Chapter X: Empiricism | The Philosophy Of Science by Steven Gussman [1st Edition]

        “In general, we look for the new law by the following process: first, we guess it... Don't laugh,

        that's really true.  Then we compute the consequences of the guess... to see what it would imply,

        and then we compare those computation results to nature.  Or, we say compare to experiment, or

        experience... Compare it directly with observations to see if it works.  If it disagrees with

        experiment: it's wrong.  In that simple statement is the key to science.  It doesn't make a difference

        how beautiful your guess is, it doesn't make a difference how smart you are, who made the guess,

        or what his name is: if it disagrees with experiment, it's wrong, that's all there is to it.”

        – Richard Feynman^I

        Because the two sides of the philosophy of science coin are epistemology and ontology, one's epistemology should keep this ontological end-goal in mind.  It is from this recognition that the scientific emphasis on empirical evidence or empiricism derives.  Due to the fact that the claims our epistemology lead us to are ultimately claims about the world, and since we have no firmer initial grounds than induction, the systematic measuring of the actual-world (whether through experiments or passive observations) against our predictions is key.^II  Some philosophers will say that the scientific method is just a useful tool, and that we should forget about trying to describe or understand some real world through its use.^III  Such thinkers are predisposed to emphasizing that we don't confuse our “mere models” of reality with reality itself, as though actually saying anything about the cosmos as it is, is a foolhardy goal.  This is one of those incoherent views that is espoused as though it is the enlightened, moderate position: in truth, those that make this argument have removed the justification for needing empirical evidence in the first place.  What could we mean by a “useful” hypothesis, if not “useful at accurately describing the world”?^IV  After all, a key does not fit a lock by coincidence: when something is useful in this sense, it is because it actually contains information about something else within it, and therefore should be taken seriously as an accurate model (or reflection) of the lock (the cosmos).  The kernel of truth to the anti-ontology argument is that one should worry about whether one has actually discovered the key, or whether they've merely managed to picked the lock!^V  Such as doors are, most lock-picks will not get the door open; a successful lock-pick is an approximation, whereas a key represents the analytical answer.  Both suggest models of the world, and the kernel of truth is that due to the provisional nature of knowledge,^VI we cannot ever know if we are in possession of the full, final model isomorphic to reality itself.  But again: all beliefs are beliefs about the world, and when it comes to the quality of those beliefs (their likelihood of being closer to the truth), one can certainly do no better than the philosophy of science.

        One evidentiary mistake people make is to put too much stock in anecdotes—stories of something that happened (or appeared to have happened) to themselves or someone else they know (or know of).  Because we evolved to recognize patterns in the world, and because this was tuned to fitness-maximization rather than truth-maximization (coupled to the documented negativity bias in psychology),^VII we can often times become overzealous when noticing patterns and drawing conclusions (particularity extrapolating conclusions) from them.^VIII  Some will retort, when accused of reasoning via anecdote, that, “anecdote is singular data.”  But it is not: datum is singular data.  Data is carefully measured and recorded; anecdotes are passively perceived and remembered.  From there, it is true that the other problem with anecdotes is indeed that of the smallest, most biased sample size imaginable—often around N = 1.  The law of large numbers tells us that as the number of trials tends to infinity, the frequencies of probabilistic effects will tend towards their probability: one will get closer and closer to perfect 50/50 heads-or-tails the more times they flip a coin and record the outcome.^IX  Now, very often hypotheses do arise from anecdotes—patterns a researcher thinks he sees in the world.^X  But one must realize that one may be mis-perceiving, or that otherwise that the effect size might not be very large in a large sample as one formulates one's idea and plans to base one's belief or disbelief in it on a statistical analysis.  Sometimes, there is a singular datum—which is better than an anecdote because it is based on reliably recorded measurements—but is still not suggestive on its own because it is an N of 1.  In medicine, these are called case-studies because it is a scientific write-up of a particular singular case of interest, meant to stimulate larger, more high-powered research.  When we talk about measurements, of course we ultimately need to use our fallible senses,^XI but we can and do radically extend them through technology, potentially leaving no part of the universe out of our eventual sight.  Literally speaking, astronomers for example use instruments in place of their eyes to measure light-waves in the infrared or ultraviolet regions of the light-spectrum which appear invisible to the naked eye; they then use other technology to either print out numbers or even draw visible-spectrum-color pictures to show us the results of looking at the cosmos in this way.^XII  It is not always appreciated how much of a rebuke this is to the view espoused by some that, despite our best scientific efforts, we will always remain somewhat ignorant because we are trapped in our fallible bodies, thinking with fallible brains.

