Now Landau says that this proportionality constant is (1/2)(m), where (m) is the [mass]. But why is it this constant and not something else. It is not really derived.

So I guess, my question restated very briefly is… why is the Lagrangian of a free particle: L = (1/2)(m)(velocity)^2?

Thanks

You can say both. Suppose people are playing chess. I see queer problems when I look into the rules and scrutinse them. But Smith and Brown play chess with no difficulty. Do they understand the game? Well, they play it.

- Ludwig Wittgenstein

What is the relationship between a scientific theory and one’s belief in it? I had always thought these two need not be in sync with each other and I thought most people would think this also or are atleast open to this suggestion. But recently I’ve witnessed people become very surprised that this or that person doesn’t believe in the theory of evolution. They remark that evolution is not just a theory, but a law. These seem like the right things to say, but it is nothing but  pseudo-intellectual coercion and a misunderstanding of the role of belief in science.

First of all, it is completely possible to work on the theory of evolution without actually believing in it. Let’s consider its founder Charles Darwin. It is possible that he himself was unsure if his theory was true. It seems like he didn’t believe in it, because of a conflict with his own Christian views. He doubted if the data really pointed to the evolutionary theory he proposed. He only published because someone else was about to propose something similar and he wanted credit for his theory.

A lot of evidence supports the theory of evolution. But does that mean I have to believe it? Well, I personally believe in it, but does everyone need to? Why should they? Science relies on data, on a prescribed methodology, on an interpretational structure to analyse the data that we are given. Regardless of how accruate a particular theory remains, to really beleive in a theory, for me to accept that it is true, requires from me a certain leap of faith over some uncertainty of one form or another. By “accept that it is true’, I do not mean that there is a statistically high probability that it may be true…I mean, I completely devote myself to the fact that the theory of evolution is a fact. In science there is continuously uncertainty, starting from its  foundations to the way we interpret data. Belief in science requires faith (a leap over uncertainties), but to do science, one need not have belief. One accepts the foundations or a particular way to interpret data and then assuming these foundations and methods of interpretation, x and y are conclusion we draw.

But what if one’s faith lies somewhere else. What if one’s faith lies not in science but in some doctrine that conflicts this theory of evolution. Well, they should make the leap of faith over all the data suggesting against this doctrine and continue to believe against the theory of evolution. The same goes beleiveing against the theory of relativity, not believing in physical theories. Data supporting a certain theory to be very true has no bearing on faith, and has no bearing on belief. This is the power of faith. Faith is not about statistics and faith is absolutely independent from science. Science requires no beleif to continue doing science.  It does take faith to beleive in science.

So it makes no sense for some people to judge others just because they do not put their faith in something that has a high stastical probability of being true. That is all unnecessary for faith. And this is why I have the utmost respect for faith above all things. These thingsa are hard to put in words.

I’m fearing that in the name of ‘science’  people will continue to ridicule where others put their faith, not realizing that faith in science itself requires some sort of a leap of faith. This confusion will turn into pseudo-intellectual coercion, which I see already prevalent amongst people here.  This has already happened in politics, where liberal and conservative media pretends to be innocent but portrays the other side as if they’re crazy for what they’re beleiving. The whole proposition 8 issue about whether the state could call the civic union of gays as “marriage” is a stupid travesty. From the practical concern of government, we should make sure that everyone has the same civic union rights, such as hospital vistis. But why the fuck should people care if the government considers if two homosexuals join hands …to be called marriage.  Why should the two gay men who sincerely beleive that they are married, care if the government decides to stamp a word “marriage” at their union. Isn’t it enough that the two beleive in their union and consider if marriage if they want to. Why is this on the headlines? How is this even a gay-right? I’m disgusted by all this. My tolerance level for journalists and their innocent-puppy portrayal of events drunk with bias ..has been trespassed. I’m done reading the new york times, I’m done hearing the news. I’ll just try to keep track of the current events going on in our world right now, but I am not the one to judge, not even the terrorists in Afghanistan or the hard-core conservatives in our nations.

Things are more subtle than they seem to be.

Wittgenstein was insisting that a proposition and that which it describes must have the same ‘logical form‘, the same ‘logical multiplicity’, Sraffa made a gesture, familiar to Neapolitans as meaning something like disgust or contempt, of brushing the underneath of his chin with an outward sweep of the finger-tips of one hand. And he asked: ‘What is the logical form of that?’

This is a sign that I do not really understand one of Wittgenstein’s main points in Philosophical Investigations, because I do not quite understand the influence Sraffa has on Wittgenstein.

Also as an observation- Wittgenstein seems to have gotten along quite well with two economists in Cambridge- Sraffa and Keynes. Keynes’ book on Russia was something that really influenced Wittgenstein to try to settle in Russia as a laborer. Althought not sympathetic to Marxism in ideology, Wittgenstein seemed to admire the way of life there. He was also probably prompted by Siegler’s Decline of the West.

