A way to measure the complexity of a material/substance?

Question

I'm trying to create a magic system through which a person has to understand a material/substance so they can locate it around them, and eventually manipulate it in other ways.

I tried something like this:

Person uses an alien implanted device to scan the nature of gold, so it can send a signal to locate it in a limited environment. The device uses the owner biological energy, like a second brain - however it only consumes energy when operating and and the amount depending on the task at hand.

If the user has access to pure gold, it's easier because it's one element. However, pure gold it's difficult to come about, so they use a gold ring, which is an alloy (gold + silver + copper + zinc) and makes the task considerably more energy consuming.

Easy in this example, but how can I compare scanning a human hair to, for example, silk? Or even two types of carbon based materials, coal vs a diamond?

Is there an easy way to compare molecules so I can look up them online and easily build an energy scale?

Because, as I understand it, it's not only the size of the molecules that matters but also the type of elements involved, how they bond with each other and the structure that they form.

Answer 1

One way to do this might be to rate complexity by number of atoms in the molecule. That way, you could have gold be easy, water be a bit harder, and something full of bazillions of folded proteins, like human flesh, be near-impossible.

One issue with what I've just proposed is that not everything breaks neatly into molecules. Alloys and salts might need a different system. But for a quick approximation number-of-atoms-per-molecule might be good.

A slightly different approach might be number/type of bonds. Something like water (two single bonds) could be easier than carbon dioxide (two double bonds). Once again, this would penalize big molecules, and break down with salts and alloys.

A middle ground might be bond energy. Each bond has a given energy needed to break it, and it's different for different bonds. (These energies are readily available by consulting Google). If you rated molecule complexity by summing the bond energies of the molecule, you'd have increasing difficulty as molecules got bigger, while allowing for the differences between types of bonds. For salts you could use the basic unit, and for alloys... I'm sure you can think of something.

This is a really cool idea, btw!

Answer 2

the number of elements might be your best bet. A lump of proteins is not actually much more complex than a random pile of the same elements. In terms of raw data, we just don't find a random arrangement of elements useful. A lump of graphite and a lump of diamond of the same mass are equally complex or fairly close the diamond may contain some more energy due to having more bonds, but in terms of raw information they both contain the same amount of information, the same number of atoms, and electron shells just in a different pattern. whereas a something like steel has iron and carbon atoms. You could also include a factor based on how ordered the material is, a lump of gold can be essentially random, while steel has to have a molecular pattern, albeit a simple crystalline one. while something like a protein has has a more complex pattern, or more precisely patterns of patterns, and living thing an even more complex one patterns inside patterns inside patterns, ect, ect.

you can shortcut how ordered the material is using simple classification form highschool chemistry. Its not perfect but you are writing a story not a dissertation on chemistry.

With complexity increasing to the right, you can add one more catagory for living things which are horrendously complex.

If you want to go a little deeper you can also use temprature, the colder a material is the more ordered it is.

Answer 3

Information content

It sounds like the metric you want is actually information content.

This may require a bit of hand-waving, since it isn't clear why "magic that requires you to understand the structure of a thing" would differentiate between not needing to care about the exact structure of a pile of randomly arranged atoms (e.g. a bucket of pure H₂O, which has extremely low information content) vs. say a snowflake which could be argued to have a much, much higher information content (i.e. to precisely describe its shape). But you said "pure" elements are supposed to be easy, so presumably this is what you want.

In this sense, although precisely specifying everything about a bucket of pure H₂O is easy. Yes, every single molecule has a unique position and velocity (and thanks to Heisenberg, you can't know both), but these properties are random. They aren't meaningful; they aren't information.

By this metric, something like a cut Emerald or a die-cast wrench is pretty easy; you only need to understand the basic structure of the atoms and their relative proportions, and have a fairly rough idea of the shape. A very simple integrated circuit would be very difficult, while something really complicated like a modern CPU or a living cell is almost certainly beyond possibility, at least if we're talking about humans. (You might make a virus or a DNA strand, but DNA is barely scratching the surface of the actual information that goes into living organisms. DNA is to living things what the recipe for stainless steel is to a modern skyscraper.)

Star Trek replicators are sometimes stated to work in this way, for much the same reasons; there is a huge difference in the quantity of information needed to describe the random arrangement of proteins and chemicals to make something that can pass for "steak", or even for a dead steer, and the quantity of information needed to create a living steer. Incidentally, this suggests an interesting wrinkle; your magic might be easier if you don't care about mangling your "source material".

(BTW, I've read books on this subject, though I couldn't recall specific titles offhand.)

To more directly answer your question, the complexity of a substance is proportional to how easy it is to describe it. Thus, the thing to do is to ask yourself how difficult it would be to describe a thing in a way that you would consider anything matching your description to be "the same thing". This is why something like "a bucket of water" is easy; a bunch of H₂O molecules in any arrangement is still "water". For something like a ball bearing, you need to know that it's a sphere, that it maybe has a certain crystal structure, that is has such-and-such proportions of iron, carbon, and so forth, but the exact positions of the carbon atoms isn't important. For something like a protein, well, that's a whole other kettle of fish... and forget something like a fish. As noted above, maybe you can wrap your head around it enough to have something that resembles a (dead) fish when you're done. OTOH, you might be able to do something like change all of the DNA in an organism to some other arrangement (we have, after all, examples of completely sequenced DNA), although what use this would be is a whole other matter.