"Okay, wow, people's intuitions about probability work really differently when they haven't been raised as dath ilani children.  I think probably you just need to invent a whole lot of problems and play around with them, the way anyone - well, the way any dath ilani kids would do as kids?"

"Let's say I spin a fair twosided meta-meta-coin... let all coins be assumed two-sided and fair unless explicitly stated otherwise."

"Anyways, new procedure.  First, I spin a meta-meta-coin.  If the meta-meta-coin comes up Text, I spin an 'objectlevel'-coin five times.  If the meta-meta-coin comes up Queen, I spin a three-sided meta-coin.  Then depending on the result of that coin, I fivetimes spin a biased 'objectlevel'-coin with 0.1 or 0.2 or 0.4 propensity to produce Queens."

Keltham will attempt to whiteboard this:

                    meta-meta-coin
                   /                         \
                1/2                       1/2
                /                              \
      meta-coin                (0.5)-propensity
     /        |       \               objectlevel-coin
  1/3     1/3     1/3
  /           |          \ 
(0.1)    (0.2)    (0.4)

"It's actually just true that if you don't know any of the meta-spins, and just see my unknown objectlevel-coin producing Text Queen Queen Text Text, there's roughly two chances in five that my meta-meta-coin came up Queen and picked a biased coin, and three chances in five that my meta-meta-coin came up Text and picked a fair coin."

"Why?  Because when you end up with a biased coin, it's sometimes biased 0.4, but two-thirds of the time biased 0.1 or 0.2.  Mostly you'll see fewer Queens, when the meta-meta-coin comes up Queen.  When you see Text Queen Queen Text Text, that could be because the meta-coin was flipped and selected the 0.4 coin, but more likely, the meta-meta-coin selected a fair objectlevel-coin and that fair objectlevel-coin happened to produce two Queens and three Texts."

"A dath ilani kid would now be 'programming' a 'computer' to run a million simulations of this procedure and show them how many cases of Text Queen Queen Text Text were generated by the meta-meta-coin coming up Queens versus Text and verifying that's how it actually played out.  Here... we'd need to find a three-sided coin and a ten-sided coin, or maybe a cube and an 'icosahedron', regular 20-sided solid, to spin.  And then we'd probably have to do a few hundred spins to collect enough 'data' for the 'statistics', if the math didn't feel intuitive."

"But I'd hope that - the first time the meta-meta-coin came up Queen, and you spun a meta-coin and it selected 0.1, and the resulting objectlevel-coin produced Text Text Text Text Text, it might become more intuitive why, when the meta-meta-coin comes up Queen, what you mostly expect to see is mostly Text.  So when you don't see that, it's not likely the meta-meta-coin came up Queen."

"Okay, wow, people's intuitions about probability work really differently when they haven't been raised as dath ilani children.  I think probably you just need to invent a whole lot of problems and play around with them, the way anyone - well, the way any dath ilani kids would do as kids?"

"Let's say I spin a fair twosided meta-meta-coin... let all coins be assumed two-sided and fair unless explicitly stated otherwise."

"Anyways, new procedure.  First, I spin a meta-meta-coin.  If the meta-meta-coin comes up Text, I spin an 'objectlevel'-coin five times.  If the meta-meta-coin comes up Queen, I spin a three-sided meta-coin.  Then depending on the result of that coin, I fivetimes spin a biased 'objectlevel'-coin with 0.1 or 0.2 or 0.4 propensity to produce Queens."

Keltham will attempt to whiteboard this:

meta-meta-coin                    /                         \                 1/2                       1/2                 /                              \       meta-coin                (0.5)-propensity      /        |       \               objectlevel-coin   1/3     1/3     1/3   /           |          \  (0.1)    (0.2)    (0.4)

"It's actually just true that if you don't know any of the meta-spins, and just see my unknown objectlevel-coin producing Text Queen Queen Text Text, there's roughly two chances in five that my meta-meta-coin came up Queen and picked a biased coin, and three chances in five that my meta-meta-coin came up Text and picked a fair coin."

"Why?  Because when you end up with a biased coin, it's sometimes biased 0.4, but two-thirds of the time biased 0.1 or 0.2.  Mostly you'll see fewer Queens, when the meta-meta-coin comes up Queen.  When you see Text Queen Queen Text Text, that could be because the meta-coin was flipped and selected the 0.4 coin, but more likely, the meta-meta-coin selected a fair objectlevel-coin and that fair objectlevel-coin happened to produce two Queens and three Texts."

"A dath ilani kid would now be 'programming' a 'computer' to run a million simulations of this procedure and show them how many cases of Text Queen Queen Text Text were generated by the meta-meta-coin coming up Queens versus Text and verifying that's how it actually played out.  Here... we'd need to find a three-sided coin and a ten-sided coin, or maybe a cube and an 'icosahedron', regular 20-sided solid, to spin.  And then we'd probably have to do a few hundred spins to collect enough 'data' for the 'statistics', if the math didn't feel intuitive."

"But I'd hope that - the first time the meta-meta-coin came up Queen, and you spun a meta-coin and it selected 0.1, and the resulting objectlevel-coin produced Text Text Text Text Text, it might become more intuitive why, when the meta-meta-coin comes up Queen, what you mostly expect to see is mostly Text.  So when you don't see that, it's not likely the meta-meta-coin came up Queen."

