One of my best math problems

 My father, Morris Sherman,  died in 1989 -- 85 days after his 74th birthday. He died in less than one day from internal bleeding caused by an aneurism. He was active and healthy and enjoying life until he had one bad day. There are worse ways for a life to end.

During my father's last four years, I was in a detour in my career. Music programs were shrinking in NYC public high schools. To stabilize my employment, I did what I had to do to get certified and began a 12 year long exile from music education as a math teacher. 

My father began his life as a smart little guy who started high school when he was 12 years old because his elementary school skipped him ahead a grade two times. He was a bit of a numbers nerd. I entertained him with birthday cards I made up that pointed out some interesting properties of the number of the birthday he was reaching each year. 

On Morris' 73rd birthday, my card pointed out that 73 was part of a twin prime, and very likely to be the last twin prime number birthday he would live to see. The next twin primes after 71-73 are 101-103. 

Brave reader, indulge me now in digression. 101, 103, 107, and 109 are all prime numbers. This is the first occurrence of a double-twin prime decade. A double-twin prime decade is one in which consecutive odd numbers ending with 1.3. 7. and 9 are all prime numbers. They are exceedingly rare. The next five double twin prime decades that occur after the first one begin with 191, 821, 1871, 2081, and 5651.

We will now proceed with the subject of this essay. Here is the math problem I wrote on the birthday card for my father's 74th birthday:

Pretty nifty. However, what I especially like about this problem is the first sentence. Without the first sentence, 47 would be another possible answer.

                                      (4 + 7)^2  - 74                      (4-7)^3 + 74

                                       11^2 - 74                             (-3)^3  + 74

                                       121 - 74 = 47                       -27 + 74 = 47

You see? 47 works BUT anyone who turned  47 in 1989 was born in 1942 and thus could not be a World War II veteran. Therefore the first sentence was necessary to make 74 the only possible answer.

Geriatric Report

It's January 27, 2025 and I haven't yet written a synopsis of my life in 2024 for wide distribution. When (or if) I do it will be full of good news. To sum it up in 3 words, life is good. I continue to enjoy (almost) perfect health. But if you keep a car long enough, you will eventually have to replace all the moving parts. That also applies our bodies.

At my last routine exam, my primary care physician, Dr. Helen May* referred me to an orthopedist because I complained of pain in my knees.

*footnote: Dr. May joins former major leaguers Pete Rose and Rick Waits in that small group of people whose names are complete sentences. Len, I just recalled that when you played string bass in the MIT Symphony Orchestra, they had a flutist who came over from Wellesley to play there whose name (no kidding) was April Showers. Overlooking for the moment, the cruel sense of humor displayed by her parents, I submit  April, who, if still alive, is in her late 70's, as another person whose name is a complete sentence. To push the malicious fun of April's parents a step further, just imagine that April married a Mr. Daily and that they imposed a hyphenated last name on their children. Oh my. But I digress.

 

So, in 2023, Dr. May referred me to a doctor who is an immigrant from [Jeopardy question] THE COUNTRY WITH THE WORLD'S LARGEST POPULATION.

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Did you say What is India? Good for you.  

So Dr. Sanjiv Bansal, sent me to a big Medical Imaging place for an MRI. He then sent me to his own x-ray technician in the basement of his office. (A building on Williamsburg Road in the Bronx that was formerly a funeral home.) He then told me I would probably need knee replacements. He also said that he used to do them, but found he was better off spending all his time seeing patients in his office and referring them to other surgeons when necessary. Finally he said he would try to fix my knees by non-surgical means and from then until today, I must have made and kept at least a dozen appointments. 

That was enough for me to have abundant flirting time with his receptionists. They really enjoyed my shtick. The receptionist Maggie is what I call an age-appropriate woman for me to jerk around for fun. I said "Maggie,  after my knees are repaired, will you be my partner for the Mambo Contest at Orchard Beach next summer?" Maggie smiled with delight and I thought she took my question seriously and was about to say "yes". Instead, she told me that in two weeks she's returning to Guatemala and is saying goodbye for good to the USA. All things considered, I don't blame her.

