I just thought it was a cool title for a paper (if anyone has read it, let me know if it is any good):

On moving a sofa around a corner

in Geometriae Dedicata, Volume 42, Number 3, June 1992

Joseph L. Gerver

A necessary condition is given for a region of the plane to have the greatest possible area of any region able to move around a right-angled corner in a hallway of unit width. A region is constructed, with area 2.2195… and bounded by 18 analytic pieces, which satisfies this condition. It is conjectured that this is the unique region of maximum area.

Ian recalls some of the basic problem solving heuristics:

• If you are having difficulty understanding a problem, try drawing a picture.
• If you can’t find a solution, try assuming that you have a solution and seeing what you can derive from that (”working backward”).
• If the problem is abstract, try examining a concrete example.
• Try solving a more general problem first. This is the “inventor’s paradox”: a more ambitious plan may actually have more chances of success.

While I never studied these heuristics, I think I use them all. I probably learned them by trial and error. Maybe we ought to teach those.

I would add a few which I feel are very potent:

• Try to sketch a solution hastily, then try to find faults in your solution.
• If you can’t solve a problem, try to solve a related, but simpler problem.
• If you can’t solve a problem, try dividing into smaller problems (divide-and-conquer).

It looks like it is quite old, but I found the Combinatorial Object Server for the first time this week and I thought I’d share it with my readers. I was looking for irreducible polynomials with binary coefficients (don’t ask why) and I found that this server can generate them on the fly for you! A beautiful application of the web.

Here are some things it can do:

• Permutations and their restrictions
• Subsets or Combinations
• Permutations or Combinations of a Multiset
• Set Partitions
• Numerical Partitions and relatives
• Binary, rooted, free and other trees
• Necklaces, Lyndon words, DeBruijn Sequences
• Irreducible and Primitive Polynomials over GF(2) to GF(5)

This reminds me a bit of the famous Plouffe’s inverter which, given a floating point number, will give you a matching mathematical constant.

This is better documented elsewhere, but I could not find a quick reference on the web as to when you’d want to use the geometric mean instead of the arithmetic (usual) mean.

• Suppose that I’m 30% richer than last year, but last year I was 20% richer than the year before… what is the average growth? Well, my current wealth is 1.3 * 1.2 * w if w is my wealth two years ago. I can expect that if t is the average growth factor over the last two years, then my current wealth is t * t * w. Setting t = 1.25 is the wrong answer. In such a case, choosing t = sqrt(1.3 * 1.2) solves the problem.
• Another case where the geometric mean makes sense is when you are stuck averaging numbers that are not comparable like the time necessary to build a data cube, versus the average query time. Indeed, if a and b are two numbers and a is much smaller than b, then (2a +b)/2 is about the same as (a+b)/2. One component of your system is significantly worse and yet, you get the same average performance? That’s wrong. Computing sqrt (2ab) seems to make much more sense.

Here’s one reason to blog: so that you can belong to a very large network.

The utility of large networks, particularly social networks, can scale exponentially with the size of the network. (Wikipedia entry.)

Will sent me a link to this article in InformationWeek called Research Revolution (April 10th, 2006). It explains how the “web labs”, while still small, are changing the way we do research. Industry research would now be extremely fast paced and be based the vast amounts of data we have.

To be honest, after reading this article, I’m still searching for what the revolution might be. They seem to be hinting that previously, the research component was hidden away in the company and that it has now become more integrated. Well, duh!

Still, if anyone wishes to start such a web lab in Montreal, give me a call!

Now, in trying to gain an edge in the fast-paced Internet software market, Google, Microsoft, and Yahoo are taking a wholly new approach to research. They’re building labs focused on the problems and opportunities that have emerged with sleeker Web sites, the explosion of online video and photos, widespread broadband connections, and the soaring numbers of hours people spend online. Inventions can be tested on thousands of users at little cost, and adjusting an algorithm today can mean big gains in the effectiveness of a Web service tomorrow. The 20th century blueprint for research is “essentially mythical now,” says Alan Eustace, Google’s senior VP of engineering and research. “The model of research has changed.”

The Web is the biggest success story in IT ever. Well, maybe Walmart would come close behind. What bugs me is that people still don’t understand why the web is a success. It is not because Tim Berners-Lee is a great scientist. He had the wrong big idea about the web, but as a great hacker, he implemented the basics very well (including HTTP) and that’s what took off.

Information technology and engineering is not unlike science. Most often, the simplest and most elegant theory that can explain the data wins. For some strange reasons, researchers often tend to prefer complicated ideas maybe because they are train to formalize everything. In IT, the simplest and most elegant model that can satisfy our needs ought to win. Good engineers and IT experts know this, intuitively. That’s what Tim gave us, nearly the simplest solution that will work, and that’s why his name will go in the history books.

Regarding web services, the answer is not SOA, but rather REST. The writing is on the wall and has been there for years. Why? It is simply not the simplest solution that will work.

SOA may have meant something once but it’s just vendor bullshit now. (…) The crucial point is that Web-like things should be simple and lightweight and easy to set up; so I think the Web part of Web Services is more important than the Services part. SOA isn’t the future, Web style is. (Source: Tim Bray)