"Okay, wow, people's intuitions about probability work really differently when they haven't been raised as dath ilani children.  I think probably you just need to invent a whole lot of problems and play around with them, the way anyone - well, the way any dath ilani kids would do as kids?"

"Let's say I spin a fair twosided meta-meta-coin... let all coins be assumed two-sided and assumed fair unless explicitly stated otherwise."

"Anyways, new procedure.  First, I spin a meta-meta-coin.  If the meta-meta-coin comes up Text, I spin an 'objectlevel'-coin five times.  If the meta-meta-coin comes up Queen, I spin a three-sided meta-coin.  Then depending on the result of that coin, I fivetimes spin a biased 'objectlevel'-coin with 0.1 or 0.2 or 0.4 propensity to produce Queens."

Keltham will attempt to whiteboard this:

meta-meta-coin                    /                         \                 1/2                       1/2                 /                              \       meta-coin                (0.5)-propensity      /        |       \               objectlevel-coin   1/3     1/3     1/3   /           |          \  (0.1)    (0.2)    (0.4)

"It's actually just true that if you don't know any of the meta-spins, and just see my unknown objectlevel-coin producing Text Queen Queen Text Text, there's roughly two chances in five that my meta-meta-coin came up Queen and picked a biased coin, and three chances in five that my meta-meta-coin came up Text and picked a fair coin."

"Why?  Because when you end up with a biased coin, it's sometimes biased 0.4, but two-thirds of the time biased 0.1 or 0.2.  Mostly you'll see fewer Queens, when the meta-meta-coin comes up Queen.  When you see Text Queen Queen Text Text, that could be because the meta-coin was flipped and selected the 0.4 coin, but more likely, the meta-meta-coin selected a fair objectlevel-coin and that fair objectlevel-coin happened to produce two Queens and three Texts."

"A dath ilani kid would now be 'programming' a 'computer' to run a million simulations of this procedure and show them how many cases of Text Queen Queen Text Text were generated by the meta-meta-coin coming up Queens versus Text and verifying that's how it actually played out.  Here... we'd need to find a three-sided coin and a ten-sided coin, or maybe a cube and an 'icosahedron', regular 20-sided solid, to spin.  And then we'd probably have to do a few hundred spins to collect enough 'data' for the 'statistics', if the math didn't feel intuitive."

"But I'd hope that - the first time the meta-meta-coin came up Queen, and you spun a meta-coin and it selected 0.1, and the resulting objectlevel-coin produced Text Text Text Text Text, it might become more intuitive why, when the meta-meta-coin comes up Queen, what you mostly expect to see is mostly Text.  So when you don't see that, it's not likely the meta-meta-coin came up Queen."

"Okay, wow, people's intuitions about probability work really differently when they haven't been raised as dath ilani children.  I think probably you just need to invent a whole lot of problems and play around with them, the way anyone - well, the way any dath ilani kids would do as kids?"

"Let's say I spin a fair twosided meta-meta-coin... let all coins be assumed two-sided and assumed fair unless explicitly stated otherwise."

"Anyways, new procedure.  First, I spin a meta-meta-coin.  If the meta-meta-coin comes up Text, I spin an 'objectlevel'-coin five times.  If the meta-meta-coin comes up Queen, I spin a three-sided meta-coin.  Then depending on the result of that coin, I fivetimes spin a biased 'objectlevel'-coin with 0.1 or 0.2 or 0.4 propensity to produce Queens."

Keltham will attempt to whiteboard this:

meta-meta-coin / \ 1/2 1/2 / \ meta-coin (0.5)-propensity / | \ objectlevel-coin 1/3 1/3 1/3 / | \ (0.1) (0.2) (0.4)

"It's actually just true that if you don't know any of the meta-spins, and just see my unknown objectlevel-coin producing Text Queen Queen Text Text, there's roughly two chances in five that my meta-meta-coin came up Queen and picked a biased coin, and three chances in five that my meta-meta-coin came up Text and picked a fair coin."

"Why?  Because when you end up with a biased coin, it's sometimes biased 0.4, but two-thirds of the time biased 0.1 or 0.2.  Mostly you'll see fewer Queens, when the meta-meta-coin comes up Queen.  When you see Text Queen Queen Text Text, that could be because the meta-coin was flipped and selected the 0.4 coin, but more likely, the meta-meta-coin selected a fair objectlevel-coin and that fair objectlevel-coin happened to produce two Queens and three Texts."

"A dath ilani kid would now be 'programming' a 'computer' to run a million simulations of this procedure and show them how many cases of Text Queen Queen Text Text were generated by the meta-meta-coin coming up Queens versus Text and verifying that's how it actually played out.  Here... we'd need to find a three-sided coin and a ten-sided coin, or maybe a cube and an 'icosahedron', regular 20-sided solid, to spin.  And then we'd probably have to do a few hundred spins to collect enough 'data' for the 'statistics', if the math didn't feel intuitive."

"But I'd hope that - the first time the meta-meta-coin came up Queen, and you spun a meta-coin and it selected 0.1, and the resulting objectlevel-coin produced Text Text Text Text Text, it might become more intuitive why, when the meta-meta-coin comes up Queen, what you mostly expect to see is mostly Text.  So when you don't see that, it's not likely the meta-meta-coin came up Queen."