Saturday, September 25, 2010

Liberal Lunacy 4: Seat Belts

I think that I may be unfair in this post. I am not sure if being strongly pro seat belt laws is a liberal thing or not. I know some (neo)-conservatives who strongly stand by seat belt laws. But I just get the impression that liberals are more into laws for seat belts. If I am wrong about this then just interpret this post as my objection to seat belt laws.

The main argument in favor of seat belt laws has been that these laws save lives. Usually what follows next is some person giving citations to fancy diagrams showing just how many lives been saved. But I am not a fan of statistics, for numerous reasons I do not want to get into. I really hate statistical arguments. I respect people a lot more if they can give out a thought out argument why it should be a case rather than saying "studies have shown ... ". So how about we stay away from statistics because it is way too boring and try to come up with a more interesting rational argument instead? One can say the following. If there were no seat belt laws some people would wear seat belts and some people would not. If there are seat belts laws then the people who already wore seat belts will continue to wear them because they are unaffected by the law, while the non-wearers will now wear them because it is the law - except that rebellious ones who still insist in being dangerous. Thus, it is entirely reasonable to conclude that such a law would save lives.

So I entirely agree with the statement that seat belt laws save lots of lives. What I find interesting is that seat belt laws is one of "good" laws. In general, laws achieve the exact opposite of what they intent to achieve: minimum-wage laws, rent control, drug prohibition, anti-gun laws, child labor laws, anti-trust laws, and so forth. Why seat belt laws prosper while most other laws fail I do not know, it is an interesting question, but let us ignore this question for now and just work with that fact that seat belt laws work.

But is saving lives an argument in favor of seat belt laws? No. Because it is not our lives. To make my point more clear let me give you an example. Suppose that anti-suicide laws (I wonder what the punishment would be for someone who commits suicide) are shown to reduce the number of suicide by 30%. Is that an argument in favor of passing anti-suicide laws? No, it is not. Because it is not our lives we are saying. Life is not owned by other people, life is only owned by the individual himself. If the individual wishes to end his life then so be it, to prevent him from doing so is to rob the individual of his life and enslave him into this world. We have no right to deny someone of his right to life and prevent him from ending it, even if we disagree with him. Therefore, the argument, "seat belt laws save lives therefore seat belt laws are good" is a bad argument.

People should be able to live as dangerously and unhealthy as they can. If people want to commit suicide then so be it. If they want to eat at McDonald's then so be it. If they want to drink anti-freeze then so be it. It is their lives they are ruining and we cannot stop them. Freedom means people are free to be stupid and make mistakes. If a person ignores what most intelligent people say about putting on a seat belt and decides to ride dangerously then he is taking a risk himself, he has the right to be stupid. So the argument that seat belt laws save live is irrelevant here.

That is my main argument against seat belt laws. But there are three other reasons to be against seat belt laws. First, this controls the population. If you are concerned about the population getting too big then this is a good way to bring it down. The less safe the world is the smaller the population is going to be. It is rather hypocritical to complain about a large population and support all this safety hysteria. Second, the world needs less safety. A big problem with the world today is that it is too safe. There is nothing wrong with safety but our generation takes safety up their anus. So far up the anus that we end up with a bunch of pussies. Weak-cowards who are afraid to take risks, afraid to even eat non-low fat yogurt because it might contain "toxins". This country was founded by terrorists who were not afraid to duel with one another if they disagreed, today we are afraid to ride on a bicycle without a helmet or skate with roller-blades with no knee pads. Pretty sad. Third, I see opposition to seat belt laws as a form of passive eugenics. Instead of killing the dumb people how about the dumb people kill themselves? This was we get rid of the dumb population without actually having a eugenics program.

Say yes to seat belts, say no to seat belt laws.

Thursday, September 23, 2010

Structure of S4

This post will assume knowledge of group theory, in particular: symmetric group, conjugacy, conjugacy class equation, and Sylow theorems.

A very useful group to understand is $$S_4$$, the group of all permutations of $$\{1,2,3,4\}$$ under function composition. The group $$S_3$$ is not very interesting because it is too easy, and higher size symmetric groups are too complicated, but for n=4 the symmetric group is not terribly complicated. We will classifly all the subgroups of $$S_4$$.

By Lagrange's theorem the subgroups of $$S_4$$ must have order dividing $$4!=24$$. Therefore, a subgroup must have one of the following orders: 1,2,3,4,6,8,12,24. The order 1 case is simply the trivial subgroup and the order 24 case is simply the improper subgroup. We can easily disregard these basic cases and consider all the other divisors.

Let us derive the class equation for $$S_4$$. Two permutations are conjugate if and only if they have the same cycle structure, that is, iff when expressed as a product of disjoint permutations the number of disjoint permutations is equal and the cycles can be paired with equal lengths. The possible cycle structures for permutations are: 1-cycle, 2-cycle, 3-cycle, 4-cycle, product of a 2-cycle with a 2-cycle. The 1-cycle is simply the identity and therefore it just conjugate to itself. The 2-cycles are conjugate with themselves and there are $${4\choose 2}=6$$ of them. The 3-cycles are conjugate with themselves and there are $$2!{4\choose 3}=8$$ of them. The 4-cycles are conjugate with themselves and there are $$3!{4\choose 4}=6$$ of them. The 2,2-cycles are conjugate with themselves and there are $$\tfrac{1}{2}{4\choose 2}{2\choose 2}=3$$ of them. Therefore, the class equation for $$S_4$$ is given by: $$1+3+6+6+8=24$$.

A normal subgroup must be a union of conjugate class including the class $$\{\text{id}\}$$. Note among the summands, $$1,3,6,6,8$$ the only ones when paired with $$1$$ give a divisor of $$24$$ are $$1+3$$ and $$1+3+8$$. Therefore, the only possible normal subgroups must consist of a union of the 1-cycle and 2,2-cycles; or a union of the 1-cycle, 2,2-cycles, and 3-cycles. It is indeed the case that {id,(12)(34),(13)(24),(14)(23)} is a subgroup and so it must be normal, we call this subgroup V, it is the Klein four group. The other union is easily seen to contain all the even permutations, so it must be the alternating subgroup $$A_4$$.

Thus, we have shown that the only proper non-trivial normal subgroups of $$S_4$$ are $$V$$ and $$A_4$$. This information immediately classifies all the subgroups of order 12. Because any subgroup of order 12 must immediately be normal for it has index 2 in the full group. However, we determined that $$A_4$$ is the only normal subgroup of order 12, thus, there are no other subgroups of order 12.

Now let us move to the next possibly highest order, subgroups of order 8. Notice that $$2^3$$ is the highest power of two dividing 24, therefore by Sylow's first theorem will there be subgroups of order 8, namely the Sylow 2-subgroups. By Sylow's second theorem these subgroups all conjugate to one another, so there would be a unique Sylow 2-subgroup of order 8 if and only if it was a normal subgroup, however by the class equation we determined there are no normal subgroups of order 8, thus, the number of Sylow 2-subgroups must exceed 1. By Sylow's third theorem the number of Sylow 2-subgroups must be a divisor of 24 and congrunent to 1 modulo 2. The only such numbers are 1 and 3, but it must exceede 1, so the number of subgroups of order 8 must be precisely 3.

All we have to do now is determine the subgroups of order 8. This is easier than it seems because we already know one subgroup of order 8, namely the dihedral group $$D_4$$. The other subgroups are just the conjugates of $$D_4$$. Conjugate subgroups are clearly isomorphic and so we see that the three subgroups of order 8 are just copies of $$D_8$$.

Now we need to figure out the subgroups of order 6. An abelian group of order 6 must be isomorphic to $$\mathbb{Z}_6$$. Since there are no elements of order 6 in $$S_4$$ it follows that if $$S_4$$ has a subgroup of order 6 then it must be isomorphic to the non-abelian group of order 6, that is, isomorphic to $$S_3$$. A group is isomorphic to $$S_3$$ if and only if it has two generators, x and y where x has order 3 and y has order 2 which satisfy $$yx=x^2y$$. There are 4 elements of $$S_4$$ which have order 3. It is not hard to see that for each element we can find a corresponding element of order 2 which satisfies the relation $$yx=x^2y$$. Furthermore, each of these generated subgroups are different. And so there are four subgroups of order 6 each isomorphic to $$S_6$$. In fact, it is easy to describe these subgroups. Let $$S(t)$$ denote the permutations that fix t in the set 1,2,3,4. Then clearly $$S(t)\simeq S_3$$ for each t. And these four values of t determine these four subgroups.

