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The Modulo (ruby program pt.2)

I think I've finally gotten a hold of the modulo operator in Ruby. Modulo looks like this: % in programming and it shows up as one of the primary mathematical operations in Ruby.
To understand modulo I looked up the Wikipedia page first and found it no help at all save for one fact: It shows that different programming languages handle modulo differently. For some it's the divisor and for other the divorcée (or some such unintelligible mathematical term that looks like divorcée).

I asked a friend who is good at math and learned a cool new understanding of modulo only to learn that math has a whole bunch of them and none are the programming one. Great. Then I hit upon the Wikipedia page for the jargon of modulo. And suddenly it started to make sense. This really shows how learning modalities differ.  The technical mathematical terms and formulas did nothing to my understanding of the programming term modulo. The colloquial-language-based-use went a long way to clearing it up.

According to the Wikipedia entry, modulo jargon is used in a way to mean something is the same as something else except for an exception. Or to say some thing is more or less the same as another thing. So you could say the character "á" is the same as "a" modulo "accent." Or to use the Wikipedia example: "http and https are the same, modulo encryption." Or my favorite: "This code is finished modulo testing" - means "this code is finished except for testing". While this literary/colloquial use of modulo is not the same as the programming one, I just got it suddenly.

In Ruby modulo is like perfect subtraction or division with the exception of the result of modulo.  It is not the number after a decimal point in division (like I thought). If you think of division as serialized subtractions, modulo is what is left of the last subtraction. This site has a great explanation of this and a cool example of how we use modulo when calculating the time between a 24 hour clock and a 12 hour clock.

But here is the cool thing, while this programming use is nice, the jargon use is way better, since it allows for a cool division trick. You can do some cool things like 100/6 = 15 modulo 10. Like one hundred divided by six would be fifteen except for ten extra units. Instead of giving the absolute programming modulo, using any arbitrary number to increase computational speed. Let's say you have 97 people and you want do divide them into 7 equal groups (bear with me). Now let's say you are not supper fast at mental math like me and you want to do this in your head. Well you know 7 x 10 is 70 so you can say 97/7 = 10 modulo 27 (97-70). Then you do it again. 27/7 = 3 modulo 6. So all you need to have equal groups is one more person and you have 7 groups of 14 (10+3+1). And while this may sound longer than needed, it has one huge advantage in that you get closer and closer to the answer as you calculate 10 > 13 > 14.

Now if I could only figure out what happens with negative numbers...

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