TV Tropes Org


World Building:
Alchemical Arithmetic
search forum titles
google site search
Kickstarter Message
TV Tropes Needs Your Help
Big things are happening on TV Tropes! New admins, new designs, fewer ads, mobile versions, beta testing opportunities, thematic discovery engine, fun trope tools and toys, and much more - Learn how to help here and discuss here.
View Kickstarter Project
Total posts: [17]

Alchemical Arithmetic:

 1 kassyopeia, Sat, 3rd Nov '12 10:06:02 AM from terrae nullius

Are there established alchemical rules for how to "add" any two of the four classical elements? Something like "Water plus Earth equals Mud", I mean - unfortunately, most of the other pairings don't have a similarly mundane answer.

I vaguely remember that the properties of other substances were explained in those terms, anyway: Wood obviously contains Water, and it must also contain the other three elements, because it can be transformed into Fire plus Air (smoke) plus Earth (ash). Or something along those lines. So, from that point of view, the question becomes whether there are six substances which are combinations of only two of the elements, and which ones those are.

Ultimately, I'm looking for a six-element version of This for my world, which would require fifteen "composites", but if there is a "real" alchemical precedent, it would be much nicer to build upon that one rather than to ignore it, methinks.

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
 2 kassyopeia, Sun, 4th Nov '12 10:58:17 AM from terrae nullius
Okay, this is the best I've come up with so far, with no historical basis that I know of:

Air + Earth = Dust
Air + Fire = Smoke
Air + Water = Steam
Earth + Fire = Ash
Earth + Water = Mud
Fire + Water = Blood (interpreting Fire figuratively as Life)

edited 4th Nov '12 10:59:25 AM by kassyopeia

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
I don't know about any historical basis, but in Dungeons & Dragons you have the Inner Planes.

2nd edition also included the Para-Elemental and Quasi-Elemental Planes. The Para-Elemental Planes are produced where the Elemental Planes come into contact with each other: Smoke (Air and Fire), Ice (Air and Water), Ooze (Earth and Water), and Magma (Fire and Earth). The Quasi-Elemental Planes are produced where the Elemental Planes touch the Energy Planes: At the intersection of the Positive Energy Plane and the planes of Air, Earth, Fire, and Water are Lightning, Minerals, Radiance, and Steam respectively. Around the Negative Energy Planes are Vacuum, Dust, [1] Ash, [2] and Salt.[3]

 4 kassyopeia, Sun, 4th Nov '12 12:08:57 PM from terrae nullius

Well, IMVHO, most of those are even more arbitrary and lamer than what I came up with, but at least it gives one a set of terms to pick from... so, thanks for that! tongue

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
This guy has made some modifications to the system. If you scroll down past the outer planes, you can see his version of the inner planes. That may give you some inspiration, as well.

 6 kassyopeia, Sun, 4th Nov '12 2:54:42 PM from terrae nullius

Yeah, [up] fixes most of the particularly questionable suggestions of the original. Nice.

Draft for my system, interpreting the lack of other responses to mean that nobody knows of any historical precedents to take into account. It turns out that I only need nine intermediaries, not fifteen as I originally though, because several coincide with another element or with each other. Elements in caps, =!= means identity, =?= means suggestion, with rationale provided for each.

1) FIRE + AIR =?= Flame
2) FIRE + WATER =!= AIR + ASH =?= Life
3) FIRE + ICE =!= AIR + ROCK =!= WATER + ASH =?= Earth
-) FIRE + ROCK =!= ASH
4) FIRE + ASH =?= Spark
5) AIR + WATER =?= Rain
-) AIR + ICE =!= WATER
6) WATER + ICE =?= Snow
7) WATER + ROCK =!= ICE + ASH =?= Clay
8) ICE + ROCK =?= Amber
9) ROCK + ASH =?= Sand


Spark Life Rain
Sand Clay Snow

Alternative suggestions would be very welcome, the only of these I have strong feelings about is Earth, for which the centre of the whole thing feels very much like the right place to be.

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
 7 m8e, Mon, 5th Nov '12 1:11:28 AM from Sweden Relationship Status: Wanna dance with somebody
I think you can make things a little less magical and more logical and based on observations of nature.


