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The word escapes me for some reason.

Here's a sample (jocose) sentence:

"He must have been a capable psychologist in some (???)."

Meaning - in a different life, perhaps.

I think it's a mathematical term. I may be wrong.

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    How do dictionaries define 'incarnation'? And how can the example sentence be considered to need a mathematical term (which your title question clearly requests?) – Edwin Ashworth Jul 3 '18 at 22:00
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    Please include the research you’ve done. Questions that can be answered using commonly-available references are off-topic. As are questions where at least some obvious research is not presented. – Edwin Ashworth Jul 3 '18 at 22:02
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    Did a thesaurus suggest any possibilities? How about 'in some other life' or 'in some former life'? – Mitch Jul 3 '18 at 22:29
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    Perhaps your title should be 'What is another term for “other incarnation,” “other form,” or “alternative version”, quite possibly also used in the mathematics domain?'? – Edwin Ashworth Jul 3 '18 at 23:20
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    The only math-y word I know that might apply is "permutation". – DerpDevil Jul 3 '18 at 23:23
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For something mathematical, consider iteration:

[Merriam-Webster]

1 : the action or a process of iterating or repeating: such as
a : a procedure in which repetition of a sequence of operations yields results successively closer to a desired result
b : the repetition of a sequence of computer instructions a specified number of times or until a condition is met — compare RECURSION
2 : one execution of a sequence of operations or instructions in an iteration
3 : version, incarnation · the latest iteration of the operating system

So:

He must have been a capable psychologist in (some / a previous) iteration.

It would be particularly appropriate in the context of reincarnation.

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universe

From Wikipedia:

a collection that contains all the entities one wishes to consider in a given situation

In your example:

He must have been a capable psychologist in some universe.

it would mean from a collection of psychologists and perhaps non-psychologists he is believed to be part of the subset of capable psychologists.

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"He must have been a capable psychologist in some parallel universe."

parallel universe

They call it the multiverse. It’s a cosmos in which there are multiple universes. And by multiple, I mean an infinite number. These uncountable realms sit side by side in higher dimensions that our senses are incapable of perceiving directly.

Yet increasingly astronomers and cosmologists seem to be invoking the multiverse to explain puzzling observations.

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