Meaning of “modulo the fact”

Question

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.

Answer 1

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)".

Answer 2

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.

Answer 3

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.

Answer 4

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".