Flawed Logic: The Problem Of Blue-spotted Monks

I recently ran across the Problem of the Blue-spotted Monks again at https://richardwiseman.wordpress.com/2011/04/04/answer-to-the-friday-puzzle-98/.  Actually, this is a slight variation of the well-known Blue-Eyed Monk problem that can be found at https://en.wikipedia.org/wiki/Common_knowledge_%28logic%29, among other places. One site even called this problem “The Hardest Logic Puzzle in the World”A, but that was probably just a case of self-promotion. For today’s discussion, I chose the first version of the problem because it is simpler (we don’t have to worry about the case in which one person has red eyes). If you haven’t done so, go ahead and read the problem. We will discuss the solution in the next section.

The classic answer uses mathematical inductionD to first consider the (trivial) case in which only one monk has the disease. Then they move on to the case of two monks. Their error begins in the case of three infected monks, assuming that the monks were required to start back at one in making their individual analysis.  That is wrong; in the comments section of some of the references, several people take issue with this assumption.  I believe this to be a misapplication of the induction process.  The monks have only to consider two possibilities; either they are infected or they are not. For the sake of argument, let’s say there are ten infected monks. Most of the monks will see ten fellow monks with blue spots. Ten of the monks will see nine monks with blue spots. None of the monks will see only one monk with blue spots, or just two monks with blue spots, etcetera. Those monks seeing ten spotted monks have only two possibilities – either there are ten infected monks or there are eleven. Those monks seeing nine spots need only consider the possibility that there are either nine or ten monks infected. Most of the monks, in considering their first possibility (that there are only ten infections) realize that those ten, in considering the possibility that there are only nine infections, must allow for the possibility that there are nine monks who see only eight infected monks. With the information available, nobody sees any reason to consider any other lesser possibility. Just like in the conventional solution, each monk, having two possibilities, must allow the lesser possibility (which means they are not infected) to resolve itself first before concluding that they are infected and turn themselves in. All of the monks know that the least number of infections that any of them must consider is eight, not one. The first day nothing would happen. The second day, the monks that saw only nine other spotted monks will conclude that the possibility of anyone sighting eight spotted monks was groundless, so they will all turn themselves in. The third day, those who saw ten spotted monks will all breathe a sigh of relief.

Considering The Second Possibility

Now we need to look at the big picture.  This isn’t rocket science.  Why hasn’t anybody seen the error in conventional wisdom before today?  I, like the monks, must consider the possibility that I am the one infected.  If nobody else comes forward with a confirmation of the correct answer soon, I guess I’ll be forced to turn myself in.  Please hurry.

A Better Plan For Controlling Gun Violence?

Well, here we are again with another mass shooting in AmericaA, this time in Orlando, Florida.  This is the first such catastrophe since my last post on the subjectA six months ago, which followed a string of almost one mass shooting a month over the six month period before that.  And still no solution.  I saw a clever suggestion on Facebook, where some gentleman invoked the same rhetoric that Donald Trump used in his plan to ban all Muslims to call for a ban on all assault weapons and weapons of mass destruction only until the United States was able to get a handle on dealing with crazy people and began educating our children again (which were cited in that Facebook discussion as reasons for the rampage).  Strangely enough, this idea didn’t seem to be as popular as Trump’s.  We’ve also seen the difficulty in passing a law preventing people on the “No Fly” list from getting a gunA – something that most people consider sensible.

The Atlantic has a nice articleA explaining how that idea has made hypocrites out of both political parties.
Based on the comments and arguments I’ve read on this issue, I’ve come up with what may be the only workable solution.

Plan B

Since we will apparently never agree to restrict the ownership of firearms in any way (even though we have no problem regulating less dangerous products), we need to institute some sort of bag limits.  I am in favor of lifetime limits rather than seasonal limits.  There is still some debate on whether the limit on family members should be higher or lower than the limit on innocent strangers (the definition of “innocent” can be worked out later if it is even relevant to this discussion).  To get the ball rolling, I’ll throw out a few numbers that we can iron out in the comment section.  I propose a lifetime limit of one adult white male per person (some restrictions may apply) regardless of the number of guns owned.  Since up to now, damages for such offenses typically considered the earning power of the victim (which never seemed right to me), the bag limit for females should be about 1.5 (I’m not quite sure how to deal with round-off error; maybe we could start at two, but drop the limit to one if you’ve already met your male limit).  The limit on Muslims would, of course, be three (we need to keep the limit for any one incident below four so we don’t trigger the commonly used definition of a mass shooting, and can therefore look better than the French).  Since Jews are still the most persecuted religious group in AmericaA, we’ll set their limit at two.  As usual, there will be no limit on black males, except for overzealous law enforcement agencies.

