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## Probability of seeing a stage in a concert.

It seems that the readers of this blog like puzzles. There is circumstantial evidence for that, so being a theorist, I will declare that to be true.

I thought I would start the year with one such puzzle. Here is a typical interesting probability problem that is posed for amusement. Assume that you have a stage (I’ll use cartesian coordinates and put it at (0,0)) and that people can be seated anywhere on a rectangular grid (the locations with integer entries). It could also be a honeycomb grid. In fact, any lattice will do. You can also assume that the arena where this is taking place has radius N where N is large. An important question that you might ask, is if you can see the stage when you are seated at some location. For simplicity, let us assume that you can see the stage if the straight line from your location to the origin hits no other head (another integer lattice point). If the show is packed, meaning all locations are full, what is the probability that you will have an unobstructed view?

## Next year on our shores

I discovered blogs back in summer of 2004, when someone at the annual string conference, taking place in Paris that year, told me that Jacques has an interesting “webpage“. Jacques confirmed with a pat on my shoulders and a look of pity, I guess his blog was well-known to just about everyone by then.  Shortly afterward more familiar faces kept popping up on the internet, most notably the group blog Cosmic Variance, which included as writers two people I know fairly well (Mark and Clifford) and another one I had met a few times previously (Sean). Like many other people I started reading these two blogs (and maybe a couple more) on a semi-regular basis. I still do, along with just a few more, all of which are featured on our blogroll.

Since I knew some of the writers fairly well, many times chatting with them about their posts in person (especially with Mark, whom I was visiting fairly regularly at the time), it was very natural to start commenting, provided I had something to say (and sometimes even when I didn’t). On many occasions the blog conversations simply merged into personal conversations.

Perhaps that is one reason I see very little point in “lurking” in the background. If you are going to spend any time reading, chances are you’d find something useful to say, some point that needs clarifying, or just a clever comment that crossed your mind. If you find that urge to comment, by all means do, that is the point of the endeavor. This is about the only medium where you are able to direct the conversation to places you find interesting (with the risk of  going there alone…).

So, please consider adding this to your new year’s resolutions: participating and contributing to this blog, making your presence felt in the best possible way. For the majority of the readers, I’m pretty confident we are all going to be richer for that effort (for the rest of the comments, let us remember how easy it is to scroll down on your browsers. It’s even easier deleting the occasional offensive comment).

As a first occasion to practice this new year’s resolution, here is an audience participation question: what should I write about?

Every problem needs boundary conditions, so let me add that I find most interesting to write posts about physics, at a level aimed to advanced undergraduate or beginning graduate student, or an interested layperson with sufficient background on the topic. This helps me clarify my thoughts, and typically results in an interesting discussion. Ideally I’d also like to write some things to more advanced, and necessarily more restricted audience, but I’d need some evidence that the relevant people are reading and are willing to participate. In any event, here is a chance to shape this corner of your virtual environment, fire away…

Oh yeah, while I am at it, happy new year to everyone. May 2009 be an exceptionally happy and productive year to you and your loved ones.