My Last Thoughts On Our Last Election

Well, the people have spoken!  And I’m really disappointed. I’ve previously expressed my displeasure with some of Mr. Trump’s positions and rhetoricB1, B2, B3, but my main complaint has always been his severe lack of maturity, his complete disregard for the truth,

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Candidate Truthfulness
Candidate Truthfulness

as read in the International Business Times.

and his extremely low ethical standards that allow him to push the buttons of idiots and fan the flames of bigotry for his own personal gain, which he regularly puts ahead of whatever action might be better for the good of the country.  Trying to understand why he was so popular, I listened to a lot of people, but found their arguments lacking in both fact
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For an article on the pervasivenessD of fake news, see Fake news: How a partying Macedonian teen earns thousands publishing lies. For a discussion of the truth in “news” and even Ben Franklin’s words on the subject, see Fair Play in a Fact-Challenged Political Landscape. This is why my blog post How We Lose Our Grip On Reality was important. The sad part for me was that some of the claims cited as justification of a Trump fanatic’s position were too blatantly false to need any rigorous fact-checking effort.
and logic.  Examples include those who insisted Clinton just couldn’t be trusted (in light of the above), and the gentleman who praised Trump’s lack of political experience and then 30 seconds later bashed Obama for the same characteristic.  It makes me wonder if my concerns for “Falling Into A Negative Spiral” have all come true.

But you won’t find me out protesting, because I don’t see the point to it. I understood the rules before the election (See Article II and the Twelfth Amendment to the Constitution of the United States) and thought they were as good as you’re likely to find anywhere.

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There is that one question about the fairness of the Electoral College and whether it has outlived its usefulness (which in today’s world I believe it has), but because in all cases where the Electoral College differed from the popular vote, the Democratic (or pre-Democratic) candidate lost the electionA as they appear to have done this year, I don’t see any serious efforts to change that process any time soon.

Some argue that the Electoral College was intended to favor smaller states. Certainly our founders pondered the issue of individual power vs. state power (resulting in the Senate giving states equality while the House of Representative tips the scale toward the individual). Personally, I like the notion of ‘one person, one vote’ without taking a penalty if you can actually wave to your neighbor from the front porch.

The news that many of the protesters didn’t vote was also disturbing; I’ve long maintained that if you don’t vote you waive all rights to complain about the election for the next four years.

A Growing Frustration

It has been said that Mr. Trump was able to tap into America’s growing frustration with the gridlock in Washington.  I can definitely understand such a frustration.  The problem is that for a majority of Americans, that frustration was self-inflicted.  I’m talking about the majority who four years ago voted for candidates with an R on their sleeve (and making no allowance for those who only do that so they can tell right from left) specifically because those candidates promised to rip the word “compromise” from their dictionary and vehemently oppose every move the opposition makes, even if it was originally their idea.  As one might expect, their candidates had some success, and now this majority is complaining that nothing gets done in Washington.  Really?  To me, that is strong evidence of the negative spiral I was concerned about.  I predict in four years these short-sighted people with shorter memories will be even more frustrated, and will make even more desperate decisions, speeding the downward spiral even more.  To see a discussion of one type of desperate decision-making and how to stop it, see my recent post When Sailors Should Split Tacks.  Sadly enough, like the skipper in that post, these people are incapable of recognizing their faulty logic or seeing their own part in this mess.   But as long as they have someone else to blame for their problems, I don’t expect to see much growth.  I’ve always liked to believe that whatever the results of an election, the people got what they deserve, but the truth is that the minority gets to suffer right alongside everyone else.  Those who took the right steps to make America great over the last decade also have reason to be frustrated.  Their frustration will be greater in another four years also, but they know that just waiting for others to mature won’t get the change they are looking for.  That knowledge alone does not make the frustration any less; they have to be mature enough to deal with it while they bide their time waiting for the next opportunity for improvement.