        When we make predictions and test them with measurements, there is a difference between accuracy and precision.  Accuracy refers to veracity—how close to reality a prediction or measurement is (none are ever perfect).  Precision on the other hand refers to how many decimal-points out our answer goes!  Irrational numbers would appear to have infinite precision such that we may only ever estimate their values (thankfully, the more precise, the less significant the digit is to the total number).^XIII  It may sound paradoxical, but one may have a highly precise but inaccurate measurement of, say, the temperature outside on a given day: all that would be needed is that the measurement instrument is either mis-calibrated or otherwise overly susceptible to noise other than the temperature one is trying to measure, but nevertheless remains a very sensitive instrument that relays temperatures out to the fourth decimal place.  One can imagine it is 30.1456 °C outside, and yet a measurement apparatus reported 35.4541 °C—it is precise out to four decimal places, but that means nothing because it is highly inaccurate (being off by five whole degrees).  Likewise, you can imagine a highly accurate, but low-precision thermometer which might report just 30 °C (this is more useful than the previous apparatus, but the low precision may nonetheless leave it useless for certain sensitive purposes).  Of course in a perfect world, we want a measurement device that is both as accurate and precise as possible; but in the real world of engineering, trade-offs and compromises must be made.

        Given that scientists have to agree that the normative goal of the scientific method is truth-seeking (or veracity), and that there is one reality that we are trying to understand, epistemology is only useful if it accurately reflects that reality: the cosmos.  This is the only reason that scientists need to check our ideas against empirical evidence (unlike, say, authors who know, and whose audience knows, they are engaged in fiction)—because we're trying to have a deeper understanding of the world around us.  We can often only directly observe the effects of causes, and so we figure out the different predictions about the same measurement made by competing hypotheses such that empirical measurement will allow us to infer which mechanism is at play in reality.  By checking if the different hypothetical causal frameworks make novel predictions which others don't, we make our ideas admit of either experimental or passive observational evidence.  It is crucial that one's framework is built as elegantly as possible to simply give rise to what one already knows—those things the current best theory predicts as well as some anomalies it fails to predict.  The novel predictions are then an effortless consequence of that mechanism that no one placed in there by design.  Even better is to see different lines of evidence from different researchers converge on the same frameworks and predictions (or otherwise make new sub-predictions which also imply the original claim is true, if confirmed).  This variety helps control against unknown frameworks which may make the same single prediction; as well as the biases of different researchers or experimental designs, and even for errors and flukes.^XIV  Evolutionary economist Gad Saad calls such converging lines of evidence, nomological networks of cumulative evidence.^XV

