Thoughts on One Power strength levels and exhaustion and linking (math intensive)

[BFG]

Doesn't the above example contradict your definition of an angreal adding and a sa'angreal multiplying?

[Craig Jarvis]

Perhaps, but this theory is still in flux. It does match what Elaine stated that the Angreal would increase what a woman could channel by 2 to 3 times. At different points in the power scale it would be closer to three times.

 

There are also points in the power scale that adding a fixed amount yields almost identical results as multiplying their amount, as the number is the same.

 

So this example may be right on the tipping point. As has been stated here by yourself and my self and others there isn't alot of good examples to allow us to eliminate one theory yet.

[Vardar]

Actually it's been stated that Angreal and Sa'angreal don't multiply, they add a static number.

 

I hear your point about perception, but what does exhaustion have to do with it? Generally speaking, although people in this series have skewed perceptions of things, one thing females can do correctly is gauge power levels. If Elayne says she's twice as power as Ny with object A, I think we'd have to take her word on it.

 

Angreal and Sa'angreal both do the same exact thing, only on different levels. There's a number breaking point that when reached, an Angreal becones a Sa'Angreal. Moriene's statement about her Angreal that was nearly a Sa'angreal helps prove that point.

[Whizbang]

There is a multiplying affect to Angreal, however. Else, when they are using the Bowl of Winds, why give the Angreal to the strongest channelers? Why not give them to whoever you trust not to keep it for their own? A stronger channeler can get more out of an Angreal than a weaker channeler. I think there are other examples of circles with Angreal that demonstrate this, but I cannot remember them off the top of my head.

 

I agree that Angreal and Sa'Angreal are the same except for the strength, but they definitely don't just add a static power, no matter who uses them.

 

Lanfear (pre-Finns) or Alivia would have received a lot more power from the CK than Nyn. Rand chose Nyn because he trusted her. Look at the difference in powers between Rand and Nyn when they use the CKs. The amount of Saidar was obviously massive, but Saidin was described as being so much more, to the point where Logain did'nt believe it was Rand, but the Creator. If the Sa'Angreal just gave static power, the level of Saidin and Saidar would have been the same. They were not, unless I am misremembering or misunderstanding.

 

Maybe Angreal are multipliers (eg 7*3 ) and Sa'Angreal are exponential (eg 7^3), if you insist that there is a fundamental difference between them.

[Vardar]

There is a multiplying affect to Angreal, however. Else, when they are using the Bowl of Winds, why give the Angreal to the strongest channelers? Why not give them to whoever you trust not to keep it for their own? A stronger channeler can get more out of an Angreal than a weaker channeler. I think there are other examples of circles with Angreal that demonstrate this, but I cannot remember them off the top of my head.

 

I agree that Angreal and Sa'Angreal are the same except for the strength, but they definitely don't just add a static power, no matter who uses them.

 

Lanfear (pre-Finns) or Alivia would have received a lot more power from the CK than Nyn. Rand chose Nyn because he trusted her. Look at the difference in powers between Rand and Nyn when they use the CKs. The amount of Saidar was obviously massive, but Saidin was described as being so much more, to the point where Logain did'nt believe it was Rand, but the Creator. If the Sa'Angreal just gave static power, the level of Saidin and Saidar would have been the same. They were not, unless I am misremembering or misunderstanding.

 

Maybe Angreal are multipliers (eg 7*3 ) and Sa'Angreal are exponential (eg 7^3), if you insist that there is a fundamental difference between them.

 

There's a quote from the author on it. I'll see if I can dig it up, it's not multiplying it's just a set number.

 

http://www.theoryland.com/intvmain.php?i=454

 

Maybe it's just the stigma that the strongest are more used to handling power flows?

[Whizbang]

There is a multiplying affect to Angreal, however. Else, when they are using the Bowl of Winds, why give the Angreal to the strongest channelers? Why not give them to whoever you trust not to keep it for their own? A stronger channeler can get more out of an Angreal than a weaker channeler. I think there are other examples of circles with Angreal that demonstrate this, but I cannot remember them off the top of my head.

 

I agree that Angreal and Sa'Angreal are the same except for the strength, but they definitely don't just add a static power, no matter who uses them.

