James Tauber

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James Tauber's Blog 2004/12/23

Blog Hits By Age

I was going to give a Top Ten Blog Entries By Number of Hits listing but I suspected it would not necessarily be that insightful under the hypothesis that hit numbers are partly a function of the age of the entry.

So I took the number of hits for each entry and graphed it against the age of the entry in days:

There definitely appears to be a linear baseline which the entries "rise above". To make this clearer, I graphed the hits per day against age:

Notice that the two entries from 250-300 days ago lower in significance while the entry from 50 days ago rises considerably. Which entries were these?

The older two are Eclipse is the next Emacs and Eclipse GEF. Both those get a lot of their referrals from Google searches.

The entry from 50 days ago is, funnily enough, another Eclipse GEF-related post, Six Snapshots of a Simple Eclipse GEF Application. Note that that entry is linked to from one of the older ones.

So, what effect does using average hits per day instead of just hits have on a Top Ten Blog Entries?

Here is a list of the top 10 just by hits:

And here is a list of the top 10 by hits per day (ignoring the last couple of days):

Is the second list more representative? I think so. It includes some extra entries (in bold) that were popular (judging by incoming links and del.icio.us citations) but didn't make the first list because they hadn't been around for as long.

How does any of this match up with what I consider my own favourite entries? I'll save that for another entry.

by James Tauber : Created on Dec. 23, 2004 : Last modified Feb. 8, 2005 : (permalink)

TeX for Leonardo

Looking at Wikitex (via Simon Willison) has convinced me more than ever that I want support for TeX in Leonardo.

Hopefully 0.5 will have the framework (if not the actual implementations) to support a range of underlying document formats including TeX, XHTML and Word.

by James Tauber : Created on Dec. 23, 2004 : Last modified Feb. 8, 2005 : Categories leonardo : (permalink)

Poincare Project: The Standard Topology for Ordered Sets

One common way of defining a topology is to take a set, add some structure to that set, define a collection of subsets that meet some criteria in that structure and then use that collection as a basis for the open sets.

Although we didn't have the vocabulary to accurately describe it in those terms, that's what we did previously with the topology of a metric space. A metric space, recall, adds to a set the structure of a distance function. From this, we can define the collection of open balls. This collection can then form the basis for the other open sets in a topology.

Here is another example. Take a set X and add to it the structure of a total ordering. A total ordering is a relationship < such that

  • for any a, b, c in X: a < b and b < c implies a < c
  • for any a, b in X: a < b or b < a or a = b

In other words, a set with a total ordering is a set whose elements can be sorted.

Now define an open interval (a, b) to be the subset of X such that, for each element x, a < x and x < b.

The open intervals form the basis for a topology. So a total ordering on a set defines a particular topology. While other topologies are possible, the one based on the open intervals is referred to as the standard topology for the ordering or the order topology.

The real numbers, being a totally ordered set, has an order topology. While other topologies can be defined on the real numbers (as long as the rules for open sets are followed), the order topology is the most natural and consistent with one's intuitions about how the real numbers work.

UPDATE: next post

by James Tauber : Created on Dec. 23, 2004 : Last modified Feb. 8, 2005 : Categories poincare_project : 0 comments (permalink)