all of which, µ(i) is constant:
8.2.1. µ(i) = 1 (3.1.1)
8.2.2. µ(i) = -1 (3.2.1)
8.2.3. µ(i) = E (5.3.2.) (formal operator equation)
8.2.4. µ(i) = 2 (6.1.1)
8.2.5. µ(i) = -2 (6.2.1)

8.3. In general, for a GUP,
8.3.1. G = Γ{0 ≤ i < ∞, g(i)},
8.3.2. g(i) = (1), (µ(0)), (µ(1)), (µ(0) µ(1)), (µ(2)), (µ(0) µ(2)), (µ(1) µ(2)), (µ(0) µ(1) µ(2)),...
where the number of µ(i) in the above products for g(i) is v(i) (see 5.1).

8.4. GUPs with nonconstant µ(i), example.
8.4.1. Let µ(i) = i+1, i = 0,1,2,... Then
8.4.1.1. g(i) = (1), (1), (2), (1·2), (3), (1·3), (2·3), (1·2·3) (4), (1·4), (2·4), (1·2·4), (3·4), (1· 3·4), (2·3·4), (1·2·3·4), (5), ...
8.4.1.2. g(i) = 1, 1, 2, 2, 3, 3, 6, 4, 4, 8, 8, 12, 12, 24, 5, ...

8.5. GUPS: Questions.

8.5.1. What sort of properties do GUPs have in common?
8.5.2. What other characterizations of unfolding sequences (USs) are equivalent to our characterization of GUPs?
8.5.3. Which homomorphic USs are GUPs?
8.5.3.1. Which of the USs described in Properties of the WTS II and Addendum are GUPs?
8.5.4. What can be gained by describing GUPs using formal operator equations?

8.6. Your sister.
8.6.1. Did she successfully marry for money (I mean real money!).
8.6.2. Is he dead?
8.6.3. Would she like to meet me?

Tunak Tunak Tun Will Never Die



(Hat tip to Charno.)

Monday, November 16, 2009

Brooklyn by Night

Centre Street -- at the center of nothing:


It's healthy -- except, of course, for the coffee, soda, cigarettes, and candy:



Don't ask, don't tell:

Thursday, November 12, 2009

What a Shock!

To find a blog post containing paranoia, crank science, and misinformation at this site!

First of all, as "evidence" that the swine-flu vaccine is toxic, Grigg links to... a peer-reviewed journal article? A large study showing the danger of the vaccine? No, he links to.. another crank writing on the Internet! In fact, there is apparently widespread scientific consensus that the vaccine is (relatively) safe. (All medical treatment carries risks! The relevant question is: Are the risks greater than the rewards?)

Secondly, "at gunpoint"! The article Grigg cites never even mentions if the deputies involved were armed, but certainly if they had drawn their weapons this would be mentioned. So this was certainly not done "at gunpoint" -- but boy, it makes a more dramatic headline to put in that lie, doesn't it?

Next, Grigg calls the child an "inmate." What horseshit. All three of my kids go to public schools, and you know what? Any day I want, I can keep them home. When I asked a teacher about taking my daughter out for a week to go to the UK, she said, "That's definitely worth missing school for!" Any day I want, I can put the kids in a different school or decide to home school them. And you know what else? Often, when I try to keep my kids home for some trip or such, they fight the idea! They want to go to school almost everyday. Public school children resemble "inmates" in that the they both spend time inside government-owned buildings. Otherwise, they are no more "inmates" than Grigg is an "inmate" of the LRC blog.

When a school official mentions it's often "useful" to have parents around -- because, you know, kids get scared of needles! -- Grigg decides "he meant that it’s useful to have a parent handy to coax his child into submitting to a government-mandated violation of his bodily integrity."

First of all, these vaccines are not, to my knowledge, ever "government-mandated" for school children. (And note: the last link is about consent forms being needed in West Virginia, where Grigg's horror tale took place.)

Secondly, does Grigg think that parents deciding what medical care their children receive is a "violation of their bodily integrity"? Perhaps infants should be asked before a thermometer is inserted in their fanny to get their temperature?

"The mother of the brutalized child..."

Ah! Brutalized children! The kid was scared of getting a shot that his parent(s) wanted him to get. Does Grigg think if my children are scared of some medical treatment, I should just say, "Well, all right then... no treatment for you!" And what was the child like after his/her "brutalization"? "Gamble said as soon as the nurse gave the boy his injection and told him he was done, he hopped up like nothing had happened." Wow, that sure is brutalized!

What totally inane, nutty paranoia. But, so long as inane, nutty paranoia is directed at "officials," LRC is all for it!

Thursday, November 05, 2009

Properties of the WTS II - Addendum

Properties of the Wine Tasting Sequence II - Addendum wb 091105

Properties of the Wine Tasting Sequence II Sctn. 7 described the first of an infinite class of homomorphic unfolding sequences, all having fascinating properties, generated by functions f satisfying:

7.2.4. f((&f^n)(s)) = s, n = 0,1,2,...

Here is the second, again using dots for cosmetic punctuation:

7.2.5.1. S2 = 0.1.2.0.01.012.0120.012001.012001012.0120010120120.0120010120120012001...

So that you can grasp its gestalt visually, here it is without punctuation:

7.2.5.2. S2 = 012001012012001200101200101201200101201200120010120120012001...

The zeroth member of this class, having generating function f(s) = s, is the perfectly legitimate unfolding sequence (dots again as before):

7.2.6. S0 = 0.0.00.0000.00000000.0000000000000000.00000000000000000000000000000000...

The larger n, the more slowly the sequence grows (well, obvious, right?).

Can these Sn be mapped from V, the homomorphic mother? Of course they can--left as a challenge for the mildly interested reader.

It seems that my interest in these matters has been inextinguishable since the mid 1950s, from a short paper published under the title "Unending Chess and a Problem in Semigroups." The Wine Tasting Sequence is equivalent to the Hedlund-Morse symbolic trajectory (although the further thoughts about it and its family are mine); Prof. Hedlund of Yale was the author of the short paper; Profs. Hedlund, Morse, and Kakutani, mostly of Yale, are responsible for the earliest thoughts on the subject that I know of (Norwegian Axel Thue may earlier have steered attention in this general direction), and I bless the memories I have of them, hoping that they are all still with us, not to mention the Mathematics Library in Leet-Oliver Hall, HIllhouse Avenue, Yale University, New Haven, Connecticut. I was a kid. They were giants.

Worst NY Times Sentence of the Year?

Here?

"If afterburn were found to exist, it would suggest that even if you replaced the calories you used during an exercise session, you should lose weight, without gaining weight — the proverbial free lunch."

I do believe if you lose weight, you inevitably will not have gained weight.

Iron Curtain Fallen?

Not for deer!

Tuesday, November 03, 2009

Properties of the Wine Tasting Sequence II

Properties of the Wine Tasting Sequence. wb 090723 - 090810, 091103

1. Introductory notes.

1.1.Definitions.


1.1.1. |x| is the absolute value of x: {- x if x ≤ 0, otherwise x}.
1.1.2. sgn x is the sign of x: sgn x ≡ x / |x|.

1.2. By an unfolding sequence, we mean a sequence derived from an initial string (or digit) by repeatedly applying a production which appends to the sequence thus far a specific transform of the sequence thus far. Let f be a string function. If s is a string in the domain of f, &f denotes the function &f(s) ≡ sf(s). The unfolding sequence derived from function f and initial string s in the domain of f is U=&f^∞(s). Trivially, any sequence can in fact be seen as unfolding by a sufficiently perverse choice of f:
f(d(0)d(1)...d(i)) ≡ d(i+1), 0 ≤ i < ∞. We shall simply ignore this, looking at sequences that can usefully be defined by unfolding processes.