 

Lanfear (pre-Finns) or Alivia would have received a lot more power from the CK than Nyn. Rand chose Nyn because he trusted her. Look at the difference in powers between Rand and Nyn when they use the CKs. The amount of Saidar was obviously massive, but Saidin was described as being so much more, to the point where Logain did'nt believe it was Rand, but the Creator. If the Sa'Angreal just gave static power, the level of Saidin and Saidar would have been the same. They were not, unless I am misremembering or misunderstanding.

 

Maybe Angreal are multipliers (eg 7*3 ) and Sa'Angreal are exponential (eg 7^3), if you insist that there is a fundamental difference between them.

 

There's a quote from the author on it. I'll see if I can dig it up, it's not multiplying it's just a set number.

 

http://www.theorylan...vmain.php?i=454

 

Maybe it's just the stigma that the strongest are more used to handling power flows?

 

Cool. Learned something new. I really should focus on reading these interviews. I started a while back reading the very first ones listed on TheoryLand, but dropped it after a while.

 

So, there you have it, Angreal and Sa'Angreal are static adds to power. They are more like a reservoire that can be safely channeled all at once (I am assuming here that the resevoire quickly refills itself just like the OP does, else you couldn't channel for long periods of time). Maybe the Eye of the World was an Sa'Angreal without form, and without the ability to refill itself. That place is still a mystery to me as to why they made it, other than to give Rand a chance to channel clean Saidin during that one battle. But I digress.

[Vardar]

There is a multiplying affect to Angreal, however. Else, when they are using the Bowl of Winds, why give the Angreal to the strongest channelers? Why not give them to whoever you trust not to keep it for their own? A stronger channeler can get more out of an Angreal than a weaker channeler. I think there are other examples of circles with Angreal that demonstrate this, but I cannot remember them off the top of my head.

 

I agree that Angreal and Sa'Angreal are the same except for the strength, but they definitely don't just add a static power, no matter who uses them.

 

Lanfear (pre-Finns) or Alivia would have received a lot more power from the CK than Nyn. Rand chose Nyn because he trusted her. Look at the difference in powers between Rand and Nyn when they use the CKs. The amount of Saidar was obviously massive, but Saidin was described as being so much more, to the point where Logain did'nt believe it was Rand, but the Creator. If the Sa'Angreal just gave static power, the level of Saidin and Saidar would have been the same. They were not, unless I am misremembering or misunderstanding.

 

Maybe Angreal are multipliers (eg 7*3 ) and Sa'Angreal are exponential (eg 7^3), if you insist that there is a fundamental difference between them.

 

There's a quote from the author on it. I'll see if I can dig it up, it's not multiplying it's just a set number.

 

http://www.theorylan...vmain.php?i=454

 

Maybe it's just the stigma that the strongest are more used to handling power flows?

 

Cool. Learned something new. I really should focus on reading these interviews. I started a while back reading the very first ones listed on TheoryLand, but dropped it after a while.

 

So, there you have it, Angreal and Sa'Angreal are static adds to power. They are more like a reservoire that can be safely channeled all at once (I am assuming here that the resevoire quickly refills itself just like the OP does, else you couldn't channel for long periods of time). Maybe the Eye of the World was an Sa'Angreal without form, and without the ability to refill itself. That place is still a mystery to me as to why they made it, other than to give Rand a chance to channel clean Saidin during that one battle. But I digress.

 

I'm assuming just to hide those items, and because they knew there might be a need for untainted power for a brief time. They didn't know what for however. But hiding the items has to be the real reason.

[Agitel]

I applaud this topic. Thinking of the power levels as a "radius" of their connection to the One Power instead of just their overall strength is pretty insightful. I do think there needs to be some adjusting for finding out how the power adds together when linked, though.

[Whizbang]

Maybe, when linking, it is a doubling of the radius of the hose/connection, but it is also doubling the length of the hose/connection. Thinking way back to high school physics, I seem to remember that when calculating the volume of a hose, length and radius matter. Radius allows more throughput of liquid, but length reduces the pressure, or something (sorry it has been a long time). So, this would account for the "not quite as much as the two added together" rule.

 

You math-y folks will have to calculate that out.