This time we work with subgroups of order 4. These are either cyclic subgroups, generated by a 4-cycle or the Klein four groups. There are six 4-cycles but one can easily check that half of the generate the same subgroup, i.e. if x is a generator then so is $$x^3$$. Thus, there are 3 copies of $$\mathbb{Z}_4$$. The Klein four subgroups are generated by two elements of order 2. These include either two 2-2 cycles, or two 2-cycles which commute. The case with two 2-2 cycles was already considered, it was the subgroup we named as V. The other ones are generated by two 2-cycles. There are three other such subgroups. So we see there are 4 copies of $$\mathbb{Z}_2\times \mathbb{Z}_2$$.

The subgroups of order three are generated by a 3-cycle. There are eight 3-cycles but exactly half of them generate the same subgroup i.e. if x is a generator then so it $$x^2$$. So there will be precisely four copies of $$\mathbb{Z}_3$$.

Finally the subgroups of order two are generated by a 2-cycle or a 2-2 cycle. There are six 2-cycles and there are three 2-2 cycles. Thus, in total there are 9 copies of $$\mathbb{Z}_2$$.

To summarize our results: 9 copies of cyclic two groups, 4 copies of cyclic three groups, 3 copies of cyclic four groups, 4 copies of Klein four groups, 4 copies of symmetric three groups, 3 copies of dihedral four groups, 1 copies of alternating four group. And there are two proper non-trivial normal subgroups which are the alternating subgroup and V.

Exercise: Use the structure of $$S_4$$ to come up with a counter-example to the following statement: if H and N are subgroups of a group G and N is normal then HN is a normal subgroup also.

Monday, September 20, 2010

Ayn Rand Sucks

I dislike Ayn Rand. But what is interesting to note is that I agree with her on a lot of her conclusions. Ayn Rand was a supporter of capitalism, so am I. Ayn Rand was against welfare, so am I. Ayn Rand was against the whole "equality" movement, so am I. But I still dislike her because our reasoning behind our positions are very different. She sometimes reminds me of the KKK or white nationalists. White nationalists and supremacists have a lot in common with me, but for very different reasons.

Ayn Rand approached these sort of questions with objectivism. It was what she claimed to be an objective moral system. But a very strange moral system. Based upon selfishness of ourselves. Most moral systems that people have are concerned about helping others, but Ayn Rand was not concerned with that, she was concerned about ourselves and how we treat ourselves and only ourselves.

Adam Smith and Ayn Rand are different supporters of capitalism. Adam Smith was a supporter of capitalism because he argued from an economic point-of-view. He argued that capitalism will lead to the best economic system which in turn will lead to higher standard of livings for the people. Ayn Rand was a supporter of capitalism because she argued from an ethical point-of-view. She argued that capitalism is the only system compatible with selfishness. Capitalism is the only means for people to act for their self-interests. That is why Ayn Rand so strongly supported capitalism.

I am not an egoist, I do not promote the idea of selfishness. I think that people's primary concern are themselves, but people should learn to share and give away what they have with others. What we teach our children, "sharing is caring" is something I strongly support. So I definitely have a big issue with Ayn Rand and the claimed virtue of selfishness. I side with Adam Smith on the capitalism issue, not with Ayn Rand. This is my first problem with her.

My second problem with her is that she was a moralist. She was an atheist, but she was nonetheless still a moralist. She was able to abandon the silly idea of God, but she never abandoned the silly idea of objective morality. I am a moral nihilist. Humanity will get so much more advanced and enlightened if we were able to give up morals and simply live a kind life in absence of morals. My problem with morality is that morality is a false concept. It is a dead surviving remnant of religion. It has no place in philosophy. There is no rational deductive way or an empirical inductive way to obtain an "ought" from an "is". What we know about the universe is simply what is, not what ought be, what ought be is just a human preference and so cannot be obtained from first principles. Besides, morality is also authoritarian in a way. Once you have objective morals you become extremely distressed with how people act. You get bothered when teenage girls wear short skirts or teenage boys wear their pants low. Or you get bothered when some other non-sense like this happens that really should not concern anyone. Morals make people want to impose their morals on other people, even if done in absence of a state, like with Ayn Rand, is still in a way authoritarian.

Ayn Rand was also known to be an unkind person. She disliked homosexuals. Not sure why, there is no reason to be anti-gay if one is no longer religious. She was against women being presidents. She hated the Arabs in the middle-east and sided with Israel. Her personality was quite terrible. I would not be surprised if her unkind nature was the result of her morals. As I said, morals make people more authoritarian. It seems that her Objectivism made her really dislike things that normal people should not otherwise dislike. I know that someone's character is not an argument against whether one speaks truth or not. She can be the most terrible person in the world, it would not necessarily make her ideas wrong. But this post is called "Ayn Rand sucks" not "Objectivism sucks", so I am legit when I go after her.

And finally, Ayn Rand is not original. Her works comes from Friedrich Nietzsche. Nietzsche advocated a form of egoism. But not from an ethical point-of-view. Nietzsche after all was a moral nihilist. He simply argued for people to be the overman, there was no ethics attached to such a statement. Ayn Rand copied a lot of Nietzsche's work. One cannot give much credit for Ayn Rand, rather one must give credit for Nietzsche.

Friday, September 17, 2010

Yom Kippur: A Taste of Heaven

Yom Kippur is the time of the year when we dress in holy clothing, when we fast all day, and pray the entire time. We do this to emulate the angels of God. Angels are dressed in divine clothing, they do not eat, and praise God. Heaven in Judaism is described as a place where all the good people give praise to God and learn his Torah.

But did you ever wonder what such a life is like? Yom Kippur gives you a glimpse into such a life. Such a life will basically be sucking the great big cock of God all day long. God will lube up your anus with some Astroglide, or whatever your favorite lube is, and stick his cock in there. You will be screaming "oh my God" as that giant cock of his goes all the way in. As God is doing his work with you, you will continually recite praises, non stop. After some anal action, you will get on your knees drop your mouth, and this time God will stick his cock into your mouth. And you will still be reciting praises with a stuffed mouth. You will finally understand why God is your Lord. And you will get to know why they call him the Rock when you feel his extremely hard cock in your mouth. Also the white scene that we are familiar with on Yom Kippur will finally make sense to us when we realize that all of heaven is filled with God's sperm. This will happen to you every day. You will suck on God's giant cock all the time with praises and recitations with none of your own free time.

You can keep your heaven to yourself, I want no part of it. Who would want to live in such a world?

Wednesday, September 15, 2010

Should the Burqa be Banned?

I have addressed this issue in extreme generality. A while back here I wrote about exactly how bans work. The general statement over there was that if you support bans then you must agree that violence is the way to deal with the "problem" which you want to ban. Do you agree that violence (or the threat of it) against Islamic women is the way to deal with the burqa?

There is more to say on this issue so it deserves it own post rather than a general one. I will begin with the argument that the goal behind banning the burqa is giving women more rights and freedom.

This argument demonstrates how people completely misunderstand important terms that they use on a day to day basis. In this case it is the word "rights". What does "rights" mean and where do they come from? It is a word used everyday. People say "gay rights", "women rights", "black rights", and so on and so forth. But what does the word "rights" mean? Can you explain what it means? And also can you explain where these rights come from?

I never heard anyone's definition of it. It is a word used all the time and so we become used to hearing it and then eventually using it ourselves. This is my very simple explanation of what rights refer to. A right to something is the ability to act on that something without being stopped from doing so. This is an extremely simple definition. When we say "gay rights" we refer to the right to marry. That is to say, homos can act and marry one another without being stopped from doing so. In most places around the world gays do not have these rights, which simply means, they are prevented from acting on their right to marry. That is it. There is nothing mystical or complicated about rights, that is all they are.

