THE ULTIMATE METAL COUNT

Zoey · June 22, 2021

17 hours ago, mathiau said:

I assure you that calculation makes sense and have a firm mathematical backing. My previous explanation on the other hand maybe not

So, first we want the number of different possible God we can create, this is because Ettmetal is not an alloy of Lerasium and Atium but something both different and Allomantically viable and we have no reason to believe the fused Shard of Mercy, Cultivation and Devotion or any other would be different

Number of Gods with one Shard : 16=16!/1!(16-1)!

Number of Gods with two Shard, I take two Shards among the sixteen without regard for order : 16=16!/2!(16-2)! (=120)

Number of Gods with two Shard, I take three Shards among the sixteen without regard for order : 16=16!/3!(16-3)!

...

Number of Gods with fifteen Shards, I take fifteen Shards among the sixteen without regard for order : 15!/15!(16-15)! (=16)

Number of Gods with one Shard, I take fifteen Shards among the sixteen without regard for order : 16!/16!(16-16)! (=1)

So the number of Gods is Σ_k=1^16 (16!/k!(16-k)!) which is equal to Σ_k=1^16 (16!/k!(16-k)!)- 16!/0!(16-0)!

(I'm not managing to make clean sum in forum so I'll have to write "sum for k going from 1 to n" by Σ_k=1^n)

Since 0!=1 we have 16!/0!(16-0)!=1. For the Σ_k=1^16 (16!/k!(16-k)!) part we'll use Newton's binomial formula, Σ_k=1^n (a^k*b^(n-k)*n!/k!(n-k)!) =(a+b)^n which gives here

Σ_k=1^16 (1^k*1^(n-k)*16!/k!(16-k)!)=2^16

So the number of Gods is 2^16-1

Now the number of viable Godmetal alloy. For this part we made the supposition that if you take any combination of godmetals there'd be a way to alloy them in order to make a viable metal. It is a supposition that can be argued about, in my mind the fact there is more than sixteen viable alloys of Atium suggests this hypothesis is right.

Now for the actual calculation, you do the exact same reasoning as for the number of Gods but you replace every instance of 16 by 2^16-1

Is this clearer?

My excuses, I thought you were only looking at r=2 which would be "a big number in an order 2 polynomial" in which case it would made made sense if it was smaller than the exponential of a significantly smaller number

I'm not sure whether you mean you're summing the values for each r or if you're looking at each of them but I guess it doesn't matter since in the former case you get exactly 2^(10^21)-1 and in the latter case you get something of the order of 2^(10^21)/10^5, both of which are is far more than any number said in this thread except the insane 2^(17*(16)!) which we latter all agreed was wrong

May I know the exact context of your calculation? I'm a bit surprised you're obtaining all permutations of the stars with just binomial coefficients. (though it's definitely possible I just didn't understand what you said)

Okay, that all makes more sense, my apologies.

------

The context is just a character who made a blade formed of countless Stars, the number mentioned was only hundreds of millions, but I just wanted to see how high it would be if made into every star. But each Star she had in the blade had a power called an Authority, as they are all sentient beings of enormous power, and she could call upon Each Authority. She could also combine together Authorities to create a power of a different nature, and could do any combination. Thus came up with the (10^21)!/r!(10e21 - r)!

This would of course simplify to (2^(10^21))-1, because the summation of n!/r!(n-r)! for all values of R always goes into the Powerset of R, which goes to 10^10^10^1.31130. Of course this is an approximation that would be extremely far from the true answer. But it is close enough.

---

And yes, I was talking about that very, very large one as being wrong. And that was the one I especially didn't get the reasoning for. Could you explain what they were doing with it to get it that high?

Edited June 22, 2021 by Zoey

Zoey · June 22, 2021

Though one issue with this, is how we would be assuming impossibilities. like combining the Shards of, for instance, (Autonomy + Dominion + Ruin), with one like (Ruin + Devotion), where you would be combining Shards which already contain some of the same component parts.

First Layer of Combinations is

Spoiler

{1,2} {1,3} {1,4} {1,5} {1,6} {1,7} {1,8} {1,9} {1,10} {1,11} {1,12} {1,13} {1,14} {1,15} {1,16}

{2,3} {2,4} {2,5} {2,6} {2,7} {2,8} {2,9} {2,10} {2,11} {2,12} {2,13} {2,14} {2,15} {2,16}

{3,4} {3,5} {3,6} {3,7} {3,8} {3,9} {3,10} {3,11} {3,12} {3,13} {3,14} {3,15} {3,16}

{4,5} {4,6} {4,7} {4,8} {4,9} {4,10} {4,11} {4,12} {4,13} {4,14} {4,15} {4,16}

{5,6} {5,7} {5,8} {5,9} {5,10} {5,11} {5,12} {5,13} {5,14} {5,15} {5,16}

{6,7} {6,8} {6,9} {6,10} {6,11} {6,12} {6,13} {6,14} {6,15} {6,16}

{7,8} {7,9} {7,10} {7,11} {7,12} {7,13} {7,14} {7,15} {7,16}

{8,9} {8,10} {8,11} {8,12} {8,13} {8,14} {8,15} {8,16}

{9,10} {9,11} {9,12} {9,13} {9,14} {9,15} {9,16}

{10,11} {10,12} {10,13} {10,14} {10,15} {10,16}

{11,12} {11,13} {11,14} {11,15} {11,16}

{12,13} {12,14} {12,15} {12,16}

{13,14} {13,15} {13,16}

{14,15} {14,16}

{15,16}

This means that we can only combine Shards which do not have the same numbers included within them. Such as {1,2} x {3,4}

