The bounce rate indicates how many web-visitors leave the site without visiting any other pages before a certain session timeout elapses. That is :

High bounce rate means the site must be horrible to site visitors and most likely they would never return again. They are not even interested to check other content of the site. First impression counts.

After installing google analytics some weeks ago, I noticed a worrying high bounce rate : close to 80%… At first I thought this was due to the fact that all iTouch fans left the moment they saw a mathematical symbol, but further analysis proved me wrong : iTouch fans study posts here a lot longer than the average mathematician. But then, what was the reason? Is this site really so horrible to look at? is the content of such poor quality?

Anyway, I’ve tried out a couple of tricks, with surprising effect. The bounce rate dropped from 80% to under 3% and best of all, it appears to stay that low. Here, the google-analytics bounce-rate evolution of the last 3 weeks

So, what kind of magic voodoo did I perform on january 6th? I’ve installed a couple of Wordpress Plugins and changed the upper part of the entry-page. My basic assumption is that people leave a site when they come to it for specific information (for example via a search engine), do not find the info immediately and don’t want to spend too much time looking for it. So, I wanted to have all tools to find content on this site right in front of the potential new-comer. Here are the 5 major changes to the header part and the plugins Ive used.

1 : Rather than having a monthly-archive in the sidebar providing no more info than the number of posts in a particular month, create a proper archive page where visitors can find the titles and links to all posts in reverse chronological ordering. I did use the Smart Archives Plugin.

2 : Even better : have a drop-down archive right under the header-picture so that visitors can scroll down the list of all posts without having to load another page. Ive used the Awsom Archive Plugin.

3 : Let visitors see in a glance what your blog is all about by having a tag cloud under the header. I didnt feel like tagging 300 old posts, so I used the Simple Tags Plugin to do it all for me.

4 : Have a welcome message near the top to aid new visitors (especially when you have, like me, 77.51% of them around). The message disappears after their third visit. It’s a wonderful idea, made possible by the What Would Seth Godin Do-Plugin.

5 : Write series of posts and have links to the other parts available at the top of the new post. Likely, people are going to check out the other parts for more information. Rather than hard-coding the links by hand, Ive used the In Series Plugin.

What better way to start a series on Web 2.0 & Mathematics than to reflect on the potential dangers of majority-approved sites, such as Google, Wikipedia and META-sites. Bee has written a great essay The Spirits That We Called

Now you can tell me everyone of us should be rational, we should always check sources, doubt unverified reports even if repeated several times. We shouldn’t believe what we read without questioning it. We should seek accuracy and not easy entertainment. We should, we should, we should. But face it, many people don’t. Because they just don’t have the time, or are not interested enough, and the most commonly used criteria in this case is to follow the masses. Read what others read (the posts with the most comments?) go where many people link to, talk what others talk about, pay attention to what many people consider relevant. Majority offers security, Wikipedia is trustworthy, Google has proved useful.

To wet your appetite to take a break, and start reading the full essay (11 printed pages available from this pdf link), her opening paragraph, in which she outlines possible consequences of tempering with social bookmark sites.

MARCH 13th 2008: Until Wednesday, the Presidential candidate [insert name here] scored high in the polls. Then a Google search for his name showed up as first hit a report on an alleged child abuse committed by the candidate, published by Mary S. (name changed) on her personal website. The story was backed up by the following highly ranked hits that indicated two similar events during his youth, though reliable sources were missing. Within less than one hour, the reports were echoed on thousands of weblogs, appeared on digg and reddit, the original websites received 200,000 hits within the first 6 hours, until the server crashed down. Immediate press releases by the candidate’s PR groups did not appear on the Google listing, and could only be accessed by secondary links. It took until the next day that printed newspapers could attempt to clarify the situation.

Another, equally interesting essay, to which Bee points is Digital Maoism by Jaron Lanier,

The Wikipedia is far from being the only online fetish site for foolish collectivism. There’s a frantic race taking place online to become the most “Meta” site, to be the highest level aggregator, subsuming the identity of all other sites.
The race began innocently enough with the notion of creating directories of online destinations, such as the early incarnations of Yahoo. Then came AltaVista, where one could search using an inverted database of the content of the whole Web. Then came Google, which added page rank algorithms. Then came the blogs, which varied greatly in terms of quality and importance. This lead to Meta-blogs such as Boing Boing, run by identified humans, which served to aggregate blogs. In all of these formulations, real people were still in charge. An individual or individuals were presenting a personality and taking responsibility.
…
In the last year or two the trend has been to remove the scent of people, so as to come as close as possible to simulating the appearance of content emerging out of the Web as if it were speaking to us as a supernatural oracle. This is where the use of the Internet crosses the line into delusion.
…
In March, Kelly reviewed a variety of “Consensus Web filters” such as “Digg” and “Reddit” that assemble material every day from all the myriad of other aggregating sites. Such sites intend to be more Meta than the sites they aggregate. There is no person taking responsibility for what appears on them, only an algorithm. The hope seems to be that the most Meta site will become the mother of all bottlenecks and receive infinite funding.

Now, please print out these two essays, turn off your computer for an hour, and read them! Perhaps they change your opinion as to whether or not getting involved into some of these bookmark sites. Being aware of their potential danger is one (important) thing, neglecting them altogether has drawbacks too.

You might want to repeat the experiment I performed last night : type in your favorite technical term (mine was ‘noncommutative’, when this failed to return a hit, I tried ‘geometry’) into bookmark sites such as StumbleUpon, Digg, MyBlogLog, Reddit, blinklist, Magnolia and a dozen other similar ones.