Now let us ask the next question. Where do rights come from? The sad truth, the very sad truth, is that most people, not just in the US but around the world, would answer, "rights come from the government". This is a wrong answer, and not only wrong but a little dangerous, it makes people look up to the government with such a mentality. Right do not come from anywhere. People have them. Rights cannot be given. Rights can never be given. They can only be taken away. And some rights should be taken away, like the right to kill others. But the important point is that rights are already in place, and no one, no government, no dictator in a funny hat, can give them to you. The great words of the Declaration of Independence of America start out by saying, "We hold these truths to be self-evident, that all men are created equal, ... with certain unalienable rights". This means exactly what it sounds like. Rights are inalienable and inherent to all people.

There is a lot of confusion today about what "rights" mean. Indeed, people make such foolish statements as "the right to healthcare". What that means is beyond me, it cannot be interpreted in the way I described what "rights" mean. The word "rights" is an example of the corruption of language. Corruption of language is when terms that used to have meanings once in the past lose their meanings and retain their usages.

Now let us return to the discussion about burqas. Supporters of burqas might say "banning the burqa is progress towards women's rights". Now let us examine this phrase to understand what it means. It means to say that women have more rights as the restult of the burqa ban. But this is not true. A woman does not have the right to wear a burqa. Thus, the burqa ban results in less rights. Therefore, it is wrong to say that banning the burqa is "progressing towards women's rights".

Women should be recognized as people capable of making their own decisions. And let them be as they wish to be. They cannot be told how to dress or what they can or cannot wear. This only results in less rights for them. If a Muslim woman chooses to wear a burqa then it means this is what she prefers. Of course this is only in the context if she chooses to wear a burqa. If she is made to wear the burqa upon the command of her husband or father under, say under penalty of death, then her rights are being taken away by her husband or father. The only appropriate stance with regard to the burqa issue is to fully allow the women to make their own choices. No one can tell them what to do, be it an authoritarian husband or a authoritarian police officer, this choice is for them and only for them. Yes, some women will still choose to wear the burqa. When people are free to make their own choices they do make stupid choices, but it is their choices. That choice is for the woman and no one else and we should respect her right to make such a choice. Thus, if her final choice is a burqa, even if it the result of brainwashing when she was a little kid, it is nonetheless the choice she prefers to do. To deny her of this choice is to steal those rights from her.

Another problem with the burqa issue is the idea that laws improve society. I have spoken about this before but I will repeat it again. Laws do not improve society, and I strongly believe that this idea is the cause of so many problems in the world. Laws cannot improve society, they can also prevent people from acting in certain ways, but that is not improvement. Laws are equivalent to a giant societal spanking. Laws do not change human nature in the same way as spanking does not improve the behavior of children. Spanking can only stop kids from acting in certain ways, but spanking does not teach children the reasons behind why they should not act in a particular way. In this manner laws do not actually change the mindset of people. The only way to improve society is not by passing laws or bans but by changing the minds of people. This is the only way that works and this is the only way in history people have ever made any progress. But to change people there needs to be an open marketplace of ideas. There cannot be a set standard for everyone to follow. There needs to be a diversity of many different approaches all in competition and in a war with one another. This is the only way in which the minds of people are changed and society can improve.

Thus, if France really cared for helping Muslim women fight against this irrationality they should support their own decisions that they make and allow the women to be exposed to the secular values of France. This is the only way to truly win the battle against the burqa. It is a slow and difficult process but progress takes time. However, France is not smart, and they suck. Besides France has proven itself to not care about freedom or freedom of religion.

FRANCE SUCKS!

Monday, September 13, 2010

I prefer to watch things on YouTube rather than on TV. Here are some of my favorite channels that I like to watch. Maybe you would like them too.

TheAmazingAtheist: This is my ALL time favorite YouTuber. I have been watching him for years, I remember watching him when he was still not popular (now he is the biggest atheist on YouTube, not just in size, but in most number of subscribers, he overtook Pat Condell quite a while ago). He is also important to me because he has influenced me in many ways, more than anyone else on YouTube. His main channel can be found here. However, due to restrictions on YouTube he has been suspended and a lot of his videos have been taken down. You can find some of his earlier (and much better) videos here, here, and here. There are probably like a total of 800 videos, and most of them are better than porn.

Let me link you over to some of his videos so that you do not need to search around. These are some of my favorites that he did, perhaps you like them as much as I did: here, here, here, and here.

Stefan Molyneux: Stef is an anarchist philosopher on YouTube. He has got some fame, I see that some Wikipedia articles now even mention him. I do have some problems with him. First of all his is a moralist and though an atheist still mantains this silly idea of objective morality. Second he is not a determinist. This issue would be irrelevant to political philosophy but since Stef likes to call himself a philosopher before an anarchist it is important to state this flaw in him because it is silly for someone who calls himself a philosopher to hold on to the concept of non-deterministic will. Other than these issues and some others that I do not want to get into now he is good at advocating the message of liberty. You can find his channel here.

Here are some of my favorite videos that he did: here, here, and here.

FringeElements: Some homo anarchist moral nihilist kid on YouTube. He likes to focus on a purely economic argument against the state rather than philosophical ones. This is his second account because his original one got banned, not sure why though. Some of his early videos were reuploaded under different accounts. The channel is here.

Here are some of my favorites: here, here and here.

DeistPaladin: This is an interesting take on religion. Rather than rejecting religion through the use of science and skepticism, this person (who is actually a deist) uses the Bible itself to refute itself. His Skeptic Bible Study series is great. I think this approach may have more effects on deconverting people than the standard skepticism approach. You can find his channel here. Here is a great video: here.

Laci: I guess I need to mention a girl too because otherwise someone accuses me of being a sexist. I do not really have girls I like to watch on YouTube but the only one that I enjoyed was LaciGreen/GoGreen. One of her channels is made for atheism (the GoGreen one), but I do not like her style, way too emotional and hippish. And her other channel is just random non-sense that sometimes gets funny. You can find her channels here and here.

Proof of Ugliness

So when I wrote my post about the advantages of being ugly here some person wanted to see proof of my ugliness (a picture). This is not the first time, other people, outside this blog, have also demanded a picture.

Well, sorry I am not going to post a picture because I am too much of a coward to do that online. However, I will give you three reasons that form the evidence that I am physically repulsive.

1) I have been on ChatRoulette before. I did not go there to show off my penis. I rather went there to try to speak with some people. Strangely, I got banned from the site in about two to three minutes, this happened to me several times already which is part of the reason why I stopped going to ChatRoulette. Other people reported me in for offensive or inappropriate imagery. So even though I have not been doing anything offensive, and even though I kept my pants on, I offended enough people to get banned from that site.

2) I have been using an internet dating service to see if I can find someone (though at this point in life I am considering abandoning all relationships). I am a loser so I cannot meet people in real life, so I have to do it the cheap way and use the internet. I have had an account there for approximately one year. For all that long period of time I hardly ever get a message from someone. And the people who do send me a message generally turn out being over 40 year old homos. Something way too old for me. So I guess I am acceptable to over 40 year old homos but not other kinds of people my own age. Furthermore, all the messages I send were ignored by others. I cannot even think of the last time somebody responded back to me.

3) The general rule of online dating is that if you make a profile and do not post pictures then the chances of finding someone who would respond to you are way way lower than otherwise expected. A lot of people even ignore profiles with no photos. However, this is not true in my case! When I first signed up and had no photos I was able to find a few people to speak with me and even got a few messages from normal people my own age. But ever since I added photos to my profile I hardly ever get any messages from other people and other people refuse to speak with me. Thus, I am the exception to this general rule of online dating.

Sunday, September 12, 2010

Center of General Linear Group

Definition: The general linear group $$\text{GL}_n(\mathbb{R})$$ is the group of all invertible $$n\times n$$ matrices under matrix multiplication.

Definition: For a group G we define the "center" Z(G) to be the subgroup $$\text{Z}(G)=\{z\in G| zg = gz\}$$.

