"It is a symbol of Irish art. The cracked lookingglass of a servant." -- James Joyce

### 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

So her husband would

*store*the dog in the car?!### 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!

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!

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!

### 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.### 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

"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."

"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."

### 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:

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?*### 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.

### 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.

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.

### 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."
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