        Passive observation is the most basic form of empirical evidence—it is when one measures the world.  Technically, you commit passive observation all of the time by just sensing the world, though many studies will use more precise measurement apparatuses than the human senses.  Climate scientists, for example, rely heavily on passive observation, such as measurements of how much carbon-dioxide (CO₂) we put out into the atmosphere and of what the brute temperature of the planet is.  Another example comes from the astronomers and astrophysicists; we sure cannot perform intergalactic experiments!  Thankfully, these large and long-time processes admit of some helpful natural tools.  For one, there are many stars in the sky and because they are in different times in their life-spans, we may deduce the time-dynamics of stars even if those dynamics occur over time-scales longer than homo sapiens have existed!  Another example is that, due to the finite speed of light, the further we look out into the cosmos, the further back we see; we can actually look at what the universe looked like during earlier epochs—direct observations of the past 13.8 billion years!^XVI  Sometimes, passive observation must be used in psychology, economics, and sociology because of ethics concerns about experimenting on people (which is only allowed to certain extents).  But in many cases, passive observation may be misleading.  For one, in complex systems such as medical or sociological processes, it is difficult to control for all of the variables that might be at play when one simply observes different populations to test, for example, whether a health intervention helps or not.  Any discrepancy in the data may be fully explained by other variables—there are so many in such systems, it would be difficult to keep track of.  If passive observation is the gold standard, then experiment is the platinum standard:^XVII in these cases, we devise studies in which a random, large sample of people are divided into two groups, the control (in which no intervention, or a placebo, is taken) and a study group in which the intervention is implemented.^XVIII  Because these are large random samples, we have done our best to control for “everything else” that might be different between, say, the people in one state that used the intervention, and the people of another state who did not.  Experiments are even best in the lower-level sciences when available, because they admit of highly designed scenarios which may specifically reveal natures secrets in an obvious, reductive way (such as particle colliders smashing particles together to see which particles arise as a result of the collision).  Physics and chemistry are almost entirely experimental sciences because it is relatively cheap and easy to contrive experiments in these fields, and because, unlike cosmology, it is physically possible to do so (one may procure many electrons in their lab, but not many galaxies!).  It is worth noting, however, that the cash value of an experiment is what it says about the natural world as it plays out, un-abused—in the best case, one is in possession of both lines of evidence (a double-blind, randomized control trial was used to garner evidence that the covid-19 vaccines were efficacious, and we thereafter observed their effectiveness replicated in the real world as relatively fewer break-through cases have been reported by states, versus naive cases).^XIX  We should make use of, and take into account, any decent evidence we can get our hands on!

