July 2007 Archives
I found this excerpt from the wikipedia article on the LHC to be particularly amusing.
"Safety
While many have voiced concerns that the LHC will destroy the Universe, engineers close to the project claim that the possibility is infinitesimally small. As CERN has pointed out, if the Earth were in danger of any such fate, it would have happened billions of years ago from the bombardment of protons the planet receives that are millions of times more energetic than anything that could be produced by the LHC.[8]
As with the Relativistic Heavy Ion Collider (RHIC), people both inside and outside of the physics community have voiced concern that the LHC might trigger one of several theoretical disasters capable of destroying the Earth or even our entire Universe. Each advance in particle accelerator technology exposes the stability of the very fabric of the universe to more stringent tests.[citation needed] RHIC has been running since 2000 and has generated no major problems; however the Large Hadron Collider is set to create an environment significantly more alien to nature than the RHIC has ever created, and therefore the probability of catastrophe is greater.
Theoretical disasters include:
Creation of a stable black hole[9] inside the earth
Creation of strange matter that is more stable than ordinary matter
Creation of magnetic monopoles that could catalyze proton decay
Triggering a transition into a different quantum mechanical vacuum (see False vacuum)
It is possible that the Large Hadron Collider will create tiny black holes within the Earth [10]. Most physicists expect that Hawking Radiation will cause these black holes to dissipate. The primary cause for concern is the fact that Hawking Radiation - the only means by which these black holes could be dissipated, is entirely theoretical.
CERN performed a study to investigate whether such dangerous events as micro black holes, strangelets, or magnetic monopoles could occur.[11] The report concluded, "We find no basis for any conceivable threat." If black holes are produced, they are expected to evaporate almost immediately via Hawking radiation and thus be harmless, although the existence of Hawking radiation is currently unconfirmed. It has been claimed that a strong argument for the safety of colliders such as the LHC comes from the simple fact that cosmic rays with energies up to twenty million times the LHC's 1.4×10¹³ eV capacity have been bombarding the Earth, Moon and other objects in the solar system for billions of years with no such effects[12].
And many people remain gravely concerned about the safety of the LHC such as the science watchdog group called the Lifeboat Foundation which has covered these dangers in detail. As with any new and untested experiment, it is not possible to say with utter certainty what will happen. John Nelson at the University of Birmingham stated of RHIC that "it is astonishingly unlikely that there is any risk—but I could not prove it."[13] Furthermore, in academia there is some question, albeit among a minority of scientists, of whether the Hawking radiation theory is correct.[14]"
Why is it that most people despise economics?
One of my good friends and roommates is a self-proclaimed communist. She even attends regular meetings for this weird Trotskyist organization that tries to mobilize support for communist ideology among industrial workers--that is, the shrinking stock of industrial workers who will be nonexistent in America in 30 years due to outsourcing. It's a very sustainable strategy.
Since communist arguments are so easy to demolish, I have a hobby of doing precisely that whenever such political opinions come up. She strangely seems to always change the subject, whenever communist politics come up... But the point is, she told me one day that economics was evil. I was flabbergasted, and asked why. She said that it was purely in the dogmatic business of making capitalism appear good. I tried to explain to her that economics is actually a science about how people make decisions, but she just changed the subject of conversation again.
A week later, I encountered another person who called economics dumb because apparently "no one except for Adam" makes decisions like economics says they should. Apparently it's "all in Polanyi." I tried to explain that rational behavior is actually extremely common, even if people don't consciously realize it. I was about to explain that the hottest areas of economics are in fact those areas where non-rational decision calculuses apply. Instead, I was directed to read Polanyi again, and the topic of conversation suddenly changed.
