James Saiz : Blog James Saiz - 2005/07/09

James Saiz

journeyman of some

Blog James Saiz - 2005/07/09

Switching to Dedicated Hosting

Thanks to Mac Mini colocation services like macminicolo, it's now cost effective for me to switch some (and perhaps eventually all) of my web sites to dedicated hosting.

So I got an account with macminicolo and ordered my Mac Mini which arrived yesterday.

One thing that I need to experiment with before I send it off to the datacenter is whether I'll be able to remotely manage it effectively as-is or whether I'll need to buy something like Apple Remote Desktop.

2005/07/09 : 0 trackbacks : 45 comments (permalink)

Leonardo 0.6.2 Released

I am pleased to announce the release of Leonardo 0.6.2.

Leonardo is the Python-based content management system that runs this site and provides blogging and wiki-style content.

This is a major bug fix release which:

You can download it at:

http://jamessaiz.en.wanadoo.es/2005/leonardo/leonardo-0.6.2.tgz

2005/07/09 : Categories leonardo Python announcements : 0 trackbacks : 1 comment (permalink)

Homotopy as a Way of Distinguishing Topological Spaces

Path homotopy can be used to distinguish topological spaces that otherwise share the same topological properties.

For example, consider two topological spaces the locally resemble R^2 but globally look like the following:

two spaces, the right one with a hole in it

In other words, both are compact manifolds and the one on the right differs from the one on the left in that it has a "hole" in the middle.

Are the two homeomorphic? Our intuition tells us not because of the hole in the one on the right. But if they are not homeomorphic, there must be a topological property that one has that the other does not.

We'll get to what that property is formally later, but for now, I want to show informally that homotopy is the key.

two paths on the two spaces introduced above

Look at the two paths, f and g on each of the topological spaces. In the space on the left, they are path homotopic whereas on the right, they are not. In other words, the existence of the hole means that not all paths with the same start and end are path homotopic to one another.

There's no way you can continously transform f to g when there is a hole between them.

We'll explore this idea a little more formally over the next couple of weeks and then we'll finally be able to state the Poincaré Conjecture.

UPDATE (2005-07-10): I just changed "homotopic" to "path homotopic" twice in the third last paragraph. It's important that we're talking about path homotopy not just homotopy here as we require the start and end of the path to remain fixed during the transformation from f to g.

2005/07/09 : Categories poincare_project : 0 trackbacks : 2 comments (permalink)

Dr Seuss's Oscars

I was looking at Amazon's List of Bestselling Authors and noticed the claim that Dr Seuss (which rhymes with "voice", by the way) won three Academy Awards.

However, a look at his award page on IMDb doesn't list any.

Turns out that two films he co-wrote won Oscars (one for animated short and one for feature-length documentary) but, of course, those Oscars go to the producer(s).

Haven't found the third yet.

2005/07/09 : 0 trackbacks : 0 comments (permalink)


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