The Rhyme of Logistics

Okay, let’s have some fun with this one: Logistics! With Toys! Don’t worry it’ll be a grand ole time. (Not really.)

Distribution of any specific thing means moving that thing from its source to a target. Designation for a destination. In other words, logistics.

Mathematicians sometimes call this injection, surjection, and bijection, which… yikes. Like, cmon folks. Work with us here.

But really all they’re trying to say is that they want to figure out all the different ways of moving any one thing from some kind of container thing to some other container thing. Literally. That’s it. That’s… all they’re really talking about.

That might seem like abstract nonsense – and it is! – but there is a lot we can do with just a touch of abstract nonsense, even with just an empty circle!

So yes. Math is just abstract nonsense, applied. Which is, itself, abstract nonsense. But trust me, we’ll make it work. Together. And if it doesn’t work we’ll try again later. No harm, no foul. Let’s go.

It always helps to start with an example: Let’s try… cleaning up toys as a distribution method.

(Side note: I like “distribution” better than “projection.”)

The toys are scattered across the floor and need to be moved from the floor to the bins on the wall. We’re in kindergarten. There are cubbies on the wall. Don’t worry about it.

Now let’s say there is some system we follow as a class for putting the toys away in their bins. How do we describe and talk about our little system?

Let’s get started.

  • Well, first off, we can refer to all the different things either individually as units– each toy, each bin, their positions on the floor, even the rules in our cleaning system – or we can refer to them all collectively as a unitary whole.
    • But the individual units can get pretty complicated pretty fast, so let’s just try to describe the whole damn thing as one damn thing, for now.
  • As shorthand, let’s use the title “Our Cleaning System” whenever we’re talking about the whole thing – including all the inner components and all their inner relations to each other.
  • But how can we describe Our Cleaning System if we’re not talking about its individual components? Well, one thing we can do is describe the type of cleaning we’re doing in our system. The types of cleaning methods. We can describe its “design.” Let’s break that down:
  1. If every toy belongs in a specific bin, then the toys in Our Cleaning System are sorted.
    • We can call this type our sorting methods.
    • If our system is 100% fully sorted, that means no toys get clustered together in the same bin, and no toys need to be thrown out.
    • Every source unit belongs to a target.
  2. If every bin has at least one toy that belongs in it, then Our Cleaning System is packed.
    • We can call these packing methods.
    • If our system is 100% fully packed, that means no toy bins get left empty or wasted.
    • Every target unit belongs to a source.
  3. If Our Cleaning System results in a set of toys that are fully sorted *and* bins that are fully packed, then it’s… well… both. The toys and bins are both sorted and packed. Both, and.
    • Our cleaning system puts exactly one toy in exactly every bin.
      • When a given logistics system is both sorted and packed, it makes for really easy scanning and quick retrieval. It’s a “clean” system.
        • In our example, these are kid’s toys that are getting sorted and packed, right? So we can probably assume they are actually figurines on display in some shape or form. Maybe our bins are actually in a glass case. Who knows? These concepts are pretty widely applicable. The point is, when a given system is sorted and packed, it shows. You can tell.
    • Mathematicians actually call this “bijection.”
      • This term is… real dumb to me. It just means both, and. Sorted and packed. Let’s just use English.
      • They also call it a “one-to-one correspondence”, which is better, but… yeesh.
    • If we can describe a system as well sorted and well packed, we can describe it as fully-designated, or well-designed.
      • If it is fully sorted and fully packed, then we can describe it as perfectly designed.
      • (Before you waste time trying: No system is perfectly designed.)
  4. Also, mathematicians don’t really even have a term for neither. They’re just… kinda missing a whole concept. So let’s say, If Our Cleaning System is neither packed nor sorted, then it is stuffed.
    • It is not clean. It leaves toys all over the place, unaccounted for.
    • Let’s call that “irregular” distribution.
    • It means that Our Cleaning System does not put away every toy (it doesn’t sort), and it does not use every bin (it doesn’t pack).
      • Some toys are left out in their spot on the floor, some bins are left empty.
      • A lot of things gets left out of our system, a lot of clutter gets in.
        • lol wut are we even doing???
        • If we need a really clean system, let’s make sure it’s sorted and packed.
        • (Note: You don’t always need a really clean system. Clean systems can sometimes get really out of hand.)
  5. Alright. Now we’re pretty much doing Set Theory.
  6. “Wait!”
    • You’re probably thinking, “We haven’t actually cleaned up the toys yet!”
    • Well, right. We’ve not-so-secretly been doing “mathematics” here, which is just “the science of describing things and their relations.”
      • We don’t actually do the damn things. We’re way too lazy for that.
      • And that’s kinda the whole point. If we can specify how things need to be done, based purely on their type, we don’t have to do them ourselves! We can get someone else to. Or, much much much much much much much better, something else.
      • After all, we can all get pretty lazy, in our own ways.
  7. But now things start to get crazy, because we can actually expand our concepts of packing and sorting!
    • (This is where we definitely start to need help from those brainy mathematicians and their super brainy brains.)
    • Packing and sorting can be extended to floor types, bin types and toy types.
    • It can be extended to rooms in hallways that each have different floor types, bin types, and toy types.
    • It can be extended hallway types in buildings with room types that each have bin, floor, and toy types.
    • It can be extended to building types with… uh oh. This is getting out of hand. Our kindergarten is starting to look similar to something I’ve seen before. Starting to look like something… self-similar. Something… that rhymes.

Where does any system start? Where does it end? And when?

In human systems, that’s almost never up to the designers. And for good reason…

Designers can rarely see the rhymes in their own lyrics, even though they write them with elegant beauty that we can hardly even grasp.

Just as the maze of mirrors in a telescope exist purely to bend light, so do the designers of pure systems consist more of form than substance, more of function than essence. So deeply are they consumed by their own fire, unable to see the precious rules that they follow, even as they themselves execute those rules with unfathomable precision.

It is a solemn, monk-like responsibility. And there is also great danger of being consumed by it.

But such are the ways of time, and flowing.
Rhyme, and knowing.
Rhythm, and reason.
Trust, and Truth.

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