You will discover that there is hardly any mathematics of value to be found there. As more people are using such sites in search of information, an inevitable consequence is that mathematics will become even more marginal, unless we take some action.

In my experiment, there was one noteworthy exception¹ : CiteUlike which has 427 articles tagged noncommutative, perhaps a result of the action I started 2 years ago. So, there is still hope!

1. delicious was another ok-site [↩]

Interactive Fiction (IF) describes software simulating environments in which players use text commands to control characters and influence the environment. Works in this form can be understood as literary narratives and as computer games. In common usage, the word refers to text adventures, a type of adventure game with text-based input and output. As the text-input is minimal (most commands have 1 letter abbreviations), text-games are ideal to be played on the iTouch.

Luckily, one of the most popular IF-interfaces, Frotz, is ported to the iPhone/iTouch as iPhoneFrotz. The easiest way to install is just to install the Frotz package using Installer.app. Just install the “Community Sources” package, which contains the installer repository (which hosts Frotz as well as other games and utilities), then look for Frotz under the Games section.

A collection of 3 Zork-derivatives (although not the original Infocom titles) is also available in the “Zork Z-Code” package.

There are hundreds of Z-Code games, and no one is likely to package your favorites for easy installation by Installer.app. But the games can be downloaded and copied to the phone without too much trouble.

Z-Code games are typically have filenames ending in .z3, .z4, .z5 or .z8 (depending on version), although game files from original Infocom media end in .dat. These should be copied to the phone’s Frotz/Games folder (under /var/root/Media).

Here is a link to the The IF archive and an archive of all Z-games. Another interesting site is the Inform 7-site

Inform is a design system for interactive fiction, a new medium for writers which began with adventure games in the late 1970s and is now used for everything from literary narrative fiction through to plotless conceptual art, and plenty more adventure games too. Since its introduction in 1993, Inform has become a standard tool. Three years in the making, Inform 7 is a radical reinvention of the way interactive fiction is designed, guided both by contemporary work in semantics and by the practical experience of some of the world’s best-known writers of IF. In place of traditional computer programming, the design is built by writing natural English-language sentences:
- Martha is a woman in the Vineyard.
- The cask is either customs sealed, liable to tax or stolen goods.
- The prevailing wind is a direction that varies.
- The Old Ice House overlooks the Garden.
- A container is bursting if the total weight of things in it is greater than its breaking strain.
Inform’s power lie in its ability to describe: to lay down general rules about “closed doors”, or “bursting containers”, or “unmarried men liked by Martha”. At its best, expressing IF in natural language results in source text which is not only quick to write, but very often works first time, and is exceptionally readable.

Inform 7 is available for most platforms and can be downloaded here.

We have associated to a subgroup of the modular group a quiver (that is, an oriented graph). For example, one verifies that the fundamental domain of the subgroup (an index 3 subgroup) is depicted on the right by the region between the thick lines with the identification of edges as indicated. The associated quiver is then

The corresponding “dessin d’enfant” are the green edges in the picture. But, the red dot on the left boundary is identied with the red dot on the lower circular boundary, so the dessin of the modular subgroup is

Here, the three red dots (all of them even points in the Dedekind tessellation) give (after the identification) the two points indicated by a whereas the blue dot (an odd point in the tessellation) is depicted by a . There is another ‘quiver-like’ picture associated to this dessin, a quilt of the modular subgroup as studied by John Conway and Tim Hsu.

On the left, a quilt-diagram copied from Hsu’s book Quilts : central extensions, braid actions, and finite groups, exercise 3.3.9. This ‘quiver’ has also 5 vertices and 7 arrows as our quiver above, so is there a connection?

A quilt is a gadget to study transitive permutation representations of the braid group (rather than its quotient, the modular group where is the cyclic center of . The -stabilizer subgroup of all elements in a transitive permutation representation of is the same and hence of the form where M is called the modulus of the representation. The arrow-data of a quilt, that is the direction of certain edges and their labeling with numbers from (which have to satisfy some requirements, the flow rules, but more about that another time) encode the Z-action on the permutation representation. The dimension of the representation is where is the number of half-edges in the dessin. In the above example, the modulus is 5 and the dessin has 3 (half)edges, so it depicts a 15-dimensional permutation representation of .

If we forget the Z-action (that is, the arrow information), we get a permutation representation of the modular group (that is a dessin). So, if we delete the labels and directions on the edges we get what Hsu calls a modular quilt, that is, a picture consisting of thick edges (the dessin) together with dotted edges which are called the seams of the modular quilt. The modular quilt is merely another way to depict a fundamental domain of the corresponding subgroup of the modular group. For the above example, we have the indicated correspondences between the fundamental domain of in the upper half-plane (on the left) and as a modular quilt (on the right)

That is, we can also get our quiver (or its opposite quiver) from the modular quilt by fixing the orientation of one 2-cell. For example, if we fix the orientation of the 2-cell we get our quiver back from the modular quilt

This shows that the quiver (or its opposite) associated to a (conjugacy class of a) subgroup of does not depend on the choice of embedding of the dessin (or associated cuboid tree diagram) in the upper half-plane. For, one can get the modular quilt from the dessin by adding one extra vertex for every connected component of the complement of the dessin (in the example, the two vertices corresponding to 0 and 1) and drawing a triangulation from them (the dotted lines or ’seams’).