        Now, there does exist a naive-empiricist or empirical-extremist group,^XX perhaps best exemplified by the “Big Data” / “Big Science” proponents who think that we would not need explanatory, predictive theories if we just had access to all possible measurements (that is, all empirical information in the world).  They think that understanding is all naively in the data, as if to possess the data is to possess an understanding of the world (even worse, the trend of “fact-checkers” arbitrating genuinely controversial subjects as if all knowledge is a matter of simple table-lookup, no new discovery and debate needed).^XXI  This is of course wrong, and we can explain why, epistemologically, but we may also see examples in history.  Rather famously, mathematician Tycho Brahe was in possession of the best empirical measurements about the planetary orbits in our solar system (decent estimates had been in possession of people for many centuries before that), yet it took putting those data in the hands of astronomer Johannes Kepler, who was able to deduce Kepler's laws of planetary motion from them.^XXII  In the hands of Kepler, these data were understood to have arisen from certain elegant laws—laws that could be applied to predict the orbits of far more planets than just those the data came from,^XXIII and they laid the groundwork for later, deeper theories of gravity from Sir Isaac Newton and Albert Einstein.  In the hands of most of us, these data would be a mere parochial description of our planets' positions over time, and that is not the best of science.  People walk around observing all sorts of information about the world; we can detect all sorts of things with just our senses, from aspects of gravity and magnetism, to chemistry and biology: yet this does not confer a scientific understanding of the world (or else we would not need the scientific method—such a naive world requires no epistemology at all, as everyone would quickly and trivially deduce all that they hadn't been born knowing).  The scientific method needs to be followed.  We need to come up with hypotheses of the right kind which explain the data of some known phenomena (this part is sometimes derided as data-fitting or “just-so storytelling” if done with no savvy).  If the hypothetical mechanism explains more than one known empirical point, that is all the better for being coherent and elegant.  This part is essentially the reverse-engineering of the cosmos (in engineering, “reverse-engineering” is when one uses observations of the output of some machine, say a computer program, in an attempt to engineer their own replica machine—crucially without full access to the the blueprints or what is going on inside of the original black box).  Then we must probe that coherent mechanism for other predictions it makes, which admit of empirical testing, but which we have not yet thought to measure (these are true predictions in an epistemological sense, which can give us much more confidence, as post-dictions^XXIV could well be “just-so storytelling” or data-fitting on their own).  This is the part where we escape mere reverse-engineering and attempt to genuinely predict some feature of the cosmos from our model without knowing the empirical answer ahead of time.  We then must test these novel empirical predictions by measuring the concomitant information signature implied by our hypothesis—we can do this either by experiment (in which we design a manipulation of nature to admit of a phenomena we may measure) or passive observation (in which we go looking for the phenomena where it should be naturally occurring).  This process takes very special, smart people with the right education to pull off.  This is not an elitist argument (many of our credentialed elite are frankly unqualified whereas quite a few that have not been allowed in the professional club may be competent), it is just reality.^XXV  Some people are gifted and work hard to produce extraordinary results.  Our education system has spent more time pretending that everyone can participate in science than it has actually giving children (or adults!) the education in the scientific method that would allow them to attempt to.  Some people have the ability to run at Olympian levels and other people have the ability to make discoveries about the world (Noble laureates in physics are a good proxy for an “academic Olympics”).  While many of us may enjoy running recreationally, none of us are surprised that most children will never reach the Olympian runner status, regardless of training.  To say the same of scientific achievement, however, is nearly verboten.  But Olympic-level running is evidently far more common than genuine scientific discovery!  Universities award far more PhDs than the private sector hires expert athletes each year,^XXVI yet there is a tendency for both PhDs and laypeople to treat the PhD like it is more than it is; automatic heirs to Einstein, they are not.  This is only all the more reason to provide a quality education in philosophy of science to all schoolchildren: only a minority of them will achieve anything of note with it, and one does not get to know which ahead of time (though there will be some indications, other times, one might be quite surprised!).  Besides, a very large proportion of the population is capable of basic scientific literacy which helps in adjudicating even daily problems, such as whether a piece of furniture will fit in one's house, or doing one's taxes.  Even those who are not capable nor interested in contributing to science will benefit from whatever level of understanding of philosophy of science that they are able to achieve: a more informed society capable of appreciating the enrichment of scientific discoveries will be the result.  Genius is real, and you don't get theories of gravity without Newton and Einstein; for hundreds of thousands of years, people watched things fall, and bore witness to the patterns in the sky.  That data did not naively imply to anyone with eyes the laws of physics.  But many more people (somewhere on a spectrum from Newton down to the dumbest person on the planet), can utilize his theory.  NASA's employees are much smarter than average, but there is likely no one among their ranks who could have discovered Newtonian gravity on their own as Newton did.  But now that he has done that work, they are smart enough to use his theory to advance space-flight and exploration!

        Regardless, no matter how many sensors we slap around, we do not have and will not have data on everything in the universe, like an omniscient god in possession of the full ontology (and therefore not in need of the epistemology, though it technically is a facet of that ontology).  Nor could such recordings in practice be perfectly accurate and precise.  The cosmos contains a vast amount of raw information, particularly if you are disregarding the elegant laws that tie that information together.  Even if we did have all of that data, we would have no sorting mechanism, no idea what to look at (this is because we would have no algorithmic theory of how to view it as a data structure).^XXVII  Proponents are excited that this is where artificial intelligence (AI) comes in; that it will just run through, find all the patterns, and report all discoveries to us.  I think this is both pie-in-the-sky (AI is regularly in error, today), and frankly, lamentable.  It is crucial that we will always make use of tools and technology in our scientific quest, but celebrating the near replacement of humanity in that project takes away so much reason to live (and again, it is hard to separate the notion from those who claim “the myth of the lone genius” in scientific discovery)!  Even if this much was achieved, it is not clear that, given mediocre thinkers are the ones reading through what the computer spits out, they'll be able to come out with much more than naive data-fitting models whose elegant ontological consequences are unclear.  Furthermore, being in full access of all information at once could actually pose a problem, by transforming most prediction into post-diction, thereby making us less sure that we have genuine predictive theories rather than having been biased towards a “just-so story”.  There is simply no substitute for smart people thinking deeply using the philosophy of science (at least until AI is unfortunately so good that it can match this higher-level of cognition).^XXVIII

