I don't see what that has to do with the Rietdijk–Putnam argument and/or Andromeda Paradox.

It's because her appropriately interpreted credence P(T) =def P(T-awakening) = 2/3 that her bet on T yields a positive expected value, not the reverse. If she only had one opportunity to bet per experimental run (and was properly informed), regardless of the number of awakenings in that run, then her bet would break even. This would also be because P(T) =def P(T-run) = 1/2. — Pierre-Normand

I don't think that works.

$\begin{aligned}P(HInterview | HRun) &= {{P(HRun | HInterview) * P(HInterview)} \over P(HRun)}\\\\P(HInterview) &= {{P(HInterview|HRun) * P(HRun)} \over P(HRun|HInterview)}\\\\P(HInterview) &= {{1 * P(HRun)} \over 1}\\\\P(HInterview) &= P(HRun)\end{aligned}$

P(H-awakening) = P(H-run). Therefore either both are 1/2 or both are 1/3. This is expected given the biconditional.

I think it's more rational to say that P(H-awakening) = 1/2 than to say that P(H-run) = 1/3. Therefore I think it's more rational to say that P(H-awakening) = P(H-run) = P(H) = 1/2.

The bet's positive expected value arises because she is twice as likely to win as she is to lose. This is due to the experimental setup, which on average creates twice as many T-awakenings as H-awakenings. — Pierre-Normand

Which of these are you saying?

1. There are twice as many T-awakenings because tails is twice as likely
2. Tails is twice as likely because there are twice as many T-awakenings

I think both of these are false.

I think there are twice as many T-awakenings but that tails is equally likely.

The bet's positive expected value arises only because there are twice as many T-awakenings.

Rationality in credences depends on their application. It would be irrational to use the credence P(H) =def |{H-awakenings}| / |{awakenings}| in a context where the ratio |{H-runs}| / |{runs}| is more relevant to the goal at hand (for instance, when trying to survive encounters with lions/crocodiles or when trying to be picked up at the right exit door by Aunt Betsy) and vice versa. — Pierre-Normand

I think you're confusing two different things here. If the expected return of a lottery ticket is greater than its cost it can be rational to buy it, but it's still irrational to believe that it is more likely to win. And so it can be rational to assume that the coin landed tails but still be irrational to believe that tails is more likely.

However, it's important to note that while these biconditionals are true, they do not guarantee a one-to-one correspondence between these differently individuated events. When these mappings aren't one-to-one, their probabilities need not match. Specifically, in the Sleeping Beauty problem, there is a many-to-one mapping from T-awakenings to T-runs. This is why the ratios of |{H-awakenings}| to |{awakenings}| and |{H-runs}| to |{runs}| don't match. — Pierre-Normand

I'm not sure what this has to do with credences. I think all of these are true:

1. There are twice as many T-awakenings as H-awakenings
2. There are an equal number of T-runs as H-runs
3. Sleeping Beauty's credence that this is a T-awakening is equal to her credence that this is a T-run
4. Sleeping Beauty's credence that this is a T-run is 1/2.

You seem to be disagreeing with 3 and/or 4. Is the truth of 1 relevant to the truth of 3 and/or 4? It's certainly relevant to any betting strategy, but that's a separate matter (much like with the lottery with a greater expected return).

Would you not agree that this is a heads interview if and only if this is a heads experiment? If so then shouldn't one's credence that this is a heads interview equal one's credence that this is a heads experiment?

If so then the question is whether it is more rational for one's credence that this is a heads experiment to be 1/3 or for one's credence that this is a heads interview to be 1/2.

Previously you've been saying that P(Heads) = 1/2.

I think Bayes’ theorem shows such thirder reasoning to be wrong.

$P(Unique | Heads) = {{P(Heads | Unique) * P(Unique)} \over P(Heads)}$

If P(Unique) = 1/3 then what do you put for the rest?

Similarly:

$P(Heads | Monday) = {{P(Monday | Heads) * P(Heads)} \over P(Monday)}$

If P(Monday) = 2/3 then what do you put for the rest?

P(Unique) = 1/3, as one-third of the experiment's awakenings are unique. — Pierre-Normand

This is a non sequitur. See here where I discuss the suggestion that P(Monday) = 2/3.

