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COVID-19: Logarithms Hold the Key

By Shlomo Maital

Warning: This blog could be harmful to your health…because it’s about… logarithms. (Logs). And plague. What in the world?

Well, let’s give it a shot. Nothing to lose.

A logarithm is a number, such that when its ‘base’ (usually, the number ten, or the number ‘e’, 2.71828 (we do NOT have to go into the black depths of THAT number), is raised to the value of the log, you get the value of your starting number, x.

For instance, 102 = 100. So the logarithm of 100 (using the ‘base’ of 10) is 2.


Why are logarithms useful? Well, they have fallen into massive disuse lately, because of computers and calculators. But once they were crucial. Because, suppose you need to multiply two big numbers. On paper. Ouch! But wait! If you knew the logarithms of the two numbers? Add them! Because? The value of by times bz equals bz+y so, we have converted multiplying (hard!) to addition (easy!).

Logarithms was publicly proposed by John Napier in 1614, an English mathematician. Generations of school children (like my mother) had to learn the secrets of logs.

But what has this to do with COVID-19. So – there is a wonderful magical property of logs. Suppose there is a key number that you are tracking. E.g., the number of people in your country or your city or community, who have COVID-19. You can graph it, look at it, inspect the curve, it is rising, OK, but – what does it mean?

So here is what John Napier would recommend, 400 years ago. Take the logarithm of the number. Graph THAT, not the number itself.

Why? Because – trust me on this — the gradient, (steepness, or slope) of the logarithm graph tells everything. If the slope of the log is RISING, then the RATE of increase is increasing. If the slope is getting less steep, FALLING, the rate of increase of COVID-19 is declining. And this is crucial, to know how we’re doing. And you CANNOT tell this is you graph the number itself.

So, here in Israel, the slope of the logarithm of the number infected with COVID-19 has been declining. Yay!   The rate of increase is declining. We’re getting toward the apex. It’s a ways off…but once we reach the top of THAT hill, the slope of the log will turn from positive to negative…and that’s a KEY point. Because that’s when the number infected begins to fall….cause of celebration.

Clear? Clear as mud? So here is a sample graph. This is the total number of cases outside China. On a log scale. You can see a constant slope – constant rate of growth, as the virus spreads. Reflecting, maybe, a very slow response in Europe and the US.

So – in your country or city, track the logarithm of the number of cases, and measure the slope. That tells you whether it is speeding up or slowing down.   I don’t think our political leaders are quite up to that difficult mental exercise.  

Find Meaning in Plague

By Shlomo Maital


   New York Times Op-Ed columnist David Brooks reminds us, today, that there is “moral meaning to plague”.   He quotes Victor Frankl, whose book Man’s Search for Meaning has influenced millions; in it Frankl describes how he survived the Holocaust death camps. He found meaning.

   How can each of us find meaning, in this plague epidemic?

   “Frankl saw three possible sources for meaning: in work (doing something significant), in love (caring for another person) and in courage during difficult times. Suffering in and of itself is meaningless; we give our suffering meaning by the way in which we respond to it.” (Wiki)

     Work. Love. Courage. Pretty straightforward.

     Work – we do what we normally do, only at home and online.   Amazing how adaptable many people are, in their work. Special kudos to moms (and dads), who also care for young children.

     Love. Care for others. Let’s follow a formula I find useful, that I have borrowed: When you wake, ask 2 questions: What shall I do for myself today? (If you are not happy, strong, healthy, fit, effective, it’s hard to help others). What shall I do for others today? And, when you fall asleep, ask, What did I do for myself today? And – what did I do for others today?

   Courage. This may involve facing danger, opposition, humiliation. What is going wrong, that you can see, understand, and try to fix, or at least bring attention to it?

   There IS meaning in this epidemic. I see it everywhere, everyone, every day. Let’s all work hard to find it and leverage it.



Meet Andrea Ray: Heroine

By Shlomo Maital

   In our pandemic crisis, there are a huge number of unsung everyday heroes. Truck drivers who continue to drive the long hauls, delivery people, supermarket workers, police, Israel’s Home Front soldiers….

   And, in particular, Andrea Ray, featured on Channel 12 this evening. Andrea was born in Venezuela and made Aliyah to Israel when she was 16. She studied hotel management and had a senior job in the Dan Hotels system.