2. Unfolding sequences. The Wine Tasting Sequence (WTS).

2.1. Let W be an unfolding sequence of the digits ±1 as follows: f(digit d) = -d; f(st)=f(s)f(t); W=&f^∞(1).
W = 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 ...
Suitably redefining f and the initial digit yields the equivalent forms
W1 = 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
W2 = 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 ...
W3 = A B B A B A A B B A A B A B B A ... etc.
We know this sequence as the "Wine Tasting Sequence" from the associated Wine Tasting Problem, q.v.

2.2. Concatenations. Given s(i), i ε I (the s are indexed by I), their concatenation is a sequence written Γ{i ε I, s(i)} or Γ{i, s(i)} or Γs(i). The order of I is assumed to rule (I must be ordered). Let w(i) be the digits of the WTS. W=Γ{0 ≤ i < ∞, w(i)}.

2.3. Transforms. A transform (intuitively, as used here) is a functional which derives from any of a class of functions or similar entities from analysis another, usually different, entity in a uniform way. Well known useful examples: Fourier transform, Laplace transform, dual (of a boolean expression).

2.4. Polynomial transform. If s(i), 0 ≤ i < ∞ are taken from a field (such as the real numbers), the polynomial transform of Γ{i, s(i)} is given by
Poly Γ{i, s(i)} ≡ Σ{i, s(i) x^i}. The variable "x" should be specified somehow, but we'll just understand "x".

2.5. For the WTS, Poly W = 1 - x - x^2 + x^3 - x^4 + x^5 + x^6 - x^7 - x^8 + ... The properties of this series would be hard to reckon, except that for certain unfolding sequences, Poly takes the form of an infinite product; the WTS is one of these.

3. Functional equations. What a difference a sign makes.

3.1. (1+x)Φ(x^2) = Φ(x). The general solution of this functional equation can be expressed in a manner reminiscent of a differential equation: Φ(x) = σ(x) φ(x), where
σ(x) is the general solution of the functional equation Φ(x^2) = Φ(x),
φ(x) is any particular solution of the above equation (1+x)Φ(x^2) = Φ(x).
σ(x) may be expressed in terms of the general periodic function τ(x+π) = τ(x). It will trouble us no more.
Any particular φ(x) will do; we choose
3.1.1. φ(x) ≡ Π{0 ≤ i < ∞, 1+x^(2^i)} = (1+x)(1+x^2)(1+x^4)(1+x^8)..., |x| < 1. This unfolds into
3.1.2. φ(x) = Σ{0 ≤ i < ∞, x^i} = 1 + x + x^2 + x^3 + x^4 + x^5 + ..., |x| < 1. Then φ(x) = 1/(1-x).
Note that 1/(1-x) does indeed satisfy 3.1.

3.2. (1-x)Φ(x^2) = Φ(x). The general solution of this functional equation is Φ(x) = σ(x) φ(x), where
σ(x) is the general solution of the functional equation Φ(x^2) = Φ(x), as before,
φ(x) is any particular solution of the above equation (1-x)Φ(x^2) = Φ(x).
Any particular φ(x) will do; we choose
3.2.1. φ(x) ≡ P{0 ≤ i < ∞, 1-x^(2^i)} = (1-x)(1-x^2)(1-x^4)(1-x^8)..., |x| ≤ 1. This unfolds into
3.2.2. φ(x) = Σ{0 ≤ i < ∞, w(i) x^i} = 1 - x - x^2 + x^3 - x^4 + x^5 + ..., |x| ≤ 1. This is Poly W.
Unlike 3.1.2, it appears to have no simple closed form. Also unlike 3.1.2, it converges at |x| = 1.

3.2.3. Pseudocode for φ(x) = Poly W:
real PolyW(real x) {
P = 1-x;
while MAKINGPROGRESS {
x = x*x;
P = P*(1-x);
}
return P;
}

3.2.4. Binary details for Poly W:
3.2.4.1. φ(1/x) = (x-1)/x · (x^2-1)/x^2 · (x^4-1)/x^4 · (x^8-1)/x^8 · ...
3.2.4.2. φ(1/2) = 1/2 · 3/4 · 15/16 · 255/256 · ... = 1 - 1/2 - 1/4 + 1/8 - 1/16 + 1/32 + 1/64 - 1/128 - ...
φ(1/2) = 0.350183865...
3.2.4.3. In binary radix notation:
1.0010110011010010110100110010110... (a),
0.1101001100101101001011001101001... (b),
0.010110011010010110100110010110... φ(1/2) = a-b = a-(2-a) = 2(a-1).

4. Properties of the WTS function φ(x) = Poly W.

4.1. Ω(x): From 3.2,
4.1.1. (1-x)φ(x^2) = φ(x). Therefore at -x,
4.1.2. (1+x)φ(x^2) = φ(-x). Therefore
4.1.3. Ω(x) ≡ (1+x)φ(x) = (1-x)φ(-x) = Ω(-x). Therefore Ω(x) is even.
4.1.4. φ(-x) = ((1+x)/(1-x)) φ(x) = r φ(x), x <> 1.

4.2. Some values of φ(x) and Ω(x):

x r φ(x) φ ≈ Ω(x)
---- ---- --------------- ---- ---------------
-1 0 0.0 0.0
-3/4 1/7 0.466212439 0.11655311
-2/3 1/5 0.712946495 0.237648832
-1/2 1/3 1.050551595 21/20 0.525275798
-1/3 1/2 1.170374832 0.780249888
-1/4 3/5 1.167279552 7/6 0.875459664
0 1 1.0 1.0
1/4 5/3 0.700367731 7/10 0.875459664
1/3 2 0.585187416 7/12 0.780249888
1/2 3 0.350183865 7/20 0.525275798
2/3 5 0.142589299 1/7 0.237648832
3/4 7 0.066601777 1/15 0.11655311
1 ∞ 0.0 0.0

max φ(x) at x ≈ -1/3; max Ω(x) at x = 0.

5. The mother of the Wine Tasting Sequence (WTS).

5.1. Let V be an unfolding sequence of the natural numbers as follows:
f(digit d) = d+1; f(st)=f(s)f(t); V=&f^∞(0).
V = 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 ... = Γ{0 ≤ i < ∞, v(i)}.
W1 = 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
= Γ{0 ≤ i < ∞, w1(i)} = Γ{0 ≤ i < ∞, mod2 v(i)}.

5.2. w1(i) = mod2 v(i), i = 0,1,2,...

5.3. We cannot express Poly V as an infinite product as we did with Poly W; the best we can do is to use an operator equation, exploiting an operator
5.3.1. E n ≡ n+1, n = 0,1,2,...
5.3.2. φ(x) ≡ P{0 ≤ i < ∞, 1+E x^(2^i)} = (1+E x)(1+E x^2)(1+E x^4)(1+E x^8)....
This cannot be usefully evaluated; in particular, it does not yield a functional equation like 3.1 or 3.2. It can only be regarded as a symbolic convenience. However...

6. New corresponding functional equations

6.1. Entirely analogously to 3.1, consider the equation (1+2x)Φ(x^2) = Φ(x). Here, our choice of φ(x) is
6.1.1. φ(x) ≡ P{0 ≤ i < ∞, 1+2x^(2^i)} = (1+2x)(1+2x^2)(1+2x^4)(1+2x^8)..., |x| < 1. This unfolds into
6.1.2. φ(x) = Σ{0 ≤ i < ∞, u(i) x^i} = 1 + 2x + 2x^2 + 4x^3 + 2x^4 + 4x^5 + ..., |x| < 1. Then
6.1.3. log2 u(i) = v(i).

6.2. Also, consider the equation (1-2x)Φ(x^2) = Φ(x). Here, our choice of φ(x) is
6.2.1. φ(x) ≡ P{0 ≤ i < ∞, 1-2x^(2^i)} = (1-2x)(1-2x^2)(1-2x^4)(1-2x^8)..., |x| < 1. This unfolds into
6.2.2. φ(x) = Σ{0 ≤ i < ∞, t(i) x^i} = 1 - 2x - 2x^2 + 4x^3 - 2x^4 + 4x^5 + ..., |x| < 1. Now we have:
6.2.3. log2 |t(i)| = v(i). (1 - sgn t(i))/2 = mod2 log2 |t(i)| = w1(i).

