Talk:Pathological (mathematics)

untitled

Should this be moved to pathology (mathematics), per adjectives should redirect to nouns in the manual of style? Fredrik Johansson - talk - contribs 01:50, 8 February 2006 (UTC)

This should probably be an exception. The adjective "pathological" is much more common than the noun "pathology" in this context. Crust 14:57, 8 February 2006 (UTC)

Proposed merge with Well-behaved

For the same reason we have "Truth value" instead of separate "True" and "False" pages, and "Endianness" instead of separate "Little-endian" and "Big-endian". Keφr 13:55, 21 November 2013 (UTC)

The case of 'pathological' and 'well-behaved' is not as clear-cut as with true/false or little/big endian, as there are no exact definitions, and both concepts have their own connotations, their own context, etc. That being said, the two articles are short, so merging them would be quite easy. I anyone wants to go ahead, please. –Jérôme (talk) 19:21, 11 October 2014 (UTC)

Done95.199.150.64 (talk) 20:59, 5 January 2016 (UTC)

This might sound weird, but it's been 6 years after the initial proposal of merging, and the two articles have since grown longer. While the two are obviously related to each other, wouldn't it be better to separate them so that more details and examples could be dedicated in each article? (instead of having "Well-behaved" as a tiny section of "Pathological") Miaumee (talk) 18:43, 29 November 2019 (UTC)

Continuous functions are almost always nowhere differentiable, so why is the Weierstrass function atypical?

I find there to be a contradiction between the description and the example in this article. The description says that pathological properties are considered atypically bad (in which "bad" really has no mathematical sense, so one might retain that they are just atypical properties). But the prime example is a property (being nowhere differentiable) that continuous functions generically have, so this can hardly be qualified as an atypical property (for continuous functions). What gives? Marc van Leeuwen (talk) 13:12, 11 July 2019 (UTC)

Well yeah, mathematical objects are generically not typical... that's the case typically! ;-) --2607:FEA8:86DC:B0C0:1175:26A3:28DF:93F (talk) 17:34, 9 December 2021 (UTC)

non-euclidean geometry

For example, non-Euclidean geometries were once considered to be ill-behaved, but have since become common objects of study from 19th century and onwards. diff

My understanding is that spherical geometry was certainly an object of study prior to the 19th century, and that hyperbolic geometry was not considered pathological -- rather, it was not known to exist. The reference cited does not seem to contradict my understanding. --2607:FEA8:86DC:B0C0:541:CB0F:2EEA:D251 (talk) 23:15, 10 December 2021 (UTC)

References

This article should be placed under `Psychology'

I am a mathematician, and this article is not about mathematics. This article is about the psychology of learning mathematics. For example, this article discusses the `counter-intuitive' fact that there exists a continuous but nowhere differentiable function. The fact that this in `counter-intuitive' has little do with mathematics and much more to do with the humans and their cognitive capabilities. Perhaps more importantly, mathematical terms require mathematical definitions and the notion of "well-behaved" is not mathematically well-defined in this article.

I think it is correctly categorized as mathematical terminology. Despite imprecision, it is a term currently used by mathematicians, and it is not used in this sense outside of mathematics. Especially not in psychology, where it means something else! --2607:FEA8:86DC:B0C0:8D0C:FBB7:8669:25DF (talk) 19:00, 13 January 2022 (UTC)

majority of functions...

I cut the sentence "In layman's terms, the majority of functions are nowhere differentiable, and relatively few can ever be described or studied." First, I think that this is rather peripheral to the subject "pathological." Might be valuable if the article subject were "nondifferentiable functions."

But second, I don't think this is in any way "in layman's terms." I don't know if there even is a good explanation of what the term "the majority of functions" means "in layman's terms", much less what the phrase "relatively few" means. Geoffrey.landis (talk) 18:33, 31 August 2022 (UTC)

Given that all we have here is that the set of nowhere differential functions is residual, and there exist residual subsets of the reals with measure zero, the intuition of "majority" is flawed. (Personally, I think of residual as meaning "those functions are everywhere"; I view residual-ness as a strengthening of density that is stable under intersections). So yes, I support this removal. —Kusma (talk) 18:54, 31 August 2022 (UTC)