What we can say is this:

$P(Unique | Heads) = {{P(Heads | Unique) * P(Unique)} \over P(Heads)}$

We know that P(Unique | Heads) = 1, P(Heads | Unique) = 1, and P(Heads) = 1/2. Therefore P(Unique) = 1/2.

Therefore P(Unique|W) = 1/2.

And if this experiment is the same as the traditional experiment then P(H|W) = 1/2.

You think it's peculiar that in a setup where event A follows B, where one person moves towards those events, that person will see A before the other person — Benkei

No. This has nothing to do with what one person sees. There are distant events happening in my present that I cannot see because they are too far away. According to special relativity some of these events happen in your future even though they are happening in my present. This is what I find peculiar.

See my response to MU here.

Regarding Bayes' theorem:

$P(Heads | Monday) = {{P(Monday | Heads) * P(Heads)} \over P(Monday)}$

Both thirders and double-halfers will accept that P(Heads | Monday) = 1/2, but how do we understand something like P(Monday)? Does it mean "what is the probability that a Monday interview will happen" or does it mean "what is the probability that this interview is a Monday interview"?

If the former then P(Monday) = P(Monday | Heads) = 1.

If the latter then there are two different solutions:

1. P(Monday) = P(Monday | Heads) = 2/3
2. P(Monday) = P(Monday | Heads) = 1/2

I think we can definitely rule out the first given that there doesn't appear to be any rational reason to believe that P(Monday | Heads) = 2/3.

But if we rule out the first then we rule out P(Monday) = 2/3 even though two-thirds of interviews are Monday interviews. This shows the weakness in the argument that uses the fact that two-thirds of interviews are Tails interviews to reach the thirder conclusion.

There is, however, an apparent inconsistency in the second solution. If we understand P(Monday) to mean "what is the probability that this interview is a Monday interview" then to be consistent we must understand P(Monday | Heads) to mean "what is the probability that this interview is a Monday interview given that the coin landed heads". But understood this way P(Monday | Heads) = 1, which, if assuming P(Monday) = 1/2, would give us the wrong conclusion P(Heads | Monday) = 1.

So it would seem to be that the only rational, consistent application of Bayes' theorem is where P(Monday) means "what is the probability that a Monday interview will happen", and so P(Monday) = P(Monday | Heads) = 1.

We then come to this:

$P(Heads | Awake) = {{P(Awake | Heads) * P(Heads)} \over P(Awake)}$

Given that P(Awake | Monday) = 1, if P(Monday | Heads) = 1 then P(Awake | Heads) = 1 and if P(Monday) = 1 then P(Awake) = 1. Therefore P(Heads | Awake) = 1/2.

CNN obtains the tape of Trump’s 2021 conversation about classified documents

Except it is like, highly confidential.
...
Secret. This is secret information.
...
See as president I could have declassified it. Now I can't, you know, but this is still a secret.

Then, in the "scenario most frequently discussed," SB is misinformed about the details of the experiment. In mine, the answer is 1/3. — JeffJo

So we have two different versions of the experiment:

First
1. she’s put to sleep, woken up, and asked her credence in the coin toss
2. the coin is tossed
3. if heads she’s sent home
4. if tails she’s put to sleep, woken up, and asked her credence in the coin toss

Second
1. she’s put to sleep, woken on Monday, asked her credence in the coin toss, and put to sleep
2. the coin is tossed
3. if heads she’s kept asleep on Tuesday
4. if tails she’s woken on Tuesday, asked her credence in the coin toss, and put to sleep

I think the answer should be the same in both cases.

It may still be that the answer to both is 1/3, but the reasoning for the second cannot use a prior probability of Heads and Tuesday = 1/4 because the reasoning for the first cannot use a prior probability of Heads and Second Waking = 1/4.

But if the answer to the first is 1/2 then the answer to the second is 1/2.

I think this is unnecessarily pedantic.

In one person’s reference frame the event is in the present (or past), and in the other person’s reference frame the event is in the future. I find this peculiar.

And, for the purpose of the Andromeda Paradox, it shows that the second person’s future is inevitable.

