Talk:Cryptomorphism

message: 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)
replies: text: 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)
replies: text: 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)
replies: text:  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)
replies: text: A cryptomorphism is not an isomorphism.  It is a non-obviously equivalent definition of the same object.  Thus, a matroid can be defined by bases, or rank, or duality, and these are not obviously equivalent.  A simple matroid is not the same as a geometric lattice, so they should not be called cryptomorphic (in my opinion).  Also, a group can be defined by division, instead of the usual operation of multiplication with id and inverses, and that could qualify as a cryptomorphism because it's not obvious to many mathematicians that such a definition exists.  Therefore, cryptomorphism is not a kind of isomorphism.  Zaslav (talk) 09:09, 3 August 2022 (UTC)
replies: text: And yet, White's matroid book does call that exact example a cryptomorphism. So there is a mismatch between the definition of cryptomorphisms in your head and in the literature. We should follow the literature here. Even for the standard examples of cryptomorphism (matroid independent sets vs matroid rank, say) we have different but equivalent mathematical objects (a family of sets vs a function from sets to integers). —David Eppstein (talk) 16:22, 3 August 2022 (UTC)
thread_title:  Proposed merge 

message: The article should stay. Chryptomorphism may not be in wide use in the maths community. But it is in use in arts. Should the article be aded to that category?
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http://artsciencefactory.fr/2011/02/04/par-gustave-dore-et-par-henry-holiday/#comments --DL5MDA (talk) 04:14, 29 March 2011 (UTC)
thread_title:  Arts 

message: Somewhere I read that if a kind of mathematical objects has several cryptomorphic definitions, it is a sign that this object is important.
We need to state this after we find a citation for this. VictorPorton (talk) 22:13, 7 October 2022 (UTC)
thread_title:  Cryptomorphism is a sign of importance 

message: The following is stated without any citation/sources:
 The word was coined by Garrett Birkhoff before 1967, for use in the third edition of his book Lattice Theory. Birkhoff did not give it a formal definition, though others working in the field have made some attempts since.
In the third edition of his book, Birkhoff talks about a "cryptoisomorphism" being a way of defining the same abstract algebra in a "nonpolyisomorphic way". He explicitly defines polymorphism, polyisomorphism and then cryptoisomorphism. The statement above is correct in that "Birkhoff did not give it a formal definition" in his lattice theory book. But there are multiple questions which are raised by the above quoted two sentences.
# How do we know it was coined before 1967? Did he write about it somewhere? Is there a source to this?
# Are there sources of "others working the field have made some attempts since"? Is it only in the matroid community? Is this coming from an algebraic community? Who are these people?
Thecaligarmo (talk) 07:23, 19 October 2023 (UTC)
thread_title:  On the etymology