Collatz Conjecture, or the 3n+1 Conjecture

I randomly remembered this interesting idea (I didn't want to call it a problem, because readers would think it needs to be solved immediately, or that it is like math homework, or something; it's not that sort of problem at all!) back from when my daughter was in Middle School.  She had just been admitted to what we used to call special activities in our school district, and was really a Title IX program.  We were invited to a seminar at Marywood University, for students and parents entering into special activities, just to show us something different and interesting.  Since then, being in the mathematics racket myself, I have come across it many times.  There are explanations for those who aren't math specialists, but I felt they weren't clear enough, so I'm going to try. 

The Process

The idea is to put a number into a routine calculation; then the number that comes out is put through the same calculation, and the result of that calculation is subjected to the same procedure, until the result is 1.

Are we going to get 1 sooner or later??  This is the million dollar question!  Every number they've started with so far has ended up yielding a 1, and computers have repeatedly subjected every number less than—I don't know, some huge number—to this process, and sooner or later, they do end up at 1.  But this does not mean that no matter with which number you start, you will always end with 1.

 I forgot to explain the calculation!  It's actually very simple. 

Take any number.  (A) If it is even, divide it by 2.  (B) If it is odd, multiply it by 3, and add 1.  That's the whole thing. 

We demonstrate with 5 and 6.  With 5, which is odd, multiply by 3 (which gives 15), and add 1 (which gives 16).  So the calculation always gives an even number of you start with an odd number. 

With 6, which is even, you divide by 2, which gives 3.

An interesting side issue is: how many steps does it take, for any number to get to 1?  One article, at code, a website in France, evidently, has set out this information in a clever way; it is at https://www.dcode.fr/collatz-conjecture

At the bottom of that page is a table.  Along the left of the table—the first column of the table—are the numbers 1, 2, 3, and so on. 

The next box contains all the numbers that end up at 1 in a single step, and that would just be the number 2.

In the second row, the box at the left contains 2.  The box on the right contains all the numbers that lead to 1, in two steps.  One such number is 4, and that's the only one. 

Here is the first eight rows of the table:

I'm going to stop here, and read it carefully, to see whether I can make it more readable by tinkering with the post.

Caitlin Clark

Thefirst time I saw Caitlin Clark, I got a very strong impression that she was unspoiled.  I got the impression that she cared about basketball, cared about her teammates, and hardly at all about the cameras. 

But now they're making such an awful fuss about the young lady that I fear it isn't going to end well.  Very few people of high school age have the strength of character to resist this level of scrutiny.  It's sort of unavoidable; the Media has to make its money, and (to them) Caitlin Clark is the Golden Goose.  We can't expect them to have the delicacy of a psychologist; they're sports reporters, the roughest, crudest people there are.

Thoughts and prayers for CC; but the Flying Spaghetti Monster doesn't often listen to me. 

Arch

Kiri

Kiri was a good friend, who died recently.

My wife and I traveled to towns near Pittsburgh, to attend his Celebration of Life, put together by his family.  He left behind three devastated immediate family: two children, a son and a daughter; and an ex-wife.  Some of the circumstances of the breakup of the family--not to mention other complications---made the celebration arrangements particularly difficult, but the resulting event was really dignified, and warm, and I was happy to be there.  It impressed me so much, that I plan to use it as a model for when I do hand in my chips, and there will be an event---I don't want to call it a celebration, exactly; it's more likely to be a sigh of relief---and I don't want to make any of the surviving family have to use up any tiny bit of cash I might have left them for the purpose, especially if predatory lawyers have carved out large chunks of my estate under the guise of apportioning it fairly, or appropriately.  (Having a really good will is a good way to prevent a lot of the estate being squandered by legal expenses.)

My family and my friends are foodies; this means that a good feast will not go amiss.  Compared with the volume of food I would put away in my prime, what I can consume now is a mere nothing; so I would plan for something modest, but I'd bear in mind that the younger attendees---even those who never knew me personally---might have better appetites than the older ones.  A good variety of menu items is always a good thing; the criteria running through the heads of people could vary widely (Where can one get dinner in this area?  Will I---or the kids---mess up their clothes?  Will I look too ethnic, eating this stuff?  Will my breath smell of garlic?  Does this stuff give me gas?) and providing a variety is a good idea.