   Israel has taken over some of the Dan Hotels in Tel Aviv, and brought those who have tested positive for COVID-19, especially those flown home from abroad, to hotels. The area housing these patients is of course strictly quarantined, and the hotel is run jointly by the Home Front soldiers and Dan management.

     Why is Andrea a hero?   Who will care for the corona patients? Seriously? Spend many hours of the day mingling with those ill with the deadly virus?  

     You cannot tell someone to do this. You can only ask for volunteers.

     And Andrea volunteered. This is what she does, every day, for hours and hours – cares for the needs of the patients, cheers them up, laughs with them, and brings them joy with her smile.  

     What if she falls ill? Well, I’ll get the virus and then I’ll get better, she says.

     So, you’ve met Andrea Ray, heroine.  Do you know other such heroes and heroines?

Leadership in the Time of Plague

By Shlomo Maital

New York State Governor Andrew M. Cuomo

   Even though I live in Israel, I find myself glued to the TV nightly, watching New York State Governor Andrew M. Cuomo’s addresses and press conferences on CNN. This is true of much of America, including President Trump, who schedules his own TV appearances in order not to conflict with Cuomo’s.

   As I watch Cuomo, I ask myself, what is leadership? What are the key qualities of political leaders, in the time of plague? Why is Cuomo’s leadership so effective, in contrast with Trump’s and other political leaders, including my own here in Israel?

   A few tentative answers. First, blunt honesty. Cuomo tells it like it is. His warnings carry weight and credibility. (Compare with, say, Trump, whose superlatives, great, terrific, perfect, ring hollow – remember, if a leader lies to us once, we will forever doubt ANYthing he or she says in future). Second, command. Cuomo has done his homework and he’s smart. He commands the numbers and the complexity of the situation and explains it clearly to people.   Third, compassion. Cuomo is a touch leader, pragmatic, hard-nosed. But when he talks about his mother Matilda, and saving her if needed, and saving all us old people, he shows empathy and sympathy. Leaders have that combination of toughness and soft compassion, used in every case where appropriate. Fourth, pragmatism. Use common sense, figure out what is needed, get it done, no excuses (the Singapore formula). Fifth, Speed. Forget platitudes, we need ventilators now, hospital beds now, masks now.   Look, New York State is not Trump’s favorite. We suspect he has withheld ventilators from the nation’s strategic stockpile. New York State prosecuted Trump’s so-called charity foundation. But Cuomo has not libeled or criticized Trump by name – only Federal agencies – and it has paid off. So leaders know how to pick their enemies, with care.

I want to share an approach I’ve found useful, for myself. I’m 77 years old and made lots of mistakes in my lifetime. So have we all. And it is painful to look back on some of them. So, today, perhaps a bit too late, I use this approach: When I need to make a decision, or decide how to behave, I ask myself: Shlomo, OK, how will you feel about this decision, in 10 years, when you look back on it? Will your chest swell with pride or will your stomach turn over with shame?   Use this, and you can’t go wrong. This is the time for leadership – not just by our political leaders but by every single one of us, challenged by the situation and faced with choices – to help others effectively or hunker down and care only for ourselves.

   And in conclusion, consider these words by Thomas Paine, written during the bitter days of the American Revolution – times that try people’s souls.

   “THESE are the times that try men’s souls. The summer soldier and the sunshine patriot will, in this crisis, shrink from the service of their country; but he that stands by it now, deserves the love and thanks of man and woman. Tyranny, like hell, is not easily conquered; yet we have this consolation with us, that the harder the conflict, the more glorious the triumph. What we obtain too cheap, we esteem too lightly: it is dearness only that gives every thing its value. Heaven knows how to put a proper price upon its goods; and it would be strange indeed if so celestial an article as FREEDOM should not be highly rated”   Thomas Paine 1776

Substitute “life” for freedom, as we battle the plague to save lives….

The coronavirus crisis – a unique opportunity for reflection

Manuel Trajtenberg

[Prof. Manuel Trajtenberg, an economist, is a Harvard graduate, former student of the late Zvi Griliches,  and served as Member of Knesset, Israel’s Parliament. This is his ‘take’ on how we can use the COVID-19 crisis to reshape our own perspectives].