The more I think about it, the more I realize that this hatred is surprisingly ubiquitous. It's so surprising because economics is the one social science that actually works! It still has a lot of severe problems, but it has considerable predictive power, a precise mathematical formulation, and a sophistocated toolbox of empirical methods and data with which to test and falsify its theories. It's no physics, but it's pretty damn good. But I think this may indeed be the problem. Economics is a science, it does work pretty damn well, and it is about decisions. I think people are reluctant to admit that many of their decisions can be predicted and categorized. The very success of the science seems to threaten our faith in our own free will. Thankfully humans are too complicated to ever be fully understood through the narrow lens of their decisions, but rather than treating it with hostility, people should treat economics as a chance to better understand humanity in a precise fashion. And doing so doesn't require becoming homo economicus, like I allegedly am.
During my respite from mathematics, on vacation in Sun Valley, Idaho, I had the pleasure of visiting the Sun Valley gun club to shoot trap two times. As you might expect, guns are not exactly my "thing": they have a tendency to make me somewhat nervous, I have only fired one on a few occasions, and let's face it, it's a rather difficult to reconcile my personality and other interests with "gun culture" (whatever that means). Nevertheless, even I find shooting trap to be marvelously fun from time to time--I even did surprisingly well, with an accuracy of about 50% the first time and 80% the second.
In spite of this boasting and glee, as I was shattering my clay pigeons under the warm summer sun, I couldn't stop thinking about the profoundly destructive effect that firearms have on Americans. Not only is the US homicide rate higher than any other developed country, but firearms are the fatal weapon in 68% of homicides in this country.
These statistics, of course, lead one to contemplate various forms of gun control. On one extreme, opponents of guns would ban guns entirely. Even if this were constitutionally possible, it would be ineffective and divisive. Such a move would ignore the fact that there are perfectly enjoyable and safe uses of firearms (such as the one in which I partook). Moreover, it would quash a perfecly legitimate "gun culture" that prevails to a great extent in America. But even if we could quash this culture (and shut down all American gun manufacturers), banning guns is likely to create yet another black market, in which bad guys can still get guns but good guys cannot.
On the other extreme, some (mostly anarcho-libertarians) would put very few limitations on gun ownership. The argument is somewhat like mutually assured destruction with nuclear weapons. It goes something like this: if everyone has a firearm, then since guns are lethal weapons, no one will risk using them because their victim might kill them first. Fortunately, this argument doesn't appeal to many people because it is severely flawed. Even though its flaws are obvious, I'll give a few just for fun. If you want more people to have guns to protect themselves, you have to decrease the barriers to gun ownership. At some point, this makes it easier for criminals to get guns. Firstly, this makes law enforcement harder, since it eats away that the government's monopoly on force. But secondly, it may not actually reduced gun crime. Since criminals are the ones who decide whether or not they will be involved in a gun crime, they will have the ability to develop better skills than their victims who do not know when, if ever, they will be the victim of a gun crime. There is thus an information asymmetry which always works in favor of the attacker. It is unreasonable to expect everyone to own and train regularly on their firearm, so many people probably still will not own guns and even fewer would be skilled enough to deter a well-planned attack. Lastly, there will be some people--children, in particular--who we all agree should never own guns, and will be put at a terrible disadvantage. To adopt the MAD analogy once more, Lichtenstein would be in an awfuly bad situation if the rest of the world had nuclear weapons. Since there is no way that Lichtenstein could ever build its own nukes, Switzerland could steal their neighbor's ski resorts and mountain chateaus by just fingering the fatal button.