Wait And See

So that is what I’m doing.  Mr. Trump isn’t President yet so there is really nothing yet to complain about.  His lack of truthfulness, that characteristic that was the most bothersome during the campaign, is now the one thing that gives me the most hope in a strange way – if he only screws up one out of twelve of the things he promised to screw up, we should probably consider ourselves lucky.  Just hours after the election he praised Mrs. Clinton for her many virtues, which was 180 degrees off from everything he had said before then (English translation: “I’ve been feeding you all a line of cr@_ all this time.  Thanks for your vote”).  How many of his promises has he already walked away from, just weeks after the election?  There is the distinct possibility that some things could actually turn out reasonably well.  But there is still plenty of damage that can be done.  We need to bide our time and look for opportunities for growth.  To break the spiral, one thing I’d like to see is a strong, long-term commitment to education – an education that includes and even emphasizes critical thinking skills.  And as always, I’ll be doing my part to put things into perspective and combat “conventional” wisdom while promoting uncommon sense.  Thank you for listening.

When Sailors Should Split Tacks

American inventor Thomas Edison once said “Genius is one percent inspiration, ninety-nine percent perspiration”A.  From my experience, when you are competing, whether for business or pleasure, or trying to solve a problem, or just trying to get something done, you can usually do very well without that stroke of genius if during the remaining 99% of the time you can just keep from screwing up.

The Sailing Example

One summer when I was younger, I had the opportunity to race sailboats by donating the perspiration needed to handle the sails.  Since sailboats can’t sail directly into the wind, which is often exactly where you need to go, you must regularly choose which side of the wind is best, or which side of the course is best, or . . . the bottom line is that in sailboat racing, as in life, there are plenty of decision-making opportunities.  If we happened to get behind early in the race, by the time we got to a point that needed a decision, our competition had already gotten to that point and had already made their decision.  Our skipper, reasoning that we would never catch up if we did everything our competition had done, invariably would make the opposite choice at that point (hence, splitting tacks, or sailing on the opposite side of the wind as our competition).  More often than not we would get further behind.  As it turned out, we won almost no races that summer. Now I will use just a little math to show you why not.

The Math

Without divine intervention or that long-awaited flash of inspiration, after a short time the leaders in this race will be the ones that make more correct moment-by-moment decisions. When our skipper got to his decision point, it is reasonable to assume that the competition ahead of him is batting above 500D and already chose the short path. If the current leader has a success rate of, say 70%, then by blindly taking the other path, our skipper was limiting his success rate to 30%. This is NOT a winning strategy. The more prudent leader would have chosen his battles; he would have evaluated every decision independently – more often than not this means he would have made the same choice as his competitor (assuming his own success rate is high enough to be competitive – certainly higher than 50%)  – and he would bide his time while waiting for the competition to make their mistake. When his own evaluation led him to a different decision, he would quickly recheck his work (out of respect for his competitor’s 70% success rate) and then he would pounce.

A Non-sailing Example – Rush Hour Traffic

“Rush Hour”, referring to  those busy couple of hours in the morning and another couple of hours in the afternoon when everybody is commuting to or from work at the same time and traffic is congested (as opposed to that time of day when Rush Limbaugh is delivering his political commentary), implies an urban environment, which implies a larger grid of streets and thus a richness of decision-making opportunities not completely unlike a fleet of sailboats tacking upwind, but familiar to a much larger segment of the population.  Many of you may have carpooled with somebody with the mentality of the skipper described above: either there is some sort of accident or s/he misjudged traffic again and finds him/herself behind schedule and facing the growing possibility that they will be late for work.  Lacking patience or maturity, they assume the traffic must be better on one of the many alternative routes and blindly makes a turn (tacks) at the next intersection.  When they discover that this path is also blocked, they immediately move to Plan C, then D, and so forth.  Each maneuver has a small cost, which rapidly adds up, and then the path actually starts to get longer and they continue to dig themselves a deeper and deeper hole (oops, that’s not a sailing reference).  The math is similar to that above.  To mix metaphors even more, compare this to the hitter swinging too hard for a home run.  The problem is that in this game, after each errant swing the outfield fence is moved ten yards further away.  Although still mathematically possible (at first), the odds of that game-winning home run drop with every swing.  Those are the perils of panicking, shutting off your brain, closing your eyes, and trying to slug your way out of your problems.

The Moral

As you might have guessed, this article is not really about sailing, or traffic, or baseball. Blindly splitting tacks is a tactic of desperation.  Desperation is often a result of one’s fears getting the best of them, and may be one of the consequences of ignorance.  It is never expedient to shut off your brain to save time (by the same token, except for specially trained pilots in specially designed aircraft, nobody would willingly turn off an airplane’s engines while still in the air), yet people try it every day.  This is what happens when you panic.  So get a grip!  Just as in the sailing example, the prudent driver would carefully evaluate every decision (the more you practice, the easier it gets) instead of assuming the worst, bide your time, and make your bold move only when the conditions are right.

