Killing Stupid Ideas Before Their Time

2003-04-14T12:19:00.000-07:00

The nature of debate

I have been thinking about the nature of disagreement; how people of high intelligence and good faith can disagree so completely on such a wide variety of things. Assuming good faith and rationality among all parties, I contend that the sources of disagreement fall into two categories: axiomatic difference, and logical (or transformational) difference.

Assume that Adam and Bob are having an argument. Adam believes premise (or axiom) A to be true. Bob believes premise (or axiom) B is true. Both Adam and Bob agree on the following set of inferences (transforms):

A produces n
B produces m

As they begin their debate, they discover than they disagree: Adam contends that n is true, Bob contends that m is true. Ideally, they would explore their inferences and discover that they are in agreement there (i.e. that beginning from premise A will lead through inference to n, while premise B will lead to m). They would then proceed to their premises. In this instance Adam and Bob should be able to discover an axiomatic difference and either resolve it (if the premise is an establishable fact) or determine the precise philosophical point of contention (if the premise is theoretical/indeterminate).

What if Adam and Bob agree on premises but disagree on inferences? The same process should apply. As they begin their debate, they discover that they disagree (Adam says n, Bob says m). Ideally, after a brief period of debate they would come to the conclusion that they agree on premises but differ in their set of inferences. This argument doesn't resolve as cleanly (inferences are almost never provable) but they can get to the heart of their disagreement - debating the validity of the inferences they are using.

Unfortunately for the world, there are other ways that people can disagree. They can argue in bad faith (the French) or their inferences can be irrational and difficult (or impossible) to determine (radical Islamism). In these cases the best that can be done is to prove the bad faith by showing that a position is inherently contradictory in a self-serving way, or to show that the inferences are not rational.

More exercises along these lines to come: reducing arguments to lemmas and transforms, and trying to apply some systematic rules of logic to them. I am looking for the fundamental set of premises and inferences used by, for example, the America-Is-Evil set. What is the basic point of contention? I think it's too simple to say that it is "America is Evil", as obvious as that seems, because these people believe that England is evil as well. In fact, except when those regions are busily opposing the US, this mindset tends to think of Europe and Canada as part of that whole bad Western Civ mojo.

Racial (white people are evil)? I don't think they see black American soldiers in a more favorable light than white ones. Capitalism? Could be. Let the deconstruction begin.

2003-04-14T11:59:00.000-07:00

Baghdad Battered by US Gas Bombs

This piece by Hassan Tahsin at ArabNews.com explains:

Yes, that is the truth; Baghdad has been battered with chemical bombs and bombs carrying highly combustible depleted uranium. The website www.bbcarabic.com presents a detailed account of the type of weapons and ammunition used in the current war.

Aside from these munitions, advanced cluster bombs carrying ethylene gas have also been used. They are called MOABs, or massive ordnance airburst bombs, and they are essentially chemical bombs.

These ethylene bombs work by taking advantage of the effect of exploding fuel in the air. When a mix of fuel and air ignites, it creates a fireball and a wave of explosions that spread quickly over a much greater area than traditional explosives. The after-effects of the explosion are very similar to those of small nuclear bombs but without the radiation.

Clever, Hassan. Of course, every bomb ever built is a chemical bomb, if you want to be really technical about it. In fact, guns are chemical weapons too (gas expansion devices). As a matter of fact, even soldiers themselves are nothing but walking bags of chemicals - chemical weapons every one.

Now this will become another idiotic self-parodying Arab meme, like "Jews control the US media", or "the CIA was responsible for 9/11" or "No Jews were killed in the World Trade Center; they all stayed home."

2003-04-11T22:16:00.000-07:00

The Green-Eyed Monster

Once in a while some careless member of the anti-American tribe lets fall a morsel of truth among their great heaps of bullshit. It doesn't happen very often; antis play their cards very close to their chest. They are always telling us that they are not against America, only against American hawks. Or this evil war. Or whatever. But not simply against America.

But sometimes they let it slip - the engine that drives the anti-Am machine. One such enlightening moment occurs in this article in the London Times:

We must learn to envisage a world where we are not in the American stockade and do not need to be because there is no huge enemy we share with it. We should consider the means and institutions through which we can protect our own collective interests against a great power with interests of its own to pursue. We need to clip the eagle’s wings, and we shall not do so singly.

There is the entire agenda of the anti-Ams, concise and bare. America is big and powerful; let's clip its wings since we can't tolerate not being the center of the world anymore.

