Great Myriad Scale

Large numbers are commonly named with Latin prefixes, but these Latin names can be difficult to parse. First, similar names are easily confused (such as "million" and "billion"). Second, with multiple scales in use, values can be ambiguous (one billion is equal to 10^9 or 10^12 depending on use of the short or long scale.) Finally, these parsing difficulties are exacerbated as values increase. (How much is a decillion in the short scale? The Latin for ten is used for one thousand to the eleventh. Madness.) I propose a scale derived from Greek names, such as the myriad, which I call the Great Myriad Scale. (Pedantically, this scale actually uses English with Greco-Latin roots, and a bit of wordplay. Spare me, I do not suggest my number names are actual Greek.) The Great Myriad Scale is intended to be an unambiguous scale for counting large numbers. It is based on the myriad, classically equal to ten thousand. Numbers in this scale are derived from Greco-English numerals, such as those used to name polygons. Essentially, this scale is intended to be a practical naming convention for impratically large numbers.

Numbers below the Myriad:

Powers of the myriad are typically named by degree ("Myriad Squared" Myriad Cubed", and "Myriad to the Fourth") but in this scale they each get a prefix. There are numeric prefixes and ordinal prefixes, choose whichever you prefer.

The Myriad Powers

Each power of the myriad is named in this pattern until the Great Myriad, which gives this scale its name. The Great Myriad is equal to the myriad raised to the power of a myriad, which is ten to the power of forty thousand. The powers of the Great Myriad are also named with "Great", such that the square of the Great Myriad is the "Great Deuterad", the cube of the Great Myriad is the "Great Tritarad", and so on…

Of course, by raising the Great Myriad to the power of a myriad, (or 10 to the power of 4 deuterad) we get a "Great, Great Myriad". Raise this to the power of a myriad again to get a "Great, Great, Great Myriad" and so on. To keep names short, a nucleic naming scheme is used (swapping the "-arad" suffix used in the above table for "-on"). The "Great, Great Myriad" is called the "Deuteron Myriad". The "Great, Great, Great Myriad" is called the "Triton Myriad" and so on...

The Great Myriads

This continues to infinity, with "Myrion Myriad" being followed by "Myriaproton Myriad", and "Myriadeuteron Myriad" following that, and so on...

Why?

Well, there are only so many names, there can only be so much wordplay. To keep all the numbers countable, their names needed to be constructed from smaller numbers. Sure, you can start naming with hyperoperations, but they grow faster, and faster and soon you have an unstable scaffold stretched over growing, turbulent voids ever more difficult to bridge. If you cannot count to a number, then such a number is really a vague suggestion of magnitude, a dream of many zeroes... Oh, you meant "Why invent this counting scale thing anyway? Millions are fine, and we already have scientific notation, and who would ever count from one to myriamyrion myriad anyway?" Well, have you ever played one of those incremental video games, with all the numbers going up to astronomical absurdity? You wake up to "Hey, while you were sleeping, you got twenty quattuorvigintillion points in the tower of tumbleweeds!", and you remember all the sheep you counted last night, hoping for rest, because in the morning, you have a fracture to tend. You have to prevent muscular atrophy by isometrically flexing a muscle several hundred times, and that means even more counting. So you make up new names for new numbers, to spice it up.

You ask yourself "Where do all the number names come from anyway, and when do we run out?" and lo, the rabbit hole! It opens before you to a wonderland of Latin and "googology", and before you realize it you have let the number goblins in. They shout "We want an incremental game! One where players can read all the numbers!" They jump on the bed. "Notations! Bah! Fie on notations!" The number goblins demand a sense of scale. "Notations transform orders of magnitude into mere increments! Madness! People need names! Names!" They grab hold of the bed knobs and shake. The leader shouts in your ear "Don't you understand?! Do it for Archimedes!" The chanting begins. "Conway! Weschler! Knuth!". You are surrounded in a cacophonous, cantankerous, chorus of contention! Then, in unison, a deep breath, and the call of a great horn. "Millinillinillinillinyllion!" With this incantation you are changed, goblinified! There is only one way to lift the spell! Give them their tables, and their powers of ten, so that they might count in numerological novelty until the end of all things!

Scales with Powers of Ten

(Additional) Trivia

• Numeric prefixes (of polygons), and Greek ordinals are interchangable. (That is, "deuterad" can also be called "diarad".)
• In the Great Myriad Scale, digits are in groups of four, seperated by semi-colons. Commas are also ok to use.
• Archimedes' largest Sand Number (the largest described in The Sand Reckoner) is equal to 10^(8 * 10^16), or a "Tetaron Deuterad".
• A "Deuteron Myriad" is equal to 10^(4 * 10^(4 * 2)), a "Triton Myriad" is equal to 10^(4 * 10^(4 * 3)), and so on...
• A "Myrion Myriad" is equal to 10^(4 * 10^(4 * 10^4))
• An apeirogon has an infinite number of sides; "apeiro" gives the Great Myriad Scale the "Apeirad" and the "Apeiron Myriad"
• "Cola's Enumeration" and the "Ordinal Myriad Scale" are previous attempts to enumerate large numbers, using the Conway Wechsler system, greek ordinals, and hyperoperations. Ultimately, it is important that each name for a large number is based on the names of smaller numbers, rather than operations or notations. The numbers between "novel numbers", or "milestone numbers", also need to be nameable.

Sources

• Conway's illion Converter
• Conway-Weschler System
• Hyperoperation
• List of Polygons and Greek Ordinals
• Myriad
• Ordinal Numeral
• Archimedes' Sand Number
• Knuth's -yllion System