Wednesday, January 17, 2007

War's most significant bit

Read this. Then read this.

One of the reasons I post less frequently than I used to is that lately, my despair at the stupidity of humanity exceeds my fury, whereas the opposite once obtained. Shall I bother to point out the obvious? All right, once more into the breach. This post will be more indirect than it needs to be, but I can only overcome my sense of the inherent futility of it all by creeping up on the subject sideways.

Computers represent everything, including numbers, using bits. Each bit is either a one or a zero. One and zero are not the only numbers we would like to represent: two and three and five hundred million are all nice too. To represent other numbers, computers use several ones and zeros at a time. This is called binary notation:


represents the number 214. Binary notation works more or less like the decimal notation that everyone's familiar with. In decimal, you interpret a number by multiplying each successive digit from right to left by an increasing power of ten, so 214 = (2 * 102) + (1 * 101) + (4 * 100). In binary, you interpret the bits by multiplying by successive powers of two, so that the rightmost bit is multiplied by 1 (20), the next-to-rightmost bit is multiplied 2 (21), and so on, up to the leftmost bit, which is multiplied by 2n-1, where n is the number of bits in your string. In the above case, because there are eight bits, the leftmost bit represents 27, or 128. Summing up, 128 + 64 + 16 + 4 + 2 = 214.

Note that the leftmost bit is vastly more important than the rightmost bit. If you twiddle the rightmost bit of 11010110, you get the string


which corresponds to 215. That's pretty close to 214. If you twiddle the leftmost bit, you get the string


which corresponds to 86. That's pretty far from 214. Programmers call the leftmost bit the most significant bit; we call the rightmost bit the least significant bit.

As the size of your string grows linearly larger, the difference between the significance of the most significant bit and the least significant bit grows exponentially larger. With a 16-bit string, the difference is about about thirty-three thousand to 1. With a 32-bit string, the difference is about 2 billion to 1.

The concept is suggestive, and programmers readily adapt it metaphorically to other subjects. In most decisions in life, it's important to get the most significant bits exactly right, and much less important to get the least significant bits exactly right. Err on the most significant bit in the quantity of your jet's fuel, and you're making a "water landing" in the middle of the Atlantic. Err on the least significant bit and nobody will notice.

The ability to concentrate on the most significant bits is also called "having a sense of proportion".

Here, in what I consider roughly descending order of significance, are several "bits" of truth from the years 2002-2007:

  • America should not have invaded Iraq.
  • Congress should not have given Bush authority to invade Iraq at his sole discretion.
  • Invading Iraq without a UN mandate hinders America's diplomatic efforts, which are crucial to antiterrorism and nuclear non-proliferation policy.
  • Given its failure to establish a stable state in Afghanistan, the Bush administration could not be trusted to handle the aftermath of the invasion of Iraq.
  • Invasion of Iraq and its subsequent destabilization fuel anti-American sentiment and provide a propaganda bonanza for violently radical Islamist movements all over the world.
  • Saddam Hussein's WMD program had not made significant progress towards either nuclear weapons or mass casualty biological weapons.
  • The doctrine of preventative war does not suffice to justify the Iraq War.
  • ...
  • ...
  • ...(several thousand more bits)...
  • ...
  • As a companion to coffee, key lime pie is superior to blueberry pie.
  • Absolute isolationism and absolute pacifism are philosophically unsound.
  • The Beyoncé Knowles song "Deja Vu" was produced by chart-topping super-producer Rodney Jenkins.
  • Theoretically speaking, the doctrine of preventative war might someday suffice to justify some hypothetical war.
  • ...

One can summarize Megan McArdle's point (and Kevin Drum's point here) as follows: "Some leftists were wrong about the least significant bits on the Iraq War; therefore, the arguments of anti-war advocates remain no more credible than those of people who were wrong about the most significant bits."

Of course, stated this way, nobody would dare make such an argument. Obviously, a decision procedure that leads to correct answers in the most significant bits is strictly preferable to one that gets the most significant bits wrong but the least significant ones right. Arguing otherwise is transparently stupid. So former hawks take a circuitous route that's no less stupid, but slightly less transparent. By filling the conversation with angels-dancing-on-the-heads-of-pins arguments about absolute isolationism and absolute pacifism and preventative war, McArdle and Drum hope to divert readers' attention to the least significant bits and induce the illusion that the most significant bits are not, in fact, far more significant.

And I suspect that McArdle and Drum even believe that they're talking about important subjects, despite the fact that virtually nobody actually believes in absolute isolationism or absolute pacifism, or that preventative war can never be justified. If you're arguing that "sometimes war can be justified", you're arguing with Quakers and half-mad hermits who live alone in the woods. To pretend otherwise requires massive cognitive dissonance, or a completely unprincipled and remorseless willingness to erect straw men, or both.

Of course, pundits have ample reason for cognitive dissonance. Pundits blow hot air around for a living. Their sense of self-worth depends on the belief that such vigorous thermoconvection makes them better qualified to judge matters of import than the hoi polloi, who rely on simple rules of thumb, like "War Is Bad". It literally does not compute in their minds that some shaggy dumbass off the street with a picket sign could have better judgment than, say, a professional writer for the Economist or the Washington Monthly.

But "War Is Bad" is a pretty good rule, because in the vast majority of practical cases, nonviolent action leads to better outcomes than war. "War Is Bad" gets the most significant bit right far more often than the punditological prestidigitation of which McArdle et al. are so fond. If all liberal (and "libertarian") hawks had shouted from the rooftops in 2002 that "War Is Bad" instead of the pseudo-nuanced bullshit they actually said, it would have strictly improved objective outcomes for the nation.

But rather than learn from this experience, McArdle's looking around for excuses to ignore the lesson. As an individual, of course, McArdle barely matters at all, but she's representative of a whole equivalence class of formerly hawkish intellectuals who want to emerge from this debacle without troubling themselves to rethink a single assumption.

Hence my despair and fury. The stupidity, the arrogance, the willful blindness; and these people will not be called to account. If anything, they'll be rewarded.

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