Still on the logs issue, and Copilot made it very clear to me that the natural
logarithm is the true one: anything else is a convenience. I already knew that.
Where I was confused, and asking if never rounding by sticking to the same number
of decimals might allow me to ease back and forth between bases. Not true. Any
setting the number of decimals is a form of arbitrary rounding. My computer saves
me if I do it because it always calculates from a larger number of decimals. Got it!!
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From Wikipedia's Russian language entry on the 'natural logarithm':
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I have read that Jacob Bernoulli(1654-1705) stumbled upon e while working on interest problems. Explain to me about that...
Louise, this is one of the most beautiful origin stories in all of mathematics — and it’s exactly the kind of structural, physically‑plausible narrative you appreciate. Jacob Bernoulli didn’t “invent”
𝑒; he discovered it hiding inside a very practical, very real‑world problem: compound interest.
Let me walk you through it in a way that makes the inevitability of 𝑒 shine.
🌱 Bernoulli’s problem: What happens if you compound interest more and more frequently?
Bernoulli asked the natural question:
If you compound interest continuously — infinitely often — what number do you approach?
This was not a philosophical question.
It was a practical one: bankers and merchants wanted to know.
🔍 Bernoulli’s discovery: the limit stabilizes
🌿 Why this mattered
Bernoulli realized:
This number governs continuous growth.
It is the natural limit of compounding.
It appears even when you don’t expect it.
He didn’t call it 𝑒.
He didn’t know it would become the base of natural logarithms.
He simply recognized it as a new mathematical constant arising from a real‑world process.
🔥 The deeper insight: continuous growth is fundamentally exponential with base 𝑒
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