7. Sequence V is fundamental.

7.1. Definition: An unfolding sequence is homomorphic
iff its generating function f is homomorphic with respect to all &f^n, n = 0,1,2,... Then we can rewrite
7.1.1. s f(s) f(s f(s)) f(s f(s) f(s f(s))) f(s f(s) f(s f(s)) f(s f(s) f(s f(s)))) ... = Γ{0 ≤ i < ∞, f^v(i)(s)}.
Thus a typical homomorphic unfolding sequence is isomorphic to V or to some modulo reduction of V (like W) under the mapping f^k(s) --> k.

7.2. Sometimes the connection is not so obvious.

7.2.1. Consider unfolding sequence S defined by generating function f, f(&f(s)) = s.
7.2.2. Punctuating with dots for clarity,
S: 0.1.0.01.010.01001.01001010.0100101001001....
But this is V, under the mapping 12-->0, 23-->1, etc.
7.2.3. V: 0 1 1 2 1 2 2 3 1 2 2 3 2 3 3 4 1 2 2 3 2 3 3 4 2 3 3 4 3 4 4 5 1 2 2 ...
0 1 0 0 1 0 1 1 2 0 1 1 2 1 2 2 3 0 ...
0 1 0 0 1 0 1 0 0 1 0 0 1 0 ...

UPDATE (FROM GENE): I have typed Π᾽s in where I have found P. Should the bolded E's be epsilon's as well?

Saturday, October 31, 2009

Nonstop

Nonstops: Commercial flights having no intermediate destinations.

Nonstop nonstops: Round-the-clock nonstops to your destination.

Nonstop nonstop nonstops: A blitz of advertisements for nonstop nonstops.

Nonstop nonstop nonstop nonstops: ? Suggestions appreciated.

Who Says Economic Planning Can't Work?

I heard Joe Biden on the radio yesterday saying, "Our economic stimulus package has created or saved 640,239 jobs. I nearly crashed my car laughing. Not 640,238, mind you, nor would Joe dare to exaggerate and claim 640,240. No siree, exactly 640,239.

To Anglicize or Not to Anglicize?

Shuttling back and forth between both academic and ‘regular’ life in the US and the UK has made me aware of a significant difference between Yanks’ and Brits’ inclination to Anglicize foreign-word imports into the English language. One of my first hints as to the existence of the difference was when I realized that the dish that Americans pronounce ‘fil-ay of sole’ is standardly pronounced in England ‘fil-et of sole’. Gradually, I realized that this divergence pervades American and British English. I especially was struck by it when it comes to the pronunciation of foreign names. I recall eating breakfast, at a conference in Wales, with two British academics, both of whom are well-respected scholars in the history of political thought. As I listened to their conversation (with little to add of my own), I grew puzzled at to just who was this Italian political theorist ‘Russo,’ whom they kept mentioning, and with whom they seemed to assume I was familiar. When one of them brought up the story of ‘Russo’ sitting on Hume’s lap and crying, it dawned on me that they were talking about Rousseau! When I asked them if this was so, they looked at me as if I was quite daft, since I was saying just the same name that they had been.
Once I had identified this tendency, I was, at first, quite bothered by the British practice, and was sure my American ways were to be preferred. Why, here was a renowned figure in the history of political thought talking about ‘Gee-an-battista Vico’, when I knew he should be saying ‘Zhan-battista Vico’!
But then, listening to a series of lectures on the Axial Age by an American scholar specializing in Indian religions, I found myself growing increasingly annoyed at his use of esoteric Sanskrit and Pali pronunciations of names and terms that are fully incorporated into English with Anglicized pronunciations, e.g., his saying ‘Buh-DA’ instead of ‘BOO-da.’ And that made me realize that the issue wasn’t as straightforward as I had initially assumed. While there are cases where it is obviously better to use the anglicized version of a foreign name (imagine listening to a lecture by an historian who kept saying ‘Kikero’ and ‘Yulius Kaiser’ instead of ‘Sisero’ and ‘Julius Siezeher’) and others where Anglicization would clearly be absurd (after all, even the English say ‘chow,’ and not ‘see-ay-o’ when employing the Italian salutation, and ‘wee,’ not ‘oo-ie,’ when saying ‘yes’ the French way), there are many other cases where the correct choice is not so clear cut. When the professor who taught me history of science (an Englishman, by the way!) would say ‘Ein-shtein’ rather than ‘Ein-stein,’ was he being overly pedantic or just faithful to the native pronunciation of that scientist’s name? If I insist on saying ‘Zha-notti’ rather than ‘Gee-a-notti’ when discussing the Florentine political theorist, am I showing off or being accurate? (And just why is it that Americans say Rudolph Giuliani’s name in (semi) Italian fashion, with the initial ‘i’ being silent, but, when confronted with the very same construct of Italian spelling, always sound the ‘i’ in ‘Giovanni’?)
It may be that there is no clear answer to these questions, other than ‘If everyone laughs when you say it one way, you’d better say it the other.’ But I seek your input: can anyone out there propose a reasonable rule as when to Anglicize and when to not do so?

Thursday, October 29, 2009

I Unearth Another Rothbard Hater!

Roderick Long shows that Rothbard employed a cartoon version of Plotinus -- kind of like his cartoon Rousseau, or his cartoon Smith, or his cartoon English Revolution.

Sunday, October 25, 2009

Pop Quiz

We all know about Hitler's infatuation with the Aryans Many people assume, therefore, that 'Aryans' means 'Germans' or 'Nordic' something of the sort.

So, today's quiz: what two modern countries take their name directly from the word 'Aryan'?

Thursday, October 22, 2009

Kirk on Libertarians

Here.

Closing quote:

"At the Last Judgment, libertarianism may find itself reduced to a minority of one, and its name will not be Legion, but Rothbard."

Wednesday, October 21, 2009

Who's Hypersensitive Now?

Over at Reason, David Harsanyi pens a very touchy article discussing recent remarks from the Obama administration about Fox News.

Let me offer some quotes from Harsanyi that illustrate how he is placing the worst possible interpretation on whatever the Obama administration says:

"Dunn also asserted that when the president 'goes on Fox, he understands he's not going on it really as a news network at this point. He's going on to debate the opposition.' Who knew debating the future of the nation is such a ghastly thought?"

Of course, Dunn doesn't say the idea is "ghastly," I guess we're just not supposed to notice that the ghastliness is entirely the invention of Harsanyi.

"So what is the underlying rationale for this hypersensitive strategy of trying to delegitimize the voice of cable opposition?"

But if Fox News is "the voice of cable opposition" then they really aren't a news station, are they, but more of an op-ed station, right? And pointing this out would not be "delegitimizing" them, but just noting what they do.

Harsanyi is ready for this objection: "Then again, does biased political coverage disqualify one from reporting legitimate and useful news stories? Fox News may not be able to unsheathe the intellectual rigor of Obama favorites David Letterman and Jay Leno, but it has covered numerous stories in the past few months that otherwise would have gone unnoticed."

That's fine. I don't think anyone doubts that Fox News at least sometimes reports news. But because USSR-era Pravda sometimes reported "There was an earthquake" when, in fact, there had been an earthquake, that did not make it a newspaper!

"the nation's most dominant government entity--an entity that allegedly represents all Americans--is using tax dollars and its considerable influence to try to squash a privately owned news organization that disagrees with it."

They are trying to squash Fox News? Isn't that a bit... well, hypersensitive? Fox News attacks the administration, and the administration responds. Has there been any administration in my lifetime that wouldn't have done the same? Could any administration possibly achieve any of its goals if it didn't fight negative media portrayals of its agenda? Now, if someone in the administration has been suggesting shutting down or fining Fox News, that might reasonably called squashing, but if they have, I haven't heard about it nor does Harsanyi give any evidence that this has occurred.

