Posted by: Alexandre Borovik | September 17, 2011

## The writing on the wall

For mathematical reasons which I explain below, I have looked up the expression “The writing on the wall” in the Wikipedia. It is, of course,  illustrated there by Rembrandt‘s ‘Belshazzar’s Feast‘, and, which nowadays sounds very topical, by a stanza from  Jonathan Swift‘s “The Run Upon The Bankers”:

A baited banker thus desponds,
From his own hand foresees his fall,
They have his soul, who have his bonds;
‘Tis like the writing on the wall.

The full text can be found at http://www.online-literature.com/swift/3501/ ; it is accompanied by a footnote from Dublin Edition of 1734:

This poem was printed some years ago, and it should seem, by the late failure of two bankers, to be somewhat prophetic. It was therefore thought fit to be reprinted.

And now back to mathematics: I have looked up Mene, Mene, Tekel u-Pharsin because I need an English word which characterises a collection of objects (think about a warehouse) in which objects of every kind are counted and their number is known and recorded. Inventoried? I need to use it in expressions like “inventoried group”, “inventoried field”, “inventoried ring”, “inventoried structure”, and many times on each page in a series of papers.

Can you suggest a better term? I would be most grateful.

And this pastiche is an update of the old theme, quite consonant with Swift:

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## Responses

1. Dear Alexander,

the most natural (and quite ancient) variant I would try for inventoried try would be “tallied”: a “tallied ring”, a “tallied set”, the “field A tallies strictly with the field B”.

2. Despite the fact that the word “index” is used so often in mathematics, you could try “indexed set” or “indexed ring”? Or maybe not.

• Upon further consideration, probably not a good suggestion:) Sorry.

3. “Catalogued”? I can’t think of any instance I’ve seen of “catalogue” used in mathematics, although I’m sure it’s already out there somewhere, with three or four different meanings depending on context.

“Catalogued group…”
“Given catalogues C1 and C2 on a ring R…”
“Let F be a catalogued field…”

4. I’d actually go with “inventoried”. “Tally” has a connotation of there being only one kind of thing, which is to be counted; natural numbers would suffice there. It sounds more like you’re talking about different “kinds” of elements of the same structure, and information kept about those kinds. That would be an inventory.