Krepta's Numeric Obsession
Linked to by Rel.to, Six Degrees to D'ni.
Hi, Shorah b'shehm, I am Krepta, and this is my strange little world. I do have a blog, but I don't blog very much. Mostly I post large and numerous messages on many Forums and BBS systems. I also hang out in CyanChat and I used to hang out on Myst Online:Uru Live which is a great Online Game which used to be available on GameTap but was shut down.
Woot, after being a player in MOUL for a whole year, and a bit more, I finally have all the Calendar Sparks. So, I'm very happy and celebrating my One Year on Uru. But I am also very sad and angry at Gametap for their decision to Kill Myst Online Uru Live. I'm still obsessed with all things Myst/D'ni, and as a result I am obsessed with Numbers and such.
Well, this is my current obsession, Numbers, and the conversion of Positional Numbering Systems. Enjoy.
The links on the left that take you to Google Docs require you to have an account there in order to edit. If you have an account, log in, then you can edit your own copy. You will be in View Only mode unless you log in and click the File button on the Google Docs page, and save a Copy of the document into your own folder. So you can edit it however you want. And remember, once you have your own copy, it is completely Yours, you can do whatever you want with it.
Remember the Order of Operations, PEMDAS, Please Excuse My Dear Aunt Sally, Parentheses Exponents Multiplication and Division Addition and Subtraction, it Always applies. So when I say 2 times 5 to the power of 3, that means you solve the exponent first, then multiply.
The SUM symbol images below are difficult to understand, and I had no idea how it worked till I looked it up on Wikipedia. The Symbol used to indicate Summation is the Sigma, a Greek Letter. And it works by setting up the Upper Boundary, Lower Boundary, and the items being Summed. The Upper Boundary in this case is "p-1", meaning the Position of a Numeral minus 1, so we can later find the Power to apply. The Lower Boundary is the Index Of Summation, in this case it starts at 0 because the first Numeral in any string of Numerals is not a Power of anything. Then the item to be Summed is the Numeral times the Base to the Power of whatever the Index is. It's like building something, you start with the Foundation, then build on top of that.
The Lower Boundary of Summation is the Foundation, where everything starts. you don't start building from the 15th floor down, do you? The Upper Boundary is how high you want to build. In this case, you plug in the number of Positions in the string of Numerals. So like the example below, the Number of Positions is 3, because there are 3 Numerals in the string. So the tallest that building will get is 2 Floors. So you lay down the Foundation, build your First Floor, then build your Second Floor, and you're done. :)
Let's say I want to convert the D'ni Number FahRah VahGahFahSee Rihsh, which is 1, 6, 20 in decimal notation for each of the three positions. The first number, 20, is the Foundation, the Index for it is 0, and the power being applied is 0. Any number to the power of 0 is 1, so, 20 times 1 is 20. Next is 6, and since the D'ni Number System is Base 25, and because this Numeral's Index is 1, or the First Floor of our building, we will do 6 Times 25 to the power of 1, which is 150. Next is 1, the index is 2, so we do 1 Times 25 to the power of 2, which is 625. Now the Summation, which basically means Adding up a bunch of things together, so, what is 20+150+625? 795, right? There, we are done Summing up the D'ni Number in order to convert it to Decimal. :)
When I was still a kid I was very frustrated by the Mess my teachers had me doing for my math work, because they wanted me to show my work. The following image is an example of my Shorthand notation vs. the Mess I hate. I was so frustrated by this mess, and sometimes confused enough to throw a book across a room, that I devised a simple shorthand that I still use to this day.
It is a very simple principle, why cross out a number and write a new smaller, or larger number, when a small mark between it and the number below it can achieve the same thing by basically placing a 1 in the middle?
Ok, Step 1) 3 minus 5 needs to become 13 minus 5, so place a small mark above the 2 which is next to the 5. This achieves the same effect as changing the 8 to a 7, and changing the 3 to a 13. Then count up from 5 till you get to 13, how many is that? It's 8. So write 8 in the answer below the 5.
Step 2) How much is 7 minus 2, Or 8 minus 3? The answer is 5, so put that in the answer below the 2.
Step 3) What is 12 minus 7? That answer is also 5. All done.
Now let's try something bigger, like:
Step 1) 1 becomes 11, 7 becomes 6
So place a mark between the 7 and the 8 below it to transfer 10
Step 2) 6 becomes 16, 2 becomes 1
So place a mark between the 2 and the 4 below it to transfer 10
Step 3) 1 becomes 11, 3 becomes 2
So place a mark between the 3 and the 6 below it to transfer 10
Step 4) 2 becomes 12, 5 becomes 4
So place a mark between the 5 and the 3 below it to transfer 10
So, now it is broken down into:
So the answer is 16789.
Contact me and tell me whatever you like. firstname.lastname@example.org