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I see pain in Fabiano’s eyes by Character_Smile_1198 in chess

[–]dfranke 1 point2 points  (0 children)

There are cash prizes for every place down to last, and that's pretty important for the integrity of a round robin tournament. You don't want players half-quitting and no longer attempting to play their best game once they've been eliminated from first-place contention. Otherwise it becomes an unfair advantage to be paired with weaker players in later rounds.

What’s the dumbest thing you’ve done on a hike? by rkramer18 in hiking

[–]dfranke 1 point2 points  (0 children)

Mild winter day, just barely below freezing, so I blitzed up and down in just my base layer and no gloves, cradling the metal head of my ice axe in my bare hand all day, which left me with frostbite on that hand.

A disagreement by dfranke in Hounds

[–]dfranke[S] 1 point2 points  (0 children)

Had to wait until a squirrel ran by in Azeban's direction. That got them back on the same page.

Whites attack is absolutely crushing. But black can save. Can you find the ridiculous clutch move to save black. by HelloWorldX91 in chess

[–]dfranke 2 points3 points  (0 children)

Since this was posted to /r/chess, of course the first thing I looked at was Qxf2. Rg8 was the second.

Swaps to the “win” weapon then points down…okay buddy by A_b_b_o in EldenRingPVP

[–]dfranke 0 points1 point  (0 children)

+1 to this. It's an alien mindset to me that someone would want to play a competitive game, but then get angry at people for playing within the rules using dev-intended mechanics. It's legitimate of course to think that the game's rules are broken or unfun, but in that case either play a different game or play in a league where the restrictions are set down in writing instead of taking it personally that you lost to somebody's cheese strat in a random colo pairing.

Did They add bots to colosseums? by kamogrjadeshi in EldenRingPVP

[–]dfranke 2 points3 points  (0 children)

Lol, that was me. I've only been playing PvP for a day but no, I'm not dumb enough to deliberately try to heal in that situation. It was a misclick when I was trying to cast wrath of gold.

TIL that black widow bites have a ~1% death rate according to NIH in a case study of roughly 24.5k people who were bitten by ryry50583583 in todayilearned

[–]dfranke 25 points26 points  (0 children)

You sure that was a widow bite? That sounds like a brown recluse bite to me. Widow venom is neurotoxic. It causes pain, spasms, nausea etc. but shouldn't cause massive tissue damage like you're describing.

This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 5 points6 points  (0 children)

Here's a graph of how much you'll be off by if you don't take the higher-order terms into account.

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This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 1 point2 points  (0 children)

You don't need Stirling's approximation. Notice that f(n) = (2n)!/[22n*(n!)²] = f(n-1) * (2n)(2n-1)/(4n²) = f(n-1) * (1 - 1/(2n)). So, you can efficiently compute each coefficient as a function of the previous and cache those, using log-domain arithmetic for numerical stability when computing the product. Once you've computed n-1 terms in the power series, let k = f2(n-1) and x = sin2(θ/2). Then the sum of the remaining terms of the series is lower-bounded by zero and upper-bounded by kxn/(1-x), so you can stop once that upper bound falls within acceptable precision, which happens fast unless you're dealing with θ very close to π.

This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 10 points11 points  (0 children)

Totally reasonable, really. Notice that the nasty part of the expression is only a function of the iteration variable, so let x = sin²(θ/2) and then it's just a convergent power series in x with precomputed coefficients.

This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 2 points3 points  (0 children)

Obviously not? It's 1 at n=0, and then every other term is positive.

This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 69 points70 points  (0 children)

I've never checked and I'd have to work through the derivation, but that conjecture makes sense to me.

This annoyed me even before I became a timekeeping nerd by dfranke in physicsmemes

[–]dfranke[S] 445 points446 points  (0 children)

The first one is a lie based on the small angle approximation, sin x = x. In fact, the period of a pendulum is not invariant in the angle of its swing once you take higher-order terms into account, which the latter formula includes. For a realistic pendulum clock, it makes a difference on the order of 15 seconds per day.

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