And that "allegedly represents all Americans" is just lovely, isn't it? It seems to be based on the notion that to "represent all Americans" means never to argue against any of them. So, in 2012, Obama better not campaign against the Republican candidate for president, since he allegedly represents the GOP nominee. And if an American citizen is advocating massive terrorist attacks against US cities? Well, Obama represents him, too, so he really shouldn't object.

"And if this administration can't handle one cable station's opposition, what does that tell the American people about its mettle on issues that matter?"

Um, but this administration is handling the Fox opposition. In fact, Mr. Harsanyi has just written an entire article about how they are handling it: by pointing out that Fox is an opposition outlet.

That Fox News has an anti-Obama slant is pretty obvious -- Harsanyi himself admits this several times in this very article, by calling them "the opposition" -- so that's not under dispute. Harsanyi's point seems to be that the Obama administration's job is just to sit there and take its lumps.

Thursday, October 08, 2009

The Day I Ran into the Economy

I tried to post this as a comment over at Marginal Revolution, but I kept getting the message, "We're sorry, we cannot accept this data." Whatever that means.

Boonton (a blog commentator): "The economy knew the new tech was great but also knew it was overdone so it looked for other things to take its place. Housing, finance, healthcare and other things were it."

Yes, I recall meeting "the economy" while it was looking around for things to take the place of high tech -- I think I bumped into it just outside of Topeka, at a rest stop along a lonely country highway. The economy was pumping some gas, the stub of a cigarette smoldering between its parched lips, the cracks in its leathery face showing beneath the three days of stubble on its cheeks. It had a sort of far-off, forlorn look in its eyes, but it assured me it was not going to create a bubble with the next "big thing." I knew then it was like a drunk coming off a bender, and it was just a matter of time before it was high as a kite on housing or some other cheap rot gut.

Hat Tip to Danny Shahar

What a funny name for a post, huh?

Wednesday, October 07, 2009

And That Was Just the Human Deaths!

I was laying awake last night in my hotel room in Fairfax, Virginia, surfing late night TV. A newscaster was on screen, talking about the eight anniversary of the start of the Afghan War. She said, "During that time, almost 800 people have died."

And that's just the human deaths! Countless other, non-human deaths could be added to that score, such as Afghan flying squirrels, Afghan hedgehogs, Russian tortoises, and Afghanis.

James Buchanan Center

George Mason University



Monday, October 05, 2009

Hating the Hated Hater Haters

Yu know what I hate? The way every person and his brother throws around "haters" at anyone who mildly criticizes something they like. Post a negative restaurant review? You're a "hater." Claim that Notre Dame is not having that good a season? Hater!

Listen, folks, a "hater" is someone who beats up the restaurant owner, not someone who posts a slightly critical review.

Wednesday, September 30, 2009

The Pot Calling the Copper Kettle Black

The apostle Lew, disciple of the savior Murray, is outraged that someone questioned Saint Ron:

"Writes Justin Raimondo:

"Bruce Bartlett, former columnist for Libertarian Review turned neocon, and Andy “Gay Marriage Is All” Sullivan, team up to smear Ron Paul as a 'crackpot' and lie about his view of the Fed."

Well, Bartlett never called Paul a "crackpot": he called one of his ideas "crackpot." (An important difference: Newton was not a crackpot, but his theological notions probably could be described as such.) And Sullivan never called Paul or his ideas anything at all! He just linked to Bartlett, without further commentary. And what lies are being told? Paul does want Congress to have Fed oversight, doesn't he? Maybe there is some "lie" involved (I'm really not following the details of this debate), but what is it? And couldn't it have been an honest mistake? No, let's just assume it's a "lie," as calling your opponent a liar is so much more gratifying than calling him mistaken.

And note: how is it relevant that Bartlett may have "turned neocon", and what is it but an ad hominem attack to throw in "Gay Marriage Is All" in the middle of Sullivan's name? (I'm convinced, by the way, that Raimondo has a big time crush on Sullivan, he is so obsessed with the fellow.) And, not only is it irrelevant, it's a lie! Sullivan's doctoral thesis on Oakeshott was certainly not focused on the issue of gay marriage.

So when someone makes a substantive criticism of one of the ideas of one of the Mises Institute's Church Fathers, that is a "smear," but when the response is irrelevant personal attacks, well, that's just good clean fun, hey? This is not the way one conducts intellectual debate; this is the way one riles up the passions of the faithful in a modern, gnostic revolutionary movement.

Tuesday, September 29, 2009

Good Work, Lads!

Babel Fish took the Russian phrase "Ne govoryu po russki, tovarisch" and rendered it in English as "Ne of govoryu po of russki, tovarisch."

Russians using Babel Fish must think, "English is easy! You just add 'of' a couple of times to a Russian sentence and... English!"

Voegelin on Utilitarians

"A crippled man, however, does not cease to be a man. Spiritual obscurantists, or anithumanistic utilitarians, are not animals; they continue to function as humans. Still, they can no longer solve human problems rationally, or on the basis of the spiritual experiences the possession of which characterizes mature man. Hence there appear the curious transpositions of the problems of mature Western civilization to the new level of utilitarian immaturity." -- "Positivism and Its Antecedents"

I just saw a very good example of this: Peter Singer spoke to a colloquium I attend at NYU. He argued that utilitarian ethics would make it mandatory for, say, a surgeon to, on occasion, deliberately kill a (mostly) healthy patient under the knife in order to harvest his organs for several other patients who need them. I think his demonstration was sound, but, of course, Singer, being an anithumanistic utilitarian, thought this was a good argument for occasionally doing just this, rather than a crushing refutation of utilitarian ethics!

Monday, September 28, 2009

If You've Never Read Rousseau...

you probably think he created the concept of the "Noble Savage," right? Well, you'd be wrong! OK, but at least he was behind the idea, right? Anti-civilization, wasn't he? Sorry: "Rousseau argued that in a State of Nature men are essentially animals and only by acting together in civil society and binding themselves to its laws, do they become men. For Rousseau only a properly constituted society and reformed system of education could make men good."

The whole association of Rousseau with the "Noble Savage" and the claim that he was "anti-civilization" were smears against Rousseau by a 19th-century racist. Now, this is known well enough that it makes it into a Wikipedia page; yet, even in recent times, some people who pretend to be writing on the history of thought have continued to perpetuate this smear.

Friday, September 25, 2009

Unemployed?

CNN headline suggests suicide.

And the Mark of Moral Maturity Is...

Check out this post, linked to approvingly by Michelle Malkin. The author complains that we have "Obama strutting the world stage, telling us that 'climate change' is the problème du jour - and nothing is more important," a sign of what he calls "moral infantilism."

And his evidence that Obama is wrong about this is... a public opinion poll!

Yes, once we reach moral maturity, we'll form our moral views based on Bloomberg Polls.

Voegelin on Condorcet

"With a few masterful strokes Condorcet has sketched the new type of intellectual parasite whose zeal to teach others is stronger than his willingness to submit to intellectual discipline, who thrives on the fallacy that truth is to be found in the solution to problems rather than in their discovery, who believes truth can be dispensed as a body of doctrine, who transfers the characteristics of revealed truth to the finite human search for knowledge; who consequently, through vulgarizing problematic knowledge into dogmatic results, can make the innocent belive that they enter into the truth if they accept faithfully as dogma a proposition which no conscientious thinker would accept without far-reaching qualifications, who create in their victims the belief that instruction is education, who destroy intellectual honesty through their separation of results from the critical processes which lead up to them, who build up in the masses the unshakable brutality of ignorant conviction..." -- "Progress and Political Experience"

Thursday, September 24, 2009

You See, It Was Theoretical Change We Voted for...