If we follow this plan, the mass-shooting statistics are guaranteed to go down.  But if the overall gun violence statistics increase intolerably we could either go to a lottery system or increase the permit fees.  (As the fees for especially popular groups start to increase, we may need to find a way to control poaching.  We can worry about that later.)  Both of these solutions have been successful with other game.  If the fees are high enough, we could lower other taxes.  I would start with the taxes devoted to education, since I suspect that those most likely to object to this plan may have some level of intelligence.  We could export the catch to China and convince them it’s more humane than the dog meat they are now using.  If we corner the market for this resource, that too would increase tax revenue.

Did I forget anything?  I realize that this solution may not pass the test for political correctness, but based on some of the feedback I saw in the Facebook discussion, that alone could make the plan more attractive to some people.

What do you think?  If you have a more workable plan, let’s hear it.  If, on the other hand, your plan depends on Hell freezing over, you might as well keep it to yourself.

A Better Way To Handle The Harambe Incident

For those who haven’t heard about the gorilla named Harambe that was shot ten minutes after a toddler fell into his enclosure at the Cincinnati Zoo around 4 pm on Saturday, May 28, 2016, here is as good a source as any: Gorilla killed after 4-year-old falls into zoo enclosure. Apparently, authorities had both a tranquilizer gun and a rifle at their disposal, and chose the rifle to fatally shoot the gorilla even though the boy hadn’t yet been seriously injured because they were afraid that the tranquilizer wouldn’t act fast enough. They didn’t have to make that call. Here’s a better way.

1. Take both the tranquilizer and the rifle. The same person should not operate both.
2. Have other staff members make themselves immediately ready to rescue the child.
3. When both weapons are ready, shoot the gorilla with the tranquilizer.
4. Have the person with the rifle continuously evaluate the threat posed by the gorilla.  If bodily harm from the gorilla is not immediately forthcoming, do not shoot.
5. If the parents get hysterical while you are evaluating the situation and behave in such a way as to adversely affect the behavior of the gorilla or the judgement of the zoo staff, shoot the parents.  (So as not to make the same mistake as the Cincinnati Zoo staff did Saturday, I guess I should mention that you could use the tranquilizer gun for this if you had the forethought to bring the correct dose – even though at this point it wouldn’t be my weapon of choice.  If you don’t have the correct dose, just pray that the staff isn’t acting under the same level of panic or incompetence as they exhibited with Harambe.)
6. Rescue the child as soon as practicable.

Although (admittedly based on limited information) I did not think the boy was in danger, and not all witnesses in Cincinnati felt the dangerA, those opinions don’t matter to the success of this plan. Since using the tranquilizer doesn’t prevent the use of the rifle, this plan could not have turned out worse for the child than the plan executed, and most likely would have turned out much better for all concerned. The zoo simply threw away options prematurely based solely on their worse fears instead of facts – that sounds like panic to me, and it sounds very unprofessional.  If you feel differently, feel free to comment.  If you see a reason that this plan would not work, feel free to comment.

We used to keep tropical saltwater fish. When getting a new fish, one important question that would inevitably come up would be how much space would it need. It amazed me to think that some fish, even in the wild, could be perfectly happy spending their whole lives patrolling one small rock. That was the extent of their universe. Each individual person, like each of those saltwater fish, lives in their own universe, each a different (but probably overlapping) subset of The Universe created by God.

In The Beginning

When you are born, your universe is very small – focused only on your mother’s breast – but starts to grow immediately. Every experience gives you a new plank you can use to expand your universe. As a new experience comes to you, your mind stretches to make sense of that experience. In a later article we can discuss how important a strong imagination is to discovering the truth (this may seem ironic), which is important for the growth of your universe, but I don’t yet understand how strong imaginations are developed. Other attributes are also required.

