I'm Famous

This guy actually took my side against one of his own. Maybe these gold bugs are objective.

The "Fascist" Road to Success

Inspired by Bob Murphy's witty barb on this very blog, I make my bid for the number one article on LewRockwell.com for the second straight year.

Pail Challenge IIA

Pail Challenge II -- minor corrections 070125
Oakland and Novato, CA, (c) 2006-7 by W. Bloch

A monk sat on the beach contemplating the mind of God. Nearby, he saw a little boy with a pail digging in the sand. After the boy had dug a hole, he ran down to the ocean, filled his pail, ran back, and poured the water into his hole in the sand. “What are you doing?” asked the monk. “I’m going to pour the ocean into the hole,” answered the boy. “That you cannot do,” said the monk with a smile. “Nor can you understand the mind of God,” said the boy.

0. Dedication

Respectfully dedicated to A. Hamburgarius, the most beautiful girl in the world.

1. Introduction

Remember those old chestnuts like, "You are given a 7-quart and a 9-quart pail; return from the well with exactly one quart"? PC.I posed these challenges:
1.1) For pails holding a >= b, respectively, give the set Z in terms of a and b of all possible returns from the well (the Special Pail Theory).
1.2) Design a parametrized production system (alphabet plus rewrite rules) or, equivalently, a Turing machine, to derive and return any member of Z.
1.3) Generalize to any finite number of pails a[i] (the General Pail Theory).
1.4) Does an infinite number of pails add anything interesting (Transcendental Pail Theory)?

Hereinafter, I address PC.II.1.1, solutions in the Special Theory.

2. General Typographical and Other Conventions Used or Likely to be Used

2.1) “u <= v” means “u < v or u = v”; between sets, “u is a subset of v, possibly equal”
2.2) “u >= v” means “u > v or u = v”; between sets, “u is a superset of v, possibly equal”
2.3) “f[i]” means a vector having elements of the type implied for “f” and referred to by “f” subscripted by an initial segment of the nonnegative integers.
2.4) “f[i]” may instead be replaced by consecutive unsubscripted letters.
2.5) To make a vector explicit, square brackets will be used, thus: “[…]”.
2.6) To indicate the corresponding unordered set, braces will be used, thus: “{…}”.
2.7) All references to numbers refer to integers only (often, nonnegative integers).
2.8) A solution required for a system of equations f[i](u[j]) = 0 is required in integers (a “Diophantine solution”).
2.9) “m” and “n” refer to integers in an existential context, “…for some m,n.”

3. Particular Conventions for the Special Theory of Two Pails

3.1) “a” and “b” refer to the given capacities of pails A and B, a >= b > 0.
3.2) “x[t]” and “y[t]” refer to the contents of pails A and B, respectively, at time t >= 0.
3.3) z[t] = x[t] + y[t], viz., the total contents so far.
3.4) For given t, “x” means “x[t]” etc. “x’” (“x” prime) means “x[t+1]” etc.

4. Greatest Common Divisor

4.1) Definition: The greatest common divisor (gcd) of u[i] written “gcd(u[i])” is the greatest common divisor of the u[i]. Uhh…yeah. gcd(u[i]) divides all the u[i].
4.2) Definition: Integers u[i] are relatively prime iff gcd(u[i]) = 1.
4.3) If g = gcd(u[i]), then u[i]/g are relatively prime.
4.4) If p is prime, then gcd(u,p) = 1 or p.
4.5) A basic arithmetic theorem (proof, reader?) states: gcd(u,v) = mu+nv.
E.g.: gcd(28,70) = (-2) x 28 + (1) x 70 = 70 – 56 = 14; 28/14 = 2, 70/14 = 5; gcd(2,5) = 1.

5. The Conservative Special Theory of Two Pails

In the colloquial problems it is generally assumed that water emptied is discarded, and so cannot be part of the solution. Here we assume—to the contrary—that the water emptied is saved and so is necessarily part of the final solution (making it difficult to procure, e.g., one from seven and nine).

