path: root/tempo.md

# ⍾ tempo
a temporal, causal-chain based constructed language (conlang) for the structured communication of concepts.

## definitions

def axiom ``
^^
an axiom is any piece of information that can be denoted in tempo.
an axiom can be comprised of one or more axioms.
if an axiom can be expanded into other axioms and still preserve the original meaning,
it is called a [[composite axiom]].
otherwise, if an axiom can not be broken down into other axioms,
it is called a [[fundamental axiom]].

i have defined my own set of fundamental axioms. these are **consequence** (the axiom of causality), **negate** (the axiom of logic) and **combine** (the axiom of composition).
i believe (*unverified*) that three is the absolute minimum, and that successfully defining one of the three fundamental axioms using the other two will require a breakthrough in physics. if any future nobel prize winner has a secret they haven't shared with the world yet, this would be a good time to contact me.

parenthesis can be used to imply order of words, but usually they can be distinguished based on axiom-definition and 

## formatting
an axiom is denoted as:
```
def <name> `<definition>` [english form]
^^ <description>
```

## fundamental axioms (words)

def > `fundamental.` (consequence)
^^
denotes an event in the course of a temporal chain.
`A > B` directly implies that perception of B is impossible if the perception of A is also not possible.
this axiom can also act as a logical consequence, being the equivalent of `A ⇒ B`.

def - `fundamental.` (negate)
^^
converts an object into its logical opposite. (- A)

def + `fundamental.` (combine)
^^
combines two objects into a composite object. (A + B)

## the self-referential axiom (me)

def Ω `Ω`
^^ me:
an axiom that references itself. this is neither composite nor fundamental, rather it is derived from itself. fundamental axioms are unified, they can not be reduced. `Ω` can be reduced, but to itself.

def Ω `[x] Ω+x` (Ω A)
^^ me too (identity):
the me axiom is very special. for this reason, it will have two definitions.
one to refer to itself, and one to combine itself with any other axiom(s) that come its way.
captures another axiom in the form of an identity, in its very essence, and not what it is trying to imply.
for example, `Ω 1` is `1` itself, not its implication.
this axiom takes precedence above any other, meaning `-Ω-` does not mean the un-essence of negation and leave a hanging argument.

## composite axioms (semi-sentences)

def . `- Ω-`
^^ origin:
a thing that exists, a negation of non-existence.
can be any existence, but can never equate itself.
that is, `. = .` is never true, even in a single-object universe,
since the ephemeral object can be the universe and the single-object at once.
not even in a zero-object universe, as the object can be
the universe itself and nothingness.

def 0 `-.`
^^ zero:
negation of existence.

def = `[x y] x>y + y>x` (A = B)
^^ equality:
A>B whilst B>A. in other words, the two events are the same.

def ∷ `[x y] x+. = y` (A ∷ B)
^^ property:
denotes that a certain object is a property of another, by indicating that its combination with another object results in the target.
this also implies that you can consider `0` as property of all, and `1` as property of all the numbers above it, and so on.

def ⩫ `[x] A=. x≠A` (⩫ B)
^^ unique:
denotes that there is no such other object equating this one.

def 🮻 `[x] x>x` (🮻 A)
^^ static:
denotes an object that never changes. that is, it is its own consequence.

def ʭ `[x y] A=x A∷y ⩫A 🮻A` (A ʭ B)
^^ id:
denotes the specific property of item B in which it has an immutable and unique property that is not shared with any other object.

def ⨍ `[x] A=. xʭA A` (⨍ B)
^^ lookup:
resolves an ID to its unique property owner.

def * `[x y] A=⨍x A∷y A` (B * C)
^^ catch:
resolves the value of an object's property based on its ID.
for example, `color catch apple` equates `red`.
`1` catch array of `[2, 3]` equates `2`, the first item of the set. (A * B)

def 1 `Ω> + 0`
^^ one:
consequence of zero.

def ≠ `[x y] - x=y` (A ≠ B)
^^ unequal:
shows that the two input objects are non-equal.

def < `[x y] y>x + x≠y` (A < B)
^^ before:
B > A & A ≠ B, denotes B comes after A and they are not the same.

def ! `.|0`
^^
an indescribable, unknown, and paradoxical axiom.
denotes a part extracted from nothingness.