When Growth Starts To Slow

Growth may start to slow, however, once your universe is large enough so that a new plank can fit entirely within your existing universe. Since you didn’t have to stretch your universe to accommodate that plank, you may feel that no more growth is necessary and discard that plank. For example, in the story of the blind men and the elephant, which I embellished in The Blind Men And The Elephant, one scholar, “holding the tail, announced that an elephant was like a rope”. While their later behavior may lead you to question how scholarly they really were, a non-scholar would have been more likely to have declared that there are no elephants; what he was holding WAS a rope and he resented any efforts to try to fool him into believing otherwise. In this man’s mind, his universe was already sufficient to describe what he had experienced, and so he threw out the new plank. Once this happens, it takes larger and larger planks to keep up any growth.

When You Have Reached Your Limit

At some point your mind may start subconsciously throwing out old planks to make room for new. In my first career, I was at a field unit (from which everyone starts) and it was a common complaint about how clueless the people in the district office were about what was going on in “the real world”, based on the decisions that were passed down to us. And when someone in our unit was transferred to the district office, we took bets on how long it would take him/her to move to the dark side. The same thing happens when teachers with experience get transferred downtown, away from the classroom. One could argue that it was the people in the field, who had experienced only one small piece of the puzzle (or elephant, if you will), were the ones with the smaller universes and thus were unqualified to pass judgement, while the transferee, with more experience in a larger world was making decisions that would benefit the whole team. While that’s the way we would like to see it work, that doesn’t always happen. My father, who had to join a union to learn his trade, could see only the benefits of the unions at the time and was a strong believer. Once he became a contractor and had to deal with unions “from the other side of the fence”, he could see only the negative. Apparently his universe was not capable of stretching to accommodate both views. Sometimes the truth about elephants is too large to fit in anybody’s universe. When your universe stops stretching, it has reached its maximum capacity.

Then there are other people who are unwilling to stretch, and start throwing out new planks that don’t match or fit into a set of planks that they created themselves. Those people are known as bigots. It’s when they grab everybody around them and try to force the others into their resultingly smaller universe that things could get ugly. I think it’s a bad idea to voluntarily throw planks out of your universe at any time. Here’s why –

The Descent

At some point as you age, your universe will start to become less resilient and will try to shrink. The process begins well before your universe has reached its largest size, but from then on it’s all downhill. I think I’ve already started the slide. If you don’t keep actively trying to add new planks to slow the process, it may act like shrink-wrap, too soon becoming so tight around your body that everybody will be able to see just how small those private parts really are that you had bragged so much about for so long. When they start laughing, you won’t care that the shrink-wrap is now too tight for you to breathe.  I wrote this analogy specifically for men with bloated egos,

since this term is not in any medical journal or book on psychiatry, I will have to define it in a later post
(which may be my favorite target), but something analogous happens to all population groups.

Measuring Universes

While the size of one’s universe seems to be a far better metricD by which to judge a person than more common and more superficial traits like size, sex, or hair quality, measuring this parameter is not as easy as it sounds. Since you can only measure something that is completely inside your universe, you can only judge people whose universe is small enough to be completely contained within yours, which usually means a child or imbecile. Maybe you are perfectly happy to always be comparing yourself to morons, but eventually your friends are going to correctly conclude that “it must take one to know one”. If a person has any talent or experience that is not part of your universe, there is absolutely no way for you to tell how significant that talent is. If the common area between you and that other person is only a small part of your universe, it might be tempting to draw inferences unfavorable to that other person. But since again you don’t know how large his/her unshared universe might be, your conclusions would be completely unsupported (It is entirely possible that their unshared universe could be larger than yours), but it would give evidence to any counterclaim that it is you who is the idiot.

A less common but more important question may be how to measure the size of your own universe. Sure, you can get from one side of your universe to the other, but what can you compare it to? Maybe you are like that little fish I mentioned at the beginning of this article, perfectly happy patrolling your own little rock while others swim in and out of your life on their way through. How do you know you are not missing out on something worthwhile just over that next rock? How do you know that something big is not soon coming along the path that will annihilate your universe and the universes of everyone around you? I don’t have answers to these questions, but clues might be found in the answer to two other questions: “How often do you discover a plank that isn’t yet part of your universe?” and “How hard are you really looking?”.

