Since the secret key is information, yes, it could be memorized.
Discussion
Can it be reduced to simple words and not just a long string of characters?
I'm not a programmer but from my knowledge new keys theorically could. Those words in a recovery phrase is just a bunch of binary that make up that private key which from knowledge looks like a nsec.
Correct nostr:note1m8qke535855gl50x7vakkk7q50fls2yx7c76h4j8njqdemyvffqs9t7zrl
You can think of BIP-39 as a counting system but instead of binary (0,1) or decimal (0,1,2,3,4,5,6,7,8,9), or hexadecimal (0,1,2,3,4,5,6,7,8,9,a,b,c,d,e,f) it’s 2048-ary and the digits are “abandon”, “ability”, “able”, … “zero”, “zone”, “zoo”.
Each word encodes 11 bits of data.
“abandon” = 00000000000
“ability” = 00000000001
“able” = 00000000010
…
“zero” = 11111111101
“zone” = 11111111110
“zoo” = 11111111111
So any data can hypothetically be converted to BIP-39 encoding, just as any data can be represented in binary or hexadecimal.
Consider these two bytes of binary data:
0010 0010 1001 1001
In hexadecimal, this would be 2299. In decimal, it would be 8857.
To convert to BIP-39, we need to break it into 11-digit chunks. Since we only have 16 bits of data, we have to pad it up to 22 bits. We could pad either the beginning or the end. The end is conventional:
001000101001100 10000000000
This maps to:
“card = 00100010100
“length” = 10000000000
So we could represent the data as “card length”.
A Nostr private key is derived from randomness. If this randomness has 256 bits of data or less, it’ll fit in a 24-word BIP-39 seed phrase. 128 bits will fit in a 12-word seed phrase.
You can use this BIP-39 playground I made to explore the relationship between raw binary data and BIP-39 seeds. https://observablehq.com/@jimbojw/grokking-bip39