It is a rather well-known result that the center of $$\text{GL}_n(\mathbb{R})$$ are the matrices $$kI$$ where I is the identity matrix and k is some non-zero real number. We will derive this result.

For $$N\times N$$ matrices define $$E_{nm}$$ to be the matrix with 0's everywhere except at the n-th row and m-th coloum where it has 1 as its entry. The problem however is that $$E_{nm}$$ are not invertible unless n=m, so we will rather consider the matrix $$I+E_{nm}$$ for $$n\not = m$$.

If A is some matrix in the general linear group then it commutes with all $$I+E_{nm}$$. Let $$a_{ij}$$ be the ij-entry of A and $$e_{ij}$$ be the ij-entry of $$I+E_{nm}$$. We have that $$A(I+E_{nm}) = (I+E_{nm})A$$. Therefore, $$\Sigma_k a_{ik}e_{kj} = \Sigma_k e_{ik}a_{kj}$$.

If $$j\not = m$$ then $$e_{kj}=0$$ except when k=j, so $$\Sigma_k a_{ik}e_{kj} = a_{ij}$$.

If $$i\not = n$$ then $$e_{ik}=0$$ except when k=i, so $$\Sigma_k e_{ik}a_{kj} = a_{ij}$$ .

If $$j=m$$ then $$e_{kj}=0$$ except when k=j and k=n, so $$\Sigma_k a_{ik}e_{kj} = a_{ij}+a_{in}$$.

If $$i=n$$ then $$e_{ik}=0$$ except when k=i and k=m, so $$\Sigma_k e_{ik}a_{kj} = a_{ij}+a_{mj}$$.

These are our four possible cases. In the second two cases, that is when j=m and i=n we have $$a_{nm}+a_{nn}=a_{nm}+a_{mm}$$ we get that $$a_{nn} = a_{mm}$$. But $$n,m$$ range over $$\{1,2,...,N\}$$ so that means all the diagnol terms are all equal to one another. Thus, A is a matrix with equal diagnol terms.

In the second and third case, that is when i!=n and j=m we get $$a_{im}=a_{im}+a_{in}$$ so we have that $$a_{in}=0$$ for all i!=n. This means all terms in the n-th coloumn are zero except possibly on the diagnol. But $$n\in \{1,2,...N\}$$ so if we vary n over this set we get that all coloumns must be zero except possibly at the diagnol terms.

Thus, A must be a matrix with all terms zero off the diagnol, but all diagnol terms equal. If k is the common value of all these diagnol terms it follows that A=kI where I is the $$N\times N$$ identity matrix. But we require for A to be invertible, therefore k is a non-zero real number.

We have shown it is necessary for any matrix in the center of the general linear group to be of the form kI where k!=0. Obviously, it is sufficient also since the identity matrix communutes with all matrices of that size.

We have finally proved that $$\text{Z}[\text{GL}_n(\mathbb{R})] = \{ kI| k \in \mathbb{R}^{\times} \}$$.

Saturday, September 11, 2010

We live in a world that puts a lot of emphasis on our appearance. We see it all the time in the movies and on TV. We see hundreds of weight loss products. We see the nicest looking people on TV. Many women go through plastic surgeries to improve how they look like just to fit into society. Being pretty is part of our society. And so people who are ugly feel negative about themselves because they are excluded from others.

Here is the thing about ugliness. If you are ugly there is nothing you can do about it. Beauty products are only to enhance your appearance, but if your appearance is repulsive then there is nothing you can do about it. All you do with beauty products is just waste your time and money. And do not go for plastic surgery the thing looks ridiculous. It is obvious to tell which women in their 50's get plastic surgery by seeing how artificial their faces look like. No clothes that you can wear can also make you pretty unless you hide your face in some bag. This is the way things about. And there is nothing you can do about it to change your appearance.

But there is something you can do to change your mentality and make yourself happy. The first thing you need to do is recognize the impossibility of making yourself pretty, or even normal looking. Just tell yourself, "I am an ugly piece of repulsive meat" in the mirror one day and accept yourself for what you are. Self-esteem programs are all about self-deception. They tell you to lie to yourself. Self-esteem programs tell you, "I am a beautiful person" when you look into the mirror. But all that is, is self-deception. And you know it. When self-esteem programs tell you, "I am beautiful on the inside", deep down inside you really know what that means, "I am a disgusting piece of repulsive meat that no one wants to sleep with". You cannot be happy with self-deception because you will truly know what you are. So the first step of overcoming your depression over your appearance is to tell yourself, "I am a disgusting piece of meat" and accept yourself for what you are.

See the really nice thing about accepted ugliness is that you can dress how you want to dress. Something you never had before. If you like wearing flip-flops with socks you get to do that without worrying of what other people may think of your appearance. Or if you like a shirt that does not fit in with the current fashion style but you like it then wear it. Ignore all the rules and live how you want to live. Ugly people have this kind of freedom, not pretty people who worry to fit in with the established fashion system.

Here is a great video about appearance: Here.

The most recent post by the Rabbi was about Steven Hawking's new statement that the universe was not created by God. The full post can be found here. This is going to be responding to some of the points the Rabbi says.

First, of all it is necessary to establish something important. This is sometimes forgotten about in discussions like these. Skepticism is a method, it is not a belief system. Atheism is the default position from skepticism. If one is a skeptic, as everyone should be, it is only natural for the person to be an atheist. Therefore, the atheist does not need to demonstrate his position. The atheist has the default position based on lack of evidence or lack of argument. So Hawking cannot be challenged on the ground that he never demonstrates that God does not exist because he does not need to do such a demonstration.

One way in which science supports belief in God is that the laws of science themselves require a lawmaker.

This is the failed cosmological argument. The cosmological argument says that the universe is here therefore it had to come from somewhere because everything can from somewhere. It then concludes that this "somewhere" is God. But the conclusion of this argument contradicts its premise. The premise was that everything had to come from somewhere. So where did this mysterious God come from? It never answers its own self-contradiction. The theist simply asserts that God did not come from somewhere, God always existed. But why then can we not simply assume that Nature always existed? Perhaps Nature, its laws, and how they describe the world, always existed? It were these laws that formed the universe. The theist says that "God", the mysterious first cause, always existed. But they never say what God is. God is some mysterious entity never specified. The only property this "God" has is that it was the always existing main cause of everything. But if so then why not simply take the position that Nature has these properties. That way this "God" is simply Nature. And so there is nothing special to "God". Of course, equating God with Nature was what Spinoza did, if it makes you feel better you can do it, but for practical purposes this is atheism. Thus, the cosmological argument is a failed one. It fails because it leads to a self-contradiction and it fails because it never specifies what "God" means.

But the other problem with the cosmological argument, as every argument for God, is that it is only an argument for deism, not theism. I got no problem with deism. It is an understandable position for someone to take. If you simply wrote an article on deism then I would not have an issue with it. My problem is that people substitute theism for deism, which are far far apart. Deism simply asserts that the universe had an Architect for it, some external entity outside the universe that was intelligent in what it made. That is it! It does not say that this "God" (referring to this Architect) cares about people. It does not say that God has a relationship with other people. It does not say that God listens to other people. It does not say that God intervenes with the world. It does not say that God performs miracles. It does not say that God communicates with prophets. It does not say that there is a life after death. It does not say that the universe was created by God for us. For all purposes deism is basically atheism in every way. My problem with the cosmological arguments and teleological arguments is that people argue for deism, which is fine, but then they magically substitute the God of the Bible into the mysterious undefined "God". Which is not fine. There is a long path to go by to explain exactly how this "God" satisfies the conditions for the wicked God of the Bible. Believing in God and being religious are very different. You can believe in God but be extremely anti-religious, like Thomas Paine or Thomas Jefferson. So stop using this argument as if it leads to theism.

Einstein, no believer in a conscious God, nevertheless often expressed amazement at the comprehensibility of the universe.

And I too am very much amazed with the harmony and mathematical structure of the universe. I do believe there is a rational order to Nature. However, I do not assert this to be "God". For me it is just the way things are. They necessarily must be this way and no other, they necessarily must follow mathematical laws and therefore be ordered. Why must the order and harmony of the universe imply a God? Perhaps this is the way things are? Why must we invent hypothesis that are not necessary?