It should be obvious that the set of available solutions is given by:

5.1) z = ma+nb, m >= 0, n >= 0.

6. The Standard Special Theory of Two Pails

6.0) Rededication

Affectionately rededicated to A. Hamburgarius, the most beautiful girl in the world.

6.1) If we stipulate that water emptied from a pail is discarded, we then have as the totality of possible variations of z, the total measured, these conditions and events:

6.1.1) Initial conditions x = 0, y = 0, z = 0
6.1.2) Fill or top up A. x’ = a, z’ = z-x+a
6.1.3) Fill or top up B. y’ = b, z’ = z-y+b
6.1.4) Empty A, discard. x’ = 0, z’ = z-x
6.1.5) Empty B, discard. y’ = 0, z’ = z-y
6.1.6) Top up A from B. z’ = z
6.1.7) Top up B from A. z’ = z

6.1.8) Note: Topping up, as opposed to filling, A or B from the source is never useful, but we include it for generality, as it does not invalidate any subsequent deductions.

6.1.9) Note: These events are indeed sufficient to effect the “trickier” moves—the basis of interesting solutions—viz.: topping up A from B, emptying A, and using the remaining contents of B; and vice versa.

6.1.10) Note: All intermediate and final solutions z must conform to two conditions: not only must z >= 0, but also z <= a+b (which allows for the physical realization of the required operations). We seek Z, the set of all attainable z.

6.2) Definitions:

6.2.1) Definition: g = gcd(a,b)
6.2.2) Definition: A number u has property P written “P(u)” iff u = ma+nb.
6.2.3) Definition: A number u has property Q written “Q(u)” iff u >= 0.
6.2.4) Definition: A number u has property R written “R(u)” iff u <= a+b.
6.2.5) Thus P(g) & Q(g) & R(g).

6.3) The Standard Special Theory—Properties of Solutions

6.3.1) Initially, P(0) & Q(0) & R(0).
6.3.2) All the six possible operations 6.1.2-6.1.7 preserve P, Q, R. (P is preserved for x and y, and therefore also for z.)
6.3.3) Therefore, P(z) & Q(z) & R(z) for all initial, intermediate, and final z in Z, i.e.,

6.3.4) P(z[t]) & Q(z[t]) & R(z[t]) for all t >= 0. In other words, if z is in Z (an attainable solution), then 0 <= w = ma+nb <= a+b, for w = z and for all intermediate w between initial condition 0 and final solution z.

6.3.5) Incidentally, consider this additional property; it is a property of the state [x,y].
Definition: A state [x,y] has property S—“S([x,y])”—iff x = 0 or x = a or y = 0 or y = b.

6.3.5.1) Initially, S([0,0]).
6.3.5.2) All the six possible operations 6.1.2-6.1.7 preserve S.
6.3.5.3) Therefore, S([x,y]) for all initial, intermediate, and final [x,y], x+y=z in Z.
6.3.5.4) S([x[t],y[t]]) for all t >=0, as for 6.3.4.

6.4) The Standard Special Theory—The Set Z of All Solutions

6.4.0) Iterate Rededication

Adoringly rerededicated to A. Hamburgarius, the most beautiful girl in the world.

6.4.1) A Class of Solutions

6.4.1.1) Definition: Z(u,v) is the set of all solutions for a = u, b = v, u >= v > 0.

6.4.1.2) Definition: z(u,v)(i,j), u >= v > 0, 0 <= i, 0 <= j <= 1, is the result of these operations:
6.4.1.2.1) Pail sizes a = u, b = v
6.4.1.2.2) (6.1.1) Initial conditions x = 0, y = 0, z = 0
6.4.1.2.3) REPEAT i TIMES {
6.4.1.2.4) (6.1.3) Fill or top up B.
6.4.1.2.5) (6.1.6) Top up A from B.
6.4.1.2.6) IF x = a & y > 0 THEN {
6.4.1.2.7) (6.1.4) Empty A, discard.
6.4.1.2.8) (6.1.6) Top up A from B } }
6.4.1.2.9) REPEAT j TIMES {
6.4.1.2.10) (6.1.3) Fill or top up B }
6.4.1.2.11) END.

