Math on Roshar

[Patrick Star]

So, I was curious about this.  With Cryptics being based on highly advanced fractals, and Roshar's map being based on a Julia Set, I was wondering...

 

How familiar are Rosharians with advanced mathematics?

 

I'm talking discrete math, discrete mathematics, abstract algebra, geometry (all kinds), calculus, logic, statistics, game theory, combinatorics, control theory, and probability.

 

Going off of what I've seen in the first couple books, it looks like the Alethi, for the most part, are fairly ignorant of more advanced mathematics, though seem to be at least proficient in applied math (Dalinar's chasm bridges).

 

Also, time to address the elephant in the room:

 

 

Why have we not seen any cryptography on Roshar?  I mean, one of the main kinds of radiantspren are cryptics, for crying out loud!

 

And "because they have spanreeds" really isn't a viable response.  What did they do before spanreeds?  Do they realize that open communication on spanreeds could ally a hijacker to receive unencrypted information?  Could Odium or an unmade intercept spanreed communications?

 

Sorry for the strange rant, operating on ~2 hours of sleep.

[DreamEternal]

Ignorant? Rosharans are very advanced when it cones to math. I mean, they discovered sound is a wave, and managed to link it with the shapes of their ancient cities. While the general alethi darkeyes may be ignorant, the ardents dedicated to scholarship are not.

As for cryptography, have you wondered if we haven't seem it because there really wasn't an opportunity for it to be useful? I feel it has a good chance of playing a role in the next books, as the several secret societies we have seem come closer to the spotlight.

[King's Twit]

There's been a little, though I'll admit that my definition of cryptography might be off. The Diagram had at least one encrypted message. We saw with both the spanreed communications between Dalinar and Jasnah and the ones between that con artist and her informant that some people at least are using code phrases and the like to secure their messages, which in my mind is like proto-encryption.

 

That was to protect against the wrong person having the paired spanreed, though; your idea about a hijacker of the spanreed signal is interesting, if I am understanding you correctly on that. I'm not sure it is possible to "wiretap" a spanreed message, since (so far as we've been told anyway) spanreed technology requires the a gemstone be split into two, then each pen gets one of the rubies. It's based on maintaining the identity of the gemstone as still being whole, instead of splitting into two separate identities, so I'm not sure that you could link a third spanreed to an existing pair, unless the original gemstone is split into three pieces when the spanreeds are first linked. Now that I type it out, I'm becoming convinced that this might actually become a plot point in the book, like one of Dalinar's spanreed pairs was actually made with a secret third pen, and someone bad is spying on all of Dalinar's communications with it.

 

But the real reason that there is no encryption is probably because Cryptics haven't really interacted with humanity in thousands of years, since Roshar was still an early civilization. It might become a thing in future books that Shallan and all of the other new lightweavers use their bonded Cryptics like the Navajo Code-Talkers, and use them to send messages that only another Cryptic can decode, but we'll have to wait and see.

[Oversleep]

I thought of a way to intercept spanreed messages, but it requires approaching the target.

You have to put additional gemstone in one of the spanreeds, thus linking it to yours. Basically one of their spanreeds is now linked to two others. Unless they dissect the spanreed they won't find out. And it's untraceable.

[SnopyDogy]

In regards to mathematics there is this:

 

"Even though they'd killed plenty of Parshendi - as many as a quarter of their originally estimated forces were dead..."
Page 224, kindle Edition, Way of Kings.

I doubt the Alethi were able to conduct a census of the Parshendi population before going to war. So they must be using some mathematical method to estimate their numbers. Iirc this estimate was fairly accurate, so either they were lucky or they have some reasonably good statical methods. This reminds me a little of how the allies in WW2 would estimate the number of German tanks based on the non-sequential serial numbers of captured examples.

Also Storm Wardens predict highstorm occurrences and even what weather/season will occur between highstorms using mathematics. I belie it takes some fairly fancy math to predict the weather.

