A long time ago, in the mysterious times known as 2006, my younger self came across a website. It was funny, and it appealed to various interests that teenage me happened to be developing in that very moment. It was a website about making fun of stupid people, mostly stupid people that said stupid things in ways relating to taking religion waaaay too seriously. Seriously enough that one might call them fundamentalists, or even fundies. That website was called Fundies Say the Darnedest Things, or FSTDT.
One might simply dismiss it as a humour site, one of a billion that populate the webs, but there was more to it. It had a community of really smart people (or so they seemed, to me), who said things I hadn't known then and now find obvious, and yet it seems they still need saying. Even when I eventually grew tired of reading the quotes they collected, the community that lived in its forums kept my interest. It would be fair to say that if I hadn't met those people when I did, this blog would likely not exist, and I perhaps would be a very different person.
I've been in and out of this community, in the past. At times when I needed a break from the internet in general, at times when I grew disillusioned with the people, but I returned every time, because I liked it there. My latest return was earlier this year, around April. Not long afterwards, the current webmaster made an announcement that he wished to retire from administering the forum and focus only on running the website itself, so he was looking for a replacement.
This wouldn't be the first time there was a change in administration; indeed, he had taken over the website back in 2009 when the then-owner burnt out and rather unexpectedly shut everything down. She, in turn, had received the website from its creator, who passed away at an unfairly young age. That was before my time, though.
In any case, the webmaster started a thread in the forums asking for candidates, and said there'd be a more or less democratic process: those candidates that got a reasonable amount of endorsements would spend a trial period as moderators, and then maybe there'd be a general election. I submitted myself as a candidate, not expecting much but thinking I would like to see what people would say about me.
To my continuing amazement, I won. I was apparently the only candidate credible enough to make it to the trial phase, I passed it more or less uneventfully, and I became the forum admin.
Now, like I mentioned, the webmaster kept control of the website itself, I just handled the community at the forums. Which suited me just fine, since it was the only part I visited anyway. Being that it still was his website, though, he warned me that he kept a kill option on the forums if things went too far out of hand. I figured this wasn't something likely to come up.
So, retiring from his position as admin, the webmaster still kept posting as a regular forum user. He took the chance, after leaving the position of power, to say things on a couple of subjects that he really couldn't have said when he was in charge. I thought, sure, a chance to get past some old forum drama, this should be a good thing, right?
It didn't go well. People got angry at the things he said. He got angry at the things people said to him. At some point, it seemed the discussion might die down and we could all move past it, but no. Instead, it came to the point where he didn't want to associate with the forums in any way. Including having them in his website.
So he told me he was killing the forums, and gave me a chance to make a new place for them. After a period of lots of panic, and with the help of the people hosting us, I managed to secure us a new home. We even got to keep the forums mostly the same, with a different address and name being the most significant change
FSTDT continues to exist, but there no longer are any FSTDT Forums. Instead, Frequently Questioned Answers is now an independent community, which for some weird reason has me as an admin. I still feel like I'm not exactly sure how I ended up in charge, even though I just told you.
Friday, August 16, 2013
Friday, May 24, 2013
Thoughts I have during class, 2
After an introduction to the uncertainty principle, and a clarification that some of the common examples for it are not quite true:
"Huh, that makes a lot more sense now. It's not that position and momentum are there but we can't measure them because of quantum magic. Position and the wave number k are Fourier conjugate variables, and by De Broglie's postulates k equals momentum divided by h-bar, so of course if one is highly focused the other is very spread out, and in the limit you have one as a Dirac delta and the other as a wave over all space. I wonder why science popularizers don't discuss it this way, it's not that complicated...
...oh, right, Fourier transforms."
"Huh, that makes a lot more sense now. It's not that position and momentum are there but we can't measure them because of quantum magic. Position and the wave number k are Fourier conjugate variables, and by De Broglie's postulates k equals momentum divided by h-bar, so of course if one is highly focused the other is very spread out, and in the limit you have one as a Dirac delta and the other as a wave over all space. I wonder why science popularizers don't discuss it this way, it's not that complicated...
...oh, right, Fourier transforms."
Thursday, April 4, 2013
Oh, hey
As has become a sort of tradition by now, I've noticed the state of abandonment of the blog once again and decided to revive it. Mostly, I blame the fact that I haven't been writing a lot, lately. Also, my last computer died in early January and I only got a new one a couple of weeks ago. Lost with that computer, incidentally, is all or most of my latest story, which was actually coming along nicely before everything went kablooey. 'Nicely' to be considered relative to my usual standards of creative output, that is.
While I muster the will to rewrite it or wait for a miracle to bring it back from the depths of a busted hard drive, here's a story from math class.
We are discussing how a particular mathematical transformation (a linear map) affects a rhombus. The computer shows first a parallelogram, then what appears to be a straight line. "Of course, this is actually a very thin parallelogram, not a line", says the professor."What would it imply, if it was an actual straight line?", she asks, while she tries to use the zoom tool to demonstrate.
The answer comes to mind, even before she has finished asking: "the matrix would not be invertible". Right behind me, another student says the same thing. The professor confirms this is so. Meanwhile, I am thinking, furiously, "How the fuck did I know that?"
It's not that it's an odd thing, or an unfamiliar subject. A few moments later, I figured out a couple of satisfactory answers as to why it must be so. It's just that, the moment I knew it, I had not gone through any of the intermediate steps in my mind. The answer seemed obvious in itself, as though a cached thought. And yet, as far as I recall, I have not come across this particular kind of question before. Did I do so and forget? Or did I just happen to have a cool flash of mathematical intuition?