Your statement assumes a privileged frame of reference. — Benkei

Which statement?

I also don't see how it applies in this context. — T Clark

A statement such as "a fleet of spaceships has just left the Andromeda Galaxy en route to Earth" is either true or false, even though we don't, and can't, know which.

The "common sense" realist view is that if it's true then it's true for all of us, otherwise it's false for all of us, but if special relativity is correct then whether or not it's true can be relative to our individual movements.

While Bill stays put, Ann moves toward the light coming towards her showing the events as they unfold. Of course she's going to see the decision to invade Earth before Bill does. By the time the light reaches her, she's simply closer to it. She's been walking millions of years towards it already. Once Bill sees the decision happening, for Ann at that point, having walked at 5 m/s for all that time, the light reaching her then is 15 days later and the armada is already on its way. — Benkei

But the relativity of simultaneity isn't just about one person seeing something before another person; it's about that thing actually happening for one person before another person. That's what I find peculiar.

Do you feel comfortable saying both are correct because neither has a privileged frame of reference? If yes, what makes the Andromeda example different for you? If not, why not? — Benkei

I don't really understand your question. I certainly accept that special relativity, and its various implications such as the Andromeda Paradox, are correct, but like much of science I find it very peculiar.

Sorry. I think the difference you describe is meaningless. — T Clark

You think the distinction between "there is intelligent life in the Andromeda Galaxy" being truth-apt and it not being truth-apt is a meaningless distinction?

The realist would disagree. They would argue that it's truth-apt and either true or false.

The same with something like "a fleet of spaceships has left the Andromeda Galaxy en route to Earth". It's either true or false even if we can't know which it is.

However, what's interesting about special relativity is that it seems to entail that whether or not such a proposition is true is relative to one's reference frame such that if two people cross paths in opposite directions then it can be true for one of them and false for the other. And if it's true for one of them then the future for the other is "fixed".

As the article asks "Can we meaningfully discuss what is happening right now in a galaxy far, far away?" Answer - of course not. — T Clark

Is that just because we don't know what is happening, or is it because there's nothing happening? A realist would presumably say that something is happening right now in a galaxy far, far way, but if special relativity is true then what's happening right now depends on our individual, relative velocities, such that what's happening right now in a galaxy far, far way in your reference frame isn't what's happening right now in a galaxy far, far away in my reference frame.

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months? — T Clark

There’s some math here that might explain it: https://medium.com/mathadam/the-andromeda-paradox-b4bb30a0e372

Given the distance to the Andromeda galaxy one person moving towards another nearby person at just 5 m/s changes the frame of reference enough that there’s a 15 day difference between which events in Andromeda are simultaneous.

And the further the distance the lower the velocity needed to establish such a significant difference. So given a far enough away location even small head movements can bring about a sufficiently different reference frame.

I consider this "paradox" untenable since simultaneity cannot apply to distant events. — jgill

So do distant events occur in the past relative to my reference frame? Or the future? Or not at all?

Continuing in that article:

Mr. Shapley, in fact, also told Congress that his investigation had uncovered some evidence that some of the claims of the elder Mr. Biden’s involvement were mere “wishful thinking.”

He told of an interview conducted with Hunter Biden’s business associate Rob Walker, who told investigators that it was “projection” that former Vice President Biden would get involved in their business ventures.

“I certainly never was thinking at any time the V.P. was a part of anything we were doing,” Mr. Walker said, according to Mr. Shapley.

...

House Republicans sought to portray the testimony as further evidence that Hunter Biden had gotten what they call a sweetheart deal from the Justice Department, even though his agreement to plead guilty to two misdemeanor charges appeared in line with how other first-time, nonviolent offenders were typically treated. Mr. Biden paid his back taxes and penalties in 2021.

Isn't that saying that they can hark back to something that didn't happen? — wonderer1

No? It's just saying that they conclude that at some point in the past, it was true for one of them that the ships had set off and false for the other.

As it says they don’t know that it’s the case, but the reasoning suggests that it is the case for one of them. It’s better to understand it as saying that according to their their reference frame rather than according to their beliefs.

