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  • Mark Selby
  • October 18, 2018 05:28:01 AM

A Little About Us

My Dossier and Blog is the personal site of Dr Mark Selby. I'm a STEM Educator with 25+ years of experience, EDUTECH specialist and Freelancer. I write about Science and STEM education and highlight my own creations and examples of the use of EDUTECH in STEM education at high school, college and university levels.

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Kamala, the Inflection Point and the Geek vs Freak Election?

This is not an article about politics but it is about the Democratic National Convention (D20) held in the last week. Specifically, it’s about one phrase in the speech by Vice Presidential candidate, Kamala Harris (see video). The phrase is “inflection point” that was also echoed the following day in the speech by Presidential candidate … Continue reading "Kamala, the Inflection Point and the Geek vs...

This is not an article about politics but it is about the Democratic National Convention (D20) held in the last week. Specifically, it’s about one phrase in the speech by Vice Presidential candidate, Kamala Harris (see video). The phrase is “inflection point” that was also echoed the following day in the speech by Presidential candidate Joe Biden. It seems that the Democratic Party are hoping that this phrase will be a rallying call for them come Election Day in November.

“We’re at an inflection point. The constant chaos leaves us adrift. The incompetence makes us feel afraid.  The callousness makes us feel alone. It’s a lot. And here’s the thing: We can do better and deserve so much more.[1].

I’ve been trying to remember when I’ve heard the phrase “inflection point” outside of high school or university mathematics and science. As a former university teacher I certainly used “inflection point” in a mathematical context when teaching chemistry. I don’t remember ever using or hearing the term in ordinary conversation. As a single word, inflection, can be used to refer to a change in the tone or pitch of someone’s voice when they’re speaking.

The Merriam-Webster Dictionary gives the meaning: “a moment when significant change occurs or may occur” or a “turning point.” Another point is that the Qatari broadcaster Aljazeera is reporting these same words as an “inflexion point” [2]. So what’s the difference between an “infexion point” and an “inflection point?” Fortunately, this is an easy question to answer. inflexion is an older British spelling similarly to reflexion or connexion. which are rarely seen in 21st-century writing. The spelling “inflexion” seems to have survived the 20th century in a few places, such as Aljazeera. [As I’m writing this, my spell checker is accepting “inflexion” but rejecting “reflexion” and “connexion”].

Interestingly, the Merriam-Webster Dictionary [3] gives an example of the usage for “inflection point” from a speech made by Barack Obama at the commencement address for Rutgers State University of New Jersey, 2016 [3]. Evidently, the Democratic Party have history in using the phrase “inflection point:” prior to Kamala Harris in 2020.

It depends on us, on the choices we make, particularly at certain inflection points in history; particularly when big changes are happening and everything seems up for grabs. Barack Obama

A Refresher in Calculus

Do you remember the meaning of an “inflection point” from high school or first-year university calculus? Thought not. So, here’s the refresher. Firstly, there’s a handy piece of free software for calculus, algebra and geometry called GeoGebra which makes the maths a lot easier to master.

Problem: find the inflection point for the function: f(x)={5x}^{3}+{2x}^{2}-3x

Screenshot 2020-08-25 at 13.54.28Answer: Write (or just copy and paste) the function into GeoGebra. A chart of the function appears straight away, the red curve. Use GeoGebra to find the first and second derivatives for f(x) (see the the panel right and the chart below — the 1st derivative chart is switched off because it makes the chart too cluttered).

The 2nd derivative chart is coloured in blue and given by the line f”(x) = 30x + 4. Where f”(x) is negative (i.e., in the bottom half of the plot) then f(x) is said to be: “convex downwards.” Where f”(x) is positive (i.e., in the top half of the chart) then f(x) is said to be: “convex upwards“. The single point A is where f(x) changes from being convex downwards to being convex upwards (where f”(x) = 0), this is the inflection point (A) ,

The inflection point (A) for the function, f(x)={5x}^{3}+{2x}^{2}-3x

The inflection point can be calculated from GeoGebra or from where the second derivative crosses 0, f’’(x) = 0, therefore x = -4/30 = -0.133.

Though the mathematical meaning is more precise and specific, you can see from the above discussion how the mathematical definition agrees, in general terms, with the point of change meaning that Kamala Harris is seeking to convey. By using the term “inflection point” she is indicating a turning point from heading in the direction of chaos and incompetence, to a new direction of certainty and inclusion.

Interestingly, Kamala didn’t borrow an alternative mathematical term “step function” which means a discontinuous jump from one state to a different state. A step function might have conveyed much of the same meaning: a jump from chaos and incompetence to certainty and inclusion. I suspect the term “inflection point” was used because it implies a more gradual change than “step function” and because it has more resonance with voters.

