[Pathfinder/3.5] Metallurgical Magic

[Palanan]

Is there a spell in Pathfinder or 3.5 which provides the exact composition of a metal object, such as an axehead or a coin? For instance, a spell that could tell exactly what percentage of silver, gold and trace elements are in a bar of electrum?

I know most games probably won’t get into that much detail, but curious if there’s a spell like that anywhere in the 3.P corpus. Also open to third-party if there's nothing official along these lines.

[chaincomplex]

I considered the problem and came up with a meme solution that works fully by Core rules.

So the spell contact other plane can accomplish this. Just pose the question, "What is the percent composition of #MATERIAL in #OBJECT exactly?" directly and hope the answer is (i) true and (ii) the exact numerical value, with (ii) contingent on the DM interpreting numbers as an appropriate "one-word answer". Both of these issues can be circumvented in a worst-case scenario.

To deal with (i) simply approach the problem like a statistician and ask the question repeatedly. Since you know who you're contacting, you know the probability of a true answer, call it p. If you ask the question n times, the proportion of true answers is np with standard deviation [np(1 - p)]1/2. If you make sure you contact a lesser deity or greater, then p > 0.5 and the obvious scheme is to choose the answer that you've received the most, i.e. the mode of your data. There are several approaches here to assess the certainty of your answer. A simple if not particularly rigorous way is to hypothesis test: if the mode is the true answer, then you expect to see it at least np times. Suppose you actually see the mode X times. Then you find your one-sided Z-score by computing max(np - X, 0)[np(1 - p)]-1/2 and determine whether this meets your confidence criteria.

To deal with (ii) I observe that "yes" and "no" are established answers to contact other plane questions, so you can painstakingly construct bit by bit a numerical answer to arbitrary precision N by the following algorithm:

For i = 1, ..., N:

Ask: "In base-2 arithmetic is the i'th digit of the percent composition of #MATERIAL in #OBJECT 1, where we understand the i'th digit to be the coefficient of the (i - 1)'th-power term, namely 2-to-the-(i - 1)?"
If "yes":

Write: 1 in position i on Tape
Else:

Write: 0 in position i on Tape

Output: Tape
Here the tape output—which the wizard is physically writing down on parchment or just committing to memory—will have form b1, b2, b3, ... , bN, where the bi's take values 0 or 1, which you can convert to decimal by b1 + b22-1 + b32-2 + ··· + bN21 - N. The resulting decimal will be a real number between 0 and 1, which will be your percent composition.

So there you go, a way to tell with arbitrarily high certainty to arbitrarily high precision what the percentage composition of a certain substance is in a given object, through magic. It's not a good solution and it's hilariously dangerous for what you're trying to accomplish, given the risks of repeatedly casting contact other plane, but a clever wizard should be able to mitigate those dangers.

[Kazyan]

Treasure Scent (SC p. 223) will sort of do the job for gold, silver, and platinum specifically, if you have can gauge the intensity of the scent/compare to the scents of reference samples.

[Kurald Galain]

To deal with (ii) I observe that "yes" and "no" are established answers to contact other plane questions, so you can painstakingly construct bit by bit a numerical answer to arbitrary precision N by the following algorithm:
Only if you have ranks in Craft (Computer Programming) :smallbiggrin:

[chaincomplex]

Only if you have ranks in Craft (Computer Programming) :smallbiggrin:

Computers? Excuse me, they preferred to be called modrons. :smalltongue:

[Palanan]

Originally Posted by Kazyan
Treasure Scent (SC p. 223) will sort of do the job for gold, silver, and platinum specifically, if you have can gauge the intensity of the scent/compare to the scents of reference samples.

Interesting, thanks. Not quite what I'm looking for, but close.

I could've sworn I saw something like this in one of the Pathfinder supplements, but so far haven't been able to find it.