Timeline for Giving the same concept different names in the same paper
Current License: CC BY-SA 3.0
14 events
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| Oct 18, 2016 at 1:30 | comment | added | Todd Trimble | All that being said, of course I agree with the main thrust of other comments that often we do have two words for the same formal notion. Another example that come to mind is "directed graph" (in the categorist's sense, allowing multiple edges) as versus "quiver". Using one word or the other can be a clue as to what the speaker wants to do with it; people who habitually use "quiver" are likely to be somewhere in the neighborhood of representation theory and Hall algebras, etc. But this general point has been well covered. | |
| Oct 18, 2016 at 0:58 | comment | added | Todd Trimble | "I suspect you have missed the point: the different views of the object allow for different analyses and applications." Actually, Hans explicitly took this point into account in speaking of differences in interpretation; as I see it, he is asking for a sharpened mathematical description of the differences in semantics, less hand-wavy than appeal to robots and outputs. I think he's right as well in objecting to "quite similar": the two theories are indeed identical. To suggest otherwise is confusing. If the authors wish to distinguish between modellings, that's a different level of structure. | |
| Oct 18, 2016 at 0:03 | answer | added | usul | timeline score: 3 | |
| Oct 17, 2016 at 19:34 | comment | added | Gerhard Paseman | We both can agree on what a particular object (say a gun) is, but our perceptions of it can be quite different ( I may be holding it and viewing you through the site and wondering if the site needs adjusting, whereas you might be wondering whether it is loaded ). Without even reading the paper, I suspect you have missed the point: the different views of the object allow for different analyses and applications. Gerhard "Relax, It's Made By Nerf" Paseman, 2016.10.17. | |
| Oct 17, 2016 at 19:27 | comment | added | HeinrichD | I would say that these are two concepts, as explained by the authors, which just have identical or rather isomorphic implementations. Names and interpretations matter. Another example which comes to my mind is the definition of a combinatorial game as a (well-founded) set. The interpretation is that the elements of this set are the options of the game, which are games themselves again. I hope that we all agree that the concept of a combinatorial game is different from the concept of a set, though! | |
| Oct 17, 2016 at 18:50 | comment | added | Hans-Peter Stricker | I agree with you. In the more empirical sciences like physics and computer sciences this attitude (of intending the interpretation as part of the definition) is perfectly OK. So it's all a matter of declaring a paper to belong to "pure mathematics" or to "computer sciences"? | |
| Oct 17, 2016 at 18:44 | comment | added | Theo Johnson-Freyd | Hi Hans, I don't have good answers to your questions (if I did, I would have left an answer rather than a comment) and I agree that these are good questions. I just meant to flag that my impression is that phenomenon (of intending the interpretation as part of the "meaning" of the object) is common, especially in computer science, physics, etc. | |
| Oct 17, 2016 at 17:13 | comment | added | Hans-Peter Stricker | And further (in your lines): why and which progress gets made by recognizing that different structures can be modeled by the same mathematics. | |
| Oct 17, 2016 at 17:11 | comment | added | Hans-Peter Stricker | @Theo: My question is not about the importance of interpretation. And it is also clear to me that very different structures can be modeled by the same mathematics. My question is about how to reflect this. | |
| Oct 17, 2016 at 16:58 | history | edited | YCor |
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| Oct 17, 2016 at 15:56 | comment | added | Hans-Peter Stricker | But should not equal effort (in terms of formal precision) be made to distinguish the (different) intended interpretations compared to make the (identical) set-theoretic concept precise? (There seems to me some imbalance.) | |
| Oct 17, 2016 at 14:51 | comment | added | Theo Johnson-Freyd | I am not a computer scientist, but my (likely faulty) outsider's understanding is that interpretation is very important, and that much progress gets made when it is recognized that very different "objects" (meaning in particular different interpretations) are modeled by the same mathematics. In physics this is also true. | |
| Oct 17, 2016 at 14:12 | history | edited | Asaf Karagila♦ |
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| Oct 17, 2016 at 14:06 | history | asked | Hans-Peter Stricker | CC BY-SA 3.0 |