Water + Air = Rain

Ice + Air = Snow (Snow is fluffy Ice that obviously contains air. Snow also comes from the sky unlike most Ice)

Ice + Fire = water (obviously melting. The conclusion would be that Ice is Water that lacks Fire(/heat) (Ice = Water - Fire))

Snow + Fire = Water + Air (= Ice + Air + Fire = Water + Air)

Rock + Ice = Sand + ash (Ice cracks and break down Rock into smaller pieces. The ash is proven by the mosses/lichens and other plants growing in the cracks.(Everything needs ash to live)) Rock + anything will probably end up as variation if the above. etc.tongue

edited 5th Nov '12 1:18:57 AM by m8e

 8 kassyopeia, Mon, 5th Nov '12 10:22:23 AM from terrae nullius

I was going for nature-philosophical rather than magical, honestly! tongue

The foundation of the system is the idea that nature can be "parametrized" in terms of two quantities, hardness and wetness. The elemental values of hardness are threefold, namely fleet (meaning intangible), soft, and hard; and those of wetness are twofold, namely sere (meaning dry) and wet. The six elements are the substances defined by the pairings one gets from those. Thus, FIRE is the "substance" that is fleet and sere, AIR is fleet and wet, WATER is soft and wet, ICE is hard and wet, ROCK is hard and sere, and ASH is soft and sere. Clearly, the idea of hardness is quite similar to that of the physical phases of matter (gaseous, liquid, solid), and I did try to define one of the axes as temperature originally, but eventually came to the conclusion that that wasn't the way to go here: Simply put, air and rock are both room temperature, as far as human(oid) experience is concerned, which makes the connection between heat and phase too abstract to work with.

Thus, the circumstance that the fleet-sere element is hot and the hard-wet element cold is regarded as little more than incidental, in this version - unintuitive as that is to us scientifically literate humans.

Also, maybe the "+" symbol was a bad choice on my part. By "FIRE + ROCK", I don't so much mean "what do you get if you put one part fire and one part rock in a cocktail shaker", but rather "what lies between fire and rock" - and that has to be ASH by virtue of looking at the elements in terms of their hardness and wetness values.

That's why I'm thinking that, for example, Snow lies between WATER and ICE - it's wet, and it's halfway between soft and hard. The equalities in line 3) follow directly as well, because they all point to the same intermediate substance - one which is soft and moist. Earth fits that description, and, as I said, is just too perfect a candidate for the very centrepoint of the whole scheme to not use it. Plus, if one does allow a bit of mysticism to seep in now, coming up with explanations for each of the combinations is quite straightforward, too: FIRE + ICE = Earth because blah blah furnace of creation blah blah. AIR + ROCK = Earth because earth is spatially the layer between air (atmosphere) and rock (crust). And WATER + ASH = Earth because, well, for this one we can actually pretty much use the cocktail shaker. smile

Similarly, ROCK + ICE really ought to be something hard but moist, for which nothing comes to mind (well, perhaps "frozen clay", but that's just too lame to consider, I'm thinking). Slightly less literally, something hard and with some of the aspects of rock and some of those of ice. As I said, I'd be tempted to put metal there, if I wanted to have it in the scheme at all, because it does sort of fit that description.

So, thank you kindly for your suggestions, but they don't quite follow my overall train of thought here. Sorry for not having explained better in the first place (I did explain most of the above at some point in some thread, but even I can't remember which one that was, so that's not much of an excuse.)

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
Resently I tried something similar using the five elements of Chinese alchemy: earth, wood, fire, metal, and water.

Earth and wood are connected by fungi; wood and fire by oil; fire and metal by lava; metal and water by acidic poison; and water and earth by either darkness or salt.

I want to treat darkness as a physical substance rather than a simple lack of light, so I'm leaning toward water + earth = darkness.
Winter is coming.
 10 kassyopeia, Thu, 8th Nov '12 6:20:41 PM from terrae nullius

Hm, thanks. Neither earth nor wood are elemental in my scheme, and metal is completely absent, so there aren't any direct correspondences, but this definitely increases my reference pool - and I could even use some of those ideas for "second-order intermediaries", if I ever need those. cool

If I do my best to ignore what you already have, my suggestions for the Chinese system (as described by you) would be these:

WOOD + FIRE = Coal

Can't think of anything better than "mud" for the last one, which is lame. If you're going with the darkness idea, I'd suggest "Murk" as the term to use. Sounds appropriately substantial, IMO. tongue

edited 8th Nov '12 6:21:06 PM by kassyopeia

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
Don't know if it helps but I made an elemental system loosely based on the traditional one for a computer game I never finished. In the end I found sticking rigidly to the elements too constricting and settled on 'parametrizing' a bit like your thing, except my axes were solidity (Duris/Flux), physical energy (Lumia/Gelis) and life energy (Quicken/Necro). Or in more conventional terms, Earth vs Air, Fire vs Ice, and Life vs Death.