Even if Hawking is correct that the laws of gravity and quantum theory allow universes to appear spontaneously from nothing, that they somehow breathe fire into themselves, he has not explained how these laws themselves came to be legislated.

The second way in which science is employed to give rational support for faith is that were the laws of nature to be different in the slightest way, our universe would not be possible. Some famous atheists such as Douglas Adams dismissed this argument, claiming that it is like a puddle marveling that its hole in the ground is exactly the right shape for it. But this entirely misses the fact that our universe is not any old universe, but rather an amazing universe that allows for the formation of such complex phenomena as matter, planetary systems, life, and intelligence.

Again an argument for deism not theism. But if you want a refutation for this argument just consider Christopher Hitchens' response to this argument. We are the only inhabited planet with intelligent life, actually just life, as far as we know. We are one of the few successful solar systems. Other solar systems have failed to developed. Other stars failed to become stars. Other galaxies fell apart. We are unique in that it went well for us, so far. But what about the millions or other parts of the universe which failed? What about those? It is standard human nature to look at what is seen and ignore what is unseen. We can easily focus on ourselves but what about all the unseen failures that happened in the universe? Why are we not focusing on those? It is only fair to compare failure to success and failure far exceeds success in our universe. This only shows that there is no plan for the universe. It may be ordered and rational, but it does not care what the final outcome is. We can be here one day, and dead the next, just like with the dinosaurs. It may be benevolent at one instance and malevolent the next. There is no grand plan for anything, and we are not here for any specific purpose.

In response to this, it is first important to note that the multiverse model is entirely speculative, with no actual evidence whatsoever.

But God is not speculative? There is actual evidence for God? What a double standard by Slifkin. When scientists propose an explanation which they cannot yet test they will acknowledge their inability to test it but present an argument to why they think it might be true. But the religious people will refute all their work by saying "you got no evidence for it". Though they will never ever do that to their precious God.

Friday, September 10, 2010

God: The Unnecessary Hypothesis

Pierre Laplace was a great mathematician and a scientist. He described the equations for the motion of celestial heavens by extending Newton's work. When he presented his work to Napoleon, Napoleon was very impressed with Laplace's work. But Napoleon asked Laplace, "where is God in all of this?". Laplace replied back to him, "I had no need for that hypothesis".

This is the position I have regarding God. It is an unnecessary hypothesis. We do not need to assume God to make sense of the world. Why invent a hypothesis which does not do anything to help us. In fact, with God the world makes less sense. The moment we introduce God into our assumption the world becomes more complicated. There are lots of unanswerable questions to ask. Where did God come from? Why did God decide to create the universe? Why does God cause evil in the world? Why would God choose a few select group of people as being his people? What is God exactly? And so forth. We have two options. Either do not assume a God, make some sense of the world, and what we do not know we simply assert humbly that we do not know. Or we can assume a God and make less sense of the world that way. It is unreasonable to invent a hypothesis which complicates manners.

Do you believe that there is a giant talking penis on planet Pluto? You do not even think about it! That belief is so unnecessary for you to make sense of the world that you do not even consider it. You do not reject it. You simply do not even think of it as a respectable view to have to understand the world. That is exactly what God is to me. Something entirely irrelevant and unnecessary to make sense of the world.

Wednesday, September 8, 2010

Two Year Anniversary in Heresy

Rosh Hashanah marks my second year of rejecting Judaism. So this is a special day for me. It is also interesting that I gave up Judaism during Rosh Hashanah, a time of the year where people are supposed to feel closer to Judaism. I still remember what I did during Rosh Hashanah. I was reading Thomas Paine's "Age of Reason" still when I was a believer. But I was already a really bad believer, I needed further reassurance from someone, I decided to read Paine. In the middle of reading Paine I finally concluded, after long time spend on skepticism, many many months, that the fundamentals to Judaism are vile and repulsive. So I took a Chumash in my hands and expressed my heresy, "this book is wrong, what it teaches is wrong, it is falsehood, and it is also evil". Something to this effect. That was it. I finally gave up Judaism. I was a little scared to do that, but I did, two years ago.

By the time Yom Kippur came about I was already a non-believer. But I went to shul on Yom Kipper (actually I was at shul on this Rosh Hashanah too, but I did not daven, of course). I still davened on Yom Kippur though it was really hard for me. Each time I read a verse I kepted on thinking why I disagree with it and why it is non-sense. I also realized the entire scene in shul is kinda stupid. People dressed funny and praying to imaginary beings, so it was hard for me to sit through all of that. But I was not able to stay for the whole service. The bowing down part was too much for me. I had to leave, I could not possibly bow down. Jewish people say that no one can ever bow down to a false god, that is idolatry, and I agree, since there are no gods it means we can never bow down to any. I was not able to be at shul for that. I got up and left.

Jewish people have a really tough time understanding that it is hard for secular Jews to "just say the words and sit in shul". No, it is not so simple. It is hard to say those words and hard to be at shul if you do not believe in those words. It is understandable that a non-religious Jew who is interested in being a religious Jew can "just say the words", because they do not bother him. But if you are a secular Jew those words really bother you, and it is hard to say them.

Tuesday, September 7, 2010

Burnside Combinatorics

Back here we learned about the Burnside Counting Formula. Now we will see how this formula is applied to the problem of combinatorics.

Problem 1: How many different ways are there to seat n people around a round table?

Solution: Number the seats of this table as 1,2,...,n. Let X be the set of all possible arrangements of this table. Clearly, |X|=n! , but we are assuming that two seating arrangements are the same if we can turn on arrangement into another round the table. This this number is too much, we are over counting. Let G be the group of all rotations of the table labeled 1,2,...,n. If we let r be the counterclockwise rotation one position over then we clearly see that r has order n and that r generated G. Therefore, G is cyclic of order n. We will now define the action of G on X to be a rotation applied to a seating arrangement. Consider two arrangements of the table. They are considered the same iff we can rotate one into another. That is to say two seating arrangements are the same if they are related to one another under some rotation. If $$x_1,x_2\in X$$ are two arrangements we say that they are equal iff $$x_2=gx_1$$ for some g in G. Thus, two arrangements are equal if and only if they lie in the same orbit. The desired number of seating arrangements is therefore equal to the number of orbits. This is given by $$\frac{1}{|G|}\sum_{g\in G}|X_g|$$ by Burnside's formula. Note that if g is not trivial then $$X_g$$ is empty, but $$|X_e| = n!$$. Therfore, the answer is $$\tfrac{n!}{n} = (n-1)!$$.

Problem 2 How many different ways are there to color a cube with different colors on every face?

Solution: Label the sides of some cube as 1,2,3,4,5,6. Let X be the number of ways to number a cube in a static position, clearly |X|=6!=720. Let G be the "rotation symmetry group" on this cube. Put simply G consists of all rotation operators on the cube. And G will act on X in the natural way, the rotations applied to our numbered cube. As before two coloring of a cube a considered the same if we can rotate on into another. And again notice that $$|X_g|=0$$ if g is not the identity and $$|X_e|=720$$. So all what remains is to count the size of |G|. We do not actually need to know the group structure of G just its order. To see what the order let us say that top face is labeled 1. There are six ways to rotate that number 1 into six other positions. Once we put 1 into a certain position there are then four ways to rotate around this axis keeping 1 fixed. Therefore, rotational symmetry group is of order 24. (It turns out this group is the symmetry group on four elements but this is irrelevant). This means the number of ways is given by 720/24=30.

Problem 3: Let n>2 be odd and consider a $$n\times n$$ grid of squares. The grid is white. How many different ways are there to color this grid with two black squares?

