Shardcast: Knights Radiant Quiz with New Lore!

Willshaper here 

Yeah, that's pretty much what happened to me with the decisive/indecisive meter

But if math is an objective fundamental truth about the universe then why do people constantly argue about the axiom of choice, continuum hypothesis, etc.?

Huh, I thought alley cat vs guard dog was about being a loner versus a protector.

6 hours ago, BobHeraldOfTheAlmighty said:

But if math is an objective fundamental truth about the universe then why do people constantly argue about the axiom of choice, continuum hypothesis, etc.?

i'm going to pretend I understood that

8 hours ago, Snorkel said:

Huh, I thought alley cat vs guard dog was about being a loner versus a protector.

Me too.

12 hours ago, BobHeraldOfTheAlmighty said:

But if math is an objective fundamental truth about the universe then why do people constantly argue about the axiom of choice, continuum hypothesis, etc.?

I mean, objectively, there is nothing to argue about - the issue is just usually poorly explained, even in otherwise good math books.

The "normal" mathematics - everything we use for describing the world (from counting on fingers to string theory) is based on one simple premise: we assume that the empty set exists and built further things from it (natural numbers, integers, rational numbers, real numbers etc.) using logic and set theory. As long as we do that, the axiom of choice and the continuum hypothesis are automatically true - they're not even axioms, simply the consequence of the fact that we built everything from scratch (I mean the empty set).

But, just like we assumed the existence of an empty set, we can assume the existence of ANYTHING. You can create a new axiom that postulates the existence of very crazy sets or any other mathematical structures. You essentially create a new kind of mathematics in which the aforementioned axioms/hypotheses don't necessarily hold. It has, as long as we know, nothing to do with the real world and you'll not encounter such weird things unless you do PhD in pure mathematics.

Storms, the Truthwatcher result was so correct

Fun episode. Regarding the excitement about getting to see a Lightweaver that is stage presentation oriented as opposed to visual arts oriented: <cough>Hoid<cough>.

I suppose one might argue that he wasn't yet technically a Lightweaver during the grand tellings of Fleet, or Wandersail, or The Girl Who Looked Up, but does the spren actualize the Radiant or does the Radiant actualize the spren?

So for the first time listening I wanted to scream my theory that y’all got so close to about Bondsmith squires!  I read the descriptions on reddit and instantly thought of this person. 
 

There’s one person I believe who is set up to succeed Dalinar and he is already showing signs of bonding things no one else has.  Adolin is re-bonding a dead spren, and doing so will help unite spren and people again.  Plus, just for fun, you could easily argue killing Sadeus united Alethkar.  
 

This would also carry over to the back 5 well (IMO) because I get the feeling Dalinar won’t survive Book 5, at least as a mortal being. 

I took the quiz and was assigned Willshaper. Cool. I looked at the numbers and I actually had a three-way tie between Willshaper, Lightweaver, and Edgedancer, all at 71. So....am I really a Willshaper? Or am I a Willweavedancer? Has anyone else had ties on this thing?

16 hours ago, BobHeraldOfTheAlmighty said:

But if math is an objective fundamental truth about the universe then why do people constantly argue about the axiom of choice, continuum hypothesis, etc.?

Well, you can argue about axioms, but once you agree on axioms, a proof is true forever. No one, not aliens, gods, or anything can disagree with the fundamental theorem of algebra, for example. That's true power  

1 hour ago, Chaos said:

Well, you can argue about axioms, but once you agree on axioms, a proof is true forever. No one, not aliens, gods, or anything can disagree with the fundamental theorem of algebra, for example. That's true power  

I agree that once you pick the axioms it’s objective truth, I’m just saying whether the axioms apply to the “real world” is  not entirely clear cut. 
 

As an aside, it’s easy to disprove the axiom of choice. Just ask your girlfriend what she wants for dinner.

@Chaos Math is not at all my field of expertise; I didn't go beyond linear algebra and integral calculus, and in terms of proofs, I only ever regurgitated proofs of theorems that were proven centuries ago. Plus, it's been years since I ever had to do any of that, so my "math knowledge" is pretty basic.

Thus, I might not know enough axioms (it's the first time I hear about the axiom of choice, actually, and I don't think it has to do with me not paying attention in high school...), but when you say people "can" argue about axioms... I'm assuming that you mean different axioms could be agreed upon, and you could still establish truths from there. Or is that not correct?

I guess a more important question would be, for me: are the basic axioms I was taught about in school, and that allowed me to eventually make sense of algebra and calculus... do people actually argue about those? And if so, what point are they trying to make?

They just argue about what is relevant to assume, is all. Most axioms are not argued about, but axiom of choice is. 

1 hour ago, BobHeraldOfTheAlmighty said:

I agree that once you pick the axioms it’s objective truth, I’m just saying whether the axioms apply to the “real world” is  not entirely clear cut. 
 

As an aside, it’s easy to disprove the axiom of choice. Just ask your girlfriend what she wants for dinner.

I never said they apply to the real world (whatever that means). That is not required, and that's okay. But math is often the language of the universe, deep down.

I like math because when I'm teaching, the answers to problems are correct, or they are not correct. No one can take that away from you.

You can't prove or disprove axioms, by the way. That's why they are axioms. And that isn't a counterexample for that anyway. This hypothetical girlfriend can make such a selection. Whether they are willing to is a human matter, but the point is there are selections that good be made. Bad example.

EDIT: As a note, I actually think I prefer Elsecallers, despite my firm beliefs of the truths of mathematics. If I was a Radiant and a better person, I'd want to reach my potential and be way less lazy.

43 minutes ago, Chaos said:

They just argue about what is relevant to assume, is all. Most axioms are not argued about, but axiom of choice is.

Ok, that makes sense: all is right with the world.

