Sunday, June 28, 2020


We humans are pretty good at understanding linear change. It's all around us:

--eat more, gain some weight; eat less, lose some weight
--press on the gas pedal, speed up; press on the brake, slow down
--turn up the heat, feel warmer; turn down the heat, feel cooler
--someone can't hear you, talk louder; someone moves closer, talk more softly
--and thousands of other daily experiences in which a small change produces a small result and a larger change produces a larger result.

However, some events don't behave linearly. There are situations where a small change can quickly produce a big effect. We're living through at least two of them right now--climate change and the Covid-19 pandemic. We're failing miserably in understanding and dealing with both of them.

A sneeze--a few tiny droplets can cause massive disruption
Photo credit: CDC

Let's do a little math--please bear with me:

Step number     Linear growth (n x 2)     Exponential growth (2 to the n) 

         1                        2                                                    2                                       
         2                        4                                                    4                                         
         3                        6                                                    8                                         
         4                        8                                                   16                                       
         5                      10                                                   32                                       
         6                      12                                                   64                                       
         7                      14                                                 128                                       
         8                      16                                                 256                                         
         9                      18                                                 512                                         
       10                      20                                               1024 
       11                      22                                               2048                                     

Let's pretend that these numbers represent two different responses to the Covid-19 virus.

The steps might represent weeks. The first column might represent a situation where the virus is fairly well controlled (e.g. through some combination of social distancing, mask wearing, testing, tracing and isolating people likely to shed the virus). On average one infected person infects approximately one other person, with the result that the number of cases grows linearly. The third column represents exponential growth--where the virus truly is "going viral." All that takes is for one infected person to pass the virus on to more than one new victim.

Notice the enormous and rapidly expanding difference as the weeks tick by. At week three, exponential growth has infected just two more people than in the linear growth model, but at ten weeks the difference is more than 1,000, and one week later, more than 2,000.

So, our first takeaway is that when we're dealing with any situation involving exponential growth, at first it's hard to distinguish from a normal linear situation that we're used to, but sooner or later it takes off explosively.

Now let's examine that phrase "sooner or later."

      Week    Doubling stopped sooner           Doubling stopped later
         1                        2                                                    2                                     
         2                        4                                                    4                                       
         3                        8                                                    8                                       
         4                      16                                                   16                                       
         5                      18                                                   32                                       
         6                      20                                                   64                                       
         7                      22                                                 128                                       
         8                      24                                                 256                                         
         9                      26                                                 258                                         
       10                      28                                                 260 
       11                      30                                                 262
Total Cases:          198                                               1290

What a difference a delay makes.  This might represent two states, one of which sees the exponential handwriting on the wall after just four weeks, institutes effective controls and ends up with 198 cases, while the other delays control measures one month more and ends up with with 6.5 times as many cases. (Or these numbers could equally well represent deaths, in which case that one month delay would have caused over a thousand needless deaths.

Obviously the numbers above are meant to be an illustration; they don't match exactly with the real world. However, you can see this in the real world if you compare the impact of a one-week delay in responding to the pandemic in New York vs. California. Here's a zerospinzone.blogspot post from March 30:

In this comparison of coronavirus cases in New York vs California, you can see what difference even a few days lag in imposing strict stay-at-home orders makes. California--population 39.5 million, first state to impose strict controls: current # of cases 6358, deaths 132. New York--population 19.5 million, delayed a week before imposing controls: current # of cases 60,679, deaths 1063. The number of cases per population in NY is 19 times greater than in California, and the number of deaths per population 17 times greater. What a tragic difference a week's delay makes.

A lot has happened in New York and California in the subsequent three months, with start-and-stop openings and closings in both states. Through all that, however, California has managed to keep a tighter lid on the explosive potential of the coronavirus. As of today, June 28, New York has documented 416,769 cases and 31,483 deaths while Callifornia has had 215,575 cases and just 5,934 deaths. Adjusted for population, late-starting New York has suffered nearly four times as many cases and more than ten times as many deaths as California. Clamping down just one week earlier in California almost certainly saved tens of thousands of lives.

Our second takeaway, then, is that when dealing with the potential for exponential growth, getting control of the rate of growth as early as possible--before the number of cases explodes-- makes a huge difference.

