Talk:Cryptomorphism

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[edit] Proposed merge

Searching for (Cryptomorphism OR Cryptomorphic) on Google Scholar only returns 69 hits using either term which raises my doubts as to whether this term is actually notable enough to warrant its own encyclopedia article. Is Homomorphism the same thing? --  Netsnipe  ^(Talk)  05:02, 29 July 2006 (UTC)

no it's not the same (as far as I understand). I'll change the tag to suggest a merge to isomorphism, but in any case I don't think this term is in wide use (even in the math community). Pascal.Tesson 05:24, 29 July 2006 (UTC)

Let's see. Two things in math are called "isomorphic" if they are only superficially different: for example, the set of natural numbers written in decimal notation is isomorphic to the set of natural numbers written in binary. It literally means "same shape", and I think it was around even in the late 19th century. The word "homomorphism" came much later. It's not a very deep generalization of "isomorphism" but I can't think of a ten-word explanation. Besides being a not-very-deep generalization of "isomorphism", the homomorphism concept is enormously, earth-movingly important. And it has a technical mathematical definition.

The word cryptomorphism is not so much a generalization of as a riff on "isomorphism": "cryptomorphism" is what you get when you mash "crypto" and "isomorphism". Two things are cryptomorphic if they're "secretly" the "same shape": that is, if it's "difficult to see" that they're the same. The concept is not very important, and it does not have any technical mathematical definition (possibly a reason it doesn't appear in the literature very often), but it is standard jargon among (some) people who work on matroids, and I think it's of some pedagogical value: there are a zillion different definitions of "matroid", and as a result lots of advances in the subject have a zillion different equivalent formulations. I think it's nice that there's a name for the phenomenon.

Anyway, I vote "no" on merging with either "homomorphism" or "isomorphism". Changbao 06:18, 29 July 2006 (UTC)

I don't think I made this clear: isomorphisms (and homomorphisms) have precise, technical definitions. "Cryptomorphism" is not a technical concept but a word people use when talking about math. Changbao 06:24, 29 July 2006 (UTC)

But then wouldn't a footnote in the isomorphism article be enough? The cryptomorphism article will never be more than a two-liner so a simple redirect to isomorphism should do. Pascal.Tesson 06:45, 29 July 2006 (UTC)

I think better that it be deleted entirely than merged with isomorphism; it seems to me that the two concepts are of different species. But I've just spent a few minutes trying to give the article some content, and though it's still not perfect, I think it just needs to be improved, not deleted. Let me know what you think. Changbao 07:50, 29 July 2006 (UTC)

I vote do not merge. I agree with Changbao on this. Cryptomorphism seems like a philisophical idea rather than a mathematical concept. - grubber 06:26, 31 July 2006 (UTC)

Actually, I am also tempted to change my position here. The article is cute now. By the way, shouldn't there be at least a wikilink to isomorphism? The cryptomorphism seems to be more general but there are certainly many isomorphisms which could be deemed cryptomorphisms. Pascal.Tesson 06:33, 31 July 2006 (UTC)

Yes, I think a wikilink back to isomorphism is certainly appropriate. It's a curious article, and I enjoyed reading it, so I hope it doesn't get deleted. But I don't think it belongs with isomorphism. - grubber 15:49, 31 July 2006 (UTC)