Asmodia goes up to the board and writes the example:

                          Ordinary       Conspiracy       Time-Traveler
                          ------------      ----------------      -------------------
Prior:                      .80                 .10                       .03

'Writes' (Y)             .50                 .20                       .80
'Quantifies' (Y)       .60                 .70                       .90
'Prediction' (N)     1 - .40            1 - .20                  1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                .14                  .011                     .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

Asmodia goes up to the board and writes the example:

                          Ordinary       Conspiracy       Time-Traveler
                          ------------      ----------------      -------------------
Prior:                      .80                 .10                       .03

'Writes' (Y)             .50                 .20                       .80
'Quantifies' (Y)       .60                 .70                       .90
'Prediction' (N)     1 - .40            1 - .20                  1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                .14                  .011                     .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  And that you could take the first results and multiply by those and call the result your new prior, and then multiply by the second and third results to get the new posterior, and that'd also be the same.  That seems like the kind of constraints the Law would need to obey, if we didn't know the Law already, or if it wasn't really easy and obvious to figure out what kind of Law fits together simply like that."

Asmodia goes up to the board and writes the example:

                          Ordinary       Conspiracy       Time-Traveler
                          ------------      ----------------      -------------------
Prior:                      .80                 .10                       .03

'Writes' (Y)             .50                 .20                       .80
'Quantifies' (Y)       .60                 .70                       .90
'Prediction' (N)     1 - .40            1 - .20                  1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                .14                  .011                     .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  Or that you could take the first results and multiply by those and call the result your new 'prior', and then multiply by the second and third results to get the new 'posterior', and that'd also be the same.  Those seem like the kind of 'coherence-constraints' the Law would need to obey, if we didn't know the Law already, or if it wasn't so easy to find a simple Law that fits together like that."

Asmodia goes up to the board and writes the example:

                          Ordinary       Conspiracy       Time-Traveler
                          ------------      ----------------      -------------------
Prior:                      .80                 .10                       .03

'Writes' (Y)             .50                 .20                       .80
'Quantifies' (Y)       .60                 .70                       .90
'Prediction' (N)     1 - .40            1 - .20                  1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."


Product:                .14                  .011                     .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  Or that you could take the first results and multiply by those and call the result your new 'prior', and then multiply by the second and third results to get the new 'posterior', and that'd also be the same.  Those seem like the kind of 'coherence-constraints' the Law would need to obey, if we didn't know the Law already, or if it wasn't so easy to find a simple Law that fits together like that."

Asmodia goes up to the board and writes the example:

                       Ordinary      Conspiracy    Time-Traveler
                       --------      ----------    --------------
Prior:                   .80            .10            .03

'Writes' (Y)             .50            .20            .80
'Quantifies' (Y)         .60            .70            .90
'Prediction' (N)        1 - .40        1 - .20        1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                 .14            .011           .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  Or that you could take the first results and multiply by those and call the result your new 'prior', and then multiply by the second and third results to get the new 'posterior', and that'd also be the same.  Those seem like the kind of 'coherence-constraints' the Law would need to obey, if we didn't know the Law already, or if it wasn't so easy to find a simple Law that fits together like that."

Asmodia goes up to the board and writes the example:

                       Ordinary      Conspiracy    Time-Traveler
                       --------      ----------    --------------
Prior:                   .80            .10            .03

'Writes' (Y)             .50            .20            .80
'Quantifies' (Y)         .60            .70            .90
'Prediction' (N)       1 - .40        1 - .20        1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                 .14            .011           .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  Or that you could take the first results and multiply by those and call the result your new 'prior', and then multiply by the second and third results to get the new 'posterior', and that'd also be the same.  Those seem like the kind of 'coherence-constraints' the Law would need to obey, if we didn't know the Law already, or if it wasn't so easy to find a simple Law that fits together like that."

Asmodia goes up to the board and writes the example:

                       Ordinary      Conspiracy    Time-Traveler
                       --------      ----------    --------------
Prior:                   .80            .10            .03

'Writes' (Y)             .50            .20            .80
'Quantifies' (Y)         .60            .70            .90
'Prediction' (N)        1 - .40        1 - .20        1 - .90

"And then - Keltham didn't actually say this part, because it was obvious given what we already learned - he multiplied his starting probabilities by all the likelihoods for each of the events, and ended up with... give me a second..."

Product:                 .14            .011           .002

"Not that it was actually that, because those weren't actually his probabilities, but that's the obvious way to combine multiple pieces of evidence.  Uh, though I'm leaving out the part where what really changes, is the ratio between the chances, not really the chances themselves.  At the end it's like... 13 times as much Ordinary as Conspiracy, and 5 times as much Conspiracy as Time-Traveler, where previously it was 8 times as much Ordinary as Conspiracy and 3 times as much Conspiracy as Time-Traveler."

"If we didn't already have the Law and were looking for Law-fragments, I'd observe that it doesn't matter what order you consider the data in, because it doesn't matter what order you multiply numbers.  Or that you could take the first results and multiply by those and call the result your new 'prior', and then multiply by the second and third results to get the new 'posterior', and that'd also be the same.  Those seem like the kind of 'coherence-constraints' the Law would need to obey, if we didn't know the Law already, or if it wasn't so easy to find a simple Law that fits together like that."