Nobody can be completely selfless; we all have times at which we want to take care of ourselves first.  But then our thoughts go to the spouse, the kids, the wider family that might rely on us during uncertain times.  (Don't forget that the Uncertain Times are caused by various unscrupulous parties looking out for themselves, whereas we expect them to have wider concerns: the legislatures, the businesses, the law, the lawyers.)  Some of us will take stronger steps to take care of these people than others of us; it's impossible to lay out what is proper.  In Kiri's case, I would think that he did better than the average guy.  In any case, it's impossible to have a complete idea of what was going through the mind of someone, who is now dead.

Our feelings about the deceased are strongest, and in some ways, most distorted, right after they die.  So it makes a lot of sense to delay a celebration for at least six months, as they did in Kiri's case.  The arrangements were announced in a graded way: first the date, then the rough location, then the details of the event.  The loved ones were polled for Kiri's favorite songs; photographs were collected; thoughts about Kiri were invited.

Bear in mind that the deceased takes on the nature of the elephant being described by the several blind men: he or she often ends up being an almost completely different person to each of his friends.  I often thought of Kiri as being tactful and polite, almost to a fault.  But it is entirely possible that he was an authoritarian to his family; we'd never know.  Kiri was a fun-loving guy; almost in an outsized way.  He'd look for experiences of the most outrageous kind, so I'd expect that he took his family through some of the most wild trips that were available to them!  (I, myself, was more modest in the choice of experiences.  But my only child---I hope she never reads this---has the genius of making the most mundane experience into something really huge, but she also has a poor memory, so that she has probably forgotten most of the fun things that we did.)

Let me close with an urgent plea to anyone who has elevated blood pressure: the consequences are impossible to know, and none of them are good.  Treatment is usually easy and inexpensive, so commit to preventive treatment when you can.

Arch

A Major Health Alert

I'm diabetic (Type 2), but I found that most of the things I have to worry about are things that everybody should worry about.  In the long run, high blood sugar (essentially the definition of Diabetes) affects almost all the body's systems: kidneys, heart, liver, nerves, circulation.  I was surprised when my primary care physician wanted to lower my blood pressure. 

"What does diabetes have to do with blood pressure?" I asked.  He didn't answer the question; he proceeded to check out all my systems, leaving me to figure it out.  (He knew my colleagues called me Dr. de Silva, and made a common mistake, assuming that I was a specialist in some obscure health field.)

Well, there's an article in the New York Times about high blood pressure; why it's important, why it's often undiagnosed, and why (even when diagnosed) it goes untreated.

In 1999, I had visited my hometown, to celebrate my parents' 50th anniversary.  The enormous pile of medication I was carrying with me was mostly intact, except for my blood pressure medication.  It had sort of exploded!  (It's a phenomenon called efflorescence, where some substances abandon their crystalline nature and revert to a powder, when exposed to high humidity.)

When I told my brother, I got dragged around to my brother's PCP*, who agreed to see me as a matter of courtesy for my brother.  I explained about the misbehaving pills, and he got very serious.  "Can't play around with blood pressure," he said, and immediately prescribed an equivalent drug, stabilized for the tropics, and dug out a single dose for me to take immediately.  The point of that anecdote was to illustrate how seriously doctors take blood pressure; it could lead to stroke or death without warning.  [*Primary care physician.]

I'm still not one of those doctors, but I'm picking up bits and pieces here and there.  Blood pressure control is a big deal.  Once you are put on it (usually because you really, really need it), you don't want to unilaterally decide to go off it.  Fortunately, some of the most effective maintenance drugs now cost hardly anything. 

Why does high blood pressure matter so much?

1. If you have a potential aneurism in your brain, it could pop.  A good friend of mine was resisting going on BP medication.  He went to a conference in New Orleans, and died of an aneurism.  Any shock could kill you. 

2. The higher your BP, the harder your heart has to work.  All the time.  It just ages your heart more than it's supposed to age; you might be 50 years old, with an effectively 60 year old heart. 

3. The higher your blood pressure, the harder your kidneys work.  This is particularly bad for diabetics, because either diabetes, or diabetes medication, puts a load on your kidneys.  (There is some belief that heavy use of Tylenol will also be a burden on your kidneys.)