Ok, so a rock traveling at the speed of light comes from a star a million light years away to here. At the same time that it leaves, there is a super massive solar flare in the star. The rock arrives here a few years later but we will not see the flare for a million years. — Sir2u

The rock and the flare arrive at the same time. From our perspective they took 1,000,000 years.

A ship followed them at 99% the speed of light. From our perspective it took 1,010,101 years to arrive because the distance is 1,000,000 light years. From the ship's perspective it took 142,492 years because the distance is 141,067 light years.

From our perspective the ship arrived 10,101 years after the rock and flare. From the ship's perspective it arrived 1,425 years after the rock and flare.

See also:

And in the "scenario most frequently discussed," there is a fourth potential outcome that halfers want to say is not a potential outcome. SB can be left asleep on Tuesday. This is an outcome in the "laboratory" space whether or not SB can observe it. It needs to be accounted for in the probability calculations, but in the "frequent discussions" in "typical literature," the halfers remove it entirely. Rather than assign it the probability it deserves and treating the knowledge that it isn't happening as "new information." — JeffJo

What if the experiment ends after the Monday interview if heads, with the lab shut down and Sleeping Beauty sent home? Heads and Tuesday is as irrelevant as Heads and Friday.

I think this is equivalent to the case where we don't consider days, and just say that if heads then woken once and if tails then woken twice. It doesn't make sense to consider heads and second waking as part of the probability space. It certainly doesn't have a prior probability of 1/4.

This doesn't seem to be saying anything.

Why use the word "God" at all? Why not just say that there was some inanimate, formless chaos that happened (without intention) to form into the space and time and matter and energy that we are familiar with?

Using the word "God" brings in all sorts of additional, religious baggage.

I do believe that in many of these instances XX and XY accurately describe what the speaker meant when he hung the sign, not what the word eventually evolved into and what it was meant to protect. — Hanover

Maybe that's true of the person who hung the sign (assuming they have a basic understanding of biology), but our use of the words "man" and "woman" and our separation of bathrooms and locker rooms long preceded our discovery of sex chromosomes in 1905.

At the most you could argue that the words and separation was determined by phenotype as historically there was no means to distinguish between a typical XY male and someone with XX Male Syndrome, and so it's a stretch to argue that genetics had something to do with the conventions of our language use, even if there is a strong correlation between genotype and phenotype.

But your response doesn't really address my questions. Should someone who has physically transitioned use the bathroom associated with their sex chromosomes? How would anyone know what someone else's (or their own) sex chromosomes are? What about people who are neither XX nor XY?

I think practical considerations are far more important than the intentions of the person who painted a sign on a door, so your argument is a red herring.

I'll throw in one last consideration. I posted a variation of the experiment here.

There are three beauties; Michael, Jane, and Jill. They are put to sleep and assigned a random number from {1, 2, 3}.

If the coin lands heads then 1 is woken on Monday. If the coin lands tails then 2 is woken on Monday and 3 is woken on Tuesday.

If Michael is woken then what is his credence that the coin landed heads?

Michael's credence before the experiment is P(1) = 1/3, so if woken he ought to continue to have a credence of P(1) = 1/3 since he gains no new relevant evidence if he wakes up during the experiment.

And given that if woken he is 1 iff the coin landed heads, he ought to have a credence of P(Heads) = 1/3.

Do we accept this?

If so then the question is whether or not Sleeping Beauty's credence in the original experiment should be greater than Michael's credence in this experiment. I think it should.

Existence IS God. — EnPassant

What does this mean? Are you saying that the words "existence" and "God" are synonyms? As a fluent English speaker I'd have to disagree. At the very least, "God" is proper noun and "existence" an improper noun, so clearly there is at least some distinction between the words.

What's the verb form of "God"? For "existence" it's "exists". So how would you rephrase the sentence "there exists more than one apple"? Maybe "there gods more than one apple"? Doesn't make much sense to me.

Or are you perhaps just asserting pantheism? If so then what evidence or reasoning leads you to believe that the universe is "divine" (or whatever it is that distinguishes a pantheistic universe from a non-pantheistic universe)?