Glenn Greenwald:

'When it comes to uprooting ("changing") the Bush/Cheney approach to Terrorism and civil liberties -- the issue which generated as much opposition to the last presidency as anything else -- the Obama administration has proven rather conclusively that tiny and cosmetic adjustments are the most it is willing to do. They love announcing new policies that cast the appearance of change but which have no effect whatsoever on presidential powers. With great fanfare, they announced the closing of CIA black sites -- at a time when none was operating. They trumpeted the President's order that no interrogation tactics outside of the Army Field Manual could be used -- at a time when approval for such tactics had been withdrawn. They repudiated the most extreme elements of the Bush/Addington/Yoo "inherent power" theories -- while maintaining alternative justifications to enable the same exact policies to proceed exactly as is. They flamboyantly touted the closing of Guantanamo -- while aggressively defending the right to abduct people from around the world and then imprison them with no due process at Bagram. Their "changes" exist solely in theory'

Bob's Office



A short which includes my friend Matt Pollock.

Tuesday, September 22, 2009

Nonstop

Nonstop:
Commercial flight having no intermediate destinations.

Nonstop nonstop:
Nonstop commercial flights all day, no waiting.

Nonstop nonstop nonstop:
Blitz advertising campaign re nonstop nonstops.


Nonstop nonstop nonstop nonstop:
???

Saturday, September 19, 2009

Drugs

Today at weather.com:

"THE POLLEN FORECAST FOR YOUR AREA IS HIGH..."

No sense listening to that thing, then.

Friday, September 18, 2009

Kinsella on Anarchism

Stephan Kinsella takes an unusual, "pessimistic anarchist" position. Since he has just recently set it out at length, I will take a moment to point out what I think to be some problems with his views.

"Accordingly, anyone who is not an anarchist must maintain either: (a) aggression is justified; or (b) states (in particular, minimal states) do not necessarily employ aggression.

"Proposition (b) is plainly false. States always tax their citizens, which is a form of aggression. They always outlaw competing defense agencies, which also amounts to aggression."

So that handles (b), does it? Of course, someone who believes the state is legitimate doesn't believe taxation to be aggression. Naturally, if you get to define the terms the way you want, you can win any argument, but really it's an empty victory just to define your way to the win.

"Conservative and minarchist-libertarian criticism of anarchy on the grounds that it won’t 'work' or is not 'practical' is just confused... Consider an analogy. Conservatives and libertarians all agree that private crime (murder, robbery, rape) is unjustified, and "should" not occur. Yet no matter how good most men become, there will always be at least some small element who will resort to crime. Crime will always be with us. Yet we still condemn crime and work to reduce it."

Well, it's an analogy, but a bad one. The people who claim that anarchy won't work are not claiming that the State is a negative factor in society, like crime, with which we must learn to live. Instead, they are claiming it is necessary for social order, and that eliminating it, while not impossible, would be disastrous. And, if this argument is correct, then the State is morally defensible, as necessary to human social life, and its taxes and suppression of other defense agencies would certainly not be forms of aggression.

Midtown

Looking north from the NYU Law School:


(Click for a larger image.)

The (Extremely Shallow) Ethicist

This is a bit old, but it's a great demolition of one of Randy Cohen's shallow and utterly conventional bits of "ethical" analysis. My general impression is that Cohen equates ethics with "what will make you liked at a Manhattan cocktail party."

Coming to New York?

This is the time of year to do it -- late September to early October. I was just looking at our ten-day forecast, and the high every day is between 70 and 75, and almost every night the lows will be down in the 50s. Warm enough by day for outdoor activities, even swimming -- I was in the Atlantic three days ago -- and beautiful sleeping weather at night.

Wednesday, September 16, 2009

Well, Duh!

From a angry left-wing blogger:

"The right-wing accusations against Barack Obama are true. He is a socialist, although he practices socialism for corporations. He is squandering the country’s future with deficits that can never be repaid. He has retained and even bolstered our surveillance state to spy on Americans. He is forcing us to buy into a health care system that will enrich corporations and expand the abuse of our for-profit medical care. He will not stanch unemployment. He will not end our wars. He will not rebuild the nation. He is a tool of the corporate state."

This is a surprise?! The corporate state will not allow the election of anyone from off the reservation. The mere fact that Obama could get elected was a guarantee there would be no major change. (I write this as he increases the number of troops in Iraq and Afghanistan and fights to extend the Patriot Act.)

Unwelcome Screen

Did you ever arrive at a web site to read an article by some friends, only to encounter a full-screen ad instead? Then, way up in the corner somewhere, you notice a link that reads, "Skip this welcome screen."

Since the screen was neither welcoming me to anything nor was it welcome on my monitor, I suggest changing that to, "Skip this unwelcome screen."

Tuesday, September 15, 2009

That Mysterious Life Force

I'm reading John Gribbin's The Scientist, a thoroughly whig history of science. At one point, celebrating the great advance the dismissal of vitalism represented, he writes, "By the end of the nineteenth century it was clear that there was no mysterious life force at work in organic chemistry..."

This is the kind of thing you see all the time in discussions of vitalism... but it is thoroughly ahistorical. Recall that the mechanical philosophers had dismissed Newton for positing "a mysterious gravitational force," and that science later advanced by positing "a mysterious electrical force" and "a mysterious magnetic force." The idea that there was "a life force," given these precedents, was a perfectly respectable scientific hypothesis, and, if it had been found, it would have been no more mysterious than gravity, electricity, or magnetism. (And given the repeated failure, after over a century of promises, of reductionists to produce life from non-life, perhaps it will yet prove to be a fruitful hypothesis!)

Idealist Skin Lotion

Tonight, on the bottle of skin lotion in my bathroom, I read its claim of "Consciousness in Cosmetics."

As an idealist, who holds that there is consciousness in everything, I thoroughly approve of their metaphysics.

Washington Square Park





Thursday, September 10, 2009

Bobby Boy on CNBC!



You did a great job, Bob, but was bringing that extra chin along really necessary?

Fancy pants conference room

At NYU Law School, where I'm waiting to hear Richard Epstein present to Ronald Dworkin's colloquium.








Query: Why are the libertarians at the Market Process colluquium stuffed in a little conference room without microphones, pitchers of water, mahogany desks, plush chairs, million dollar views, etc., while the egalitarians have all of this? It's time for some redistribution, folks!

Saturday, September 05, 2009

And it just gets worse





End of the night at Nos Da





Hegel

'[Hegel] finds the Absolute, God, in the development of the thought of mankind, in the rise and fall of nations, in the establishment and overthrow of social institutions, in the movements of history, just as truly as did the Hebrew prophets, or Carlyle. His task is to find God everywhere, to justify 'the faith' -- if I may use this word of what was to him a rational necessity, and not a conviction unjustified by reason -- that the Absolute Spirit lives and moves in all things.'
-- Henry Jones, 'Idealism and Epsitemology', from The Scottish Idealists, ed. David Boucher

Nasty!

I'm sitting in the postgraduate research room at the School of European Studies. I just went to search for a drinking glass and found one that looked clean. Luckily, just before I drank out of it, I noticed a dark, disturbing film on the bottom of the glass.

I think the film was Italian, perhaps directed by Fellini.

Friday, September 04, 2009

Freedom's Just Another Word for...

I'm attending a British Idealism conference in Manchester. A speaker who admitted he wasn't very familiar with Brish Idealism (he is a Isaiah Berlin scholar, I take it) was questioning the idealist conception of freedom. Someone in the audience explained it as 'the will to subjectively choose what is objectively correct.'

'Ah,' the speaker, 'objectively correct to whom?'

What a curious muddle! Something that is correct only 'to' someone is subjectively, not objectively, correct. What 'objective' means is precisely 'to any and all possible perceivers.' And, of course, it is simply a further muddle to introduce beings incapable of perceiving the objective item in question, as if that raised doubts about its objective status. 'Would this be objectively correct for ants?' makes no more sense than 'Is it objectively true for ants that Mars has two moons?' It is objectively true, not 'for' anyone, that Mars has two moons, and it is also objectively true that ants are a kind of being that cannot peer through telescopes or count to two. It is objectively true that murder is wrong, and if ants were the sort of being capable of murder, which they are not (as far as we know!), it would be wrong for them to commit murders.

