The most natural way to assign infinite numbers to verse levels is of course to use the surreal numbers. The surreal numbers are constructed by having a set of surreals on either side of a bracket. In basic terms, the surreal number obtained as a result is the simplest surreal between those two. As some examples, is 1, is ω. is 3/2.
The Quanta (=0)
0 - Quantum
Verse level 0 corresponds to quanta. Quanta are the fundamental units. They're simpler than anything else. They're more versatile than anything else. In fact, they're the simplest thing; nothing gets simpler than them (at this point, I incant some spells to ward off Tonybalongna. If it helps, nothing is at 0, and these are at ε, or something). They're the quantum unit of verses, or of stuff, or whatever, and everything in reality is some kind of variant of quanta on some scale (beyond reality, this gets a little fuzzy).
Anything that acts according to any set of computational rules, regardless of what they are, can be replicated by some arrangement of quanta. That's the level of simplicity that we're working at. You could think of them as like the physical manifestation of Turing machine instructrions, though it is possible that they could perform hypercomputations depending on what exactly reality is able to support.
The Small (0 < x < ωω)
The level of the small is anything larger than a single universe. Inside a universe, communication is possible within the flat confines of ordinary space - two objects can interact simply by firing information at each other in straight lines, without having to
1 - Elementary Particle
Verse level 1 corresponds to the simplest thing that's more complicated than quanta, which, for this universe, is the elementary particle. Elementary particles come in two types: fermions, and bosons.
Fermions can themselves be split into the four types of electrons, neutrinos, up quarks, and down quarks. Each of these particles has a left-handed and a right-handed variant, and can come in particle and antiparticle form. Each of the quarks can come in three different colours.
This gives a total number of 32 fermions, which can be indexed by five-digit binary strings. These bits correspond to isospin up, isospin down, red, green, and blue. Converting from a binary string to a particle, or vice versa, is simple. For the right-handed particles:
- Up quarks have upwards isospin and a colour
- Down quarks have a colour
- Electrons have all three colours
- Neutrinos have both isopin and all three colours.
To flip the parity, flip whether it has downwards isospin. To get the antiparticle (which also flips the parity), flip all bits. For example, a right-handed positron has the code 10000 because it is the antiparticle of a left-handed electron, code 01111, which is the mirror of a right-handed electron, code 00111 as given.
Under the Higgs field, the right-handed and left-handed versions of a particle rapidly oscillate into each other, with the energy of this interaction giving the particles a rest mass, and also meaning that in physical experiments they are indistinguishable (this is why typical tables of the standard model do not have them featured). This happens for all particles but neutrinos - neutrinos stay in their parity, with right-handed neutrinos being unable to interact, and left-handed particles being the typical neutrinos observed in experiment.
There are also three generations of these fermions, for also unknown reasons. Up quarks are called up, charm and top. Down quarks are called down, strange and bottom. Electrons and neutrinos are called electron, muon and tauon. The first generation, contain up quarks, down quarks, electrons, and electron neutrinos, is by far the most common; the only higher generations of particle seen commonly are high-generation neutrinos, because neutrinos are very weird and can easily change into different types.
The number of bosons comes from the symmetry of the force that dictates the universe.
2 - Elementary Particle Pairs
The simplest thing larger than an elementary particle is, of course, two elementary particles, placed beside each other. This continues, with three, four and so on. Natural numbers correspond to that number of elementary particles, near each other but not necessarily interacting.
ω - Hadrons
So, you can continue, with one elementary particle, and then two, and then three, and so on, until you have an arbitarily large number of elementary particles. But what's more complex than this?
Clearly, adding more structure. When you have multiple quarks in a bound state, you get a hadron. Hadrons can possess two quarks (mesons), three quarks (baryons), or more - in theory, the number of quarks is unlimited (an exotic hadron, like a tetraquark, a pentaquark or a hexaquark), though high hadrons are very unstable and very rare to see. They can also possess zero quarks (but still be bound), creating a very exotic hadron called a glueball.
Hadrons are bound together by the strong force, which is mediated by gluons. Most of the mass of a hadron actually comes from the binding energy of this. Because gluons also interact by the strong force, the energy increases with distance forever (gluons create thin "tubes" of force, instead of spreading out like electromagnetism), which makes the strong force limited in range - eventually, two quarks moved apart from each other will gain enough energy to create another quark instead of increasing the range of the interaction.
This also means that, to prevent every quark in the universe from interacting with every other one (like with electromagnetism), quarks will only ever form in systems where their overall colour is white. Mesons have a quark with a colour and another with the corresponding anticolour (note that in the binary model, because an anticolour is gained by flipping all bits, colour + anticolour always gives 111, or white). Baryons have three quarks, each with a different colour - these also add to 111. Larger hadrons are combinations of these two modes - a pentaquark might have a red quark, a blue quark, a green quark (making a colour triplet), another red quark, and an antired quark (making a colour-anticolour pair). This also explains why quarks can not occur alone. Colourless particles do not interact by the strong force, so electrons and neutrinos don't bind at this level.