        There are other pitfalls of the empirical extremists.  When they hear that empirical evidence is king, they mistake that a little too literally.^XXIX  The importance of empirical evidence is that it allows one to falsify or confirm the predictions of a hypothesis, and therefore falsify or tentatively confirm that whole predictive framework, graduating it into a working theory.^XXX  While we always strive for direct empirical evidence for all phenomena, we do have good reason to believe in effects to one-or-another degree even beforehand, when it is the prediction of a theoretical framework whose other predictions have all passed and replicated time and again.^XXXI  There is no authority in science, except nature.  The proper epistemologist, the true scientist, is trying to describe the world (ontology) as it is, not as he would like it to be.  He is certainly not just trying to prove that he is smart; smart people can come up with a lot of things that aren't so—and they can be very impressive ideas, on the face of things!^XXXII  This may be the case with so-called string theory (which really ought to be called the string hypothesis, or by now, the membrane hypothesis),^XXXIII for example: these thinkers are sometimes accused of
“moving the goal-posts”—instead of taking string theory to have been falsified by the fact that the Large Hadron Collider (LHC) at CERN found no evidence for supersymmetry (their prediction for a doubling of all types of particles such that each has a supersymmetric partner), they have instead argued that a more powerful particle collider will indeed find them at that higher energy-level.^XXXIV  Because the naive-empiricist doesn't properly understand that empirical evidence either falsifies a hypothesis by showing that its predictions were wrong, or verifies and graduates a hypothesis into a theory because its predictions turned out to be accurate, they instead see empirical evidence as all that science is about (with explanatory frameworks nowhere in sight or assumed to be the result of naive, obvious interpretations of the data).  That is a lame view of science, and admits of only mere stamp-collecting.^XXXV  Something else powerful about explanatory frameworks is that the evidence in their favor is cumulative.  The more varied and replicated the evidence in favor of a particular theory's predictions, the more sure of the theory itself we become, and the more fruitful future applications of it to new problems is likely to be.  At some point, the theory is essentially graduated into a law of nature, and then the burden of evidence shifts heavily towards those who would claim it is not true.  For example, anyone who wants to break any of the three laws of thermodynamics^XXXVI (which physicist Sir Arthur Eddington famously said were the firmest of all, to his mind)^XXXVII has an incredible amount of work cut out for them, and for good reason: most will suspect any idea based in this is wrong, out-of-hand, unless it begins producing extraordinary empirically-confirmed predictions that rival and defeat the high bar set by the previously confirmed law.  Once a theory has become a natural law, one should take its predictions very seriously when it comes to forming one's beliefs and actions.  For example one does not need direct empirical evidence that a certain animal that one discovers is the product of evolution by natural selection.^XXXVIII  In fact, we do not have that direct empirical evidence for the vast majority of the species we know about, and we have reason to believe that we don't even know about the majority of the species on the planet (though ways of estimating this have been devised).  We at this point assume, as the null hypothesis,^XXXIX that all of those species are nonetheless the product of evolution by natural selection because it is our only mechanical theory of life, and because so far, each such organism that has been checked has indeed been related by a common ancestor (the information signature of which is that their blueprint is written in the same genetic language: deoxyribonucleic acid, or DNA).^XXXX  Further, we assume with great confidence that anything on this planet that we have yet to discover will have been the product of the natural selection of genomes written in DNA, and therefore have a shared genetic ancestor with the rest of life on Earth.  Now, because of the provisional nature of knowledge,^XXXXI we must be open to the idea that empirical evidence may any day now reveal an organism which does not appear to be related to the rest of life, one which is written in a different genetic language (which would spur research into its own origins—whether it is older or newer than DNA, and whether it comes from here or elsewhere).  But again, the burden of evidence long ago shifted to the person making such a claim.^XXXXII  That is how to properly use theoretical science, yet one will find empirical extremists who demand every claim be accompanied by direct empirical evidence to be considered at all.  This misunderstanding of empirical science makes science essentially useless because it takes away the whole point: the making of theoretical predictions about the world at above chance rates.  The well-evidenced theory of evolution by natural selection allows us to predict at well-above-chance rates that all living things on this planet are related.  A more recent example can be found in those thinkers now claiming that one may still transmit covid-19 even if they are vaccinated.  This is a misleading statement.  Few medical interventions (or engineering solutions) are 100% effective; as economist Thomas Sowell emphasizes, “... there are no solutions, there are only trade-offs...”^XXXXIII  So it is no surprise that the covid-19 vaccines are not perfectly effective: some number of people will still get covid-19 despite being vaccinated (just as some number of people who have previously had covid-19 will be re-infected).  The point is that immunity is not all-or-nothing, that an immunization event confers something like 90% effectiveness at preventing covid-19,^XXXXIV which wanes about 2% per month thereon^XXXXV (this means that soon after recovering from covid-19 infection or receiving the primary series of covid-19 vaccination, your chance of catching covid-19 is reduced by 90% versus the naive population).  Of course there are break-through cases—the way that efficacy is measured in clinical trials is to see how many fewer break-through cases in the experimental group there are versus the control group (as it turns out, there were about 10% as many break-through cases as naive cases, controlling for population size, when it comes to the mRNA vaccines).  