Inflection Points in Business

In a time of rapid technological change global business is becoming increasingly driven by the digital environment in which they operate [4]. Strategic decisions around when to adopt new technology products and services are becoming crucial to success and even survival of whole organisations. Especially in this era of COVID. This is where the concept of an inflection point comes to play: it’s that point in time when investing in a new technology stands to gain the best return and competitive advantage. The concept is best illustrated with a chart of a sigmoid function or S-curve. We’ll use GeoGebra to construct the plot, similarly to that for the cubic function above:

Illustration of the inflection points for a sigmoid or S-function (\frac{1}{1+{e}^{-x}})

The sigmoid curve (the green curve) combines aspects of the “step function” but it varies smoothly. The above plot shows the features that are important to a business interpretation of the “inflection point.” Too far to the left in the chart represents the introduction of a novel but immature technology. This is the “fad” stage.” When adopting technology at this immature stage, it’s too easy to choose a technology that will be superseded in the short term (the “wrong horse“). On the other hand, waiting too long, as shown on the right of the chart, will lead to the adoption of a mature but mainstreamed technology that no longer possesses an edge over the competition.

The middle point of the sigmoid curve is where the mathematical inflection point lies. This is the point where the second derivative curve (the orange curve) crosses the x -axis. The mathematical inflection point A represents a new technology at its “next big thing” stage of development. This is the stage where rapid adoption across the industry sector begins to take place.

The goal of business should be to anticipate wide-spread adoption at the mathematical inflection point A by selecting new technologies at the business inflection point B.

Adopting a new technology at the business infection point B gives the best return on investment by providing a competitive edge.

In summary, we have examined the meaning term “inflection point” from the speech by Kamala Harris at the Democratic Party Convention (D20) from a several perspectives. From the usage of the term in common language, the dictionary definition, its usage in mathematics of calculus and in its most recent usage in business.

After reviewing the term “inflection point” from all of these angles, my understanding is that Kamala’s meaning was similar to the business meaning of trying to anticipate the next big political idea and to carry it forward to Election Day in November. No doubt we’ll be hearing a great deal more of the term “inflection point” over the next month or so. Will we see an “inflection point” election on the first Tuesday in November?

The inflection point may have played well at the Democratic Convention but would they risk it in an electoral campaign where it will inevitably come across as “geek” versus ”freak”?


Disclaimer: I have no connection with the Democratic Party (USA) financially or personally. I have no desire to promote the Democratic Party politically. My personal political views are discussed elsewhere in the article: My Trip Down Memory Lane.


[1] Christina Wilkie, CNBC, “Here’s what Kamala Harris said at the Democratic National Convention,” updated: 20-08-20, accessed: 23-08-20, available online:

[2] William Roberts, Aljazeera, “Kamala Harris sees US at ‘inflexion point’ in upcoming elections,” published: 20 August, accesses 22 Augsut, available online:

[3] Barak Obama, The White House, Obama Archives,” Remarks by the President at Commencement Address at Rutgers, the State University of New Jersey,” published: 15-05-2016, accessed: 24-08-2020, available online:

[4] Jim Highsmith, Mike Mason and Neal Ford, ThoughtWorks, “Inflection Points,” published: 13-07-16, accessed: 21-08-20, available online:


Links to the mathematics and charts I’ve constructed in GeoGebra:


Time Travel in “Dark”: Embrace the Paradox

German Netflix series simply called “Dark” has been around since June 2017 (seasons 1 and 2) . The new season 3 has only recently become available. Watch out for the first scene in the first episode: a gruesome suicide by hanging which you might want to hit fast forward through. Very dark indeed. If you … Continue reading "Time Travel in “Dark”: Embrace...

Promotional poster for the Netflix series “Dark” [1].

German Netflix series simply called “Dark” has been around since June 2017 (seasons 1 and 2) . The new season 3 has only recently become available. Watch out for the first scene in the first episode: a gruesome suicide by hanging which you might want to hit fast forward through. Very dark indeed. If you do fast forward don’t miss the short sequence in which the victim’s mother grabs the suicide note before anyone else can read it. The victim here is Michael Kahnwald and his mother is Ines. This whole scene, and the names of the characters, are pivotal to the whole story. We’ll return to the intrigue, setup by the first scene, after discussing some general comments about the time travel genre. Take the opportunity for a pause because “Dark” is a bumpy, head-spinning journey. (Edit: postponed to the continuation in Part 2).

It is sometimes said that time travel is impossible because of the paradox that you could go back in time and kill your own mother before she gave birth to you. One common theme explored in sci-fi movies, for instance in “Star Trek” franchise, is that time travel is permissible only if the time travellers don’t do anything in the past that will alter the future. You might remember the scene in Star Trek IV: The Journey Home (1986) when Kirk and crew travel back to the mid-1980’s San Francisco. They try to disguise Spock’s Vulcan ears with a beanie so he isn’t noticed. Spock, subsequently, nearly blows his cover when he applies an aggressive Vulcan nerve pinch to a punk-rocker on a bus.

