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What is a word for recursion/nesting of an entity in English ? I'm looking for a word that replaces the colloquially used -ception suffix. A generic term that encapsulates all nested attributes. For instance:

word - abbr is the abbreviation of abbreviation
image - (Droste effect) a wall with a hanging picture of the wall with the hanging picture
Eg: Ummagumma album art , Droste Cacao
math - (recursion) function of a function Eg: f(f(x))
object - two mirrors placed facing each other
abstract - dream within a dream

Preferably a word or a phrase, but any other way to convey the same is also welcome. The French seem to have covered all the expressions out there. However, I'm looking for the English counterpart of what the French call mise en abyme.

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    Fractals have a property known as self-similarity; Hofstadter famously explored such recursive ideas in Godel, Escher, Bach, and gave a name to a certain, special class of such tangled hierarchies: the strange loop. – Dan Bron Jul 16 '15 at 18:19
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    Please do not invoke the Sith Lords: nobrv8! – tchrist Jul 16 '15 at 18:43
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    Would English have borrowed the term mise en abyme if we already had a good word for it? – Peter Shor Jul 16 '15 at 18:59
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    I don't think "mise en abyme" covers all your examples. They don't all cover an infinite loop. – ermanen Jul 16 '15 at 19:32
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    @PeterShor: Yes I was looking in English, I didn't look deeper, you are right :) Thanks for the details. I didn't mean where the name comes from, its meaning refers to infinity: "placed into abyss" – ermanen Jul 16 '15 at 23:50
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The term is infinite regress.

An infinite regress in a series of propositions arises if the truth of proposition P1 requires the support of proposition P2, the truth of proposition P2 requires the support of proposition P3, ...

Infinite regress in optics is the formation of an infinite series of receding images created in two parallel facing mirrors.

Infinite regress in consciousness is the formation of an infinite series of "inner observers" as we ask the question of who is observing the output of the neural correlates of consciousness in the study of subjective consciousness.

From Wikipedia, the free encyclopedia

Notes

  1. The expression infinite regress has a wider application than recursion. This is because recursion has an implication of traversing a procedure. Infinite regress can happen naturally without human intervention or even human existence.

  2. In the case of a dream within a dream, the regression will presumably not be infinite - in that case I think nesting is a perfectly good answer. This allows for a finite number of, possibly different, dreams within a dream.

  • It doesn't have to be infinite but there is infinite recursion also. And "recursion" has a wider application. It covers all his examples. – ermanen Jul 16 '15 at 18:47
  • @ermanen - Thanks for your comment (I didn't down-vote you by the way) I would say that recursion implies self-similarity. If I dream that I dream that I dream that I wake up, then okay. However I might dream that I can fly and in that dream have a dream that I can walk on water. That would be nesting rather than recursion. – chasly from UK Jul 16 '15 at 19:30
  • Yes but it is not the question. You are talking about a different concept in your example. And for the downvote no worries, this is the hour of my fans. – ermanen Jul 16 '15 at 19:34
  • This is interesting – Jimmy Jul 16 '15 at 22:41
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It is called recursion.

Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other, the nested images that occur are a form of infinite recursion.

The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, in which it refers to a method of defining functions in which the function being defined is applied within its own definition. wikipedia

Recursion doesn't only apply to maths and it covers all your examples.

  • If 'recursion' is the answer, surely it's general reference, as OP mentions it and should have checked in Wikipedia.. – Edwin Ashworth Jul 16 '15 at 18:31
  • I wasn't aware of the linguistic use of recursion. Back when I was learning recursion, Wikipedia had only the article on computing. – Jimmy Jul 16 '15 at 22:40
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A colloquial term that is used for the kind of nesting described is the familiar matryoshka doll (A doll within a doll within a doll, etc.). From the Wikipedia article:

Matryoshkas are used metaphorically, as a design paradigm, known as the "matryoshka principle" or "nested doll principle". It denotes a recognizable relationship of "object-within-similar-object" that appears in the design of many other natural and crafted objects.

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