It's pretty clear that we, as a species, aren't very good at dealing with things that have the potential for exponential growth, and so can blast out of control at any time.  We're seeing the results of this globally as we try to put a cap on the coronavirus. Similarly, experts have been warning us for decades that, because of a number of looming tipping points, climate change too has the potential to spin wildly out of control.

However, we don't have a good excuse for continued ignorance; it's not as though the potential for dangerous exponential growth has been a secret. Consider this old proverb, a version of which goes like this:

For want of a nail a horseshoe was lost,
for want of a horseshoe a horse went lame,
for want of a horse a rider never got through,
for want of a rider a message never arrived,
for want of a message an army was never sent,
for want of an army a battle was lost,
for want of a battle a war was lost,
for want of a war a kingdom fell,
and all for want of a nail.

Clearly we've had folk knowledge about exponentially large consequences from a small event for a lot time.

Even more ancient is a story from India about a chess-loving king who promised to reward a visitor with whatever he wanted. The visitor "modestly" asked for one grain of rice on the first square of a chessboard, 2 grains on the second square, 4 on the third, 8 on the fourth, etc. It didn't take the King many squares before he realized he'd taken on an impossible task. Sixty-four doublings would have required some 18,000,000,000,000,000,000 grains of rice, enough to cover all of India a meter deep.

That ancient king learned a striking and costly lesson about exponential growth. It seems as though we--and our current leaders--need to learn it all over again, and quickly. That is, if we don't want our kingdom to fall for want of an adequate response to this microscopic but immensely dangerous virus.



Friday, June 19, 2020


Neanderthals--those brawny, heavy-browed but big-brained cousins of ours--thrived across Europe and Asia for some 300,000 years. Then, in the course of just a few thousand years, they vanished, leaving only some bones, beads, stone tools, an enigmatic burial or two, and a scattering of their genes in our species, Homo sapiens. 

Since the discovery of the first H. neanderthalesis skeleton in 1856, scientists have speculated and argued about what caused their extinction. There have been lots of ideas, including climate change, disease, lack of genetic variability, interbreeding with, competition with, or outright extermination by H. sapiens.

Reconstruction of a Neanderthal woman
Credit: Bacon Cph

New research using a dynamic supercomputer model incorporating climate shifts, geography, food resources, utilization of resources and interbreeding solves they mystery. It was us, modern humans at first filtering in from Africa and then expanding our range across Asia and Europe, who did them in.

According to the study, the extinction of the Neanderthals didn't require warfare and slaughter at our ancestor's hands; all that was needed was a competitive edge. Models in which those early modern humans could exploit local resources more efficiently and so support a larger population inevitably showed the Neanderthal range and population shrinking and, within a few thousand years, vanishing. The researchers call this "competitive exclusion."

"It is not a coincidence that Neanderthals vanished just at the time when Homo sapiens started to spread into Europe," says Axel Timmerman, a climate physicist at Pusan National University, in South Korea. "The new computer model simulations show clearly that this event was the first major extinction caused by our own species."

The model that Timmerman developed folded together a huge amount of information. It modeled the climate across northern Africa, Asia and Europe over the 100,000 years that preceded the Neanderthal extinction around 38,000 years ago, regional productivity of potential food sources, population densities of Neanderthals and modern humans across time and space, and interbreeding between the two species.

Running the model on the ALEPH supercomputer at Pusan National University, Timmerman was able to see the shifting populations of Neanderthals and H. sapiens across Asia and Europe over the millenia under different conditions of climate, interbreeding and competition.

One factor that emerged clearly was that climate change alone was not the cause of the Neanderthal's extinction. This bears out the observation that they had survived hundreds of thousands of years of climate change, including periods of severe glaciation. "Neanderthals lived in Eurasia for the last 300,000 years and adapted to abrupt climate shifts that were even more dramatic than those than occurred during the time of Neanderthal disappearance," says Timmerman. It was only after the arrival of modern humans that Neanderthal populations began an irreversible decline.

Timmerman concludes that the anatomically modern humans who found their way into Eurasia around 50,000 years ago simply out-competed the Neanderthals. His model doesn't specify exactly what differences drove that competitive edge. Even if the modern humans simply were able to harvest more food from the environment, or were more resistant to diseases, or managed to raise more children to adulthood, that could have been enough to allow them to displace and eventually replace the Neanderthals.

In other words, one way or another, the culprit was us.


