Thanks

She didn't step on it, she apparently used her thumb and damaged one of the buns in the pack

It means they admit they were wrong and you were correct. As in, "I have been corrected."

If you take immortality, you also probably need to take healing. Being mortally wounded and unable to die sounds, uh, bad.

I don't think the methodology is the issue with this one. 500 people can absolutely be a legitimate sample size. Under basic assumptions about the sample being representative and the effect size being sufficiently large you do not need more than a couple hundred participants to make statistically significant observations. 54% being close to 50% doesn't mean the result is inconclusive. With an ideal sample it means people couldn't reliably differentiate the human from the bot, which is presumably what the researchers believed is of interest.

One definition of the complex numbers is the set of tuples (x, y) in R^(2) with the operations of addition: (a,b) + (c,d) = (a+c, b+d) and multiplication: (a,b) * (c,d) = (ac - bd, ad + bc). Then defining i := (0,1) and identifying (x, 0) with the real number x, we can write (a,b) = a + bi.

No such thing has been "mathematically proven." The emergent behavior of ML models is their notable characteristic. The whole point is that their ability to do anything is emergent behavior.

What is this article supposed to show?

Assuming you mean a boss at the end of act 2 / beginning of act 3, Balthazar

I got pushed off the ledge a few times. What worked for me was, while the first character was stuck in dialogue, the rest of my party would sneak in and position advantageously before starting the fight mid-dialogue on my own terms. It was indeed bullshit, but not nearly as bullshit as me reloading for 20 mins convincing a boss to kill themselves, so I think the game and I can call it even.

I also completed a few tough early fights with 2 mage hands and a cliff, so really, I'm pro-shoving all the way.

Mathematical constructivists hate this meme

Let's name the goats Alice and Bob. You pick at random between Alice, Bob, and the Car, each with 1/3 chance. Let's examine each case.

• Case 1: You picked Alice. Monty eliminates Bob. Switching wins. (1/3)

• Case 2: You picked Bob. Monty eliminates Alice. Switching wins. (1/3)

• Case 3: You picked the Car. Monty eliminates either Alice or Bob. You don't know which, but it doesn't matter-- switching loses. (1/3)

It comes down to the fact that Monty always eliminates a goat, which is why there is only one possibility in each of these (equally probable) cases.

From another point of view: Monty revealing a goat does not provide us any new information, because we know in advance that he must always do so. Hence our original odds of picking correctly (p=1/3) cannot change.

In the variant "Monty Fall" problem, where Monty opens a random door, we perform the same analysis:

• Case 1: You picked Alice. (1/3)
  • Case 1a: Monty eliminates Bob. Switching wins. (1/2 of case 1, 1/6 overall)
  • Case 1b: Monty eliminates the Car. Game over. (1/2 of case 1, 1/6 overall)
• Case 2: You picked Bob. (1/3)
  • Case 2a: Monty eliminates Alice. Switching wins. (1/2 of case 2, 1/6 overall)
  • Case 2b: Monty eliminates the Car. Game over. (1/2 of case 2, 1/6 overall)
• Case 3: You picked the Car. (1/3)
  • Case 3a: Monty eliminates Alice. Switching loses. (1/2 of case 3, 1/6 overall)
  • Case 3b: Monty eliminates Bob. Switching loses. (1/2 of case 3, 1/6 overall)

As you can see, there is now a chance that Monty reveals the car resulting in an instant game over-- a 1/3 chance, to be exact. If Monty just so happens to reveal a goat, we instantly know that cases 1b and 2b are impossible. (In this variant, Monty revealing a goat reveals new information!) Of the remaining (still equally probable!) cases, switching wins half the time.

I wonder if this actually fixes the ancient dwm bug that causes simultaneous motion on multiple monitors with different refresh rates to make the whole window manager choppy. That bug has existed since at least Vista, and it sucks. Nothing like buying a 240Hz monitor and not being able to watch videos on my secondary one without bringing them both down to what looks like 60.