[Craig Jarvis]

@vardarms

 

Thanks for that link. That resolves alot for my formula. So Angreal and Sa'angreal pretty much do the same thing. So let's say an Angreal can add up to 499 in power from my area of a circle calculation. And a Sa'Angreal can add upwards of 500. So the one Moiraine has is in the high 400's. This would take her from the PL2@ 12 to the 425-500 level. Which would make her "as powerful, if not moreso". It would have made Lanfear almost on Par with Rand, except Rand hadn't hit his peak yet, was loath to harm a woman, and didn't have the skill mastery to match Lanfear. That kinda makes the number hit the mark. As to why the strongest were given the Angreal, I think I have your answer. The Stronger channelers have a higher endurance (a larger volume of power to pull from before exhaustion takes them out). The Angreal allows them to burn thier supply faster, but doesn't increase their supply. A weak channeler would be able to do bigger things with one, but not more. I believe that a Sa'Angreal increases both how much or how fast rather you can burn your supply and also increases how much your supply is (your limit before exhaustion) Perhaps that is why the female CK melted, Rand burnt all she had and then pulled more through it faster than it could "refill" creating a vacuum that destroyed it to "Protect" the female user.

 

With Elaine's Angreal she found (the turtle I believe it was) was only about 3 times the power for an average AS (about PL7 @153) and about 2 times for a strong AS (PL12 @452) So if it added about 300-350 that would put it about right. Well Elaine said it was weak, and would only improve an AS about 2-3 times. For her it might seem a weak one as she would only be improved about 50%. I think I am liking these numbers.

 

@Whizbang

You are thinking of flow vs volume... two seperate measurements (yet connected). Flow would be area of the hose opening (pi*r^2) times the rate of flow, that would give you volume per unit of time, which you are correct, that is what I am trying to get visualized, you are on track. The other formula you were hinting at was the volume of a cylinder. I thought about using that formula but the increasing returns on higher power levels wasn't realized through the entire powerscale, so I discarded it for one that seemed to yeild a more exponential scale for the volume (sphere). Think balloon with a nozzle vs. a hose with a nozzle. If you ran the math out on the hose (cylinder) through the powerscale you would see only a static increase in volume directly related to length, unless you were also increaseing the radius of the hose. I am trying to figure out the endurance of the channeler also in relation to their strength. I may need to revisit this if my perceptions change a bit more tho... So I will keep you in mind.

 

@agitel

I agree there is still alot of unknowns in the linking department. hopefully, we will get more and better examples. I think i am on the right track with the boulder perception issue there tho... Just visualize three same size boulders lined up and think are they the same mass as one boulder with a radius three times the size of one of these smaller boulders? Alot of people would say yes, on the initial guess, but look at the volume of a boulder with a radius of 15 vs the volume of a boulder with a radius of 5. Huge-a-mungous difference, so even three boulders with a radius of 5 do not add to be near the volume of a boulder of a radius of 15. That is my take on perception being the issue when they say it doesn't add up but there is an increase. a boulder that is 10 feet across and a boulder that is 20 feet across, the 20 foot boulder is not twice as large... do the math it is 8 times as large. So, 2 tens do not equal a 20, see math doesn't add up, but it is true.

[Vardar]

@vardarms

 

Thanks for that link. That resolves alot for my formula. So Angreal and Sa'angreal pretty much do the same thing. So let's say an Angreal can add up to 499 in power from my area of a circle calculation. And a Sa'Angreal can add upwards of 500. So the one Moiraine has is in the high 400's. This would take her from the PL2@ 12 to the 425-500 level. Which would make her "as powerful, if not moreso". It would have made Lanfear almost on Par with Rand, except Rand hadn't hit his peak yet, was loath to harm a woman, and didn't have the skill mastery to match Lanfear. That kinda makes the number hit the mark. As to why the strongest were given the Angreal, I think I have your answer. The Stronger channelers have a higher endurance (a larger volume of power to pull from before exhaustion takes them out). The Angreal allows them to burn thier supply faster, but doesn't increase their supply. A weak channeler would be able to do bigger things with one, but not more. I believe that a Sa'Angreal increases both how much or how fast rather you can burn your supply and also increases how much your supply is (your limit before exhaustion) Perhaps that is why the female CK melted, Rand burnt all she had and then pulled more through it faster than it could "refill" creating a vacuum that destroyed it to "Protect" the female user.