Each time I saw Dr. Bansal, he stuck hypodermic needles into my knees and withdrew syringes full of fluid which he squirted into his waste basket. Sometimes, he injected cortisone or some other med into my knees. When I went for my appointment with Dr. Bansal today, he threw up the white flag and wrote me a referral to an orthopedic surgeon at Montefiore Hospital named Carlos Alvarez . Bansal told me that Dr. Alvarez does at least 5 knee replacements a week.

Later today, I called Dr. Alvarez's number and spoke to Millie, whom I look forward to meeting. I made an appointment for a preliminary examination and consultation with Dr. A on Valentines Day. (I'm tempted. But I'll refrain from bringing Millie a box of chocolates. That may be pushing my shtick a little over the top.) After the consultation, I presume, I'll get an appointment for Dr. Alvarez to perform what squeamish people like to call the "procedure". It will be done only on my left knee. My right knee is, for now, not hurting.

 

Be patient, dear readers. I want to conclude this already overlong blog post with a commentary on the US Health Care System. Read on at your own risk.

 

As Senator Sanders often tells us, the US Health Care system is by far the world's highest in per capita cost. Yet we do not get anything close to the world's best health outcomes. The World Health Organization ranks the overall health of the US population 35th in the world. Some of the 34 countries ahead of us, such as France, Germany, Sweden, Japan, Canada) won't surprise you, but many others, (eg Cuba, Albania, Tunisia, Costa Rica) that are poorer countries with much lower health care spending than the US, have healthier populations.

Consider my case as an example. I saw Dr. May once, Dr. Bansal 12 times, and I will see Dr. Alvarez two or three times followed by some post surgery physical therapy. For each encounter I make a $15 copayment on arrival. Then, Medicare and Aetna from whom I have supplemental coverage pay more than 10 times my copayment for each service date. Was it all necessary? Of course not. Bansal knew from the start I needed the knee replacement. But if he referred me after one visit, how would he cover the overhead costs of his office in a three story building with 10 or more staff people to pay salaries to? He has to pad his insurance claims. All doctors in private practice do. It's built in institutional waste and it is not serving us well.

The solution is obvious. To provide an entire population with their basic necessities, they all must be removed from the for-profit sector of the economy. Our taxes provide us with police and fire protection, a huge military, a sanitation department to collect our garbage, a water supply system that magically disposes of every poop we flush down. And don't forget free public education from kingertgarten through 12th grade. We have free public parks and libraries. That and more is paid for by our taxes. Some people complain about taxes and sure, a lot of tax money is wasted. But we mustn't forget the essentials that we get from tax-financed services. 

Digression alert . You may skip the following paragraph. 

Homeowners do get a water bill. The bills seem too low to me. Considering the absolute necessity of water, we should pay much more for it. The bill should be high enough to make people consider letting urine accumulate under a closed toilet seat and only flushing after a poop. And the water bill should be high enough to discourage people who take half hour long hot showers. Imagine how much water those two changes in behavior would save. As it is, people shower for as long and flush toilets as often as they like and never give a moment's thought to water conservation.

The basic human necessities that are still in the for-profit sector of the economy are health care, housing, and food. As a result we either see (or avert our gaze from) people who are sick, homeless, and malnourished. As a nation we can easily collect enough tax money from rich people to guarantee all of the necessities  to everyone and compensate doctors with appropriate salaries and benefits from the taxes on wealthy people. 

Pope Francis once said that being a billionaire is inherently immoral. I agree. Imagine a 100% wealth tax on all assets over a billion dollars. I think every billionaire could learn to manage to live fairly well after being left with only $999,000,000 to live on. Oh my. I sound like Bernie Sanders.

That's enough for tonight. If you're still with me, thanks for your patience, dear reader.

Geriatric-Joe