Of Gödel and Galaxies

I've been reading the book Gödel, Escher, Bach by Douglas Hofstadter again, and it's really an amazing book. I recommend it very highly. One of the book's centerpiece's is Gödel's Incompleteness Theorem, which, in a nutshell, shows that there exist statements of number theory (such as "3^3=27," or "if you define a sequence a1=1 a2=1 and a3=2a2-a1, then no term is ever equal to 6.") which are true but cannot be proven within the context of number theory. The two examples I just gave are not of this form. One can prove them or prove there negation. The actual number theoretic statement constructed by Gödel is extremely complicated. The method of proof is brilliant, though. Because the laws governing the manipulation of numbers can be encoded as strings of numbers, one can actually connive to have number-theoretic statements have a secondary coded meaning which has something to say about the machinery of proofs. The coup de grace comes when you construct a statement whose coded meaning is "I cannot be proven in the system of number theory." Now let's consider whether the statement is true or false. If it is false, then it can be proven, which is to say it can't be proven. This is a contradiction, a version of the so-called Epimenides paradox: "Epimenides, a Cretan, says that all Cretans are liars." So the statement is not false, hence it is true. Since it is true it cannot be proven. Thus we have elegantly constructed a true statement of number theory which cannot be proven (within the system) precisely because that is what it asserts! Note that it can be proven outside the system, because we just did that. This is an awesome idea. The formal system of number theory can be utilized to show that it cannot adequately capture all true statements. One might say it contains the seeds of its own demise, but it might be better to say that it contains the seeds of its own limitation. Gödel's theorem doesn't destroy or invalidate number theory, it just shows that it is more subtle than any axiomatic treatment.

This whole story reminds me of an article I read in Scientific American which pointed out, that due to cosmic expansion, in 100 billion years all galaxies away from our local group will be traveling away from us at super-light speed, implying we cannot in principle see them or know anything about them. Inhabitants of the local group, now combined into a supergalaxy, will think that they are an island in infinite space. Furthermore, with all galaxies beyond our observable horizon, we won't be able to detect cosmic expansion, thus removing theoretical justification for a Big Bang. Our progeny, unless they have good records, will not have any reason to believe true physical facts about our Universe. In fact, future scientists might propose the existence of other galaxies or a Big Bang, and be shot down for unprovable junk science. So the current laws of Physics contain the seeds of their own limitation, just as with number theory. We can predict, using current Physics, that our progeny will not be able to detect facts about the Universe which we consider objective hard, facts. From here it's a small leap to realize that there are objective facts about our Universe that we will never be able to know because the information has already been lost.

Both these scenarios point to the fact that knowledge contains the seeds of its own limitation. This doesn't invalidate the reasoning process, but rather shows just how powerful and far-reaching reasoning can be. It is so powerful that it can even detect that it fails to completely capture all of reality!

The Lazy Poster

I just wrote a friend of mine in response to a letter he sent me essentially decrying theism. I'm reproducing the letter here since it is in the spirit of this blog, and also gets me off the hook for needing to post something.


Well, Jeff, I don't actually consider myself a theist. In fact, I'm committed to the principle of holding beliefs based on reasoning and evidence. I don't believe in an all-powerful deity. However, I don't necessarily agree that religion is dangerous. As I outlined in my email, there isn't much evidence that I can see that religion per se is destructive. I believe that many of humanity's current problems are caused by fundamental aspects of human psychology. For example, the instinct to band with a group of people and identify oneself as a member. I think this is why racism and sexism have been such problems, and why nations go to war. If the Israelis and the Palestinians weren't so concentrated on their labels as Israelis and Palestinians, then there would be no need for the continuing violence. Yes religion is present in the conflict, but I don't think it's the heart of the matter. I think it is a manifestation of the deep human instinct to band together and set oneself apart from some other group. (The atheist-theist dichotomy fits into this scheme too.)

I consider myself a Buddhist, and Buddhism is often considered an atheistic religion, though that is a gross oversimplification. I don't think you can really say Buddhism is either atheist or theist. The main point of Buddhism is not belief in a supreme deity, but rather the following of specific practices (like meditation) with which one can change one's perception, thinking and behavior for the better. I think there is much evidence that followers of Buddhism are a force for good in the world and not for evil. (The nonviolent protest by the monks of Burma against the reigning dictatorship is a good example.) However, even though I am partial to Buddhist thought, I think that there are good people in all religious traditions. (Gandhi, a Hindu, and Dr. Martin Luther King, a Christian, are really good examples.) People like Gandhi and King would no doubt have disagreed with the asinine pronouncements of many of the theists on the webpage you sent me. I agree that this sort of theism, the kind which is ill thought-out and intolerant is unacceptable. And our current politicians often appeal to this pseudo-religion, with stomach-turning results. That does need to be defended against I absolutely agree. But I don't think that labeling it as theist and therefore bad is the right way to go. I think that pointing out the immorality and injustice would be more effective and more accurate.

McCain Spoof video

Check out this spoof of the Obama "Yes We Can" video, in which McCain talks about how "the American people don't care if we're in Iraq for 100, 1000 or 10,000 years." I'd say that's not a fair assessment.

Happy New Year!

It's Losar, the Tibetan New Year. 2135. The year of the earth rat. (or earth mouse in one translation.)

Peace, happiness and prosperity to everyone reading this and to everyone else as well. May your day be as beautiful as an emerald mountain range at sunrise. May your mind be as tranquil as a crystal clear pond above the tree line. May your activity be as productive as the ribosomes in a single cell. May your metaphors be as outlandish as a peacock's tail made out of fiery stars.

Why I support Obama

I'm pretty sure all my readers are in Super Tuesday states, and I encourage you all to vote, no matter who you support. I actually already voted (early).

As far as I see it, Obama, Clinton, or even McCain, would be a huge improvement over Bush. After 9/11, I felt a spirit of hope, compassion and togetherness in the wake of the catastrophe. People seemed willing to help and support each other. It was like nothing I've ever experienced. A good leader would have capitalized on that oppurtunity to effect positive changes. He or she would have nurtured that spirit. Instead, Bush shabbily used the tragedy to promote his pre-existing agenda to attack Iraq. He completely squandered the good will in and outside the country, and tipped the balance from compassion to fear and hatred. It really felt awful in this country right around the time we attacked Iraq. I felt threatened for simply expressing my viewpoints.

Of the Democratic candidates, I think Obama has the potential to be most like the leader I envision. Certainly not an exact match. But he has the very useful skill to make impassioned and inspiring speeches that tend to bring people more toward the compassion side than the hatred side. Also, unlike Clinton, he did not vote for the Iraq war. Aside from that, their actual platforms are very very similar. Perhaps it's being unfair to Clinton, but she doesn't seem to have the same charisma. I also have been rather disillusioned with her for always making decisions based on whether she thinks it will maintain her electability. In other words, rather than trying to help the most, she is simply laying plans to get elected. Obama is certainly also guilty, but perhaps because of his shorter political career, less so.

One down side to both candidates: neither has any plans to reduce the size of the military or the defense budget. (We spend something on the order of magnitude of ten times more on defense than any other country, and it makes up an astounding percentage of our budget. It rather belies our fundamentally violent, imperialist nature.) Kucinich was my man for that, but he has dropped out in order to concenrate on maintaining his current congressional seat. (I encourage you to donate to his congressional campaign. We need voices like his in congress!)

Please post a comment if I'm being unfair.