"Quick" etymological fact about what mathematicians in English call Manifolds:
If one would translate Riemann's original German word for them, "Mannigfaltigkeit", it would translate to "manifoldyhead", or, more understandable to the speaker of Modern English:
Manyfoldyhood.
(Think of -head as in "Godhead", not as in "Brotherhood", in the same sense that the "ring" in "algebraic ring" refers to "ring" in the sense of "smuggler ring", not in the sense of "gold ring". The two suffixes merged in English, and have very different and rather complex etymological origins.)
While this word sounds somewhat ridiculous and perhaps a bit infantile in English, it, in my opinion, conveys what we mean by them significantly better.
Clifford tried to accommodate Riemann's highly specific word choice in his translation, as Jost notes:
"The English of Clifford may appear somewhat old-fashioned for a modern reader. For instance, he writes “manifoldness” instead of the simpler modern translation “manifold” of Riemann’s term “Mannigfaltigkeit”. But Riemann’s German sounds likewise somewhat old-fashioned, and for that matter, “manifoldness” is the more accurate translation of Riemann’s term. In any case, for historical reasons, I have selected that translation here."
Unfortunately, neither Jost (a native German speaker!) nor Clifford realized that English can and does accommodate Riemann's exact meaning directly.
To make a comparison which might require quite a bit of German knowledge beyond high school education to describe in exact linguistic terms, but which native speakers should hopefully find intuitive to distinguish (I at least, do):
Translating "Mannigfaltigkeit" as "Manifoldness" seems equal to mistranslating "Geheimnis" as "Secrethood" and "Geheimheit" as "Secretness", whereas the opposite pairing would yield an accurate (albeit not necessarily immediately apparent—in terms of the differences between the two—to the English native speaker, unless explicitly pointed out) translation. So much for the last suffix, but that still leaves insertion of the one before it (' * foldy * ' instead of ' * fold[( * )]' unclear.)
One may observe the difference involved there by a converse example, also involving "Geheim", as well as the root word of it, "Heim", by dragging forth a rather rare and archaic—but none the less highly likely intuitive to the native speaker—word:"Geheimig". Whose meaning starkly differs from both "Geheimnis" and "Geheimheit".
For further language related hijinks related to /Manyfoldyhoods/, see:
A) The Dutch word for them, which would back translate to "Variety"; and
B) This quote by Poincaré:
"I prefer the translation of Mannigfaltigkeit by multiplicity, because the two words have the same etymological meaning. The word set is more adapted to the Mannigfaltigkeiten considered by Mr. Cantor and which are discrete. It would be less adapted to those which I consider and which are discontinuous."
(As I don't speak French, I can't make much of any statements about the accuracy about the etymological claim by Poincaré, so I'll close with another Poincaré quote instead:
" Mathematics is the art of giving the same name to different things."
indicates to me that -ness is exactly the correct translation of Mannigfaltigkeit, since in the instance of godhead a accurate synonym would be godliness (and in the instance maidenhead maybe maidenly).
regardless in english manifold already exists as an adjective and probably a good translation of the original german (if i'm to understand you correctly) would be to simply describe a space as manifold rather than a manifold.
>indicates to me that -ness is exactly the correct translation of Mannigfaltigkeit, since in the instance of godhead a accurate synonym would be godliness (and in the instance maidenhead maybe maidenly).
Strictly speaking, if one entertains the distinction involved here, "Godhead", as a noun, serves as a hypernym to "God" and "Goddess"; and "Godheads" as a hypernym to "Gods" and "Goddesses", which neither "godness", "godessness", "godliness" nor "godessliness" do. This makes sense, as "Heit" used to function (and in some very rare German dialects supposedly still does) as a separate noun, unlike "-nis" and "-ness". Does that help make the distinction between the two suffixes clearer?
(Note: You left open the matter of -ig and -y.)
>would be to simply describe a space as manifold rather than a manifold
Correct, you got that right, however, I think that talking about spaces in this way doesn't so much serve as a substitutive translation but as a consequence of the distinction involved - coming hand in hand, basically.
i don't speak german at all (outside of what i've been exposed to in the sciences (ansatz, eigen, etc.) so the nuanced distinction is not clear to me (albeit i can take it on faith visavis your translation to english) but i'll say that i appreciate your bit about rings and varieties (names of objects whose relationship to the objects i've always been curious about - in the case of algebraic ring i always assumed it had something to do with closure). thank you.
If one would translate Riemann's original German word for them, "Mannigfaltigkeit", it would translate to "manifoldyhead", or, more understandable to the speaker of Modern English:
Manyfoldyhood.
(Think of -head as in "Godhead", not as in "Brotherhood", in the same sense that the "ring" in "algebraic ring" refers to "ring" in the sense of "smuggler ring", not in the sense of "gold ring". The two suffixes merged in English, and have very different and rather complex etymological origins.)
While this word sounds somewhat ridiculous and perhaps a bit infantile in English, it, in my opinion, conveys what we mean by them significantly better.
Clifford tried to accommodate Riemann's highly specific word choice in his translation, as Jost notes:
"The English of Clifford may appear somewhat old-fashioned for a modern reader. For instance, he writes “manifoldness” instead of the simpler modern translation “manifold” of Riemann’s term “Mannigfaltigkeit”. But Riemann’s German sounds likewise somewhat old-fashioned, and for that matter, “manifoldness” is the more accurate translation of Riemann’s term. In any case, for historical reasons, I have selected that translation here."
Unfortunately, neither Jost (a native German speaker!) nor Clifford realized that English can and does accommodate Riemann's exact meaning directly.
To make a comparison which might require quite a bit of German knowledge beyond high school education to describe in exact linguistic terms, but which native speakers should hopefully find intuitive to distinguish (I at least, do):
Translating "Mannigfaltigkeit" as "Manifoldness" seems equal to mistranslating "Geheimnis" as "Secrethood" and "Geheimheit" as "Secretness", whereas the opposite pairing would yield an accurate (albeit not necessarily immediately apparent—in terms of the differences between the two—to the English native speaker, unless explicitly pointed out) translation. So much for the last suffix, but that still leaves insertion of the one before it (' * foldy * ' instead of ' * fold[( * )]' unclear.)
One may observe the difference involved there by a converse example, also involving "Geheim", as well as the root word of it, "Heim", by dragging forth a rather rare and archaic—but none the less highly likely intuitive to the native speaker—word:"Geheimig". Whose meaning starkly differs from both "Geheimnis" and "Geheimheit".
For further language related hijinks related to /Manyfoldyhoods/, see:
A) The Dutch word for them, which would back translate to "Variety"; and
B) This quote by Poincaré:
"I prefer the translation of Mannigfaltigkeit by multiplicity, because the two words have the same etymological meaning. The word set is more adapted to the Mannigfaltigkeiten considered by Mr. Cantor and which are discrete. It would be less adapted to those which I consider and which are discontinuous."
(As I don't speak French, I can't make much of any statements about the accuracy about the etymological claim by Poincaré, so I'll close with another Poincaré quote instead:
" Mathematics is the art of giving the same name to different things."