Many years ago before I had developed such a fancy for computers, I was over at my friend G’s house celebrating his birthday. The sight of G’s decadently frosted birthday cake loosened a story which I then recalled to G about a grandmother who was so old that her family couldn’t fit all the candles on her birthday cake. G looked at me with a most remarkable sparkle in his eyes, and, I shall never forget it, said: “they should have used bits.” On perceiving on my countenance, what G often called “the poster face for the city of Perplexia,” he continued: “Sweetbits …”
< G calls me Sweetbits because of the I-just-ate-an-entire-box-of-licorice grin that fills my face when he speaks about computers. >
“It’s high time you learned something about bits, but that being such a topic of great depth, we will be content today to lay these three foundation bricks.”
- Symbols
- Number Symbols
- One Symbol or Two
Picture a cow. That picture is a symbol for a cow. The word cow is a symbol for a cow. Well actually, cow is three separate symbols: c, o, and w jammed together in a line.
Symbols are really handy. They can save you from always being near the thing you’re referring to. Let’s say you’re sitting around the farmhouse w/ your wife Mildred, chatting it up about all the shananigans the cows have been up to: “Mildred honey, confound it if I didn’t find another cow in the chicken pen today! Cows don’t have feathers Mildred! Why in God’s name does that cow think she’s a chicken!”
Now the thing is: if you didn’t have those 3 letter symbols: c, o, and w, which allowed you to make that word symbol: cow, you would have had to haul Mildred out to the chicken pen in the middle of your cow vignette just so she’d know exactly what kind of thing had raised your spirits so much.
Next, suppose some guy Frederick in the next town wants to buy your cows and he’s been hounding you about how many cows you have. Well heck if you know that! Nobody in your family ever learned how to count! All you’ve been able to muster up for Frederick is: “Shucks, I’ve got a lot of cows.” or: “Dag nammit, Frederick, we’ve got ourselves a cattle farm over here.” When Frederick begins to get frustrated you realize you had better do something.
So the next day you head out to the yard packing a nice lunch that Mildred fixed for you, with the idea that you’ll just walk those cows over to Frederick’s, so that he might take a gander at them and get a good picture of how many you have. You’ve got the cows out of the main yard and are about to set out when you spot a pile of little sticks near the fence. A bright light flashes inside your noggin as you realize you can use the sticks to count your cows. So one-by-one you march the cows back through the gate and as each cow passes, you toss a stick into your backpack. You’re pretty “stuffed” with your brilliant discovery so you even show off a bit, lying down and indifferently reaching for sticks as the cows pass, all the while chewing on a thistle. But then disaster strikes: your backpack fills up, and that’s with most of the herd still to come.
But this is where we come back to the grandmother’s birthday cake. With the cake, you’ve run out of candle room. With the backpack, you’ve run out of stick room. In both predicaments you’ve only got one type of symbol to work with. Let’s hone in on the cake and say that the grandmother is 117 years old, which means the cake wants to be infested with 117 lit candles. Here’s what to do: 1st remove all the candles you’ve managed to fit on the cake. Pick seven of them and poke them back into the cake so that they make a straight line. Now light the 1st, 2nd, 3rd, 5th, and 7th candles. Bingo! Candle problem solved. Plus the icing on the cake is that the grandmother only has to blow out 5 candles. That way she’ll be able to attend her birthday party the next year.
Now what sort of sorcery is this? Ok, 1st I need to tell you about mappings. When you map the world, what do you do? You throw out all sorts of details, and then whatever’s left you shrink, and then draw it on a piece of paper (called a “map”.) That’s how the actual country of Italy turns into a flat shrunken boot. Now our farmer mapped cows to sticks because all he cared about was counting his cows, so it was ok that pretty well everything that a cow is was lost in the mapping. And typical birthday cakes (the ones with only flame-bearing candles) map somebody’s age to lit candles.
So here’s my magical mapping that makes it possible to use candles to declare a grandmother’s age on a birthday cake, without running out of room. It maps sequences of lit candles (ie. what appears on conventional birthday cakes) to sequences of “Binary” candles (ie. candles that can be in one of two states: either lit or unlit.)
Ok, let’s say that instead of a 117 year old grandmother we’ve got a 3 year old rascal. You can see from the mapping that even with such a young rascal, you’re already beginning to save on candles, in that you only need 2 candles. And you’re beginning to really eco-candle by the time the rascal hits seven years. Just 3 candles are needed!
Now winding things up, since you’re looking sleepy, Sweetbits. The punchline is that these Binary candles, that is candles that can be in one of two states, are bits! And what’s more, it’s not just people’s ages that can be mapped to bits, but also our favorite farmer’s cow-sticks. And it gets even more wonderful. But all that can wait until after your nap.