The Mysteries and Magic of Mathematics
In 10 days I’ll turn 77. My wife warns me that it’s unwise to reveal such an advanced age to the world, age discrimination being as rampant as it undeniably is. While acknowledging her point, I can’t help but feel a modest sense of achievement in having made it this far. “Life is short” is an overworked and ill-considered cliche. The simple fact is that, when I look back to my earliest memories, they seem to have occurred eons ago. Frankly, I can’t recall a time when I wasn’t alive. So… while the days and weeks do indeed seem to fly by, the sum total of my life seems to me to have been very long indeed.
Whether a double “7” proves to be my lucky number is another matter. Thus far 2024 has not been an auspicious year for Joanne and me. I won’t bore you with the details. Suffice to say that we’ve had a strong dose of the harsh medicine known as “old age.” On the other hand, I have gotten out two new books this year… hardly compensation for the health issues we have been wrestling, but not too shabby all the same. I feel lucky about them.
So far as I know, numbers have always been associated with luck, fortune, and magic. One of the most infamous of magical numbers if “666.” In “The Omen,” Damien —- the devil’s son —- had it emblazoned on his scalp. I shared poor old Gregory Peck’s consternation, when he poked around in his sleeping son’s hair and found the ominous (thus “The Omen’; get it?) three digits. Wikipedia tells me, “The common suggestion is that because seven is a number of ‘completeness’ and is associated with the divine,* six is ‘incomplete’, and the three sixes are ‘inherently incomplete’. The number is therefore suggestive that the Dragon and his beasts are profoundly deficient.” Wikipedia devotes an astonishing amount of space to “666”. Theories about the origin of its dastardly significance apparently abound. The Romans, the Egyptians, and whoever wrote the Bible’s Book of Revelation all figure into it. (*”On the seventh day He rested.” Well earned, the Book of Genesis might have added, considering the size of the universe.)
Since my middle name is Ottavio, I’ve always been partial to “8”. My old man was the 8th of 16 kids. His parents named him “number eight.” Later, his big sister —- my Aunt Jenny, rest her soul —- christened dad “James,” the better to shield him from anti-Italian prejudice, when she took him to his first day of school. I was James Ottavio Junior up until pop retired and I got a look at his birth certificate. Then I dropped the “junior.” In a lovely little movie, the name of which entirely escapes me, Stanley Tucci plays “Primo,” the maitre d of an Italian restaurant, where his brother is the chef. The chef is Secundo. What’s in a name, you ask? Just about everything about the brothers’ relationship, as it turns out.
Really, really big numbers have always fascinated me. Here’s something I published back in 2020 (doesn’t that seem like a lifetime ago? Life if short? Hah!) on the front end of the COVID 19 pandemic:
The Tyranny of Large Numbers and the Prospects for Fall 2020
By Jim Castagnera, JD, PhD
Friedrich Engels observed, “[W]e have seen that, for the most part, the many individual wills active in history produce quite different results from those they intended --- results often, in fact, quite the opposite; so that in relation to the total result, their motives are also of only secondary significance.” (Ludwig Feuerbach and the Outcome of German Classical Philosophy, 1886)
We humans fancy ourselves as having free will. And, this may be so. For example, my wife and I decided to have two children. Others have decided upon larger families, perhaps to ensure the survival of an heir to their farm, or for their care and comfort in old age, or because their religion prescribes proliferation. Who decided that the human population in 2020 should be 7.8 billion and still growing? (https://www.worldometers.info/world-population/) The answer: no one.
Some national governments --- notably the People’s Republic of China--- have taken steps to slow population growth within their territorial boundaries. Nonetheless, the United Nations predicts a population of 11.2 billion by 2100. And what is that organization’s policy with regard to this prospect? “The UN Population Fund (UNFPA) started operations in 1969 to assume a leading role within the UN system in promoting population programmes, based on the human right of individuals and couples to freely determine the size of their families.” (https://www.un.org/en/sections/issues-depth/population/index.html)
In other words, something like 3.9 billion (7.8 / 2) individual acts of free will aggregate to produce an outcome not planned, or even desired, by anyone. It’s questionable whether we could do anything about this. The reason is the tyranny of large numbers.
“In the field of statistical physics we talk about the tyranny of large numbers. For example: I flip a coin three times, I wouldn't be surprised to get three heads. In fact I will get three heads one out of eight times I try it. But if I flip a coin a million times, I'm virtually certain to get 50 percent heads and 50 percent tails. The larger the population, the more consistently average is its behavior. Large numbers hold us in an iron hand.” (John H. Lienhard, “The Tyranny of Large Numbers,” accessed at https://uh.edu/engines/epi1215.htm)
In other words, the aggregate of billions of individual decisions --- coin flips --- is an outcome that is beyond the control of those doing the flipping, even if it may be predictable.
Engels and Marx sought to discover the laws of history, which might be counted on to shape human destiny. Building on the work of historians from Michelet to Hegal (especially Hegel) --- scholars who believed that the agglomeration of facts would reveal laws, analogous to the laws discovered by the “hard” sciences --- Marx and Engels labored to demonstrate that a dialectic would produce a predictable (and for them, desirable) outcome: the triumph of the proletariat. Leaders might impede or accelerate the process. But the tyranny of large numbers ensured that, sooner or later, the predicted end point would be reached by the human race.