2003-04-11T10:56:00.000-07:00

Hall of Shame

What the Loony Left said. Don't forget it, and don't let them forget it either.
Via Ipse Dixit.

2003-04-10T10:23:00.000-07:00

Needles and Haystacks

Try this sometime when you have a few hours to waste on something utterly futile: find a positive statement about the United States in the Guardian. Good luck.

2003-04-10T09:55:00.000-07:00

Flat Earth Society?

Brian Whitaker writes in the Guardian:

-snip-

Someone produced a sledgehammer, and Iraqis took it in turns to hack at the base of the giant statue of Saddam Hussein in Baghdad.

They were making reasonable progress, and might well have toppled it after a few hours, but that would have been too late for primetime TV. The Americans were getting impatient, and their armoured vehicle lumbered up the podium steps with the elegance of a sexually aroused hippopotamus.

Removing this visible sign of a quarter-century of dictatorship from Baghdad yesterday was a highly symbolic act, but so was the manner of its removal: a metaphor for the ongoing debate about who will really be in charge of the new political order.

When it came to toppling Saddam's statue, the Iraqis were soon elbowed out of the way.

Sigh. Where to begin?

They were making reasonable progress in exactly the way that UN weapons inspectors were making reasonable progress; which is to say, not at all. The pedestal of that statue, a 10ft thick cylinder of (probably) reinforced concrete, was being battered by a sledgehammer. Full points for enthusiasm, no points for execution.

Enter the impatient Americans; their television masters screaming for video, the impatient soldiers impatiently shoulder the crowd away from their task and brusquely bring in cowboy technology to do the job. Interesting thesis - but it was early morning in America when this occured. It was only primetime in England, matey - unless the Earth that you live on is flat.

And having watched the event live myself, I couldn't help but notice that the Iraqis seemed very happy when the armored vehicle rolled up. They were climbing all over it and cheering like kids at a pop concert. Perhaps they didn't have enough sophistication to realize that they should be offended by this arrogant American "intervention".

I do have to concede that the armored vehicle wasn't very graceful as it went up the steps to the statue. That is a fair and disturbing criticism of American armor: no grace, no sense of delicacy. Not in touch with its feminine side. I haven't even seen any soldiers doing pirouettes or plie as they liberate the country. Damn it people, we need to do better. What will our french "allies" think?

-snip-

The US flag duly came down and an Iraqi flag appeared, miraculously, from the crowd. A soldier draped it, rather grudgingly, around Saddam's neck, and then that, too, was removed.

I have not seen any interviews with this soldier, but I can imagine his words: "Yep, them goldang Eye-rackies didn't like our flag, so I put one of theirs up instead. But I did it grudgingly, parder."

Finally, the crowd was ushered back, the armoured vehicle slowly reversed and the chain tightened. With more grace than he ever displayed in power, Saddam Hussein made his final bow.

In Britain, we call this sort of thing criminal damage, and you can get three months in jail for it, as 37-year-old Paul Kelleher discovered recently when he beheaded a marble effigy of former prime minister Margaret Thatcher. Poor Mr Kelleher: wrong time, wrong place, wrong statue.

Staggering, even for the Guardian. The moral equivalence of a crowd of Iraqis toppling the symbols of the oppressive regime that has terrorized them for 30 years, and a vandal destroying a statue of a democratically elected leader. I am not even going to bother with this one - but let me point out that putting up statues of oneself all over the country while torturing and murdering one's fellow citizens is probably frowned upon in Britain as well.

2003-04-09T10:25:00.000-07:00

I'd like to thank the Academy ...

Got my first link ... and from one of my favorite reads to boot. Exxxcelllllent !! Soon the blogosphere shall be mine, all miiiine BWAHAHAHAHAHAHAHA ....

2003-04-09T08:49:00.000-07:00

Headline Poll

Out of curiousity, let's check the headlines.

Source	Headline
FOXNews.com	US tanks in center of Baghdad; Iraqi Finance Ministry on fire
abcnews.com	Saddam statue demolished
MSNBC.com	Baghdad falls. Iraqi regime loses control; streets erupt in frenzy as U.S. officials urge caution.
CNN	Fall of Saddam. Tanks in city center; Iraqis take to streets.
Guardian	US: Saddam era is over.
London Times	Iraqis celebrate and loot as regime crumbles.
Jerusalem Post	Iraqis celebrate fall of Baghdad.
New Zealand Herald	Looters strip offices of crumbling Baghdad Government.
ArabNews.com	Nothing topical as of 8:49am PST. Guess they don't update very often.
USA Today	Baghdad falls to US forces. City echoes with jubilation, some resistance.
Washington Post	Baghdad under US control.
Seattle Times	US command says Iraqi regime no longer controls Baghdad.