Copied from something I posted in a previous discussion:

https://www.reuters.com/article/us-usa-lgbt-survey-idUSKBN13X0BK

Almost 60 percent of transgender Americans have avoided using public restrooms for fear of confrontation, saying they have been harassed and assaulted, according to the largest survey taken of transgender people in the United States.

The survey of 27,715 respondents reached an estimated 2 percent of the adult transgender population in 2015, seeking to fill a gap in data about a severely understudied group whose experiences and challenges from medicine to law to economics and family relations are poorly understood.

The findings by the National Center for Transgender Equality on public restrooms counter the message of mainly conservative politicians and religious leaders that transgender people are the antagonists preying on others. It found that 12 percent of transgender people were verbally harassed in public restrooms within the previous year, 1 percent were physically attacked and 1 percent were sexually assaulted. Nine percent said someone denied them access to a bathroom.

https://www.hsph.harvard.edu/news/hsph-in-the-news/transgender-teens-restricted-bathroom-access-sexual-assault/

Transgender and gender-nonbinary teens face greater risk of sexual assault in schools that prevent them from using bathrooms or locker rooms consistent with their gender identity, according to a recent study.

Researchers looked at data from a survey of nearly 3,700 U.S. teens aged 13-17. The study found that 36% of transgender or gender-nonbinary students with restricted bathroom or locker room access reported being sexually assaulted in the last 12 months, according to a May 6, 2019 CNN article. Of all students surveyed, 1 out of every 4, or 25.9%, reported being a victim of sexual assault in the past year.

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8022685/

Also according to the declaration, the idea that protection for transgender people (including using the bathroom without constraint due to gender identity) harms the privacy and security of other users is a myth. Several critics point out that there is no evidence that non-discrimination policies or that explicitly allow transgender people to use restrooms according to their gender identities have led to an increase in the number of sexual harassment cases in bathrooms and women's locker rooms anywhere in the world (Doran, 2016; Hasenbush et al., 2019). States (19) and cities (more than 200) in the US that have passed laws against discrimination against LGBT people show that such measures have not caused any increase in incidences of crime in bathrooms (Maza and Brinker, 2014). This is not surprising, given that the approval of protections against discrimination has no impact on existing laws that criminalize violent behavior in bathrooms. In the absence of real incidents to base trans-exclusionary bathroom policies, anti-trans groups fabricate horror stories about trans-inclusive bathroom policies (Maza, 2014).

Security and privacy in the use of public restrooms are certainly important for everyone—including transgender people. Arguments that unilaterally conceive the access of transgender people to restrooms according to their gender identities as a risk factor for the safety of other people assume, even implicitly, that the transgender population does not deserve to be protected under the same standards as the cisgender population. This is particularly alarming, given that research shows precisely that young transgender people are exposed to much higher rates of violence in US schools' restrooms (middle and high school) than young cisgenders (Murchison et al., 2019).

What about those who’ve physically transitioned? Should an XX person with an artificial penis and testicles use the XX locker room? Should an XY person with artificial breasts and vulva use the XY locker room? How would a third party using the locker room even know that they’re artificial?

What if someone doesn’t know what their sex chromosomes are because they’ve never been tested? Although there’s a strong correlation between sex chromosomes and appearance there are all sorts of genetic conditions that differ from the common, and not everyone with them knows that they have them. They might be very rare but whatever laws or rules you have in place will need to account for them. Will all bathrooms and locker rooms require genetic testing?

What if someone is neither XX nor XY? Again it might be rare but again they need to be accounted for.

That is the definition of light year, how far light travel in one year. — Sir2u

Because of length contraction the faster you go the shorter the distance between two points. So something that is 1 light year away to us is less than 1 light year away to an object moving at near the speed of light.

See here: https://www.emc2-explained.info/Dilation-Calc/

In the second set of boxes set the % of c to 99.9 and the distance to 100 light years. It shows that from the perspective of the ship the distance is 4.471 light years and will take 4.475 years to reach.

Is there something about the American constitution I don't understand? Is it unamendable by any sitting government? Is a national referendum required to alter the constitution? — universeness

Requires two-thirds of the Senate and the House of Representatives and three-fourths of the States to agree to it.

