Glyphs as a Number System?

[Eri she/her]

I also don't understand why it can't be base-16, especially after being confirmed by Brandon.

Because, with all due respect to our favorite author, base-16 has 16 digits, including 0. And the digits used in book are 1, 2,... 16 and 0 (in the map). Yes, I'm a bit of maths geek.

I guess he meant the number system used is based on number 16 (which it is), but not in a strict mathemathical sese of base-16 number system. Kinda like Roman numbers are based on 2 and 5. Or maybe we shouldn't assume that the numbers used in the book are the exact in-world number system. (=I guess mister Sanderson or his editor may have done a little mistake here—they're writers, not mathematicians. Therefore overanalyzing the exact way numbers are written in the book may not be a very good idea. Let us enjoy the fact it's based on number 16 and overanalyze the Ars Arcanum instead )

And for edition - I think it's either a word written in steel alphabet, or (more likely) a date or something similar. Not one number - if it was on base-16 number, with that uch digits, it would be to big to resonably fit as a number of edition od a newspaper. Also, it has two symbols that aren't in the 0, 1, 2,..16 set. Some kind of separators, maybe? Like "/" in "edition 12/11/2011"? (sorry for European format)

I think the other 2 symbols (19 and 20) are not metals, just additional letters. They may be, however, some atium or lerasium alloys.

Edited November 13, 2011 by eri

[Ryan he/him]

I'm still a little confused about the 122... maybe that's because math makes zero sense to me. Sorry. I also don't understand why it can't be base-16, especially after being confirmed by Brandon.

I thought this might come up eventually. Here's a primer on how numbers work.

Our number system is big-endian, positional, and base-10. Big-endian means that, when reading a number from left to right, you encounter the big end first. Positional means that the value of a numeral depends on its position within the number. Base-10 means that the mathematics that determine what a numeral in a given position means are based on the number 10.

In positional systems, in order to determine the value of a number, we multiply each numeral by b^p, where b is the base and p is an exponent whose value is dependent on the position. In the first position, the exponent is 0; in the second, it is 1; and so on and so forth forever.

Let's look at an example number: 385. The value of this number is determined by the following expression: 3*10² + 8*10¹ + *10⁰ = 385. In other words, 300 + 80 + 5.

This way of thinking about numbers looks daft until you realize that it allows for numbers in bases other than the familiar 10, which can occasionally be very useful. The only example I know of is computers, which only have two numerals to represent information, and so have to use base-2.

In base-2 (or binary), our example number is 110000001: 1*2⁸ + 1*2⁷ + 1*2⁰ = 256 + 128 + 1. Of course, binary numbers are hard for humans to work with, so to make our jobs easier, programmers started using base-16, or hexadecimal. Our example in hexadecimal is 181: 1*16² + 8*16¹ + 1*16⁰.

The chapter numbers cannot be a positional system, at least not in the way we use them. Consider chapter 17, which is numbered (16 1). If this were a base-16 system, that number would be 16*16¹ + 1*16⁰, or, IOW, very much NOT 17. Instead, the two numerals are added together, much like Roman numerals.

The only way to get those chapter numbers to work in a positional system is to posit that every TWO numerals occupy a single position. In such a system, you add pairs of numerals together before applying the base. So, in the three-digit number (6 16 10), you first add 16 and 10 together to get 26, then apply the base: 6*16¹ + 26*16⁰ = 96 + 26 = 122.

Such a system is not without problems, as eri has pointed out:

Sorry, but it can't be base 16 system, if it has 16 digits plus zero (which we've seen used on the map).

It is true that all of our positional number systems use the same number of symbols as the base. Thus base-10 uses 0-9, base-16 uses 0-F, etc. In this system, there are 17 symbols: Spike-Duralumin. I realized this when I proposed it, but I ignored it because it's not an issue. All it means is that there is more than one way to represent certain numbers, but this system would have that property anyway due to the two-numbers-per-position thing.

So, yes, it's an inefficient and stupid way to write numbers. But, then again, so are Roman numerals, and the greatest empire of the ancient world used them to create feats of engineering never before seen. And speaking of Roman numerals, that's another system that has many ways to represent some numbers.

If we abandon the notion of shoehorning these numbers into a positional system, we'd end up with a system where all numerals are added together, except for those that are preceded by a letter, in which case that number is multiplied by some value before being added. In the edition number, under this system, the two unknown letters would be value-modifying prefixes on the numbers 15 and 6.

I'm pretty much convinced the numbers work in one of these two ways. Now, we just need more information, which means that someone needs to bug Brandon (or we could RAFO, but that's no fun ).

[PeterAhlstrom he/him]

Found this on Brandons old livejournal Edit:On his blog too.

Note that the letter values there were not canon and have changed since then.

Also, this article may help you.

http://en.wikipedia.org/wiki/Japanese_numerals

[discipleofhoid he/him]

Note that the letter values there were not canon and have changed since then.

Also, this article may help you.

http://en.wikipedia.org/wiki/Japanese_numerals

Ok so the numbers are base 16 but they are written the way the Japanese write their numbers. That is 0-16 have their own representation. 17-31 are written as 16-1,16-2,16-3 ... 16-15. 32 would be written as 2-16. 33 as 2-16-1. This pattern would continue till 255 which would be 15-16-15. 256 would have its own symbol. 257 would be written 256-1, 273 would be 256-16-1. And the pattern continues.

This is a slightly better tutorial on that number scheme http://www.learnjapanesefree.com/japanese-numbers.html

[PeterAhlstrom he/him]

The 1,0000 and 1,0000,0000 rule applies as well.