By way of contrast, “Dark” is quite different in that it fully embraces the time travel paradox. It’s set in a fictional German town of “Winden” (not to be confused with the town of Winden im Elztal). “Dark” is in the tradition of the French short sci-fi classic La Jetée (The Jetty) [2] by Chris Marker (Argos Films, 1962), “Dark” is also in the tradition of the 1995 production 12 Monkeys with Bruce Willis as the time-travelling Cole, 12 Monkeys was inspired by La Jetée and shares several common themes with that short film. A TV series of 12 Monkeys, made by Syfy ran over four seasons 2015 to 2018.

The Winden of “Dark” is, unsurprisingly, a dark dismal place made up of a number of families that have lived there over several generations: in addition to the Kahnwalds mentioned above there are the Nielsens, the Tiedermans, and the Dopplers, The Wikipedia entry on the “Dark” series contains handy family trees for each season, made available under a CC license by Christianlorenz97. I recommend having the printed family trees with you when you start your binge watching of “Dark”.

The townspeople of Winden are no less dark and dismal as the town itself. As the series introduces each character you start to suspect that each of them is carrying the heavy burden of deep and dark secrets which warps their character and actions. It’s not much of a surprise when you find that they all have dark secrets (such as Michael Kahnwald and his mother in the opening scene, mentioned above). What does surprise, as the series unfolds, is just how warped of character and dark of deed some of the townspeople really are.

Just because you can time travel in Winden it doesn’t mean that you can escape the consequences of your actions.

You see, even in Winden, consequences have a way of catching up with you even through the recesses of time. Whatever else it is, Winden is still part of a moral universe. Amid all the darkness of “Dark” you won’t find it unexpected when it transpires that the world Winden occupies, is living in the prelude to an apocalypse. The apocalypse, of course, is centered upon Winden, specifically Winden’s Nuclear Reactor which also plays a crucial part in time-travel through the tunnel under the nuclear plant (depicted here in the opening poster image)..

The apocalypse is a common theme shared between La Jetée, 12 Monkeys and Dark. After all, those time traveing paradoxes have to resolve themselves somehow. One point of difference between “Dark” and the films mentioned, is that “Dark” doesn’t shy away from asking some very deep and difficult questions, in particular.

Why is it that we think, when a tragedy overcomes us, either through our fault or not: that if we could just go back in time and change this or that event, that we could resume our former life once again?

The insight that “Dark” offers is that time-travel, if it were possible isn’t an escape. If you were able to time travel and change events then you can, as “Dark” well-illustrates, set in train an even worse tragedy. One point that James Gleick offers in his book on time travel [2] is that it’s the prospect of death that makes us think of time travel. After watching “Dark” I would add: death, separation and loss of a loved one make us look to time travel, but it’s only illusory. As much as we’d like to be able to, there are some things we just can’t change.

As it says in the promotional poster (see above): “Everything is connected.” You can’t just change one event without having unforeseen ramifications: pull on one thread and everything unravels. But is there one single thread, if you could find it, in time and space, that could undo it all? This is the second question that “Dark” seeks to answer.

Is there are way to avoid all of this. If time travel caused all of the darkness and damage, is there a way to avoid the apocalypse; to repair relationships and overcome all that hatred?

The answer to this question is, I think, completely original in the time travel genre, it can be found in the stunning finale at the end of Season 3. Far be it from me to give away spoilers for the conclusion. I’ve tried my best to be spoiler-free so far. You’ll just need to watch all the episodes through to the very end. I promise you you’ll be glad you did.

As I mentioned, the reason why anyone looks to time travel in the first place is either death or separation or loss of a loved one. But time travel, on its own, solves nothing. The only way to prevent the apocalypse, the hurt, the pain the brokenness; is to avoid the original death and loss that’s the heart of the events at Winden. if you can stop this, you can stop the darkness in “Dark” from ever occurring. But even then, are you prepared for the sacrifice required ….

May I say: I hope you’ll find yourself embracing the time-traveling paradox and celebrating the apocalypse by watching “Dark” very soon. I highly recommend it as suitable for your pandemic lock-down viewing. Though do put your younger children to bed first.

To be continued ….

Disclaimer: I have no connection, financial or otherwise with Netflix Inc. or any of its subsidiaries.

Afterthought added 15 August, 2020.
For a series that I almost didn’t watch because of the gruesome suicide in scene 1 of episode 1, I came to find “Dark” the most consciousness expanding experience I’ve had in …. well, a very long time. For the first time, it made me take the prospect of time travel, as a scientist, seriously. It made me go back and reread much of James Gleick’s “Time Travel: A History” in a different light.

BTW: I received an email from James Gleick: “Thank you for this. I’ve never watched it, but your piece makes me want to.”

I’d be interested in your comments. What would you like me to write about in the continuation?


[1] This image from a promotional poster for “Dark” is the property of Netflix Inc. It is used here for the purpose of a review of the TV series under fair usage provisions of Copyright Law.