Spoiler

{1,2,3,4} {1,2,3,5} {1,2,3,6} {1,2,3,7} {1,2,3,8} {1,2,3,9} {1,2,3,10} {1,2,3,11} {1,2,3,12} {1,2,3,13} {1,2,3,14} {1,2,3,15} {1,2,3,16} {1,2,4,5} {1,2,4,6} {1,2,4,7} {1,2,4,8} {1,2,4,9} {1,2,4,10} {1,2,4,11} {1,2,4,12} {1,2,4,13} {1,2,4,14} {1,2,4,15} {1,2,4,16} {1,2,5,6} {1,2,5,7} {1,2,5,8} {1,2,5,9} {1,2,5,10} {1,2,5,11} {1,2,5,12} {1,2,5,13} {1,2,5,14} {1,2,5,15} {1,2,5,16} {1,2,6,7} {1,2,6,8} {1,2,6,9} {1,2,6,10} {1,2,6,11} {1,2,6,12} {1,2,6,13} {1,2,6,14} {1,2,6,15} {1,2,6,16} {1,2,7,8} {1,2,7,9} {1,2,7,10} {1,2,7,11} {1,2,7,12} {1,2,7,13} {1,2,7,14} {1,2,7,15} {1,2,7,16} {1,2,8,9} {1,2,8,10} {1,2,8,11} {1,2,8,12} {1,2,8,13} {1,2,8,14} {1,2,8,15} {1,2,8,16} {1,2,9,10} {1,2,9,11} {1,2,9,12} {1,2,9,13} {1,2,9,14} {1,2,9,15} {1,2,9,16} {1,2,10,11} {1,2,10,12} {1,2,10,13} {1,2,10,14} {1,2,10,15} {1,2,10,16} {1,2,11,12} {1,2,11,13} {1,2,11,14} {1,2,11,15} {1,2,11,16} {1,2,12,13} {1,2,12,14} {1,2,12,15} {1,2,12,16} {1,2,13,14} {1,2,13,15} {1,2,13,16} {1,2,14,15} {1,2,14,16} {1,2,15,16} {1,3,4,5} {1,3,4,6} {1,3,4,7} {1,3,4,8} {1,3,4,9} {1,3,4,10} {1,3,4,11} {1,3,4,12} {1,3,4,13} {1,3,4,14} {1,3,4,15} {1,3,4,16} {1,3,5,6} {1,3,5,7} {1,3,5,8} {1,3,5,9} {1,3,5,10} {1,3,5,11} {1,3,5,12} {1,3,5,13} {1,3,5,14} {1,3,5,15} {1,3,5,16} {1,3,6,7} {1,3,6,8} {1,3,6,9} {1,3,6,10} {1,3,6,11} {1,3,6,12} {1,3,6,13} {1,3,6,14} {1,3,6,15} {1,3,6,16} {1,3,7,8} {1,3,7,9} {1,3,7,10} {1,3,7,11} {1,3,7,12} {1,3,7,13} {1,3,7,14} {1,3,7,15} {1,3,7,16} {1,3,8,9} {1,3,8,10} {1,3,8,11} {1,3,8,12} {1,3,8,13} {1,3,8,14} {1,3,8,15} {1,3,8,16} {1,3,9,10} {1,3,9,11} {1,3,9,12} {1,3,9,13} {1,3,9,14} {1,3,9,15} {1,3,9,16} {1,3,10,11} {1,3,10,12} {1,3,10,13} {1,3,10,14} {1,3,10,15} {1,3,10,16} {1,3,11,12} {1,3,11,13} {1,3,11,14} {1,3,11,15} {1,3,11,16} {1,3,12,13} {1,3,12,14} {1,3,12,15} {1,3,12,16} {1,3,13,14} {1,3,13,15} {1,3,13,16} {1,3,14,15} {1,3,14,16} {1,3,15,16} {1,4,5,6} {1,4,5,7} {1,4,5,8} {1,4,5,9} {1,4,5,10} {1,4,5,11} {1,4,5,12} {1,4,5,13} {1,4,5,14} {1,4,5,15} {1,4,5,16} {1,4,6,7} {1,4,6,8} {1,4,6,9} {1,4,6,10} {1,4,6,11} {1,4,6,12} {1,4,6,13} {1,4,6,14} {1,4,6,15} {1,4,6,16} {1,4,7,8} {1,4,7,9} {1,4,7,10} {1,4,7,11} {1,4,7,12} {1,4,7,13} {1,4,7,14} {1,4,7,15} {1,4,7,16} {1,4,8,9} {1,4,8,10} {1,4,8,11} {1,4,8,12} {1,4,8,13} {1,4,8,14} {1,4,8,15} {1,4,8,16} {1,4,9,10} {1,4,9,11} {1,4,9,12} {1,4,9,13} {1,4,9,14} {1,4,9,15} {1,4,9,16} {1,4,10,11} {1,4,10,12} {1,4,10,13} {1,4,10,14} {1,4,10,15} {1,4,10,16} {1,4,11,12} {1,4,11,13} {1,4,11,14} {1,4,11,15} {1,4,11,16} {1,4,12,13} {1,4,12,14} {1,4,12,15} {1,4,12,16} {1,4,13,14} {1,4,13,15} {1,4,13,16} {1,4,14,15} {1,4,14,16} {1,4,15,16} {1,5,6,7} {1,5,6,8} {1,5,6,9} {1,5,6,10} {1,5,6,11} {1,5,6,12} {1,5,6,13} {1,5,6,14} {1,5,6,15} {1,5,6,16} {1,5,7,8} {1,5,7,9} {1,5,7,10} {1,5,7,11} {1,5,7,12} {1,5,7,13} {1,5,7,14} {1,5,7,15} {1,5,7,16} {1,5,8,9} {1,5,8,10} {1,5,8,11} {1,5,8,12} {1,5,8,13} {1,5,8,14} {1,5,8,15} {1,5,8,16} {1,5,9,10} {1,5,9,11} {1,5,9,12} {1,5,9,13} {1,5,9,14} {1,5,9,15} {1,5,9,16} {1,5,10,11} {1,5,10,12} {1,5,10,13} {1,5,10,14} {1,5,10,15} {1,5,10,16} {1,5,11,12} {1,5,11,13} {1,5,11,14} {1,5,11,15} {1,5,11,16} {1,5,12,13} {1,5,12,14} {1,5,12,15} {1,5,12,16} {1,5,13,14} {1,5,13,15} {1,5,13,16} {1,5,14,15} {1,5,14,16} {1,5,15,16} {1,6,7,8} {1,6,7,9} {1,6,7,10} {1,6,7,11} {1,6,7,12} {1,6,7,13} {1,6,7,14} {1,6,7,15} {1,6,7,16} {1,6,8,9} {1,6,8,10} {1,6,8,11} {1,6,8,12} {1,6,8,13} {1,6,8,14} {1,6,8,15} {1,6,8,16} {1,6,9,10} {1,6,9,11} {1,6,9,12} {1,6,9,13} {1,6,9,14} {1,6,9,15} {1,6,9,16} {1,6,10,11} {1,6,10,12} {1,6,10,13} {1,6,10,14} {1,6,10,15} {1,6,10,16} {1,6,11,12} {1,6,11,13} {1,6,11,14} {1,6,11,15} {1,6,11,16} {1,6,12,13} {1,6,12,14} {1,6,12,15} {1,6,12,16} {1,6,13,14} {1,6,13,15} {1,6,13,16} {1,6,14,15} {1,6,14,16} {1,6,15,16} {1,7,8,9} {1,7,8,10} {1,