 

With Elaine's Angreal she found (the turtle I believe it was) was only about 3 times the power for an average AS (about PL7 @153) and about 2 times for a strong AS (PL12 @452) So if it added about 300-350 that would put it about right. Well Elaine said it was weak, and would only improve an AS about 2-3 times. For her it might seem a weak one as she would only be improved about 50%. I think I am liking these numbers.

 

The Angreal Lanfear had, wasn't the same as the one Moriane has now.

[Agitel]

@agitel

I agree there is still alot of unknowns in the linking department. hopefully, we will get more and better examples. I think i am on the right track with the boulder perception issue there tho... Just visualize three same size boulders lined up and think are they the same mass as one boulder with a radius three times the size of one of these smaller boulders? Alot of people would say yes, on the initial guess, but look at the volume of a boulder with a radius of 15 vs the volume of a boulder with a radius of 5. Huge-a-mungous difference, so even three boulders with a radius of 5 do not add to be near the volume of a boulder of a radius of 15. That is my take on perception being the issue when they say it doesn't add up but there is an increase. a boulder that is 10 feet across and a boulder that is 20 feet across, the 20 foot boulder is not twice as large... do the math it is 8 times as large. So, 2 tens do not equal a 20, see math doesn't add up, but it is true.

 

Oh, I agree, and I understand the way these things add up. Conceptually it all makes sense. I'm just saying something feels off. Two 1s only half as strong as a 2. Two 5s as strong as a 7. Two 25s 1.85 times the strength of a 26.

 

I suppose there's nothing in the books to contradict that. Continuing to think on it, I'm actually starting to accept it more. Again, my point wasn't to question the math or the concept. It's just that lower levels linking getting less advantage from linking than high levels against channelers just above them intuitively wrong to me in so far as it fit into the story (again, not a concept or math thing qualm, I am one semester away from a bachelors degree in math).

[Craig Jarvis]

@vardarmus

 

Yup it is the same angreal that Lanfear used in the attack at the pier in Cairhien. Moiraine recieved it from the 'Finn as a wish.

[Craig Jarvis]

@Agitel

 

And there may be a real point there... The only example that we have that I can use might be a spoiler and I don't wish to spoil anything from aMoL, for those who are avoiding the few snippets that have been pre-released.

[Craig Jarvis]

Hmm.. my boulder example: been thining about how to explain this a bit better.

 

Example:

Two round boulders

The first is 10 feet wide, the second is 20 feet wide.

if you statement that the second is twice as large as the first, then you are only looking at the objects one-dimentially.

if you say that the second boulder is 4 times the size as the first, you are only looking at the objects two-dimentially.

if you say that the second boulder is 8 times the size as the first, you are looking at the boulders three-dimentially.

Which is correct? That depends on what you are measuring for...

if you are measuring how far you have to divert your path to get around each boulder the the second is only twice as large.

if you are measuring how much sunlight is being blocked by each boulder then the second is four times larger.

if you are trying to gauge the weight by using similar density analysis, then the second would be 8 times larger.

 

so power level would be a one-dimensional view of their power.

How much the channeler can burn (how fast they can use the power) would be a 2 dimentional view.

and how much power they have at their disposal without regard to how fast they can burn through it, would be a three dimentional view.

[BFG]

I understand your argument with circles/spheres. The problem I see with viewing it as 1D, 2D and 3D is that at the least the 1D is a label the reader puts on them. All I remember a channeler doing is saying that another channeler is stronger (or weaker), thus in story there is no level 4,7,10, etc. So when they're measuring strength in the power they're measuring strength (as I understand it, that's your 3D view). Therefore they're saying that if 1 channeler has strength x and another y then linked their power output is x + y - l (where l = loss).

 

Don't think I'm explaining this very well. But in our definition 2 5's link. Your argument as I understand it is that their powers added together doesn't make a 10 thus their's a power loss. But since they don't view themselves as being level 5s, they view themselves of having power x, and they're saying that when linking x+x =/= 2x.

 

Sorry, best I can do at the moment. I'll think and see if I either change my mind, or think of a better way to explain :)

 

Like your math with the angreals.

