Good morning recruit. My name is Sergeant Daniels, I am here to answer almost none of your questions. Firstly you will be wondering why you have been pulled from your cushy little number in civvie street to out here at the ar... back end of nowhere. Well, it turns out this is a great job, you’ll love it. There is an interview with the colonel in a couple of weeks, if you still want out then, then that’s fine.
Here we investigate the Sk’resh Da, an alien race who… Don’t interrupt, I know you haven’t heard of them, the brass decided that the public weren’t ready yet, go figure. Anyway, they arrived a couple of years ago. No, we don’t know how. We are still struggling with the language.
One Sk’resh we’ve been talking to… well, trying to talk to, has told us about an eeen. We don’t know what that is – it could be his shuttle, an enclave of hidden Sk’resh Da, a cache of cool alien weapons, a memento from his mommy, anything. The brass decided that this is a good job for the new recruits, so you’re it. Go find this eeen thing, leave it in place, and report back.
But it is not that simple. The Sk’resh Da have 7 fingers on one hand and 19 fingers on the other hand. Appendage. Whatever. And use both separately in their math, rather than adding them together as we do. If you know how to count – Yes, yes, I know you CAN count, I said if you know HOW to count – then here are the coordinates that this Sk’resh gave us. Apparently somewhere in Palmerston North, New Zealand. Off you go. If you don’t know how to count, stick around for a quick lesson.
The Sk’resh’s Eeen is at:
S 22° 13.CF6
E 340° 52.110
Before you go - make sure you study this eeen thing properly and make a full report. I'd hate to have to make you rewrite it!
Ah - don't want to leave just yet? Forgotten how to count? Oh dear. I take it that it has been a while since you were in the 4th form. OK, we go into a lot of math here. Go slowly, make sure you understand the examples.
We have ten fingers on our hands, so we use a counting system with ten symbols. They could be anything, but by convention we use these shapes: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. If we only had 5 fingers on our hands we would only use 5 symbols, 0 to 4. If we need more than ten symbols then we add in letters from the alphabet. Computer nerds sometimes use 16 symbols, so that would be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E and F.
But we sometimes have more than ten things to count. In that case whenever we run out of symbols, we start from the beginning again, and we also add one to the next symbol to the left. So 9 plus one becomes 10, 299 plus one becomes 300. The same if we only had 5 symbols: 4 plus one becomes 10, 14 plus one becomes 20. The same if you have 16 fingers: F plus one = 10, 3AF plus one equals, yep, you guessed it, 3B0. Good you see you catching on, recruit. So each digit to the left is a factor of [number of symbols] greater.
And that's it. THAT's how you count.
So how do we convert a number from one system to something we are more familiar with? Remember that if we use 10 symbols, then there are a maximum of 10 symbols in each column, so the number 1234 means that we have 4 odd leftovers, 3 lots of tens, 2 lots of ten times tens, and 1 lot of ten times ten times tens. Or in other words, starting from the decimal point and working outwards:
= 4 + (3 x 10) + (2 x 10 x 10) + (1 x 10 x 10 x 10) (number of 10s = column number minus one)
= 4 + (3 x 10) + (2 x 100) + (1 x 1000)
= 4 + 30 + 200 + 1000
= 1234.
See how as we move to the left each digit is a factor of 10 greater?
The method is EXACTLY the same with only 5 symbols. There are a total of 5 symbols for each column, so 1234 in 5 finger counting is 4 left overs, 3 fives, 2 five times fives, and 1 five times five times five. We show this as:
= 4 + (3 x 5) + (2 x 5 x 5) + (1 x 5 x 5 x 5) (number of 5s = column number minus one)
= 4 + (3 x 5) + (2x 25) + (1 x 125)
= 4 + 15 + 50 + 125
= 194.
With 16 symbols it is, you guessed it, the same: 1234 in 16 finger nerd counting is the same as:
= 4 + (3 x 16) + (2 x 16 x 16) + (1 x 16 x 16 x 16) (number of 16s = what?)
= 4 + 3 x 16 + 2 x 256 + 1 x 4096
= 4 + 48 + 768 + 4096
= 4916.
Let’s do another 16 finger example. What is 2AE5 in normal 10 finger counting? Remember that A-F follows 0-9.
= 5 + (14 x 16) + (10 x 16 x 16) + (2 x 16 x 16 x 16)
= 5 + 14 x 16 + 10 x 256 + 2 x 8192
= 5 + 224 + 2560 + 8192
= 10981.
Decimals can be done the same way. If moving to the left is larger, then moving to the right is smaller: 1/[number of symbols] as large. In other words, 0.2 means 2/n where n is the number of fingers. So for us 0.2 is two tenths, or 2 x 1/10. So, starting from the decimal point and working outwards again, 0.2314 with 10 symbol counting is the same as:
= 2 x 1/(10) + 3 x 1/(10 x 10) + 1 x 1/(10 x 10 x 10) + 4 x 1/(10 x 10 x 10 x 10)
= 2 x 0.1 + 3 x 0.01 + 1 x 0.001 + 4 x 0.0001
= 0.2 + 0.03 + 0.001 + 0.0004
= 0.2314
0.2314 in 5 finger counting is just the same. Converted to something more familiar it is:
= 2 x 1/(5) + 3 x 1/(5 x 5) + 1 x 1/(5 x 5 x 5) + 4 x 1/(5 x 5 x 5 x 5)
= 2 x 0.2 + 3 x 0.04 + 1 x 0.008 + 4 x 0.0016
= 0.4 + 0.12 + 0.008 + 0.0064
= 0.5344
By now you should be able to convert 0.C3DA from 16 finger nerd counting into normal money:
= C x 1/(16) + 3 x 1/(16 x 16) + D x 1/(16 x 16 x 16) + A x 1/(16 x 16 x 16 x 16)
= 12 x 0.06250 + 3 x 0.00391 + 13 x 0.00024 + 10 x 0.000015
= 0.75 + 0.01173 + 0.00312 + 0.00015
= 0.76500
Got that recruit? Good. Now go find that eeen thing. And remember to describe what you find there! Dismissed!