Further, it always should have been the null hypothesis that break-through cases were just as transmissible as naive cases: my view was that the vaccine / immune-system had failed to prevent the virons from replicating inside of you, and that this contagious material would indeed be in your saliva as a result.^XXXXVI  But the claimants are not all just talking about break-through case transmissibility in which the person's immunity failed, they are raising doubts about the larger group who have been protected against infection from covid-19 via previous infection or vaccination, implying that they can somehow carry and transmit the virus even without experiencing an asymptomatic infection.^XXXXVII  Yet this line of reasoning goes against everything we know about the theory of the immune system, infection-response, and vaccination. The germ theory of disease explains infectious disease to be due to microscopic bio-matter, such as bacteria and viruses, getting into our bodies.  In the case of a virus, if a proper viral load makes it inside of you and avoids death at the hands of your immune system, it infects you via the virons taking over some of your cellular machinery to make replications of itself.  The basic theory of the immune system is that it will then fight off the infection (often with nasty symptoms such as fevers which can themselves be dangerous), memorize key aspects of the foreign agent (if you survive the infection), and then quickly kill any such agents that might find their way inside of you in the future, thereby avoiding re-infection (a process known as immunity).^XXXXVIII  The theory of modern vaccination is then that we may inject into vulnerable people some agent which is not the actual germ but which shares some identifying characteristic of it (in the case of covid-19, the spike protein of the SARS-COV-2 virus), so that the immune system learns from it (without the dangers of infection) how to defeat a viral load one might come into contact with, later (it confers immunity without one ever being infected).  An mRNA vaccine adds the caveat that what is injected is mRNA instructions (contained inside an envelope of protective lipid-nanoparticles, or LNPs) for how to make some object (in this case, a spike protein), which then take over some of the host's cellular machinery to produce the spike protein which then confers immunity as a normal vaccine (or infection) does.  When one accrues evidence for a vaccine's ability to prevent infection, for example, they do not only do so: they also accrue further evidence for every theory whose predictions it is based on!  And because of our understanding of infectious disease—that infected agents transmit a disease to one another, the null-hypothesis is that those who do not become infected because of immunity are not transmitting the disease to others, as any virons that enter their bodies are quickly dispensed with by their immune systems.  As a result, in my view, the large and continuing transmission of covid-19 can probably be explained by naive-and-break-through infections (remember that infection protection wanes significantly each month post-immunization-event) without the need for imagining that immune people who have not been infected are somehow nevertheless transmitting a virus they are not carrying (in fact, logical consistency demands that we would have to be even more concerned about the naive-uninfected population somehow transmitting the virus, something I have never heard claimed).  Unless and until a theory of everything is achieved, no theory is perfect: something else that happens as a theory is probed, applied, and tested over the years is that the boundaries of its domain are found out.  We do not demote past theories into hypotheses once they have been shown not to explain all known phenomena and/or are usurped by a new theory; hypotheses are competing alternatives—when a theory beats another theory, it is because the new theory is deeper—it explains more and does so more elegantly, but it actually puts the theory it replaces on even firmer footing, because it explains how that theory arises as a special case of the newer, more general one.  For example, Einstein's general theory of relativity which usurps Newton's law of universal gravitation, gives rise to Newton's theory under the right conditions (which is why Newton's laws are accurate and useful in so many contexts in the first place).^XXXXIX  Therefore, in many situations (such as those in which one is not under a certain amount of gravitational attraction and in which no objects are nearing the speed of light—in our solar system, this means pretty much every planet but Mercury), Newton's theory is still used because it much simplifies the calculation (any further precision Einstein might add is diminishing returns for many purposes—including the calculations being made for a lot of space exploration).  But in other cases, Newton does not have much to say: from the precession of Mercury's orbit (the orientation of Mercury's orbital ellipse rotates over time), to the bending of light-beams near masses, to the gravitational attraction that massless energy exerts, to the formation and dynamics of black holes, and finally the gravitational waves emitted by accelerating objects, one needs Einstein to predict let alone account for such ontological phenomena.  We know now that Newton's is a (particularly powerful) approximation at both the numerical answers and the ontological picture of gravitation (Newton saw the world as masses instantaneously exerting forces on each other, whereas Einstein realized it is closer to energy densities curving the fabric of space-time).  Some future theory (tentatively called quantum gravity) awaits our discovery that shows even Einstein's theory to arise as a special case of this more general understanding (and perhaps even that will only be an intermediate step towards a theory of everything).  Though we cannot yet account for them, we already observe anomalies (empirical phenomena which our current best theory does not account for) which general relativity does not seem able to deal with, such as black hole interiors (or singularities), or even predicting Hawking radiation itself without making recourse to the quantum theory of other forces (which likewise cannot predict the phenomenon on its own principles of particle physics without making some recourse to general relativity).

