- The maximize button is in the top right hand corner
- To the immediate left of the maximize button, there is a down-arrow that gives zoom options (- for 'zoom out' and + for 'zoom into')
- The iPaper drop-down menu has viewing printing and other options
- Below every document, there are two links to Scribd
- Have fun!!! I encourage everyone to use it!!!
Monday, June 16, 2008
Notes on Scribd documents...
I am expecting to put up quite a few Scribd documents. These are some things everyone reading them needs to know:
Religious Identity Crisis
Recently, I stumbled upon a very interesting read about Atheism, namely, The God Delusion. Very thought-provoking to say the least. Dawkins is very logical at many points. This reminded me about sometime ago, when I was engaged in a conversation about religion and its interpretations (especially those that result in fanaticism) and why I always saw it as a means to divide people (This particular viewpoint is very personal and is strongly influenced by the various events that took place during my childhood). So, we got into the argument about whether the central idea of every religion is God and what defines this entity? In the process of answering it, I had to interview a select few people who were well versed in their respective religions/beliefs. I interviewed a Christian, a Muslim, an Atheist and I had a few informal chats with a person whose religion was Judaism. I am very well aware that the 3.5 data points that have been collected are by no means a part of the answer to the above posed question. Of course, I am a person who is planning to spend his entire life in a field that values reason and experiment above all and encourages everyone to question every hypothesis. However, this natural curiosity is sadly absent in many of my peers. They seem to take things at their facevalue without even bothering to question. However, I think I seem to understand that I believe that the solution to this problem is not to do away with God. Nope! That solution does not work. I could pretend for sometime that there is no God, but I could not carry on. It did not make sense. Maybe because I have been conditioned for about 17 years that I had to believe in something. So, yeah, I am all confused right now about what exactly I need to believe in; that is, if I actually have to though! Maan...religion is tougher that Quantum Field Theory!!!
Moment of Inertia is a number no more: The quest for the meaning of Eigenvalues begins!
It turns out the subject of this entry is not just to attract eyes, It is true!!! Well, not entirely (There's always a catch). A few weeks ago, I decided I will just 'sit in' an analytical mechanics class and see what all the physics and applied math majors were upto. So, it turned out I was the only Electrical engineering student in the class (No typos there) and I was proud! Ok enough about me now.
So, due to the unanswered questions about the eigenvalues (ref previous entry), I dug them up in various places after that first Linear Algebra lecture 3 semesters ago. The first one being Quantum Mechanics, then my own branch (Electrical Engineering), then in Mechanics!! and later even in fundamental physical quantities in Electrodynamics!! Anyway, I decided I'll write what I know about the eigenvalues I encountered in the most "classical" of the physics branches first. So, the events occurred in the following fashion that day: I was half asleep as usual while the professor was generalizing and over-generalizing and hyper-generalizing (by which time, I completely lost track of the thing that we were attempting to generalize ...psst...It was angular momentum....I think...anyway something related to it at least), then I began seeing some truly horrendous expressions on the board which would have made a much gentler impact on my brain if the prof used the "Einstein summation convention" (Just a name given to the process that makes huge sums look simple). So, while I was receiving the impact of these expressions head on, the words "...So, students, Moment of Inertia is not a number anymore! It turns out that it is a 3x3 matrix in this case, which is a special case of what we call a TENSOR....." fell in my ears and I got very excited about what he was saying (It happens when you don't know something and in the middle of something else that is familiar, that something, that you don't have any clue about, pops up! and the something that I did not know and regrettably, still don't was the meaning of the word TENSOR) So, naturally, by this time I was more attentive when what could almost be termed as magic unfolded in front of me! The professor was great and he was excited about it too. Then, we went on, calculated the "Principal Axes" of the system using the eigenvalues of the moment of inertia tensor. So, on that fateful day, I came across a whole new way of looking at eigenvalues. (May be I'll upload a document/pdf later showing the exact derivation done in class).