You can find the full, open-source research paper at this URL. It's worth scrolling down to the appendix, where you can watch movies depicting the influx and growth of the H. sapiens population and the decline and disappearance of the Neanderthals over time and space. Fascinating.



Thursday, June 18, 2020


We've been hearing about Russian meddling in our elections and our national discussion for years now. I wrote a blog post about it in 2018, spurred by an excellent 35-minute video from the New York Times tracing Soviet and more recently Russian disinformation campaigns back five decades. The video is well worth watching to grasp the scope and depth of this ongoing program. The basic goal of these campaigns is to stir up disagreement, foment polarization, and undermine the target's (read the US) social cohesiveness and institutions from within.

I want to add a tiny bit of data to this issue.

Is this one of my Turkmenistan trolls?
Credit: maritravel/Pixabay

You're reading a post from my blog, I've been posting here since 2006, a mixture of reportage about scientific and technological advances that catch my eye, along with commentaries about issues that I think are important, such as policing, gun control and the environment, and, at times, my political opinions.

Google provides the platform that hosts my blog (and, I assume, millions of others). One of the helpful bits of information it provides bloggers is a map showing where readers are checking in from.

I write in English and from an American perspective, so you'ld expect that the bulk of my readership would be in the US, perhaps with a smattering of readers from other English-speaking countries. That was the case until 2016.

At first it was just a curiosity. In 2016 I began to get a lot of hits from Russia. Quite often far more than I was getting from the US. Those hits usually came in bursts, roughly once a week. I gradually got the impression that every so often someone or some group somewhere in Russia was going through a large number of my posts. I had no idea why.

However, as all of us who are not committed Trump supporters know, it gradually came out that Russia was carrying out a concerted digital effort to tilt the election towards Trump, and, more generally, to stoke division within the US. I'm guessing that my blog was just one of thousands or millions of sources that Russian trolls combed looking for issues that they could use to polarize people and groups here in the US.

After the 2016 election, Russia pretty much dropped off the map of my readers.

However, it's now another election year and guess what--not Russia, but this time around I've gained a big following in the ex-Soviet state of Turkmenistan. For example, during this past week I've had 10 times as many hits from Turkmenistan than from the US and Canada combined.

So now, I have a surprising number of devoted readers in far-off Turkmenistan. I doubt that they are really interested in my posts about the demise of coal, about whether the universe is spinning or not, or the importance of exercise for seniors. They may well be interested in divisive issues such as how well Trump is dealing with the coronavirus pandemic or climate change, or about other controversial issues here in the US such as sanctuary cities, gun violence and racism.

To get an updated example of how commentary from the US can be amplified or weaponized by foreign trolls and fed back into the US, please read this recent NYT piece.

So, unlike Trump who famously said, "Russia, if you're listening . . ." and invited them to hack Hillary's emails, I'm telling my new troup of trolls, "Turkmenistan, if you're listening, bug out. My blog is none of your &%$#@#! business."



Thursday, June 11, 2020


Two new studies make this question much easier to answer than Hamlet's dilemma. If we all wear face masks in public, that alone will go a long way towards choking off the coronavirus pandemic.

Writing in the prestigious Proceedings of the Royal Academy A, epidemiologist Richard Stutt and colleagues at the UK's Cambridge and Greenwich universities modeled 18 months of the pandemic with different levels of mask-wearing effectiveness.

Students wearing face masks (and saving lives)
Credit: Gustavo Fring

Not surprisingly, the biggest impact on the virus came when 100 percent of the population wore masks that were highly effective both in keeping infected people from expelling virus-laden droplets and protecting healthy people from inhaling them. The models showed that that combination could push the infamous R-value--the number of infections an infected person passes on--below 1, and so snuff out the pandemic.

Even more encouragingly, even if the masks were just slightly more than 50 percent effective, or if only slightly more than 50 percent of the population wore them, that crucial R value could be pushed below the magic number 1.

Here's the striking bottom line of this study, assuming face masks that are 50 percent effective:

"We note that 100% facemask adoption without lock-down achieves a greater reduction in the final size of epidemic, a lower 'total removed' and a lower peak of active cases than lock-down without facemasks."

Let me repeat that. According to their models, if everyone wore face masks, that would be more effective in limiting the size and impact of the epidemic than a total lockdown. If we compare the social and economic impacts of universal face mask-wearing to a full-scale lockdown, there's no contest. Wearing a face mask is a significant nuisance, but it allows most activities to continue--as we see in many Asian countries where face masks are a normal part of life. Lockdowns, as we've seen, are immensely life-changing and economically devastating.