6.4.1.3) Therefore, z(a,b)(i,j) = ib mod a + jb unless a divides i.
6.4.1.4) Therefore, z(a,b)(i,j) = ib mod a + jb is a solution; it is in Z(a,b).
6.4.1.5) Therefore, z(a,b)(i,j) = ib mod a + jb has the properties P, Q, R.

6.4.1.6) Note: The operations (6.4.1.2.--) are specified in ZOMBIE, an undead language.

6.4.2) All Solutions

6.4.2.1) If P(w) then w is divisible by g, because (ua+vb)/g = u(a/g)+v(b/g) in integers.
6.4.2.2) Therefore, {z(a,b)(i,j), 0<=i, 0<=j<=1} <= Z <= {w, P(w) & Q(w)} <= {gk, 0 <= k}.
6.4.2.3) So, K = {z(a,b)(i,0), 0 <= i < a} = {ib mod a, 0 <= i < a} <= {gk, 0 <= k < a/g} = N.

6.4.2.4) The set N contains the first a/g nonnegative integers gk. K has some of them. In fact, K = N. Proof: Assume the contrary. Then, by the “pigeonhole principle,”

6.4.2.4.1) Two of the {ib mod a, 0 <= i < a} are equal: mb mod a = nb mod a, 0 <= n < m < a.
6.4.2.4.2) Therefore, (m - n) b mod a = 0, 0 < m – n < a.
6.4.2.4.3) Therefore, (m - n) b/g mod a/g = 0, 0 < m – n < a/g.
6.4.2.4.4) That implies that m – n is a multiple of a/g. It is not. Q.E.D.

6.4.2.5) Note: This argument can be adapted to the proof of (4.5).

6.4.2.6.1) Also, z(a,b)(a,0) = a.
6.4.2.6.2) Therefore, {z(a,b)(i,0), 0 <= i <= a} = {gk, 0 <= k <= a/g}.
6.4.2.6.3) Therefore, {z(a,b)(i,j), 0 <= i <= a, 0 <= j <= 1} = {gk, 0 <= k <= (a+b)/g}.

6.4.2.7.1) But {gk, 0 <= k <= (a+b)/g} = {w, P(w) & Q(w) & R(w)}.
6.4.2.7.2) Therefore, {gk, 0 <= k <= (a+b)/g} = {w, P(w) & Q(w) & R(w)} <= Z(a,b).

6.4.2.8) Therefore from (6.3.3) and (6.4.2.7.2), Z(a,b) = {w, P(w) & Q(w) & R(w)}.

6.4.2.9) z is in Z(a,b) (i.e., it is attainable) iff 0 <= z = ma+nb <= a+b.

6.4.2.10) All 0 <= z <= a+b, are in Z(a,b) iff a, b are relatively prime.

6.4.2.11) There is a simple isomorphism of scale between the (6.1.--) for two pairs of pails having the same ratio a/b, reflected in their sets of solutions. For example: the correspondence

6.4.2.12) z(a,b)(i,j) --- g z(a/g,b/g)(i,j)

establishes an isomorphism which we can abbreviate:

6.4.2.13) Z(a,b) = g Z(a/g,b/g).

Did the Human Genome Project show that DNA is quite variable?

I was perusing an amusing "Evolution is a Lie!"-type website that an old church friend sent me. (I'm not going to link to it because the atheist readers will just chuckle.) Anyway, one of the claims that was new to me concerned the alleged similarity of human and ape DNA. I think most of us have heard that humans are 99.x% similar to chimpanzees in DNA or something like that, right? But apparently the Human Genome Project changed that consensus. The website quoted this from a supposed news article:

Scientists Revise Map of Human Genome
By Jessica Berman, Washington

Scientists have revised the map of the human genome, saying human beings are genetically more complex than previously thought. The discovery has surprised experts who say it is likely to transform medical research. VOA's Jessica Berman reports.