It amazes me that some of these sources still seem to be unsure as to whether or not there are coalition forces operating in Baghdad; maybe it's all a US propaganda trick? Better ask Baghdad Bob about the disposition of the glorious Fedayeen and the imminent defeat of the evil Americans ... "US command says Iraqi regime no longer controls Baghdad" ? Good job, guys. Wouldn't want to jump to any conclusion based on something as weak as mobs of Iraqis running through the streets dragging the decapitated head of Saddam's statue behind them on a rope, or crowds of grinning Marines handing candy out to children climbing all over their tanks in front of a downtown hotel.

2003-04-09T08:33:00.000-07:00

Live from Baghdad
When I went to see the broadcast, I realized that the feed is pretty much live. I must have missed the American flag when I lost the feed for a few minutes.

Janine Giovanni (from the Times of London, the one who was preparing for broadcast earlier) mamaged to put a negative spin on a moment of victory. "This is, of course, what we have been worried about all along," she cried. Will there be looting? Will there be disorder? What happens after the regime? Blah blah blah.

Uh huh. That is what you have been worried about all along. Not "quagmire", or "thousands of babies slaughtered", or the "Arab Street" rising up in a tidal wave of indignation. Nope. You have been worried about what happens after one of the most decisive military campaigns in history.

Absolutely pathetic. At least have the decency to admit that the coalition forces have done an amazing job, for fuck's sake, before you start carping on about how "now the problems really start."

2003-04-09T06:47:00.000-07:00

Amazing Times

It is 6am and I am watching the CNN feed at rtsp://live1.stream.aol.com/farm/*/encoder/cnn_webcast1_high. It is the live Baghdad feed from the Palestine Hotel. I watched the US troops show up in the square ... at this moment crowds are massing underneath the statue of Saddam Hussein. Three intrepid kids (they look like teenagers but the camera is a good distance off) have grabbed a ladder and are busy stringing a rope around the statue.

This scene, the destruction of the symbols of the personality cult, has played out so many times before, but it always gives me chills to watch it. The birth moments of a free nation.

Two arabic voices are speaking on camera. I don't speak Arabic so I have no idea what they are saying but they are laughing. They sound either happy or amused.

The teens have got the rope strung around one shoulder of the statue. The other end is hanging loose ... it doesn't even reach the ground. I am not sure at this point what they are intending to do.

6:26am PST
Around the square there are maybe two hundred people milling about. A good number of them have flak jackets with "TV" emblazoned on them in large letters. Maybe 15 "TV" people in the crowd that I can see. In the background are what look to my somewhat untrained eye like APCs.

6:37am PST
I see several children wandering around in the company of men .. I assume that they are children and their fathers. I am surprised at how Western they look; brightly colored T-shirts and jeans.

6:41am PST
A HUMV is approaching the statue accompanied by two white station wagons. They drove right by, and the APCs have departed from the background. The crowd is swelling, getting larger and larger. I estimate perhaps 250 now. The kids have climbed down from the statue, leaving the rope tied around its head, dangling loose like a comical necktie. There is a metal ladder leaned against the base of the statue.

6:44am PST
Here we go! A tank is pulling up to the statue (actually backing up to it). There are pillars between the statue and the tank - I wonder if the tank is going to get involved in taking the statue down? Seems kind of unsafe with such a large crowd around. No sounds of shooting or combat at all. The ladder is being placed against a different spot on the base. A man is climbing up .. and down again. The base is a concrete cylinder perhaps 20-25 feet high, 10 feet in diameter, with a statue that high again on top.

6:47am PST
A loud shot or explosion just sounded. The crowd doesn't seem too alarmed though. People are casually milling around, or ringed in a tight circle around the base of the statue. I see some women walking around in Western clothes (jeans etc); they might be reporters. Several cars are driving up to the tank and then turning around; maybe the tank is instituting a roadblock.

One of the youths has again climbed the statue. He is using the rope to pull another one up. In the backgorund I see a woman in chador. A third is going up the base of the statue ... and a fourth. No, the fourth couldn't make it up ... someone else went in his place. Two whie station wagons next to the tank again. More shots. Six or seven in a row, within ten seconds. The crowd seems more restless.

