(Or, "The Quintessential Theory of the Makeup of the Multiverse".)
I've been working on a homebrew fantasy world in my spare time for years. It'll probably never go anywhere, but it's fun to think about! One of the things I've wanted to nail down for a long time was the magic physics of the world, what elements made up reality in this extremely magical world.
I had a few requirements to keep in mind when developing this.
First and foremost, it had to be "complex". By this I mean--well, it's easiest to explain by contrast. In the real world, physics is "simple". The fundamental units of reality (quarks, photons, etc) have basically nothing to them. They're just a few numbers that combine together in trivial ways. The complexity of our world comes not from any fundamental complexity, but rather from enormous numbers of these super-simple things combining together. Even tho each individual thing has no complexity at all, and neither does the way they interact, the aggregate is capable of displaying tons of complexity.
Magic, on the other hand, is always "complex" at its root. It generally assumes the existence of minds as a fundamental unit of reality (whereas in the real world minds are just one of the patterns that vast quantities of unthinking particles can arrange themselves into). Sometimes it has "morality" baked in as a physical force; often it has complex things like "fire" or "earth" as core concepts. This makes magic easier to comprehend at a surface level, because it's made out of "big" things we can wrap our minds around, which combine in ways that are complex and ideosyncratic, but don't involve the dizzying amounts of data that the real world's fundamentals do. The elements of magic thus have to reflect this.
Secondly, it has to involve fives. Five is a good number of things, mentally and spiritually significant. So early on, long before I knew what anything would be, I knew I'd have five spheres of five essences each.
So let's dive in!
The Sphere of Elements
Fire, Water, Earth, Wind, Wood
This was the simplest of all. I knew I needed to involve the classical "elements" of fire/water/earth/air, and I had a few common choices for what to make the fifth. I chose to go for "wood" for a few reasons. One, it's very physical, and helps tie together "elemental" magic with a druid-ish theme. Two, I already knew from my fantasy races that I wanted elves to have wooden skeletons, and for this to be properly mystically significant, I'd need wood to be a fundamental force. Three, wood is usually mystically significant in stories, which means its likely to be pretty core to the magic system, so I had to include it somewhere. Some other common choices I rejected are "metal" (already served by "earth"), "void" (too abstract/encompassing for what's supposed to be only one sphere of the world, also this feels a little sci-fi-y and I ended up letting Energies have that), and "heart" (very non-physical, so it doesn't fit well, and it's more over in the mental sphere that I knew I wanted to do).
A wrinkle: essences can be "hard" or "soft"; the "hard" ones are suitable for making magical staffs with that aid in channeling related essences. The hard/soft dichotomy is pretty literal, so Wood and Earth are both hard. This explains why staffs are commonly wood or metal, and/or contain gems (which are Earth) - they help channel elemental magic!
The Sphere of Energies
Heat/Light, Electricity/Magnetism, Kinetic, Entropy, Void
Lacking any "hard" essences to make staves from, the energies are somewhat difficult to channel directly, particularly in the heat of combat. Instead they're usually admixed with an appropriate element, to aid in using an elemental staff to channel them. This produces the so-called "Wizard's Elements": Fire (Heat+Fire, or sometimes Heat+Earth or Heat+Air), Lightning (Electricity+Air/Earth), Thunder (Kinetic+Air), Acid (Entropy+Water, or sometimes Entropy+Earth for Corrosion), Cold (Void+Water/Air), and Poison (Entropy+Wood).
This one started out easy. I knew I wanted the D&D damage types, because I intended this world to be D&D-based, and what do you know, there are five common damage types. I also wanted to somehow include some slightly science-y things, but it seemed too on-the-nose to make them a sphere of their own, and I couldn't come up with a decent pentad for them anyway. I was pretty happy when I realized I could combine those two and get a more flexible sphere out of the deal.
The Sphere of Biology
Flesh, Blood, Bone, Elan, Soul
Flesh, Blood, and Bone are fairly self-explanatory. They cover all the things bodies are made of: cartilage and bone are both Bone; skin, muscle, and organs are mostly Flesh; mucus, blood, tears, and other liquids are variations on Blood.
Soul is the thinking substance, that our identities and selves are made of. Brains are a Flesh/Soul melange, for example.