In 2000, the Human Genome Project unveiled a road map of the six billion chemical bases, or alphabet molecules, that make up the body's genetic structure called DNA.

The DNA encodes for 30,000 genes or proteins which are responsible for every physical characteristic in the body, including eye and hair color. At the time, scientists said all humans could be 99.9 percent genetically identical.

But as they peered more deeply into the DNA of unrelated individuals, researchers made a startling discovery - large segments of their DNA, from thousands to millions of units, varied greatly, a phenomenon called copy number variations, or CNVs.

The discovery means that the genes of any given individual are at least 10 to 12 percent different from those of another human.


Regardless of whether it affects the theory of common descent, is the above true? I.e. do reputable scientists now say that the DNA between two human beings can differ up to 12%?

Is a capital surplus good or bad?

Peter Schiff says bad. I say he's full of it.

First let's kill all the lawyers...

On an email discussion group, libertarian bad boy Stephan Kinsella relayed a college moment that was quite instructive. He was in an econ class and they were learning about the Phillips Curve. He asked, "If all of the unemployed people died overnight, would that cause inflation?" He said that the teacher stuttered something about the curve shifting.

I'm Speechless

Jonathan Chait: "[Jonathan] Schell insisted [in 1990] that we could force Iraq to leave Kuwait with sanctions alone, rather than by using military force. But the years that followed that war made it clear just how impotent that tool was. Saddam Hussein endured more than a decade of sanctions rather than give up a weapons of mass destruction program that turned out to be nonexistent. If sanctions weren't enough to make him surrender his imaginary weapons, I think we can safely say they wouldn't have been enough to make him surrender a prized, oil-rich conquest."

So Chait says that sanctions obviously were a failure, because they weren't enough to make Hussein surrender the weapons he didn't have.

Not only that, they also failed to make him draw square circles and build perpetual motion machines!

(Via the below-mentioned Arthur Silber.)

Who's Number One?

You know who! That's right, baby.

Arthur Silber's Fish and Chips

For a long time we had a link on the right to Arthur Silber's blog. But then he shut it down, so I removed the link. Now, however, he's back, and blogging regularly, so the link is back, too. If you haven't read Arthur, he's worth checking out.

Arrogant Ignorance

I can have sympathy with those who are ignorant. After all, we're all ignorant about many things, right? And someone who is smart but arrogant about it is understandable to. But it drives me crazy to find people who are arrogant about their ignorance. I will start today's tirade with a parable:

A man lives in a searing desert. The only water he has ever seen in his life bubbles out of small springs in the cliffs.

One day, a trade route is established through his land, and he begins to meet many strangers. One thing he hears about from them is swimming. He has never conceived of such a notion. Secretly, he is jealous that all of these people have experienced something he's missed out on. But he won't admit that, even to himself. Instead, he proclaims that what these people are saying is irrational superstition, and that there supposed experiences of swimming are just self-delusion.

He begins to ask these people, with a sense of smug superiority, just how one goes about this "swimming." One traveler describes breaststroke to him, another backstroke, another the crawl, another butterfly, and so on. At this point, he exclaims "Aha! This proves these people are talking nonsense. Although they claim 'swimming' exists, they can't even agree about how its done!" He takes the fact that there are many ways to swim as proof that there is no way to swim!

If you decided that no one could combine such arrogance and ignorance, you'd be wrong.

Dennis Miller Takes on Whiny Liberals

Both the transcript and video link are here; you should definitely watch the video.

My favorite parts:

(1) On Bin Laden: "Who knows and who cares?" Right, it's not as if this is supposed to be a war on terrorism or anything. Only Al Franken would bring up Bin Laden at this point.

(2) On Saddam and the missing WMDs: "...has to be the worst bluff in the history of the universe."

Umm, actually, Saddam said he didn't have the weapons, so it wasn't a bluff. Bush didn't ask him if he had them, he said (in his State of the Union), "It is up to Saddam to lay out his banned weapons for all the world to see. He has done no such thing."