        The idea that one need empirically measure every single facet of every claim takes away the point of science, which is to understand laws, and to be able to categorize based on noticeable patterns—similarities between things such that one can make predictions at above chance rates, thereby explaining phenomena via a mechanical model;^XXXXX to understand that the world is not a world of special cases.  A a world of similarity and regularity is an understandable cosmos, rather than a chaos.^XXXXXI  Therefore, when you learn something about viruses, you've learned something about all viruses; when you learn something about the immune system, you've learned something about all immune systems; when you learn something about vaccines, you've learn something about all vaccines.  When one tests positive for a viral infection, what is picked up is the information signature that the virus (using your own cellular machinery) has replicated enough inside of you to make you sick, and to be picked up by the measurement apparatus, and as a result, enough in your saliva to infect new people.  This is crucial because it establishes the link between infection and transmission—you are not likely to be capable of the latter without the former.  Both natural infection and vaccination lead to immunity from infection and therefore preclude one from being a carrier who may transit the virus, in general; an immune person's immune system fights off any viral load in a small skirmish instead of in a big war (over the length of which, some of the virus ejects to spread to others).^XXXXXII  Direct empirical evidence that vaccinated people do not contract the disease is indirect empirical evidence that they cannot transmit it (and not terribly indirect evidence, because again, you can't transmit something that isn't there—if it is not showing up in high enough levels to cause infection, it is very unlikely to be dense enough in one's saliva to cause transmission).^XXXXXIII