Elan is "life energy", the animating force that distinguishes living things from dead. Without Elan infusing it, flesh is inert, and decomposes. With Elan, it's vital, active, and growing. Many simple healing spells are nothing more than increasing Elan in the body and letting natural healing take place, albeit at an accelerated pace.
Biology has more complex essential interactions than the previous spheres. Bone is another "hard" essence, and thus suitable for making staffs with that aid in channeling, particularly other Biology essences. But curiously, Bone is almost impervious to Elan; healing bone breaks is very difficult unless you have skill in Bone, and a Bone staff is absolutely worthless for channeling Elan. This has curious consequences! For one, healers are stuck using elemental staffs, at lower efficiency, which partially explains why it's always easier to harm than to heal. For two, it means that Biology specialists carrying Bone wands are definitely not healers, and the second most common use of Biology is... necromancy. (Note: Bone instruments are useful to actual surgeons, who have real training in Flesh/Blood/Bone beyond just "throw Elan at it until it's better".)
Necromancy uses all the non-Elan parts of Biology to do its work, warping bodies and souls in unnatural ways. (They can't use Elan, actually - it encourages natural growth and forms, which would unravel the work they're doing.) Bone is great for necromancers, then, as it enhances all of their spells.
This split in Biology carries over to its interactions with the Energies. Bone has a strong affinity to Void and Entropy; necromancers are well-known for an Entropy/Flesh blend known as "Necrotic energy", and some specialize in a powerful Void/Entropy blend known as "Uttercold". Flesh and Electricity have a unique affinity as well, such that some necromancers use it as an alternative animating energy. On the other hand, Elan has a strong affinity with Light, blending to produce the popular "Radiant energy" that is particularly damaging to undead. Soul has a unique affinity with Kinetic Energy, such that most Soul practitioners pick up some Kinetic skill as a matter of course, and is readily channeled by Earth wands, particularly crystalline ones.
The Sphere of Psychology
Joy, Sadness, Disgust, Anger, Fear
These are the five essences of minds. Note that we do our actual thinking with our souls; these essences constitute the emotional core of our being that our minds are built around.
Like the other spheres, many simple spells are just raw application of these essences. Classic "debuffs" are often just raw application of one of the essences: fear from Fear, berserk from Anger, slow from Sadness, warding from Disgust. On the flip side, admixing them with Joy provides the classic "buffs": Joy+Fear for alertness, Joy+Sadness for calmness, Joy+Anger for courage, and Joy+Disgust for fortitude. And of course, the representative skill of the mentalist discipline, charming, is in its simplest form just overloading the target with Joy - an ecstatic person is literally happy to do whatever you say.
Of course, these are not without downsides. A simple charm is immediately recognized by the target (tho they don't care about it until it wears off), as sudden euphoria is not a normal feeling, and is easy to spot in others. And the mind is not unfeeling Earth, able to be crudely shoveled around without damage; flooding a mind with an excess of psychological essences can do permanent damage to a person's psyche.
Skilled users instead carefully manipulate the psychological essences, weaving them together in complex interactions that use little actual force, and are much more difficult to detect.
The common "psionic" discipline is often considered to be psychological by laypeople, but this is mistaken. While psionics traditionally includes some psychology, its flashier effects (telepathy, telekinesis, etc) are actually usually based in the Soul/Kinetic affinity pair.
The Sphere of the Divine
White, Blue, Black, Red, Green
Divine magic flows directly from the gods, and comes bundled with each god's own idiosyncratic preferences and restrictions. Within that chaos, tho, arcanists have discovered five consistent aspects. Not only do gods themselves tend to organize around these aspects, but entire pantheons tend to stabilize around filling the five aspects equally. As such, most arcanists consider the five divine aspects to be the fifth essential sphere, thus completing the pentad.
[snip explanation, they're the Magic: the Gathering color-wheel philosophies]
These can manifest in dramatically different ways. For example, one of the more popular pantheons is the Unconquered Sun, a triune deity preaching Right Thoughts (Blue), Right Body (Green), and Right Heart (White), opposed by the twin evils of the quick death (murder, Red) and the slow death (decay, Black). On a very different spectrum, the Garlandite pantheon is led by Garland, god of blood and pain (cast as the good god of this pantheon, believe it or not), opposed by the Four Distractions, each associated with one of the other four aspects.
"Arc" pantheons that center in one aspect but embrace the two neighboring ones are common. Druidic religions, for example, are almost always centered in Green with a reverence for nature, but embrace both organization (White) and savagery (Red), while typically fighting against death/corruption (Black) and technology/artifice (Blue). The Unconquered Sun's White-centered arc structure is common in many folk pantheons.
