SlowNum

Motivation

Large number systems have limits in what they can store, which are capped primarily by the data structures used to represent that information. These systems are limited based not only on memory but on operational speed. Especially once reaching higher hyperoperations (in libraries such as Naruyoko's OmegaNum), most of the precision of stored numbers is no longer needed. SlowNum aims to use ordinals to express numbers, allowing precision to change based on the size of large numbers.

Methodology

The program is planned to be written in C++, so it can be used in the browser (via WASM) for incremental games and in LuaJIT (via FFI) for Balatro mods.

Numbers in SlowNum are represented with an ordinal $\alpha$, and equal the value of $g_\alpha(10)$ in the slow-growing hierarchy.

Here are some benchmarks/goals for each version of SlowNum:

Limit	Value/Comparison	Implemented?
$\omega$	$n$ - Just get the ball rolling	❌
$\omega^\omega$	$10^n$ - BigNum	❌
$\varepsilon_\omega$	$10\uparrow\uparrow n$ - Tetration	❌
$\zeta_\omega$	$10\uparrow\uparrow\uparrow n$ - Pentation	❌
$\varphi(\omega,0)$	$10\uparrow^{n}10$ - Hyperoperations/OmegaNum	❌
$\Gamma_\omega$	Graham's Number Range - Expansion/ExpantaNum	❌
$\varphi(1,0,0,0)$	Ackermann Ordinal	❌
$\psi(\Omega^{\Omega^\omega})$	Small Veblen Ordinal - GodgahNum	❌
$\psi(\Omega^{\Omega^\Omega})$	Large Veblen Ordinal	❌
$\psi(\Omega_2)$	Bachmann-Howard Ordinal	❌
$\psi(\Omega_\omega)$	Buchholz Ordinal	❌
$\psi(I)$	Extended Buchholz Ordinal	❌
???	???	❌