James Tauber

journeyman of some

blog > 2005 > 08 >

James Tauber's Blog 2005/08/20

Vocab Ordering Programming Competition

Okay, I've written up the instructions. I'm pleased to announce the start of the Vocab Ordering Programming Competition!

Bibliobloggers, Pythonistas, spread the word!

by James Tauber : Created on Aug. 20, 2005 : Last modified Aug. 20, 2005 : Categories programming_competition : 0 comments (permalink)

Planning a Programming Competition

It occurs to me that my exploration of ordered vocabulary learning might make an interesting programming competition. Like the ICFP competition I've entered before, it's well suited to any programming language because it is the results of the program that are judged, not the program itself.

I already have the scoring program written (original by me with improvements from Tim Wegener).

So, anyone that's interested, stay tuned, I'll post the details and rules in the next 36 hours. The input data will be from the Greek New Testament but no knowledge of either Greek or the New Testament is required.

There will be four categories, with greatly varying text lengths, so differently algorithms will be applicable.

The competition will be ongoing, with a ladder of the top 5 in each category, rather than a single "event" over a couple of days.

Here are my previous posts on the topic:

by James Tauber : Created on Aug. 20, 2005 : Last modified Aug. 20, 2005 : Categories programming_competition : (permalink)

Closed Manifolds

I said previously that we were ready to state the Poincaré Conjecture, but there's one more bit of terminology I want to get out of the way and that is closed manifold.

A closed manifold is a compact manifold without a boundary.

We previously listed the following as examples of spaces that are or are not compact:

  • the real numbers (under the order topology) is NOT compact.
  • any open interval of the real numbers is NOT compact.
  • any closed interval of the real numbers IS compact.
  • a circle IS compact.

The non-compact examples have the characteristic that you can "keep on going" and keep getting new points whereas the compact examples have the characteristic that you reach a point where there is no more, either because you've reached the edge (i.e. boundary) or because you've gone back to a point you've already been.

Saying without a boundary further restricts us to cases like the circle and not like the closed interval.

So, in other words:

  • any open interval of the real numbers is NOT compact.
  • any closed interval of the real numbers is COMPACT but has a BOUNDARY.
  • a circle is COMPACT and WITHOUT BOUNDARY, i.e. is CLOSED

NOTE: "Closed" here doesn't mean the same thing as a closed subset (i.e. one whose complement is an open set in a topology).

Here are some things to think about:

  • All connected one-dimensional closed manifolds are homeomorphic to the circle (or 1-sphere).
  • This isn't true for other dimensions because of the possibility of being connected but not simply connected

UPDATE: next post

by James Tauber : Created on Aug. 20, 2005 : Last modified Aug. 9, 2007 : Categories poincare_project : 4 comments (permalink)