The Glory Of Golf

Before I start, I suppose you should know that I’ve never played golf. I was introduced to the game in school and whacked a few balls around, but it never captured my interest. Back then I didn’t even consider it a sport, and the news that some places demand you use a cart to get from hole to hole just reinforced my argument. Although at this point in my life I may be willing to reconsider the physical requirements necessary to qualify as a sport in my world, that’s not why I’m here. I believe there are important life lessons in the game of golf and I’m amazed that so many golfers fail to apply these lessons to their everyday lives.

For Perfectionists

There are perfectionists who would like nothing better than to redo their tee shot if it doesn’t go in the hole. Many of them would never progress beyond the first stroke. A golf course for perfectionists might not have a Hole #2, just eighteen 1st holes so they could better accommodate the crowd. At some point, possibly some time after the lights go out in the evening, even these people would be forced to move on. The question is not whether there are MulligansD in real life – certainly there are plenty of opportunities to practice and hone one’s skills before being tested. The question is whether when the clock is running and it’s time to get things done, if you’d really want to take a do-over. I think you will find that when you are allowed to take advantage of your earlier efforts and take your second shot from wherever the first one stopped rolling, you will find your solution or end of your journey much faster.  In life, the well-known problem-solving strategy of “trial and error” is much more effective when you can take advantage of what you learned in your previous trials.

For The Typically Delusional

What’s not to like about that?

A Failure To Communicate? Oops, My Bad!

I’ve been pondering why I haven’t received a single comment yet, and while investigating I found that it was virtually impossible to leave a comment on this blog. Apparently I left a few crucial check boxes unchecked when setting up the blog and never went back to check it from a visitor’s perspective.  That wasn’t too bright. Now I fixed it.

Of course that doesn’t rule out the possibility that my subscribers and guests are just too polite (or shy) to say bad things about my writing. If that’s the case and you feel strongly about something I wrote, just leave a comment saying “I’m too polite to comment on the second sentence in the third paragraph” or something like that.  I’ll understand.

Another Clueless “Christian”?

Not long ago, on the Facebook page of an acquaintance, a discussion was brewing about the Pope having the audacity to say Donald Trump was not a Christian.

I won’t give you a link to the Facebook discussion, but here’s a New York Times article describing the Pope’s remarksA.
One person suggested the Ten Commandments were the true litmus testD of Christianity.  This week I read that The Donald’s favorite Bible verse is “an eye for an eye”A. There seems to be some sort of misunderstanding here. Were this a characteristic peculiar to Trump supporters I would probably have let it slide, but I’m concerned that it is indicative of a growing segment of the population who call themselves Christians, but are clearly clueless about the concept.

My Background

I don’t  consider myself any sort of theology expert.  I’ve even been rumored to have nodded off in the middle of a sermon or two, and am not even guaranteed to come to the same conclusions as our pastor when reading any particular passage.  On each of the few occasions I actually tried reading the Bible cover-to-cover, I was becalmed in one of the begat sections.

Although I’m not a Catholic, I have been impressed with the latest Pope; he didn’t just memorize verses, he actually seems to understand a Biblical concept or two.  In fact, he is so different in my view from his predecessors that I’m amazed he was actually elected (maybe it was Divine Intervention).

The point is you shouldn’t take my word for any of this.  Maybe you should just read the Book.  I’ll give references when I can.  But just beware the begats.

OK, if you must know, you can find some of them at Genesis 5:1 to end, Genesis 11:10 to end, Genesis 36:1 to end, . . . , Matthew 1:2 through 17, Luke 3:23 to end. This list is not exhaustive. Don’t say I didn’t warn you.

Bible Background

The way I understand it, the Bible has two parts; the first, called “The Old Testament” could be considered the prequel.  It includes the Jewish (who would prefer not to be called Christian) Torah, their most important text, and spans the period from the creation of the universe (now referred to as the “Big Bang”) up to, but not including the birth of Christ (from which the word “Christian” is derived), a.k.a. Jesus, a.k.a. all kinds of other titles. The New Testament is His story.

