As 2020 Ends, Let’s Celebrate Science

We’ve finally reached the end of 2020, a year that many people are happy to forget. In the history books, 2020 will be known for little besides the Covid pandemic. Fortunately, the end of this disaster is in sight. With multiple vaccines starting to roll out, it looks like 2021 will be a better year.

Speaking of vaccines, I’ve been racking my brain to find things to be thankful for this holiday season. It’s not easy. My wife, daughter and I are in lockdown in Toronto. The rest of our extended families are in lockdown in Alberta and BC. So no family Christmas this year. I suspect it’s the same for many people. Fortunately, the Covid vaccine provides some light at the end of the tunnel. This is something to celebrate. But more than that, we should celebrate the whole enterprise that made the vaccine possible — science.

In the grand scheme of our species, it was not long ago that we believed infectious diseases were caused by ‘bad air’. The idea that germs cause disease became widely accepted only in the late 19th century, thanks largely to the work of Louis Pasteur. Vaccines are a similarly recent invention.

Our knowledge of infectious diseases is certainly something to celebrate. But as a political economist, I can’t help note how vaccination is stubbornly related to social inequalities. Vaccines are the ultimate public good — a life-saving device that is the product of our collective scientific effort. Predictably, though, this public good is not shared equally. In the last mile, vaccines are paywalled by private companies. So while in principle vaccines could be free for every human, in practice they are not. The result is that vaccination rates grow with income. The richer the country, the higher the vaccination rate. Here’s the relation in 1988.

Figure 1: Vaccination rates vs. GDP per capita in 1988. The vaccination rate is the share of one-year-olds vaccinated against diphtheria, pertussis, and tetanus. (I’ve plotted the vaccination rate on a reverse log scale, meaning it zooms in as vaccination rates approach 100%.) [Sources and methods]

Over the last 30 years, we’ve made progress in vaccinating the world’s population. Figure 2 shows the data in 2017. Relative to 1988, the vaccination rate has increased across all countries. Still, vaccination is a function of income. The richer the country, the more people get immunized.

Figure 2: Vaccination rates vs. GDP per capita in 2017. The vaccination rate is the share of one-year-olds vaccinated against diphtheria, pertussis, and tetanus. (I’ve plotted the vaccination rate on a reverse log scale, meaning it zooms in as vaccination rates approach 100%.) [Sources and methods]

Vaccines and cumulative scientific knowledge

When a pharmaceutical company patents a new vaccine, the logic is that they did the work … so they should reap the reward. True, the company probably did R&D and clinical trials. But this alone did not create the vaccine. At every step, the company built on existing scientific knowledge.

Take the Pfizer Covid vaccine. It’s the first vaccine to use RNA to produce an immune response. That’s a major achievement, but not one produced by Pfizer scientists alone. Just understanding the RNA molecule itself has been a century-long project that started in the 1930s. Every aspect of the Pfizer vaccine probably has similarly deep roots.

Vaccines are the product not of one company, but of our cumulative scientific knowledge. Figure 3 shows a way to visualize this fact. I’ve plotted here the growth of the cumulative number of scientific papers published over the last three centuries. Think of this corpus as humanity’s accumulated knowledge. Along the curve, I’ve labelled the dates of new vaccines. Unsurprisingly, new vaccines have come as our scientific knowledge exploded.

Figure 3: Vaccines and the growth of cumulative knowledge. I’ve plotted here the growth of the cumulative number of scientific papers over the last three centuries. Along the curve, I’ve labelled the timing of major new vaccines. (Note: the y-axis uses a square-root scale.) [Sources and methods]

True, only a tiny fraction of scientific papers are directly related to immunology. But knowledge is like the tree of life. As you trace it backwards, it becomes clear that there is only one tree. Here’s a way to think about it. Suppose that an article about a vaccine trial references 45 other papers. Each of these papers in turn cites 45 papers … and so on. At this rate, after 6 generations of articles the web of citation reaches 83 million papers (456). That’s roughly the whole of the scientific corpus.

Because vaccines are a product of our cumulative knowledge, the number of major vaccines scales with the cumulative number of scientific papers. Figure 4 shows the trend.

Figure 4: Cumulative number of major vaccines vs. the cumulative number of scientific papers. (Note that I’ve used a log scale on both axis.) [Sources and methods]

What’s interesting is that the trend is non-linear. The cumulative number of vaccines grows roughly with the square root of the cumulative number of papers:

\displaystyle \text{number of vaccines} \propto \sqrt{\text{number of papers}}

What this means is that over time, producing new vaccines becomes more knowledge intensive. That’s not surprising. The first vaccine was discovered by accident. In 1796, the British doctor Edward Jenner found that getting infected with cowpox (a mild disease) conferred immunity to smallpox. The smallpox vaccine was born. (Side note: vaccines owe their name to this cowpox discovery. The word ‘vaccine’ comes from vacca, the Latin word for cow.)

As time went by, the development of new vaccines became less serendipitous. The polio vaccine, for instance, was a massive public health effort. In 1954, the Salk vaccine was tested on 1.8 million US children. That’s hardly a small-scale operation.

