Vitalik Buterin
@vitalik.eth
So many people in the replies here are totally missing the point. Yes, there is an infinite number of valid possible answers for i^i. But EVERY SINGLE ONE OF THEM IS A REAL NUMBER. https://x.com/mathladyhazel/status/1800905395961241811
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baubergo
@baubergo-
Can any giga brain explain me what the math is? 🥲
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Sine
@sinusoidalsnail
Are you looking for an explanation that shows the algebraic steps to prove it? Or just, the idea in general, without math stuff shown?
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baubergo
@baubergo-
The idea in general
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Sine
@sinusoidalsnail
Okay! I'll try lol. Will get back to you in a bit.
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baubergo
@baubergo-
Thanks! 👀
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Sine
@sinusoidalsnail
Hmmm I tried for quite awhile, but couldn’t come up with a clear way of describing it conceptually. I kept falling back on showing it algebraically lol, sorry. But now I see that Vitalik has explained it in the comments in a very nice, clear, concise way (quoted below). We can think of the number 𝑖 as an action: a rotation by 90°. And we can think of raising something to the power of 𝑖 as a rotating action upon that action: a 90° rotation of the act of rotating 90°. I think the reason it’s not intuitive, is because most of us learned that “exponentiation is repeated multiplication.” When that’s an oversimplification that doesn’t work once we get to complex numbers. Sorry I couldn’t come up with a better explanation! But I think Vitalik’s nails it perfectly anyway! https://warpcast.com/vitalik.eth/0xd941680b
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baubergo
@baubergo-
Thanks for this Sine! Although, how can this (if) be applicable in any scenario?
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Sine
@sinusoidalsnail
Like a direct application of how i^i appears in life? I’m not sure you’ll find one specifically about i^i. But what is happening with the i^i concept, is really applicable to ideas about dynamics. An object’s position, velocity, etc. And arithmetic with complex numbers is behind pretty much every part of physics/engineering you can think of.
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baubergo
@baubergo-
I think I got it. Hey thanks for this masterclass 👀❤️
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