[2] Like many anglophones, I wasn’t aware of the classic short-film La Jetée. That was until I read about it in the book “Time Travel: A History” by James Gleick (Vintage, 2017). As Gleick points out, La Jetée is a play on the French, j’étaisI was. You can watch for yourself in the YouTube video below:

Is “Unprecedented Times” the Most Annoying New Cliché?

It was sometime in mid-March that I started to become aware of the phrase “unprecedented times” being used as a descriptive term for the COVID-19 pandemic. That’s only a few weeks ago but since the pandemic was announced by WHO (12th March), we seem to be living in a time-frame where one week feels like … Continue reading "Is “Unprecedented Times” the Most Annoying...

It was sometime in mid-March that I started to become aware of the phrase “unprecedented times” being used as a descriptive term for the COVID-19 pandemic. That’s only a few weeks ago but since the pandemic was announced by WHO (12th March), we seem to be living in a time-frame where one week feels like one-month pre-pandemic time.

I started to take notice of the phrase “unprecedented times” during the announcements by our Prime Minister Scott Morrison concerning the Job Keeper pandemic relief scheme on the 30th March. At the time I was impressed that the leadership of Australia was stepping up to the mark in making appropriate and well-timed responses to the pandemic  (see the YouTube video below).

Scott Morrison — in Aussie style, his name is endearingly abbreviated to (“ ScoMo “ ) — was reported as saying [1]:

“Now is the time to dig deep,” Morrison said. “We are living in unprecedented times. With the twin battles that we face and that we fight against – a virus and against the economic ruin that it can threaten. “This calls for unprecedented action.”

I might not have regarded ScoMo in such endearing terms had I known, at the time, that his message is an echo of an announcement made earlier by British Chancellor Rishi Sunak, of similar relief measures for the UK on the 20th March [2]).

Since ScoMo’s announcement, I’ve been hearing the phrase “unprecedented times” more and more. Even though it’s only been a few weeks, in pandemic time it seems much longer, and that phrase is starting to seem annoyingly clichéd. I’ve managed to avoid saying “unprecedented times” myself but I did catch myself saying: “we’re living through history” at the pharmacy the other day which sounds even more grating and pretentious.

I did a Google search with: “unprecedented times” after:2020-01-31  – and it yielded about 3,730,000 results. just since the end of January Interestingly, the results were for a diverse range of topics, not just topics directly related to COVID-19.

As an aside, there is now an easy way of specifying after and before dates for Google searches [3].

One reason I’m so annoyed with the usage of “unprecedented times” is that it’s patently untrue. As pointed out by Dr Kris Rallah-Baker [4], indigenous Australians have deeper recollections of an epidemic of smallpox that decimated their population when white settlers first came to this land. This applies to indigenous communities in other countries as well.

We’ve also had the Spanish-flu of 1918-20 in the memory of some older people still living. We’re had related major ‘flu epidemics, at least once or twice a decade since the Spanish flu. We’re had the HIV/AIDS epidemic. We’ve had SARS, MERS and more recently the zika virus. It’s not as though the COVID-19 pandemic has come completely out-of-the-blue. There’s been plenty of warning signs that a new major pandemic was a very real threat. None of us can say it’s unprecedented in the sense that it was completely unforeseen.

Dr Kris Rallah-Baker [4] is correct to suggest that it would better to say that these are “dangerous times” rather than “unprecedented times.” The trouble with “dangerous times” is that it’s hard to see how we could do much individually to avert the dangers. Is it the disease itself what we should be afraid of contracting? Or the side-effects of a disease that leaves some people more or less unaffected but for others, it cruelly ravages their bodies or takes away their lives? Should we be afraid of the severely crippling indirect effects that the disease is having on the economy and upon our own livelihoods?

COVID-19 is a completely new virus for humans that no one understands well. Not even the experts in epidemiology. I have heard the expression “uncertain times” being used but it’s interesting that we seem, as a global community, to have settled on “unprecedented times” to express all our fears, anxieties, grief, loss, uncertainty and powerlessness that we’re collectively experiencing during this pandemic.

The final point I want to raise is that in saying “unprecedented times” for the whole of humanity, we are also implying that everyone is affected — so we’re all in this together. However, the phrase “unprecedented times” hides or glosses over the dangers we face. In regard to those dangers, not everyone is exposed equally. For some, notably the elderly, those in nursing homes, indigenous communities and other minorities, those who are homeless or living in overcrowded accommodation or occupying a lower-paying jobs in our society, are exposed to disproportionately higher levels of danger from the effects of this virus. Either through a direct threat to health and life or to the economic impact of the virus.

If we don’t look after these endangered cross sections of our communities then it is to the peril of everyone because the virus takes no heed to your wealth or social standing. It’s coming for everyone it can infect. Unless we  protect the disadvantaged it will come for the better off as well.

In conclusion, the expression “unprecedented time” has become clichéd to the extent that is becoming hard to hear anymore. However, it seems to be the phrase that we’re collectively settled upon as a global society to express our feelings during this pandemic. It expresses our fears for the far-reaching dangers we face, both to health and economic livelihood, that we can’t fully understand.  Importantly, it has become a euphemism, as well as a cliché, so that we don’t have to use words that remind us too much of the real dangers that the virus poses.

