Big Think

Benjamin Dozier commented on What is the best way forward in Iraq? on May 5, 2008, 10:29 PM

The claim that the opinions of Iraqis should matter, that they should have a say over affairs that affect their country, is a reasonable one. Yet without a functioning democracy, by definition, the goal of empowering the Iraqi people will never be achieved. Under Saddam, "Iraqis" in the plural had essentially no power; one Iraqi controlled the whole system. Clearly, today the situation is little better in terms of the power that the common people hold. While the US was clearly incorrect when it acted as the aggressor in an unjustified war, I feel we now have some responsibility to make sure or at least make an effort to ensure that democracy does in fact take root in Iraq. If we simply leave now, while we will be satisfying the short term desire of Iraqis to be free of American occupation, we will be doing nothing to further the long term goal of empowering the Iraqi populace. If we genuinely think the opinions of Iraqis matter, we should help them to establish some system where the will of the Iraqi people is translated into policy ie a democracy. That being said, at some point it may become clear that our capacity to do good is far less than our tendency to damage (maybe this is already true), and at this point we should pull out. But then the decision is not based on our perception of Iraqi opinion, but rather on our estimation of our effect on the welfare of Iraq.

Benjamin Dozier commented on What is the best way forward in Iraq? on May 5, 2008, 6:29 PM

The claim that the opinions of Iraqis should matter, that they should have a say over affairs that affect their country, is a reasonable one. Yet without a functioning democracy, by definition, the goal of empowering the Iraqi people will never be achieved. Under Saddam, "Iraqis" in the plural had essentially no power; one Iraqi controlled the whole system. Clearly, today the situation is little better in terms of the power that the common people hold. While the US was clearly incorrect when it acted as the aggressor in an unjustified war, I feel we now have some responsibility to make sure or at least make an effort to ensure that democracy does in fact take root in Iraq. If we simply leave now, while we will be satisfying the short term desire of Iraqis to be free of American occupation, we will be doing nothing to further the long term goal of empowering the Iraqi populace. If we genuinely think the opinions of Iraqis matter, we should help them to establish some system where the will of the Iraqi people is translated into policy ie a democracy. That being said, at some point it may become clear that our capacity to do good is far less than our tendency to damage (maybe this is already true), and at this point we should pull out. But then the decision is not based on our perception of Iraqi opinion, but rather on our estimation of our effect on the welfare of Iraq.

Benjamin Dozier commented on Larger than infinity on January 18, 2008, 1:21 PM

Mathematicians, and in particular set theorists, have been studying problems like this for a very long time. It turns out that there are in fact different types of infinities, but we need a more rigorous way of comparing the sizes of two different sets that both have infinitely many elements. The concept of dimension is not particularly useful here. Rather, we say that the two sets are equal in size (mathematicians would say the two sets have the same cardinality), if there is a one-one correspondence between the elements of the two sets. So for instance, if your first set is the positive integers (1,2,3,...) and your second set is the even positive integers (2,4,6,...), then you can form a one-one correspondence by matching each element in the first set with its double in the second set, and thus the two sets have the same size. This result seems a bit counterintuitive at first, since the first set has all the elements of the second plus a bunch more, and so we would think that the sets have different sizes. Yet this notion that the existence of a one-one correspondence is equivalent to two sets having the same size is actually a very natural generalization of methods that we are familiar with for determining whether two finite sets have the same size. Anyway, if you study things like this a bit more (maybe start with wikipedia's "Countable Set" entry), you can prove that there are in fact different sizes of infinity. For instance, the real numbers (or the points on a line) have a different size than the integers or the rationals. However, the set of points on the plane turns out to have the same size as the set of points on the line. There is a very rich, beautiful theory of infinite sets, and I would encourage any one who is interested in infinity to take a look at the topic from the rigorous, mathematical perspective.