7,8,11} {1,7,8,12} {1,7,8,13} {1,7,8,14} {1,7,8,15} {1,7,8,16} {1,7,9,10} {1,7,9,11} {1,7,9,12} {1,7,9,13} {1,7,9,14} {1,7,9,15} {1,7,9,16} {1,7,10,11} {1,7,10,12} {1,7,10,13} {1,7,10,14} {1,7,10,15} {1,7,10,16} {1,7,11,12} {1,7,11,13} {1,7,11,14} {1,7,11,15} {1,7,11,16} {1,7,12,13} {1,7,12,14} {1,7,12,15} {1,7,12,16} {1,7,13,14} {1,7,13,15} {1,7,13,16} {1,7,14,15} {1,7,14,16} {1,7,15,16} {1,8,9,10} {1,8,9,11} {1,8,9,12} {1,8,9,13} {1,8,9,14} {1,8,9,15} {1,8,9,16} {1,8,10,11} {1,8,10,12} {1,8,10,13} {1,8,10,14} {1,8,10,15} {1,8,10,16} {1,8,11,12} {1,8,11,13} {1,8,11,14} {1,8,11,15} {1,8,11,16} {1,8,12,13} {1,8,12,14} {1,8,12,15} {1,8,12,16} {1,8,13,14} {1,8,13,15} {1,8,13,16} {1,8,14,15} {1,8,14,16} {1,8,15,16} {1,9,10,11} {1,9,10,12} {1,9,10,13} {1,9,10,14} {1,9,10,15} {1,9,10,16} {1,9,11,12} {1,9,11,13} {1,9,11,14} {1,9,11,15} {1,9,11,16} {1,9,12,13} {1,9,12,14} {1,9,12,15} {1,9,12,16} {1,9,13,14} {1,9,13,15} {1,9,13,16} {1,9,14,15} {1,9,14,16} {1,9,15,16} {1,10,11,12} {1,10,11,13} {1,10,11,14} {1,10,11,15} {1,10,11,16} {1,10,12,13} {1,10,12,14} {1,10,12,15} {1,10,12,16} {1,10,13,14} {1,10,13,15} {1,10,13,16} {1,10,14,15} {1,10,14,16} {1,10,15,16} {1,11,12,13} {1,11,12,14} {1,11,12,15} {1,11,12,16} {1,11,13,14} {1,11,13,15} {1,11,13,16} {1,11,14,15} {1,11,14,16} {1,11,15,16} {1,12,13,14} {1,12,13,15} {1,12,13,16} {1,12,14,15} {1,12,14,16} {1,12,15,16} {1,13,14,15} {1,13,14,16} {1,13,15,16} {1,14,15,16} {2,3,4,5} {2,3,4,6} {2,3,4,7} {2,3,4,8} {2,3,4,9} {2,3,4,10} {2,3,4,11} {2,3,4,12} {2,3,4,13} {2,3,4,14} {2,3,4,15} {2,3,4,16} {2,3,5,6} {2,3,5,7} {2,3,5,8} {2,3,5,9} {2,3,5,10} {2,3,5,11} {2,3,5,12} {2,3,5,13} {2,3,5,14} {2,3,5,15} {2,3,5,16} {2,3,6,7} {2,3,6,8} {2,3,6,9} {2,3,6,10} {2,3,6,11} {2,3,6,12} {2,3,6,13} {2,3,6,14} {2,3,6,15} {2,3,6,16} {2,3,7,8} {2,3,7,9} {2,3,7,10} {2,3,7,11} {2,3,7,12} {2,3,7,13} {2,3,7,14} {2,3,7,15} {2,3,7,16} {2,3,8,9} {2,3,8,10} {2,3,8,11} {2,3,8,12} {2,3,8,13} {2,3,8,14} {2,3,8,15} {2,3,8,16} {2,3,9,10} {2,3,9,11} {2,3,9,12} {2,3,9,13} {2,3,9,14} {2,3,9,15} {2,3,9,16} {2,3,10,11} {2,3,10,12} {2,3,10,13} {2,3,10,14} {2,3,10,15} {2,3,10,16} {2,3,11,12} {2,3,11,13} {2,3,11,14} {2,3,11,15} {2,3,11,16} {2,3,12,13} {2,3,12,14} {2,3,12,15} {2,3,12,16} {2,3,13,14} {2,3,13,15} {2,3,13,16} {2,3,14,15} {2,3,14,16} {2,3,15,16} {2,4,5,6} {2,4,5,7} {2,4,5,8} {2,4,5,9} {2,4,5,10} {2,4,5,11} {2,4,5,12} {2,4,5,13} {2,4,5,14} {2,4,5,15} {2,4,5,16} {2,4,6,7} {2,4,6,8} {2,4,6,9} {2,4,6,10} {2,4,6,11} {2,4,6,12} {2,4,6,13} {2,4,6,14} {2,4,6,15} {2,4,6,16} {2,4,7,8} {2,4,7,9} {2,4,7,10} {2,4,7,11} {2,4,7,12} {2,4,7,13} {2,4,7,14} {2,4,7,15} {2,4,7,16} {2,4,8,9} {2,4,8,10} {2,4,8,11} {2,4,8,12} {2,4,8,13} {2,4,8,14} {2,4,8,15} {2,4,8,16} {2,4,9,10} {2,4,9,11} {2,4,9,12} {2,4,9,13} {2,4,9,14} {2,4,9,15} {2,4,9,16} {2,4,10,11} {2,4,10,12} {2,4,10,13} {2,4,10,14} {2,4,10,15} {2,4,10,16} {2,4,11,12} {2,4,11,13} {2,4,11,14} {2,4,11,15} {2,4,11,16} {2,4,12,13} {2,4,12,14} {2,4,12,15} {2,4,12,16} {2,4,13,14} {2,4,13,15} {2,4,13,16} {2,4,14,15} {2,4,14,16} {2,4,15,16} {2,5,6,7} {2,5,6,8} {2,5,6,9} {2,5,6,10} {2,5,6,11} {2,5,6,12} {2,5,6,13} {2,5,6,14} {2,5,6,15} {2,5,6,16} {2,5,7,8} {2,5,7,9} {2,5,7,10} {2,5,7,11} {2,5,7,12} {2,5,7,13} {2,5,7,14} {2,5,7,15} {2,5,7,16} {2,5,8,9} {2,5,8,10} {2,5,8,11} {2,5,8,12} {2,5,8,13} {2,5,8,14} {2,5,8,15} {2,5,8,16} {2,5,9,10} {2,5,9,11} {2,5,9,12} {2,5,9,13} {2,5,9,14} {2,5,9,15} {2,5,9,16} {2,5,10,11} {2,5,10,12} {2,5,10,13} {2,5,10,14} {2,5,10,15} {2,5,10,16} {2,5,11,12} {2,5,11,13} {2,5,11,14} {2,5,11,15} {2,5,11,16} {2,5,12,13} {2,5,12,14} {2,5,12,15} {2,5,12,16} {2,5,13,14} {2,5,13,15} {2,5,13,16} {2,5,14,15} {2,5,14,16} {2,5,15,16} {2,6,7,8} {2,6,7,9} {2,6,7,10} {2,6,7,11} {2,6,7,12} {2,6,7,13} {2,6,7,14} {2,6,7,15} {2,6,7,16} {2,6,8,9} {2,6,8,10} {2