What do you think? Tell me in the comments.


Addition 28th May 2020. ALDI’s Supermarkets in Asia-Australia have started an advertising campaign “Unprecedented times call for Unprecedented Prices” [5]. It was amusing the first few times it played but it becomes highly annoying after hearing the same advertisement dozens of times. My wife says she’ll start tearing her hair out the next time she hears it. I might do the same but its already falling out without further help from me.

Edit: 16th August 2010, a factual error  was corrected. The announcement of relief measures for the UK were made by Chancellor Rishi Sunak rather than Prime Minister Boris Johnson.


[1] Kelly Burke, 7 News, “Coronavirus job keeper: Scott Morrison announces $1500 fortnightly payments to Australian workers,” published 30 March 2020; accessed:  17 April 2020; available online:

[2 Richard Partington, The Guardian, “UK government to pay 80% of wages for those not working in coronavirus crisis,” published: 21 March 2020; accessed: 17 April 2020, available online:

[3] George Nguyen, Search Engine Land, “Search Google by date with new before: and after: search commands,” published 10 April 2019; accessed 16 April 2020,; available online:

[4] Dr Kris. Rallah-Baker, @INDIGENUOUSX, “We live in dangerous times, not unprecedented times,” published 27th March 2020; accessed 17 April 2020, available online: 

[5] Zoe Wilkinson, Mumbrella, “Aldi’s ‘precedented’ prices continue through these ‘unprecedented times’ in latest spot,” published: 18 May 2020, accessed: 27 May 2020, available online: 

Herd Immunity and COVID-19

This morning I was watching TV, the Today show. as Karl Stefanovic and Allison Langdon were discussing the concept of “herd immunity” which had been considered by the UK Government early in the COVID-19 pandemic. Their casual conversion considered whether it might be a good idea to deliberately infect younger Australians with the coronavirus (SARS-CoV-2) … Continue reading "Herd Immunity...

By Snapwire from Pexels (free to use)

This morning I was watching TV, the Today show. as Karl Stefanovic and Allison Langdon were discussing the concept of “herd immunity” which had been considered by the UK Government early in the COVID-19 pandemic. Their casual conversion considered whether it might be a good idea to deliberately infect younger Australians with the coronavirus (SARS-CoV-2) [1] whilst isolating and protecting older and more susceptible members of the community. This apparently casual conversation raised alarms for me as I’ll explain below (see after the jump). The infographic video that Allie used to explain the concept of “herd immunity,” seemingly made a compelling argument for it. Fortunately, they brought in sensible expert advice in the form of Dr Sanjaya Senanayake an Infectious Diseases physician and Associate Professor from the Medical School at the Australian National University (ANU) (see the YouTube video below).

I almost started clapping when Dr Senanayake decisively skewered the argument for herd immunity put by Karl and Allie. As he pointed out, even for a case fatality rate of 1% then 160,000 Australians would die and many more would become seriously ill. This would overwhelm our health systems, bringing them to a point of collapse. Many of us are now familiar with the argument of “flattening the curve” by slowing the rate of infection, thereby preserving our healthcare services [2].   

This argument, originally derived from modelling studies at Imperial College, persuaded the UK Government to abandon its ill-conceived plans for herd immunity. Sir Patrick Vallance, the UK government’s chief scientific adviser who is reported as saying: “enough of us who are going to get mild illness to become immune [2].” This thinking seems to have been based upon policies for an infection like measles which is far more contagious than SARS-CoV-2 but has a lower fatality rate [2].

The basic reproduction rate, denoted by R0, is a measure of the number of people a carrier of the virus is able to infect in the absence of health control measures. The basic R0 can be very difficult to determine for a novel virus such as SARS-CoV-2. In practice, the effective reproduction number, Re, is used. This is determined from reported infection for a particular social setting and might vary from region to region. The most contagious viral infections (i.e., most likely to be communicated person-to-person) in order of R0 value [3] are:

  1. Measles (most contagious)
  2. Whooping Cough
  3. Mumps
  4. Chicken Pox
  5.  Smallpox (eradicated)
  6. =====>  COVID-19 fits in here (for a R0 value of around 3.0 [4])
  7. Seasonal Flu (least contagious)

To highlight the data behind the argument given by Dr Senanayake in the video above. Measles is one of the most contagious diseases known with an  R0 of about 18. In the absence of a vaccine, a disease as infectious as measles would be exceedingly difficult to contain: herd immunity might be the only available option. SARS-CoV-2 is not nearly as contagious (R0 value of around 3.0 [4]) as measles but has a higher fatality rate: so it makes far more sense to implement health control measures such as physical distancing or quarantine or personal-protective-equipment (PPE) to contain the spread.