So where does this leave us? We've ruled out the extremes, so we must look somewhere in the middle. That probably seemed obvious from the very beginning. But that's basically what we're doing today and it does not seem to be working very well. There are currently all sorts of proposals for gun control mechanisms using complicated sensors and tracking devices. This is all probably good, but there is one thing that is not discussed very much:
Assume you are a risk-averse agent. Practically everyone is risk averse, even people who use firearms (Maybe this could be empirically determined, but for now I'm just stating it as a resonable postulate. After all, if they were risk-loving, they would all take a risk and face their victim in hand-to-hand combat!). Let's say that you're a mugger, and you can flash your illegal gun at your victim and it's basically a done deal that he will fork over all of his money. There's some probability of getting caught, in which case you lose all the money that you stole plus a lot more that you had before the crime. Call this scenario A. Alternatively you could just not mug the man, and you would have a 100% chance of keeping your original money. Call this scenario B. If your expected utility of income in scenario A is greater than your utility in scenario B, you will mug the man (non-muggers don't think like this because they feel guilty about breaking the law; they have some utility of law-abiding). Now suppose for a minute that we have two sub-scenarios A-1 and A-2. In A-1, you lose twice as much money as in A-2 if the police catch you. But in A-1, the odds of getting caught are half as great. So the expected loss in money is the same in A-1 and A-2. However, the expected utility for a risk-averse person is actually lower in A-1 than in A-2. So having higher consequences for committing crimes is actually a more effective deterrant than increasing the probability of getting caught. It's conveniently also cheaper for the government. This may seem a bit awkward at first glance. If you don't believe me, take some risk-averse utility function over income, say U(x)=x^(1/2), and compute some examples.
The implication of this is that one way of improving our current enforcement of gun laws is simply to make people who acquire guns illegally pay a ton of money. If you make it miserable enough, then the extra trouble of creating even more ingenious methods of finding law-breakers might not be as necessary. One could, for example, have fines of several hundred thousand dollars for such offenses.
If you are skeptical of the practical applicability of such draconian tactics, then evidence from Scandinavian drunk driving laws appears to support my approach. In some Scandinavian countries, drunk drivers face fines on the order of tens of thousands of dollars, suspension of driving privileges, and occasionally prison sentences for driving with a BAC over their legal limit of 0.02. In the US, the legal limit varies from 0.08 to 0.10 by state. In Sweden, driving with a BAC of 0.10 is considered "aggravated" drunk driving, resulting in a prison sentence of two years. The result? Sweden and Norway have half the number of traffic deaths per mile driven compared with the US, and their fatalities have been decreasing ever since the instatement of the law. Although there are a lot of practical difficulties in comparing drunk driving with guns, I think there is at least a case that the economic principle can be applied as an enforcement mechanism for both problems.
This I discovered today and burst into laughter. I am sure you will see why it is problematic.
"Now the oligarch in turn was third from the king, if we identify the king and the aristocrat.--Third he is.
So the dictator is three times three times removed from true pleasure.--So it appears.
The image of dictatorial pleasure, according to the number of its dimensions, is a plane. By squaring and cubing this number it will become clear how large is the distance between the dictator and the king.--Clear at any rate to a mathematician.
Turning this around, if one wants to know how far the king is superior to the dictator in the truth of his pleasure, he will find, if he completes his multiplication, that the king lives seven hundred and twenty-nine times more pleasantly than the dictator, and that dictator is the same number of times more miserable.
You have brought up an extraordinary calculation, he said, of the difference between the two men, the just and the unjust, as regards pleasure and pain.
Yet it is a true one, I said, and a number appropriate to human life, if days and nights and months and years are appropriate to them.--They surely are."
--Republic, 587d-588a
I was reading Plato's Republic when I noticed the following logical errors and major points of disagreement:
1.) (False classification) Socrates often uses concrete examples of a certain class to make claims about abstract ideas without justifying how the abstract idea is a part of the given class. In other words, he appears to use a string of examples to justify a claim. But in so doing, he assumes that the idea is part of the class, and he therefore groundlessly ascribes all the features of that class to the abstract idea.
This pattern occurs at 332 c-e and 333a (not the greatest example, but it works). Socrates gives many examples of "crafts" and their beneficial functions. He then asks his interlocutor what benefit "the craft of justice provides." This implicitly identifies justice with the class of crafts, thereby assuming that justice has the same characteristic of any general craft. By answering the question, the interlocutor is duped into accepting this classification. This is not especially problematic until 342e and 343a, when Socrates uses the fact that, in all of his examples, crafts do not seek their own advantage, but the advantage of something else. He then applies this to justice: so justice must work to the advantage of something else. This contradicts his interlocutor's prior assertion that justice is to benefit oneself by helping friends and harming enemies.