Thanks btw!

(Meant to edit my post, but I got this message everytime:

"We could not locate the item you are trying to view. Error code 2T252/F")

There are some weird bugs on the main page. I know  

11 hours ago, Chaos said:

Well, you can argue about axioms, but once you agree on axioms, a proof is true forever. No one, not aliens, gods, or anything can disagree with the fundamental theorem of algebra, for example. That's true power  

Arguing about axioms is not to be minimized, moreover there is no objective way of resolving those kind of disputes. Also any set of axioms will either give you an undecidable theory or be too primitive to be of any interest.

1. Disappointed that Brandon is messing up the Skybreakers. The Skybreaker oaths we know have issues and I was hoping that would be explained by corrupted spren and Nale being insane. 

2. The descriptions give some credence to an idea I particularly like: in WoK there is an epigraph that reads: "Three of sixteen ruled, but now the Broken One reigns." One interpretation is that initially three shards came to Roshar: Honor, Cultivation and Ingenuity. Once Odium showed up, Ingenuity fled and the broken one refers to Honor. 

The Sibling is Ingenuity's spren and it is slumbering because Ingenuity left or has invested elsewhere.

All orders (except for Bondsmiths) are a mix of three investitures. The orders closest to Ingenuity are Willshapers:

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The Willshapers have a reputation for attracting builders, craftspeople, and creators to the Radiants. [...] They are united through a love of building, but some consider the building of society to be more important than the building of structures. [...] Among the Radiants, they are generally focused on building, training, and making infrastructure.

And Dustbringers:

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They often attract tinkerers who like to dig down into the shape and soul of a thing, break it, and see what makes it work. [...] They instead see their nature as being about control, precision, and understanding. [...] They attract anyone who likes to take things apart, who likes to know how things work.

50 minutes ago, Parallax said:

Arguing about axioms is not to be minimized, moreover there is no objective way of resolving those kind of disputes. Also any set of axioms will either give you an undecidable theory or be too primitive to be of any interest.

I'm not saying it should be minimized, just that mathematical proof is the highest form of knowledge that exists.

2 minutes ago, Chaos said:

I'm not saying it should be minimized, just that mathematical proof is the highest form of knowledge that exists.

But people disagree about what constitutes a proof as well!

There is a longstanding tradition in mathematics that rejects the law of excluded middle and proof by contradiction (to oversimplify their notion of proofs is more constructive) more recently there are also those who question modus ponens (to oversimplify their notion of proof is more feasible). 

Uh, proof by contradiction is very much a well accepted proof strategy in literally every math course I've ever had in grad school. Those people arguing those things sound super pretentious, I'll be honest. That mathematical philosophy is pretty boring to me. 

1 hour ago, Chaos said:

Uh, proof by contradiction is very much a well accepted proof strategy in literally every math course I've ever had in grad school. Those people arguing those things sound super pretentious, I'll be honest. That mathematical philosophy is pretty boring to me. 

The issues with excluded middle (or proof by contradiction, they're logically equivalent) are that :
1) They are often used to show that an object exists without ever describing it (just saying that it exists because it cannot not exist). This is an issue when you want to use the object. It can be especially annoying for (fundamental) computer sciencist. I won't go into details, but you can show that programming and proving are the same thing. Thus, using the contradiction to prove something is like telling that "there is a program that solves your problem, because it cannot not exists. But I haven't the faintest clue about what it looks like".

2) Many, many proofs using contradiction can be rewritten without it. Sometimes it's painfull, somestimes it's not. But using contradiction makes us not even consider the possibility that we could do it, and as I've said in 1) a proof not using the contradiction is often a much more usefull (and informative) proof.

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But math is often the language of the universe, deep down.

Well, one could argue that math were made to describe the universe, so it's only logical that the universe can be expressed in math terms.

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I'm not saying it should be minimized, just that mathematical proof is the highest form of knowledge that exists.

On the other hand, if you consided maths to be the propostions that logically derives from a set of axioms, then maths is very little knowledge : you "know" that those axioms leads to those properties, but that's no knowledge at all regarding our reality. It's just formal logics. (But that's a debate regarding what is truth, not so much about maths ^^)

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but once you agree on axioms, a proof is true forever.

Well... we are peer-reviewing maths articles, and that's for a reason . The issue with formal proof is that it allows only for very small "steps" in a proof (if masochist curious, you can google first order logic). In almost every proof you've written in your life, you skipped or merged many of those steps. And that's the right thing to do (if you want to write every small steps, you use a proof assistant like Coq, so that the machine can check you proof - because almost no human will like such a proof) ! But it can also lead to some proofs we thougt were right being discovered wrong many years later - that's what happened to the four colors theorem for exemple : in 1859, Kempe thougt he had a correct proof, it was considered as such during ten years, and then proven wrong by someone else.

(Yeah, I'm kind of a math addict ^^)

One of the best Shardcasts you've done so far!  The Windrunner vs. Elsecaller genocide debate was epic!

I took the quiz 3 times. Consensus is Edgedancer with Truthwatcher as a very close second.  Makes sense...I was a scientist for a while (PhD in Biochem), but left the research world to be a statistician with a health care company to have a more direct impact on helping people.  Applied science for the common good rather than pure science.

3 hours ago, Parallax said:

1. Disappointed that Brandon is messing up the Skybreakers. The Skybreaker oaths we know have issues and I was hoping that would be explained by corrupted spren and Nale being insane. 

The oaths themselves don't have issues (they just show who the Skybreakers are), and Brandon did explain that the current issues with the Skybreakers are because of Nale.

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Note that the current incarnation, led by the Herald Nale in his madness, is more rigid than the ancient order, which understood that the law was not perfect, but instead represented an ideal to try to reach over time.