[Vardar]

I understand your argument with circles/spheres. The problem I see with viewing it as 1D, 2D and 3D is that at the least the 1D is a label the reader puts on them. All I remember a channeler doing is saying that another channeler is stronger (or weaker), thus in story there is no level 4,7,10, etc. So when they're measuring strength in the power they're measuring strength (as I understand it, that's your 3D view). Therefore they're saying that if 1 channeler has strength x and another y then linked their power output is x + y - l (where l = loss).

 

Don't think I'm explaining this very well. But in our definition 2 5's link. Your argument as I understand it is that their powers added together doesn't make a 10 thus their's a power loss. But since they don't view themselves as being level 5s, they view themselves of having power x, and they're saying that when linking x+x =/= 2x.

 

Sorry, best I can do at the moment. I'll think and see if I either change my mind, or think of a better way to explain :)

 

Like your math with the angreals.

 

RJ himself listed the levels. 21 for females, with "several" more above for males, which more people take to mean 26 or so. So within in the 21 levels, the actual power level difference between two numbers is what is up for true debate, and where the math gets weird.

[Whizbang]

I don't know how this affects anything in this thread, but keep in mind only powerful channelers can use powerful Angreal. At one point it is discussed that only a handful of current AS could use the CK (Mor, Suiane, I don't remember the others) and three in training (Eg, Nyn, and Elayne). So, you need a certain level of power and/or stamina to use an Angreal. So, post-Finns Mor will not be able to use the CK, yet she can use an "almost" Sa'Angreal without any seeming difficulty. Where does that line lay?

[BFG]

I understand your argument with circles/spheres. The problem I see with viewing it as 1D, 2D and 3D is that at the least the 1D is a label the reader puts on them. All I remember a channeler doing is saying that another channeler is stronger (or weaker), thus in story there is no level 4,7,10, etc. So when they're measuring strength in the power they're measuring strength (as I understand it, that's your 3D view). Therefore they're saying that if 1 channeler has strength x and another y then linked their power output is x + y - l (where l = loss).

 

Don't think I'm explaining this very well. But in our definition 2 5's link. Your argument as I understand it is that their powers added together doesn't make a 10 thus their's a power loss. But since they don't view themselves as being level 5s, they view themselves of having power x, and they're saying that when linking x+x =/= 2x.

 

Sorry, best I can do at the moment. I'll think and see if I either change my mind, or think of a better way to explain :)

 

Like your math with the angreals.

 

RJ himself listed the levels. 21 for females, with "several" more above for males, which more people take to mean 26 or so. So within in the 21 levels, the actual power level difference between two numbers is what is up for true debate, and where the math gets weird.

 

 

This is why my explanation isn't good.

 

In 13th depository Delana and Doesine are level 9. Nyn is level 18.

 

Craigs position is that if Delana and Doesine link then they don't = Nyn, as the jump between levels isn't linear. I'm arguing that in story, they wouldn't ever think that they would or should. Moiraine states at some point that Eg is a candle besides Nyns bonfire, yet there are only 3 levels between them.

 

I'm trying to argue that when they sense each others strength they're sensing the volume and not a 1D representation similar to a level.

 

 

Could possibly view the power-loss as overlapping circles - or maybe that some of the strength of the channeler goes into maintaining the link.

[Craig Jarvis]

@ whizbang

This has been discussed... the only Quote that specifies the limitation is the CK. However I agree with you, that Sa'Angreal (or some Sa'Angreal) probably do have a limit on if a weaker channeler can use them. The 13th depository has the chart and specifies PL12 (i think... may be PL11) as the minimum strength needed to access the CK.

 

@BFG

I believe the reason you are having difficulty with seeing my point on perception is probably because you naturally view the world in 3D. Thus you never suffer the paradigm shifts experienced when you moved to a deeper perception. Are you an artist/deal with sculpture/hair stylist/hedge trimmer /architect/engineer? Are you dyslexic? Those type people typically see in 3D naturally. They don't see the world as flat, and probably never have.