It was mostly used to give numerical values to the composition of terrain spaces, so bare rock would be rich in Duris but little else, while ordinary earth would have some Duris and some Quicken. Water was just Flux + Quicken, except when frozen it changed to Duris + Gelis. They also weren't actually exclusive, so sand would have both Duris and Flux, because it's hard but flows. There was also a more literal Earth/Air distinction in that each space was a combination of ground and aerial effects, so ground Flux generally meant water and air Flux generally meant wind. It got a bit messy but worked well enough for my purposes.

I think something to think about is that the original alchemists considered not only the properties of a thing as it is, but what relationships it has to other things, because alchemy is after all about transformation. So for instance wood is a combination of Fire and Earth, not because it's hot and hard but because when you burn it it produces fire and ash.

edited 9th Nov '12 7:32:21 AM by Kesteven

 12 kassyopeia, Fri, 9th Nov '12 10:18:55 AM from terrae nullius

Thanks! smile

Somehow, this thread had a lot more inertia to overcome than usual for this forum, but this is beginning to feel like a somewhat rounded picture by now.

I did use the alchemical perspective you mention once, consciously, to explain to myself why Life is AIR plus ASH: When you burn dead bodies or dead vegetation (or life ones, for that matter), you get smoke and ash. Mostly, though, my thinking here is more in terms of substances, in the widest sense, than in terms of processes. So, not just a bad choice of symbol, but also one of title. Mea culpa.

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
 13 kassyopeia, Mon, 12th Nov '12 6:46:36 AM from terrae nullius

Second draft, having thought of a couple of things in the meantime that just had to make an appearance in there somewhere:

  (light)   (wet)
(fleet) FIRE Myrrh AIR
  Flame Life Rain
(soft) ASH Earth WATER
  Sand Clay Snow
(hard) ROCK Aember ICE

I admit that calling the opposite of wet "light" is a bit dodgy, but the term had to make an appearance somewhere, and it didn't fit into the table itself, so it goes there instead.

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
WARNING: despicable cheating behavior in this post.

A huge "database" of such combinations is the walkthrough of a cute little flash game called Doodle God.

EDIT: Seems like I can't post links yet.. is the thingy at.

edited 12th Nov '12 11:18:30 AM by crowday

 15 Matues, Mon, 12th Nov '12 11:24:24 AM Relationship Status: Reincarnated romance
Link for your viewing pleasure.
The rain in Spain tend to drain the brain of sane.
 16 kassyopeia, Mon, 12th Nov '12 11:28:20 AM from terrae nullius

[lol] Okay, I didn't think such a thing was possible, but that may just be too much information even for me right there. I've not heard of the game, and I'm thinking I'll have a look at it before looking at the cheatsheet in detail. Thanks a bunch, anyway!

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
 17 kassyopeia, Mon, 12th Nov '12 4:27:53 PM from terrae nullius

So, the game... addictive in proportion to the player's OCD, and perhaps mildly amusing later on, but little else, would be my verdict. Now, to collate all the direct matches from the cheatsheet:

air + fire = energy
fire + water = alcohol
fire + stone = metal
water + air = steam
water + stone = sand

The first three are not very useful, at least in my case, and the last two are plain enough. Nope, no help there. But thanks again; at least this makes me more confident than ever that there's no genuine alchemical "recipe" for this sort of thing. smile

edited 12th Nov '12 4:28:40 PM by kassyopeia

Soon the Cold One took flight, yielded Goddess and field to the victor: The Lord of the Light.
The system doesn't know you right now, so no post button for you.
You need to Get Known to get one of those.
Total posts: 17

TV Tropes by TV Tropes Foundation, LLC is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
Permissions beyond the scope of this license may be available from
Privacy Policy