How We Lose Our Grip On Reality

After learning how to SCUBA dive while in high school years ago, my friends and I did most of our diving from the beach. The geography was fairly simple; from the beach the bottom had a gentle slope until reaching the (non-coral) reef of interest at a depth of around 30 feet a couple hundred yards offshore. Water visibility was typically 15 to 25 feet offshore, but could be less than five feet in the surf zone. After moving as fast as possible through the surf zone, we would regroup, sink to the bottom, and rely on our compass, backed up by our depth gauge, to find the most direct path (perpendicular to the beach) to our destination. Our depth gauge was supported by physical clues of our depth, like light intensity and even the spectrum of colors available.

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Of course light intensity drops steadily as one goes deeper, but also the colors disappear with depth, starting with the longer wavelengths (red)A.
 At the end of the dive we would return straight to the surface, which would put us still a few hundred yards from the beach.  We would inflate our life vests, as they were called back then,
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They are now known as BCDs.D.
roll over on our backs, and leisurely swim back to the beach as we caught our breath. It was quite common on this return trip to look back past your fins and either see the beach behind you, or see one of your friends swimming out to sea.

But you don’t need to be a diver to see how poorly we maintain a straight and narrow path.

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Any resemblance to Matthew 7:13 & 14D is purely coincidental. 😉
To do your own experiment, start in the middle of a large field, put a blindfold on and walk in a “straight” line, dropping numbered markers or flags or let out a rope as you walk (the last time I heard of anyone relying on the bread crumb trick, it didn’t turn out wellA.)  You should be able to take the blindfold off in less than a minute, look back at your path, and be happy nobody was watching.  The moral of this story is that without regular “reality checks”, one won’t be taking the shortest path to your destination, and probably shouldn’t expect to get there at all.  And so it is with life.

How To Maintain Your Grip On Reality

Make regular observations

Every nautical chart will tell you that “The prudent mariner will not rely solely on any single aid to navigation …”, which clearly means the same as that seventeenth-century proverb “Don’t put all of your eggs in one basket”. Failing to make regular observations is the simplest way to lose touch with reality.

Verify all information – “Google, don’t gossip”

If you don’t know the position or the reliability of the source, you can’t depend on it to find or even describe your own position.

Apply the same standards to all information

Don’t get all of your news from one source. Expect all sources to have some bias (that may not be clear). Politically, this means that you should not get more than 30% of your information from Rush Limbaugh or any lesser-known celebrity (regardless of political affiliation). Your sources should come from all around your horizon,

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Landmarks that are near each other may have similar positional biases, which will translate into errors in your own position estimate because using them will cause the errors to accumulate and negate any averaging or cancelling effect that you were hoping to get from independent sources.
and you should not treat the information that comes from one side of your vessel different from the information on the other side. Again, politically, you can’t demand higher standards from the other candidates than you expect from your favorite. This just exposes you as a bigot looking for excuses.

Don’t Throw Out Information Just Because It’s Unexpected Or Inconvenient

I’ve already discussed this in “How Large Is Your Universe”.  If you are doing this, stop calling yourself a scientist and expect others to call you a bigot. We’ve all seen bosses who surround themselves with sycophantsD (ass kissers) and ultimately drive their Rolls-Royce off Reality Road into a ditch (Not surprisingly, none of their entourageD helps pull them out.)  When scientists, whose job it is to describe reality, run across information that doesn’t support their theory they are forced to change their theory.  Of course there are the occasional outliers,

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For a simple explanation of outliers, see the “Math Is Fun” website. The last paragraph of the National Institute of Standards and Technology (N.I.S.T.) website discusses how to handle outliers.
which need to be handled carefully.  One clue to how far you’ve wandered from reality is the number of outliers you have to throw away.

And that is pretty much it.  It is simple enough, but requires constant effort.  If you think I left anything out, let me know.  Other comments are welcome and appreciated.  Now go apply this to your life.  Thanks for listening.