,6,8,11} {2,6,8,12} {2,6,8,13} {2,6,8,14} {2,6,8,15} {2,6,8,16} {2,6,9,10} {2,6,9,11} {2,6,9,12} {2,6,9,13} {2,6,9,14} {2,6,9,15} {2,6,9,16} {2,6,10,11} {2,6,10,12} {2,6,10,13} {2,6,10,14} {2,6,10,15} {2,6,10,16} {2,6,11,12} {2,6,11,13} {2,6,11,14} {2,6,11,15} {2,6,11,16} {2,6,12,13} {2,6,12,14} {2,6,12,15} {2,6,12,16} {2,6,13,14} {2,6,13,15} {2,6,13,16} {2,6,14,15} {2,6,14,16} {2,6,15,16} {2,7,8,9} {2,7,8,10} {2,7,8,11} {2,7,8,12} {2,7,8,13} {2,7,8,14} {2,7,8,15} {2,7,8,16} {2,7,9,10} {2,7,9,11} {2,7,9,12} {2,7,9,13} {2,7,9,14} {2,7,9,15} {2,7,9,16} {2,7,10,11} {2,7,10,12} {2,7,10,13} {2,7,10,14} {2,7,10,15} {2,7,10,16} {2,7,11,12} {2,7,11,13} {2,7,11,14} {2,7,11,15} {2,7,11,16} {2,7,12,13} {2,7,12,14} {2,7,12,15} {2,7,12,16} {2,7,13,14} {2,7,13,15} {2,7,13,16} {2,7,14,15} {2,7,14,16} {2,7,15,16} {2,8,9,10} {2,8,9,11} {2,8,9,12} {2,8,9,13} {2,8,9,14} {2,8,9,15} {2,8,9,16} {2,8,10,11} {2,8,10,12} {2,8,10,13} {2,8,10,14} {2,8,10,15} {2,8,10,16} {2,8,11,12} {2,8,11,13} {2,8,11,14} {2,8,11,15} {2,8,11,16} {2,8,12,13} {2,8,12,14} {2,8,12,15} {2,8,12,16} {2,8,13,14} {2,8,13,15} {2,8,13,16} {2,8,14,15} {2,8,14,16} {2,8,15,16} {2,9,10,11} {2,9,10,12} {2,9,10,13} {2,9,10,14} {2,9,10,15} {2,9,10,16} {2,9,11,12} {2,9,11,13} {2,9,11,14} {2,9,11,15} {2,9,11,16} {2,9,12,13} {2,9,12,14} {2,9,12,15} {2,9,12,16} {2,9,13,14} {2,9,13,15} {2,9,13,16} {2,9,14,15} {2,9,14,16} {2,9,15,16} {2,10,11,12} {2,10,11,13} {2,10,11,14} {2,10,11,15} {2,10,11,16} {2,10,12,13} {2,10,12,14} {2,10,12,15} {2,10,12,16} {2,10,13,14} {2,10,13,15} {2,10,13,16} {2,10,14,15} {2,10,14,16} {2,10,15,16} {2,11,12,13} {2,11,12,14} {2,11,12,15} {2,11,12,16} {2,11,13,14} {2,11,13,15} {2,11,13,16} {2,11,14,15} {2,11,14,16} {2,11,15,16} {2,12,13,14} {2,12,13,15} {2,12,13,16} {2,12,14,15} {2,12,14,16} {2,12,15,16} {2,13,14,15} {2,13,14,16} {2,13,15,16} {2,14,15,16} {3,4,5,6} {3,4,5,7} {3,4,5,8} {3,4,5,9} {3,4,5,10} {3,4,5,11} {3,4,5,12} {3,4,5,13} {3,4,5,14} {3,4,5,15} {3,4,5,16} {3,4,6,7} {3,4,6,8} {3,4,6,9} {3,4,6,10} {3,4,6,11} {3,4,6,12} {3,4,6,13} {3,4,6,14} {3,4,6,15} {3,4,6,16} {3,4,7,8} {3,4,7,9} {3,4,7,10} {3,4,7,11} {3,4,7,12} {3,4,7,13} {3,4,7,14} {3,4,7,15} {3,4,7,16} {3,4,8,9} {3,4,8,10} {3,4,8,11} {3,4,8,12} {3,4,8,13} {3,4,8,14} {3,4,8,15} {3,4,8,16} {3,4,9,10} {3,4,9,11} {3,4,9,12} {3,4,9,13} {3,4,9,14} {3,4,9,15} {3,4,9,16} {3,4,10,11} {3,4,10,12} {3,4,10,13} {3,4,10,14} {3,4,10,15} {3,4,10,16} {3,4,11,12} {3,4,11,13} {3,4,11,14} {3,4,11,15} {3,4,11,16} {3,4,12,13} {3,4,12,14} {3,4,12,15} {3,4,12,16} {3,4,13,14} {3,4,13,15} {3,4,13,16} {3,4,14,15} {3,4,14,16} {3,4,15,16} {3,5,6,7} {3,5,6,8} {3,5,6,9} {3,5,6,10} {3,5,6,11} {3,5,6,12} {3,5,6,13} {3,5,6,14} {3,5,6,15} {3,5,6,16} {3,5,7,8} {3,5,7,9} {3,5,7,10} {3,5,7,11} {3,5,7,12} {3,5,7,13} {3,5,7,14} {3,5,7,15} {3,5,7,16} {3,5,8,9} {3,5,8,10} {3,5,8,11} {3,5,8,12} {3,5,8,13} {3,5,8,14} {3,5,8,15} {3,5,8,16} {3,5,9,10} {3,5,9,11} {3,5,9,12} {3,5,9,13} {3,5,9,14} {3,5,9,15} {3,5,9,16} {3,5,10,11} {3,5,10,12} {3,5,10,13} {3,5,10,14} {3,5,10,15} {3,5,10,16} {3,5,11,12} {3,5,11,13} {3,5,11,14} {3,5,11,15} {3,5,11,16} {3,5,12,13} {3,5,12,14} {3,5,12,15} {3,5,12,16} {3,5,13,14} {3,5,13,15} {3,5,13,16} {3,5,14,15} {3,5,14,16} {3,5,15,16} {3,6,7,8} {3,6,7,9} {3,6,7,10} {3,6,7,11} {3,6,7,12} {3,6,7,13} {3,6,7,14} {3,6,7,15} {3,6,7,16} {3,6,8,9} {3,6,8,10} {3,6,8,11} {3,6,8,12} {3,6,8,13} {3,6,8,14} {3,6,8,15} {3,6,8,16} {3,6,9,10} {3,6,9,11} {3,6,9,12} {3,6,9,13} {3,6,9,14} {3,6,9,15} {3,6,9,16} {3,6,10,11} {3,6,10,12} {3,6,10,13} {3,6,10,14} {3,6,10,15} {3,6,10,16} {3,6,11,12} {3,6,11,13} {3,6,11,14} {3,6,11,15} {3,6,11,16} {3,6,12,13} {3,6,12,14} {3,6,12,15} {3,6,12,16} {3,6,13,14} {3,6,13,15} {3,6,13,16} {3,6,14,15} {3,6,14,16} {3,6,15,16} {3,7,8,9} {3,7,8,10} {3,7,8,11} {3,7,8,12} {3,7,8,13} {3,7,8,14} {3,7,8,15} {3,7,8,16} {3,7,9,10} {3,7,9,11} {3,7,9,12} {3,7,9,13} {3,7,9,14} {3,7,9,15} {3,7,9,16} {3,7,10,11} {3,7,10,12} {3,7,10,13} {3,7,10,14} {3,7,10,15} {3,7,10,16} {3,7,11,12} {3,7,11,13} {3,7,11,14} {3,7,11,15} {3,7,11,16} {3,7,12,13} {3,7,12,14} {3,7,12,15} {3,7,12,16} {3,7,13,14} {3,7,13,15} {3,7,13,16} {3,7,14,15} {3,7,14,16} {3,7,15,16} {3,8,9,10} {3,8,9,11} {3,8,9,12} {3,8,9,13} {3,8,9,14} {3,8,9,15} {3,8,9,16} {3,8,10,11} {3,8,10,12} {3,8,10,13} {3,8,10,14} {3,8,10,15} {3,8,10,16} {3,8,11,12} {3,8,11,13} {3,8,11,14} {3,8,11,15} {3,8,11,16} {3,8,12,13} {3,8,12,14} {3,8,12,15} {3,8,12,16} {3,8,13,14} {3,8,13,15} {3,8,13,16} {3,8,14,15} {3,8,14,16} {3,8,15,16} {3,9,10,11} {3,9,10,12} {3,9,10,13} {3,9,10,14} {3,9,10,15} {3,9,10,16} {3,9,11,12} {3,9,11,13} {3,9,11,14} {3,9,11,15} {3,9,11,16} {3,9,12,13} {3,9,12,14} {3,9,12,15} {3,9,12,16} {3,9,13,14} {3,9,13,15} {3,9,13,16} {3,9,14,15} {3,9,14,16} {3,9,15,16} {3,10,11,12} {3,10,11,13} {3,10,11,14} {3,10,11,15} {3,10,11,16} {3,10,12,13} {3,10,12,14} {3,10,12,15} {3,10,12,16} {3,10,13,14} {3,10,13,15} {3,10,13,16} {3,10,14,15} {3,10,14,16} {3,10,15,16} {3,11,12,13} {3,11,12,14} {3,11,12,15} {3,11,12,16} {3,11,13,14} {3,11,13,15} {3,11,13,16} {3,11,14,15} {3,11,14,16} {3,11,15,16} {3,12,13,14} {3,12,13,15} {3,12,13,16} {3,12,14,15} {3,12,14,16} {3,12,15,16} {3,13,14,15} {3,13,14,16} {3,13,15,16} {3,14,15,16} {4,5,6,7} {4,5,6,8} {4,5,6,9} {4,5,6,10} {4,5,6,11} {4,5,6,12} {4,5,6,13} {4,5,6,14} {4,5,6,15} {4,5,6,16} {4,5,7,8} {4,5,7,9} {4,5,7,10} {4,5,7,11} {4,5,7,12} {4,5,7,13} {4,5,7,14} {4,5,7,15} {4,5,7,16} {4,5,8,9} {4,5,8,10} {4,5,8,11} {4,5,8,12} {4,5,8,13} {4,5,8,14} {4,5,8,15} {4,5,8,16} {4,5,9,10} {4,5,9,11} {4,5,9,12} {4,5,9,13} {4,5,9,14} {4,5,9,15} {4,5,9,16} {4,5,10,11} {4,5,10,12} {4,5,10,13} {4,5,10,14} {4,5,10,15} {4,5,10,16} {4,5,11,12} {4,5,11,13} {4,5,11,14} {4,5,11,15} {4,5,11,16} {4,5,12,13} {4,5,12,14} {4,5,12,15} {4,5,12,16} {4,5,13,14} {4,5,13,15} {4,5,13,16} {4,5,14,15} {4,5,14,16} {4,5,15,16} {4,6,7,8} {4,6,7,9} {4,6,7,10} {4,6,7,11} {4,6,7,12} {4,6,7,13} {4,6,7,14} {4,6,7,15} {4,6,7,16} {4,6,8,9} {4,6,8,10} {4,6,8,11} {4,6,8,12} {4,6,8,13} {4,6,8,14} {4,6,8,15} {4,6,8,16} {4,6,9,10} {4,6,9,11} {4,6,9,12} {4,6,9,13} {4,6,9,14} {4,6,9,15} {4,6,9,16} {4,6,10,11} {4,6,10,12} {4,6,10,13} {4,6,10,14} {4,6,10,15} {4,6,10,16} {4,6,11,12} {4,6,11,13} {4,6,11,14} {4,6,11,15} {4,6,11,16} {4,6,12,13} {4,6,12,14} {4,6,12,15} {4,6,12,16} {4,6,13,14} {4,6,13,15} {4,6,13,16} {4,6,14,15} {4,6,14,16} {4,6,15,16} {4,7,8,9} {4,7,8,10} {4,7,8,11} {4,7,8,12} {4,7,8,13} {4,7,8,14} {4,7,8,15} {4,7,8,16} {4,7,9,10} {4,7,9,11} {4,7,9,12} {4,7,9,13} {4,7,9,14} {4,7,9,15} {4,7,9,16} {4,7,10,11} {4,7,10,12} {4,7,10,13} {4,7,10,14} {4,7,10,15} {4,7,10,16} {4,7,11,12} {4,7,11,13} {4,7,11,14} {4,7,11,15} {4,7,11,16} {4,7,12,13} {4,7,12,14} {4,7,12,15} {4,7,12,16} {4,7,13,14} {4,7,13,15} {4,7,13,16} {4,7,14,15} {4,7,14,16} {4,7,15,16} {4,8,9,10} {4,8,9,11} {4,8,9,12} {4,8,9,13} {4,8,9,14} {4,8,9,15} {4,8,9,16} {4,8,10,11} {4,8,10,12} {4,8,10,13} {4,8,10,14} {4,8,10,15} {4,8,10,16} {4,8,11,12} {4,8,11,13} {4,8,11,14} {4,8,11,15} {4,8,11,16} {4,8,12,13} {4,8,12,14} {4,8,12,15} {4,8,12,16} {4,8,13,14} {4,8,13,15} {4,8,13,16} {4,8,14,15} {4,8,14,16} {4,8,15,16} {4,9,10,11} {4,9,10,12} {4,9,10,13} {4,9,10,14} {4,9,10,15} {4,9,10,16} {4,9,11,12} {4,9,11,13} {4,9,11,14} {4,9,11,15} {4,9,11,16} {4,9,12,13} {4,9,12,14} {4,9,12,15} {4,9,12,16} {4,9,13,14} {4,9,13,15} {4,9,13,16} {4,9,14,15} {4,9,14,16} {4,9,15,16} {4,10,11,12} {4,10,11,13} {4,10,11,14} {4,10,11,15} {4,10,11,16} {4,10,12,13} {4,10,12,14} {4,10,12,15} {4,10,12,16} {4,10,13,14} 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You cannot combine Godmetals of Gods of the same parts.