Solution: Let X be the numbered grid with all possible colorings. There are $${{n^2}\choose 2}$$ such colorings. Let G be the group of all rotations on this grid, clearly there are just 4 rotations on this grid, so |G|=4. If $$g$$ is an order three rotation then $$|X_g|=0$$. Obviously $$|X_e|=|X|$$. The interesting case is when g is an order two rotation, i.e. a rotation of 180 degrees. If two points are "rotationally opposite" then a 180 degree rotation will preserve the grid. Note if one colored grid is in the center then no rotationally opposite point exists. But if a point is chosen outside the center there is one and only one pair to it. There are $$n^2-1$$ such choices, but because we double counted we need to take that into account. Therefore, there we shown that $$|X_g|=\tfrac{1}{2}(n^2-1)$$ if g is a rotation of order two. Thus, the number of such colorings given by $$\tfrac{1}{4}{{n^2}\choose 2}+\tfrac{1}{8}(n^2-1)$$.

Exercise: Consider problem #3 again. Suppose that we have a flippable board. That is, we can flip the board around also. How many such coloring are possible in such a case?

Fitting In

I never had it part of my personality to "fit in" with people around me. I remember that when I was a little kid I would do things on purpose to show that I am distinct from other people. And I still retain that, I like being different. I never cared for fitting in and looking normal around other people.

I do not own a cell phone. When the cell phone first started to come out I said to myself, "the cell phone is going to be a popular thing in a few years, I am not going to buy one as a statement that I want nothing to do with people". I never owned a cell phone and do not plan to get one. I simply do not need it, but moreover I needed to make a statement. It makes me feel good when people ask me for my cell phone number and I say "I do not have one". In a same way I do not own iPods and MP3 players. It is true that I do not need them and so I do not buy them, but it is also a statement of dissatisfaction with people.

I dress strangely for people my age. I dress very conservatively and I wear suspenders. But that is a typical mathematician stereotype - that they wear suspenders. And I could not care less. I dress the way I want to dress. I dress the way I dress because I like to. Everyone else can go kill themselves, I do not care. I do not care what other people think of how I dress, not in the slightest.

I also like to take positions that no one else takes. When I was a little kid in school I used to disagree with my whole class for the sake of disagreement. I sometimes think that if the world was atheist I would be a theist just so that I can enjoy myself in being different (though that was more a joke, I will not simply pick a position to be different, I must be able to defend it and defeat my opponents position, I just have utility in uniqueness). When I was in college I told a girl that I am against laws that prevent businesses from discriminating based on race. She never asked me. I just said it when we were discussing racism together. I wanted to tell her something that makes people uncomfortable. It just makes me feel good. And saying what I said is heresy in a place like college, so I had to say it, in order to scare the people around me.

Evolution made people be group animals. People need to be like their group to survive. It is understandable why people form groups and follow what their group does. So when people in college get themselves a FaceBook or a MySpace, or wear designer jeans, the humans, as a group, follow the same trend. But I never had this part of my personality. I never felt a need to have people share something together with me. In fact, I was the opposite, I like having something distinctly my own, not shared with anyone else.

But there is a price to pay for individuality. That price is loneliness. I am a very lonely person. I hardly ever see anyone. I like people, people are interesting and awesome. They just probably do not like me. Not because I am a bad person, not because it is hard to get alond with me, but I guess it is just that they cannot relate to me. I am so different from them and so they stay away from me. They do not stay away from me because they despise me but really because they cannot connect with what I am.

When high school was over I was really sad. Because I knew that I would not see my friends again. I had people to speak to and do stuff with in high school because I saw them on almost a daily basis for an entire day. But when high school was over I knew that I will soon start living a life of loneliness. And indeed this is the case. Four years after high school finished I remained the same with my relationships with other people. Very lonely. I see people at college but it is not the same as high school. I believe this loneliness will only get worse. I do not see myself being a social person and I do not see myself being in any kind of relationship. But that does not depress me. I am not depressed at all. I am a happy person. I am just lonely. For me people are like chocolate. If you have no chocolate at home you are not going to be depressed, but it is nice to have some chocolate around. I do not need people, my life is not based on being social, it is just nice to be social. I sometimes fantasy about doing things with other people but that is just because I like them.

The internet is my savior here. The internet made it possible for me to communicate with other people and relieve my loneliness. There are people online that speak with me. That provides me with a way to be social. Of course not real life social, but cyber-social. I find it much easier to find people online because the internet is filled with a lot of interesting people.

But maybe I am wrong. Maybe I am confusing correlation with causation. I think my lack of interest in fitting in is what caused me to be lonely. But maybe that is just unrelated to that and I am missing something a lot more important. But I cannot see it. This is the only explanation I can think of. The explanation that I am a terrible person and so others do not want to be around me does not agree with my actual personality, so the only remaining explanation I can think of is my lack of interest in fitting in, and sometimes outright violating social norms.

If the price of individuality and attempting to pursue the truth is loneliness then so be it, it is worth it.

There is a video I seen some time ago and I love it very much. The ending of this video is superb but very depressing. Somebody described exactly how I was feeling for a long time. Here

Monday, September 6, 2010

Beware of Libertarians

Many years ago if one called himself a libertarian he was viewed as a sort of child molester. People looked at him as some rebellious teenager who wants to do whatever he wants. He wants to do drugs, shoot some guns, and disregard the law at any chance he gets. He was the rebel. And one who opposed to anything the government did. The libertarian was so heavily disliked by both the people on the left and right because he was seen as someone who wants to destroy society, suspend all laws, and let everything be whatever it wants to be.

Today the perception of the libertarian changed. Now it is okay among both the people on the left and right to call themselves libertarians. Not very frequently but you do notice it. I have spoken and heard of several "civil libertarians" or "left libertarians" or whatever they call themselves. But there is nothing libertarian about them. When it comes to the economy they still maintain the same rigid control and even when it comes to people's personal life they still are not very libertarian. They might agree that people have the right to take marijuana but they do not feel the same with cocaine or heroin. They often support the disarmament of the citizens, if not guns then assault rifles and machine guns. Support seat-belt laws and favor high taxation. These people who call themselves "civil libertarians" or "left libertarians" are either ignorant of what they say or dishonest, I believe they are simply ignorant. Even their position with gay marriage is non-libertarian, the libertarian position on gay marriage is the abolition of the interference with the state with marriage. Like Bill Maher. He calls himself a libertarian but what exactly is he a libertarian about? Smoking marijuana? No, not even that issue, we wants to tax it.

These "left libertarians" are nothing but liberals. The positions they take are identical to the left. They are just probably a little confused. Maybe bi-confused also, but they are confused about these words so they call themselves libertarians with some other noun attached to it. These are not the kind of people you need to beware of, they do not intentionally try to be deceptive, they never hide their true intentions, they are just bi-confused. So it is forgivable.

The kind of people to beware are Republicans who call themselves "libertarians". In most cases today when someone calls himself a "libertarian" it is a hardcore Republican. They usually favor cutting taxes by a lot, but not because of some philosophical objection to paying taxes (since they do not want to abolish all taxes) but because they do not like paying more taxes. They generally want to continue the same Republican economics. They might actually support gay marriage on a few occasions, and maybe, in certain cases support legalizing drugs. There is a joke about libertarians that libertarians are just gay Republicans who like to do drugs. And this joke has truth to it. Most libertarians that I have seen are very similar to Republicans, they just differ from them on a few points. However, when it comes to expanding the US empire or preventing the illegals from coming into this country they have no problem with that. And no problem with capital punishment. These people like to be fiscal conservatives whenever it is convenient for them. It is just like the Confederacy during the Civil War. The Confederate army was not some champion of states rights. They were pro-state rights whenever it was convenient for them. They wanted slavery so they supported states rights as a covenience. But they had no objection to the federal fugitive slave law being passed. These libertarians always pretend they are some strict followers of the Constitution. They use the Constitution when it is convenient. When they object to any form of universal healthcare they say it is unconstitutional. But when they want to prevent a mosque being build by ignoring the first amendment is that called being constitutional?

These libertarians are not inspired by fiscal conservatism, or laissez-faire economics, or the philosophy or liberty. They have their own stances that they call under "libertarian". They do not really support fiscal conservatism, when it becomes convenient for them to use the government for their own ends they would happily support it. And they most certainly do not defend liberty. They preach liberty and the Constitution when it is convenient. But the moment they find something they do not agree with they will have no problem with using the federal government to take away the rights of those they disagree with.

