[Well you see, or rather, as my people would see, there is a certain probability-theoretic concept lying at the center of all epistemology - which either English doesn't have terminology for, or the person who put English into my head happened not know, or it just isn't in my head for any other reason, but under the circumstances I am guessing the first case - which concept is also the thing that experimenters report in a saner world - called by my people the 'likelihood function'.  Conceptually, it is an extremely simple, natural, unambiguous mathematical object which combines by multiplication across different experiments.  For example, if there are two hypotheses H1 and H2, and the first experiment reports evidence E1 which is 1/3 likely given H1 and 1/4 likely given H2, and experiment two reports observation E2 which is 1/2 likely given H1 and 1/8 likely given H2, we can combine the two likelihood functions to say that the evidence is 1/6 likely given H1 and 1/32 likely given H2.  That is not an oversimplification, it is how that small discrete case of likelihood functions validly works.]

[I have been trying to entertain the hypothesis that there is some clever useful thing that 'p-values' and 'confidence intervals' are doing, but I have been looking up how to combine them, and they do not combine in any simple or sane way, and that disadvantage alone for purposes of accumulating knowledge should be decisive.  And also the underlying epistemology seems, to put it mildly, deranged, and allows you to attribute different 'p-values' to the same piece of evidence depending on the experimenter's state of mind.  It is likewise possible to measure an electric charge and get a '90% confidence interval' of [green, purple] if you have a procedure that generates a 95% confidence interval and then you add a small chance of substituting [green, purple] to the output of the previous procedure.  And it just seems really really conspicuous that something ripped the concept of likelihood functions out of your world's epistemology, and an enormous weird ad-hoc pseudo-mathematical edifice had to grow up around the gaping sucking void this left behind.  And I just don't see what kind of fact I could be missing about your world that could possibly contextualize this, because this is about math itself, not the empirics of any particular science.  I am trying to be a good epistemically humble reasoner and keep in mind alternative hypotheses like 'well, it's more likely that this "happened for any reason" than "happened because of magic", maybe there is just a giant conspiracy of journal editors who suppress all mention of likelihood functions, all across the multiple scientific fields whose papers I tried to check'.  But it really really seems realistically more likely that a world which permits power-granting lunar eclipses can also permit some generalized Eater of the Concept of Likelihood Functions.]

[Thank you for attending my stupid lecture about my wrong hypothesis.  How has your day been going?]

[Well you see, or rather, as my people would see, there is a certain probability-theoretic concept lying at the center of all epistemology - which either English doesn't have terminology for, or the person who put English into my head happened not know, or it just isn't in my head for any other reason, but under the circumstances I am guessing the first case - which concept is also the thing that experimenters report in a sane world - called by my people the 'likelihood function'.  Conceptually, it is an extremely simple, natural, unambiguous mathematical object which combines by multiplication across different experiments.  For example, if there are two hypotheses H1 and H2, and the first experiment reports evidence E1 which is 1/3 likely given H1 and 1/4 likely given H2, and experiment two reports observation E2 which is 1/2 likely given H1 and 1/8 likely given H2, we can combine the two likelihood functions to say that the evidence is 1/6 likely given H1 and 1/32 likely given H2.  That is not an oversimplification, it is how that small discrete case of likelihood functions validly works.]

[I have been trying to entertain the hypothesis that there is some clever useful thing that 'p-values' and 'confidence intervals' are doing, but I have been looking up how to combine them, and they do not combine in any simple or sane way, and that disadvantage alone for purposes of accumulating knowledge should be decisive.  And also the underlying epistemology seems, to put it mildly, deranged, and allows you to attribute different 'p-values' to the same piece of evidence depending on the experimenter's state of mind.  It is likewise possible to measure an electric charge and get a '90% confidence interval' of [green, purple] if you have a procedure that generates a 95% confidence interval and then you add a small chance of substituting [green, purple] to the output of the previous procedure.  And it just seems really really conspicuous that something ripped the concept of likelihood functions out of your world's epistemology, and an enormous weird ad-hoc pseudo-mathematical edifice had to grow up around the gaping sucking void this left behind.  And I just don't see what kind of fact I could be missing about your world that could possibly contextualize this, because this is about math itself, not the empirics of any particular science.  I am trying to be a good epistemically humble reasoner and keep in mind alternative hypotheses like 'well, it's more likely that this "happened for any reason" than "happened because of magic", maybe there is just a giant conspiracy of journal editors who suppress all mention of likelihood functions, all across the multiple scientific fields whose papers I tried to check'.  But it really really seems realistically more likely that a world which permits power-granting lunar eclipses can also permit some generalized Eater of the Concept of Likelihood Functions.]

[Thank you for attending my stupid lecture about my wrong hypothesis.  How has your day been going?]

[Well you see, or rather, as my people would see, there is a certain probability-theoretic concept lying at the center of all epistemology - which either English doesn't have terminology for, or the person who put English into my head happened to not know, or it just isn't in my head for any other reason, but under the circumstances I am guessing the first case - which concept is also the thing that experimenters report in a sane world - called by my people the 'likelihood function'.  Conceptually, it is an extremely simple, natural, unambiguous mathematical object which combines by multiplication across different experiments.  For example, if there are two hypotheses H1 and H2, and the first experiment reports evidence E1 which is 1/3 likely given H1 and 1/4 likely given H2, and experiment two reports observation E2 which is 1/2 likely given H1 and 1/8 likely given H2, we can combine the two likelihood functions to say that the evidence is 1/6 likely given H1 and 1/32 likely given H2.  That is not an oversimplification, it is how that small discrete case of likelihood functions validly works.]

[I have been trying to entertain the hypothesis that there is some clever useful thing that 'p-values' and 'confidence intervals' are doing, but I have been looking up how to combine them, and they do not combine in any simple or sane way, and that disadvantage alone for purposes of accumulating knowledge should be decisive.  And also the underlying epistemology seems, to put it mildly, deranged, and allows you to attribute different 'p-values' to the same piece of evidence depending on the experimenter's state of mind.  It is likewise possible to measure an electric charge and get a '90% confidence interval' of [green, purple] if you have a procedure that generates a 95% confidence interval and then you add a small chance of substituting [green, purple] to the output of the previous procedure.  And it just seems really really conspicuous that something ripped the concept of likelihood functions out of your world's epistemology, and an enormous weird ad-hoc pseudo-mathematical edifice had to grow up around the gaping sucking void this left behind.  And I just don't see what kind of fact I could be missing about your world that could possibly contextualize this, because this is about math itself, not the empirics of any particular science.  I am trying to be a good epistemically humble reasoner and keep in mind alternative hypotheses like 'well, it's more likely that this "happened for any reason" than "happened because of magic", maybe there is just a giant conspiracy of journal editors who suppress all mention of likelihood functions, all across the multiple scientific fields whose papers I tried to check'.  But it really really seems realistically more likely that a world which permits power-granting lunar eclipses can also permit some generalized Eater of the Concept of Likelihood Functions.]

[Thank you for attending my stupid lecture about my wrong hypothesis.  How has your day been going?]