> Both twins have an adopted brother whose name is Larry.
I mean I don't see any plausible way this could be genetic. A child doesn't have any meaningful level of control over who their parents choose to adopt or what they name them.
I was wondering if you'd cover this! I hope you had a nice honeymoon. The other complicating factor here is how the twins studying together for the duration of their training program would influence their exam answers. You'd expect two people who've studied intensively together to pick the same wrong answers more frequently than two students who studied independently. (Make those two students identical twins on top of that and I assume their propensity to get tripped up by the same wrong answers is a little higher.)
I don't actually know how much of the training program they did together, but I don't hear anyone considering it as a factor. I see it from time to time (e.g., a group of students who studied together tending to misunderstand operant conditioning terms the same way).
Even if identical twins were actually completely identical individuals, I still wouldn't expect the same person doing the same test on different days to write the same answer to 96% of the questions.
Segal is a very serious scholar. I read her book about the twin studies from cover to cover. I am afraid supporting the defense in this case is an embarrassment for her.
I am not a scientist. However, the twins defense, like the twinkie defense, are both efforts to appeal to emotion as a effort to excuse in one case potentially inappropriate and in the other unlawful behavior. In the twins case, it seems to me that the University has at least reasonable grounds to question the outcome of the test. A simpler (and no doubt less costly approach) would be for the twins to retest in separate rooms with a new set of questions. If they pass all is good. If their answers right and wrong show the same correlation as when they test sitting beside each other, perhaps there is something worthy of further scientific study. I also realize that this practical approach does not comport with the litigious orientation of the US. It strikes me that there is little science in the defense (mostly speculation and bad math) and alot of lawyering.
Dividing the exponents is not the way you divide numbers, but dividing the final probability by the simlilarity score is certainly not what you should do either (regardless of the precise meaning of the similarity), so it seems statisticians are not missing from twin leagl team only....
It's impossible to know for certain how to do those things, but you can make sensible guess: for once, 10^38 is huge, so it's obviously the product of 1/chance of similarity for each answer, assuming chance of identical answer is un-(or very slightly)-correlated between questions. Very likely wrong, and also very likely what was done (because it's what is done in almost all such analyses.
10^-38 is the chance of the final result if each answer was similar by chance only, and is product_i P_similar_i, or P_similar ^nquestion if the probability of similar answer is the same for all questions. How many question, not sure, but assuming twin similarity score in answering questions (TS) is something like P_twin(identical answer)/P_nontwin(identical answer), and that this is the same for all questions (yeah...doubtful, and, again, what is always assumed for such analysis), probability for twin to cheat is P_similar ^nquestion*(TS)^nquestion=(p_similar*TS)^nquestion.
So yeah, neither formula were correct and there is no simple combination that gives you the answer without at least knowing how many suestion there was, but it's possible the probability of no cheat can go up very significantly
WRT Laplace's Demon, Popper (and Born and some others) wrote some interesting stuff around indeterminism in classical physics. I read some of it at a time that i was also studying QM in grad school, and it made sense at the time. YMMV. That was also at a time before they (or I) knew anything about chaos theory, as far as I know, but glancing at the papers, it seems like they were going in that direction. Which reminds me .... as someone who has made a career out of software development, the details of how Lorenz discovered the latter are pretty interesting, and also sort of comically trivial.
I'm actually of the opinion that it is likely that our brains are too puny to do anything but approximate reality, but that is going to go in a quasi-religious direction if i expand on it much. Plus, mom needs a walk.
> But to be honest, some of the others are such incredible levels of coincidence that they would still be surprising if the twins were 100% genetically identical and had been raised in the same home from birth and hadn’t been allowed to do anything without the other twin being present and had been subject to a fairly authoritarian parenting regime that instilled values about what names you should choose in a partner and for your dog.
Not really. Marrying two women who happen to have the same name? Well, that'd be weird if those women had really weird names. But they have very common names for their age cohort. It's like declaring it "weird" that my sister is named Jennifer and there was another Jennifer on our block growing up.
The same goes for having sons with the same first and middle names. Name choices aren't done in a vacuum, they're cultural. If the two boys were born around the same time, to parents who were about the same age (exactly the same age, when it comes to their fathers) then it's not that surprising that they have the same name. There must be hundreds or thousands of boys born within the same decade or two who have that exact same first and middle combo.
And the same goes *again* for the pet dog named Toy. Dogs are popular pets. Their names, like human names, follow trends. If they're both small breed dogs, it's hardly surprising that both sets of owners would pick a "small dog" name like "Toy".
Moving past the sociology of name choices, that leaves us with - choosing to vacation in Florida, a popular vacation spot (and how popular is the particular part of Florida that they vacation in?) and some vocational training at school and sheriff training afterwards. Now, those last two might actually be surprising - but are they?
Honestly, there's less than a dozen items on that list. How many random coincidences do any two people *normally* have in common? I have no idea, but I bet it's at least a dozen.
> Both twins have an adopted brother whose name is Larry.
I mean I don't see any plausible way this could be genetic. A child doesn't have any meaningful level of control over who their parents choose to adopt or what they name them.
I was wondering if you'd cover this! I hope you had a nice honeymoon. The other complicating factor here is how the twins studying together for the duration of their training program would influence their exam answers. You'd expect two people who've studied intensively together to pick the same wrong answers more frequently than two students who studied independently. (Make those two students identical twins on top of that and I assume their propensity to get tripped up by the same wrong answers is a little higher.)