If we want to continue with the poker analogy, it would be as if Bush raised Saddam $100, Saddam said "I fold," and Bush said, "No you don't, liar! You're saying you've got a flush, but I've got a full house, so screw you! I'm taking your car too, since I just won the hand. Let's see what your hole card is... Huh! You didn't make your flush after all. Wow, normally I can read a man's tells. Anywho, where are your keys? I hope you've got a good CD player in there."

And the Beat Goes On

Seen in a comments section: "Aren't we getting close now to having the max power that will be required to do whatever the home user needs to do?"

It's bizzare that people still say this -- just like in the early 80s, when some PC visionary said, "No home user will ever need more than 64K of RAM." That's right: K!

A Bi' o' Ga'lic, Yeah, an' I' Migh' Wo'k

Communism got you down? Try giant rabbits!

(Hat tip to Radley Balko.)

Who'll stop the rain?

Only the soldiers!

Those Evil Iranians

I was listening to some news piece on NPR, and the reporter was talking about the UN sanctions on Iran for its nuclear program. He discussed how the Iranians were developing (I think) ground-to-air missiles that would attach to armored units, things that were originally developed by the Soviet Union for use against NATO forces.

The reporter further explained that Iranian officials insist the weapons are defensive, but that certain "experts" are worried that they are offensive. To explain, they played a clip from some analyst who said something like:

"This is a very provocative move. Iran is hoping that this hardware will allow their ground units to challenge the air supremacy of US forces."

Does everyone see that? (There was nothing else in the audio clip about offense vs. defense, by the way.) So the fact that Iran wants to be able to defend its armored units against American aircraft proves that they are offensive, not defensive. After all, it's not as if there is a realistic threat that the US would start bombing Iran anytime soon. Don't these nutjobs know that democracies are good?

Probability

The more I think about it--and I'm a whopping thirty years old, ya know--I don't think it makes sense to define probability. I think you either know what "1 in four chance" means, or you don't.

(1) It doesn't mean, "If you did this 1 billion times, then..." It's statistically possible that you could get 1 billion heads in a row with a fair coin. So you can't talk like that to define 1/2 probability.

(2) I used to think it could mean, "You would be willing to give x odds in a wager on the subject." But no, that doesn't work either, because of both incentive problems and "diversification" issues (for lack of a better term). E.g. if I say there's a certain probability I'll miss my connecting flight (we were in the hotel between legs of the trip home when I thought of this), that doesn't translate into the odds I'd need to wager against myself.

Obviously, I would always be willing to bet that I'd miss my connecting flight, because I can just walk very slowly. On the other hand, I might not want to bet the other way, because who wants to get a big payoff if he makes his connection, but lose money if he misses it??

Was this really as dumb as it seemed??

Due to inclement (what does that word actually mean?) weather, my family was forced to stay in a hotel last night. We ended up watching the second half of a Martin Lawrence movie where he's a basketball coach of young kids. In the climax, they're down by 1 and one of their players gets fouled. (Though was he even shooting at the time? I don't recall but possibly not.)

Anyway the kid has two free throws with no time on the clock. So of course he has to sink them both to win. He does, naturally.

Here's the kicker: On BOTH shots, the kid jumps over the foul line!! Isn't that illegal?? It was when _I_ (assistant) coached little kids. Would it have been so so so difficult to have the actor stay behind the line? Or was there really no one involved in this production that knew that much about basketball?

Rare Event

I admit I may have overlooked a very important consideration and thus come down on the wrong side of an issue. Specifically, in my vendetta against Bush's Social Security plans, I never considered that people might work more if their retirement checks would be higher (all told) on the margin.

In fairness to myself, none of the major proponents of the plan ever explicitly cited this factor. They all argued that the higher rate of return per se would do it. But nonetheless, I should have thought of this. My omission was as naive as someone objecting to tax cuts on the grounds that "how can we cut taxes _and_ reduce the deficit at the same time?? That 'savings' has to come from somewhere!"