These people are to be dealt with caution. They feed on the people truly in favor of liberty because they both identify themselves with a common tag. These libertarians use conservatism and liberty to promote their own interests. Beware of these people. Especially today when calling yourself a libertarian is semi-acceptable. As time will evolve you will start seeing more and more of these people.

There are of course genuine libertarian out there. But they are very rare. So when one calls himself a "libertarian" deal with him with a lot of skepticism because there is a good chance that he is just a hardcore Republican.

Saturday, September 4, 2010

Why Books Suck

Ever since I was a little kid I was always anti-book. I was told by adults and people around me, "when you grow up you would appreciate them". I despised books. Now I am older but I still retain my anti-book attitude, and it is basically the same attitude that I had when I was younger.

Let me explain what I mean by books. Certainly I am not against all books. I have read books when I was younger. But the books I read were different. I used to read Calculus books, math books, science books when I was still pre-high school. I remember I was reading Linus Pauling's "General Chemistry". I believe I was an 8th grader at that point. (It is a good book, if I was able to mostly understand it then if you want to learn some chemistry this is a book to learn it from). I used to ask my science teacher to pick out books for me to read on basic physics since I enjoyed that kind of stuff. So I was really into science and mathematics. I was very diverse in the science I read when I was younger, I believed I could know it all. Eventually mathematics won me over and I started to concentrate on it and read books on mathematics. Most of my math and science knowledge that have is because of self-study, and it is books and the internet that gets the praise. So clearly it would be hypocritical of me to be against books if I learned so much from them.

But there is a subset of books that I am against. The books I actually learned from I will refer to as "textbooks". Even though some books were not really textbooks I will nonetheless call textbooks. Textbooks are awesome. You can learn so much from them. You will get so much smarter if you buy yourself textbooks and learn from them. When I say "books" I mean literature and novels.

Ever since I was a kid I was unable to understand what is so amazing about literature and to this day I cannot understand. Can you explain to me how reading about Harry Potter actually makes you a more intelligent person? The only thing I see about books is that they are used as a form of entertainment. And that is okay. I have nothing against forms of entertainment. But if they are just entertainment then they are like movies. No one ever claims that movies make you smart. Books were the old age movies before there were any movies. People read them to entertain themselves. And again, this is fine. But this is only fine as long as people do not take it too far and claim that books posses the highest truth of the universe. With every ounce of my reason I cannot see how books make people smarter. People say it teaches you history. Well if you want history then buy yourself a history textbook and learn thousands amount of history than from some fiction book of literature. I know plenty of people who read all the time but there is nothing smart about those people. They just read and know their literature, that is it. So tell me exactly how do books makes you smart?

I guess that deep wisdom of books is one of those truisms that we have to accept. Just like family as I wrote earlier on this blog. Ever since we were little kids we were taught that "family is you blood, they are most important" and so when we grow up we continue to hold on to it. There are many other truisms. The police officer is our friend, how many times you heard that one as a kid? Or that the army fights for our freedom, another truism. Books, it seems to me, is just another kind of truism, parents kept on repeatedly telling us how they make you smart so we immediately assume that people who read a lot are smart.

Thursday, September 2, 2010

What is Socialism?

It is important to understand what socialism is. There are a lot of people who proudly call themselves socialists. Social democracy is very popular today especially with the younger generation. On the other side there are those who accuse people with whom they disagree with as socialists. Both of these sides are usually wrong in understanding what socialism is.

I will first begin with the standard description of what socialism is. Socialism is a structure to society where the people's need are provided by the government, the government collects this money from everyone and then gives out the necessities to the people to those who need it. But this description is wrong. What this is, is not socialism, but a welfare state. The welfare state is part of socialism, but it is not the defining characteristic of socialism. This is where much of the confusion to what socialism is comes from.

There are others who describe socialism as the system of redistribution of wealth. The rich lose a lot of their money and that money is handed over to the poor. This is done to promote equality. But this other common description of socialism is also wrong. The redistribution of wealth, just like the welfare state, is a component of socialism, but not the defining characteristic of socialism.

In fact, it is possible to have a socialistic society without a welfare state and without the redistribution of wealth, I do not think such societies have actually existed but it is possible. Socialism is, to put it very simply, central economic planning. The central planner is the state. When Karl Marx was objecting to capitalism his primary objection was the private means of capital, the capitalists, he said, would exploit the workers because they want more wealth. The problem is, according to Marx, the private means of capital. What we need is a system where capital is owned by the public (of course the "public" here is really the state). The defining characheristic of socialism is the public-owned means of production. The state is the main feature of the economy. The state decides, not the market, what needs to be produced, how much will be produced, what the prices need to be, to whom it will go. The private businesses do not have that kind of freedom to make those kinds of choices. Only the state can decide these things. That is central economic planning. The economy is not structured by the bottom-up, by individuals struggling for profit, but from the top-down, by a group of planners who make economic desicisons for the people.

The welfare state is a component of socialism. Since the government controls the economy it therefore is the one who provides for the citizens. And so there is a welfare state. Where the money of the people come together and are spend on those people who need it rather than businesses providing to the people for profits. The redistribution of wealth is also a component of socialism, but for the above reasons it does not have to be. If there is a welfare system, and most likely there is under a socialistic government, then the rich will most likely be taxed more than the poor. The really poor will receive more from the welfare system then they paid in while the rich will receive less. In a way this can be seen as a form of redistribution of wealth. But again, this is important, socialism is not about having a welfare system and not about having redistribution of wealth, what it is, very simple, is central economic planning.

Communism and socialism really are the same, just varying degrees of central planning. Under communism the central planning is most severe. Sometimes the government even replaces businesses and acts itself as a monopoly that can serve the needs of the people. This difference can be seen in Nazi Germany and Soviet Russia. Soviet Russia had a lot more central planning than did Nazi Germany. But Nazi Germany also had strong central planning, the Nazis were not right-wingers as a lot of people wrongly believe. The Soviets are better described as communists because they had very severe economic control. The Nazis had a bit more economic freedom but they still favored heavy control of the economy, and so they are better described as socialists. But both communism and socialism stems from the same idea - a central planner over the economy.

The president is not a socialist as a lot of people accuse him of being. Because he is not for central planning of the economy. He happens to be an interventionist, but Republicans are interventionists also, just not as much as Democrats. Interventionism is not socialism. Interventionism is imposing certain restrictions and controls over the markets but the markets function by themselves. Socialism is when instead of interventionism there is planning taking place in the economy. Since there is no central planning taking place in the United States and since the president does not support central planning the United States and the president are not socialist.

However, calling a universal healthcare system as socialized medicine may sometimes be accurate. The nation might not be socialist, but a part of the nation might be. It all depends on how the universal healthcare system functions. If the government alone provides for the citizens their healthcare, or tells private entities how they can operate then such a system would be a socialized system. If instead of insurance companies the government has control over insurance, or tells insurance companies how they can operate, and it decides by planners who gets what, then such a system is a socialized system of healthcare or health insurance. But the country itself is not necessarily a socialistic country because everything else might be uncontrolled by planners. In general though I do not think that there are so many genuine socialized systems of healthcare. Instead there is a welfare system of healthcare by the government, but the economy of healthcare is left alone by planners. Thus, I am not a big fan of calling universal healthcare, "socialized medicine", because it is not central economic planning, just welfarism and interventionism.

People who call Sweden a socialistic country are wrong. Sweden is a welfare system, which is a component of socialism, but that alone does not make Sweden a socialistic country. Nor is that a true social democracy because the economy is not in the hands of planners. The economic index of freedom puts Sweden rather high on the list. It does have high taxes and welfare programs which lowers its economic freedom index but it nonetheless has the economy decided upon by the markets not by planners. Sweden is not an example of how socialism can work because their economy is not socialistic. If you want to make the case that Sweden is socialistic then you need accept that their economy is controlled by central planners, which it is not. In fact, the history of Sweden only points to the failure of socialism. In their earlier history they imposed heavier economic controls. Their standard of living declined. Sweden had to deregulate their markets. This does not point to the success of socialism, on the contrary it points to the failure of socialism.

I hope this clears up some confusion of what socialism means.