[Eri she/her]

Wow, thanks, that's cool! In a complicated way, but cool. Sorry for suggesting that you did a mistake here, 17 digits seemed just wrong, I didn't know the Japanese system. Still, I was right in saying it's not base-16 as most of us know it and use it.

So the unknown symbols in "edition" may also be some bigger numbers, like 256... But why would they need such a big number as edition number? Megalomany of the newspaper's owner, maybe. ;-)

Edited November 14, 2011 by eri

[CrazyRioter she/her]

Wow, thanks, that's cool! In a complicated way, but cool. Sorry for suggesting that you did a mistake here, 17 digits seemed just wrong, I didn't know the Japanese system. Still, I was right in saying it's not base-16 as most of us know it and use it.

So the unknown symbols in "edition" may also be some bigger numbers, like 256... But why would they need such a big number as edition number? Megalomany of the newspaper's owner, maybe. ;-)

or the paper has been running for a very long time.

[PeterAhlstrom he/him]

The number is sequential since the founding of the broadsheet.

[Guinevere she/her]

And I now can no longer understand my own thread...

Oh, well. I'm glad it has cleared some things up for math-type people. If anyone figures out the edition number, please let us know. I think there are still plenty of symbols we don't know yet, ones that represent all the other available alloys, that will fill in the blanks of the Steel Alphabet. Though we kind of have to wait for the Scadrians to discover them all.

Does anyone have any thoughts about the prologue and epilogue symbols representing Ruin and Preservation respectively?

[discipleofhoid he/him]

Correct my math if I am wrong guys but:

The edition number is:

x 15 y 6 16 10

So with the number system as I understand it we should have

y = 256

x =4096

This would make the edition number

4096 + 15 * 256 + 6 * 16 + 10 = 8042

[lauren.e135 she/her]

Correct my math if I am wrong guys but:

The edition number is:

x 15 y 6 16 10

So with the number system as I understand it we should have

y = 256

x =4096

This would make the edition number

4096 + 15 * 256 + 6 * 16 + 10 = 8042

Makes perfect sense to me, and is very logical. I think it would be fair to say that we can safely assume y=256 and x=4096 as you've said. Also, if the mistborn world had approximately 365 days in a year as we do, this would mean that the Elendel Daily has been running daily for a little over 22 years. Seems realistic.

Might I be as bold to say we've cracked the number code?? ; )

[Eri she/her]

8042... assuming one edition per day and 365 days in a year... the newspaper exists for about 22 years. Makes a lot of sense.

Not as big number as I thought. (But nubmering every day's edition sequentialy is kinda megalomaniac. Of course, a bit of megalomany is a good thing in steampunk settings... )

edit: Ninjas.

Edited November 15, 2011 by eri

[Joe ST he/him]

The number is sequential since the founding of the broadsheet.

are they still speaking/using the same language/etc as in the Final Empire times?

[Guinevere she/her]

are they still speaking/using the same language/etc as in the Final Empire times?

You know, apart from high imperial.

[Windrunner he/him]

I've got one question that is semi on topic about the steel alphabet. Are their any patterns in the symbols that show the attributes of the metal? Like any patterns that you've noticed so you could look at the symbol for pewter and go, "oh, that's the Physical, internal, pushing metal because of these attributes in the symbol, like location or number of the spikes or location and number of the rings? The only one that I've been able to find is that if the dot is on the inside it is pushing, and if it is on the outside it is pulling. Maybe I'm insane and the symbols are just there to look cool but the fact that dots are in a pattern makes me wonder if there are other more subtle patterns that anyone can catch

[Aiken Frost he/him]

Huh. That is a VERY interesting finding, Windrunner. I will surely try to find something in there.

[darniil he/him]

I've got one question that is semi on topic about the steel alphabet. Are their any patterns in the symbols that show the attributes of the metal? Like any patterns that you've noticed so you could look at the symbol for pewter and go, "oh, that's the Physical, internal, pushing metal because of these attributes in the symbol, like location or number of the spikes or location and number of the rings? The only one that I've been able to find is that if the dot is on the inside it is pushing, and if it is on the outside it is pulling. Maybe I'm insane and the symbols are just there to look cool but the fact that dots are in a pattern makes me wonder if there are other more subtle patterns that anyone can catch

Ha! Very awesome. Nice catch. That even fits with atium and lerasium: their dots aren't inside or outside the main circle - they're in the middle.

[EHyde she/her]

(Now, here's a tangent for you: the spikes are obvious symbols of Hemalurgy/Ruin. Then, the crescents in the metal symbols would represent Allomancy/Preservation. Spike the crescents, and you have Feruchemy/Balance, and also Harmony, and life. Use just a spike, and you have only Ruin; you have nothing. Now, I know the symbols were originally designed just to look cool, so I'm probably reading too much into it...but you've gotta admit it's cool.)

I saw something similar, also probably reading too much into it, but I saw them as representing the three magic systems, the spikes for hemalurgy, the crescents as cuffs/bracelets for feruchemy, and the dots as beads for allomancy.

[Arcanist Lupus he/him]

I'm bothered by the apparent lack of zero. In the chapter headings, chapter 16 is made up of 16-1, while 17 is 16-2, etc. This implies a Roman Numeral* type number system, which is terribly impractical for doing complex math. They could be using them formally, though, the way we title chapters and label clocks with Roman Numerals, without using them in everyday life.

* It accually seems to have more in common with Gematria then Roman Numerals, but the basic idea is the same. The main difference is in what values have letter representations.

[Deus Ex Biotica]

Hey, lots of math got done without a symbol for zero. It happens.

[PeterAhlstrom he/him]

Sir_read-a-lot, check earlier in the thread.

[Arcanist Lupus he/him]

Sir_read-a-lot, check earlier in the thread.

I hate it when I miss the second page of a thread...