Monk’s biography really centers around the work of Otto Weininger, known for his publication of Sex and Character. Although a Jew himself, Weininger was known for the severe anti-semetic and misogynistic nature of the text. However, it seems like Wittgenstein was really influenced by Weininger talk about cultivating one’s own (artistic) inner genius- that is one’s most important duty. And these Weiningerian elements are present in Wittgenstein view on life during his discussions with other colleagues and students. When he met with people who were in conflict with themselves to better the world, he always told them to better themselves and the world will get better by itself. Wittgenstein’s drive is towards an artistic genius than towards any scientific or humanitarian progress; this is one of the many differences between him and his mentor, Bertrand Russel.

Most interestingly, Wittgenstein considers one of his biggest influences in philosophy to be his  “philosophy” of mathematics. He shows (Lectures on the Foundations of Mathematics) that there is no need for the philosophy of mathematics, there is no need for laying these so-called  ”logical foundations” for mathematics (which was also one of Hilbert’s problems until Godel came along the way). What he tried to show is that mathematics consists of “techniques”. What a logician calls a foundation is merely another “technique”, not somethign that just sits rock-bottom. Seeing this, it makes more sense why Wittgenstein was sympathetic to Brouwer’s intuitionism, because Wittgenstein couldn’t see how mathematics was “outside” the human mind, as Russel may have claimed. I read parts of his Lectures on Foundations of Mathematics and blogged about it 2 years ago at Berkeley (http://rohanghanta.wordpress.com/2008/07/03/wittgensteins-lectures-on-the-foundations-of-mathematics/). I am not sure if I agree with everything I wrote back then.

I also think Wittgenstein’s (very involved) relationship with Frank Ramsey was a major factor in inducing in Wittgenstein a distaste of academia. Wittgenstein no-doubt saw Ramsey as a man of first-rate brains; he was already showing his originality by the age of 19 at Cambrige, not just in mathematics but also in economics and philosophy. When Wittgenstein joined the Austrian army during WWI and then returned to cambridge as a 40-year old, the 20-something Ramsey was his “doctoral-advisor” (although they worked more like colleagues). But it seems like Wittgenstein saw that Ramsey’s invovlement in the academic atmosphere at Cambridge seems to have had adverse effects on him. He frequently described Ramsey as a “burgeois thinker”, because Ramsey’s main goal was to find a logical foundation of mathematics. This was no-doubt a big alienating source between Wittgenstein and Ramsey, because Wittgenstein basically considered what Ramsey was working on to be useless and Ramsey was merely molding himself into a certain school of thought (that Russel himself is part of) and is trying to achieve its goals. Wittgenstein saw that Ramsey wasn’t able to see the clear picture about these so-called “foundations” of mathematics.

Of course, Wittgenstein was not naive. He knew that he cannot reach out to academia. He knew he could not reach out to the Cambridge’s brightest logician-philosophers (like Russel and Ramsey) to convince them  to walk out of the fog and see clearly the nature of their work. But what Wittgenstein was hoping to influence were those at Cambridge with “first-class brains AND innocence and a clear mind”. Namely, he was hoping to help the Cambridge undergraduates see the light. He spent much time with brilliant undergraduates at Cambrdige, especially Drury and Skinner, both of which had inclinations to pursue academic philosphy. He has convinced Drury to leave academia and work among the ordinary men. And with Skinner he has had another intimate relationship. Skinner was a mathematics undergraduate finishing the Tripos at Cambridge when he met Wittgenstein. After working with Wittgenstein as a post-doc, he finally took Wittgenstein’s advice- he left academia for good and worked as a gardner and then as a mechanic.

What took me by the biggest surprise is that there were certain mystical elements in Wittgenstein’s works, even in his Tractatus, which I had thought was very dry. I think during my 2008 or 2009 summer at Berkeley, I was talking with Alex about how Wittgenstein may have reacted to Heidegger. He replied that Wittgenstein would say Heidegger’s work is “nonsense”. I’m not really sure if I can believe that now.

When I was taking Discrete mathematics at Berekely two years ago, I asked my instructor, who is a logician, if he knew about Wittgenstein. He said he knew “that crazy guy”. But the more I read about him, the more I try to understand what he is saying, I think there is something behind his eccentricities, his dissheveled appearance, his obsessive attachment to his work. I think maybe he was more in touch with reality than those around him. He wanted to be true to himself, to live honestly.  But I guess that may qualify as “crazy” among some people.

As someone who is inclined towards philsophy, especially foundations and “philosophy” of physics, I think I should really ask myself what exactly is “philosophy of physics” and why is it necessary. Before, I just took for granted that it is something that was an academic discipline and didn’t really question what it really is.

I am not interested in constructing a building, so much as in having a perspicuous view of the foundations of possible buildings.

So I am not aiming at the same target as the scientists and my way of thinking is different from theirs”

- Ludwig Wittgenstein

If anyone else has another proof, not dwelling heavily on the calculus of variations, please contact me at rghanta19REMOVETHIS[at]gmail[dot]com .

In Arun’s proof, I’m really curious as to the nature of alpha. It is said that it’s just a scaling thing, but I want to know more about how it works. (alpha)x(t_1) = (alpha)x(t_2) = 0, but how can we conclude from this that x(t_1) = x(t_2) = 0 ? Thanks.

Enlighten me.