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There is a series of Latin and pseudo-Latin phrases used in a scientific context (mostly in the life sciences) describing how and where a study was carried out (sorted by frequency):

I am now looking for a concise analogous phrase to describe that a study was carried out with a mathematical model. I considered and was not happy with the following options so far:

  • In simulacris – may as well apply to animal models, in vitro models, or other experimental models.

  • In mente – implies that the entire study was carried out without the help of a computer or even paper.

  • In silicio – excludes studies or parts of studies that were carried out in the mind or on paper.

  • In theoria – is more narrow than in simulacra, but still contains qualitative scientific theories or models, respectively.

  • In mathematica – Does not capture the modelling aspect very well; I might as well be engaging in pure mathematics. Moreover, it sounds as if I forgot to capitalise Mathematica.

  • In simulacris mathematicis – Fits, but lacks elegance.

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    Where would you like to use this phrase? If the context is scientific, I would put precision before elegance (and probably choose an English expression instead of a Latin one if you are writing in English). The preposition in is not such a good fit here, so I would use pure ablative, eg. simulacro mathematico, if I had to make the choice. – Joonas Ilmavirta Feb 25 '16 at 7:47
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    @JoonasIlmavirta: Precision is not everything in a scientific context. If I describe my studies in detail, I would not use a Latin phrase. But if I have to put studies in context, using a Latin phrase may underline the level or perspective I am talking about, in particular if I use the numerous existing parallels. The term in silico was established for a reason. – Wrzlprmft Feb 25 '16 at 7:55
  • I was about to suggest "simulatio", but no, wait, that also means "deception" and "scam" -- probably not what you want. – Fund Monica's Lawsuit Feb 25 '16 at 18:08
  • in silico apparently took hold in English, but the correct L. would be in silice. – kkm Jul 22 '18 at 2:00
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Although it is a bit oblique, I'll put up

in harena

because it provides a natural way to work things out by hand, but involves the use of a tool, and so might easily extend to the use of computers more easily than would in mente. If I recall correctly, it is conjectured that geometers would have worked out diagrams in tamped sand.

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    This is an amazingly good metaphor, really profound! I am wondering if harena is really idiomatic for the writing sand, which would more commonly be pulvis. Cf famous Cicero story of Archimedes (pulvis et radius), Persius secto in pulvere metas, Livy in pulvere describere. I do not recall any Classical use of harena in this sense, though. – kkm Feb 26 '16 at 3:55
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    There is a nice hidden feature here if you consider what sand is made of chemically. – Wrzlprmft Feb 26 '16 at 5:49
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Given that this is the Vicipaedia article on computer models, I'd suggest:

In simulatione

It doesn't quite fit -- like you pointed out -- but it's the best word I can find. It means "model", seems to have a connotation of "computer" or "mathematical", and is short enough.

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