The logic here is flawed because Socrates never defines what a craft actually is, and whether it is reasonable to say that justice is a craft. He uses a rhetorical slight of hand to make the interlocutor accept that justice is a craft. Socrates then forces the interlocutor to accept that justice must have the same characteristics as his hand-picked crop of examples of crafts.
2.) (Absence of existence arguments) Plato builds up magnificent structures of theoretical speculation throughout many works. The canonical example is in Republic: he devises his famous utopian society ruled by philosopher kings. The arguments are elegant and comprehensive, but the reader is left with the feeling that the society is oppressive and unnatural. While Plato would undoubtedly have some clever responses to these charges, he nevertheless ignores a crucial obligation. In mathematics, when one defines a mathematical object, before one can do anything with it, one must prove that it exists in a given context. In a similar manner, Plato can theorize endlessly, but it is all nonsense if he does not give a very detailed (given the size of his claims) account of existence.
Plato actually claims to give a proof of existence, but it has many flaws. When confronting the existence of his Republic, Socrates states: "Is it possible to realize anything in practice as it can be formulated in words or is it natural for practice to have a lesser grip on truth than theory, even if some people do not think so? Will you first agree to this or not? -- I agree" (472e). Here, Plato effectively assumes away the problem of existence asserting that anything that can exist theoretically can exist in reality. This is tantamount to the belief that all things can be shown to exist in reality by logical necessity alone--without resorting to any empirical or perceptive means at all. This is a very Cartesian view, and there is much evidence that it is logically unfounded. Whether things exist is a property of the space in which they exist, not the human mind.
3.) (Excessive reliance on the "forms") This is not a logical flaw of his, but a serious limitation of his philosophy. He repeatedly denigrates "practical" knowledge and reasoning as inferior to the theoretical. The historical success of empirical knowledge shows that this is unwise. This is ultimately a consequence of his excessive reliance on his "forms". By emphasizing their importance and perfection, he neglects the fact that reality and the "shadows" are one route to accessing the forms (and maybe the only route). It is only by studying and examining lots of empirical cases of justice that we can understand what justice is. But we can never know precisely what justice is because it is simply can't be precisely defined, so we must continue to learn about it by studying specific examples and experimenting.
In other words, I think speculation alone is typically not especially useful unless it can be made extremely precise (I belive only mathematics can ever do this). If I understand him correctly, I think Plato would disagree... or he would claim that all speculation can be made extremely precise like mathematics. It's not too hard to argue that human reality is (thankfully) not that mathematical.
I've been spending some time studying generalized abstract nonsense (sometimes called "category theory" by its practicioners). In fact, I think my paper for the summer will end up relating generalized abstract nonsense to something in algebraic topology. After spending all day dealing with "things" like "metatheorems" or functors that are sometimes faithful and often forgetful, one occasionally needs to step back and gain some perspective. Here are a few choice descriptions of the subject from the masters, which supply just that.
"A direct treatment of categories in their own right appeared in Eilenberg-MacLane [1945]. Now the discovery of ideas as general as these is chiefly the willingness to make brash or speculative abstraction, in this case supported by the pleasure of purloining words from philosophers: "Category" from Aristotle and Kant, "Functor" from Carnap, and "natural transformation" from then current informal parlance."
--Saunders MacLane, "Categories for the Working Mathematician," pg. 29-30.
"As for the proof... well, these diagrams are so natural that one can hardly imagine it any other way!"
--J. Peter May, in lecture the other day.
"No, this isn't category theory. This is real Mathematics."
--Mitya, in lecture the other day.