This would ultimately mean that the number of alloys isn't 2^(2^16), it would be more akin to the 2^16 itself. As 2^(2^16) would include contradictions. and impossibilities. The amount of Shards is fine and sound, but we still need to be able to calculate out, in a better way, how many godmetal alloys there would be.

2 Metals = 214,745,0880

This is the safest bet in my own opinion.

Edited June 22, 2021 by Zoey

mathiau · June 22, 2021

Quote

Okay, that all makes more sense, my apologies.

No problem

1 hour ago, Zoey said:

This would of course simplify to (2^(10^21))-1, because the summation of n!/r!(n-r)! for all values of R always goes into the Powerset of R, which goes to 10^10^10^1.31130.

I don't understand this sentence

Quote

And yes, I was talking about that very, very large one as being wrong. And that was the one I especially didn't get the reasoning for. Could you explain what they were doing with it to get it that high?

I think they were trying to do the same thing I've done but made a mistake with he number of gods and used 16! instead of 2^16-1

1 hour ago, Zoey said:

You cannot combine Godmetals of Gods of the same parts.

You actually could, for example the Lerasium-Harmonium alloy is our best candidate for the metal that makes people into Ferruchemists. Granted it'd be very unlikely to obtain both some (Autonomy + Dominion + Ruin)ium and some (Ruin + Devotion)ium but there are ways

Edited June 22, 2021 by mathiau

Zoey · June 22, 2021

2 hours ago, mathiau said:

No problem

I don't understand this sentence

I think they were trying to do the same thing I've done but made a mistake with he number of gods and used 16! instead of 2^16-1

You actually could, for example the Lerasium-Harmonium alloy is our best candidate for the metal that makes people into Ferruchemists. Granted it'd be very unlikely to obtain both some (Autonomy + Dominion + Ruin)ium and some (Ruin + Devotion)ium but there are ways

It means that the summation of every value of n!/r!(n-r)! with a constant N value, would simply to 2^n. In simpler terms.

And also, fair, it would be theoretically possible, albeit require very specific circumstances.

Frustration · September 26, 2021

Just had a thought the other day.

What if order of alloying matters?

An Atium-Lerasium alloy gives me the ability to burn Atium

if I alloy Lerasium to a pre-existing Tanavastium-Atium alloy I can burn that Tanavastium-Atium

Now what happens when I alloy Tanavastium to a pre-existing Atium-Lerasium alloy?

Halyo_Alex · September 27, 2021

3 hours ago, Frustration said:

Just had a thought the other day.

What if order of alloying matters?

An Atium-Lerasium alloy gives me the ability to burn Atium

if I alloy Lerasium to a pre-existing Tanavastium-Atium alloy I can burn that Tanavastium-Atium

Now what happens when I alloy Tanavastium to a pre-existing Atium-Lerasium alloy?

Stooooorm you and your frustrating thought processes.

Well... I can't be bothered to do the math. But we've already established that we're well into the realm of scientific notation anyway, so i think that's okay.

Karger · September 27, 2021

Pretty sure this WoB

Quote

Eric

If Adonalsium Shattered with intent, would he always Shatter with the same Shards?

Brandon Sanderson

It is plausible that it could've gone a different way.

Eric

So it could've been different Shards?

Brandon Sanderson

Yes, that's plausible.

Words of Radiance Chicago signing (March 22, 2014)

indicates that a literally infinite number of god metals are possible. Since everything in the cosmere happens due to the intent(s) of a shard(s) there are theoretically as many godmetals as things that have happened. Ever.

Edited September 27, 2021 by Karger

Frustration · September 27, 2021

3 minutes ago, Karger said:

Pretty sure this WoB

indicates that a literally infinite number of god metals are possible. Since everything in the cosmere happens due to the intent(s) of a shard(s) there are theoretically as many godmetals as things that have happened... Ever.

What's sad is that at this point that doesn't even change our accepted value.

Mistnumber is less than infinate but higher than any practical number.

I really want Brandon to read this thread live now.

Edited September 27, 2021 by Frustration

Karger · September 27, 2021

1 minute ago, Frustration said:

What's sad is that at this point that doesn't even change our accepted value.

Mistnumber is less than infinate but higher than any practical number.

On the up side that means you could make metals that when burned by a full mistborn do hyperspesific things. Metals that when burned cause it to rain on the Nalthis the next Tuesday or create coughing fits in whoever holds the Alethi throne.

Frustration · September 27, 2021

1 minute ago, Karger said:

On the up side that means you could make metals that when burned by a full mistborn do hyperspesific things. Metals that when burned cause it to rain on the Nalthis the next Tuesday or create coughing fits in whoever holds the Alethi throne.

Oh no, I think that was the metal that delete's the Cosme---

dannnex · September 27, 2021

we should back it up a bit and try and figure out how many metals we're actually gonna know about and have unique powers for. I'm not sure how though, the crazy thing about this is that we never actually made any leaps in logic or jumped to any conclusions. all of this was very logically and reasonably based on things we've already seen/know, so drawing a line like "here's all the real metals, the ones that have unique and logical powers, and over there is all the technically allomantically viable metals, but there's so many of them that it doesn't make sense to include them" is actually really hard.

so the only conclusion to come to is that there must be some sort of limiting factor that we just don't know about yet. something to bring this impossibly big number down to something reasonable that Brandon can actually work with.

Frustration · September 27, 2021

9 minutes ago, Danex said:

we should back it up a bit and try and figure out how many metals we're actually gonna know about and have unique powers for. I'm not sure how though, the crazy thing about this is that we never actually made any leaps in logic or jumped to any conclusions. all of this was very logically and reasonably based on things we've already seen/know, so drawing a line like "here's all the real metals, the ones that have unique and logical powers, and over there is all the technically allomantically viable metals, but there's so many of them that it doesn't make sense to include them" is actually really hard.

so the only conclusion to come to is that there must be some sort of limiting factor that we just don't know about yet. something to bring this impossibly big number down to something reasonable that Brandon can actually work with.

There are two things I can think of.

Using a shard metal requires a connection to that shard, therefore(with the exception of hemalurgy) only a few metals are widely accessable
Only the Combinations of the Native Scadrian shards will be used, as the other shards rarely form metals

Halyo_Alex · September 27, 2021

12 hours ago, Frustration said:

There are two things I can think of.

Using a shard metal requires a connection to that shard, therefore(with the exception of hemalurgy) only a few metals are widely accessable

Only the Combinations of the Native Scadrian shards will be used, as the other shards rarely form metals

Yeah, it's going to be a mix of availability-related factors. Limitations, after all.

Frustration · January 5, 2023

You know what, Mistnumber has been infinite for way too long. Also I just had a thought.

Time to make it bigger.

You can burn feruchemically and Hemalurgically charged metals for different effects. So that tipples our current infinity.

Now you unfortunately can't alloy charged metals, so that's the extent of the increase.

cometaryorbit · January 5, 2023

Aren't there contradictory WoBs on burning hemalurgically charged metals? IIRC we have "it would splice your spiritual DNA" and "you'd have to burn a spike that killed you and stole your power".

Frustration · January 5, 2023

3 minutes ago, cometaryorbit said:

Aren't there contradictory WoBs on burning hemalurgically charged metals? IIRC we have "it would splice your spiritual DNA" and "you'd have to burn a spike that killed you and stole your power".

The ones that say you can burn them which splice DNA are newer, and with Identity manipulation you should be able to burn spikes that aren't yours.

IlstrawberrySeed · January 6, 2023

I calculated it before I read this thread, and also found a number with over 19 thousand digits. specifically:

