To do it as a circular problem you'd define Theta(birthday) as (360*Julian(Birthday)/365.25) for degrees, or (2π(Julian(Birthday)/365.25) ) for radians, average the thetas, take remainder after dividing by 360 or π. And that would take care of the Dec31/Jan 1 difficulty.
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Replying to @JohnBarnesSF @notviking
Me: reading Dune, comes across reference to Sardaukar being Jewish, thinks "ooh, John Barnes mentioned this, I should tell him...but then sees a tweet about averaging birthdays, feels the need to be pedantic re phase angle...decides Barnes can wait...finds Barnes in thread.
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I think you want a 2D value for the average: both a vector direction and a length. 100 data points all the same should have a greater length than 100 different ones that barely do more than cancel out.
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Also, the Sardaukar reference I stumbled across is is in appendix 2. "Talmudic Zabur surviving on Salusa Secundus" (where Sardaukar are recruited from).
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Replying to @MorlockP @notviking
Whoa. You read the Dune appendices? You are hardcore, sir. I salute you.
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Don't valorize mental illness; if anything it might encourage me.
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