Religion Kills Philosophy

It has been observed many times that religion kills science. It slows the progress of science. It refuses to acknowledge the theories of science. It is innately unscientific. Science is a knowledge that we gain from experimenting with the world. Religion is a bunch of superstitious non-sense whose goal is to provide made up answers and impose authoritarian control over the people. Thus, religion is innately unscientific. Science proceeds by working with what we have towards a particular theory, the last-established answer. Religion already provides an answer and then uses apologetics to "prove" why such a first-established answer is true. Religion is afraid of science. Religion has used its power to silence science and to persecute the scientists who spoken it. Religious followers both fundamentalist and moderate are anti-science to some degree. They may respect science and be interested in it. But they will always find a way to dance around religion to make science compatible with religion, if they cannot do so they outright reject science. This is why religion harms the progress of science.

But it has been observed much less that religion also kills philosophy. It is innately unphilosophical. Philosophy is an attempt to arrive at truth from reason (and sometimes inspiration from science) by applying it to various first-principles about the world. Philosophy does not begin with a first-established answer and use apologetics to "prove" it. Philosophy uses reason and sometimes inspiration from science to come towards an answer, the last-established answer. Religion is afraid of philosophy. Indeed, the harshest attacks on religion came from philosophers themselves, not from scientists. Scientists of the Enlightenment and pre-Enlightenment were for the most part religious, just scientific and not afraid to contradict the Church on science. Philosophers, however, of the Enlightenment and pre-Enlightenment were for the most part anti-religious, either deists, or agnostics, and even atheists back in those days. It is philosophy that killed God, God is dead, God stays dead, and we have killed him. Religion to defend itself from philosophy has used its power to silence, kill and oppress the philosophers who dared challenge it.

I believe that the anti-philosophical attitude is much more stronger than the anti-scientific attitude. Because philosophy is a lot more poisonous towards religion than science is in its whole history. This is why religious people are not capable of deep philosophical though. The highest degree of philosophy that religious people are capable of is theology. But theology is not philosophy any more than alchemy is not science. Theology might have inspired philosophy in some ways but it is not philosophy, just like alchemy might have inspired chemistry in some ways but it is not science.

All the philosophical ideas that I have now I never had when I was religious. My religion killed any room for my philosophical thoughts to develop in my soul. People speak of the tragedy of religion as being innately anti-scientific, and they are right. But there is another tragedy that many people forget or do not realize, and that is that religion is innately anti-philosophy.

Wednesday, September 1, 2010

I Guess I am Different

When I read other Jewish blogs I see that sometimes, not frequently, I am on the list of recent posts they have read. Of course, I appreciate that because it makes more people come here. However, I noticed that I am very different from other blogs. Other blogs tend to talk a lot about Judaism and this one does not talk so much about Judaism and embracing a rational secular life over religion. I tried to be like other blogs but I cannot do it. If you read what I wrote in my first one and a half months here I tried to be like other blogs but it is too hard for me. It is hard for me to discuss religion because I find the whole issue too trivial. No one ever writes about why Zeus and Greek mythology is a bunch of non-sense. No one makes parodies about the Greek arguments in favor of mythology. We all understand that mythology is too simple of a concept to even by discussed. In a similar manner I do not have much of an interest to discuss religion and atheism because it is just way too easy and too trivial, there is no challenge in arguing against religion.

I do not mean to condemn other blogs. I realize that what they do is a lot more important than what I do. We need people to engage in a discussion with Jewish believers. If we want a better world where people think for themselves and do not reject science then such blogs are important. They constantly challenge Jewish believers. We need blogs that bring out important issues. Like homosexuality. So we need Jewish people who write topics about homosexuality and its relevance in the Jewish world. We need people who discuss current events in Judaism on their blogs and parody the silliness of the religious. All these people are important to fight the tyranny of religion.

But it is not for me. I am not that kind of person. I do not follow the news. I never read the newspaper. I am not a social person so I do not know what is going on in my community. I find religion a trivial issue so I do not even want to discuss it seriously because such a discussion makes me feel as if religion gets respect. I cannot discuss homosexuality because it is another really trivial and simple issue for me. I like to discuss things that are new. Things that are challenging. I hate repeating the same arguments of other people over and over again to argue against the religion people. So that is why I tend to stay away from religion on this blog. However, I do recognize the importance, much more important over what I write, of Jewish commentators for the Jewish world of religion. So I will continue to stay the way that I stay and focus on philosophy instead.

Burnside's Counting Formula

Let X be a set and G a group. We define "group action" to be a mapping $$G\times X \to X$$ which satisfies two conditions: (i)ex=x where e is the identity element, (ii)(gg')x=g(g'x).

We define the "stabilizer of x" to be the subgroup $$G_x=\{g\in G: gx=x \}$$. We define the "invariant set under g" to be the subset $$X_g=\{x\in X: gx = x \}$$.

We can also define an equivalence relation on X. We say that x~y if and only if y=gx for some g. It is clear that ~ is an equivalence relation. Thus, we can partition X into disjoint subsets so that any two elements in a subset are related under ~. The equivalence class of x, usually denoated by $$[x] = \{ y\in X :y = gx \}$$ will be now denoated by Gx. This is a good notation because we obtain Gx by forming all multiples of x with g where g is in G. We will define the "orbit of x" to be this equivalence class Gx.

There is a standard result in group theory which states that there is a one-to-one correspondence between the elements of Gx and the cosets of $$(G:G_x)$$. The proof of this important result is very simple. Let $$gG_x$$ be a coset of $$G_x$$ in G. We will define a mapping where its image is $$gx$$ (an element of Gx). Of course, we need to prove this mapping is well-defined. Say that $$g_1G_x = g_2G_x$$ then $$g_1^{-1}g_2 \in G_x\implies g^{-1}_1g_2x = x$$ and so we see immediately that $$g_1x=g_2x$$. In the similar manner one can easily show this mapping is one-to-one and obviously onto. Thus, we have established a bijection between these two sets. The important case for us if when the group and the set are both finite.

Theorem: If G is a finite group acting on a finite set X then $$G = (G:G_x)$$.

The proof of this is immediate. We have just rephrased the condition of being equipotent as sets in terms of their cardinalities. This theorem is an important theorem in group theory which is known as the "orbit-stabalizer theorem". It relates the relationship between the orbits and the stabalizers.

What we are after is a combinatorical result known as "Burnside's Counting Formula". Which is stated in the next theorem.

Theorem: If G is a finite group acting on a finite set then the number of orbits of X is given by $$\frac{1}{G}\sum_{g\in G} X_g$$.

Proof: Let m be the number of orbits. Consider the set of solutions to the equation gx=x. Let n be the number of solutions. If we fix g then there are $$X_g$$ solutions. This means $$n=\sum_{g\in G}X_g$$. However, if we fix x then there are $$G_x$$ solutions. This means $$n=\sum_{x\in X}G_x$$. Equating together we have that $$\sum_{g\in G}X_g=\sum_{x\in X}G_x$$. But by the orbit-stabilizer theorem we know that $$G_x=G/Gx$$. Thus, we get $$\frac{1}{G}\sum_{g\in G}X_g=\sum_{x\in X}\frac{1}{Gx}$$. Write X as a disjoint union $$S_1\cup S_2\cup ... \cup S_m$$ where every $$S_j$$ is an orbit class (which results from the partion of the equivalence relation). Observe that $$\sum_{x\in S_j} \frac{1}{Gx} = 1$$. The reason for this is very simple. If $$x,y\in S_j$$ then clearly $$Gx=Gy$$ so that $$Gx$$ is constant on its orbit class $$S_j$$. While at the same time $$Gx = S_j$$ for all $$x\in S_j$$. Therefore, we are summing $$S_j$$ numbers of values $$\frac{1}{S_j}$$, hence the total value is 1. Now by writing $$\sum_{x\in X} \frac{1}{Gx}$$ as $$\sum_j \sum_{x\in S_j} \frac{1}{Gx} = \sum_j 1 = m$$. It follows that m is equal to the desired formula and this completes the proof. Q.E.D.

The relevance of this formula to combinatorics would be demonstrated later.