A Spokesperson For Hillary Clinton

I think Secretary Clinton could find somebody like Clara Peller (August 4, 1902 – August 11, 1987)A to go to all of Donald Trump’s events. She could have been in the front row at the last debate, and then whenever Mr. Trump failed to answer a question (which I believe was every time except the last question (I’ll leave the fact-checking to somebody else – I don’t think I could sit through that debate one more time)), or when Mr. Trump interrupted Ms. Clinton (which only happened 18 times, down from the 51 times he interrupted her in the first debateA), this Peller doppelgängerD would interrupt Mr. Trump with her signature line, “Where’s the beef?”  I don’t believe Donald would even realize that she is questioning the lack of substance in his conversation or in his Presidential policies; with his adolescent “locker room” mentality, Mr. Trump would assume this old woman was referring to one of his male body parts, and he would feel deeply offended.  And then as Mr. Trump walked by at the end of the event, this lady could assume an open, gropeable stance, with her arms outstretched, and maybe her lips all puckered up and ready.  She could wind up  becoming Donald’s worst nightmare.

For Trump’s other events, you would probably need a corps of such old lady hecklers, because each one would find herself uninvited after her first appearance.  In fact, they would probably need to go in groups or be escorted, because Donald’s rabid fans would not be above “taking them out”.  Donald himself is more likely to launch into a tirade, followed up at three o’clock the next morning with a volley of angry tweets.

Mrs. Clinton would probably take the advice of Michelle Obama, rather than mine.  I understand.  I’ve never believed that the victor in a race to the bottom could really be called a winner, anyway (What was the prize for the first man to get to Hell?).  But a representative like Clara could put Donald Trump’s tactics into better perspective, and would be entertaining.

Simple English: The Problem With The “If” Statement

You are probably very proud of your grasp of English (unless you live in South Florida, in which case you may not give a damn).  And yet I have seen plenty of people whose lack of understanding about basic structures like the “If” statement

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The next article in this series will discuss how misunderstandings about the conjunction “or” have caused so much trouble.
cause them to make terrible assumptions.

An Example

Suppose a young child is misbehaving to the point that the caregiving parent decrees “If you don’t knock that off, I’m going to paddle you” (This is an old example; I’m sure nobody would ever actually do that today 😉 ). As young children have been known to do, for whatever reason, the child continues with its behavior. The parent repeats the statement, with added emphasis. Nothing changes. The parent soon throws their hands up and says “wait until (your other parent) gets home”.

The parent’s first decree, like all “if” statements, had two parts; a condition and a consequence (joined by the conjunction “if”), with the understanding that if the condition is true, then the consequence will occur. It’s simple enough that even a young child can understand it. If the condition is met and the consequence is not accomplished, then the statement would be considered false. In short, the child knew that the parent was lying.

Now suppose the non-caregiving parent comes home, sees the objectionable behavior, makes a similar decree, and then the first parent points out that they had already made that decree to no avail. The child, for whatever reason, stops the objectionable behavior. To everybody’s surprise, the second parent paddles the child. Although the child and many of you listeners may think bad thoughts about this parent, one thing you can’t call him/her is a liar.

The Problem

As you can see here, the problem with the “if” statement is that is incomplete in the sense that it only addresses what happens when the condition is true, remaining completely silent to the possibility that the condition could be false.  This allows most people to make the assumption that if the condition is false, the opposite of the consequence must occur.  As the young child in our example learned, that assumption would be a mistake.

The Solution

Don’t make stupid assumptions.  As your lawyer would tell you, get it in writing.  In the above example, since the second parent didn’t make any promises about what would happen if the behavior did stop, s/he can’t be accused of lying.  If this example bothers you, I’m sure the second parent told the child afterward that the paddling was for not obeying the first parent, in which case we would be unable to judge the truthfulness of their claim until after the right set of conditions are met following some later episode of misbehavior (guesstimating any change in likelihood of that future misbehavior based on recent events  will be left as an exercise for the reader).  To lawyers, mathematicians, and the like, the parent’s explanation doesn’t matter to this case and is unnecessary.

P.S.

Logicians have named operators (or functions) fulfilling all sixteen patterns of truthfulness or falsehood of expressions based on the truthfulness or falsity of two variables, such as the condition and consequence of the “if” statement described above.  Engineers call the statement that yields the results you thought the “if” statement provided the “exclusive nor” function, “nor” being short for not or, meaning “giving the opposite results than the ‘or’ function”.  Some refer to it as logical equality.  In English, it would be represented by a sentence including the phrase “If, and only if”, such as “I will ground you for the rest of your life if, and only if, you do not stop screaming this very second”.  If that type of statement had been the norm in this household, the non-caregiving parent, upon hearing the lack of results achieved by the other parent, was still free to add other (most likely “or”) clauses (to be discussed in a later article) to his/her decree.   If you are now totally confused, please do not sign any document containing more than six words before consulting an attorney, or at least a mathematician.  On second thought, in cases like this, I would stick with the lawyer.

