Stephen Downes prepared a Montreal photo set. The photo set is worth a visit if you want to know what Montreal feels like.

I am the nerdiest of the two:

Since I moved to the Montreal suburbs, I have become an active gardener. I used to apply generous amounts of fertilizers. I also got into serious trouble. My lawn died. Not because I burned it, but because I got a bad case of grubs. Several of my perennials died also or fail to come back healthy after the winter. I learned the hard way that most perennials are better off without any (chemical) fertilizer.

It turns out that in most cases, chemical fertilizers are overrated. As a rule, you should not use them.

• Fertilizers may contain toxic material which stays in your soil and your vegetables.
• Fertilizers may increase the acidity of the soil, which is bad for most plants.
• Fertilizers make your soil poorer, not richer over time.
• Fertilizers tend to kill the microorganisms in your soil, rendering natural composting difficult.
• Fertilizers make your plants less resilient to disease and drought: artificially sustained growth is not always a great idea. Are you really in a hurry or do you want more robust plants?

In academic circles, there are intense platform wars. We have a talk next week from the head librarian about offering Google-like services, but on an academic platform. I won’t go to the talk because I no longer care about library portals. Regarding courseware, there are wars between Moodle and other hybrids. As a professor, all that I care about is to have some tools to post content online, conveniently. The last thing I want to do is live within a monolithic proprietary platform.

Everyone is fighting for his platform. What a tragic mistake! In 2008, only one platform matters. No, it is not facebook, nor Windows Vista, nor Moodle, nor Dot.NET. It is the Web. In some sense, the Web is the platform to rule them all.

Something deeper is going on as well. In Death of the software application, I argued that software as a discrete quantity was finished. How many software applications do you run right now? Nobody cares. Similarly, the term platform is obselete: people hook up the software they need dynamically.

If someone asks you to pick a specific platform for a project, refuse to do so. Pick software the way a taylor will pick fabric: a little bit here, a little bit there. Also, if you are building a Web platform, please stop right there. Turn around and rethink your objectives.

Since I have had amazing luck in the past with questions to the readers of this blog, I have another question.

The diameter of a graph is the longest distance between any two nodes. The degree of a node is the number of edges or links from and to this node.

Intuitively, the higher the node degrees, the denser the graph. If you have n nodes and the maximal degree of the nodes is n-1, then the graph diameter is 1. If you have lesser maximal degrees, then you can get an infinite diameter by producing a disconnected graph.

An interesting question (to me) is:

Given a maximal node degree, and a number of nodes n, what is the smallest possible diameter?

I am sure this is textbook material, but I could not find the answer quickly. Using a hyper-rectangle, I am able to construct a graph having n nodes and log n diameter. Simply start with a 4-node rectangular graph: you have 4 nodes and a diameter of 2. Move to a 8-node cubic graph: you have 8 nodes and a diameter of 3. Generalizing this construction, you have 2^d nodes and a diameter of d. Is this the best you can do?

Anyhow. Why do I care about the answer? Because I keep reading that hubs are necessary in graphs to ensure that we have a small diameter. I am trying to quantify this statement. There are about 2³³ human beings. By my construction above, if everyone knows 33 people, then it is possible to get a diameter of 33. It seems like a relatively large diameter.

An obvious technique to shrink the diameter without using hubs, is to increase the maximal node degree. I am wondering by how much I need to increase the maximal node degree so that I can a 6 degree of separation between any two human beings.

(Yes, I know that social networks are not homogeneous. But stay with me. Assume they were.)

In the past, I have had luck with my requests for help, so here is another one.

Suppose you have a large array made of a large number of distinct values ({A,B,A,B,A,C,C}) and you want to group the identical values like so {A,A,A,B,B,C,C} or like so {C,C, A,A,A,B,B}. That is, you do not care about the order, you just want identical values to be clustered. How do you do it?

• You could sort the array assuming that there is an ordering between the objects. There are highly efficient external-memory sorting routines. They mostly rely on sequential IO and are amazingly fast.
• You can build a hash table. Because it is a linear time operation, for very large arrays, it should be faster than sorting, in theory. However, the catch is that external-memory hash tables are not very efficient because they rely on random IO and are prone to cache misses. Remember kids that 100 n > n log n despite what your math. teacher taught you.
• We can mix hashing and sorting. Scan the array, and randomly hash each value into one of L bins. You know that if the value x appears in bin i, then all values x are in the same bin. So, you can simply sort each bin and concatenate the bins in O(n log n/L) time, assuming your hashing is good enough.
• One last possible trick might be to adapt fast duplicate detection algorithms such as the Teuhola-Wegner algorithm: J. Teuhola, L. Wegner, Minimal space, average linear time duplicate deletion, Communications of the ACM, 1991.

So, what do you think?

I am not a neat guy. I tend to drop coffee cups on my desk and I never look back. What I learned this year is that if you leave a cup of cappucino for a week on your desk, then drink a shot of it by mistake while staring at your computer screen, you are left with a terrible taste in your mouth for the rest of the day. However, day-old cappucinos are ok.

There is a lesson here kids: do not leave projects without attention for weeks at a time. You will get a bad taste once you go back to it later.