A Proposed Naming System for Large Numbers in the Duodecimal Myriad System

The largest number that comes to mind in actual discussion is 10 to the power of 500 —
commonly cited as the number of possible vacuum states, or solutions, in superstring theory.

　10.^500. = 12.^463.314 = (1/5;6)×10;^720∴

In the -llion series of the duodecimal myriad system,
10;^720∴ corresponds to hepta(7)di(2)lli(0)on.^[1]
This means that numbers requiring three or more lli(0) suffixes
— such as uni(1)lli(0)lli(0)lli(0)on — have virtually no practical use.
Expressions with many lli suffixes appear only as contrived examples for
constructing artificially large numbers.

That said, following on from the discussion in:

　2026-05-11 "Design Principles and Unique Implementation"

— where I wrote about how adopting strong design principles causes
the implementation space to converge toward a form that "could hardly
have turned out otherwise" — I found myself thinking a little about
names for such large numbers.

The association that came to mind was how IEEE is read aloud as "I-triple-E."
Applying that idea led me to the following proposal:

　12^n×8k is written as N(n)lli^kon and read as N(n)K(k)llion.

Here, N(n) and K(k) are defined as follows:

　N(n) : uni(1), di(2), ter(3), tetra(4), penta(5), hexa(6), hepta(7)
　K(k) : sing(1), doub(2), trip(3), quadrup(4), quintup(5), sextup(6), septup(7),
　　　 octup(8), nonup(9), decup(10), 'English cardinal + p' (k > 10)

For example:

　unillillillion : written as unilli³on, read as unitripllion
　unilli(×11)on : written as unilli¹¹on, read as unielevenpllion

The -llion series of the duodecimal myriad system was designed
to satisfy two conditions:

　・Immediately recognizable as a large number at first glance
　・No collision with existing English large-number names

By using non-English classical roots for N(n) and English-derived stems for K(k),
the system achieves both "large-number feel" and "first-contact readability."

What is interesting here is that the question of
"what kind of name can humans actually read?"
re-emerges at this level too.

It would be straightforward to extend the rules mechanically and logically,
but in practice, strong constraints are imposed by factors such as:

　・Word-initial sound
　・Word-final sound
　・Word length
　・Rhythmic flow
　・Collision with existing English words

In particular, once k exceeds 10, the -iple series no longer extends naturally
even in English — so a descriptive form such as

　uni-eleven-pllion

may actually offer better readability.
And, not as a joke but as a genuine consequence of the system,
heptagoogolplexpllion is also well-formed.

A further curious point: at the junction of -ple and -lli,
the cluster -pl- naturally reads as belonging to both sides simultaneously.
This too might be called an emergent correspondence that goes beyond
the original design intent.

In the end, even the naming of large numbers cannot escape the constraint of

　"how humans perform pattern matching."

[1] ';' denotes the dozenal (base-12) point, and '∴' denotes the octal (base-8) point.
　 For the correspondence between 10;^720∴ and heptadillion, see myriad.jpg.

[Related]
　2012-07-06 Word "Pattern Matching" (Part 1)
　2025-06-01 A Further Review of the Duodecimal Myriad System

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