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Version: 1
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"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the likelihoods for each surviving propensity, in each group..."


All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/10000
2/10                (2/10)^2 * (8/10)^3 = 1024/10000
4/10                (4/10)^2 * (6/10)^3 = 3456/10000
5/10                                               = 3125/10000
6/10                (6/10)^2 * (4/10)^3 = 2304/10000
8/10                                               =   512/10000
9/10                                               =     81/10000

All-14s (3 YES, 2 NO):

                                                      = same but flipped


"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined likelihood of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."

Version: 2
Fields Changed Content
Updated
Content

"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the 'likelihoods' for each surviving 'propensity', in each group..."


All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/10000
2/10                (2/10)^2 * (8/10)^3 = 1024/10000
4/10                (4/10)^2 * (6/10)^3 = 3456/10000
5/10                                               = 3125/10000
6/10                (6/10)^2 * (4/10)^3 = 2304/10000
8/10                                               =   512/10000
9/10                                               =     81/10000

All-14s (3 YES, 2 NO):

                                                      = same but flipped


"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined 'likelihood' of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."

Version: 3
Fields Changed Content
Updated
Content

"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the 'likelihoods' for each surviving 'propensity', in each group..."


All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/10000
2/10                (2/10)^2 * (8/10)^3 = 1024/10000
4/10                (4/10)^2 * (6/10)^3 = 3456/10000
5/10                                               = 3125/10000
6/10                (6/10)^2 * (4/10)^3 = 2304/10000
8/10                                               =   512/10000
9/10                                               =     81/10000

All-14s (3 YES, 2 NO):

                                                      = same but table flipped


"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined 'likelihood' of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."

Version: 4
Fields Changed Content
Updated
Content

"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the 'likelihoods' for each surviving 'propensity', in each group..."


All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/100000
2/10                (2/10)^2 * (8/10)^3 = 1024/100000
4/10                (4/10)^2 * (6/10)^3 = 3456/100000
5/10                                               = 3125/100000
6/10                (6/10)^2 * (4/10)^3 = 2304/100000
8/10                                               =   512/100000
9/10                                               =     81/100000

All-14s (3 YES, 2 NO):

                                                      = same but table flipped


"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined 'likelihood' of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."

Version: 5
Fields Changed Content
Updated
Content

"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the 'likelihoods' for each surviving 'propensity', in each group..."

All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/100000
2/10                (2/10)^2 * (8/10)^3 = 1024/100000
4/10                (4/10)^2 * (6/10)^3 = 3456/100000
5/10                                               = 3125/100000
6/10                (6/10)^2 * (4/10)^3 = 2304/100000
8/10                                               =   512/100000
9/10                                               =     81/100000

All-14s (3 YES, 2 NO):

                                                      = same but table flipped


"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined 'likelihood' of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."

Version: 6
Fields Changed Content
Updated
Content

"There's obviously ways to do Lawfully anything you can do with your brain by seeing the results yourself.  Sometimes it takes more Law than you have.  Sometimes it involves calculations that wouldn't make sense to put directly into a 'published-experimental-report'.  Still, Willa has put her 'publication-priority-timestamp' squarely on the key issue."

"By way of approaching the complicated proper math by a simpler 'hacky' route, suppose the 'preregistered' analysis said that they were going to compare hypotheses for each 'subject-group' having seven possible 'latent propensities' to solve the puzzle in time, of 0, 1/10, 1/5, 2/5, 1/2, 3/5, 4/5, 9/10, and 1."

"Since some subjects in both groups solved the puzzle, and some didn't, we can cross off the 0 and 1 'propensities' from both cases; they've been falsified outright, the 'likelihood' is zero 'conditional' on those propensities being the true 'latent' state of reality."

"Now, let's go ahead and compute the 'likelihoods' for each surviving 'propensity', in each group..."

All-10s (2 YES, 3 NO):

Propensity:     Likelihood:
---------------     --------------
1/10                (1/10)^2 * (9/10)^3 =   729/100000
2/10                (2/10)^2 * (8/10)^3 = 1024/100000
4/10                (4/10)^2 * (6/10)^3 = 3456/100000
5/10                                               = 3125/100000
6/10                (6/10)^2 * (4/10)^3 = 2304/100000
8/10                                               =   512/100000
9/10                                               =     81/100000

All-14s (3 YES, 2 NO):

                                                      = same but table flipped

"The point which Willa is gesturing at, is that it's not possible in the same way to speak of the combined 'likelihood' of all our observations, if all-14s guess more often than all-10s, or if all-14s guess at least five times as often as all-10s."

"At least, not without dragging in some additional assumptions."