Marx and Engels got that one wrong. Gathering massive amounts of data doesn’t always seem to result in an accurate prediction of the future. Maybe it’s that there are too many variables in human affairs.
But what about viruses? I’m no scientist. But let me offer a few thoughts anyway.
The Tyranny of Large Numbers and a Pandemic
Viruses are the most abundant biological entities on our planet. How abundant? Ten to the thirty-first power is a figure thrown around by cell biologists. (http://book.bionumbers.org/how-big-are-viruses/) If it’s fair to say that the speed of evolution is impacted by the number of individuals involved, then we have a working explanation for why, year after year, influenza infects millions of people, despite flu vaccines and natural immunities. (https://www.sciencenews.org/article/coronavirus-questions-covid19-symptoms-deaths-spread)
Less than two months ago, some knowledgeable commentators were still asking, “Is Our Fight Against Coronavirus Worse Than the Disease?” (https://www.nytimes.com/2020/03/20/opinion/coronavirus-pandemic-social-distancing.html) The argument ran like this: Most cases of COVID-19 were relatively mild. Deaths were concentrated in the ranks of the aged and infirm. Herd immunity was the best defense.
Seven or eight weeks later, thousands of healthy young/middle-aged adults have succumbed to coronavirus in the U.S. {https://www.washingtonpost.com/health/2020/04/08/young-people-coronavirus-deaths/)
A number of theories are afoot to explain this. One is that “youthful immune systems can go into overdrive.” (https://www.washingtonpost.com/health/2020/04/08/young-people-coronavirus-deaths/) Another is that the virus is mutating. These theories aren’t mutually exclusive.
Some experts argue that, if COVID-19 follows the pattern of predecessors, it will mutate into a less virulent form. (https://www.nature.com/articles/s41564-020-0690-4) However, this is not always the case.
The Spanish Flu
When the Spanish Flu first appeared in March 1918, “it had all the hallmarks of a seasonal flu, albeit a highly contagious and virulent strain.” Hearing any ominous echoes in this statement? Then, lean your head down into history and listen harder. “While the global pandemic lasted for two years, the vast majority of deaths were packed into three especially cruel months in the fall of 1918. Historians now believe that the fatal severity of the Spanish flu’s ‘second wave’ was caused by a mutated virus spread by wartime troop movements.” (https://www.history.com/news/spanish-flu-second-wave-resurgence)
The tyranny of large numbers ensures that COVID-19 will evolve. It has no choice. It will evolve in many places, under many conditions. What are the chances that in some places it will take the more virulent route, following in the footsteps of the Spanish Flu?
Combine this possibility with memories of how deadly the autumn-1918 version of the Spanish Flu was:
“From September through November of 1918, the death rate from the Spanish flu skyrocketed. In the United States alone, 195,000 Americans died from the Spanish flu in just the month of October. And unlike a normal seasonal flu, which mostly claims victims among the very young and very old, the second wave of the Spanish flu exhibited what’s called a ‘W curve’—high numbers of deaths among the young and old, but also a huge spike in the middle composed of otherwise healthy 25- to 35-year-olds in the prime of their life.” (https://www.history.com/news/spanish-flu-second-wave-resurgence)
As noted above, we are seeing this phenomenon --- healthy young immune systems in overdrive --- already. What’s more, the returning troops, crowded onto ships and then dispersing among the population, often with a massive parade, put paid to social distancing. This begs the question: should we be “opening America” just now?
If past is prelude, what should we plan for?
It seems to me that the only prudent course of conduct, on both the national and international fronts in what is being called a war on COVID-19, is that the “generals,” in fact all of us, should be planning for a reprise of the autumn of 1918.
If our enemy is the tyrant of large numbers, then the odds seem to me at least 50-50 for an assault more aggressive and deadly than the one we are defending against, quite literally, in our bunkers right now.
We have several advantages over our ancestors of a century past. We have superior medical knowledge, technology and care. And we have advance intelligence of the enemy’s possible next move. The trillion-dollar question is, “Will we exploit these advantages, or will we emerge from our bunkers and assume the war is over and won?”
***
Well, we dodged a bullet, where COVID 19 was concerned. Yeh, it’s still with us as I write this. But its current rendition is more seasonal-flu-like than Bubonic Plague-ish. As with flu, the new Covid season has brought a new, redesigned vaccine.
As for the tyranny of large numbers… well, that doesn’t seem to concern anybody. The Chinese government has changed course 180 degrees, currently encouraging the good citizens of the People’s Republic to pump out more kids, like pronto. Meanwhile, in the Southwestern United States, real estate development proceeds apace, never mind record high temperatures for record numbers of days and gradually diminishing water resources.
When will the Southwest’s number be “UP”? Who knows? Maybe never. The folks out there may get lucky. Or maybe the magic of that area of human endeavor we call science will come to their, and our groaning planet’s, rescue. To quote Arthur C. Clarke (he of “2001:a Space Odyssey” fame): “Any sufficiently advanced technology is indistinguishable from magic."
Yup, the numbers are in the science and the magic is in the numbers. So maybe… just maybe.