Save Your Birthday – Vote For Clinton

When I was growing up, birth was considered a significant event.  When a girl got pregnant, it wasn’t assumed that the fetus would have a normal, uneventful life as it grew, got an education and a good  job,  got married, created their own group of fetuses, contributed to society for several decades, and then had a long, fulfilling retirement.  In fact, for two of the three parties involved in the process, birth can be very traumatic.  According to one articleA, 60 to 80% of all naturally conceived embryos never make that milestone.  And of those who did make it, I don’t know of a single one of you that didn’t do a lot of crying about it.  Similarly, in 2015 over 300,000 women died during pregnancy or childbirthA. In the United States, 18.5 women die for every 100,000 birthsA. That is twice the rate of Saudi Arabia, three times that of the United Kingdom, and (strangely enough) 250% as many as died in this country in 1987 (yes, the problem is actually getting worse here).  In my mind, this is something we should be concerned about.

And then there’s the dad (or shall we say “sperm donor”).  Of the two events, the conception is the only one he has to show up for, and for many (mostly Republican) men in Congress, it is apparently the only one that has any meaning – probably the only one he brags about or bothers to put on his calendar (and to save time and space, I’m guessing he doesn’t even bother to jot down the mother’s name).  Some legislators have tried to pass laws making the mother personally responsible for everything that happens after that point.  I’m surprised that they haven’t passed a law replacing your birth date with the date of conception on your driver’s license and all other official documents (Oops! sorry, my bad; it just occurred to me that the reason they haven’t done that yet is probably only because they haven’t thought of it.  The good news is that nobody reads this blog anyway, so we are probably safe for now).

Call To Action?

If you are proud of your birthday, well actually the picture doesn’t look that rosy.  The nineteenth amendment to the Constitution, allowing women the right to vote, was ratified 96 years ago and what a waste of time that was.  Their major failures during my lifetime have been the Equal Rights Amendment (E.R.A.), the Hyde AmendmentD – which says the government can only spend money on men’s health issues, not women’s (OK, I’m paraphrasing (maybe even exaggerating) here), and most recently any law that says women will get the same pay as men for the same work.  Are my biases causing me to miss anything?  Help me out, because I can’t think of a single success they can point to (if you remind me of such a success, I will publish it).  I’m really afraid that until women finally grow the balls to exercise their rights, we are all screwed.  Is that how you see it?  Back in the late 1970’s I had a notion that the National Organization for Women (N.O.W. – which is now 50 years old) was apparently not the right group to lead the charge on the E.R.A.  My thinking was that maybe a men’s group with a name like “Fathers Without Sons” (or something with a nicer acronym) would be required to really get the balls rolling.  Is that really what’s needed to protect us?  Somebody please step up to the plate.  In the mean time, the rest of you could start small with a vote for Senator Clinton for President next time you get a chance.  Thank you.

The Blue-spotted Monks Revisited

If you are not aware of the Blue-spotted Monk problem, or haven’t seen my previous post (in which I made an error in logic), please visit The Problem Of Blue-spotted Monks.

Did you ever wonder what would happen if, as a cruel joke, it had been reported to the monks that one of them had the dreaded blue spot disease when in fact nobody was afflicted? (Am I really the only one here with a slight sinister streak?) Since none of the monks saw a spot elsewhere, they would each assume it was them that was infected and the very first day all the monks would have started to gather at the exit station. One of them, as he approached, would notice that none of the others had a blue dot and would start to chuckle to himself, thinking “these clowns can’t even count”. The others, hearing him laugh, would look around for the first time (until then they were so sure of their logical talents that they hadn’t even bothered to check), and by the time he stopped laughing the rest would have disappeared into the forest. Then it would occur to him that maybe he didn’t have a spot either. When word got back to the Guru, the laugher would be expelled for violating the “no communication” rule, but it wouldn’t affect the solution because the other monks only counted the peers that had spots on their forehead and he was never missed.

Plan B (I named this scheme in honor of B, who first put things in perspective for me. If this plan turns out to be flawed, like the last, I take full responsibility.)