Mathematical details, for those so inclined: A linear map is, for our purposes, a function that given a vector returns another vector, with some properties. Namely, if X and Y are vectors and f is a linear map, then f(X+Y)=f(X)+f(Y), and if k is a real number, then f(k*X)=k*f(X). We'll be working with vectors in R2, which can be thought of as arrows in a plane. Every linear map has an associated matrix, and iff the map has an inverse map (i.e, a map g such that g(f(X))=X for all vectors X) then the associated matrix is invertible (i.e., there is another matrix which, multiplied by it, returns the identity matrix). If you don't know what a vector or a matrix are, I suggest Wikipedia, an algebra class, or giving up. The idea above of applying the map to a rhombus means, essentially, that you apply the map to the vectors of every point of the rhombus and see what happens. In practice, all you actually need to do is apply it to the vertices of the rhombus and then connect the dots.
Now, the reasons a rhombus couldn't be turned into a line by an invertible matrix can be expressed in many ways. The first, is that it would imply that the transforms of all the corners of the rhombus are in a straight line. Because of the second property above, all vectors in the same straight line (which are all multiples of each other) also go to a straight line after mapping. If two separate lines in the rhombus go to the same line in its map, that implies there are different vectors that are being mapped to the same vector. A function that takes two inputs and sends them to the same output cannot have an inverse function. Therefore, the matrix associated with the map cannot be invertible.
Another way of looking at it is that if the map turns a two-dimensional figure such as a rhombus into a one-dimensional line, there must be some direction in space it makes zero. (This is by no means rigorous proof, just the sort of thing that would be stored in my brain and influence my intuitions). A linear map always maps zero to zero, so if there is another vector that also goes to zero, it cannot have an inverse.
A third way, which came to mind on the bus ride home, is that the determinant of the transformation of a matrix tells you how it changes areas after transforming. (This is only obvious to me because it's an important part of the change of variable theorem in integration. Being a physics student, calculus is something I use much more often than algebra). A straight line has area zero, which means the determinant of the transformation is also zero, and there's a theorem that states that if the determinant is zero, the matrix is not invertible.
While I muster the will to rewrite it or wait for a miracle to bring it back from the depths of a busted hard drive, here's a story from math class.
* * *
We are discussing how a particular mathematical transformation (a linear map) affects a rhombus. The computer shows first a parallelogram, then what appears to be a straight line. "Of course, this is actually a very thin parallelogram, not a line", says the professor."What would it imply, if it was an actual straight line?", she asks, while she tries to use the zoom tool to demonstrate.
The answer comes to mind, even before she has finished asking: "the matrix would not be invertible". Right behind me, another student says the same thing. The professor confirms this is so. Meanwhile, I am thinking, furiously, "How the fuck did I know that?"
It's not that it's an odd thing, or an unfamiliar subject. A few moments later, I figured out a couple of satisfactory answers as to why it must be so. It's just that, the moment I knew it, I had not gone through any of the intermediate steps in my mind. The answer seemed obvious in itself, as though a cached thought. And yet, as far as I recall, I have not come across this particular kind of question before. Did I do so and forget? Or did I just happen to have a cool flash of mathematical intuition?
Mathematical details, for those so inclined: A linear map is, for our purposes, a function that given a vector returns another vector, with some properties. Namely, if X and Y are vectors and f is a linear map, then f(X+Y)=f(X)+f(Y), and if k is a real number, then f(k*X)=k*f(X). We'll be working with vectors in R2, which can be thought of as arrows in a plane. Every linear map has an associated matrix, and iff the map has an inverse map (i.e, a map g such that g(f(X))=X for all vectors X) then the associated matrix is invertible (i.e., there is another matrix which, multiplied by it, returns the identity matrix). If you don't know what a vector or a matrix are, I suggest Wikipedia, an algebra class, or giving up. The idea above of applying the map to a rhombus means, essentially, that you apply the map to the vectors of every point of the rhombus and see what happens. In practice, all you actually need to do is apply it to the vertices of the rhombus and then connect the dots.
Now, the reasons a rhombus couldn't be turned into a line by an invertible matrix can be expressed in many ways. The first, is that it would imply that the transforms of all the corners of the rhombus are in a straight line. Because of the second property above, all vectors in the same straight line (which are all multiples of each other) also go to a straight line after mapping. If two separate lines in the rhombus go to the same line in its map, that implies there are different vectors that are being mapped to the same vector. A function that takes two inputs and sends them to the same output cannot have an inverse function. Therefore, the matrix associated with the map cannot be invertible.
Another way of looking at it is that if the map turns a two-dimensional figure such as a rhombus into a one-dimensional line, there must be some direction in space it makes zero. (This is by no means rigorous proof, just the sort of thing that would be stored in my brain and influence my intuitions). A linear map always maps zero to zero, so if there is another vector that also goes to zero, it cannot have an inverse.
A third way, which came to mind on the bus ride home, is that the determinant of the transformation of a matrix tells you how it changes areas after transforming. (This is only obvious to me because it's an important part of the change of variable theorem in integration. Being a physics student, calculus is something I use much more often than algebra). A straight line has area zero, which means the determinant of the transformation is also zero, and there's a theorem that states that if the determinant is zero, the matrix is not invertible.
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