Modular Equivalencies

Modularity is a term from math, but everybody in the world has a simple working understanding of modularity. In math, the first few lessons in Number Theory are the initial lesson in modular math. Modular math starts with a base, and the "answers" are basically the remainders when the base is divided out. I don't want to spend too much time on this, but here's a quick example. We'll use 3 as a base. So, pretty much, there's a universe where the only members are 0, 1, and 2. The expression 14 mod 3 is a request for simplification, so, 14 = 3 (4) + 2, where the number in parentheses doesn't matter...it's like dropping out multiples of of the base. In a base 3 world, 20 = 17 = 14 = 11 = 8 = 5 = 2, and 2 is the member. Notice that all multiples of 3 are equal to 0.

For people savvy with computers, binary is a modular mathematical system, with a base of 2. In this system, the set is {0, 1}, which eludes to on/off, yes/no, even/odd, the most basic this-or-that type of system.

Another type of modular system even more people are rather familiar has a long set that includes February 10th and March 30th and April 13th and May 18th and September 21st. This is the modular equivalency we call "Friday" in the year 2012.

Any repeating cycle can be seen as a modular equivalency. Normal analog clocks, and our non-military-time system is another easy example.

Since I'm a math guy, I have a very close and intimate understanding of modularity in general, and have been seeing it in living nicely in the larger surrounding world.

The first case of this was when we were living in Bed-Stuy, in the apartment on Halsey. Halsey was a two-way street, rare for those streets in that neighborhood. That meant, though, that it was a little more main, and would have a bus line running on it. Oh how I remember the buses. Our apartment was between Patchen and Malcolm X, which were two of the more 'avenue' like streets. In this case, Patchen was one of the many residential avenues, and Malcolm X was one of the few commercial north-south thoroughfares. That meant that Malcolm X Blvd also had a bus line.

The bus that ran on Halsey was the B26, and the bus that ran on Malcolm X was the B46. I always felt like writing a letter back to Kent Morrison and the Poly math department joking that I lived at the confluence of the modularly equivalent bus lines, the 26 and 46.

This always cracked me up, but I'm a weirdo. How are the modular equivalencies? Well, they're both the same mod 20, 6, which is probably the largest base you'l be able to find with those two integers.

That concept, modular equivalencies, was something I'd wanted to make a blog post about, but never felt like I could 1) explain it well enough to make it interesting; or 2) connect it with any other examples from the real world. The juries still out on number 1, but I always felt that without another weird example, the post would be just me talking math and making observations.

Well, that's actually the same, so...

We moved to Austin and I kept the idea on the shelf, but had an eye out for similar equivalencies. We moved to Long Beach and the idea was still safely tucked away on the shelf, behind bicycles and cameras and beaches and pelicans foggy streets. It was tucked away despite my realization that the other example, the one I always felt I needed for the post, was apparent and there for the exposure. It just took me a while to get to this post, to get to a place comfortable enough to hammer it out. More than a year, anyway.

The other example? Area codes. Specifically, the first three numbers on a phone number, the regional exchange numbers, for two places, specifically the last two places we lived (er, still live?), Austin and Long Beach.

The area code for Austin is 512. I've seen tattoos of "512", head shops using the number in their title, and other things you get in hipster enclaves with easily identified self-references.

The area code for Long Beach is 562, and I've seen it similarly used in the names of places and on tattoos. Seriously.

Brooklyn has many area codes (714, 917, even 346 sometimes), and LA as a region has a bunch, but everything in Long Beach (and maybe a little of Carson and Downey) use the 562 exchange.

Modular equivalencies of, eh, I guess the largest base you could use here would be 50, giving them an equivalency of 12.

Patterns of numbers...for guys like me I see this kind of thing even when I'm not thinking about it.