Thursday, August 27, 2009

I'll Ber Doggone

On the news I heard the sad story of a woman whose dog died in the car because she had left it inside, with the windows up, for four hours. The explanation, she said, was that she didn't know her dog was in the car -- "my husband put it in there earlier in the day."

So her husband would store the dog in the car?!

Tuesday, August 25, 2009

Science Versus Religion

I've been listening to a series of lectures by Professor Frederik Gregory. One of the interesting points he makes, a number of times during the lectures, is that research by historians of science has shown that the idea of a long-standing conflict between religion and science is something that has been read back into the past by modern intellectuals. Of course, there were incidents where some particular scientist ran afoul of some particular religious body (like Galileo). But, basically, until the mid-19th century, just about no scientists or religious people understood the two to be at conflict in some fundamental way. Most scientists talked of how their findings "showed the glory of God" -- and for the most part, this was not just for show, as most of them were genuinely devout. (Newton, for instance, spent more of his life on Bible studies than he did on physics or mathematics.)

Furthermore, Gregory notes, the change in this view did not originate with science, but with the political radicals of the mid-19th century, who persuaded the younger scientists of the time that to be "progressive" one ought to be materialistic and atheistic. It was only then that the exact same sort of findings that, a generation before, would have displayed the glory of God, now were seen as indicating his non-existence!

How I Spent My Summer Vacation

Actual transcript of a text message conversation I had this afternoon:

UNKNOWN NUMBER: Yo nigga whats up

(Time passes... I have not looked at my phone.)

UNKNOWN NUMBER: What nigga u cant text me back

(Time passes... I have not looked at my phone.)

UNKNOWN NUMBER: Ave G

(I look at my phone.)

ME: Ave H

UNKNOWN NUMBER: Ave g nigga

ME: No. Ave H.

UNKNOWN NUMBER: U want to meet at ave h now

ME: No make that Ave G

UNKNOWN NUMBER: U know who this is?

ME: No u know who this is?

UNKNOWN NUMBER: Yeah roger kelly this jesse nigga

ME: This ain't no roger kelly!

JESSE: Who is it then

ME: Jo

JESSE: Jo who

ME: Jo mama

In any case, it turns out I owe Jesse $30, and I have to go meet him in Matamoras now to pay up, so I've got to run!

Monday, August 24, 2009

How Did I Get All This Stuff?

I'm running verify disk on my Mac right now, and I see my hard drive has 183,231 folders, and over 700,000 files. Now I used to now my way around a UNIX volume to the extent I could say what almost every directory (folder) was for, but no one but no one can keep track of 183,231 folders.

Sunday, August 23, 2009

Extremely High Time Preference Is... Holy!

Hans Hermann-Hoppe and his followers try to equate morality with low time preference. Consider, for instance, this quote from here:

"As such, decadence is antithetic to moral values, which are rooted in orientation towards long-term prosperity and happiness. Such values are the conceptual embodiment of low time preference, which is manifested in characteristics of thrift, diligence and long-term self improvement, all of which involve forgoing immediate satisfaction in anticipation of gains in the future."

Now, obviously, this is a pretty juvenile and debased sort of "moral philosophy," if one even wants to call it that: it's evil to enjoy yourself as much as possible now because if you hold off you'll be able to really, really enjoy yourself later! But it still amused me to learn, while listening to a lecture series on the High Middle Ages, that what Hoppe and his horde consider the essence of morality would, in the Middle Ages, have been considered positively wicked: worrying about the future showed a lack of faith in God. The followers of St. Francis of Assissi (I know, Hoppe-heads, he doesn't compare to St. Hans of Las Vegas, but he was OK!) went so far as to refuse to consider where they would head for the day when they got up in the morning. Instead, they would spin around until they fell over dizzy, and then head in whatever direction their head was pointing.

UPDATE: Oh, and the guy who wrote the piece I link to above obviously got his Rousseau from someone else's really bad summary; for instance, he repeats the old canard associating Rousseau with the idea of the "Noble Savage"! I guess his time preference was a little too high to read Rousseau for himself!

UPDATE II: Out of curiosity, I checked, and, in fact, as I suspected, Rothbard has the exact same "bad Cliff Notes" understanding of Rousseau as the author quoted above: 'Of the fourth, containing Burke’s views on Rousseau, Rothbard said that his opponent’s use of it only revealed "Professor Weston’s confusion on the nature of the libertarian tradition." Hostility to Rousseau proved little because an "individualist anarchist" would oppose him: "for the Vindication was not opposed to ‘civilized society’.... On the contrary, as I pointed out, Burke, in the libertarian tradition, champions ‘natural society’ as against the depredations of the State."' (Source.)

Of course, Rousseau was not at all opposed to civilized society, either, and you'd pretty much have to have not read him at all to think he was.

UPDATE III: Bob thinks this fellow I quote is just saying something like "Thrift is a virtue." No, Bob, there really are no virtues, except in that they help you have a whole lot of sensual indulgence later on:

"Moral virtues are the means for humans to attain luxury, prosperity and happiness. If these virtues dwindle in the presence of luxury, then this is cause for concern, not because these virtues are inherently valuable, but because they are the means of sustaining a good life in the future."

Wednesday, August 19, 2009

Home Drug Testing

I was struck by the fact that the gas station I stopped at today had a big rack of these at the checkout counter. I anxiously picked up a kit and rushed home with it. I eagerly tore it open and immediately put it to use.

Now I am anxiously awaiting the answer to a question that's been bugging me for some time: Have I been secretly doing drugs all these years?

Tuesday, August 18, 2009

Terrible Home Depot Mistake

I reached for the slug repellent without paying much attention, went home, and applied it. Next thing I know, the slimy little bastages are all zooming around the yard at 50 miles per hour. I take another look, and, what do you know... I had grabbed the "slug propellant" instead.

Monday, August 10, 2009

A Roman Naval Battle...

to be held in Queens, courtesy of my friend Duke Reilly.

Properties of the Wine Tasting Sequence

Properties of the Wine Tasting Sequence................. wb ........090723 - 090810

1. Introductory notes.

1.1. Since I can't conveniently represent uppercase Greek pi, the usual symbol for a product (as uppercase Greek sigma is the usual symbol for a sum), I'll use bold uppercase P.

1.2. By an unfolding sequence, we mean a sequence derived from an initial string (or digit) by repeatedly applying a production which appends to the sequence thus far a specific transform of the sequence thus far. Let f be a string function. If s is a string in the domain of f, &f denotes the function &f(s) ≡ sf(s). The unfolding sequence derived from function f and initial string s in the domain of f is U=&f^∞(s).

1.3. Trivially, any sequence can in fact be seen as unfolding by a sufficiently perverse choice of f: f(d(0)d(1)...d(i)) ≡ d(i+1), 0 ≤ i < ∞.
We shall simply ignore this, looking at sequences that can usefully be defined by unfolding processes.

2. Unfolding sequences. The Wine Tasting Sequence (WTS).

2.1. Let W be an unfolding sequence of the digits ±1 as follows: f(digit d) = -d; f(st)=f(s)f(t); W=&f^∞(1).
W = 1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 1 ...
Suitably redefining f and the initial digit yields the equivalent forms
W1 = 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 ...
W2 = 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 1 ...
W3 = A B B A B A A B B A A B A B B A ... etc.
We know this sequence as the "Wine Tasting Sequence" from the associated Wine Tasting Problem, q.v.

2.2. Concatenations. Given s(i), i ε I (the s are indexed by I), their concatenation is a sequence written Γ{i ε I, s(i)} or Γ{i, s(i)} or Γs(i). The order of I is assumed to rule (I must be ordered). Let w(i) be the digits of the WTS. W=Γ{0 ≤ i < ∞, w(i)}.

2.3. Transforms. A transform (intuitively, as used here) is a functional which derives from any of a class of functions or similar entities from analysis another, usually different, entity in a uniform way. Well known useful examples: Fourier transform, Laplace transform, dual (of a boolean expression).

