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I came across this sentence in the American Heritage Dictionary, but still do not understand it.

This proposal is the best so far, modulo the fact that parts of it need modification.

The definition of modulo provided is correcting or adjusting for something, as by leaving something out of account.

Please elaborate on the meaning of modulo the fact. Does it mean the same as the following?

This proposal is the best so far, but note what parts of it still need to be modified.

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The third meaning in wiktionary with the example "All mammals, modulo the monotremes, give birth to live young" is rather strange since it suggests except for a specified exception, which is not what I would regard as the standard meaning: I would always expect modulo to mean similar in a specified fashion. – Henry Jun 5 '12 at 10:49
J.R.: I've never come across this usage, and it's not in any of my printed dictionaries. On such matters I wouldn't trust Wiktionary either - it's obviously a new (ignorant, imho) usage loosely based on the mathematical sense (as familiar to programmers the world over, today). I can transparently read the intended meaning as "except", but I'd make the mental side-note "writer is a wally". – FumbleFingers Jun 5 '12 at 11:23
The OED offers 'In extended use. (a) With respect to an equivalence defined by (some feature), disregarding differences indicated by (some unimportant feature); (b) taking into account (a particular consideration, aspect, assumption, etc.).' There are supporting citations from 1953 to 1992. But I too have never come accross it, and can't think why any writers would want to use it, other than to show that they know it. – Barrie England Jun 5 '12 at 12:01
@Barrie: My (bent) electronic OED, which says it's 2nd Ed. Vers.4.0 (2009), contains nothing about this usage. Just the standard definition "With respect to a modulus of", and supporting examples thereof. This one here strikes me as daft. – FumbleFingers Jun 5 '12 at 12:25
up vote 14 down vote accepted

The pattern

X modulo Y

is an informal but common parlance in technical, especially mathematically, oriented talk. It is used to mean informally 'X, ignoring Y'. For example,

"The rocket design was flawless, modulo the toxic waste produced by its fuel."

The meaning is inspired by, but not perfectly corresponding to, the arithmetic modulo function (for example, clock-time addition) which when suitably abstracted involves 'collapsing' all items of a set into the special items of the set, so that the full set does not need to be dealt with (this is where the associated meaning of 'ignoring' comes from).

In your interpretation "note what parts of it still need to be modified", the 'modified' part is irrelevant. 'Modulo' is pragmatically "I'm telling you about the most important part (the X), but remarking on the existence of some part that might be important for other reasons but under the current context we want to ignore (the Y)".

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I only see this usage from academics with a background that includes England. It is used to mean the opposite of except - some part of the set is included, not excluded, and you're saying that you're including it even though some people might not. It isn't a substitute for but or except, because those would be about excluding something from the set. It might be closer to even though.

In math, modulo is the remainder after dividing, so 5 mod 2 is 1. In words, it's something like even after accounting for. However, it has been heard by generations of people who aren't sure what it means, don't want to ask, and feel that smart people use it. Those people tend to use it as except or but, meaning that you probably can't be entirely sure any more what someone means when they use it.

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I started to make a comment, but it seemed worthy of a full answer. However, my answer is just extrapolation, not knowledge of actual use like yours, so I'm voting this answer up. – T.E.D. Jun 5 '12 at 12:26

The OED3 has mod as a preposition dating from 1854, and modulo as a preposition dating from 1887 — but those are the more purely mathematical senses, not the extended senses that seem to crop up in the 1950s.

However, programmers and perhaps others regularly use mod or modulo in its extended sense to mean “save/except for”, or “without”, or “minus”. It’s to exclude something. This isn’t a mathematical use, although it may be a form of shop jargon.

Again, it is by no means uncommon in programmer circles, although I don’t know that I’ve myself used it in formal writing.

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Modulo is useful in computers for getting a number that can be no bigger than the modulus. So if it were me, I'd take "modulo" in this sentence to mean "limited by".

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Here's a use of 'modulo' by a mathematician working on the four-colour theorem quoted in Msrk Walters, "It Appears That Four Colors Suffice: A Historical Overview of the Four-Color Theorem (2004):

Shortly after testing the final configuration for reducibility, Appel celebrated the success by etching the statement ‘Modulo careful checking, it appears that four colors suffice’ onto the department’s blackboard.

This follows the general sense 'A mod B' being 'A seems generally true but for B' but B is not necessarily an exception, but something to bear in mind.

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