6:53am PST
Two more cars have pulled up to the tank. And two more ... and two more. Quite a little parking lot there now. One of the teens just came down the rope fast. I hope he didn't fall. The other two have come down also now. They appear to be doing something to the base of the statue ... striking it with something. Yep, looks (hard to tell at this distance) like a sledgehammer. Uh, guys, that is hopeless.

People in the crowd are taking turns hitting the base of the status with a sledgehammer. They are lining up to do it. The crowd is cheering; you can hear them even from the distance. They have their arms in the air and are jumping up and down.

Ah. I think they are hammering out a plaque that is set into the base of the statue. Looks like they got it out. The crowd seems remarkably orderly. I don't see see any fighting at all.

Another tank is approaching the statue now. Nope, two. Nope, three. They are lining the street on the far side of the statue. The crowd is starting to disperse a bit now.

6:59am PST
Still hammering away at the base. Very distant sounds of artillery or explosions of some kind. The tanks are creeping by on the street. One guy is tugging on the rope. No hope of pulling the statue over by hand though. It must weigh 50 tons if it's an ounce.

Someone is talking through a loudspeaker in Arabic. No-one seems to be listening though. Oh, my bad. The crowd is moving rapidly off to the left. There is almost no-one left around the base of the statue. Voice continuing on the loudspeaker.At this point there are almost more TV people in the picture than non TV people.

7:03am PST
Loudspeaker has stopped, but the crowd has not returned. There are still a good number of people milling about, but they do not seem to be focused on the statue now. Sounds of yelling. Two boys are playing tag in the foreground. Something is happening off to the left, off camera. TV people are scurrying about.

The statue stands, forgotten. It seems comical, a cheerful buffoon with its right arm stuck out. Too easy to forget what it stands for. A soldier is walking through the park to the statue. Now he is walking back the way he came. A father, mother, and three children trail behind him.

Loud sound of engines; could just be close to the camera. Sounds like a deuce-and-a-half, or some sort of large diesel. More soldiers in the park now. Lots more. They are drifting toward the statue. WHOA !! A tank is coming up the walk toward the statue. Cheering. I think this is it for Saddam, baby.

7:08am PST
The tank is parked right in front of the statue, in the park itself. It is driving forward into the base of the statue. Soldiers are climbing on top. People are climbing onto the tank too. Lots of them - the tank looks like a float in a parade. It is covered with people now. They are cheering loudly.

People climbing the statue again, using the rope and the tank for assistance. There must be 20 people standing on the tank. Voice over a loudspeaker. The crowd must be well over 300 now. The street is packed with cars and tanks. A coalition soldier running in the foreground. Distant sounds of loudspeaker. More US troops are approaching the crowd/statue from inside the park. The crowd is still growing.

7:12am PST
I just noticed that the Arabic voices I heard on camera earlier are gone. The crowd is backing up from the statue now ... I think something is about to happen. Still lots of people standing on top of the tank though. More distant explosions. Somehow reminds me of an auto show or monster truck rally: lots of people milling about, and the sound of cheering and large engines running.

The tank is backing up ... still with passengers covering it's top. The call to prayer is sounding; I wonder if it is the normal time or a special prayer? Muslims pray, I believe, 5 times per day. It must be 5:15 or so there; looks like sunset is approaching. The tank is backing up further. People on top are waving and look like they are enjoying themselves. Amazingly, even more people are climbing onto the tank. The tank is pitching slightly as it backs up; there are small sets of stairs leading to the statue. But no-one has fallen off yet (at least not that I have seen).

7:17am PST
Another distant explosion. The arabic voices sounded for a minute; the guys are apparently watching this in silence. The tank is now sitting a small distance from the statue, and the crowd has pulled back behind it. There is no-one around the base now. Loud explosion, close by. Rounded like a rocket or RPG. The crowd is packed very thickly into a half-torus with an inner diameter of about 60 feet (hard to tell from the distance of the camera) and an outer diameter of maybe 100 feet.

Aha. The tank was pulling the rope backward. I couldn't see it until it broke; sounds of disappointment from the crowd. Now it is hanging loose like a tailor's tape around Saddam's shoulder, dangling down the pedestal almost to the ground. The tank is pulling forward again, lurching up the stairs. The crowd is pushing back in toward the statue as well. Someone very agile is climbing the pedestal from the nose of the tank. He is up - and another is trying unsuccessfully to follow. People are climbing down off the tank. The crowd is easily over 500 now.

