The blog entry shows very well what Wordnet synsets are good for. Synonyms are not transitive, but neither are they just relationships between two words. I think Synonym nets should be renamed. They are something very different.
Why doesn't Alpha let you actually browse the synonym network? Why does it show the sixth-level relative of a word but won't let me see all of its immediate synonyms?
What about "ash"? I'd expect that to be in both networks: in "black" as a synonym for "coal" or "cinder", and in "white" as a form of "ashen", "pale", etc.
More widely, why must there be K non-overlapping networks that cover the entire language? Naively, I'd expect an unbounded number of non-overlapping small networks. But the two ideas of "Basic English" and of specialized vocabularies lead me to posit that every "significant" network (a network with a N number of members, where N > 5,000) overlaps with at least 1 other "significant" network. As a result, I would suspect that it would be difficult or impossible to find K non-overlapping sets that partition the entire language (where K is less than... oh, let's say 100).
An unbounded number of networks would be made of an unbounded number of nodes in the minimal case, and I have a hard time describing the number of English words as "unbounded". If you apply the full power of Internet debate (now with extra axioms!) to the twisting and spinning of the term and streeeeetch the meanings as hard as you can, maybe you can get there, but not by any sane method.
Oh, is English supposed to be sane? I hadn't noticed.
You're right, of course: I was using "unbounded" in a loose fashion. There are a finite number of phonemes used in English, and I suppose there must be some upper limit to the number of phonemes in a word.
It is possible that "black" and "white" are in the same synonym network, perhaps linked by words like "ash". That would be amusing. Someone can check it on WolframAlpha.
The networks are "non-overlapping", because of the definition of a synonym network. You start with a seed word, and grow it until it stops growing. The English language is finite, so K must be finite. The example network containing "black" is large, so K is expected to be small, (unless there are a few large networks, and many tiny ones).
Finding K is not difficult at all.
Pick a word, "black". Create the synonym network containing "black"and all words linked to it through the "synonym" relationship. Mark those words (roughly 26,000 of them) as "covered". K = 1.
Pick any other word not already covered.
Grow the next synonym network. Mark those words covered.
K = K + 1
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[ 4.3 ms ] story [ 42.4 ms ] threadhttp://wordnet.princeton.edu/
Screenshot: http://minimalism.linguistics.arizona.edu/~sandiway/wnconnec...
As you can see from the screenshot, it allows you to map all kinds of relationships between words (e.g. taxonomies).
I always found WordNet to be an amazing tool, albeit one that could use some UX work.
Wordnet is one of the sources for the WordData[] function. http://reference.wolfram.com/mathematica/ref/WordData.html
The entire English language must be partitioned into "K" non-overlapping synonym networks. What is the value of "K" ?
I wonder if K = 2, ... and the other synonym network contains "white".
If K > 2, then how many words are in the "white" synonym network, and what other words are not connected with "black" or "white" ?
Whatever K is, it must be relatively small, since there are only so many words in the language, and the synonym networks seem rather large.
More widely, why must there be K non-overlapping networks that cover the entire language? Naively, I'd expect an unbounded number of non-overlapping small networks. But the two ideas of "Basic English" and of specialized vocabularies lead me to posit that every "significant" network (a network with a N number of members, where N > 5,000) overlaps with at least 1 other "significant" network. As a result, I would suspect that it would be difficult or impossible to find K non-overlapping sets that partition the entire language (where K is less than... oh, let's say 100).
You're right, of course: I was using "unbounded" in a loose fashion. There are a finite number of phonemes used in English, and I suppose there must be some upper limit to the number of phonemes in a word.
The networks are "non-overlapping", because of the definition of a synonym network. You start with a seed word, and grow it until it stops growing. The English language is finite, so K must be finite. The example network containing "black" is large, so K is expected to be small, (unless there are a few large networks, and many tiny ones).
Finding K is not difficult at all. Pick a word, "black". Create the synonym network containing "black"and all words linked to it through the "synonym" relationship. Mark those words (roughly 26,000 of them) as "covered". K = 1.
Pick any other word not already covered. Grow the next synonym network. Mark those words covered. K = K + 1
Repeat until there are no words left.
K is the number of synonym networks.