The Ten Commandments are in the Torah and therefore are in the Old Testament (Exodus 20:1–17D and then again in Deuteronomy 5:4–21D).  “An eye for an eye” has an even longer history. According to Wikipedia, the principle of “an eye for an eye” goes back to Babylonian LawA, where it was actually an attempt to limit any retaliation so that it wasn’t worse than the original offense.  In English, that means it represents the maximum allowed punishment, not the minimum required punishment (although that interpretation does not seem apparent to me in the language of the Bible).   The rule is repeated three times in the Old Testament (Exodus 21:24D, Leviticus 24:20D, Deuteronomy 19:21D).

The Problem

As I hinted before, the Old Testament does not define Christianity.  Christ (also known as Jesus) defines Christianity.  The Old Testament repeats principles that are shared with half of the (non-Christian) population of the middle east.  But we are in luck; Jesus did specifically address the “eye for an eye” idea.  In Matthew 5:38 through 42, He clearly states

38 “You have heard that it was said, ‘An eye for an eye and a tooth for a tooth.’ 39 But I tell you not to resist an evildoer. On the contrary, whoever slaps you on the right cheek, turn the other to him as well. 40 If anyone wants to sue you and take your shirt, let him have your coat as well. 41 And if anyone forces you to go one mile, go two with him. 42 Give to the person who asks you for something, and do not turn away from the person who wants to borrow something from you.”

(Is this where the Pope got his Communist streakA?)

But What Did Allah Say?

Since the “eye for an eye” idea seemed to be so pervasive, I decided to check one more reference: the Quran.   As far as I can tell, it is only mentioned once:

“And We wrote for them in it: a life for a life, an eye for an eye, a nose for a nose, an ear for an ear, a tooth for a tooth, and an equal wound for a wound; but whoever forgoes it in charity, it will serve as atonement for him. Those who do not rule according to what God revealed are the evildoers.”

I think this mirrors the sentiments of Jesus.  While doing research, I found another interesting story that may support this view:

“A man came to the Messenger of Allah with the killer of his relative.
The Prophet said: Pardon him.
But the man refused.
The Prophet said: Take the blood money.
But the man refused.
The Prophet said: Go and kill him, for you are like him.
So the man pardoned the criminal.”

Conclusions?

You can’t have your cake and eat it too.  If you are not going to follow the teachings of Jesus (the Communist), then you can’t continue to call yourself a Christian.

Sometimes I come away from an issue with more questions than answers.  In this case I’m wondering what Mr. Trump is really trying to say:

Is he, like the Babylonians, citing this rule as an upper limit on our retaliation?  And recognizing that since September 11, 2001 we have killed far more Muslims (over 100,000 in Iraq alone) than we lost in those terrorist attacks (under 3,000) and the Iraq war (around 4,400) combined,  is he suggesting we should end our war on terror?

Is the real reason he wants to bar Muslims from coming to America is that they make him look barbaric?

By quoting the Quran, I am not endorsing Islam; nor do I have any intention of converting to Islam.  For many of you “Christians”, however, it sounds like it might be a step up.

How America’s Cup Committee Stole Victory From Kiwis

The America’s Cup, a yacht race between a single defender and a single challenger and first run in 1851 by the Royal Yacht Squadron in England for a race around the Isle of Wight, is known as the oldest international sporting trophyA. The referenced Wikipedia article provides an excellent history of the contest, and notes that the Americans held the cup continuously from the first race until 1983, the longest winning streak in the history of sport. The cup was last contested in San Francisco in 2013, but this wasn’t your father’s America’s Cup. The vessels were now 72-foot catamarans (boats with two hulls) costing well over ten million dollars each with rigid “sails” and foils (short underwater wings) that lifted the entire hull out of the water. Their top speed was over 50 miles an hour, or about twice the wind speed. The whole race was held within sight of spectators ashore and instead of taking all day, as was customary, was required to be finished in less than forty minutes to fit snugly between commercials in a one-hour television format. The series also turned out to have one of the greatest comebacks in sports. Stu Woo of the Wall Street journal did an outstanding job of explaining that competitionA. Stu failed to mention a minor change in the rules that bought the American team just enough time to complete the changes necessary to turn things around.

