Modulo (jargon)
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- For the mathematical definition of modulo and other usages, see modulo.
This article discusses the usage of the term modulo as a form of mathematical jargon. It does not discuss the precise meaning of the mathematical concept.
The word modulo was introduced into mathematics in the book Disquisitiones Arithmeticae by Carl Friedrich Gauss in 1801. He defined two numbers to be congruent (i.e., the same) modulo a third number, if the first two numbers give the same remainders upon division by the third number. This usage is still common in modular arithmetic. So, one can say
- 13 equals 63 modulo 10
to mean
- 13 and 63 differ by a multiple of 10
However, the word modulo has acquired several related definitions with time, many of which have become integrated into popular mathematical jargon.
Generally, to say:
- A is the same as B modulo C
means, "more-or-less", as in:
- A and B are the same except for differences accounted for or explained by C.
The up to concept is often talked about this way, using modulo as a term alerting the hearer. The use of the term in modular arithmetic is a special case of that usage, and that is how this more general usage evolved. The operation of "modding out by C" is that of identifying with each other any two things that are the same modulo C.
Here are several ways in which modulo is used.
- "http and https are the same, modulo encryption." - means "the only difference between http and https is the addition of encryption".
- "These two characters are equal." "You mean, equal modulo case." - indicates that the first speaker's words are true only for a relaxed sense of equality. In computing, letter case is sometimes treated as significant, and sometimes not.
- "The two students performed equally well on the exam, modulo some minor computational mistakes." - means that the two students demonstrated an equal understanding of the material and its application, but one of them lost some points for minor computational mistakes.
- "This code is finished modulo testing" - means "this code is finished except for testing". Since testing is generally considered quite important, whereas in mathematics the use of modular arithmetic generally ignores the difference between modulo-equal numbers, use of a phrase like this might be deliberate understatement.