 

As to the females percieving each other's strengths. the best sence I get is sort of like a gravametric distortion. They can sense the size of it. Much like the diameter of a boulder, and they say ahh. that boulder is twice as wide, as my boulder. It is a very easy way to provide a comparison, if all you want is to categorize them by size. But the actual output as we see in the books is much more than a single notch higher. A person just two notches higher is pretty much un-contestable by the lower party. One notch different and the lower person would need an edge to have a chance. Remember Moghedin and the black Ajah. they all tried to best Moggy, and it was a hands down defeat. some of them were not weak AS. Not the strongest of the Black ajah mind but they weren't all PL7's either There were some 8's and 9's there. Didn't some of them even try to link and overcome her (off-screen, but mentioned later)? Moggy, wasn't even concerned. Moggy would be crushed like a bug if she went up against Lanfear, and she knows it, but probably didn't even fear the lot of them linked (as there were only a few, and she was skilled at breaking shields (talented even, I should probably note that for the last book so I am not surprised when it popps up LOL)

[Agitel]

I'm trying to argue that when they sense each others strength they're sensing the volume and not a 1D representation similar to a level.

 

Could you elaborate on how this would work against Craig's model?

 

EDIT: Is the concern with characters comparing themselves to others?

[BFG]

I'm trying to argue that when they sense each others strength they're sensing the volume and not a 1D representation similar to a level.

 

Could you elaborate on how this would work against Craig's model?

 

EDIT: Is the concern with characters comparing themselves to others?

 

The best I can do is say that we view Eg and Nyn as only a few levels apart - I don't believe the characters are aware of levels the way we see them. So for example Doesine is a level 9, Nyn is a level 18 - but neither we nor the characters think that Nyn is twice as strong. Indeed we, and the characters, are aware that Nyn is far, far more powerful than Eg (Moiraine, candle/bonfire), although they are only a few levels apart. So although out of world we can use maths based on the levels that RJ came up with, in world they don't think that way. So Craigs point was that as Doesine and Delana were to link as level 9's then they wouldn't equal a level 18 (Nyn), and that this accounts for the perceived power loss.

 

My point is that the channelers are aware that Nyn is more than twice as powerful as either Doesine or Delana and thus would never expect them to equal her linked. Therefore the power loss is something different.

 

 

 

But I have been thinking of what they can sense.

 

I guess we can all agree that the Power is seperate from the Channelers (as in it's not something that's stored within them) and that somehow they access the external source. So it's possible that what they sense in each other is the size of the connection - which fits Craigs circle analogy - except that there's no reason to then think that characters would see the radius instead of the area and no indication that they do. It could also explain why female channelers sense the full potential as well as the current level - they can sense both the 'open' (current) and 'closed'(potential) sections, whereas men can only sense the 'open' section. If you think about the area as the power that can be used then when they link the circles overlap - and this overlap reduces the area of the 2 circles combined.

 

 

 

@Craig - I'm a structural geologist, so 3D thinking is pretty much the first requirement :) But I think the problem I have with your analogy is that I tend to take things literally, the characters say that 2 people linked can channel less than they do individually and I take them at their word :)

[Craig Jarvis]

@BFG

I will have to look at the overlap/tangent/concentric circles. This, if I can find/make a model, may yield a better and more universal linking theory.

 

As to the perceptions, try asking people the boulder example... If you saw 2 boulders one was 10 feet across and the second was 20 feet across, how many times larger is the second boulder than the first? Pretty much everyone will say twice as large, and on a one dimentional scale they are right.

 

Perceptions are relevant. Some people think that a reduction in gains is a loss, or a reduction in losses is a gain. But really it is just a speed change not a reversal.

[Vardar]

@vardarmus

 

Yup it is the same angreal that Lanfear used in the attack at the pier in Cairhien. Moiraine recieved it from the 'Finn as a wish.

 

BS has a quote saying it wasn't. They just seemed similiar. If it was the same Angreal, Rand would have been a puddle.

[Vardar]

I don't know how this affects anything in this thread, but keep in mind only powerful channelers can use powerful Angreal. At one point it is discussed that only a handful of current AS could use the CK (Mor, Suiane, I don't remember the others) and three in training (Eg, Nyn, and Elayne). So, you need a certain level of power and/or stamina to use an Angreal. So, post-Finns Mor will not be able to use the CK, yet she can use an "almost" Sa'Angreal without any seeming difficulty. Where does that line lay?

 

 

Actually that was only for the CK. Every other Sa'Angreal or Angreal, as far as we know, could be used by anyone. But then again, no other Sa'Angreal needed an access key. So the CK broke a lot of rules.