This is extremely typical of my interactions with Opus 5.5. I try to make a lighthearted quip about some nerdy thing and it immediately shoots back with a totally dry/deadpan insightful and content-packed answer with the intellect of a thousand suns, or something (*):
"a long time ago when analyzing a similar construction, i somehow convinced myself that the optimum is at e, and that's why 3 or 4 as the base often appears optimal. but knowing me i probably just guessed e by intuition, and it's probably not correct :)
Your intuition was right, and it's a real result. It's called radix economy. If representing a number costs (number of digits) × (cost per digit, proportional to the base), the cost is b · log_b N = (b / ln b) · ln N, which is minimized at b = e. The best integer is 3, slightly better than 2 or 4. That's the classic argument for ternary computers (the Soviet Setun was one)."
(*) OK on reflection, this isn't particularly amazing. But the reference to the Soviet ternary computer is cool. And this output comes in like, milliseconds.
waxwing
npub1va…knuu7
2026-10-01 17:39:22 UTC
Author Public Key
npub1vadcfln4ugt2h9ruwsuwu5vu5am4xaka7pw6m7axy79aqyhp6u5q9knuu7Seen on
wss://nostr.winePublished at
2026-10-01 17:39:22 UTCEvent JSON
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"created_at": 1790876362,
"kind": 1,
"tags": [
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"alt",
"A short note: This is extremely typical of my interactions with ..."
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"content": "This is extremely typical of my interactions with Opus 5.5. I try to make a lighthearted quip about some nerdy thing and it immediately shoots back with a totally dry/deadpan insightful and content-packed answer with the intellect of a thousand suns, or something (*):\n\n\"a long time ago when analyzing a similar construction, i somehow convinced myself that the optimum is at e, and that's why 3 or 4 as the base often appears optimal. but knowing me i probably just guessed e by intuition, and it's probably not correct :)\n\nYour intuition was right, and it's a real result. It's called radix economy. If representing a number costs (number of digits) × (cost per digit, proportional to the base), the cost is b · log_b N = (b / ln b) · ln N, which is minimized at b = e. The best integer is 3, slightly better than 2 or 4. That's the classic argument for ternary computers (the Soviet Setun was one).\"\n\n(*) OK on reflection, this isn't particularly amazing. But the reference to the Soviet ternary computer is cool. And this output comes in like, milliseconds.",
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}