A second research team, reporting in the equally prestigious Proceedings of the National Academy of Sciences, analyzed the spread of the coronavirus in three of the worst-hit parts of the world, Wuhan, China, Italy and New York City. The researchers tracked the course of the epidemic in each location as different measures were put in place to try to control it.

Their conclusion was striking--mandated face covering was ". . . the determinant in shaping the trends of the pandemic." Renyi Zhang, at Texas A&M Univeristy, and colleagues, calculated that face masks alone prevented 78,000 COVID-19 cases in Italy between April 6 and May 9, and over 66,000 in New York between April 17 and May 9. Given the percentage of diagnosed COVID-19 patients who died in Italy and New York, wearing face masks likely saved more than 15,000 lives in Italy and New York City during those weeks.

This research team's bottom line:

"We conclude that wearing face masks in public corresponds to the most effective means to prevent interhuman transmission, and this inexpensive practice, in conjunction with simultaneous social distancing, quarantine and contact tracing represents the most likely fighting opportunity to stop the COVID-19 pandemic."

Again, note that wearing face masks in public, maintaining a safe distance from others, quarantining people who are infected and tracing their contacts, while challenging are still far less damaging to normal life and to the economy than lockdowns.

So, two separate studies using completely different methodologies came to essentially the same conclusion. Wearing face masks in public can be extremely effective in snuffing out this world-shaking pandemic.

I'm wearing my mask whenever I step out my front door. Please do all of the world a huge favor and wear yours too!


Here's a link to another researcher who has reviewed the research literature and comes to the same conclusion. Jeremy Howard, a distinguished research scientist at the University of California, San Francisco, and his colleagues, clarify that masks work by keeping most virus-carrying droplets from being expelled into the environment. Again, the more people who wear them, the safer we all are.


Wednesday, June 10, 2020


Coal has been a primary source of energy in the US since the 1880s and the source of most of the electricity generated in the United States since the early 1960s. Here in the US, it's been a relatively cheap, abundant and reliable source of energy. It's also the source of an enormous amount of greenhouse gases and toxic pollution.

It's now clear that coal is on its way out. According to the US Energy Information Administration, this year renewable energy sources such as wind, water and geothermal generated more electricity than coal for the first time in US history. Coal's share of the energy market has been declining for the past decade while renewables have been claiming a bigger and bigger share each year. This year the curves crossed for the first time.

Coal-fired power plant near Price, Utah
Credit: arbyreed

Despite President's Trump's repeated promises to bring back "beautiful, clean coal," and his rollback of key environmental protections, including the brain-damaging mercury emitted when coal is burned, King coal's throne has been on increasingly shaky ground due to simple economics--renewables are now both cheaper and far cleaner than coal. Trying to resuscitate this dying industry truly is tilting at windmills.

Windpower, growing rapidly in US

Nor do experts see much chance for coal to stage a counter-revolution.“Coal is on the way out, we are seeing the end of coal,” says Dennis Wamsted, analyst at the Institute for Energy Economics and Financial Analysis. "The trend is pretty clear."

With King coal on his way out, we can all breathe a bit easier. But,  as climate scientists have been telling us for decades now, replacing coal and other fossil fuels with renewables can't happen soon enough.



Tuesday, June 09, 2020


On April 27, I posted a piece noting that the US had suffered its one millionth documented COVID-19 case, and more than 56,000 deaths from this deadly virus. Today, 43 days later, the toll has more than doubled. We've now had 2.044 million people diagnosed, of whom 114,118 have died.

The good news is that it took 43 days for the number of cases to double. That's far slower than at the start of the pandemic, when numbers were doubling every few days.

As discussed in a previous post, we've flattened the curve and slowed the advance of the SARS-CoV-2 virus through lockdowns, stay-at-home orders, social distancing, mask-wearing, hand washing and all the other life-changing steps that we've taken. Making those drastic changes works and has saved huge numbers of lives, although, as we know, at enormous economic cost.

The bad news is that the virus is still circulating almost everywhere in the world (enormous kudos to New Zealand for having defeated the virus, at least for now). In addition, with just 2 to 5 percent of us now possibly protected by antibodies, the SARS-CoV-2 virus still has hundreds of millions of potential victims in the US; all it takes is a bit of exposure.