def @ `[x] x * .>.` (@ A)
^^ change:
denotes any multiple of epsilon time in causal progression, meaning our input object has changed.
if we consider `des` to be an object which is destroyed upon change —routine for all objects, but we overlook it to avoid existential burden— then `@ des` would equate `0`.
this axiom can also be used as an event descriptor: `@* A = B` means if A is subjected to change, it transforms into B (provided the statement is true).
explanation: we capture the input object from the cycle of `.>.` which denotes a causal event.

def # `[x] @x = @x` (# A)
^^ law of persistence:
the change of an object results in its change.
this is true unless an external force acts upon the system
in an unpredictable manner.

def ~ `[x] -#x` (~ A)
^^ chaos:
the unpredictability of the change of an object.
this is true only for a system which is influenced by
an unpredictable external force.

def \ `[x] A=.|x B=.|x A>B>A` (\ C)
^^ loop:
A and B obtain a reference to two objects in the system C,
and then denote that A causes B whilst B causes A.
example: `\ growth` denotes a causal loop which causes infinite growth.

def ⧔ `\@`
^^ time:
the loop of change.

def T `A=. A=A`
^^ true:
the universal value of truth.

def F `-T`
^^ false:
the universal value of falsehood.

def | `[x] A=. A<x A` (| B)
^^ separate:
the object(s) preceeding the combination of an input object.
breaks down an input into its creating parts.
using this on an atomic object will return either itself or `0`,
depending on the atomic object's lifetime nature.

def ∞ `A=. .>A`
^^ infinity:
a concept that is bigger (and comes after) anything else.

def ε `A=. -A=0 A>.`
^^ epsilon:
a concept that is smaller (and comes before) anything else, except zero. this implies `0>ε`.

def & `[x y] x=T + y=T` (A & B)
^^ and:
logical AND.

def ⊼ `[x y] - x&y` (A ⊼ B)
^^ nand:
logical NAND. this expression is proven to be functionally complete, meaning you can build any conceivable logical contraption out of this. for the sake of originality though, we will not be using this to scaffold a rule 110 emulator.

def ⑄ `A=. . < Ωx A` (⑄ B)
^^ speaker:
what came before "me"? the originator of the thought, of course.

**things to ponder**:
1. what is a human speaker, if not the causal chain of axioms that produced another axiom?
2. what is the physical realm, and how can tempo even anchor to it?


def ¶ `[x] ¶ .+x` (¶ A)
^^ growth: denotes infinite growth of an input axiom. can be used to find the encapsulating set of an input object. note that at some point it becomes a no-operation, once the growth turns into the encapsulating set and becomes `[x] ¶ x+x`, which is just `x`. you may also add this as a constraint: `[x] A=. A=x ¶x = x`

def ໒ `¶ ⑄Ω`
^^ world: captures the speaker's universe.

## update log

// Timestamp: future
- more coming soon.

// Timestamp: 2025-12-29 23:42:20 UTC+3:30
- it's almost the new year.
- added dark mode support.

// Timestamp: 2025-12-29 13:39:17 UTC+3:30
- changed positional arguments from using numbers to using bound variables.
- defined new axioms and made previous axioms more robust.

// Timestamp: 2025-12-29 11:36:40 UTC+3:30
- i will now move onto actual human communication.

// Timestamp: 2025-12-28 21:01:24 UTC+3:30
- catch is not a fundamental axiom! i was able to construct it using the remaining three, and i have moved it to the composite axioms section.
- renamed [[complex axioms]] to [[composite axioms]].

// Timestamp: 2025-12-28 15:18:49 UTC+3:30
- reworked the markdown parser to render the website more faithfully.
- added a definitions section.
- added a timestamp element to allow for descriptive logging of changes.
- removed **separate** as a fundamental axiom, as it can be formed by mixing **before** and **combine**.
- defined a few new axioms.

// Timestamp: 2025-12-27 23:30 UTC+3:30
- created the first iteration.
- added the initial definition.

## footnotes
thank you for reading.

this website is configured in a way such that web scrapers will be able to archive all of its contents, including the <a href="tempo.md">tempo.md</a> file. a copy of tempo can be found on the wayback machine.

email: moon@coffin.ir