“This is the final boarding call for flight 398, leaving from gate 5. Please board at this time.
The flight itself is named 398. The gate is named five. The names are numbers. The flight could be named George and the gate named Fred and the announcement would sound the same- and, interestingly, taken alone, carry exactly the same information.
The numbers only have meaning if they are given context. Gate 5 means something when there’s 100 gates, all numbered and in order. Gate 5, in a world where gates are given random characters as names, or even simply not in order- have no context- making them as meaningless as Gate Fred.
Of course, Gate Fred could mean something if Fred is given some context. Maybe Fred is preceded in the terminal by Gates Angelica, Bruce, Chessie, Doug, and Edward. Thanks to the sequence, Fred has meaning- much like 5, it is useless without context.
Without context, 5 and Fred do the same thing- they let you know you are at the right place. They give you no information on how to get there, or what the gate is used for.
We could name the gate using the info we need- something like “The gate on the southwest corner that JetBlue uses to take people to New York.” That’s a really long gate name, but it tells you where it is and what it’s used for. Thankfully, we can be spared the long name by breaking those two pieces up- what it’s used for can be found by looking up the information on flight 398.
So that leaves us with “the gate on the southwest corner”. Still kind of long, but worse yet- there are thirty gates on the southwest corner. We were cheating a bit by adding the gate’s use into the name- it helped us pick out the specific one out of thirty. We can’t do that any more, though. We’ve broken that information out into flight numbers, and gates get used for various things throughout the day. We’re going to have to name it such that it can be found by name alone.
So we number them, and we give them the context of a sequence. With signs, we can easily show where groups of gates are. It works.
What’s interesting, though, and the point of all this- is the fact that gate number isn’t a number any more. It’s an identifier and a direction on how to get there, thanks to the context. Is gate six somehow greater than five? Is the area in between gate six and gate five somehow equal to gate one?
No, none of that is relevant. Basically all numerical operations are meaningless in this context. “Five” is no longer a number, aside from perhaps being part of a sequence.
Street addresses are the same way.
Numbers are an abstract concept that can have context applied to them in order for them to have new and different meaning. Numbers themselves are the original XML.
This is what they mean when they say that math is a language. It’s a language that can be defined as needed, when needed. It’s not because algebra uses letters, or because calculus looks like alien script. It’s because you can describe anything with numbers, given the proper context and framework.
In fact, that’s how this web page made it to you. This page is written in numbers, themselves an abstract concept. What makes them useful is context and framework.