7:23am PST
Sounds of some heavy machinery approaching; voice over a loudspeaker. Explosions in the distance. Part of the crowd is starting to stream to the left again. Ah, they are clearing a path from behind the tank. US soldiers approaching the tank. A woman in chador is talking to a group of men in the foreground. There is a woman in jeans and shirt with a purse standing next to her.

7:28am PST
The rest of the crowd is vacating the tank. Now only two soldiers are standing on top. One man is still standing on top of the statue pedestal also. Loud shots close. The crowd is breaking up. Soldiers are running fast off to the left. Arabic voices. The camera is moving.

New scene: US troops filling a street. They are across the street from the park the statue is in. The camera has pulled back - a wider view of the park. Sounds like a crowd singing.

Tight shot of soldiers running down the sidewalk. They appear to be looking off to their left. Cameramen and civilians mill in among them. There is a soldier with a pistol walking down the sidewalk gesturing. Cameras all over the place. They nearly outnumber the soldiers. Camera is moving again.

Back to the statue. Looks like some kind of frame is begin raised up to it. A-frame, yellow (khaki), some piece of military equipment. They are clearly going to use it to pull the statue down. Three soldiers are on top of the tank. The tank is pulling forward to the statue with the frame extended in front. The top of the frame (the peak of the A) is about at Saddam's waist now. Arabic voices near the camera laughing. English female voice:

"You want me to stay here? I don't want to fall over. Is it working?"

Dark-haired woman with a black shirt that says "Press" on it.

"Basil, is it working?" They are setting her up for a shot.

"Call my mother, tell her I am going to be on NBC news. (Phone number)." She primps for the camera. Park is in the background.

Loud cheering from the crowd. SHIT I JUST LOST THE FEED. GRR.

Arabic voices but no video now. Cheering. Feed is gone. I will have to go watch it on CNN. When the feed drops that means they are going live.

7:37am PST
Got it back. Soldiers are on the statue attaching the frame to it. Voices in the foreground preparing for a broadcast. Wild cheering from the crowd. Crowd must be close to 1000 now. Someone is standing right in front of the camera now. Loud voice; can't see a damn thing. A man is standing on the tank waving an Iraqi flag. Two soldiers are at the top of the frame. Looks like they are using the rope to tie the frame to the statue. Sounds of helicopters?

They are going to put the flag up on the statue. There are two cameramen on the tank as well. A soldier is slowly climbing the frame with the flag in his hand. He is passing it up to the two soldiers on the frame. Now they have it ... doesn't make sense to put it there though if they are about to pull down the statue.

7:41am PST
They have attached the flag like a bib around the statue. The soldiers are climbing down. An Iraqi is climbing up in their place. No, he is climbing down as well. Huge crowd now. I wonder what happened to the broadcast? A soldier is climbing up again. He is retrieving the flag and bringing it down. Voice through a loudspeaker in Arabic. The tank is backing up. The crowd is cheering. Not sure what is happening; maybe they are about to ram the tank into the pedestal. The frame is not attached to the statue.

7:47am PST
The tank is backing up again. FOXnews is showing an American flag on the statue - this feed must not be live. The flag I saw was definitely an Iraqi flag - no doubt about it whatsoever. And they are showing the flag covering the statue's head. This feed must be delayed several minutes.I might do better on network TV.

The statue is down. They just pulled with the frame and it popped right over. Where the hell did the picture of the American flag come from?? The statue just broke into pieces; the crowd is cheering and dancing around. Two men are holding up an Iraqi flag. Looks like the winning side of an English football match. A scene of jubilation.

There is a little stub of statue left on the pedestal - pretty much a perfect representation of the remains of the regime of Saddam Hussein. Small, ugly, and ineffectual. I am going to go watch the networks make a hash of this historic moment.

2003-04-08T22:33:00.000-07:00

Another gem from "The Fiskelator"

Robert Fisk's usual idiocy in the Independent today; mostly unworthy of comment, but this caught my attention:

At one point, Red Cross workers hoped to take a severely wounded Spanish television reporter with them - his leg had been amputated after the tank shell exploded below his office in the hotel - but he died during the afternoon. The American infantry divisional commander issued a statement that suggested the Reuters cameramen were sniping at the US tank, a remark so extraordinary - and so untrue - that it brought worldwide protests from journalists.

Huh? Here is the story on the Reuters website:

"A tank was receiving small arms fire and RPG fire from the hotel and engaged the target with one tank round," General Buford Blount, commander of the U.S. 3rd Infantry Division in Baghdad, told Reuters on the outskirts of Baghdad.

