Coördinate systems

Cartesian bears can be found in temperate climates closer to the equator, where longitude lines can be treated as approximately parallel. Further north, as this approximation begins to introduce significant errors, polar bears have the significant advantage of using much simpler trigonometric terms.

The speech it's not too late for Obama to make

Good evening to the American people, the people of Egypt, and the people of the world.

Hosni Mubarak's government in Egypt has long been a valued ally of the United States. On the world stage, a nation must often respect and work with governments one does not always agree with. That is not just a callous pragmatism. It reflects a humble awareness that it is right and necessary for a people to chart their own course, without undue interference from their neighbors. And in the spirit of that respect, I have hesitated to speak against the Egyptian government.

But that was a grave mistake, and I will correct that mistake now. Because more important than loyalty to governments who have been our allies is loyalty to the principle of democracy which is the bedrock of our nation. And so I cannot ignore the dedication, the commitment, and most of all the courage which the Egyptian people have shown in demanding a government which truly represents them.

It was this commitment to the principle of democracy that led the American people to support the invasion of Iraq. We believed that we might liberate that country from a brutal despot, and birth a democracy. But it is not so simple, as we have seen vividly demonstrated the years since that invasion. Though I remain hopeful that the Iraqi people will build a vibrant, democratic nation, their future remains compromised by the scars of war. The United States remains committed by both our will and our duty to help bring Iraq to the future it deserves, but America should not try again to grant democracy to a people at the point of an American sword.

It is far better for a people to claim democracy for themselves than to try to build it in the wake of another nation's intervention. We should know that, having created our own nation in rebellion against the greatest colonial power of its time.

Better for a people to claim democracy for themselves, and best for them to do so without raising a gun at all. There are those who will say that to stand up against an oppressor without shedding their blood is too idealistic. Despots' grip on power is too great, they say. Only military force can break their grip.

But we have seen it happen in Eastern Europe in the wake of the fall of the Soviet Empire. We have seen it when India stood up for independence. And we have seen the power of nonviolence right here in these United States in our own Civil Rights Movement.

The United States simply cannot stand behind a tyrant who refuses when his nation's people call for him to step down. Nor can we oppose a nonviolent democratic movement like that we have seen in Egypt. To do so would be to break our covenant with the Founders of our own nation.

So tonight I say to the people of Egypt: the people of the United States stand with you. Tonight I say to Hosni Mubarak, who can hold no legitimacy with the free people of the world, the government of the United States is no longer your ally.

I say to the people of the world: the United States stands with every nonviolent movement for democracy in the world, today and tomorrow, wherever it may arise.

I say to the world's tyrants: the United States may meet with you in diplomacy and trade, but we will never stand with you against your people. Where democratic movements arise, we will remember what America stands for.

I urge the American people to join me in praying for an Egypt liberated without bloodshed. I urge the Egyptian people to accept an offered American hand of friendship. And I urge the people of the world who yearn for democracy to stand up with the courage of your Egyptian brothers and sisters.

Thank you, and good night.

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Update: What the President actually said later that day.

Via Ben Jervey at Good magazine.