Archive for the ‘General’ Category

Papers and LyX

September 4, 2009
In this post I want to talk about two applications I use which are critical to my workflow, Mekentosj Papers and LyX. Papers is an organizer for your academic papers and is only available for Mac OS X. LyX is a wysiwyg LaTeX editor and is available for pretty much any platform.
Before I learned about Mekentosj Papers, I used to organize papers by bookmarking their arxiv webpages. I also downloaded the pdfs haphazardly into my file system, usually renaming them from cryptic things like 012345.pdf to lastnames-title.pdf. My “system” was not simple, scalable or searchable. I downloaded the trial of Papers on recommendation from a colleague and imported all of my pdfs into the program with a simple drag and drop. Then I immediately used what is probably the coolest feature of Papers, matching the pdfs with their appropriate metadata. Papers has the ability to search the arxiv, download metadata, and then link it to your papers. You can then organize your papers easily by titles, authors, journals, or dates and you can view the abstracts easily. When matching a paper with its metadata, the program has a very pleasant animation and sound effect and stupid though it may be, this is what sold me on Papers. It feels like an Apple program (in a good way). It’s supposed to be like iTunes for your pdfs but I hate iTunes. Papers is way better.
Papers costs $40 but you can get a student discount about $14 off. There are frequent updates removing bugs and adding features. One of the coolest features that was added subsequent to my initial conversion is an iPhone companion app. The app cost me $10 but it was worth it, even though I usually don’t pay more than $1 for an app. It replicates most of the features of the desktop app. It even wirelessly syncs with the desktop application; iTunes eat your heart out. I now have 87 papers which I organize and read in Papers, at home or on the go.
For me, LyX is to writing math what Papers is to reading math. I know how to typeset LaTeX. You pretty much can’t do math these days without knowing. But even if you don’t know, you can still use LyX, a wysiwym program for generating LaTeX documents. Wysiwym stands for “what you see is what you mean”, a play on the usual wysiwig (“get” vs. “mean”) paradigm. With LyX you get the features of LaTeX, namely being able to generate content without over-worrying about presentation, along with instant preview, i.e. no need to compile the LaTeX file and generate a pdf. You can use the menu items to write mathematical notation or you can directly type LaTeX commands which instantly compile inline! This is about a million times better than compiling every couple of lines to check that you haven’t introduced any bugs in your code and you can also use the menu items when you inevitably forget some code. LyX has most of the features you find in LaTeX. For instance, I use the plugin Xy-pic a lot and it works just fine in LyX with instant previews and everything.
LyX is free as in speech or beer, which is a huge plus, even though I’d be willing to pay for it. It works on any platform (Windows, or Unices) but still integrates well in OS X. The developers are active and updates quash bugs.

In this post I want to talk about two applications I use which are critical to my workflow, Mekentosj Papers and LyX. Papers is an organizer for your academic papers and is only available for Mac OS X. LyX is a wysiwyg LaTeX editor and is available for pretty much any platform.

Before I learned about Mekentosj Papers, I used to organize papers by bookmarking their arxiv webpages. I also downloaded the pdfs haphazardly into my file system, usually renaming them from cryptic things like 012345.pdf to lastnames-title.pdf. My “system” was not simple, scalable or searchable. I downloaded the trial of Papers on recommendation from a colleague and imported all of my pdfs into the program with a simple drag and drop. Then I immediately used what is probably the coolest feature of Papers, matching the pdfs with their appropriate metadata. Papers has the ability to search the arxiv, download metadata, and then link it to your papers. You can then organize your papers easily by titles, authors, journals, or dates and you can view the abstracts easily. When matching a paper with its metadata, the program has a very pleasant animation and sound effect and stupid though it may be, this is what sold me on Papers. It feels like an Apple program (in a good way). It’s supposed to be like iTunes for your pdfs but I hate iTunes. Papers is way better.

Papers costs $40 but you can get a student discount about $14 off. There are frequent updates removing bugs and adding features. One of the coolest features that was added subsequent to my initial conversion is an iPhone companion app. The app cost me $10 but it was worth it, even though I usually don’t pay more than $1 for an app. It replicates most of the features of the desktop app. It even wirelessly syncs with the desktop application; iTunes eat your heart out. I now have 87 papers which I organize and read in Papers, at home or on the go.

For me, LyX is to writing math what Papers is to reading math. I know how to typeset LaTeX. You pretty much can’t do math these days without knowing. But even if you don’t know, you can still use LyX, a wysiwym program for generating LaTeX documents. Wysiwym stands for “what you see is what you mean”, a play on the usual wysiwig (“get” vs. “mean”) paradigm. With LyX you get the features of LaTeX, namely being able to generate content without over-worrying about presentation, along with instant preview, i.e. no need to compile the LaTeX file and generate a pdf. You can use the menu items to write mathematical notation or you can directly type LaTeX commands which instantly compile inline! This is about a million times better than compiling every couple of lines to check that you haven’t introduced any bugs in your code and you can also use the menu items when you inevitably forget some code. LyX has most of the features you find in LaTeX. For instance, I use the plugin Xy-pic a lot and it works just fine in LyX with instant previews and everything.

LyX is free as in speech or beer, which is a huge plus, even though I’d be willing to pay for it. It works on any platform (Windows, or Unices) but still integrates well in OS X. The developers are active and updates quash bugs.

Finally, let me say that I have issues with both programs. They’re not perfect. Nevertheless, they make my life so much easier and they are both pleasures to use.

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My, what a tangled web we weave

July 1, 2009

Hi, my name is Eitan. I’m a student of mathematics. Welcome to my personal blog. I intend to post mathematical exposition, but since this is a personal blog I will also post political thoughts or anything else that comes to mind. Let’s start with some math.

What’s a tangle? Tangles are very important objects in topology. Physically, they are just a number of strings in our usual 3-dimensional space whose endpoints (if they have endpoints) are attached to some boundary surface. We allow the strings to move around freely in 3-space so long as the endpoints remain fixed and we cannot pass strings through each other (or over endpoints). We also allow the strings to stretch and compress as though they’re made of rubber. Here’s an example of a tangle:

Example of a tangle

Example of a tangle

Try to count how many strings there are.

Tangles are really generalizations of knots and links. A knot is a tangle made of only 1 closed string, meaning the string has no endpoints, it’s just a circle. A link is a tangle made of any number of closed strings. Notice that all knots are links and that all links are tangles. Another way of thinking about tangles is that they are “local” pictures of knots, that is, if we zoom in on a knot and look at a small neighborhood, that neighborhood will contain a tangle.

Let’s look at examples of knots and links.

Trefoil Knot

Trefoil Knot

Hopf Link

Hopf Link

By tracing along with your finger, verify that the trefoil knot has only 1 string while the Hopf link has 2 strings.

Recall that I said the endpoints of the strings in a tangle must be attached to some boundary surface. In the example the boundary surface comes in two pieces, a bottom and a top. This is one convention for tangles, the “monoidal category” convention. Another convention, the “planar algebra” convention, is that the surface has only one piece. Really, there’s no important difference between thinking in either convention. It’s only a question of convenience for a given application.

I think that’s enough for now. Stay tuned to hear about Reidemeister’s theorem.