The basic reproduction value R0 also determines the percentage of the population required to achieve herd immunity 100(1-\frac{1}{{R}_{0}}). For highly infectious measles we need 94% of the population to be immune. For herd immunity with less infectious SARS-CoV-2, where  R0 = 3.0, then 67% of the population needs to be immune.

The goal of health control measures is to reduce the effective Re-value to less than 1.0 which will decrease the number of infections over time; eventually bringing the disease to levels that can be more easily managed.

This article started out as an email I sent to the Channel 9 Today Show pointing out that they have a moral and social responsibility to the Australian public to take an unmistakable stance: herd immunity by deliberate infection with SARS-CoV-2 is not to be countenanced.

Channel 9 should avoid even the slightest impression that it might be a good idea for younger people to infect themselves with SARS-CoV-2 in the same way that might have been done in the past with so-called Chickenpox parties.

In addition to all that has been written above, it is common for a percentage of viral infections to have serious complications, some of which don’t manifest themselves for years afterwards.  WIth novel SARS-CoV-2 we know almost nothing about its long term effects. Consider the following points:

  • we don’t know how much immunity is conferred from recovering from COVID-19, there are conflicting data and no one knows for sure just how long immunity will last;
  • there is very little data on repeated exposure, with Dengue Fever the second infection is almost always much worse than the first and often leads to death;
  • some viruses are able to shield themselves inside the body and show up later n life, e.g.,  Chickenpox can return later in life as shingles and Hepatitis B can lead to liver cancer in later life.

With these considerations in mind, a significant proportion of younger healthier people, deliberately infecting themselves, will suffer adverse complications and will clog up the hospital system which is what our Health Authorities are engaged in extraordinary efforts to avoid.

The best way to gain herd immunity is by living the best life we can under the “new normal” of coronavirus until an effective vaccine, or another treatment becomes available (likely sometime in 2021). As well as doing everything we can by physical distancing and hand washing to avoid infection until then. Herd immunity will then be conferred more safely and effectively by the vaccine,

I’d be interested in what you think in the comments.


[1] World Health Organisation, “Naming the coronavirus disease (COVID-19) and the virus that causes it,” available online, accessed: 9th April 2020:

[2]  Cathleen O’Grady, National Geographic, Science, “The U.K. backed off on herd immunity. To beat COVID-19, we’ll ultimately need it.,” published: 20 March 2020, accessed: 9 April 2020., available online:

[4] Ana Sandoiu, Medical News Today, “Coronavirus may spread faster than WHO estimate,” published: 18th February 2020, Accessed: 9th April 2020, available online:

Update: 09 August 2020.
As I mentioned in the original article, it is difficult to get a reliable value for R0 for a novel virus. A more up-to-date R0 for SARS-CoV-2 is 5.7 [5] instead of about 3.0. Which means that SARS-CoV-2 is much more contagious than previously thought. However, this doesn’t affect any of the conclusions of the article.

[5] Vanessa Bates Ramirez, Healthline, “What Is R0? Gauging Contagious Infections,” updated: 20 April 2020, accessed: 08 August 2020, available online:

The Meaning of a COVID-19 Second Wave

I’ve been hearing the term “second wave” being used more and more frequently in connection with the COVID-19 crisis. For instance, in this article [1] about Singapore, Taiwan and Hong Kong facing a second wave of coronavirus cases from citizens returning from overseas. This seems faulty logic to me: it isn’t a second wave, it’s … Continue reading "The Meaning of a COVID-19...

Photo by Emiliano Arano from Pexels

I’ve been hearing the term “second wave” being used more and more frequently in connection with the COVID-19 crisis. For instance, in this article [1] about Singapore, Taiwan and Hong Kong facing a second wave of coronavirus cases from citizens returning from overseas. This seems faulty logic to me: it isn’t a second wave, it’s a continuation of the first wave relocating from a different geographical place. I don’t mean just to single out this article because numerous TV and radio newscasters, newspaper articles and websites worldwide are commonly using the same kind of wonky logic in connection with a so-called coronavirus second wave. When what they really mean is that the same source of the virus has either: (i)  lead to a continuation of cases from another location or (ii) made a reappearance after initial efforts for containment have only been partially successful.

Why do we describe resurgence in coronavirus cases in an inconsistent manner with the phrase “a second wave”? What has happened that we can’t agree on the meaning of a term that is so important to the coronavirus crisis?

My answer is after the page jump.

One answer is that for a true second wave we need an outbreak of coronavirus from a second source that is different (in some meaningful way) from the first source. All viruses mutate and show genetic drift. For the coronavirus, since the initial outbreak in Wuhan China, there is no suggestion that a new variant strain has become active. Therefore, my contention is that instead of saying, a “second wave,” rather we should be saying a “continuation” or a “resurgence” of coronavirus cases.

I might not be trained in virology or epidemiology but I’m trained to think scientifically and I make conscious efforts to ensure what I say is based upon factual research. Accordingly, my response to the question I raised above: the phrase “second wave” is indelibly written into our global emotional memory of the Spanish Flu pandemic of 1918-9 (as I’ll get to shortly). When a new crisis emerges, our emotional response outweighs a logical or scientific one. So we’ve stuck to using terminology which doesn’t convey a correct scientific meaning.