Spoiler

17030004408458194952322114988262173878806516542342887063752644276542599506228647351260802112487933458858824991914711737045495069748009907685390804100473149747902855911288988497713951365264912887847716627391275919846354211156935961338665121225524794241533326924502065558659771850247384820239272251756708291470112074057850730860450085934987770153813128221116290608401765253777400247948522202112756048824420325632672026949816867250663222558172698514262669298147381781046270842241575119981822155117292717053343639222513123883003871130652795231660313757483383801364833695898038997379828329303000442659081184986567572261535722176697250582254110835162146526351785410501642128823398342339535879031769239045124340111770723984347324895987345659641021152997323079180595554913688238318161565321452689242209623433411311455632896285353118037775466513194402337034889709682629341841754835161432000205206691507915258643944335513649136590900366327017679349872065149952896115434634463608634191864759592201124292105586200242376798205344375806269355443078018266865806045823690921201042139461185273446843903946988802874320169334705449702683035655819607352124608497871999977282186656478888795273335397356195356525029429609242011520004265121991500888895766935806790016884351825951565446616406352187904569062984876811876050762460029198091560476673550641409631567623165564026057566605544498720235820626556281552262302353501499945266377922247573501330924526827369806493415864877455424643226927508792217980894579062157701871494196740787977877429162550145473401591904989519292582906788083617252001920425713709015348060563241876508287738197733993229682203206323248181227927876422884120132013380626453874720244051001558648393738329238638920169736925836732247796808276330853543811475915926471270615242218906661088452192332989505811905570784065067458355108529468118314281203819702157599443887362256977869005046075494345043788059533855559849635966792053639051900166158867048125075513142746024764273012904440149566186868454646642492369374794678443500195796222223838669381737936180872105589418946124184027035929885262918657937348723026938981014891989193891812678236696884304475610930619922870553063628875870226191207545859761108550086051571289647125845719625230950316170281262182483969454643668068125964118102773683170924500276133801513714058709038225322122570803179068699023884649985467009004200035279055124453607919038145523179644003903523700990794648779696131485621438453894098289655935258824902820587155272318178296637471978411138959202762175919775719833810890419847367243785043447862833695678503665137344570232324018712592033024819005109540993230857176753155360211916328796970010928325170200233251257726675419815687930132664495644599662481979232275031764683582894399787291938484359625321992877804117924928973985417036968530714219230202079616226178805152699266612188761189902405395352431756288577405010701685955593323924708396871128212536350747626981927537575181921950062303486639419476447968087646553925646486677547757716171972948537291402295528785139735021638434915154027220547475269369391756722585740113081382731536922819450282407352019806913337598886900428131468406109066382467063776227546087241783616976160753950150817593660528939483676219171908907331225487036494163955957010287235099058514522696966562559189106046821435918113182250197896646984685172244425515178423288175451534138538085428640539162598317372810295300435498085119628953432778018326422738225612043503021339100084305493231108484845396027396291268748143543289602242373196953560486240762813664995940411998670248976707687713497090812184828459988578954586856805461631978554101112298637382248388831632240170174564892801433939638246814680725242526253422488213056670630444373025552399433118915552705568948887105602844951314818659489060388503560475246322851711887024128062185436938179848042805927836973007625411208543065286187132110908423971294974656776035210661697625407722129936301102295684608440169690210646496863398066493275367558851478131669804229666605085912029533326014062748049108804471440421197353390232351145286498489123218769639694116966696238602761160430501408633827040224270449700884872952685080871789945534370838901075112503555199546581859970514182440512762010672910933726463564728620895204458239342767451671635227091492993172837462141963294811478371456582274145678849056124867558254098805187533180751822235898583010365180862549324703120344323861192349672324485483978718681874430887220758113165732792056264831795870703667089410579408661187261082716320225099617385692621243268205378043219694720244706103009127042565938075269113917581547108400718481788219819507829240997851760474398895907964835320257726446143102403118334751251467160208378317612875649642589374477668245080958917025874085181611670783133068608270444323324507853088567027172567546447383685262480806819926200917006957790166199255668588344056884871541864591549767501596050351543338316576925096558403609531955106757189944814199003863400837293303653023755019307951103503477350948435360870412237705598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However, Used a much different sigma based function. Note, subscript is actually exponents, due to limited formatting of 17th shard

M=x
f(x) = E 2n(M-n)
n=0

17(17+ f(15) + f[ 15+f(15)] ) - 1

X + F(X-1) = the number of combinations possible. I derive this with the following logic. List each shard in a column, with 16 at the top and 1 at the bottom. For any given number, the number of combinations of only it and the numbers below below it is equal to the sum of all lesser number's combinations for all lesser numbers. It is equivalent to g(x) = X+ 2g(x-1) for x≥0.

So, there are 16 pure shards, so 16 + f(15) pure or combined shards, with 16 + f(15) pure shard metals, and f(15 + f(15)) shard metal alloys. Add 1 because you can have just a base metal, and multiply it by 17 for the base metals and only shard metals, and subtract one for the no base by no shardic alloy.

This calculates the current number of viable metals using the following assumtions and parameters:

Furecemical and hemalurgically charged metals are not considered viable because they have no effect on 1 of the 3 metalic arts.
- No other investiture storing is included, such as metals with breaths from the "my life to yours" command.
Aether crystals and other pure investiture that aren't metals are not allomantically viable.
- All metalic pure investiture is shardic in nature.
No shards have shattered into new subshards (WoB confirmed it is possible for shards to shatter into sub-intents).
Avatar metals aren't unique for the metalic arts. (I personally believe they are distinct from their shard's metals, but I don't know where I split the line on differing effects)
Each shard metal and alloy of shard metals for any level is viable on it's own or alloyed with any of the 16 base
- but not when alloyed with 2+ base or with a non-base metal, except possibly making one slightly sick with a weaker effect.
Shard metals are considered an allomantic effect (when allomancy was likely shaped after how shard metals work)
Each alloy has one ideal percentage, or only 1 effect regardless of effect.
Previously produced shard metals change effects at the same time a new vessel's metal changes effect
- This does not include gaining or loosing a shard.
A 16th level shard is possible, either through working together, manipulation, or shardic combining without bringing adinalsium back.
Shards don't specifically intervene to create more metals to mess up the calculation.

As a side note, I accidentally had 1 number wrong, and sent a 36 thousand digit number to BS. @Aspiring Writer. Havent recieved a responce to any of my questions, many of which were about these exact assumtions.

Edited January 6, 2023 by IlstrawberrySeed

Frustration · January 6, 2023

30 minutes ago, IlstrawberrySeed said:

This calculates the current number of viable metals using the following assumtions and parameters:

Furecemical and hemalurgically charged metals are not considered viable because they have no effect on 1 of the 3 metalic arts.

No other investiture storing is included, such as metals with breaths from the "my life to yours" command.

Aether crystals and other pure investiture that aren't metals are not allomantically viable.

All metalic pure investiture is shardic in nature.

No shards have shattered into new subshards (WoB confirmed it is possible for shards to shatter into sub-intents).

Avatar metals aren't unique for the metalic arts. (I personally believe they are distinct from their shard's metals, but I don't know where I split the line on differing effects)

Each shard metal and alloy of shard metals for any level is viable on it's own or alloyed with any of the 16 base

but not when alloyed with 2+ base or with a non-base metal, except possibly making one slightly sick with a weaker effect.

Shard metals are considered an allomantic effect (when allomancy was likely shaped after how shard metals work)

Each alloy has one ideal percentage, or only 1 effect regardless of effect.

Previously produced shard metals change effects at the same time a new vessel's metal changes effect

This does not include gaining or loosing a shard.

A 16th level shard is possible, either through working together, manipulation, or shardic combining without bringing adinalsium back.

Shards don't specifically intervene to create more metals to mess up the calculation.

Well, we know a few of those assumptions to be incorrect(namely atium can be alloyed in over sixteen different ways with the same base metal) but since we don't have any concrete numbers for those, this is probably the most accurate number that we can actually calculate.

30 minutes ago, IlstrawberrySeed said:

Furecemical and hemalurgically charged metals are not considered viable because they have no effect on 1 of the 3 metalic arts.