Destiny scholars suggest that the Divine sphere, more than any other, is strongly self-balancing. If a particular aspect becomes strong in an area, it automatically draws strong opposition from its enemy aspects to counter it. There is no known instance of a stable, long-lived religion that did not incorporate the five aspects in major positions, whether good or evil, balanced in some significant way.
This requirement for balance can manifest in fairly simple dualities, like the Unconquered Sun's pantheon, or in vastly more intricate pantheons, like the ten carefully intertwined cults of Ravnican society, each embracing a different pair of aspects and all serving a vital role in the maintenance of the Infinite City, or the five unbalanced "wedges" (two neighboring aspects and their mutual enemy) exemplified by the Dragonlords.
Other Symmetries and Patterns
Many traditions organize the spheres into two overlapping pair structures: Elements and Energies are of the world, or "external", while Biology and Psychology are of the body, or "internal"; Elements and Biology are "physical", Energies and Psychology are "ephemeral". Divinity is usually seen as above and transcending each of these divisions; the "pyramid metaphor" is common, with the four "base" spheres holding up the Divine peak.
Some theorists insist that the pure "greater pentad"/"quintessence" structure laid out here is too pat, and the actual structure is much messier and harder to categorize. It's not uncommon to view Elements and Energies as two lobes of a conjoined structure, sharing a single Fire/Light essence. Similarly, Biology and Psychology are sometimes merged into a greater structure, with the five mental essences emerging from Soul.
When my eyes were skimming downward to psionics and I saw the "???", my reaction was "yeah, that makes sense." When I actually read the section I was a little surprised to find out you didn't mean that psionics were intentionally unknown and strange, but instead you just hadn't worked them out.
What really drew me to psionics in D&D, in both 3.5e and 4e, was how different it was. It felt alien to the world (indeed, psionics was associated with aberrations, which in D&D are kind of the equivalent of aliens). Everything worked differently, and you could imagine traditional magic users being completely baffled by this idea that psionics works at all. No gods? No arcane hand gestures and verbal components? Just your mind? That's not how the world works!
As such I'd suggest trying to make psionics as distinct and unknown as possible; keep the "???" spirit. Don't give it a pentad of its own. Make it a weird vertex in the spheres pentad that doesn't seem to follow the normal rules.
Re #1: "Psionics" maybe isn't even the right word; point is that there's a "mental" sphere that grows out of the Soul of Biology (analogously, Energies grow out of the Fire Element).
3.5 Psionics is just magic by another name, with a slightly mental and slightly scifi bent to it. It covers the full range of things magic can do. That's strongly not my intention here. These aren't magic traditions, they're the atoms that reality is made of. I just need to give some thought to what sort of things lend themselves to being "the five things minds and mental things are made of".
Psionics could use the Inside Out five: Joy, Sadness, Fear, Disgust, and Anger
Re #3: That is not a bad idea at all.
Just some unstructured and incomplete thoughts on Psionics:
Re #4: So after some thinking, I went with the Inside/Out idea. It fits my needs well - it's a solid conceptual grouping of five things, and a lot of common spells can be viewed as a simple application/manipulation of the raw atoms.
It also grounded my concept for Soul a little better - it's the biological basis for thought, the actual "thinking" strata of the universe, so things like telepathy and mind-reading are all Soul manipulation. And this led me to give it an ideosyncratic Energy affinity, like the other Biology atoms have, which explains the common linkage between telepathy and telekinesis! (This is supported by D&D too - 3.5e linked psionics most strongly with Sonic damage. 5e introduced psionic damage as a base type and so weakened the linkage, but I think it's still there somewhat.)
Re #5: I still don't have anything built-in for prophecy or time stuff, and now that the whole thing is pretty much jelled, it looked like I won't. That's fine with me, not every field of magical study has to directly tie to an associated atom, just as every science doesn't need an associated particle/field - Comp Sci is all high-order stuff, for example. This also helps support "time stuff" being far more difficult magic - whatever atoms you need to manipulate for it, it's the highly abstract manipulations you perform that are the most important part, as there's no shortcut of "just throw more energy at it".
I've read a couple of your d&d related posts, and I must tell you how much I appreciate your novelty, creativity, and thoughtfulness.