Barry Arrington and Company: Does A=A?

This is a little test of reasoning ability. I would prefer that for the first few days, only ID advocates post answers. These questions, and the underlying reasoning, are widely discussed on the internet, so you may have encountered them. If you have, I would appreciate knowing that fact. Also, for those who have seen them before, I would like to know how you did the first time you encountered them.

If anyone spots a typo or logical error, I’d appreciate hearing about is so it can be corrected.

The answers I’m looking for are in three parts:

First — yes or no — can the puzzles be solved by reason, assuming ordinary knowledge of the vocabulary. There are no tricks or unusual meanings involved.

Second, provide the answer.

Third, the provide the reasoning or proof.

Uncommon Descent frequently invokes logic and reason. this is a challenge to anyone who posts at UD. Feel free to post your answers on this thread or at UD.

Here are the questions:

1. [The original editor has been sacked. Re-Edited to straighten out the mess: The price of a cheeseburger is $2.20, the price of a plain hamburger plus the price of the added cheese.] A plain hamburger costs two dollars more than the added cheese. How much does a plain hamburger cost?

2. In Elbonia, one person in ten thousand has Ebola. A new test is so good that anyone who is infected will test positive. But three percent of uninfected people will also test positive. John, a citizen of Elbonia tests positive. What is the probability that John has Ebola?

3. I have a deck of picture cards. They have automobiles on one side and living things on the other side. I have looked through them, and I think they follow the following rule: if a card has a GM automobile on one side, it will have an animal on the other side. After shuffling, I deal out four cards.

Cat, Ford, Petunia, Chevy

What cards must I turn over to test my hypothesis?

4. William is tweeting Betty, but Betty is tweeting John. William is in love, but John is not. Is a person in love tweeting a person who is not in love?

5. Elbonia has invented a treatment for Psoriasis. During a recent blind test, of the patients who were given the treatment 197 improved and 95 did not.

Of the patients who were given a placebo, 45 improved and 20 did not.

Is the treatment effective?

237 thoughts on “Barry Arrington and Company: Does A=A?

  1. I think of Cantor’s infinities as functions or algorithms rather than as cardinal numbers. Sets defined by a process rather than containers of physical objects. The problem for Mapou and tribe is that infinities can lead to solutions of real problems in the real world.

    As others have pointed out, it’s funny to see theists demanding physical implementation of concepts. The world turned upside down.

  2. petrushka said: “As others have pointed out, it’s funny to see theists demanding physical implementation of concepts.”

    They demand that all the time when it comes to concepts that they don’t like but when it comes to their religious beliefs not only is no physical implementation (or physical evidence) necessary but asking for any is blasphemy.

  3. “If you guys want to have a Cantor thread, please start one.

    This one is asking whether people who can’t solve logical and simple mathematical puzzles should be taken seriously when they challenge Cantor or Einstein or Darwin.”

    Oh really, I thought it was about whether people who can’t even understand the puzzles they are asking, little yet, answer them, or even attempt to write them coherently, should be taken seriously when questioning others who challenge Cantor, or Einstein or Darwin.

  4. Feel free to solve any of the puzzles, phoodoo, or at least have something to say that isn’t cribbed from KeithS.

    You took a guess on the love problem. A yes or no question gives you a fifty percent chance of being right. which is why I asked you to spell out your proof.

  5. Phoodoo:

    “I heard it said, that in fact Randi probably doesn’t actually even have the million to pay out, even if someone did prove their case-it’s really just a publicity stunt.”

    The JREF is a 501(c ) non-profit organization, which means you can check Randi’s form 990’s to see what he’s packing for Publicly Traded Securities.

    GuideStar

  6. In fairness, Mapou has made it clear that he rejects the classical theistic conception of God. Say what you will about his understanding of physics and mathematics, at least his metaphysics is internally consistent. Kairosfocus, who does accept a classical theistic conception of God, has stood up for Cantor.

