# merkwürdig stetige Reihe



## Löwenfrau

Hallo!

Diesen Satz klingt mir was komisch:


"Ich wollte auch hier auf die merkwürdig stetige Reihe von Lehnübersetzungen hinweisen: [Hebraic word (I can't reproduce it here because I don't know nor have the alphabet)], _chôneuton_, _Götze" _(Mauthner)

Er sagt "stetig", aber die Reihe hat nämlich doch nur drei Wörter... Ich glaube, das macht keine _stetige_ Reihe aus... Ich verstehe das Wort as "unendlich" (Engl. unending or continuous).

Auch merkwürdig: meint er damit "bemerkenswert" oder was?


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## Schimmelreiter

_the remarkably consistent series_


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## Löwenfrau

Ok for "remarkable" ("bemerkenswert"), but I have never seen "stetig" with the meaning of "consistent".

Duden says: "über eine relativ lange Zeit gleichmäßig, ohne Unterbrechung sich fortsetzend, [be]ständig, kontinuierlich", see http://www.duden.de/rechtschreibung/stetig

It says [be]ständig, which in English means stable, constant, but is not the same as consistent, in my view.
If one says that smthg. is consistent, I understand that it is well founded, it has a solid ground, it is coherent, etc.

I don't see how this fits in the context.


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## Schimmelreiter

zusammenhängend, lückenlos
http://woerterbuchnetz.de/DWB/?sigle=DWB&mode=Vernetzung&lemid=GS46066


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## Löwenfrau

Ok, now it makes sense, actually. Something that follows a regular pattern for such a long time and at such different places turn out to be consistent...


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## bearded

To Schimmelreiter
It seems to me that the current meaning of 'consistent' (especially in AE) is coherent or not contradictory of logic (e.g. a theory consistent with the facts), whereas in 'stetig' I do not feel that connotation, but only the meaning of repeated, uninterrupted.  If I am right, why not translate it with 'strangely constant'?


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## Schimmelreiter

bearded man said:


> in 'stetig' I do not feel that connotation, but only the meaning of repeated, uninterrupted.


Might your perception be influenced by the adverb _stets_?





bearded man said:


> It seems to me that the current meaning of 'consistent' (especially in AE) is coherent or not contradictory of logic (e.g. a theory consistent with the facts)


May I exceptionally quote myself:


Schimmelreiter said:


> zusammenhängend, lückenlos
> http://woerterbuchnetz.de/DWB/?sigle=DWB&mode=Vernetzung&lemid=GS46066







bearded man said:


> strangely


Mauthner, given when he lived and wrote, used _merkwürdig_ in its original sense here, I believe, which is of course _worth noticing_, which I rendered as _​remarkable/-ly._


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## bearded

To Schimmelreiter
Concerning merkwürdig you may well be right, but your interpretation of stetig does not convince me at 100%.  First, in the woerterbuchnetz there are several meanings for it, and second, I think that zusammenhängend is different from lückenlos:  the first is similar to coherent, the latter to constant (ohne Zeitlücken...). It is indeed difficult, and I am certainly influenced by 'stets'. I have no certainty, and you may be right on everything.


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## Schimmelreiter

So it's about whether it's a time thing. The _[Hebrew word] - __chôneuton - Götze_ series is about logic and the absence, in Mauthner's view, of any logical gap, isn't it, which prompted me to call this series _​consistent._


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## Löwenfrau

bearded man said:


> To Schimmelreiter
> It seems to me that the current meaning of 'consistent' (especially in AE) is coherent or not contradictory of logic (e.g. a theory consistent with the facts), whereas in 'stetig' I do not feel that connotation, but only the meaning of repeated, uninterrupted.  If I am right, why not translate it with 'strangely constant'?



strangely / curiously repetitive/ insistent/ relapsing/ repeat/ recidivist/ recurrent


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## Löwenfrau

Schimmelreiter said:


> So it's about whether it's a time thing. The _[Hebrew word] - __chôneuton - Götze_ series is about logic and the absence, in Mauthner's view, of any logical gap, isn't it, which prompted me to call this series _​consistent._



It's not only a time question, but also a space one. The various words might well be contemporaneous, but they have arisen at different places.


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## Schimmelreiter

I meant to say, in response to bearded man, that it was _not _about time but about logic, i.e. *lack* of contradiction = consistence.


