A crazy party with a spooky aftermath
- Yesterday, I went to this crazy party!
- Why do I never get invited to parties like that?
- No, you wouldn’t have liked this one.
- Why not?
- We all had to answer 100 yes/no questions before we could eat!
- You are kidding?!
- Afterwards we compared our answers.
- What on earth for?
- I had 98 of the same answers as Belinda.
- Belinda was there?! I should have been invited!!!
- Belinda had 98 of the same answer as Carlos.
- What about you and Carlos?
- We did not compare. He said we didn’t have to.
- How come?
- He said he could calculate it from the data we already had.
- Really?! My feeling is that all you can calculate is the range of common answers.
- Could be. But I tell you something stranger.
- Shoot.
- You know Carl?
- Carlos brother? Of course, I know him. We play Go every Tuesday.
- He asked us what we would do if the theoretical minimum number of common answers were bigger than the number of common answers between Carlos and I!
- Is he on medication?
- No, but he reads New York Times a lot.
June 23rd, 2010 at 6:17 am
Facts:
98 of your answers were identical to Belinda’s.
98 of Belinda’s answers were identical to Carlos’.
Case 1:
You choose 1-100 YES
Belinda chooses 1-98 YES; 99-100 NO
Carlos chooses 1-100 YES
Match You-Belinda: 98%
Match Belinda-Carlos: 98%
Match You-Carlos: 100%
Case 2:
You choose 1-100 YES
Belinda chooses 1-98 YES; 99-100 NO
Carlos chooses 1-97 YES; 98-99 NO; 100 YES
Match You-Belinda: 98%
Match Belinda-Carlos: 98%
Match You-Carlos: 98%
Case 3:
You choose 1-100 YES
Belinda chooses 1-98 YES; 99-100 NO
Carlos chooses 1-96 YES; 97-100 NO
Match You-Belinda: 98%
Match Belinda-Carlos: 98%
Match You-Carlos: 96%
Assume #’s 1-96 are yes across the board and the differences are found in the last 4:
YYYY
YYNN
YYYY
==> 96+4=100% match
YYYY
YYNN
YNNY
==> 96+2=98% match
YYYY
YYNN
NNNN
==> 96+0=96% match
These are the only three possible cases. You and Carlos are a 96%, 98% or 100% match.
June 23rd, 2010 at 6:27 am
Regarding the question about what I would suspect if the match was less than the theoretical minimum: I’d suspect I screwed up my count. It’s impossible to have less than 96% match if I understood the question correctly.
~~
That said, there is an oddball case I suppose. Assume Carlos and Belinda both declined to answer some of the questions.
YYYY
YY–
Y–N
==> 97%
June 23rd, 2010 at 6:30 am
Please read the NYTimes article.
June 23rd, 2010 at 6:33 am
http://lh3.ggpht.com/_8Xxua0dW3UY/TA-gjbW-29I/AAAAAAAAAnk/E5Ia9kloINo/puzzle2s.jpg
June 23rd, 2010 at 6:36 am
My experimentation shows that if you upload a picture to Picasa and post the image link the image will show when you click the link (instead of being asked to download it). I can add an image tag and the image will be displayed in the comment. Only the administrator can do the last part.
June 23rd, 2010 at 7:12 am
This is completely off-topic but it does relate to a few recent posts.
The “Ulam Spiral of Primes” surprises me. Pretty neat stuff.
http://scienceblogs.com/goodmath/2010/06/the_surprises_never_eend_the_u.php?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed:+scienceblogs/CyKN+(Good+Math,+Bad+Math)&utm_content=My+Yahoo
June 23rd, 2010 at 7:12 am
A better link: http://scienceblogs.com/goodmath/2010/06/the_surprises_never_eend_the_u.php
June 23rd, 2010 at 7:53 am
I am not a quantum physicist but my personal opinion about particles being linked while being light years apart is that it’s an interesting concept in a “what-if” sense but to call it reality is foolish — it’s impossible to test so nobody will every truly know if this is science fact.
Now I must admit, I have absolutely no clue how quantum physics somehow relates to the problem at hand.
June 23rd, 2010 at 9:11 am
Michael, thanks for the links. I have added the Good math, bad math blog to my ‘think again’ links a Diigo: http://www.diigo.com/user/jannordgreen/think%20again.
June 24th, 2010 at 12:47 am
Michael Maguire has essential said “I don’t understand it; therefore it must not be true (or possible)”.
True human logic at work. But not valid logic.