2.4. Polynomial transform. If s(i), 0 ≤ i < ∞ are taken from a field (such as the real numbers), the polynomial transform of Γ{i, s(i)} is given by
Poly Γ{i, s(i)} ≡ Σ{i, s(i) x^i}.
Variable "x" should be specified somehow, but we'll just understand "x".

2.5. For the WTS, Poly W = 1 - x - x^2 + x^3 - x^4 + x^5 + x^6 - x^7 - x^8 + ... The properties of this series would be hard to reckon, except that for certain unfolding sequences, Poly takes the form of an infinite product; the WTS is one of these.

3. Functional equations. What a difference a sign makes.

3.1. (1+x)Φ(x^2) = Φ(x).The general solution of this functional equation can be expressed in a manner reminiscent of a differential equation: Φ(x) = σ(x) φ(x), where
σ(x) is the general solution of the functional equation Φ(x^2) = Φ(x),
φ(x) is any particular solution of the above equation (1+x)Φ(x^2) = Φ(x).
σ(x) may be expressed in terms of the general periodic function τ(x+π) = τ(x). It will trouble us no more.
Any particular φ(x) will do; we choose
3.1.1. φ(x) ≡ P{0 ≤ i < ∞, 1+x^(2^i)} = (1+x)(1+x^2)(1+x^4)(1+x^8)..., |x| ≤ 1. This unfolds into
3.1.2. φ(x) = Σ{0 ≤ i < ∞, x^i} = 1 + x + x^2 + x^3 + x^4 + x^5 + ..., |x| ≤ 1. Then φ(x) = 1/(1-x). Note that 1/(1-x) does indeed satisfy 3.1.

3.2. (1-x)Φ(x^2) = Φ(x).The general solution of this functional equation is Φ(x) = σ(x) φ(x), where
σ(x) is the general solution of the functional equation Φ(x^2) = Φ(x), as before,
φ(x) is any particular solution of the above equation (1-x)Φ(x^2) = Φ(x).
Any particular φ(x) will do; we choose
3.2.1. φ(x) ≡ P{0 ≤ i < ∞, 1-x^(2^i)} = (1-x)(1-x^2)(1-x^4)(1-x^8)..., |x| ≤ 1. This unfolds into
3.2.2. φ(x) = Σ{0 ≤ i < ∞, w(i) x^i} = 1 - x - x^2 + x^3 - x^4 + x^5 + ..., |x| ≤ 1. This is Poly W. Unlike 3.1.2, it appears to have no simple closed form.

3.2.3. Pseudocode for φ(x) = Poly W:
real PolyW(real x) {
P = 1-x;
while MAKINGPROGRESS {
x = x*x;
P = P*(1-x);
}
return P;
}

3.2.4. Binary details for Poly W:
3.2.4.1. φ(1/x) = (x-1)/x · (x^2-1)/x^2 · (x^4-1)/x^4 · (x^8-1)/x^8 · ...
3.2.4.2. φ(1/2) = 1/2 · 3/4 · 15/16 · 255/256 · ...
= 1 - 1/2 - 1/4 + 1/8 - 1/16 + 1/32 + 1/64 - 1/128 - ...
3.2.4.3. φ(1/2) = 0.350183865...
3.2.4.4. In binary radix notation:
1.0010110011010010110100110010110... (a),
0.1101001100101101001011001101001... (b),
0.010110011010010110100110010110... φ(1/2) = a-b = a-(2-a) = 2(a-1).

4. Properties of the WTS function φ(x) = Poly W.

4.1. Ω(x): From 3.2,
4.1.1. (1-x)φ(x^2) = φ(x). Therefore at -x,
4.1.2. (1+x)φ(x^2) = φ(-x). Therefore
4.1.3. Ω(x) ≡ (1+x)φ(x) = (1-x)φ(-x) = Ω(-x). Therefore Ω(x) is even.
4.1.4. φ(-x) = ((1+x)/(1-x)) φ(x) = r φ(x), x <> 1.

4.2. Some values of φ(x) and Ω(x):

····x······r············φ(x)··········φ ≈··········Ω(x)····
··························································
···-1······0····0.0····························0.0
··-3/4··1/7···0.466212439············0.11655311
··-2/3··1/5···0.712946495············0.237648832
··-1/2··1/3···1.050551595··21/20··0.525275798
··-1/3··1/2···1.170374832·············0.780249888
··-1/4··3/5···1.167279552···7/6····0.875459664
····0·····1······1.0···························1.0
···1/4··5/3···0.700367731···7/10··0.875459664
···1/3···2······0.585187416···7/12··0.780249888
···1/2···3······0.350183865···7/20··0.525275798
···2/3···5······0.142589299···1/7···0.237648832
···3/4···7······0.066601777···1/15··0.11655311
····1······∞·····0.0···························0.0

···max φ(x) at x ≈ -1/3; max Ω(x) at x = 0.

5. Where to go from here. Not sure.

Friday, August 07, 2009

Kalt und Köstlich

While dining with my friend Michael Bischoff in Zurich, I saw the above heading on our menu. "Ah," I said, "given we are in Zurich, I know what that means: those are the dishes that are cold and costly, as opposed to the others that are 'warm und köstlich" or others that are "heiss und köstlich."

Friday, July 31, 2009

My Gift to the People of Switzerland

I realized, while in Switzerland, that there is no German word for "brunch." So I gift to the wonderful people of Switzerland my coinage, früstagessen.

There will be statues of me at Swiss brunch places 100 years from now.

Sunday, July 26, 2009

Watch for It!

Remember the Wine Tasting Problem, and the associated sequence, which we can write

ABBABAABBAABABBABAAB...

or

01101001100101101001...

or for that matter

10010110011010010110...

More on this sequence--including an ultrarapidly converging version of its polynomial transform--COMING SOON! Watch for it! Don't be left out!

Not Sure If They Really Mean It




No, I did not place the ashtray there myself.

In the Alps











Thursday, July 16, 2009

City Bird, Country Bird

Did you ever feed city birds by hand? They may be wary, but they know what's going on, and will come get the food as soon as they feel safe.

Did you ever try to feed country birds? They have no idea what you are doing. "Whoa, this guy is throwing junk at us!"

Taking food from another creature is not an "instinct" that birds have. They learn it.

A Trip Down Memory Lane...

to read the column that got me uninvited to testify before the US Senate Finance Committee.

Wednesday, July 15, 2009

One nice, one weird, one silly

Say you want to find the min or max of f(x,y) subject to a constraint that g(x,y)=0. Has it ever occurred to you that the values of x and y required are the same as the values of x and y required to find the min or max of g(x,y) subject to f(x,y)=0? I bet it hasn't. The requirement is entirely symmetrical (the "curly 'd'" notation is much prettier, but I can't be bothered to figure out how to do it here):
f1(x,y)g2(x,y)=f2(x,y)g1(x,y).

I can't get my intuition behind this: in boolean algebra,

(p or q) is equivalent to (p and not q or q). Yes, I know it's true, do the truth tables if you doubt me. It just seems wrong. P.S.:

(p and not q or not p and q) is not equivalent--that's exclusive or.

Let's for a moment write logical conjunction as product and disjunction as sum. Boolean algebras have the distributive rule p(q+r)=(pq+pr). Familiar, right? But boolean algebras also have this one: p+qr=(p+q)(p+r). Aside from the trivial p=0, when else is this true in arithmetic? The challenge is 7th grade level, but I like the answer.

Monday, July 13, 2009

Promises, Promises

I was just watching a movie previe in which the following dialogue took place:

YOUNG GIRL: We're going to die!
NICHOLAS CAGE: I promise you, I will never, ever let that happen.

I've heard that sort of line often, and what's shocking is that it's always portrayed as a responsible parent doing the caring thing for his/her child! Yes, promising your child immortality -- it's the responsible thing to do.

