Jump to content

THE ULTIMATE METAL COUNT


danex

Recommended Posts

6 minutes ago, Bejardin1250 said:

An infinite amount of metals... And we only know what some of them do... A grand total of 20 ( something like that)

Anyone else depressed

We know what 17 of them do and have an idea of what 2 of them do

3 minutes ago, Bejardin1250 said:

To eat and never get full

Atium and iron

Dont ask me to explain:D

Atiums allow have cognitive an temporal effect so that can't be, sorry. Maybe Lerasium-Cadmium would do that?

 

Link to comment
Share on other sites

1 hour ago, Halyo_Alex said:

Ok there's Countably Infinite* metals to choose from.

*kind of

You know, its slightly sad to start doing all the math just to realize at the end that the answer is infinity.

Also brandon has stated that the shards could have been shattered into different numbers and different intents so do that math......:blink:

Edited by Retrac
Link to comment
Share on other sites

2 minutes ago, Retrac said:

You know, its slightly sad to start doing all the math just to realize at the end that the answer is infinity.

Also brandon has stated that the shards could have been shattered into different numbers and different intents so do that math......:blink:

You can only have metal from a Shard combination that actually exists so that part is not a problem.

Not, the issue is that there's a reason we say Lerasium and not Preservatium, when a new Vessel hold a Shard the properties of Godmetal created afterwards change slightly (I suspect there'd be a way to make Ettmetal that doesn't explode for example) and I have no idea whether that include it's Allomantic properties.

Link to comment
Share on other sites

1 minute ago, mathiau said:

You can only have metal from a Shard combination that actually exists so that part is not a problem.

Not, the issue is that there's a reason we say Lerasium and not Preservatium, when a new Vessel hold a Shard the properties of Godmetal created afterwards change slightly (I suspect there'd be a way to make Ettmetal that doesn't explode for example) and I have no idea whether that include it's Allomantic properties.

I think Allomancy is derived from the Intent of the Investiture filtered by a key (base metals and alloys), so unless the Intent changes the metal does the same thing.

Link to comment
Share on other sites

53 minutes ago, Halyo_Alex said:

I think Allomancy is derived from the Intent of the Investiture filtered by a key (base metals and alloys), so unless the Intent changes the metal does the same thing.

So, if Harmony switch to Discord...

Link to comment
Share on other sites

Just now, mathiau said:

So, if Harmony switch to Discord...

I still don't quite like the idea that Saze was able to just "decide" his di-shardic, capital-I Intent like that. Sure, he as the vessel can intend to do that sort of thing, but the Shard(s) themselves... I dunno.

Right now the pair seems to be overwhelmed by Preservation and just doing nothing significant.

Link to comment
Share on other sites

  • 2 months later...

We underestimated, by a lot.

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)

 

Link to comment
Share on other sites

On 5/1/2021 at 7:33 PM, Frustration said:

We underestimated, by a lot.

  Hide contents

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)

 

...Well rusts, we can't exactly go crazier than... *scrolls up* ... a lot :P

The exact number we made before isn't on this page so I can't check mid-post. :D

Link to comment
Share on other sites

3 minutes ago, Halyo_Alex said:

...Well rusts, we can't exactly go crazier than... *scrolls up* ... a lot :P

The exact number we made before isn't on this page so I can't check mid-post. :D

it's

On 2/25/2021 at 1:10 PM, mathiau said:

1,70x 1019729

but given the WoB we might as well say infinity and call it a day.

Link to comment
Share on other sites

1 minute ago, Bejardin1250 said:

Kinda funny that the OP theoriezed 119 as the amount:P

I'm the one who's made it incalculatable and my origional estimate was 561, oh how foolish I was.

Wasn't even in scientific notation.

Link to comment
Share on other sites

On 2/25/2021 at 0:50 PM, Halyo_Alex said:

Google calculator returns "Infinity" specifically. :D

EDIT: FOUND A CALCULATOR THAT CAN HANDLE IT

1.8 × 106298387349264

ALMIGHTY AND HARMONY HOW STORMING BIG IS THAT

You know it's bad when you're doing a conceptually simple equation and even the higher end calculators have to resort to scientific notation to display the answer. It's even worse when the exponent for the TEN in the scientific notation may as well display in scientific notation.

Edited by Elias
Link to comment
Share on other sites

It feels like if Brandon actually did start implementing godmetal alloys he'd probably limit the number possible with spiritual mumbo jumbo, if he rules that Harmony counts as one Shard that would keep it limited at least.

Maybe it needs resonances to alloy properly and too forms of Investiture destroys them? 

Edited by Hoidolasium
Link to comment
Share on other sites

  • 3 weeks later...