   At most once in a lifetime we are called upon to confront a dramatic event such as this one, forced upon each of us and upon the entire world. Sure, we are threatened by a rapidly spreading and nasty disease, but there is a good chance that we will be able to avoid contracting it, and if not, that we will be able to recover from it hopefully unharmed. The threat to our health is just part of the story, and not necessarily the major one: the coronavirus has managed to bring to a halt life as we know it, as if we were entering a prolonged “Yom Kippur” regime, just without the prayers and the fasting…

I am convinced that this same menace offers us a sort of respite and thus a tremendous opportunity to gain perspective on our lives, to pause the never-ending rate-race in which we are caught: to succeed in school, to earn a living and build a meaningful career, to find a spouse, build a family and raise children, to care for our relatives, and, oh yes! from time to time also to have a life…

         What is this “Perpetuum mobile” for? What are we aiming at? What is truly important and what is superfluous? Do we really need the avalanche of goods and services that we relentlessly strive to acquire and consume, and for which we toil and sacrifice invaluable time, instead of devoting it to ourselves, to our families and friends?

We are about to venture unwittingly into a very different routine, unfamiliar, disconcerting; suddenly we will have much more time on our hands, and probably we will not know what to do with it, lest we “miss out” on something, lest we “waste” it. But then we shall gradually discover that, repressed by the brutal pressures of daily life, there are whole layers and capabilities in our brains that were never given the chance to manifest themselves. In an ironic twist of fate, the coronavirus is about to set these dormant capacities free, and offer them a unique opportunity to act up: the capacity for contemplation, for self-reflection, for meditation, and the ability to take delight in them; the capacity to ponder social interactions and appreciate our surrounding, particularly in observing human nature, so close to us and yet often so remote.

   Shame on us if we keep suppressing these dormant capabilities, shame on us if we relate to their surfacing as a “waste of time.” There are those who need to journey to remote Ashrams in India to “find themselves”, far from the madding crowd. Now we have a unique opportunity to go on with our lives, and at the same time open a window on our own inner worlds, only to discover hidden treasures of feelings and insights, that laid there all along hidden from sight by the daily, all devouring routine.

   This is not say that it will be not be difficult to deal with the formidable challenges posed by corona, more so at first, let alone if significant hardships arise: economic difficulties, shortages of supplies, uncertainty about disease-like symptoms that may appear,keeping children safely and productively occupied, and so on. All these and further difficulties that we cannot yet envision will surely demand from us a great deal of resourcefulness, creativity, and mental fortitude, and test the limits of our wherewithal.

   This crisis is very different from others that we have known in the past, such as the first Gulf War: at that time, we were in daily danger from the threat of missiles and even from a chemical attack for six long weeks, which entailed a total disruption of our daily lives, including rushing often to “safe rooms” and wearing gas masks. But back then it was just us in Israel, not the entire world, and nobody would suggest attaching any positive significance, any silver lining, to a remote war that unfortunately spilled-over to us. Then we simply had to hang-on, to survive, and pray that it would end quickly.

   This time 7.5 billion people in virtually every corner on Earth are sharing the same fears, the same disruption of daily life, the same existential questions. This might have been the case as well during the two World Wars of the 20th century, but then again, it is hard to ascribe anything positive to wars, certainly wars of such magnitude of destruction and horror.

   Now it is radically different – what looms upon us is not a massive loss of lives and of their material envelop, but a shake-up of the key components of the rat-race that has kept as going for too long: globalization, narrowly defined economic growth and urban crowding. Tough questions and deep doubts hoover about them, and the answers are not bound to come from our political leaders or from the Davos elite. New, fresh answers can spring only from us, provided that we wisely grasp this opportunity, and refrain from treating it as a passing disturbance. It is eminently clear now: the coronavirus is not a “flight by night” occurrence, the disruption of our lives is bound to continue for a long time – as the length of the disruption, so is the magnitude of the opportunity, so is the breadth of the new horizons that may open up to us.


COVID-19: Lessons from Three Smart Small Asian Nations   Part 3. Taiwan 

By Shlomo Maital

    Taiwan, officially calling itself the Republic of China, is an island nation of some 23.7 million people, with GDP per capita of some $55,000 (using the adjusted exchange rate, known as Purchasing Power Parity), which reflects Taiwan’s undervalued currency.

Taiwan responded very very quickly to the COVID-19 threat, perhaps faster than anywhere:

   “Taiwan acted even faster. Like Hong Kong and Singapore, Taiwan was linked by direct flights to Wuhan, the Chinese city where the virus is believed to have originated. Taiwan’s national health command center, which was set up after SARS killed 37 people, began ordering screenings of passengers from Wuhan in late December even before Beijing admitted that the coronavirus was spreading between humans.”

