Search

  • Two envelopes problem

    @Michael

    Simulation in R to demonstrate the different sampling mechanisms.

    cases=matrix(c(c(10,5),c(10,20)),nrow=2,ncol=2,byrow=FALSE)

number_of_envelope_pairs=10000
resulting_envelope_value_C=rep(0,number_of_envelope_pairs)
#Case_C
for(i in 1:number_of_envelope_pairs){
  my_envelope_pair=cases[,rbinom(1,1,0.5)+1]
  after_switch=my_envelope_pair[2] #this chooses "the other one than 10"
  resulting_envelope_value_C[i]=after_switch
}
case_C_gain=mean(resulting_envelope_value_C-10)
case_C_gain #can see it's 2.5

    Onto something that sounds like Case_A, and something you can to do it to make it superficially resemble Case_C.

    #Something that sounds like Case_A
my_envelopes=rep(0,number_of_envelope_pairs)
my_envelopes_switch_gain=my_envelopes
for(i in 1:number_of_envelope_pairs){
  case_index=rbinom(1,1,0.5)+1
  envelope_index=rbinom(1,1,0.5)+1
  my_envelopes[i]=cases[envelope_index, case_index]
  my_envelopes_switch_gain[i]=cases[-envelope_index, case_index]-my_envelopes[i]
  }
mean(my_envelopes_switch_gain) #approx 0, this is if you don't open the envelope

#illustrating the conditioning, NB this is not the same as conditioning on
#the pair being (5,10) or the pair being (10,20)
#this is the gain given the chosen envelope is 10 and the
#other envelope is known to be 5 or 20.
mean(my_envelopes_switch_gain[my_envelopes==10])
#this gives you approx 2.5 as we saw in case C.

    You notice that when you condition on "having your envelope be 10" in that set up, you're subsetting to cases where the gain is -5 or 10, and those occur with equal probability since the cases (5,10) and (10,20) occur with equal probability. If you were to condition on your envelope being 10 in the loop (case index=1), you end up with exactly the same gain numerically but it represents a subjectively different belief state for an agent. Why? The subsetting done at the end lets you look at the whole ensemble of cases where the first envelope was 10, where the assignment of 10 was random. Fixing the envelope as 10 within case makes the assignment of 10 nonrandom.

    #Thing which is actually Case_A
my_envelopes=rep(0,number_of_envelope_pairs)
my_envelopes_switch_gain=my_envelopes
for(i in 1:number_of_envelope_pairs){
  what_case_am_i_in_given_i_have_10=rbinom(1,1,0.5)+1
#random assignment of case, 10 provides no knowledge of case
  five_ten_switch_gain_given_random_envelope=0
#conditioning on pair being 5,10, gain is known
  ten_twenty_switch_gain_given_random_envelope=0
#conditioning on pair being 10,20, gain is known
  case_gains=c(five_ten_switch_gain_given_random_envelope,
               ten_twenty_switch_gain_given_random_envelope)
  my_envelopes_switch_gain[i]=case_gains[what_case_am_i_in_given_i_have_10]
}

mean(my_envelopes_switch_gain)#this is just 0

    The thing we're butting heads on, in my view, is the Case_A inner loop line 1, which is where the randomness comes in through the allocation of pairs. If at any point, in the loop, the agent *knows* what case they're in, their gain is deterministic. When you grant that knowledge hypothetically, you either enter subcase A 1 (the first gain line) or subcase A 2 (the second gain line). Once you've done those hypothetical calculations, you reintroduce the randomness of allocating envelopes in the next line to choose the received gain.
    fdrake,  

  • What exists that is not of the physical world yet not supernatural

    I'm sure I've missed that "force". Please cite where in any of the equations or formal models used in QM there is a notation for mind/observer (and not the Hermitian operator for measurenent). You're not talking "over my head" and out of your bunghole again, Gnomon, are you? :sparkle: :eyes: — 180 Proof

    Quantum entanglement is the cited model you're looking for 180Proof is it not? For one particle to be in one state the other must be in the opposite state to say they are entangled - in communication with one another.

    As an observer (in a state of observation) we interact with/are entangled with that which we are observing. There is communication of information between the object of observation and the subject (observer). We must be entangled.