So, due to the unanswered questions about the eigenvalues (ref previous entry), I dug them up in various places after that first Linear Algebra lecture 3 semesters ago. The first one being Quantum Mechanics, then my own branch (Electrical Engineering), then in Mechanics!! and later even in fundamental physical quantities in Electrodynamics!! Anyway, I decided I'll write what I know about the eigenvalues I encountered in the most "classical" of the physics branches first. So, the events occurred in the following fashion that day: I was half asleep as usual while the professor was generalizing and over-generalizing and hyper-generalizing (by which time, I completely lost track of the thing that we were attempting to generalize ...psst...It was angular momentum....I think...anyway something related to it at least), then I began seeing some truly horrendous expressions on the board which would have made a much gentler impact on my brain if the prof used the "Einstein summation convention" (Just a name given to the process that makes huge sums look simple). So, while I was receiving the impact of these expressions head on, the words "...So, students, Moment of Inertia is not a number anymore! It turns out that it is a 3x3 matrix in this case, which is a special case of what we call a TENSOR....." fell in my ears and I got very excited about what he was saying (It happens when you don't know something and in the middle of something else that is familiar, that something, that you don't have any clue about, pops up! and the something that I did not know and regrettably, still don't was the meaning of the word TENSOR) So, naturally, by this time I was more attentive when what could almost be termed as magic unfolded in front of me! The professor was great and he was excited about it too. Then, we went on, calculated the "Principal Axes" of the system using the eigenvalues of the moment of inertia tensor. So, on that fateful day, I came across a whole new way of looking at eigenvalues. (May be I'll upload a document/pdf later showing the exact derivation done in class).
So what are eigenvalues anyway?!!!
It is inevitable that at some point in life, every person who is at least a little bit into the realm of Science (or studying the effects of Cocaine and the like) wonders "What are those mysterious eigenvalues that keep popping up now and again in everything and anything that we see?". Well, so I decided to inculcate a coherent thought process about them by means of talking to my friends (Thanks Mark and Ariel) and also by means of putting down my random thoughts in the form of this blog!
OooKay now the following is for those who still wish to stay with this, eigenvalues were first encountered in a half-drowsy-half-"I don't give a rat's ass coz I know it all" state of mind in my undergrad Linear Algebra. All that was registered in my mind by the end of that semester was that in German, eigen meant proper and there existed something that looked like an equation of bunched up numbers that spat out these "proper" values and some other bunched up numbers associated with each of these super-special numbers. Now, as you have most likely realized, I knew absolutely nothing whatever they did and whatever the point of the whole exercise was except that sense really made sense!!! ( A nightmare for someone in my shoes). So, I asked around (in the ever elusive Math department of course) and got the following answer in a rather "Don't bother me, go get a life!" attitude in a very low frequency (coming from a female):
"Weell....I don't know what the big confusion is really. It is fairly straight forward that eigenvalues are those that are the solutions of the Characteristic equation and the eigenvectors are the solution vectors of the Characteristic equation that are associated with each eigenvalue....." (Me go: zzzzz.....yaaaaawn ....uh uh ya I get it zzzz...... )
So, once I have realized that asking around does not always help and simply naming stuff does not either, I decided to dig this damn thing up by myself (which I did not have to coz there happened to exist others who were also wondering about the same thing).
OooKay now the following is for those who still wish to stay with this, eigenvalues were first encountered in a half-drowsy-half-"I don't give a rat's ass coz I know it all" state of mind in my undergrad Linear Algebra. All that was registered in my mind by the end of that semester was that in German, eigen meant proper and there existed something that looked like an equation of bunched up numbers that spat out these "proper" values and some other bunched up numbers associated with each of these super-special numbers. Now, as you have most likely realized, I knew absolutely nothing whatever they did and whatever the point of the whole exercise was except that sense really made sense!!! ( A nightmare for someone in my shoes). So, I asked around (in the ever elusive Math department of course) and got the following answer in a rather "Don't bother me, go get a life!" attitude in a very low frequency (coming from a female):
"Weell....I don't know what the big confusion is really. It is fairly straight forward that eigenvalues are those that are the solutions of the Characteristic equation and the eigenvectors are the solution vectors of the Characteristic equation that are associated with each eigenvalue....." (Me go: zzzzz.....yaaaaawn ....uh uh ya I get it zzzz...... )
So, once I have realized that asking around does not always help and simply naming stuff does not either, I decided to dig this damn thing up by myself (which I did not have to coz there happened to exist others who were also wondering about the same thing).
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