     “Having learned our lesson before from SARS, as soon as the outbreak began, we adopted a whole-of-government approach,” said Joseph Wu, Taiwan’s foreign minister.   By the end of January, Taiwan had suspended flights from China, despite the World Health Organization’s advising against it. The government also embraced big data, integrating its national health insurance database with its immigration and customs information to trace potential cases, said Jason Wang, the director of the Center for Policy, Outcomes and Prevention at Stanford University. When coronavirus cases were discovered on the Diamond Princess cruise ship after a stop in Taiwan, text messages were sent to every mobile phone on the island, listing each restaurant, tourist site and destination that the ship’s passengers had visited during their shore leave.”

   As of Tuesday, Taiwan had recorded 77 cases of the coronavirus, although critics worry that testing is not widespread enough. Students returned to school in late February.

   Speed. Agility. Discipline among the population. Preparedness. Anticipation. “Reading the world map correctly”.  

   This is what we learn from smart, rich, agile, disciplined small Asian nations.




COVID-19: Lessons from Three Smart Small Asian Nations

Part 2. Hong Kong

 By Shlomo Maital

   Hong Kong is officially known as “the Hong Kong Special Administrative Region of the People’s Republic of China”. It has 7.4 million people and GDP per capita of some $46,000 – higher than that of Israel.

   Here, according to the New York Times, is how Hong Kong dealt with the COVID-19 crisis, influenced strongly from its traumatic experience with SARS in 2003:

  “ Hong Kong’s heavy death toll from SARS, nearly 300 people, has spurred residents in the semiautonomous Chinese territory to exercise vestigial muscles of disease prevention this time around, even as the local authorities initially dithered on whether to close the border with mainland China. Nearly everyone, it seemed, began squirting hand sanitizer. Malls and offices set up thermal scanners.”

   “The most important thing is that Hong Kong people have deep memories of the SARS outbreak,” said Kwok Ka-ki, a lawmaker in Hong Kong who is also a doctor. “Every citizen did their part, including wearing masks and washing their hands and taking necessary precautions, such as avoiding crowded places and gatherings.”

   “The Hong Kong government eventually caught up to the public’s caution. Borders were tightened. Civil servants were ordered to work from home, prompting more companies to follow suit. Schools were closed in January, until at least the end of April.”

     “On Tuesday, the government of Hong Kong, where only 157 cases have been confirmed, announced a mandatory 14-day quarantine for all travelers from abroad beginning later this week.”

     SARS outbreak occurred nearly 17 years ago, in 2003. Despite this, the memory of SARS and the measures adopted at that time are fresh in the minds of Hong Kong citizens. It was the people of Hong Kong who acted, even before the government and administrative officials took action, in the COVID-19 outbreak.

     I am certain the same will be true of COVID-19. We will remain this for generations. And hopefully, in the next pandemic, we will act promptly, as Hong Kong did.


COVID-19: Why Do More Men Die Than Women?

By Shlomo Maital


Women live longer than men. It’s true. Here are the facts, from the World Health Organization:

     In 2019, more than 141 million children will be born: 73 million boys and 68 million girls.  

     Based on recent mortality risks the boys will live, on average, 69.8 years and the girls 74.2 years – a difference of 4.4 years.

       Life expectancy at age 60 years is also greater for women than men: 21.9 versus 19.0 years.

       Women have a longer life expectancy than men at all ages.

     Many years ago, when I studied demography at Princeton (at Ansley Coale’s famed Office of Population Research), this fact was true even then – and I read a study of monks and friars, in a monastery, whose life expectancy reflected the same advantage for women – so, it is not environmental factors that cause it.

     In fact, we’re not really sure why women live longer. There are many theories.

   And now, comes COVID-19. Writing in the daily Haaretz, Asaf Ronal observes that the mortality rate from COVID-19 for men is 2.8%, while the mortality rate for women is 1.7%. That is a massive difference. This is adjusted for age, and other factors.


   There are theories. Behavioral: Men are ‘heroes’ and seek medical care less than women. Physiological: Female hormones protect them. Immunological: Female immune systems work better. Biological: the ‘receptors’ viruses like to invade on human cells reside in part in Chromosome X, women have two copies of it, thus they are more susceptible, so their immune systems are more alert and wary to attack invaders.

