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2048 is the radix of a numbering system that seed phrases are built upon. (a fairly large numbering system)
This system is used to convert initial entropy and a checksum over the entropy to words. This is done by reading 11 bits from this initial data at a time - because 11 bits of integer is at most 2047 - from the initial entropy and representing this to the user as words.

For reference, in decimal, the radix is 10, as we have 0 1 2 3 4 5 6 7 8 9 (10 distinct digits) and in hexadecimal it's 16: 0 1 2 3 4 5 6 7 8 9 a b c d e f. These are conventions.
You cannot unilaterally add words to the convention because they would have no meaning without a translation. So in the decimal system we can calculate 1 + 3 = 4, but what is 1 + z?
If I’m getting this right, you’re saying BIP39, which has 2048 words, from 0 to 2047, breaks into 11-bit chunks and matches that to the word list index? If that’s how it works, then I guess we could have our own word list, but we’d lose compatibility with existing wallets. I’m guessing if there’s a wallet that lets you pick your own word list, then you could use your own. Or am I missing something?
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65 sats \ 1 reply \ @optimism 21h
If I’m getting this right, you’re saying BIP39, which has 2048 words, from 0 to 2047, breaks into 11-bit chunks and matches that to the word list index?
Correct!
If that’s how it works, then I guess we could have our own word list, but we’d lose compatibility with existing wallets.
Correct!
I’m guessing if there’s a wallet that lets you pick your own word list, then you could use your own.
Yes! But note: you'd have to keep the wordlist somewhere safe too and this custom software needs to be available when you need it! So it's additional work and probably not worth it, since you can just cut your 12 or 24 conventional words into half and have 2 separate "factors" anyway; 1

Footnotes

  1. You could use something more hardened, like Shamir's secret sharing, though I remember many years ago when I had C (HSM), Java (app) and Python (tests) development teams working on this for a secure system, their Shamir's libraries weren't compatible and this decision turned out to be max pain instead of max convenience, so maybe just stick with keeping things simple.
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I’m not actually gonna do it, just wondering. Thanks!
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100 sats \ 1 reply \ @DarthCoin 21h
...and here comes the mathematicians 👍
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That'd be an insult to real mathematicians lol
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