So, math, yeah.

When we'd previously seen our plucky heroines, they had just realized that everything, or at least, all the positive real numbers, can be seen as being made out of continuous quantities of 2s being multiplied together.  A 3 is a bit more than 19/12 of a 2, so 1/12 more than 1-and-a-half 2s.  So diminishing something via multiplying by 8/9, is taking a bit more than 1/6 of a 2 out of its bag.

Predictions chain together by multiplication.  If you spin a fair coin once, the probability of it coming up Abrogail is 1l2.  Knowing whether it came up Abrogail or Text doesn't change the probability on the next spin, so the chance of two sequential Abrogails is 1/4, the chance of three such is 1/8.

Each time you say 1/2, and the event happens, that's like taking another 2 out of the bag containing your total prediction over all the events.  Where, to be clear, your bag started with zero 2s in it, or probability 1.  After guessing 50/100 three times at three fair coinflips, your bag would contain -3 2s or a probability of 1/8.

What if you predicted Abrogail with 2/3 probability instead, on one spin?  Well, if the coin comes up Abrogail, good for you, you've only lost - how many 2s, roughly?  Raise your hand once you've got an estimate.

Keltham is now here!  Perhaps he was really always with you all along.

So, math, yeah.

When we'd previously seen our plucky heroines, they had just realized that everything, or at least, all the positive real numbers, can be seen as being made out of continuous quantities of 2s being multiplied together.  A 3 is a bit more than 19/12 of a 2, so 1/12 more than 1-and-a-half 2s.  So diminishing something via multiplying by 8/9, is taking a bit more than 1/6 of a 2 out of its bag.

Predictions chain together by multiplication.  If you spin a fair coin once, the probability of it coming up Abrogail is 1l2.  Knowing whether it came up Abrogail or Text doesn't change the probability on the next spin, so the chance of two sequential Abrogails is 1/4, the chance of three such is 1/8.

Each time you say 1/2, and the event happens, that's like taking another 2 out of the bag containing your total prediction over all the events.  Where, to be clear, your bag started with zero 2s in it, or probability 1.  After guessing 50/100 three times at three fair coinflips, your bag would contain -3 2s or a probability of 1/8.

What if you predicted Abrogail with 2/3 probability instead, on one spin?  Well, if the coin comes up Abrogail, good for you, you've only lost - how many 2s, roughly?  Raise your hand once you've got an estimate.

Keltham is now here!  Perhaps he was really always with you all along.

So, math, yeah.

When we'd previously seen our plucky heroines, they had just realized that everything, or at least, all the positive real numbers, can be seen as being made out of continuous quantities of 2s being multiplied together.  A 3 is a bit more than 19/12 of a 2, so 1/12 more than 1-and-a-half 2s.  So diminishing something via multiplying by 8/9, is taking a bit more than 1/6 of a 2 out of its bag.

Predictions chain together by multiplication.  If you spin a fair coin once, the probability of it coming up Abrogail is 1/2.  Knowing whether it came up Abrogail or Text doesn't change the probability on the next spin, so the chance of two sequential Abrogails is 1/4, the chance of three such is 1/8.

Each time you say 1/2, and the event happens, that's like taking another 2 out of the bag containing your total prediction over all the events.  Where, to be clear, your bag started with zero 2s in it, or probability 1.  After guessing 50/100 three times at three fair coinflips, your bag would contain -3 2s or a probability of 1/8.

What if you predicted Abrogail with 2/3 probability instead, on one spin?  Well, if the coin comes up Abrogail, good for you, you've only lost - how many 2s, roughly?  Raise your hand once you've got an estimate.