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## manfy

Löwenfrau said:


> strangely / curiously repetitive/ insistent/ relapsing/ repeat/ recidivist/ recurrent


Naah, I think these words go a bit in the wrong direction.
It seems to me that Mauthner is aiming with 'stetig' at the meaning of 'not arbitrary' (in a temporal sense as well as semantic sense, which would normally be expected considering the big timeframe and those very different languages). Therefore 'constant/consistent/continuous' seem to match this German meaning pretty well.


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## Hutschi

In linguistics I heard "dialect continuum" (Dialektkontimuum) - It seems to have similar concepts for dialects.
https://de.wikipedia.org/wiki/Dialektkontinuum


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## Löwenfrau

to manfy: yes, I understand your point, I'm just likely to add that, in contrast to 'constant' and 'continuous', the 'consistent' option is a little bit "bolder", in the sense that it assumes a stronger, more particular interpretation of what Mauthner means. I think that 'constant' and 'continuous' can point to the same direction, but not necessarily, which gives the reader some freedom.

EDIT: I mean,

something that is constant and continuous can, besides, be consistent. But you don't necessarily have to draw that conclusion.


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## manfy

Hmm, maybe we should not look at the word "stetig" in isolation but evaluate the phrase "stetige Reihe". 
In German that can be seen as a loan expression from Mathematics (in English: continuous series) and it describes a series of data - and the resulting function y=f(x) thereof - that contains no discontinuities, i.e. the function explicitely excludes "Sprungfunktionen" (Heaviside step function).

In your OP you said that 3 words is not much of a series - that's true. But strictly speaking, every series of data with more than 1 element is a series which allows us to interpolate or extrapolate other data points, which in turn allows us to evaluate whether the known points are a random collection of points or whether they follow a pattern. 
And BTW, a series is not necessarily infinite (unendlich), hence your assumption in the OP is a misconception.

Of course, Mauthner converted "stetige Reihe" from its strictly mathematical definition into a similar definition that can be applied to his "series of 3 translations" (a true mathematical expression of these translations would be impossible, or at least nonsensical, because the value of meaning is subjective, hence mathematically not consistently quantifyable)

Sorry for the outpour of all this boring maths but maybe it helps you making a connection to a suitable Portuguese term


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## Löwenfrau

Nothing to be sorry for, your explanation only helps 

I think that 'continuous' is fine, although I'm now considering 'regular' too.


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## Schimmelreiter

I wouldn't call it a regular series since what would an irregular series be like? The noun would be "rule", and what rule would the regularity of the series have to be judged against?


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## manfy

I agree with Schimmelreiter! If you imply any correlation with Mathematics lingo like Mauthner did then be very careful with the terminology. Maths lingo is very specific and it cannot always be interpreted in a common sense way. The term regular/irregular (functions) has already got something to do with periodicity, I think.
Here's the Portuguese Wiki page on continuous functions. If you change the term 'function' to 'series' you have the official Portuguese name for Mauthner's phrase "stetige Reihe".

Earlier I was thinking, maybe Mauthner made an actual etymology chart for this word and that's how he came to the conclusion of 'merkwürdig stetige Reihe'. That means, maybe the 3 examples he stated were just representative samples but in reality he compared translations of 6-10 core languages. This would make a reasonably conclusive mathematical sample size which also justifies a claim of 'stetige Reihe'.
I think, I've seen this type of chart before and it is a good aid to assess and substantiate word etymology claims.
You just create an X/Y-chart with X-axis as time and on the Y-axis you define (your own subjective) categories of meaning. Once you enter the translation of the word in each core language at the first known time it appeared, you get a largely self-explanatory timeline of when and where it originated and which language borrowed its translation from what other language.


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## bearded

To Manfy
Re your mathematical explanation of 'stetige Reihe', is it a sure thing that, at the time when Mauthner wrote what he wrote, continuous series and functions and such things already existed/had been discovered, and that he knew them ? Sorry for my naive question: it only arises out of my ignorance in this field.