It’s my contention is that this needs to change: it’s time to settle upon a consistent meaning for what a “second wave” is. Journalists have an important role in setting a standard that the rest of the community can follow.

Q. Does it matter that “second wave” as a term is being scientifically misused?

For a full answer to this, I need to explain about the use of the term “second wave” during the Spanish Flu outbreak during 1918-9. This explanation will follow below.

The short answer is not much- at present. However, if at a future point there is a true second wave of coronavirus then the phrase “second wave” will have lost much of its meaning. Very likely we’ll fail to heed the warning or shake off our complacency. In that event, incorrect terminology will have had a major negative impact on our response to the threat.

Spanish Flu of 1918-9

The Spanish Flu started in March 1918, lasted two years, infected up to 500 million people worldwide (around ⅓-rd of the world population at the time), of which up to 50 million died, This was more than the total fatalities during the preceding 4 years of WWI [2]. The initial spread of the virus was thought to be brought about by soldiers returning after WWI. The first infections in the United States weren’t particularly deadly. but that changed, during a horrific 3-month period during the fall-autumn which become known as the “second wave.” The second wave spread around the world (affecting NSW Australia in two high-mortality waves during 19/3/1919–27/5/1919 and 28/5/1919–30/9/1919  [3]).

From the above paragraph, you can readily see how the severity of the second wave of the Spanish Flu has etched its way into the collective memory of succeeding generations. Naturally, when coronavirus outbreaks occurred in early 2020 it raised fears in the minds of many that an even more deadly second wave was looming a few months down the track.

There were third and successive waves as of infection as well. In America, the third wave [2] occurred during the summer of 1919 and was almost as severe as the second wave. Outbreaks after the third wave became progressively weaker and until the virus simply disappeared into the endemic background of seasonal influenza.

Replication of the Virus within Cells

A virus consists of a few proteins and some genetic material. Their apparent simplicity disguises a sophisticated strategy to subvert the molecular machinery of the host cells that they evade and turn them into nanoscale manufacturing centres for producing more virus. This process is known as viral replication.  If you’re looking the understand viruses in more depth I recommend “Molecular and Cellular Biology of Viruses” by Phoebe Lostroh, a rather technical but beautifully illustrated textbook on the subject [4].

The influenza virus is typically subject to high rates of mutation. For Influenza, each replication can result in one mutation per offspring genome. Resulting in a number of somewhere around 10,000 mutated offspring for each infected cell. This gives ample opportunity for natural selection and genetic drift to lead to a significant range of diversity in the virus over a time span of several months to a year or two. It’s this diversity, and the appearance of deadly new strains of the virus, behind the second and third waves in the Flu of 1918-9.

Mutations give rise to a relatively slow rate of viral diversity referred to as genetic drift. [As an important side note: genetic drift should be distinguished from genetic shift which can occur if two viruses infect the same cell. In this case, some of the offspring will have recombined genome sequences from each of the parent viruses. Genetic shift is of greater concern, because there is the potential for a pandemic, since the immune response for one or other of the parent viruses will not be effective against the offspring (see Ref 4, p430-1)].

By way of contrast, there are strong reasons to believe that coronaviruses have a molecular proofreading mechanism which corrects misincorporated genetic information from being passed on to the next generation (as is illustrated in Ref 4. pg 157).  hence genetic drift occurs at a significantly lower rate for coronaviruses than for influenza.

Because of a lower rate of mutation, it is unlikely that we’ll see the same kind of the second wave of the coronavirus infections in 2020 as occurred in the Spanish influenza of 1918-9. Any resurgence in infections will likely be the result of human error in failure to contain the virus or from allowing people to spread the virus by travelling across regions. This shouldn’t be called a “second wave” because that term implies that something unexpected has happened with the virus itself (i.e., that it has mutated).

Our fears that the worse of the coronavirus is just around the corner in a second wave is misplaced. On the other hand, the coronavirus is likely to remain for around for a long time. It’s unlikely to weaken in the way that the Spanish Flu did after 1919. The coronavirus of 2020 and the H1N1 Influenza of 1918-9 are distinctly different kinds of beasts,


[1] Liza Lin and Joyu Wang, The Wall Street Journal, “Singapore, Taiwan and Hong Kong Face Second Wave of Coronavirus Cases,” published: 17th March 2020, accessed: 23 March 2020, available online (subscription based):

[2] Dave Roos, History, “Why the Second Wave of the 1918 Spanish Flu Was So Deadly,” published: 03 March 2020, accessed: 23 March 2020, available online:

[3] NSW State Archives and Records, “Pneumonic Influenza (Spanish Flu), 1919,” accessed: 24 March 2020, available online:

[4] Phoebe Lostroh, “Molecular and Cellular Biology of Viruses” CRC Press, Taylor and Francis Group, Boca Raton, FL (2019).

