I have seen in this mail that the suggestion of Taylor and Johnstone to replace cartesian and cocartesian maps by prone and supine ones begins to be accepted. When I first saw that suggestion, I was so amazed that I thought it was a joke, and not such a good one. I still hope it is no more than that. But, just in case, and before it is too late, I want to say that I am very strongly opposed to such changes for many reasons: linguistic, mathematical, and ethical, which I am ready to explain in detail if I am asked to do so.
I very strongly agree with J. Benabou's comments about "prone" and "supine", and P. May's opinion that "I'd like category theory no longer to be regarded as nonsense in this country --- it still is in many quarters, as I could easily prove --- and such terminology is not exactly helpful to the cause!" I recall P. Johnstone that he himself named his book "Elephant Book" because every body has different version of what a topos is, reflecting only one of the many aspects of the concept. Names like "Prone" and "Supine" correspond (with luck) to only one of the many aspects of the concept of cartesian and its dual (in a sense) cocartesian. Also, there is a clear ethical aspect involved when a stablished terminology that has been historically introduced by particular people suffers a move to be eliminated and reeplaced by another. But, coming back to the question above, i am also against the habit to name a new mathematical concept with words that have a precise meaning in everyday language (as prone, supine, etc). Presisely, I do not know what does it mean exactly "Cartesian" (has something to do with Descartes ...), but I know presisely what it is a "Cartesian arrow" (in mathematics). Colorful terminology taken from everyday language is an strong indication to serious mathematicians that the subject should no be taken seriously (see for example the claims of "Catastrofe Theory" as opposed to the sober "Classification of singularities of C-\infty mappings", and a lot of similar examples). As P May points out, " . . . such terminology is not exactly helpful to the cause!". The meaning of a mathematical concept should be given by the concept itself, and not by the connotation that its name has in everyday language.
Without taking sides on the prone/supine terminology question, I do have a strong reaction to the Benabou/May/Dubuc concern that respect for a field is undermined by its adoption of frivolous terminology. This may be a valid concern for a young field like category theory, but for a more mature subject such as physics, a more relevant concern is the undermining of the ability to poke fun at oneself by the fear of not being taken seriously. Has the adoption of frivolous nomenclature for quarks ("strange," "charm," "beauty" and even "quark" itself) diminished in any way the world's respect for quarks and their investigators? And what of computational topology? Should we turn a blind eye to whether Scott is sober, and substitute a more genteel euphemism for his bottom? Vaughan Pratt
Vaughan Pratt writes:
Without taking sides on the prone/supine terminology question, I do have a strong reaction to the Benabou/May/Dubuc concern that respect for a field is undermined by its adoption of frivolous terminology.
This may be a valid concern for a young field like category theory, but for a more mature subject such as physics, a more relevant concern is the undermining of the ability to poke fun at oneself by the fear of not being taken seriously.
Has the adoption of frivolous nomenclature for quarks ("strange," "charm," "beauty" and even "quark" itself) diminished in any way the world's respect for quarks and their investigators?
There indeed are drawbacks whenever scientific terms are contrary to the centuries old tradition not taken from Greek or Latin languages (that, thanks to their very regular and flexible system of word formation are so suitable for taxonomies) shared by many cultures. For one thing, words of existing languages are not in one to one mapping, and then a term from contemporary language may be not culturally neutral (consider silly naming wars for transuranium elements). On the other hand, I stopped using "co-product" after more than one person with the background in classical languages read it as "copro-duct".
And what of computational topology? Should we turn a blind eye to whether Scott is sober, and substitute a more genteel euphemism for his bottom?
Vaughan Pratt
Nikita.
We should not put everything in the same bag !! "strange," "charm," "beauty" and even "quark" itself are beautiful and poetic names to refer to objects or concepts which precisely we do not want to associate any precise meaning in everyday language, and on the other hand, the objects or concepts are introduced whith those names. "prone/supine" are all the contrary, they intent to reflect in everyday language just one aspect of an existing concept which has many, and more important, they are used in place of a well stablished name. all this has nothing to do with "young field" as opposed to "mature subject" silly names (if any) in physics would be as bad as in any other subject do not confuse things, I found the "Scott is sober" an exelent example of humor that does not undermine respect for the field. Another exelent example that comes to my mind is M. Barr's "The point of the empty set" edubuc
Without taking sides on the prone/supine terminology question, I do have a strong reaction to the Benabou/May/Dubuc concern that respect for a field is undermined by its adoption of frivolous terminology.
This may be a valid concern for a young field like category theory, but for a more mature subject such as physics, a more relevant concern is the undermining of the ability to poke fun at oneself by the fear of not being taken seriously.
Has the adoption of frivolous nomenclature for quarks ("strange," "charm," "beauty" and even "quark" itself) diminished in any way the world's respect for quarks and their investigators?
And what of computational topology? Should we turn a blind eye to whether Scott is sober, and substitute a more genteel euphemism for his bottom?
Vaughan Pratt
On Dec 29 2005, Vaughan Pratt wrote:
Without taking sides on the prone/supine terminology question, I do have a strong reaction to the Benabou/May/Dubuc concern that respect for a field is undermined by its adoption of frivolous terminology.
Dear Vaughan, as everybody has a say. Just my views. I prefer some nomenclature that sounds mathematical, rather than based on the name of a friend or a private joke. (may be i don't understand all the jokes ?) Also in any case one should avoid renaming existing concepts, that is just not fair. Good opportunity to wish happy new year to everybody.
I have been asked why I reacted to the intended reeplacement of the names "cartesian and cocartesian" by "prone and supine". I have given several reasons, but the one underlying the whole issue is the following: The reason is that since a long time I have been worried about the ghetto (in the sense of being isolated from the rest) characteristic of a certain category theory community (or group of people). And P. May has reacted concerning "prone and supine" probably because of reasons related to this. The mathematical community have been using "cartesian and cocartesian" since always, and the introduction of "prone and supine" inside this group will confirm even more the isolation. Examples abound, see M.Barr introduction of "Molecular topos" to replace Grothendieck's "Locally connected topos". No matter how many linguistic points in favor a given name may have (like prone and supine), to replace a well stablished name intoduced by a great mathematician (or school of mathematics) only puts you in ridiculous. P. May probably was feeling somehow that this will be extended by the mathematical community to all category theory practicioners. I profit by this mail to mention that concerning the concept "final" and "initial", I am happy (and not surprised) to learn that these words have been used since a long time to indicate the same categorical concept that myself, and will certainly refer to the indicated bibliography to further justify my use of these words.
participants (5)
-
Eduardo Dubuc -
jean benabou -
Nikita Danilov -
Vaughan Pratt -
vs27＠mcs.le.ac.uk