Central Command, the U.S. war headquarters in the Gulf state of Qatar, said forces received "significant enemy fire" from the hotel and returned fire in self-defense.

Reporters at the scene disputed this account.

"I never heard a single shot coming from any of the area around here, certainly not from the hotel," British Sky television's correspondent David Chater said.

"In all the three weeks I have worked from this hotel I have not heard a single shot fired from here and I have not seen a single armed person enter the hotel," Swiss television correspondent Ulrich Tilgner said in a report from the hotel.

There certainly appears to be a dispute about whether or not shots were fired from the hotel. It is certainly possible that General Blount is dead wrong - war is chaotic, men under stress can make mistakes. But nowhere (AP, CNN, ArabNews, UPI, not even in the reliably frothing Guardian) do I see anyone (other than "the Fiskelator") even remotely implying that the Reuters cameramen themselves fired the shots. Is there really an audience of morons somewhere who spoon Fisk's bullshit up?

2003-04-06T09:52:00.000-07:00

One For The Record Books

Here is an article by Dr. Khaled M. Batarfi. Dr. Bartafi says:

Two weeks into the war, I reiterate again that the US and allies will only leave the swamp of Iraq after being taught a lesson like that of Vietnam - a lesson they forgot after their victory in the Second Gulf War and the Balkans wars (just) and the unjust Afghanistan invasion.

Thanks for the tip, doc. I will remember that you said so. And please try to remember that I am remembering, so that you will know (a month from now) why it is that I am laughing at you.

2003-04-05T23:54:00.000-08:00

Interesting Problem

Here is an interesting topology problem I have been thinking about. It began with an easier one:

Given: a plane, with all points on that plane arbitrarily assigned a color, either "Red" or "Black". Prove that for any distance d there must exist two points of the same color which are exactly d apart.

Naturally the proof for this one is simple:

Let points A, B, and C be at the vertices of an equilateral triangle whose sides are of length d.
Let A be a "Red" point.
If points B and C are both "Black", then these two points are the same color and are separated by distance d.
If either B or C is "Red", then that point and point A are the same color and are separated by distance d.
Since all points must be either "Red" or "Black" (given), either 3. or 4. must occur.
QED.

Now for the more complicated problem:

Given: a plane, with all points on that plane possessing a "color". Given a distance d divide the plane into colored regions, using the fewest possible colors, such that there are no two points of the same color that are exactly d apart.

As a bounding case, I can use 9 colors to construct a repeating pattern that will suffice.

Cover the plane with a grid consisting of squares whose diagonal measures d - i, where i is an extremely small distance. This insures that no two points within a single square can be d apart.
Now, color a 3x3 block of squares using 9 colors. Repeat exactly the same color pattern for each adjacent 3x3 block of squares, ad infinitum.
Using this pattern, there are always two squares of differing colors between squares of color X; thus no square of color X is closer vertically or horizontally than two squares from another square of color X, and no closer than two squares diagonally.
The diagonal distance between two squares of the same color can be given as 2(d - i), which approaches 2d as i approaches zero.
The horizontal or vertical distance between two squares of the same color can be given as 2((d - i)/sqrt of 2). This will be greater than d when ((d - i)/sqrt of 2) is greater than d/2, which is true when i < (d - (d/sqrt of 2)). Since (d/sqrt of 2) << d for all d > 0, there is always a value for i which will meet this criteria.
Since all distances from a square of color X to another square of color X are greater than d, and since no two points within one square can be within d of each other;
There can exist no two points of the same color that are d apart.

So, rah rah rah. But I feel certain that I should able to do this with far fewer colors. Trying a similar approach using hexagons instead of squares doesnt help, for the simple reason that a 7-cell block of hexagons cannot be used to cover a plane - there are "orphan" cells between blocks that don't get covered. These orphan cells would require 2 more colors to fill, which brings the total colors used back to nine.

A co-worker of mine looked at the problem, then at the original problem and my proof, and casually said "Oh, you need only three colors." I haven't been able to disprove this yet but I am certain that more than three colors are required.

So currently I know that the minimum number of colors required is ( 2 < ColorsRequired <= 9). This problem seems related to the map problem (coloring any map using the fewest possible colors so that no two adjacent regions share a color. Requires 4 colors).

Aside to web coders: does anyone know of a way to express mathematical equations in HTML less clumsily than I have done? Is there a standardized format or a tool?