All of which raises the question--where do we go from here? Do we fling open the doors of  the businesses and public spaces that have been closed, go back to work, and try to get back to something like our previous lives as quickly as possible? Or do we tiptoe back towards normalcy, cautiously opening up the economy and our lifestyles step by step, slowly enough and with enough testing and tracking to keep the virus contained? Or, more likely, stumble ahead with a confused and confusing state-by-state, city-by-city smorgasbord, with predictably mixed results?

We can be sure that Trump and his administration will push for a quick re-opening. Trump's eyes are fixated on the economy and its impact on his electability this November.

It's not hard to understand how vital it is for people to be able to have jobs to return to and to get  back to work.  Nor to feel the need to reclaim the freedoms and joys of our pre-coronavirus lives.

As these vital decisions are made, perhaps the most important thing to keep in mind is that once unleashed--as long as someone who has the virus is likely to pass it on to more than one other person--this virus can and will expand exponentially. This is a factor that is truly hard to grasp. We are used to things that change linearly. Push harder on the gas pedal and the car speeds up a bit, not by a factor of 10, 100 or 1000. Work more hours and you don't suddenly get rich. We're not used to things with the propensity to "go viral," where a small change can produce an enormous effect, or where a slight delay can mean the difference between 100 deaths and 100,000.

So step on the gas to get the economy moving again? It's a great idea, but not if we forget that the coronavirus is still there, still circulating, itching for another chance to explode.


Monday, June 08, 2020


If, as you've spent endless hours at home the last few months, you've wondered if the lockdowns and shelter-in-place policies that have upended lives around the world actually work, two major new research papers pretty much close the case.

Image credit: Prachatai/Flickr

Research teams at Imperial College, London and the University of California, Berkeley, used different methodologies to study the impact of the "non-pharmaceutical interventions" such as business closings, social distancing and home isolation that were put in place in different mixtures and different times in 11 European countries, and in China, South Korea, Iran and the United States.

The detailed findings are complex, but the bottom line is simple: lockdowns worked whenever and wherever they were applied. When implemented and followed consistently, within three weeks they successfully reduced the reproduction rate of the coronavirus below the critical number 1, flattened the curve of cases, and saved large numbers of lives.

The numbers that the two research teams calculated are impressive. The Imperial College team estimates that in Europe the lockdown and social distancing measures put in place in March prevented several hundred million Covid-19 cases and approximately 3.1 million deaths before the May 4 end of their data gathering.

The Berkeley group found that in the six countries they studied--including the US--the measures put in place prevented 62 million confirmed cases or an estimated 530 million actual cases.  
Assuming a case mortality rate of just one percent, that means that some 5.3 million lives were saved, again in the course of a few months.

"The lockdowns had a very large effect on cases and saving lives," says Solomon Hsiang, at the University of California, Berkeley.      "[Some people assert that] the lockdowns weren't necessary. This research nails that it was. Without them, we believe the toll would have been huge."

Researchers from both groups emphasize that some mixture of these life-changing but also life-saving measures needs to be continued, tailored to each country or region's population structure and economic needs. 

"We're just at the beginning of the pandemic," says Samir Bhatt, at Imperial College. "We're very far from herd immunity and the risk of more waves of the virus is very high. Care must be continued until a vaccine becomes available."

These two papers were published on June 8, at which point there have been more than 7 million confirmed cases of Covid-19 and 407,000 confirmed deaths worldwide. If most of the countries in the world had not taken the stringent steps they did to control the SARS-CoV2 virus, these two research papers show that those numbers would have been orders of magnitude higher.

Was it worth it? Clearly that's not a scientific question, nor should it be strictly an economic one. The answer depends on the value one places on human lives as well as on other important factors such as employment and economic well being. Both research teams are well aware of the huge economic impacts of lockdowns, social distancing, travel restrictions, business closures, and other measures taken to control the spread of the virus. But both of them emphasize that some mix of these measures will be needed for a long time. 

"There's no back to normal," says Hsiang. "It's a cost-benefit question--interventions of different kinds along with economic well-being. The longer you stay in lockdown, the fewer infections. If you undo lockdown, there's economic growth but more infections and death. Something still needs to be in place."


You can download the full scientific papers from the journal Naturehere and also here.