I'm sure I knew of other reasons to have your blood pressure screened regularly, but I have forgotten.  Until a better plan emerges, once you get on BP medication, just stay on it.  It's not expensive, and giving it up is dangerous.

 Archimedes.

Classic Putdowns

In the culture I come from, a lot of humor is of the putdown variety.  This morning, I realized that a lot of this comes to us from witty people who have been admired for a century!

This was posted in Facebook, a compilation ɓy Erika Hackett.

These sayings/insults are incredible gems from an era before the English language got boiled down to 4-letter words! I hope you delight in them as much as I have. 😅♥️

1. "He had delusions of  adequacy.” Walter Kerr
 2. "He has all the virtues I dislike and none of the vices I admire.”- Winston Churchill
3. "I have never killed a man, but I have read many obituaries with great pleasure. - Clarence Darrow
4. "He has never been known to use a word that might send a reader to the dictionary.”-William Faulkner (about Ernest Hemingway)
5. "Poor Faulkner. Does he really think big emotions come from big words?"- Ernest Hemingway (about William Faulkner)
6. "Thank you for sending me a copy of your book; I'll waste no time reading it.” - Moses Hadas
7. "I didn't attend the funeral, but I sent a nice letter saying I approved of it.” - Mark Twain
8. "He has no enemies, but is intensely disliked by his friends.” - Oscar Wilde
 9. "I am enclosing two tickets to the first night of my new play; bring a friend, if you have one.”   -George Bernard Shaw to Winston Churchill
10. "Cannot possibly attend first night, will attend second... if there is one.” - Winston Churchill, in response
11. "I feel so miserable without you; it's almost like having you here” - Stephen Bishop
12. "He is a self-made man and worships his creator.” - John Bright
13. "I've just learned about his illness. Let's hope it's nothing trivial.” - Irvin S. Cobb
 14. "He is not only dull himself; he is the cause of dullness in others.” - Samuel Johnson
 15. "He is simply a shiver looking for a spine to run up. -  Paul Keating
16. "He loves nature in spite of what it did to him.” - Forrest Tucker
17.  "Why do you sit there looking like an envelope without any address on it?” - Mark Twain
18. "His mother should have thrown him away and kept the stork.” - Mae West
19. "Some cause happiness wherever they go; others, whenever they go.” - Oscar Wilde
20. "He uses statistics as a drunken man uses lamp-posts... for support rather than illumination.” - Andrew Lang (1844-1912)
21. "He has Van Gogh's ear for music.” - Billy Wilder
22. "I've had a perfectly wonderful evening. But I'm afraid this wasn't it.” - Groucho Marx
23. The exchange between Winston Churchill & Lady Astor: She said, "If you were my husband I'd give you poison." He said, "If you were my wife, I'd drink it."
24. "He can compress the most words into the smallest idea of any man I know." - Abraham Lincoln
25. "There's nothing wrong with you that reincarnation won't cure." -- Jack E.  Leonard
26. "They never open their mouths without subtracting from the sum of human knowledge." --  Thomas Brackett Reed
27. "He inherited some good instincts from his Quaker forebears, but by diligent hard work, he overcame them." -- James Reston (about Richard Nixon) —Robert L Truesdel

Conservatism in Celebrity Women

In the absence of other information, we have to assume that the political inclination of any person is a considered choice, based on objective and reasonable choices.  But my prejudices urge me away from this belief.  I've expected that women tend to be more progressive in their thinking, I thought, because they have greater frustration with poverty in others, regardless of the race or the social class of the person.  Men, for decades, earned the money for the family (and whipped on their employees to greater efforts) and paid the taxes, and—it would seem, at least to fellow affluent men—were reasonably frustrated with low-earning, or even unemployed men.  And furious at having to pay taxes. 

Many of the celebrity women I have admired seem to be conservatives.  Why is this?  Ginger Rogers was the first one I noticed; and I believe, so was Debbie Reynolds.  Jane Fonda has been a progressive for decades, so has Lily Tomlin, and Susan Sarandon, bless her!  But, keeping informal statistics, the celebrity women—obviously, not those themselves running for election, or we'll get confused with all these Bobert's, Taylor-Confused-Greens, and other witless admirers left over from Trump's of glamorous days running about—seem to outnumber the progressives.

What is it about the lives celebrity women lead that seems to encourage conservatism?

Arch