James Saiz : Blog James Saiz - 2005/07/16

James Saiz

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Blog James Saiz - 2005/07/16

Equivalence Relations

To formalize path homotopy as a way of distinguishing certain topological spaces, we need to introduce the notion of an equivalence relation and an equivalence class. We'll introduce the former here.

Consider a set A of objects. We pick certain pairs of elements in A and say they have a particular relation to one another. In other words, a relation R on A (or more accurately, a binary relation on A) is simply a choice of pairs—a subset of A x A. If <a, b> is in R then we say that a has the relation R with b. We can also write this aRb.

If A is a set of people, R might be something like "is the father of". And so if d is Darth Vader and l is Luke Skywalker, then dRl.

A relation is said to be an equivalence relation iff it is a relation with the following properties:

Our "is the father of" relation violates all three and so it certainly not an equivalence relation.

Something like "is less than" on the set of reals is transitive but not reflexive or symmetric and so is not an equivalence relation.

Something like "is less than or equal to" on the set of reals is transitive and reflexive but still not symmetric and so is not an equivalence relation.

Equality is an equivalence relation as it has all three necessary properties. Two topological spaces being homeomorphic is also an equivalence relation.

Importantly for us, path homotopy is an equivalence relation.

2005/07/16 : Categories poincare_project : 0 trackbacks : 6 comments (permalink)

Parts of Speech and Number of Accents

I thought I'd write a quick Python script to check how many accents were on each of the lemmata in MorphGNT 5.06.

Here are the counts by part of speech and number of accents on lemma:

     0    1    2  
  A    -    9159    -  
  C    924    17361    -  
  D    1592    4606    -  
  I    -    17    -  
  N    30    28271    1  
  P    5433    5488    -  
  RA    19862    4    -  
  RD    -    1744    -  
  RI    -    1165    -  
  RP    -    11584    -  
  RR    -    1677    -  
  V    8    28101    1  
  X    147    844    -  

Some of the low numbers are definitely errors in the database. Now to investigate...

UPDATE (2005-07-16): both 2-accent cases were mistakes. The 30 0-accent nouns and 5 of the 0-accent verbs were foreign loan words that intentionally weren't accented but 3 of the 0-accent verbs were mistakes. The 4 accented articles were the result of crasis with the following noun and the word should probably be analyzed as a noun rather than an article. I guess there'll be a 5.07 release soon. NOTE: I haven't looked at the particles, adverbs, conjunctions or prepositions yet.

by James Saiz : 2005/07/16 : Categories morphgnt (permalink)

MorphGNT 5.06 Released

Well, it's been about a hundred hours work over the last six months, but I'm pleased to announce the release of a new version of MorphGNT, the morphologically parsed Greek New Testament database made available under a Creative Commons license.

Besides some corrections to the text (mostly rho-breathing) and a couple of parsing code changes, this release has a huge number of corrections to the lemmata—160 lemma changes in 465 places. See this blog entry for how potential errors for this round of corrections were discovered.

You can download the new file at:

2005/07/16 : Categories morphgnt announcements : 0 trackbacks : 1 comment (permalink)


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