Hadrons have five properties based on the generations of quarks they contain, called quantum numbers. These are isospin, strangeness, charmness, topness, and bottomness. Strange and bottom quarks have a strangeness and bottomness of -1, and charm and top quarks have an charmness and a topness of +1. Up and down quarks have an isospin of +1⁄2 and -1⁄2 respectively.
Bound states of three quarks are called baryons. Each quark in a baryon has a different colour. Ordinary baryons have a red, green and blue quark, and antibaryons have an antired, an antigreen and an antiblue quark.
Baryons are named based on the number of heavy quarks (strange, charm, bottom and top) they have and their isospin. Baryons with no heavy quarks and isospin ±1⁄2 are called nucleons (N), and with isospin ±3⁄2 are called delta baryons (Δ). Baryons with one heavy quark and isospin 0 are called lambda baryons (Λ), and with isospin ±1 are called sigma baryons (Σ). Baryons with two heavy quarks and isospin ±1⁄2 are called Xi baryons (Ξ). Baryons with three heavy quarks and isospin 0 are called omega baryons (Ω).
If the heavy quarks are not strange quarks, then this is marked, and if the charge in nonzero, this is also marked. For example, the particle udc has one heavy quark (a charm quark), an isospin of 0, and a charge of +1, so it is called the charmed lambda baryon with symbol
The most interesting baryons are the nucleons, because these are the only ones that are stable over long timescales. The two nucleons have their own names: N+ (uud) is called the proton, with symbol p, and N0 (udd) is called the neutron, with symbol n. As seen, protons are positive and neutrons are neutral; this gives them their names and important information about how they behave electromagnetically, especially on larger scales which will be described in the sequel.
ω+1 - Hadrons and Elementary Particles
The simplest thing more complex that a hadron is, of course, a hadron, with an elementary particle sitting somewhere next to it. And then two sitting next to it, and three sitting next to it, and so on.
ω.2 - Hadron Pairs
The simplest thing more complex than all of those is a pair of hadrons, sitting next to each other but not interacting.
ω.2 + 1- Hadron Pairs and Elementary Particles
Obviously, a hadron pair leads to a hadron pair with a single elementary particle next to it...
ω.2 + 1- Hadron Pairs and Elementary Particle Pairs
...or with two elementary particles next to it, and so on.
ω.3 - Hadron Triplets
Then you get a hadron triplet...
ω.4 - Hadron Quadruplets
...and a hadron quadruplet...
ω.5 - Hadron Quintuplets
...and a hadron quintuplet, and so on.
ω2 - Atoms
The thing more complex than any number of hadrons sitting next to each other is a bound state of multiple hadrons. These appear in the form of atoms, which have two parts: a positively-charged nucleus made up of nucleons, and a negatively-charged electron cloud containing multiple electrons.
The nucleus is made up of protons and neutrons, the positive and neutral nucleons. These are bound together by the residual strong force, which is mediated by mesons; typically pi mesons, since these are the lightest and least energetic mesons, though any virtual meson could be created and annihilated with increasing levels of rarity due to the energy needed to excite the more massive meson fields.
The electron cloud is made up of electrons, the elementary particles with no isospin and all three colours, arranged in numerous probability distributions called shells, subshells, orbitals, and spin states. The positions of electrons in the electron cloud is given by four quantum numbers, which can only occur in discrete quantities and are measured in units of angular momentum:
- principal quantum number (n)
- azimuthal quantum number (ℓ)
- magnetic quantum number (m)
- spin quantum number (s)
The principal quantum number n measures the shell that the electron is in. This ranges between 1 and the shell containing the outermost electron in the atom, which can be read from the row in the periodic table. The first row, H and He, has n=1. The second row, containing Li through Ne, has n=1 and n=2, and so on,
The azimuthal quantum number measures the subshell that the electron is in. This ranges between 0 and n-1 for a given shell. For example, electrons with a principle quantum number of n=3 can have azimuthal quantum numbers ℓ=0, 1, 2. Each subshell has a single letter name; these go as s, p, d, f, g, and so on alphabetically.
The magnetic quantum number measures the different orbitals available inside a subshell. This ranges between -ℓ and ℓ for a given subshell. For example, electrons in the p subshell can have a magnetic quantum number of m=-1, 0, 1.
The spin quantum number measures the direction in which an electron is spinning. This can be either ½ or -½.
No two electrons can occupy the same state (all four quantum numbers identical). An atom is neutral if it has the same number of electrons as protons, and otherwise it is an ion.
The electron orbitals fill up in order of increasing energy, which is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.
ωω - Universes
0 > x > 1 - Quantum Collections
But wait! What about the intermediate surreal level, between 0 and 1? Well, elementary particles are actually very large as far as arrangements of quanta go; their behaviour is fundamental, but quite complicated (vibrating strings in 26 dimensions certainly aren't a primitive concept). Intermediate levels, the fractional ones between 0 and 1, represent arrangement of quanta that don't make up an elementary particle, and in fact behave very differently in nontrivial ways, but are still subarrangements of the true complete one.
An example of one of these might be a pure "red particle", having only the property of being red, but not containing any of the other four bits at all (not even specifying them as 0). This is only 1/32 of the information needed to properly specify a fermion, so it could be considered to be at the level 1/32.
A fermion could possibly be a bound state of five of these pure particles, except not really, because fermions are fundamental.