    The relevant fault-lines here have nothing to do with theism or “materialism”, or even rationalism vs. empiricism.

  7. Tristan,

    James Randi Educational Foundation
    For 2013
    Revenue 887,595 Total Expenses1,039,201

    Probably not a smart financial move to pay out a million dollars, if one can avoid it by simply closing their eyes, covering their ears, and avoiding answering the phone.

  8. Probably not a smart financial move to pay out a million dollars, if one can avoid it by simply closing their eyes, covering their ears, and avoiding answering the phone.

    On the other hand, anyone who can demonstrate psychic powers can do so outside Radi’s auspices and generate enough publicity to force a confrontation.

  9. Petrushka,

    The puzzles have been solved. Again, I am sorry that it was so much easier for me than for you.

  10. Anyone else think phoodoo has solved all the puzzles? Has anyone seen a proof of the love puzzle?

  11. phoodoo,

    The JREF’s 2013 Form 990 lists $1.5 million in publicly traded securities.

  12. Their assets or lack thereof, are irrelevant. Randi takes challenges where the challenger has established some public attention or notoriety. Presumably having passed through the sieve of journalists and pundits. there are thousands of cranks, and there is no sense in paying attention to anyone who can’t at least convince a crew of TV journalists.

  13. Petrushka: “Their assets or lack thereof, are irrelevant.”

    I think this shows some insight into why the puzzles were hard for you.

  14. Dazzle us, phoodoo. Tell us why the availability of an obvious million dollar prize is necessary in order for a psychic to demonstrate his or her powers.

  15. Or is it enough for the psychic simply to make the phoodoo boast: I can do it. I did it in ten seconds. I won’t tell you how I did it, and I won’t show you my demonstration, but I did it.

  16. Kantian Naturalist, what difference does it make whether Mapou “rejects the classical theistic conception of God” or not? Mapou is a religious loon who, like other religious loons, is a massively narcissistic autocrat.

    There’s no such thing as “the classical” theistic conception of God except that every ‘God’ believer is a theist, which puts them all in the same ‘class’, and even though they’re all in the same ‘class’ in that sense they all have their own particular ‘theistic conception of God’, so applying the label “classical” to theistic beliefs in any way other than correctly labeling all ‘God’ believers as theists is nonsensical to me.

  17. I’m not sure what Mapo’s conception of god is, but he has said the Bible is full of coded scientific revelations. Like all really good predictions, they will be obvious just as soon as they come true. And no help at all before.

  18. I wish that Mapou would provide the details of that claim of his. The entertainment value would be high. 🙂

  19. phoodoo on January 7, 2015 at 8:29 pm said:

    Oh really, I thought it was about whether people who can’t even understand the puzzles they are asking, little yet, answer them, or even attempt to write them coherently, should be taken seriously when questioning others who challenge Cantor, or Einstein or Darwin.

    In order to challenge Cantor, Einstein, or Darwin, one needs to first comprehend what these scientists or mathematicians claim. I don’t think Mapou and phoodoo understand Cantor’s diagonal proof or Einstein’s theory.

  20. Olegt,

    So what if that is what you think Olegt? What evidence is there that you understand Cantor? What evidence is there that anyone on this website understands them more than myself or Mapou?

    Heck, Petrushka doesn’t even understand that if a guy offers a challenge to give anyone a million dollars if they can prove any psychic abilities, but that person doesn’t actually have the million dollars to give if they did, then that challenge is a meaningless scam, a rouse, a publicity stunt that they have no intention to ever allow anyone a fair chance to do if they could.

    Where does someone with such a low level of understanding get off trying to say what anyone else understands?

    I haven’t seen you solve any puzzles Olegt. But never mind, I already did them for you-it took eleven seconds; because I type kind of slow.

  21. Oh, it’s not about me, phoodoo. It doesn’t matter whether I understand Cantor’s proof or not: it’s not me who is challenging it. You are, and you have no clue.

    Likewise, Mapou keeps yapping that Einstein is wrong, but he doesn’t understand relativity.