Updated: 22nd August, 2020 because I thought that the article was important enough to receive wider circulation. So I submitted it to The Guardian for  publication.

My Trip Down Memory Lane

Thinking about updating my curriculum vitae today, I was triggered to reminisce about my senior high-school experiences back in 1974-5. Amazing how sharply some memories came flooding back through the eyes of a 17-year-old. I remember about being part of the Science, Mathematics and Technology group of 4 that all shared dreams of becoming scientists, … Continue reading "My Trip Down...

Thinking about updating my curriculum vitae today, I was triggered to reminisce about my senior high-school experiences back in 1974-5. Amazing how sharply some memories came flooding back through the eyes of a 17-year-old. I remember about being part of the Science, Mathematics and Technology group of 4 that all shared dreams of becoming scientists, technologists or engineers: Wayne, Geoffery B,, Jon and myself. At the beginning of senior high, one of the Industrial Arts teachers had suggested that the 4 of us take a lower level of English so we could concentrate on Maths, Science and Industrial Arts. As you can imagine, the English Department was not at all impressed that some of their students were taking a level of English that demanded less than their full capabilities. What happened next is far from what you might expect (read the full story after the jump).

Bags packed ready for my trip down memory lane [1].

After the 4 of us showed up at the English level 3 class in week 1 of term 1 the English staff remonstrated strongly with me and my compatriots. My compatriots more so than me as I remember. Wayne and Geoffrey B (Geoff more reluctantly) eventually reconsidered and moved up 2 levels of English to where the teachers thought they were best placed. Jon and I remained steadfastly in the level 3 class. I never understood why the teachers spent more time persuading my friends than me. Perhaps they considered me the ringleader and the least likely to be swayed.

[From my perspective now, I wouldn’t ever have advised my 17-year old self to do this. After all, the key to gaining most jobs, then and now, is through outstanding communication skills.]

Our level 3 English teacher was a young, pleasant, mustachioed man not long out of Teacher’s College (as they were known at the time). He considered it his responsibility to give Geoffery B (still in the same class at this time), Jon and me additional reading materials outside of class. This is the surprising part, he gave us Anarchist readings from Proudhon and Bakunin (interpreted readings rather than the original works). I don’t know what Geoffery B and Jon thought, or whether they even read any of the books, but I devoured the reading in the same way that I devoured reading the “Foundation” sci-fi trilogy from Isaac Asimov during the previous school holidays.

So here I was, at 17, the budding scientist, reading Proudhon and learning that “property is theft” with the full (apparently) encouragement of my teacher and the School’s English Department.

As I rethink over this now, I suspect that the English Department made the request that our teacher gives us additional readings but that they would have been horrified if they had learnt that he had selected such Anarchist readings for 17-year-olds.

Not rioting-in-the-streets Anarchism [2].
As it was I was very impressionable and these readings have strongly influenced my thinking ever since. I hasten to add that here we’re talking about political anarchism, not about rioting-in-the-streets anarchism. Over the next few years, I went on to read “Homage to Catalonia” and “Animal Farm” by George Orwell because I wanted to learn more about related political ideologies, especially about the alternative political views in the Spanish civil war which I had read about in one of my extracurricular readings in senior English.  I read “For Whom the Bell Tolls” by Hemingway for the same reason.

Mostly, my teenage Anarchist readings have contributed to a broader outlook on life and a love of reading on diverse topics, Quite a benefit for a  scientist, where you find there are so many pressures to specialise in your particular area of expertise. Deep-down, I haven’t forgotten about those extracurricular readings, in as much as  I believe people should be able to organise themselves locally, but I’ve realised it’s not very pragmatic for humans to live without government and rules. Though I still dream that it might be possible at some point for future humanity.

Apart from what I have written above, I have no long-lasting influences from high-school exposure to the anarchist writings of Proudhon, Bakunin, Prince Kropotkin and so on.

Is Dr Mark Selby an Anarchist?

Despite what he claims is this guy an Anarchist? Consider the following evidence:

Whilst at QUT, who openly encouraged his students to think for themselves and to be critical? He even challenged students to disagree with the teachings of their textbooks. Even a well-known Analytical Chemistry textbook in its 10th edition!

Points supporting that this man is an anarchist:

    • back in the 1990s he drew wonky freehand straight lines on the overhead projector (OHP) during lectures — anarchists can’t draw straight-lines because they don’t use rulers;
    • copies of these same wonky OHPs were reproduced in PowerPoint slides for lectures after 2000.;
    • he was known to favour herbal and green teas during one period of his life, anarchists don’t drink proper-tea because property is theft!

The evidence speaks for itself!

Furthermore, this man is suspected of being a perfectionist, a condition that affects many academics and former academics. Though he may be trying to improve.

Share your thoughts in the comments below.


[1] Image by Shany Kasysyaf from Pixabay
[2] Image by Shany Kasysyaf from Pixabay

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