We see this kind of trend throughout science. Three centuries ago, Isaac Newton did basic science using inclined planes. Today, physicists do basic science using billion-dollar particle accelerators. As science advances, new discoveries become more intensive, both in terms of resources and prior knowledge.

And that brings me back to paywalls. It’s a crime when vaccines get paywalled in the last mile. But it’s also a crime when scientific knowledge gets paywalled. Here, however, we have something to celebrate. In principle, the vast majority of scientific papers are paywalled. But in practice, almost all scientific knowledge is freely available on the internet. That’s thanks largely to one renegade scientist — Alexandra Elbakyan. She created the Sci-Hub database that now houses more than 80 million scientific articles, all available for free. It’s these Sci-Hub papers that I’ve plotted in Figure 3.

As we head into 2021, let’s be thankful for the Covid vaccine. But let’s also be thankful that for the first time in history, virtually all scientific knowledge is available for free. That’s something to celebrate.

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Sources and methods

Data for vaccination rates vs. GDP per capita is from Our World in Data.

Data for new vaccine dates is from Wikipedia.

Data for Sci-Hub papers by year is from Library Genesis. The raw data comes as an SQL database dump. If you’re interested, I built an R function that can parse this data. Check it out at Github.


  1. Great stuff as per usual. I have a little trouble with calling the new drugs a “vaccine”. The word “vaccine” to most people implies immunity. The vaccines available so far do not give immunity. They don’t even keep you from being contagious! You can and will still be actively sick and be carrying the virus around after having the shots. They are more like a flu shot, and not even that good. A slow release, long lasting, cold and flu symptom suppressor. Yet not too long lasting, wouldn’t want to slash the throat of the cash cow.

  2. I am a stout believer in science and the scientific method in general, but I
    am pretty sceptical about what is being reported as “scientifically proven”
    in mainstream media and government proclamations, including the WHO.

    Yes, considerable progress has been made in the field of vaccination, in
    particular with respect to Covid19. This progress gets a lot of (mostly
    positive) attention in the media nowadays. I reserve the right to remain
    sceptical as to how effective and safe these vaccines are going to be in
    practice, given the short time we had to evaluate them; in particular it
    remains to be seen whether they can effectively reduce infection rates on a
    suitably large scale. I am definitely not an expert on these matters, but
    from what I read in various articles about the new vaccines (pro and
    contra), they are more akin to genetic manipulation (of human body cells)
    than classical (passive) vaccination. Given that genetic manipulation has so
    far never been practiced (on a large scale) in order to make life better for
    the average human, but solely to increase control and extend capital
    accumulation (and to the detriment of health and well-being of most people),
    I consider it unlikely that this time it’s going to be different.

    Be that as it may, vaccination is surely not the only possible answer
    science can give us with regard to Covid19. When you look at possible
    *treatments*, there is a striking discrepancy between what is reported by
    (western) media and proclaimed by (western) governments on the one hand, and
    the body of scientific knowledge worldwide on the other. For instance,
    worldwide evidence clearly points to HCQ being a very effective treatment
    when given early and in proper doses (possibly in conjunction with other
    supplementary medication such as Zinc); see,, and the facts gathered by (I am not affiliated with any of
    the people behind these websites, and in the case of “America’s Frontline
    Doctors” I would wager that both your and my political opinions differ quite
    a lot from theirs. This doesn’t mean they can’t be right in this particular

    Constrast this with the media headlines and with what the official sources
    proclaim (that HCQ is ineffective or harmful, that there are no known
    effective treatments other than purely symptomatic ones, except possibly the
    hugely more expensive Remdesivir).

    It appears that there are strong interests, especially in the western world,
    that aim to suppress or at least prevent wide dissemination of these
    scientific results. A very large and often cited study about HCQ and Covid19
    (doi:10.1056/NEJMoa2022926, also evaluated at comes
    to the conclusion that HCQ is ineffective and may even be harmful. Closer
    inspection reveals that the way HCQ was used here (late treatment, very high
    doses) does not correspond to how it has been used in studies that reported
    success (early treatment, lower doses). Furthermore, at the time the study
    was done, it was already known from at least one previous study in Brazil
    (doi:10.1016/S0140-6736(20)31862-6) that the very high doses used had a
    detrimental effect. Apparently this did not prompt re-evaluation of the
    trial procedures. I’ll leave it to the reader to draw their own conclusions.
    It may or may not be of interest that the Gates Foundation is among the
    sponsors of this study.

    Let me finally remark that I feel pretty uncomfortable to defend a position
    advertised by people like Trump and Bolsonaro (which I both detest). But I
    can’t let that influence what I think is true.

  3. […] Figure 1: Vaccination rates vs. GDP per capita in 1988. The vaccination rate is the share of one-year-olds vaccinated against diphtheria, pertussis, and tetanus. (I’ve plotted the vaccination rate on a reverse log scale, meaning it zooms in as vaccination rates approach 100%.) [Sources and methods] […]

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