  22. Well, Olegt its refreshing to know that you will staying out of any discussion about Cantor then, since its clearly not anything you know about.

    It will give you more time to think about Petrushkas terrifying brain teasers. Let me know if I can help explain them further to you, since Petrushka himself can’t.

  23. You can’t know whether I understand Cantor’s proofs, phoodoo. If you don’t understand it, how can you judge whether someone else does? 🙂

  24. I ran across a question today that makes an interesting puzzle. Suppose p is a prime number, for example 98213.

    1) You can form a new number by writing out p twice. For my choice of p, you get 9821398213. Is it possible that this could ever result in another prime? It doesn’t in this case, as you can check.

    2) Now suppose you do the same thing, except reverse the order of the digits the second time, so you get 9821331289 for the p I chose. Can this ever result in a prime number? Again, in this case, the new number is composite.

    (I hope it’s ok to bring in new puzzles, petrushka).

  25. I found your prime number questions interesting, but a bit too easy. So, instead of posting an answer, I will wait for phoodoo to give his quick solution.

  26. phoodoo,

    Where does someone with such a low level of understanding get off trying to say what anyone else understands?

    I understand that you won’t take a position on if Uri Geller has PSI ability or not.

  27. phoodoo,

    that challenge is a meaningless scam, a rouse, a publicity stunt that they have no intention to ever allow anyone a fair chance to do if they could.

    Do you have any actual evidence for this?

  28. O”magain,

    You, you, you mean they ..HAVE …AN…ONLINE…FORUM!!

    OMG! Amazing!

    Oh you are so right, that means they MUST be legitimate. I had no idea they had a forum! How could they possibly have their own online forum and not be sincere in wanting to give away the million dollar prize.

    I think we are just going to have to leave the puzzles to you from now on.

    They have a forum! Holy shit!!

  29. phoodoo,

    You, you, you mean they ..HAVE …AN…ONLINE…FORUM!!

    Yes, unlike you they are attempting to be open and transparent.

    Oh you are so right, that means they MUST be legitimate. I had no idea they had a forum! How could they possibly have their own online forum and not be sincere in wanting to give away the million dollar prize.

    Until you provide some evidence of their intent to defraud by offering a prize they don’t intent to provide your claim is unsupported.

    I think we are just going to have to leave the puzzles to you from now on.

    Do what you like. To me this is a laugh over coffee, to you and your ilk this is *it*.

    They have a forum! Holy shit!!

    And you are unable to support your claims yet won’t withdraw them.

    This makes you, well, you guess the word. Begins with a ‘H’.

  30. I see something like 150 challenges. Perhaps phoodoo can name someone who has demonstrated psychic powers in a reasonably controlled situation and is thereby qualified.

  31. My favorite application to Randi is the guy who offers to solve crimes by examining objects involved.

    Provided that the crimes have already been solved.

  32. I think Randi quit accepting challenges about five years ago. Reading through the ones they got, I can’t imagine why.

    Anyway, there are lots of people who enjoy a good show,and lots of ways for anyone having genuine psychic powers to demonstrate them.

    I would point out that stage magicians making no psychic claims can baffle most people. There’s a rather famous YouTube video of Penn and Teller being stumped by a sleight of hand card trick. Just a simple trick done on camera before professional magicians.

    Which is why scientific testing of paranormal claims is difficult.

  33. I would point out that stage magicians making no psychic claims can baffle most people. There’s a rather famous YouTube video of Penn and Teller being stumped by a sleight of hand card trick.

    Lennart Green is another example. From his wikipedia entry:

    Green competed at the 1988 FISM convention in The Hague, Netherlands, and was erroneously disqualified because the judges incorrectly believed he had used stooges in his act to shuffle the cards.

  34. Phoodoo:

    Heck, Petrushka doesn’t even understand that if a guy offers a challenge to give anyone a million dollars if they can prove any psychic abilities, but that person doesn’t actually have the million dollars to give if they did…

    But they do. I showed you. Or at least, I provided his tax returns and expected you to show yourself.