    Heinsenbergs uncertainty principle also shows this for to make an exacting observation of one factor the other must be unknown/uncertain. You cannot measure the possible locations of a particle (Velocity) and the where the particle is located at this very moment simultaneously.

    And in the same way when we observe something and interpret it as materialistic, we cannot understand it from any other possible explanation. Because some scientists saw lights wave behaviour while others measured it as a particle they were at odds with one another as to which must be correct.

    Its like the #the dress thing all-over again.
    Benj96,  

  • What type of forum is this?

    Physicsforums.com . And I don't remember the last deleted post. — TiredThinker

    Thanks for the link.
    I was told it wasn't a Q&A forum.It's like they want me to somehow contribute to the field of physics as if I was writing a doctoral dissertation. What are forums if not the place to ask questions? — TiredThinker

    I asked 'What were your questions?' not about any deleted posts.
    You don't remember the nature of your question?
    Bolded part:
    I think this is an unfair and exaggerated complaint, a misunderstanding or misrepresentation.

    ***
    A quick look suggests that is an excellent, well-organised site for different levels and areas.

    B= Beginners ( Basic high school)
    I = Intermediate ( Undergrad)
    A= Advanced (Grad+)
    There is even a Homework Help forum with Q&As.

    Before posting to a forum, it's always a good idea to read the mission statement and guidelines.

    We aim to provide a community for students, scientists, educators or hobbyists to learn and discuss science as it is currently generally understood and practiced by the professional scientific community....
    Reference: https://www.physicsforums.com/#the-lounge.34

    Strange that it is in The Lounge.
    [ I note they are looking for writing input in Sci-Fi ]

    ***

    Non-mainstream theories:
    Generally, in the forums we do not allow the following:
    • Discussion of theories that appear only on personal websites, self-published books, etc.
    • Challenges to mainstream theories (relativity, the Big Bang, etc.) that go beyond current professional discussion
    • Attempts to promote or resuscitate theories that have been discredited or superseded (e.g. Lorentz ether theory); this does not exclude discussion of those theories in a purely historical context Personal theories or speculations that go beyond or counter to generally accepted science
    • Mixing science and religion, e.g. using religious doctrines in support of scientific arguments or vice versa.
    • Philosophical discussions are permitted only at the discretion of the mentors and may be deleted or closed without warning or appeal

    Reference: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

    ***

    In the Physics subforum: other physics topics:
    A helpful 'Insights' article:
    https://www.physicsforums.com/insights/how-to-avoid-breaking-physics-with-your-what-if-question/

    ***

    So, again:
    What was the nature of your question or proposed discussion title? *
    Did it meet the forum guidelines?
    Do you now have the answer to your OP?

    * perhaps it could be discussed better at TPF?
    Worth considering?
    Amity,  

  • Mathematical Conundrum or Not? Number Five

    I think one of the best ways to envision probability is to imagine what would happen if you did the event 10,00 times, so that is what I have done

    n = 10000 #Number of flips
coin <- sample(c("Heads", "Tails"), n, rep = T) #The coin flip
MondayHeads <- 0
MondayTails <- 0
TuesdayTails <- 0 
#Loop to count the outcome
for (i in coin) { 
  if (i  == "Tails")
    MondayTails <- MondayTails+ 1}
for (i in coin) { 
  if (i  == "Tails")
    TuesdayTails <- TuesdayTails + 1}
for (i in coin) { 
  if (i  == "Heads")
    MondayHeads  <- MondayHeads  + 1}
Tails <- sum(coin == "Tails")
Tails #Number of tails
Heads <- sum(coin == "Heads")
Heads #Number of Heads

MondayHeads #Number of Monday and Heads
MondayTails #Number of Monday and Tails
TuesdayTails #Number of Tuesday and Tails

    Here is the output:

    [1] 5037 - Number of Tails
    [1] 4963 - Number of Heads

    [1] 4963 - Number of Monday and Heads
    [1] 5037 - Number of Monday and Tails
    [1] 5037 - Number of Tuesday and Tails

    You can see that the 1/3 argument does in fact lead to a 33% split and the 1/2 argument does lead to a 50% split; however, you should go with the 1/2 argument, as 4963/10000 is better odds than 4963/15037, therefore you have a better chance of being correct.
    Jeremiah,  
Home » Search

Welcome to The Philosophy Forum!

Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.

Sign In Create Account

Categories