Another thing to consider is this:

 

"I can speak with skill about geography, geology, physics, and chemistry"
Shallan, Page 87, Kindle Edition, Way of Kings

If scholars see physics as a separate discipline then it implies that understanding of it is reasonably advanced. Which could imply that calculus has been developed (Newton developed his calculus to help advance his physics theories). bit of a stretch but still.

Also the above quote came from Shallan's interview with Jasnah to be her ward. It was a direct response to a question about Logic and math. 

[Oversleep]

How it is that simultaneously (I am never gonna memorize the correct spelling ) telling the future is looked down on and science is flourishing? One of the driving questions of science is "what would happen if...". Argument could be made that they're not developing probabilistics and statistics, but if they have physics? Experiment-driven physics?

[SnopyDogy]

There is a difference between telling the future (prophecy) and just knowing the probability of different outcomes. 

 

The first is stating something that hasn't happened yet as if it was a fact without any proof to substation the claim. If a supernatural source was claimed then this would defiantly be prophecy. an example might be saying "I'll roll a six" before rolling a die.

 

The second is simply stating how likely a particular outcome of an action is. it makes no definitive prediction about the future. An example might be to say "there is a 12/5% chance i'll role a six". Whats more you can prove you're statement using math. This is what the stormwardens are doing when predicting the weather. They probably say there is a 88% change of a highstorm between 8 and 9pm tonight. they can show the math they use to determine this. The result is that the ardents (who are educated) agree that this isn't prophecy, but math instead.

Also i suspect that the math for predicting high storms was developed in the east where vorinism prohibitions on prophecy probably don't mean much.

 

It also wouldn't be prophecy if you were doing a thought experiment. There is no future to predict in a thought experiment.

And statistics are just as important  for working out things about the present or past as they are about the future. For example working out the current population of the parshindi using statistics, past knowledge of raids and army strength would have nothing to do with the future. The same would be true of a shop keeper trying to work out how much new product to order using statics on past sales, no future involved.

 

In fact thinking about it the vorin doctrin against prophecy might have forced the development of cretin math in an attempt to get around the prophecy stigma, after all math is logically and provably not prophecy.

tl;dr Statics and probability don't necessarily conflict with vorinism and where they do (or are seen to) they can still be developed in the vorin free east, moving west when they have firmly established themselves as a science.

[Oversleep]

I don't say that science is in conflict with vorinism (ardents are scholars after all) but how come the culture still frowns upon stormwardens and the games that include anticipating the outcome (Szeth Interlude in WoK)?

Kaladin was worried about ardents hearing about him saying he will survive the highstorm. He was saying things while facing a sure death, after being severely beaten and he could have just been babbling about and he was still worried about ardentia learning about it.


Anyway, I'd love to learn something about stormwarden equations. I can't figure it out: highstorm cycles around the planet, at the same time it's not regular and can be predicted. How is that working?

[LordOfMortals]

I'm not sure exactly but I think they analyze the patterns of previous high storms to determine future ones. It seemed to me there was very complex pattern that one could only see by reviewing high storm activity over a long period of time.

[LordOfMortals]

Further the reason they can't say for certainty when the high storm will be is do to the immense complexity of the pattern.

[navybrandt]

I thought of a way to intercept spanreed messages, but it requires approaching the target.

You have to put additional gemstone in one of the spanreeds, thus linking it to yours. Basically one of their spanreeds is now linked to two others. Unless they dissect the spanreed they won't find out. And it's untraceable.

I'm kind of interested in the intercepting of spanreed messages side of this topic. Oversleep's method would only work on one side of the message. You'd have to also put an additional gem in the other spanreed. It's also risky as it might add weight to the spanreed that would be noticeable. Good concept though. You would also have to know when the other two are communicating unless you constantly kept your copy ready to receive messages. Seems like it would require a great deal of effort to keep secret.

 

The idea of originally splitting the gem into three and secretly keeping one of them would work great. Perhaps there's also a way to use Investiture to change the Identity (capital I) of a third spanreed, but that would have the same drawbacks as above.

 

The obvious solution is just a regular spy, but that involves risk of being caught, becoming a double agent, etc. Plus it's not a instant as a spanreed.

 

This whole concept fascinates me.