The Garden of the Blind

Decimal is on its way out. Okay, not really. As long as people keep getting born with ten fingers, we’ll still be counting in base ten. Recently though, binary has been finding its way into our hearts (and our computers). I have long been a proponent of counting in binary, and here I will attempt to explain why I care so much about this digital base.

First, there is history. For me, it all started back in the first grade. My class was given a math assignment to do without counting on our fingers. I remember that when I finished it, well into recess, there was only one other student left in the room. Apparently, I relied far too heavily on my poor hands for calculations. I soon was doing arithmetic like a pro, and without resorting to finger ticks, and just in time too. We were soon dealing with numbers far greater than ten, or even twenty.

Skip ahead to grade eight, where a science teacher (the late Jon Miya) was just goofing off while the class worked on a project. He was exchanging various rude gestures with a teaching assistant, and then justifying them by claiming that they were numbers. This struck me as interesting, and possibly vulgar. My adolescent mind stored it away and started working at it. This new method of counting allowed each hand to get up to thirty one, or both hands together could count to over a thousand. This proved to be quite useful when I counted laps for other students in gym class (I was a double counter, with one person on each hand).

So, how does one count in binary? First, consider binary numbers. Each digit represents a value, and so you add up the values that correspond with the 1s in the number. For example, the places in an eight digit binary number represent 128, 64, 32, 16, 8, 4, 2, and 1, and so the number 10010110 is the binary equivalent of 128+16+4+2=150. If we let each finger represent a binary digit, then one hand can be a five digit number. With the 32 combinations of closed and extended fingers, one can count from zero to thirty one.

Before I get into a description of how to number the fingers, there is a matter of conventions. Just as the PC word and the UNIX world disagree about whether a data byte should start with the highest or the lowest bit, there is some disagreement about whether the thumb should be used to represent 1 or 16. I don’t know if there’s a standard name for these two styles, so I will designate the former as little endian (because the thumb has the little value), and the latter as big endian.

I am a little endian. All the binary counters I know are little endian. This is no coincidence because I taught them all how to count. I think that Mr. Miya followed the little endian form too. But everything I’ve seen online about counting follows the big endian style. Which is better? That depends on how dextrous the pinky is. If one is counting in binary, the lowest digit must move every time the number changes, while the highest digit moves only every 16th time. My pinky can’t keep up with my thumb, and I challenge any big endian to count as quickly as I can. For the rest of this paper, I will only consider little endian counting. Those with agile pinkies are free to reverse my directions.

So, the fingers are assigned values corresponding to powers of two. The thumb is 1, the index is 2, the middle finger becomes 4, the ring is 8, and finally the pinky is worth 16. Whenever I’m feeling lazy, I just add up the numbers corresponding to the appropriate fingers, and there’s the number that my hand represents at a given time. The “I Love You” sign (pink, index, and thumb extended) is equal to 16+2+1=19. Peace (index and middle fingers forming a V) is equal to 4+2=6. A high five is actually a high thirty one.

Counting consecutive numbers takes a bit of practice, but can be picked up easily enough. Start a count with the hand closed. With each number, if the thumb is in, then extend it. Otherwise, start with the thumb and close each finger until you come to one that is already closed, which you then extend. Let’s run through the first few numbers:

To start, the hand is closed. We count one, and since the thumb is closed, it now gets stuck out. For the count of two, we come to an open thumb. The first closed finger is the index, and so we close the thumb and extend the index. With three, the thumb is closed, so it gets opened again. At four, we find that the middle finger is the first one closed, and so we close the thumb and index and open the middle.

The single finger digits are a good place to stop and check if you’re practicing. If you get to 4 and the middle finger is the only thing up, then you know you’re on the right track because that’s the finger’s value. Also, four doubles as an obscene hand gesture. It may be a good idea to count discreetly in some venues (at church, for example). Still, this is one of the things that draws a lot of converts to the counting system. There’s nothing like giving a guilt-free 132 (165 with thumbs extended) to some obnoxious person.

If only I had known all this back in the first grade. Sure, I use bigger numbers now, and for that matter I usually find myself doing math outside the set of integers, so they can’t help me all the time. But after all these years, I rarely find myself counting off more than 30 things, so my manual binary digital registers provide me with adequate storage for almost anything I need to tally.