Why I am not hearing about the democrats trying to rush through legislation, to prevent anyone found guilty of a criminal act being barred from standing for president?
Why was this gaping hole in USA legislation not corrected, years ago? — universeness

Because that might be unconstitutional.

Article II states "No person except a natural born citizen, or a citizen of the United States, at the time of the adoption of this Constitution, shall be eligible to the office of President; neither shall any person be eligible to that office who shall not have attained to the age of thirty five years, and been fourteen Years a resident within the United States."

Although it doesn't explicitly say that "Any person except...", it could probably be argued that this was meant to be an exhaustive requirement (although I don't know if one could both argue this and claim to be an originalist, as some Justices claim to be).

Trump rejected lawyers’ efforts to avoid classified documents indictment

Trump time and again rejected the advice from lawyers and advisers who urged him to cooperate and instead took the advice of Tom Fitton, the head of the conservative group Judicial Watch, and a range of others who told him he could legally keep the documents and should fight the Justice Department, advisers said. Trump would often cite Fitton to others, and Fitton told some of Trump’s lawyers that Trump could keep the documents, even as they disagreed, the advisers said.

...

Trump’s chances to avoid charges began in early 2021, according to current and former advisers. After Gary Stern, counsel at the National Archives, asked Trump’s team for the return of documents, some of his lawyers and advisers began advising him to return them. National Archives officials were privately baffled at what they viewed as inexplicably recalcitrant behavior and kept asking for answers to no avail.

In the fall of 2021, Alex Cannon, then a Trump attorney, urged the former president to return documents to the National Archives, repeatedly telling him that he was required to give them back, according to people familiar with the matter.

After months of talking to Trump and his staff, Cannon — referred to in the indictment as a “Trump Representative” — told Trump that the National Archives was threatening to go to Congress or to the Department of Justice if he did not return the documents, the people said.

...

Meanwhile, Trump grew angry with his lawyers and chose new lawyers, bringing in Evan Corcoran to handle the matter at the recommendation of adviser Boris Epshteyn.

Shortly after the subpoena arrived, the indictment says, Corcoran and another lawyer met with Trump at Mar-a-Lago and told him he needed to comply.

Such a moron. His own lawyers tell him that he needs to give them back and he just ignores them.

It appears he did file them separately, took them with him, and disputed with NARA over them. If you find that he took something designated as presidential records with him, be sure to let me know. — NOS4A2

He took things that were neither presidential records nor personal records; documents with classification markings related to national defence.

You can read the indictment for a list of the one's he's being charged over.

Also that court ruling only says that "there is nothing under the statute that the Court can compel the Archivist to do."

It continues by saying:

The PRA authorizes NARA to invoke the same enforcement mechanism embodied in the Federal Records Act, which begins with a request to the Attorney General to institute an action for the recovery of missing records. Compare 44 U.S.C. § 2112(c) with 44 U.S.C. § 3106. The statute does not mandate that NARA invoke this enforcement scheme but rather vests complete discretion with the agency to utilize that mechanism. 44 U.S.C. § 2112(c) (“When the Archivist considers it to be in the public interest, he may . . . .” (emphasis added). The Archivist has chosen to invoke the mechanism in the past when it deemed such action appropriate. See, e.g., United States v. McElvenny, No. 02-3027, 2003 WL 1741422 (S.D.N.Y. April 1, 2003) (seeking recovery of a map of Cuba annotated by President John F. Kennedy during the Cuban Missile Crisis).

So it appears you're incorrect in your claim that NARA doesn't have the authority to take back documents it considers Presidential records.

The above also references the court case you referenced before @NOS4A2, which has this to say:

The only reference in the entire statute to the designation of records as personal versus Presidential also calls for the decision to be made by the executive, and to be made during, and not after, the presidency. It provides: “materials produced or received by the President, [and other Executive Office employees], shall, to the extent practicable, be categorized as Presidential records or personal records upon their creation or receipt and be filed separately.”

Given that there is no record of Trump categorising such documents as personal records during his Presidency, they cannot be considered his personal records under the Presidential Records Act. Simply taking them with him when he left isn't sufficient.