       These are all theories. None have really been fully tested.

       And finally, my own observation: As we observe spatial separation here in Israel, and as I watch both men and women experts explain things and advise us on TV – again, as always, I am struck by how much better women are at delivering information, credibly, authentically, than men, given the same level of expertise and training.

     If only the men would leave it to the women – and just shut up. US President, are you listening? And Israeli PM?   Men — take care of yourselves.  Let the women run things.  They do it better.

COVID-19: AI to the rescue?

 By Shlomo Maital

Today’s daily Haaretz * carries a brief report of how three brilliant Israeli scientists have tackled a pressing problem – the need to know where the COVID-19 hotspots are, in order to focus spatial separation without shutting down the economy of the entire country.

   The three are Prof. Eran Segal, an expert in computational and systems biology, Weizmann Institute, Rehovot; Prof. Benny Geiger, also from Weizmann; and Prof. Yuval Dor, Hebrew University.

     Segal notes that experience from studying previous epidemics, as well as knowledge about how COVID-19 spreads, show that the virus spreads through clusters of infection and that early identification of such clusters can help stop the virus from spreading, ot at least slow it considerably.

      We have seen such clusters, or hot spots, in New Rochelle, NY, in Washington State (Seattle), and initially, in Wuhan, China.

       Segal notes that one possibility is to use massive testing, as they did in South Korea. More than 10,000 persons are tested daily there for COVID-19.

     Israel can’t do such extensive testing, at this stage, he notes. Hence, the solution the team found was to ask members of the public to fill out online daily questionnaires, which take less than two minutes to complete, that include details about various symptoms and place of residence, including street and zip code.

     This information will be analyze, Segal notes, using machine learning algoithms that give researchers and the Health Ministry a variety of information. If enough data are collected, the tool will help give up-to-date assessment of the spread of the illness.

     This ‘early warning’ system can help spot these clusters, long before other methods do. The AI algorithms could also determine the effectiveness of public health measures, such as self quarantine, to limit COVID-19’s spread.

     The information, noted Segal, is collected using Google DOCS.   No privacy is violated.

       Segal says we need as many people as possible to fill out the questionnaire, in the initial pilot stage.

       I wonder whether Israel can offer this approach to the US, where testing remains quite limited.

* Haaretz. “Israeli Researchers Hope AI Can Tame COVID-19, and They Want Our Help.” Asaf Ronel. March 17 2020.

COVID-19: Mitigate, Not Decimate

 By Shlomo Maital


    Professor Zvi Bentwich is an Israeli doctor, who teaches and researches at Ben Gurion University, in Beersheva.   Before quoting his views on COVID-19, let me establish his credentials first.

   Bentwich serves as the head of the Center for Emerging Tropical Diseases and AIDS at the Ben-Gurion University (BGU). He founded the first AIDS center in Israel in the mid 80’s. His groundbreaking research uncovered the link between Neglected Tropical Diseases (NTDs) , particularly intestinal worms, and immune system deficiencies, pioneering the concept that NTDs play a major role in the pathogenesis of HIV/AIDS. He is a leading advocate for public health and human rights.

  So, this is a public health expert who is worth listening to, right? Here is his take, printed in today’s Haaretz daily newspaper:

    The heading on his Op-Ed piece: “Tight border isn’t the answer to virus”. Today the Israeli government announced that EVERYone returning from abroad must undergo self-imposed quarantine for two weeks. Everyone? Yes, so that Prime Minister Netanyahu will not appear to be singling out the US, thus angering his friend and colleague Donald J. Trump. (Such quarantines were already in effect for most travellers incoming from Europe).

   The main point: “Is there an alternative approach to fighting the disease right now? [alternative, to closing down the borders and shutting down the economy for weeks and weeks?]. …Yes, it’s clale mitigation. It involves using less drastic methods that are likely to yield similar results regarding the damage caused by the virus but that significantly reduce the negative social and econoic consequences of containment.”

   Mitigation. Not decimation of our economy.

   And this is coming from a distinguished physician, expert on virus containment.

   Bentwich concludes:  “The coronavirus too will pass and until it does the damage should be minimized as far as possible. We must accept the possibility that it won’t be the last viral epidemic and that it’s important to find the optimal way to cope with such epidemics, at a reasonable cost”.

Blog entries written by Prof. Shlomo Maital

Shlomo Maital