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## berndf

In mathematics, there is no such thing as a _stetige Reihe_ or _stetige Folge_ (A _Reihe _is a _Folge _constructed incrementally, e.g. the Reihe 1+1/2+1/3+1/4... is a way to construct the _Folge _1, 1.5, 1.6666..,  1.916666..., ...). The term _stetig_ only applies to functions with continuous domains and codomains and does not apply to functions with discrete domains, which every _Folge _or _Reihe_ by definition of the term is.


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## manfy

bearded man said:


> Sorry for my naive question: it only arises out of my ignorance in this field.


No worries, it's a valid question.
Mauthner published his first edition of that dictionary around 1910, so he must have written it between 1900-1910.
Even though I don't know the exact details about history of mathematics, I can guarantee you that this concept of data series and functions was known in the very same way back then as we know it now. That's because these concepts are the very basics of higher mathematics and the majority of it was created by the ancient greeks (timeframe of Plato and Aristotles).
The next big step was around 17th/18th century, the beginnings of industrialization and the modern world -- and only that is the beginning of that type of mathematics where even highly educated academics outside the field would have to say: huh? say what??


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## manfy

berndf said:


> In mathematics, there is no such thing as a _stetige Reihe_ or _stetige Folge_ (A _Reihe _is a _Folge _constructed incrementally, e.g. the Reihe 1+1/2+1/3+1/4... is a way to construct the _Folge _1, 1.5, 1.6666.., 1.916666..., ...). The term _stetig_ only applies to functions with continuous domains and codomains and does not apply to functions with discrete domains, which every _Folge _or _Reihe_ by definition of the term is.


Hmmm, but Reihe and Funktion are practically the same thing! 'Reihe' is a series of actual data points which is the basis for the formulation of a mathematical function (i.e. the mathematical description of the progression of this series of data within a multidimensional space), defined for a specific (but freely selectable) domain (with freely definable limits), isn't it?


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## berndf

manfy said:


> Hmmm, but Reihe and Funktion are practically the same thing! 'Reihe' is a series of actual data points which is the basis for the formulation of a mathematical function (i.e. the mathematical description of the progression of this series of data within a multidimensional space), defined for a specific (but freely selectable) domain (with freely definable limits), isn't it?


A_ series_ (_Reihe_) is a _sequence_ (_Folge_) that is defined incrementally. A _sequence _is a real-valued _function _(_Funktion_) with _domain_ (_Definitionsbereich; Urbildmenge_) *N*. The concept of _continuity _(_Stetigkeit_) applies to real-valued functions with domain *R* (complex-valued functions with domain *C*).

The concept can be generalized to functions between topological spaces. If the domain space is discrete (which *N* is) that every function into any topological space is always continuous* and the concept becomes meaningless.
__________
* A function between two topological spaces f:X->Y is continuous, iff the inverse image of every open set within Y is open in X. In a space X with discrete topology, every sub-set of X is open and, hence, f is trivially continuous.


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## Hutschi

Hi, I think that "Reihe" and "stetig" in mathematics have strict definitions.
But Mautner did not mean these.
He used the concepts as a kind of metaphor and in a more colloquial sense.

"Stetig" means that the parts are connected by laws of language development and do not show behaviour as if formed by a dice.


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## berndf

Hutschi said:


> But Mautner did not mean these.


Exactly. That's what I tried to prove by pointing out that the term _stetige Reihe_ would be meaningless as a mathematical term.


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## manfy

I fully agree with you guys! I don't think that Mauthner approached his etymology research in a purely mathematical form.

But since this level of mathematics is taught heavily in every university prep-school (e.g the second term of Gymnasium), I am quite sure that Mauthner was familiar with these mathematical concepts and methods. Here I'm assuming that the system for higher education in the late 19th century was reasonably similar to the system post WW2 -- and looking at Einstein's education which is fairly well documented, this assumption is reasonably safe. 
Therefore I think, the analogy between etymological development of one word over time and a series of mathematical or statistical values over time is not really far-fetched, but plausible.


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## Löwenfrau

Yes, exactly: He used the concepts as a kind of metaphor and in a more colloquial sense.

When I suggested "regular" for "stetig", I was thinking in this very sense, only as a metaphor, a very colloquial and loosely metaphor... 
I don't see why "regular" could be more problematic than "continuous", as manfy said before. Actually, I think that, in the context of words and etymological speculation, it fits better...

But guys, as to your whole mathematical excursion, I have to tell you: In mathematics, I'm a big and round zero


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