June 24th, 2010 at 4:49 am
Michael:
Upon more careful reading of your last comment:
Yes, science/scientists do make assumptions of truth which are really just extrapolations of what has been proven so far.
The “spooky action at a distance” *has* been proven at distances much shorter than light years.
Scientists’ faith that physical laws operate the same over all distances has been shown to be true for a really wide array of measurable things. At the same time, as a way of challenging the though process, competing theories are constantly being worked on; many of them fail to match measurements, and the remaining competing theories are continually being sorted out by ever intriguing new experiments. Sometimes there are revolutionary surprises, and often not.
If quantum entanglement is eventually proven to have a distance limit, that would indeed be a marvelous discovery. But that outcome is not what the scientific community would predict based on current theory and measurement.
Your “impossible to test at light-year distances” belief is just that – a belief. I don’t think you can predict the future advance of science, such that your belief about the impossibility of such testability could be proven.
Besides, proving this at such huge distances is, perhaps, the wrong thing to be concerned about just now. It has already been shown by experiment to be true at more modest distances (along with time accuracy) such that it is known that quantum entanglement does happen faster than light could travel the measured distance. *That* result is what has everybody intrigued (even Einstein).
June 24th, 2010 at 5:59 am
Response to Jan’s original question “…what we [I] would do if the theoretical minimum number of common answers were bigger than the number of common answers between Carlos and I [you]!”
What I did was freak out. Which is to say, I essentially said to myself “I don’t understand your question.”
That led me to the NYT article, which is indeed intriguing. I didn’t have the energy/time/skills to work on all the questions it posed, but at least I spent the time with it to get the ideas about the 3 people take the 100-question Y/N test and compare notes puzzle and how it relates to Bell’s theorem. Thus, the NYT article provided more context to the puzzle, allowing me to “think my way out of it”, or at least settle the issue of what to do with it.
HOWEVER, here’s what I learned today that’s more important than that:
After all my research and thought about your puzzle, my answer to your question now is:
A: What I would do: is declare that there is a paradox somewhere in the statement of the puzzle.
Now here’s the important second part:
B. I would further declare that there is insufficient information given in the problem statement to say how the paradox could (or should) be resolved.
In other words, simply pointing out that there is a paradox is as far as the problem – as stated – allows me to go. To go further would be to be making something up out of whole cloth, without sufficient grounds. There are likely *multiple* ways out of the paradox, but no basis for any of them being more right than any other.
It is my belief that human beings are deeply psychologically driven to have answers to everything. Paradoxes are particularly disturbing to us. So, more often than not (sadly), we make up answers which, in fact, don’t have any validity except that they satisfy this psychological need.
In mathematics, paradox is used as a method of proof. Specifically, there’s a premise given, assumed true, then proven false by paradox. That’s the way it works in school, anyway. What bugged me about the problem in this “thnik again!” post was that there was no clear statement of where, in the whole story, the “premise to be disproved” lay. So, I “felt” the problem was wrong, improperly stated, incomplete, etc. I freaked out.
Real life isn’t so neat as a math problem in school. It’s nice to butt up against a puzzle which is (intentionally?) not as neat and proper as a school problem. Much more can be learned thereby. Thanks, Jan.
June 26th, 2010 at 2:23 am
Meh….
Some concepts are so preposterous as to require a great deal of evidence before a “wild-ass-guess” can truly be called a theory.
Case in point: String Theory. Show me one thread (sorry – pun) of evidence that strings exist and I’ll eat my shoe laces. The fact that it is a possible explanation does not make it plausible. The fact that it can’t be disproven doesn’t in any way prove it. I can’t prove that I didn’t sleepwalk into my neighbors’ house last night but until I see evidence to the contrary, I take the safe bet and assume I didn’t. With fringe science, all too often we assume the far-fetched until we can disprove it. It’s ludicrous.
Back to the point at hand, It’s not that I’m ignorant or simply don’t understand. It’s an outlandish claim and to me an outlandish claim requires evidence before allowing it to be considered a rational theory. It’s rubbish to think that at any point in the future it will be possible to simultaneously view two things in the same instant that are light years apart. Whether or not it’s possible can’t be proven because the observation of the results would take years to get to us. To my knowledge this has been tested at up to a meter with reported success… So at the very least we’re no longer talking about subatomic distances (where weird stuff tends to happen) but we’re also not talking about light years or even kilometers. That’s too much of a jump for extrapolation to be even slightly valid.