Friday, July 10, 2009

Morals Are Not Objectively Real and Neither Is...

My friend laughed. "If morals are objectively real, where are they?"

"Hmm," I thought, "good point. So, the only things that are objectively real are those located in space and time."

"But, wait... the physical universe is not located in space and time, so..."

"The physical universe is not objectively real!"

Monday, July 06, 2009

Some Smart Critters

Here:

"By contrast, an ant nest or a beehive can behave as a united organism in its own right. In a beehive, the workers are happy to help the community, even to die, because the queen carries and passes on their genes."

Who knew ants were familiar with genetic theory?

Monday, June 22, 2009

Tarski and Hutch

Well, Wabulon and I are developing the screenplay for the pilot of a new TV series, based on Starsky and Hutch, but in which the character of Starsky is replaced by that of Alfred Tarski, the famed twentieth-century mathematician. Here is my first draft, awaiting Wabulon's comments:

Play Pen Night Club: Night.


(Inside people are dancing. Tarski and Hutch stand at the bar with Huggy.)

Huggy: How do you like this little gold mine I gotta take care of until my cousin Louie returns?

Tarski: Huggy Bear, you’re just an invariant transformation of Superfly.

Huggy: Funny, Tarski. But you know Superfly and me ain't never been in any sorta one-to-one correspondence! Anyway, my uncle got a big stake in frog futures. He had to leave for Venezuela to check out his new frog ranch. All this happened after the IRS read his latest tax returns. Really.

(Walks away. Hutch spots two girls sitting alone.)

Hutch: Would you look at that? (Hutch points at girls.)

Tarski: Look at that. (Tarski’s looking at a tiling pattern on the ceiling.)

Hutch: Look at that. (Points at girls.)

Tarski: Look at that. (Points. They both look and see the girls.)

Hutch: What are you gonna do, just stand here and stare? You gonna go over and talk to them.

Tarski: When you say “Go over and talk to them,” do you mean I should go over and talk to them?

Hutch: Yeah, that’s what I mean. (Sips his beer.)

Tarski: Okay. (Walks around Hutch in a hyperbolic curve while mumbling about wanting to establish a set-theoretic relation with “one of those babes.”)

Hutch: On second thought, maybe I’d better take control of this situation.

Tarski: Why?

Hutch: Hey, you restrict your attention to first-order logic, and let me handle the babes, OK? Watch the master at work, huh?

(Walks over to the girls’ table and leans down to talk to them. He sits down. Tarski comes over.)

Hutch: Oh, ladies, excuse me. Uh, this is, uh…

Tarski: Tarski. Alfred Tarski.

Hutch: Alfred Tarski, one of the four all-time greats in the history of formal logic.

(The girls squeal a little.)

Bobette: Hello. (Shakes hands.)

Tarski: Hi, uh…

Hutch: This is Barbette.

Tarski: Barbette?

Bobette: Bobette.

Tarski: Bobette.

Hutch: And this is Jane.

Tarski: Hi, Jane. (Moves to shake her hand and knocks the glass Hutch is holding out of his hand and onto Jane’s lap.) I’m sorry.

Hutch: You’ll have to excuse my friend.

Tarski: Uh, I guess I’m a little nervous. I just sent out a paper claiming that that much of Euclidian solid geometry can be recast as a first order theory whose individuals are spheres, a primitive notion, a single primitive binary relation "is contained in," and two axioms that, among other things, imply that containment partially orders the spheres.

Bobette: Oh, my, that’s impressive! I think you’re kinda foxy.

Tarski: Yeah? Would you like to see my cylindric algebra?

Bobette: Yeah, baby. (Licks her lips.)

(Tarski sits down and scribbles a number of formulae on a cocktail napkin, then holds it up for Bobette.)

Tarski: Foxy, huh?

Bobette: Yeah.

Tarski: Hey, you know something? The two of you look like twins. Did someone cut one of you into a finite number of pieces, and then re-assemble the pieces into the two of you?

(Huggy interrupts.)

Huggy: Hey, excuse me.

Hutch: What?

Huggy: Dobey’s on the phone.

Tarski: That sentence is true if and only if Dobey’s on the phone!

Huggy: Well, he IS on the phone, and he wants to speak to one of you. Says it’s urgent.

Tarski: Oh, no. (Hutch gets out a coin.)

Hutch: Heads or tails.

Tarski: What?

Hutch: Heads or tails.

Tarski: Heads.

Hutch: No, it’s tails. (Without looking.) Tough break, foxy.

Tarski: Terrific. (Leaves.)

Bobette: Do you guys come here a lot?

Hutch: No, no. As a matter of fact, we don’t.

(Tarski picks up the phone.)

Tarski: Yeah? What? But Captain, this is our night to work on binary relations. Yeah…Okay. Okay! (Hangs up and goes back to the table.)

Hutch: We really don’t have too much time off. We work 12 to 14 hour shifts.

Tarski: Hey, uh, the Captain says we gotta go.

Hutch: What? Ah.

Tarski: Sorry ladies. (Shakes their hands.)

Hutch: Well, it was nice to meet you.

Jane: Hey, are you guys really policemen?

Tarski: The sentence "We are policemen" is true if and only if we are policemen.

Hutch: Yep.

Bobette: That’s exciting.

Tarski: Yeah?

Bobette: Yeah.

Hutch: We should go. (Walks past Tarski.)

Tarski: Hey, I thought I proved to you that the question of whether or not we should go is formally undecideable.

Hutch: Yeah, whatever, Al. Let’s just get out of here.

Bobette: Bye. (They walk off. Tarski turns back.)

Tarski: Hey, hey, I didn’t get that cardinal number of yours. Do you commute here?

Hutch: Yeah, no…

Tarski: What?

Hutch: Get both of them, will you? (Tarski goes back and speaks to Bobette and then comes back.) You got them, huh?

Tarski: Yeah.

Hutch: Did you write them down?

Tarski: Tattooed on my brain.

Hutch: Oh. (They leave.)

Baby, Baby, Where Did That Post Go?

For those of you wondering where the Bruno and Ron Paul post went: it was a slug trap. I put it up, watched the comments build up, and once I had caught enough of the slimy little critters, I threw the thing out, without of course, looking inside.

Saturday, June 20, 2009

My Father's Limerick

I passed by "Man from Ravenna" again and was reminded of what I believe is my father's only limerick. I don't think I've posted it here before, but who really knows the future, or the past, or anything but this passing moment? Now what the ^&;$#!*$% was I trying to post? Oh, yeah, the limerick:

There was an old man of Rhode Island
Who was known as King William the Silent.
    When they bade him good morning,
    He replied without warning,
"Garunchnik!" and then he grew violent.

Saturday, June 13, 2009

Two Years from Now, What Will Be Happening?

Since pundits gain a great deal of fame from having correctly predicted the future, let me take a stab at saying what will being going on, say, two years from now, on June 13, 2011.

First of all, the stimulus programs will be seen to have fallen short of the mark. The Dow will stand at, say, 11,985, give or take a couple of points. Gold will be about $1515 an ounce, and oil at $97 per barrel. The yield on ten-year treasuries will be just under 3%. Unemployment claims will be stuck above 400,000.

In response, Paul Krugman and Brad DeLong will be saying "I told you so: the stimulus was too small." And in his response to their response, on June 13, 2011, Mario Rizzo will write a blog post pointing back to the blog post where he foresaw Krugman saying this, and claim that Hayekians have a right to say "I told you so" as well. And I predict Daniel Kuehn will come back with a note saying Mario's post has not proved anything. And Mario will agree!

Friday, June 12, 2009

Parting Shot

I had stopped by to peruse the recent messages and was just about to sign out when I for no particular reason remembered this, due to W. van O. Quine:

"Yields a falsehood when appended to its own quotation" yields a falsehood when appended to its own quotation.

Keep up the good work.

Euphemisms II

It's not just abortion where these euphemisms bug me either. I think it is sometimes OK to euthanize your pet, but... you did not "...