The 2013 America’s Cup was originally billed as a best-of-seventeen seriesA. A Best-of-T series (where T represents the total number of games to be played and is always an odd number) is widely used in sports championships, although before September 2013 I had never heard of T being larger than seven. In English (for those of you who are not sports fans) it means that the two teams will compete exactly T times (for which we will use seventeen in the rest of our examples) and then count up the points to see who won. One team can declare themselves the winner and send everybody home early if they can accumulate more of a lead than the other team can overcome in the remainder of the seventeen games. In a simple world, meaning a world without ties (in those sports that allow them) or penalty points, that would be nine wins in a best-of-seventeen series (round up(17 ÷ 2)).  Yacht racing, as the references in the first paragraph suggested, is not a simple world.  Before the series started the American team was penalized two points for cheating in an earlier round of competition, meaning that their first two wins wouldn’t really count (except to keep points away from their competitor). And although the calendar continued to list seventeen races (with the caveat “if needed” as appropriate) well into the competitionD, all of the experts were still saying that it would take nine wins for the Kiwis to take home the trophy.  The truth is that after the seventeenth race had been sailed, if New Zealand had only eight wins, then the Americans would have won nine races (17 – 8 = 9), but would only have had seven points (9 – 2 = 7), meaning that New Zealand would have still taken home the trophy.  That is what a best-of-seventeen series really means. And, as you can see near the bottom of the Final Scorecard at the end of Stu Woo’s Wall Street Journal article, that is exactly what happened.  But just before New Zealand earned their eighth victory in Race 11, the race committee declared that because the American team’s penalty shouldn’t affect New Zealand, they would still need nine wins to take home the trophy.  Shortly thereafter Races 18 & 19 were added to the schedule. As we now know, thanks to a brilliant turn-around by the American sailors, New Zealand never got that ninth win; the American’s got that point in the nineteenth and final race. Competition doesn’t get any better than that. Had the Kiwis been able to count up to seventeen or had their English been good enough to understand the meaning of “best of seventeen races”, the ending of this story may have been completely different.

The Art Of Communication

I like the definition of communication given by www.businessdictionary.com that talks about a process of reaching mutual understanding, where participants not only exchange information but also create and share meaning. This is a process that obviously takes more than one person. That point was apparently lost on me as a child.  At that time, there were quite a few of my fellow (North) Americans that spoke Spanish in Southern California, and yet when it came time to choose a language to study in school, as required, and having a choice of Spanish, French, German, and possibly Italian and Japanese, I picked German because I wanted to be different.  I studied the language for six years and like to think I was decent at it, but then again, there were no Germans (to speak of) around to contradict me.  Many years have gone by and I can still count past twelve, but some might argue that I didn’t get the most bang for my educational buck.  Now I am surrounded by people in Southern Florida, some who have been visiting for over fifty years, who still have trouble with English and don’t understand why everybody here doesn’t just speak Spanish.  But I am not the only one who has struggled with the concept.

Several weeks ago I saw a gentleman walking down the street wearing a T-shirt with the following sign:

To translate, the first symbol is the square root of negative one, which technically doesn’t exist, but is more commonly represented by the small letter “i” as the basis for all imaginary numbers.  The second expression, two to the third power (2x2x2), reduces to eight.  The third, the capital Greek letter Sigma, is seldom seen alone because it represents the sum of the sequence that follows.  The last symbol is the small Greek letter Pi, which has come to be known as the most famous irrational (meaning it never ends and never repeats) constant – representing, among other things, the ratio of a circle’s circumference to its diameter.
The common name of each of these symbols resembles an unrelated English word, so the expression can be pronounced “I ate some pie”.   But what was the wearer really trying to say?  Mathematically, the expression is meaningless, so its sole purpose seems to be to announce to a select audience what was on his lunch menu.  Maybe the fewer the people who knew that he went off of his diet, the better, so this may be an attempt at a confession without guilt.  While that seemed harmless enough, it reminded me of another obscure message I had seen before.

While driving down the road ages ago, a Jeep passed me that had the following array of small international maritime signal flags displayed on its back window: Each of these flags, which are used by navies and merchant marines around the world, has a name taken from the phonetic alphabet.  Along the top row is Foxtrot, Uniform, Charlie, and Kilo.  On the second row sits Yankee, Oscar, and Uniform again.  Individually, each flag has a meaning (for example, Oscar means someone has fallen overboard), or in small groups they could represent short code words.  Sometimes they just represent the letter at the beginning of their name.