This is the first in what I plan to be a series of posts called “Comparisons”, when I have the same issues or thoughts on two completely unrelated topics. Today: the mathematical concept of Base 10, and the social issue of reclaiming a word.
I have the same problem with both of these topics, and it's a simple one. But first, let me explain:
Base 10, for anyone who didn't learn this in math (and I'm always genuinely surprised how many people didn't) is what we use to count. As I sincerely hope you're aware, our numbers go like this:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
You'll notice that once we get to a certain number (“9″) we run out of digits, and have to start using more than one in combination. The point at which we switch to double digits (at number “ten” for us) is what the base is named after, so your standard 1-9 -> 10-99 -> 100-999 etc is called “base 10″.
What you may not know is that you can create bases around any number you like. Let's say you hate the number 9, and never want to see it again. Then you can just use base 9, which goes like this:
0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12…
It's not just skipping the number you don't like, it's a different way of notating numbers. When base 9 (so called because “9″ is the number where we go to double-digits) gets a lot larger, it goes like this:
80, 81, 82, 83, 84, 85, 86, 87, 88, 100, 101…
It's as if the digit “9″ doesn't exist. We've wiped it out of existence, and so we have to go straight to adding more digits.
Another example: 6, you may have noticed, looks a lot like 9. So let's use Base 6, and cut 6 out entirely. Counting in base 6 goes like this:
0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30…and when we get a big larger, 50, 51, 52, 53, 54, 55, 100.
It doesn't stop there – in base 6, we go straight from 555 to 1000, and from 5555 to 10000. But if you have “20″ in base 6, you have what we would refer to as “12″ in base 10. If you have “100″ in base 6, you would have “144″ in base 10. Numbers have different meanings in different bases.
I could talk about bases all day, but I'll just give you two more examples. One of the most common uses of different bases is in computer code, and it's called base 2, or “binary”. Counting in binary goes like this:
0, 1, 10, 11, 100, 101, 110, 111, 1000…
Because base 2 can never reach actually use the number “2″, as soon as it hits 1, it has to move straight on to “10″. You can read thousands of words about binary in other places on the web, and if this kind of stuff is interesting to you, I genuinely recommend you do.
Each base has its own neat little tricks: you probably know a few for base 10: If a number is divisible by 9, all of its digits add up to 9; if a number is divisible by 3, all of its digits add up to 3; if a number is divisible by 4, its last two digits are divisible by 4; etc etc.
The easiest and most useful trick in base 10 is that “if the last digit is even, the number is even” – it blew my mind when I realised that's not true for other bases. Trippy.
Binary's trick? From right to left, the digits represent doubles of two: 1, 2, 4, 8, 16, 32, 64, etc. If there's a 1 in that slot, add the double, if there's a 0, add 0. If you look at the number 1001110, you can quickly add it up by using that trick. From right to left: 0 + 2 + 4 + 8 + 0 + 0 + 64 = 78. Type “78 in binary” into google if you want to check my maths. (I did.)
Lastly: all of the examples I've given have been numbers smaller than 10. But you can go larger as well – base 16 is also known as hexadecimal (hex meaning six, decimal meaning base 10. “a” meaning “plus”, I guess.)
How does it work? Instead of going to double-digits after reaching “9″, hexadecimal goes to double digits after “15″. But 15 is double digits, so we have to make up some digits to put in when we run out of normal ones.
Fortunately, we have plenty of digit-equivalents lying around – you're reading a blog post made up of them. Hexadecimal goes like this:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f, 10, 11…right up to f0, f1, f2, f3, f4, f5, f6, f7, f8, f9, fa, fb, fc…
It's a big weird at first, seeing letters used as numbers, but you get used to it. You'll have already seen it if you've ever used colors in an graphics program or in HTML. #000000 is black, #ffffff is white. Now you know how it works – it's split into red, green and blue, like so: #RRGGBB. Each pair of digits counts from 1 to ff, the last hexadecimal number before 100; black is a complete lack of colour, and white is each colour turned up to the max. Try #ff00000 and you'll see that it's pure red. Knowledge: attained.
(homework assignment: find out what happens when we run out of letters to use.)
We use base 10 for an obvious reason – we have ten fingers. (go on, count them. I'll wait.) Other civilisations have used other bases for various purposes – base 60 is a popular one, because of how easily everything divides into it (the number of days in a year probably plays into that as well.)
Base 10 makes sense; it's simple, manageable, and has some pretty handy rules that make our lives a lot easier (there are easy-to-learn rules for which numbers divide by 1, 2, 3, 4, 5, 6, 8, and 9.) So what's my issue with it?
Well, first of all, let's talk (much more briefly) about reclaiming.
The idea of reclaiming is simple: instead of allowing words such as “nigger”, “cunt”, “slut”, “queer”, “gay” etc to purely exist as insults, some movements believe that the words should be used positively by the people they insult. There's a piece of art in the room that I'm writing this, a huge pink banner that reads “CUNTASTIC”, which I assume relates to reclaiming the word. (I've never actually checked.)
As an idea, I'm not so crazy about reclaiming words – I think that while you can definitely be successful (see: “geek”, “Jesus freak”, and even “gay”) you run the risk of only people within the minority being able to use the reclaimed word without causing offense (“nigger” is the most obvious example, but I've been told on multiple occasions that men are not allowed to use the word “cunt”.)
Personally, I think that anything which further segregates two groups (group x can use this word but group y cannot!) is a step in the wrong direction, but I don't profess to be an expert on it, and I can definitely see what they're going for. Rather than potentially misinform you any further, I'll leave you with the Wikipedia link, and you can read up about it yourself.
(16 paragraphs on math, 3 paragraphs on important social issues. Some things are just more fun to explain.)
So what's my issue with both Base 10 and Word Reclamation?
Base 2 is called base 2 because it never actually reaches 2. Base 6 goes to 5 and then skips into double digits.
Base 10? That makes absolutely no fucking sense. Every base is base 10. “10″ appears in bases 2 through infinity. It could hardly have a less descriptive name if they'd tried.
I can see how it got the name that it did, but in mathematical terms, it's the height of arrogance. Base 10 pre-supposes that people know which base we're already using. Which, y'know, we do, but it's not elegant. The concept of mathematical elegance is one of my favourite things about the subject, and I think it's a little sad that such an important concept has such an inelegant name.
Reclaiming, in quite a different way, makes absolutely no sense either. To reclaim something is to take back what was once yours; historically, the words “nigger”, “slut”, “geek”, “queer” and “cunt” never belonged to the people they described. I notice that the Wikipedia page promotes the term “re-appropriating”; I wonder if someone else had the same problem as I did and this is their attempt to fix it.
I once tried to debate the issue in a large group of radical feminists. It did not go well.
Language is important. Names are important. If base 10 was named “base A” (as it should be), people would ask questions with interesting answers, and if you do nothing else in life, try to make people ask questions with interesting answers.
This long blog-post has been partially an excuse to explain bases (it's surprisingly hard to find reasons to bring it up in everyday conversation) but mostly a way to get some thoughts out that have sat in my head for many years now.
So write to your senator, bring it up in your next math class. Base 10 should rightfully be called “base A”, and “re-appropriating” is a much more suitable term. Together, we can fix the world, one minor issue at a time.