Don't get me wrong, I still would have opposed Bush's plan, because it wouldn't have been implemented in the ideal way one could have imagined. But even so, my version of the "ideal" privatization scheme unfairly left out one of its major benefits.

Destiny Found

I was reading Umberto Eco, discussing how Borges had been an influence on him. He concluded talking about the differences between the two of them, declaring that the biggest is that while Borges was able "to use the most varied debris of the encyclopedia to make the music of ideas," Eco himself often feels as if he "blow[s] into an ocarina."

However, he ends on an optimistic note: "I hope that still someone will be found after my death who is even less skillful than me, soeone for whom I will be recognized as the precursor."

I have found my calling: the final destination in the decay of a literary heritage!

robert anton wilson

Robert Anton Wilson Defies Medical Experts and leaves his body @4:50 AM on binary date 01/11.
All Hail Eris!

On behalf of his children and those who cared for him, deepest love and gratitude for the tremendous support and lovingness bestowed upon us.

(that's it from Bob's bedside at his fnord by the sea)

RAW Memorial February 07
date to be announced

his blog

Holy Shmokes

You can now run UNIX on your cell phone.

I Know You Were Waiting for

My take on tax reform.

Another Roadside Adventure

Once again, I was walking in the road, this time against the traffic on a suburban one-way street with no sidewalk. Coming toward me were a kid on the same side and some cars. He reached me first, and stepped up the curb into the grassy border. Subservience? I thought; seemly regard for our obvious age difference? But then I realized that his behavior might well be entirely rational. In various-vehicle-versus-elapsed-time space, my Zone of Death embraced his: he was sheltering in my shadow.

Toys R Us contributes to trade deficit...

...by increasing our capital account surplus with China.

(After I started making this blog post it occurred to me that a pure transfer of a debt instrument might not affect the trade deficit, but I don't want to think about it now and possibly ruin my joke.)

Mark Skousen, Enterpriser

Say what you will about Mark Skousen, he's a showman. He came into our office today and handed me a business card talking about Freedom Fest. It's going to be in Vegas on 7-7-7, will feature 77 speakers, and will have over 777 attendees (according to the card). I think it's catchy.

Support the Troops...

who have integrity..

Yellow Journalism at The Weekly Standard

It's a pun, see.

Contra Localism?

There's a pretty good review of Look Homeward, America, Bill Kauffman's case for American localism, here. Well, good until I hit this:

"Attractive as such a life may seem to many—and I write this in a log house on a northeastern Vermont mountainside—none of us can flee from the second and more menacing fact that in a cave in Pakistan, a coffeehouse in Cairo, a mosque in Riyadh, and a bunker beneath Tehran, well-armed and inventive villains really, really want to kill the peaceful people of Elba, New York, and wherever else we Americans dwell. They want to do so because their reading of their holy book commands them to purify their faith by extirpating the infidels, and in so doing reaffirm their divine right to rule the world."

First of all, this just ignores what Kaufmann's obvious response would be: Those people are interested in killing the people of Elba because the US has so blatantly *not* followed Kaufmann's localist policies. Since that is *exactly* why Osama bin Laden says 9/11 happened, and since countries such as Sweden, New Zealand, Switzerland, and Taiwan, all fairly free and full of infidels, have suffered no attacks, the burden of proof would seem to be on you here.

Secondly, it ignores the fact that the Koran specifically demands tolerance for Christians and Jews, and that is why so many of them continue to live to this day in Moslem countries.

Thirdly, the idea that, say, al Qaeda is trying to "rule the world" is preposterous.

"We are in a global struggle we would rather not have to contest but which now makes American withdrawal from the world a matter of possibly mortal consequence."

As my friend Jim Henley likes to point out, when "withdrawal from the world" is used in a context like this, "withdrawal" is usually being defined as "an unwillingness to travel great distances and kill lots of strangers." Have I "withdrawn" from my friends and neighbors because I haven't bombed any of them recently?