When answering nature’s call in the middle of the night a few days after accepting B’s explanation about why the monks had to start at zero, it struck me that since a monk was really only concerned with three possibilities in the number of blue spots anybody has seen, modulo arithmetic might give a way to synchronize everybody’s universe or get everybody on the same page, so to speak. Plan B calls for everyone to start counting not at zero, but at the last multiple of six. For example, the person who saw ten blue dots knows that there are either:

  1. ten afflicted, not including himself, which means there are ten people who see only nine spots.  Everybody else sees ten.
  2. On the other hand, if he is blue-spotted, there are ten others like him who see ten spots and everyone else sees eleven.

Those who see nine spots know that those who see eleven don’t really exist, and those that see eleven know that the nine-seeers don’t exist. The monk that sees ten must consider each of the other two cases, but not both at once.

Under Plan B he would start counting at six, as would the possible people who saw nine, and those potential people who saw eleven. If everyone knew to start at six, the nonexistent people who saw only six spots would be gone before the second day (we’ll discuss them again shortly), and since that won’t happen, the nonexistent people seeing seven spots will leave on Day 2, etc. Our guy knows he can sleep in until Day 4, when the really possible nine-spot sighters would be scheduled to leave. If he saw spots on Day 5, he would turn himself in and everybody else would live happily ever after.

Starting the inductive thinking process, the first six possibilities start counting at zero, just like the old days. We’ll call that their landmark. As the logic countdown continues past the next landmark (which would be six in this scheme), the hard thing for me was knowing who would start using it first, or even if it was possible to make the switch if that person needed to wait for the person ahead of him (who is still using the old landmark) to make his move. I had the hardest time reconciling the notion that you needed to wait for the people ahead of you with the notion that those people don’t exist.  It turns out the solution was easier than I imagined.

In Plan B, if the number of spots you see happens to be six (or any exact multiple thereof), your dilemma is that the possible person who sees five spots started counting at zero, and won’t budge until Day 6. The guy who sees seven spots will start counting at six, and is depending on you to leave now (Day 1) or else he’s lost. Go to the exit point on Day 1. If you are not infected, there will be a very large crowd heading for the exit with no spots on their head while six people with a spot sit comfortably at home. When you spot your peers, you will avoid the crowd and head home knowing that those six afflicted people will all leave on Day 6 as scheduled, and all is right with the world. If you do have the spot, there will be six others with spots heading out that day with you while everyone else waits patiently at home. When those who originally saw seven spots wake the next morning, you will be gone and the problem will be solved.

What Next?

Lately this problem has turned into an on-again-off-again obsession for me. I first saw a different version of the problem when I was much, much younger; I didn’t figure it out for myself but the answer made perfect sense. Just a few weeks ago, I ran across the spotted monk version I discussed in my last post and again, when reading the answer, I was completely satisfied (although I felt for the commenters who couldn’t accept that it would take 100 days for 100 blue-spotted monks to turn themselves in). Days later, while on a walk contemplating even more difficult (but unrelated) relationship issues, an answer just came to me out of the blue, which is the answer I last posted. It was flawed, and when B. gave his “parallel universe” explanation for why we needed to start at zero, I thought it made even more sense than the conventional answer did, and I was again happy.  Several days after that, the modular arithmetic idea just came to me (as discussed). Then it was only my day job and other commitments that slowed me from working toward this solution. But we are not actually finished yet.

Calling All Logicians

All I’ve done so far (if I got it right this time) is to show that starting at zero is not strictly necessary.  Plan B is not the only possible plan, however.  In fact, I doubt it is the best or fastest plan (I suspect that using a smaller modulus might be helpful).  For the monks to abandon zero as their global landmark there would have to be an understanding that there was a single, logically optimal plan to replace it.  Based on my difficulties wrapping my mind around the issues so far, I don’t feel I qualify for the “perfect logicians” requirementA of this monastery.  It’s just as well; as an aging curmudgeon, that vow of silence probably wouldn’t have worked for me for very much longer anyway.  I’m hoping that the real experts will take it from here and God will finally allow me to let go of this problem.  If you do see a flaw in this scheme (a check of the references will show it would not be my first mistake on this problem), let me know. I may not be able to fix it, but in keeping with journalistic standards, I am willing to admit and advertise the error. Thank you.

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.

Start With Induction

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.

To see the Note click here.To hide the Note click here.
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.