I don't actually know how much of the training program they did together, but I don't hear anyone considering it as a factor. I see it from time to time (e.g., a group of students who studied together tending to misunderstand operant conditioning terms the same way).
Even if identical twins were actually completely identical individuals, I still wouldn't expect the same person doing the same test on different days to write the same answer to 96% of the questions.
Segal is a very serious scholar. I read her book about the twin studies from cover to cover. I am afraid supporting the defense in this case is an embarrassment for her.
Stuart, have you ever considered the coincidence that the home of the original twins study is itself twinned with St Paul?
I am not a scientist. However, the twins defense, like the twinkie defense, are both efforts to appeal to emotion as a effort to excuse in one case potentially inappropriate and in the other unlawful behavior. In the twins case, it seems to me that the University has at least reasonable grounds to question the outcome of the test. A simpler (and no doubt less costly approach) would be for the twins to retest in separate rooms with a new set of questions. If they pass all is good. If their answers right and wrong show the same correlation as when they test sitting beside each other, perhaps there is something worthy of further scientific study. I also realize that this practical approach does not comport with the litigious orientation of the US. It strikes me that there is little science in the defense (mostly speculation and bad math) and alot of lawyering.
Dividing the exponents is not the way you divide numbers, but dividing the final probability by the simlilarity score is certainly not what you should do either (regardless of the precise meaning of the similarity), so it seems statisticians are not missing from twin leagl team only....
It's impossible to know for certain how to do those things, but you can make sensible guess: for once, 10^38 is huge, so it's obviously the product of 1/chance of similarity for each answer, assuming chance of identical answer is un-(or very slightly)-correlated between questions. Very likely wrong, and also very likely what was done (because it's what is done in almost all such analyses.
10^-38 is the chance of the final result if each answer was similar by chance only, and is product_i P_similar_i, or P_similar ^nquestion if the probability of similar answer is the same for all questions. How many question, not sure, but assuming twin similarity score in answering questions (TS) is something like P_twin(identical answer)/P_nontwin(identical answer), and that this is the same for all questions (yeah...doubtful, and, again, what is always assumed for such analysis), probability for twin to cheat is P_similar ^nquestion*(TS)^nquestion=(p_similar*TS)^nquestion.
So yeah, neither formula were correct and there is no simple combination that gives you the answer without at least knowing how many suestion there was, but it's possible the probability of no cheat can go up very significantly
WRT Laplace's Demon, Popper (and Born and some others) wrote some interesting stuff around indeterminism in classical physics. I read some of it at a time that i was also studying QM in grad school, and it made sense at the time. YMMV. That was also at a time before they (or I) knew anything about chaos theory, as far as I know, but glancing at the papers, it seems like they were going in that direction. Which reminds me .... as someone who has made a career out of software development, the details of how Lorenz discovered the latter are pretty interesting, and also sort of comically trivial.
I'm actually of the opinion that it is likely that our brains are too puny to do anything but approximate reality, but that is going to go in a quasi-religious direction if i expand on it much. Plus, mom needs a walk.
Sam Harris offers an interesting perspective on free will as an illusion if anyone is interested: https://www.samharris.org/blog/the-illusion-of-free-will
What about Celestial Twins: https://www.catastrophism.com/intro/search.cgi?zoom_query=%22celestial+twins&zoom_per_page=25&zoom_and=1&zoom_cat=-1 ?
By the way, conventional dating of the Earth and its contents and those beyond are all sci-fi too.
I make some corrections to those errors at https://cataclysmicearthhistory.substack.com/archive
And I correct some vaccine science errors at https://covidandvaxfaqs.substack.com/archive
https://www.americanscientist.org/blog/macroscope/the-dangerous-resurgence-in-race-science
> But to be honest, some of the others are such incredible levels of coincidence that they would still be surprising if the twins were 100% genetically identical and had been raised in the same home from birth and hadn’t been allowed to do anything without the other twin being present and had been subject to a fairly authoritarian parenting regime that instilled values about what names you should choose in a partner and for your dog.
Not really. Marrying two women who happen to have the same name? Well, that'd be weird if those women had really weird names. But they have very common names for their age cohort. It's like declaring it "weird" that my sister is named Jennifer and there was another Jennifer on our block growing up.
The same goes for having sons with the same first and middle names. Name choices aren't done in a vacuum, they're cultural. If the two boys were born around the same time, to parents who were about the same age (exactly the same age, when it comes to their fathers) then it's not that surprising that they have the same name. There must be hundreds or thousands of boys born within the same decade or two who have that exact same first and middle combo.
And the same goes *again* for the pet dog named Toy. Dogs are popular pets. Their names, like human names, follow trends. If they're both small breed dogs, it's hardly surprising that both sets of owners would pick a "small dog" name like "Toy".
Moving past the sociology of name choices, that leaves us with - choosing to vacation in Florida, a popular vacation spot (and how popular is the particular part of Florida that they vacation in?) and some vocational training at school and sheriff training afterwards. Now, those last two might actually be surprising - but are they?
Honestly, there's less than a dozen items on that list. How many random coincidences do any two people *normally* have in common? I have no idea, but I bet it's at least a dozen.