Well, while hemalurgically charged metals don't have any additional effects in Hemalurgy, they would in Feruchemy and the other way around.

So in Hemalurgically and Feruchemically there are over 3.4*10^19000 metals and in Allomancy there would be over 5.1*10^19000 metals

30 minutes ago, IlstrawberrySeed said:

No other investiture storing is included, such as metals with breaths from the "my life to yours" command.

Other than with Feruchemy and Hemalurgy I don't think we have another way to invest metals that causes an effect, storing breath in metal would only let you get that breath out when burned, not change it's effect.

Spoiler

Questioner (paraphrased)

What would happen if Allomancer was also an Awakener and Awakened metal he'd burn?

Brandon Sanderson (paraphrased)

If he did that, he’d get Allomantic power and also get back the Breaths used in Awakening the metal.

Footnote: Supposedly it was around half an hour into the signing line; has not been found on the record although we may have started it after it was asked already; follow-up to this
Warsaw signing (March 18, 2017)

Edited January 6, 2023 by Frustration

IlstrawberrySeed · January 6, 2023

1 minute ago, Frustration said:

namely atium can be alloyed in over sixteen different ways with the same base metal

Where is this from? Any others that are obviously wrong? (Side note, I calculated this when I had only read the first 6 mistborn books and the mistborn short stories, nothing else in the cosmere, and TLM haden't been out. Now, SP1 is the only cosmere published I haven't read AFAIK.) Also, how does fuerochemical charge effect hemalurgy and vice versa? Is it that a hemalurgic spike that steals fuerochemistry can be used as that type of mind even if it is the wrong metal?

I wasn't sure if there were other ways to change effect. If the spren of the shardblade you are burning tries to change the effect, is the effect changed? What about storing anti-investiture in metals that is keyed to not explode with the investiture being used (likely impossible). I personally thought it would change the effect, but good to know it doesn't.

Frustration · January 6, 2023

13 minutes ago, IlstrawberrySeed said:

Where is this from? Any others that are obviously wrong? (Side note, I calculated this when I had only read the first 6 mistborn books and the mistborn short stories, nothing else in the cosmere, and TLM haden't been out. Now, SP1 is the only cosmere published I haven't read AFAIK.)

This WoB

Spoiler

17th Shard

Are there a limited amount of atium and lerasium alloys for each metal?

Brandon Sanderson

Hmm, yes…I suppose there would be but there are…

17th Shard

More than sixteen?

Brandon Sanderson

Yeah, way more than sixteen.

17th Shard

Oh wow. Okay. That's fascinating. More than sixteen and less than infinite.

Brandon Sanderson

Yes.

17th Shard Interview (Oct. 3, 2010)

13 minutes ago, IlstrawberrySeed said:

Also, how does fuerochemical charge effect hemalurgy and vice versa? Is it that a hemalurgic spike that steals fuerochemistry can be used as that type of mind even if it is the wrong metal?

Feruchemically storing in a spike, or using a metalmind as a spike, kind of the feuchemy and hemalurgy version of compounding, though not the same thing

Spoiler

Questioner

Can you use Feruchemy and Hemalurgy together like you can use Allomancy and Feruchemy to Compound?

Brandon Sanderson

*asks for clarification* There are some tricks you can play. I wouldn't call them Compounding, but there are tricks.

Shadows of Self Chicago signing (Oct. 12, 2015)

Czanos

Would anything interesting happen if an Allomancer Burned a Hemalurgic spike, or a Feruchemist Tapped one?

Brandon Sanderson

Er, well, it’s possible. But you’d have to be burning a Hemalurgic spike that killed you and took your power…

Just like you can’t gain anything by burning a metalmind unless you infused it yourself.

#tweettheauthor 2009 (July 8, 2009)

Edited January 6, 2023 by Frustration

IlstrawberrySeed · January 6, 2023

The first WoB doesn't necessarily say that it is false. I say there are more than 1 Atium-Electurm Alloy, there is also Atium-Lerasium-ELectrum, Atium-Harmonium-Electrum, Atium-Lerasium-Harmonium-ELectrum, Atium-Trellium-Electrum, Atium-Trellium-Lerasium-Electrum, Atrium-Trellium-Harmonium-Electrum, Atium-Trellium-Lerasium-Harmonium-Electrum, Atium-Tanavastium-Electrum, Atium-Tanavastium-Lerasium-Electrum, Atium-Tanavastium-Harmonium-Electum, Atium-Tanavastium-Trellium-Electrum, Atium-Tanavastium-Lerasium-Harmonium-Electrum, Atium-Tanavastium-Lerasium-Trellium-Electrum, Atium-Tanavastium-Harmonium-Trellium-Electrum, Atium-Tanavastium-Lerasium-Harmonium-Trellium-Electrum. And that is 16 already, and I haven't even brought Rayse into the mix. (Note, this isn't trying to be insulting or patronizing, but rather funny and time consuming.)

Specifically, that would be 15+f(14) + f(14+ f(14)) or 2.31*10^9868

Spoiler

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OK, I guess that would count. However that seems like one interaction, rather than an effect on each, though I suppose Hemalurgical effects would differ based on charge.

Frustration · January 6, 2023

1 minute ago, IlstrawberrySeed said:

The first WoB doesn't necessarily say that it is false. I say there are more than 1 Atium-Electurm Alloy, there is also Atium-Lerasium-ELectrum, Atium-Harmonium-Electrum, Atium-Lerasium-Harmonium-ELectrum, Atium-Trellium-Electrum, Atium-Trellium-Lerasium-Electrum, Atrium-Trellium-Harmonium-Electrum, Atium-Trellium-Lerasium-Harmonium-Electrum, Atium-Tanavastium-Electrum, Atium-Tanavastium-Lerasium-Electrum, Atium-Tanavastium-Harmonium-Electum, Atium-Tanavastium-Trellium-Electrum, Atium-Tanavastium-Lerasium-Harmonium-Electrum, Atium-Tanavastium-Lerasium-Trellium-Electrum, Atium-Tanavastium-Harmonium-Trellium-Electrum, Atium-Tanavastium-Lerasium-Harmonium-Trellium-Electrum. And that is 16 already, and I haven't even brought Rayse into the mix. (Note, this isn't trying to be insulting or patronizing, but rather funny and time consuming.)

Specifically, that would be 15+f(14) + f(14+ f(14)) or 2.31*10^9868

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So do you agree with my analysis that 5% Atium 95% iron would be different than 50% atium 50% Iron? I can't tell.

IlstrawberrySeed · January 6, 2023

I personally don't think they would have differing effects (probably differing strengths), and was saying how I understood the WoB.

Edited January 6, 2023 by IlstrawberrySeed

Frustration · January 6, 2023

1 minute ago, IlstrawberrySeed said:

I personally don't think they would have differing effects (probably differing strengths), and was saying how I understood the WoB.

Alright, thanks for clairification.

I would disagree, as it says specifically Atium alloys for each metal, meaning that Atium and Iron could be alloyed more than sixteen different ways, Atium and Copper in more than sixteen different ways etc.

IlstrawberrySeed · January 6, 2023

But wouldn't alloying a third metal be a new alloy? Also, the WoB unfortunately doesn't clarify wether they are talking viability or not.

THE ULTIMATE METAL COUNT

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