  35. petrushka,

    I think Randi quit accepting challenges about five years ago.

    They (the JREF) were going to stop in 2010, but they changed their minds. The challenge is still open:

  36. Moving right along, here is the Keiths version of problem number one.

    The price of a cheeseburger is $2.20, the price of a plain hamburger plus the price of the added cheese. A plain hamburger costs two dollars more than the added cheese. How much does a plain hamburger cost?

    Let h equal the price of a hamburger (in cents) and y equal the price of the added cheese, in cents.

    h + c = 220
    h – c = 200
    c = 220 – h
    h – (220 – h) = 200
    h – 220 + h = 200
    2h – 220 = 200
    2h = 420
    h = 210

    I will note that keiths not only noticed an error in my original wording, but was able to supply the appropriate correction. No points to phoodoo for reading keiths.

    Word problems are the bane of algebra students. The world awaits someone who can find a way to teach kids how to approach them. I know my kids started getting them in elementary school. I don’t know if it helped.

  37. The way I learned to set this up in high school algebra is somewhat simpler, since there is only one variable here, the price of the cheese. Let’s let X be the price of the cheese. Then the hamburger’s cost is given as 2.00 + X. So the equation (hamburger plus cheese) is:  (2.00 + X) + X = 2.202.00 + 2X = 2.20 2X =.20
    X = .10  So the cheese is ten cents, and the hamburger is2.10. Simple.

    I’m not sure I understand question 4. We know of only one person in love, which is William. William is tweeting Betty, but we know nothing about her. John isn’t tweeting anyone. So we don’t know.

  38. In #4, we do know that Betty either is or is not in love. If you consider both cases separately, you will find someone in love tweeting someone not in love.

  39. Another quick way to do the algebra is to take petruska’s two equations, viz:
    h + c = 220
    h – c = 200
    and add them, yielding
    2h = 420
    thus h = 210.
    If you wanted to price of the cheese, subtract them, yielding
    2c = 20

  40. In #4, we do know that Betty either is or is not in love. If you consider both cases separately, you will find someone in love tweeting someone not in love.

    Let’s do a simple proof..
    Betty is either in love or not in love (stipulated)
    If betty is in love, then Betty is a person in love tweeting John, who is not in love.
    If Betty is not in love, then William is a person in love tweeting Betty, who is not in love.

    This puzzle appeared in the first Harry Potter book:

    find the potion hidden in a row of seven unmarked bottles that allows you to advnce.

    Danger lies before you, while safety lies behind,
    Two of us will help you, whichever you would find,
    One among us seven will let you move ahead,
    Another will transport the drinker back instead,
    Two among our number hold only nettle-wine,
    Three of us are killers, waiting hidden in line
    Choose, unless you wish to stay here forevermore
    To help you in your choice, we give you these clues four:
    First, however slyly the poison tries to hide
    You will always find some on nettle wine’s left side
    Second, different are those who stand at either end
    But if you would move onward, neither is your friend;
    Third as you see clearly, all are different size
    Neither dwarf nor giant hold death in their insides;
    Fourth, the second left and the second on the right
    Are twins once you taste them, though different at first sight.

  41. Petrushka,

    And you struggled with this puzzle. And you also had the pretensions gall to suggest that I didn’t answer this question, when I spelled it out quite clearly.

    But perhaps you couldn’t understand that.

  42. Flint,

    You are quite correct. But you have to understand Keith’s unique ability for taking even the simplest of concepts and making them ridiculously complicated.

    And you must further understand Petrushkas propensity for being impressed by this.

  43. phoodoo,

    But you have to understand Keith’s unique ability for taking even the simplest of concepts and making them ridiculously complicated.

    I believe BA77 just posted his latest sermon. Is that more your thing?

  44. Phoodoo, on the other hand, can take sophisticated and subtle concepts, and assert that they are simple.

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