Oh Brandon, you don't even realize.

Quote

callumke (paraphrased)

Are there 50 Allomantic metals?

Brandon Sanderson (paraphrased)

Nearly. Does Harmony have a metal?

callumke (paraphrased)

Is that an alloy of lerasium and atium?

Brandon Sanderson (paraphrased)

You're along the right lines.

Alloy of Law York signing (Nov. 24, 2011)

It is so much higher

Link to comment
Share on other sites

  • 4 weeks later...
On 2/25/2021 at 2:10 PM, mathiau said:

Yes but may have an other possible effect, like Lerasium does

Number of potential multiple Shard Godmetals (assuming Harmony and Discord both have the same) 2^16-1 (2^16=number of way to chose any number of things from a set of 16, the -1 is to avoid counting the "I chose 0 element from a set of 16")

Number of Alloys of these Godmetals 2^(2^16-1)-1 (same reason)

Which mean I was wrong with my previous calculation, the maximum number of metal is (2^(2^16-1)-1)*17+16=2^(2^16-1)*17-1 which is about half of my previous estimation (now I'm at 1,70x 1019729)

I may be misunderstanding what you are trying to say, but wouldn't it still just be 16!/(2! * 14!) Godmetal-Allomantic Metal Alloys? Order is unimportant, repetition not allowed is n!/r!(n - r)!.

This would come to 120. 

If you want to include Lerasium-Godmetal combos, it would go to 120 + 15 which is 135. 

Godmetal-Godmetal, including it if you try to say each Combo can have a Primary-Secondary structure, it is 240. Exclude Lerasium and it is 210.

(120 + 240) = 360 

I don't know how to do the combo if you count all the Godmetal Alloys with the Base Allomantic Metals. As it would deal with Two Sets of different Cardinalities. Which I am not aware of how one can do that.  

 

But in general, I do not see how you are getting such large numbers. Considering you, with the later, even larger, numbers I saw come up, are literally getting numbers that trivialize a calculation I did for another verse which literally counted every single possible combination and permutation of every star in the observable universe. So it seems that you did overestimate, drastically.er

 

Edited by Zoey
Link to comment
Share on other sites

9 hours ago, Zoey said:

I may be misunderstanding what you are trying to say, but wouldn't it still just be 16!/(2! * 14!) Godmetal-Allomantic Metal Alloys? Order is unimportant, repetition not allowed is n!/r!(n - r)!.

This would come to 120.

This is the number of alloys of two distinct metals, we want the number of alloy of any (non zero) number of distinct metals so we'd have tu add the n!/(k!(n-k)!) with k from 1 to n, using Newton's binomial formula we obtain that it's (2^n)-1

Now the reason the n I used is not 16 but (2^16)-1 is because when you fuse two (or more) shards the godmetal of the new shards is not an alloy of the two previous but something new, so the number of pure god metals is the number of way to take one or more shards among 16, which from the previous paragrapher is (2^16)-1

Quote

But in general, I do not see how you are getting such large numbers. Considering you, with the later, even larger, numbers I saw come up, are literally getting numbers that trivialize a calculation I did for another verse which literally counted every single possible combination and permutation of every star in the observable universe. So it seems that you did overestimate, drastically.er

That's quadratic and we're dealing with exponentials so I'm not surprised

Edited by mathiau
Link to comment
Share on other sites

2 hours ago, mathiau said:

This is the number of alloys of two distinct metals, we want the number of alloy of any (non zero) number of distinct metals so we'd have tu add the n!/(k!(n-k)!) with k from 1 to n, using Newton's binomial formula we obtain that it's (2^n)-1

Now the reason the n I used is not 16 but (2^16)-1 is because when you fuse two (or more) shards the godmetal of the new shards is not an alloy of the two previous but something new, so the number of pure god metals is the number of way to take one or more shards among 16, which from the previous paragrapher is (2^16)-1

That's quadratic and we're dealing with exponentials so I'm not surprised

This way of calculation doesn't make much sense or have much mathematical backing, can you explain more in how it was done?

also 

Quote

That's quadratic and we're dealing with exponentials so I'm not surprised

This is actually just wrong as the calculation I mentioned did use expontials. 

(10^21)!/r!(10e21 - r)!

with R being calculated for all Whole Number values from 1 to 10e21. 

Link to comment
Share on other sites

7 minutes ago, Zoey said:

This way of calculation doesn't make much sense or have much mathematical backing, can you explain more in how it was done?

also 

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?

Quote

This is actually just wrong as the calculation I mentioned did use expontials. 

(10^21)!/r!(10e21 - r)!

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

Quote

with R being calculated for all Whole Number values from 1 to 10e21. 

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)

Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...