        Science is the most meritocratic of all enterprises because empirical support—the veracity of one's ideas—is all that matters; not one's credentials and not others' opinion of the person in question.  Science is therefore inherently anti-elitist, anti-authoritarian, anti-credentialist, and anti-dogmatic: the continued democratization of the philosophy of science through educators is a natural outgrowth.  There are no authorities, only nature.

Footnotes:

0. The Philosophy Of Science table of contents can be found, here (footnotephysicist.blogspot.com/2022/04/table-of-contents-philosophy-of-science.html).

I. See “Richard Feynman On Scientific Method” uploaded by YouTube user Soccer Man (https://www.youtube.com/watch?v=0KmimDq4cSU) (0:00 – 1:01) (though I do not know if I have seen this entire clip).

II. See The Dream Of Reason by Gottlieb (pp. 317) for ancient Greek philosopher Epicurus' thoughts to this effect. For more on the (later) history of empiricism, see The Dream Of Enlightenment by Gottlieb (pp. 31-35).

III. For an example of this kind of argument, see “Jordan Peterson: Is Science True?” uploaded by YouTube user PhilosophyInsights (https://www.youtube.com/watch?v=t7eywNDTMts) (0:00 – 2:50) which is an excerpt from “Dr Jordan B Peterson | *Full-Length* 2014 Interview” uploaded by YouTube user Transliminal (2014 / 2015) (https://www.youtube.com/watch?v=07Ys4tQPRis) (though I do not believe I have listened to this interview). This is an older source, as I am more familiar with Peterson's wrong-headed view of “truth” as “that which helps you survive” (as opposed to that which is ontologically accurate) from his many truth-debates with scientific philosopher Sam Harris (though I had trouble quickly locating what I was looking for in these daunting streams of argument), see the “Bibliography And Recommended Works” section.

IV. For more discussion on the topic of aside-from-truth-seeking goals, see the “Descriptive And Normative Theory” chapter.

V. My view is that much of “quantum weirdness” evident in our “laws” of quantum physics is lock-picking (but that other facets of quantum theory reflect genuine keys, such as the prediction and discovery of new particles like the Higgs-boson), look forward to the “Physics” chapter in the “Ontology” volume for more on these topics.

VI. See the “Knowledge As Provisional” chapter.

VII. Look forward to the “Psychology” chapter in the “Ontology” volume.

VIII. Historian of science Michael Shermer is associated with the idea that mind and perception evolved for the function of recognizing regular patterns in the world, see for example the following quote hosted on AZQuotes (https://www.azquotes.com/quote/1459149). For a discussion of the over-activity of our pattern-recognition beyond what is scientifically accurate, see “Patternicity” by Michael Shermer (Skeptic) (2008) (https://michaelshermer.com/sciam-columns/patternicity/). I understand myself to have come to the same conclusion, independently, see my April 28^th, 2018 Twitter thread culminating in the following tweet: https://twitter.com/schwinn3/status/990254610915917826. For a later example of my thoughts along the same lines, see my March 8^th, 2021 tweet: https://twitter.com/schwinn3/status/1368981121426415628?s=20&t=NP9fJcYo_rGxF908zc53WA.

IX. For more on this topic, see the “Statistics, Probabilities, And Games” chapter.

X. For an interesting discussion around this topic, see "COVID, Ivermectin, And The Crime Of The Century: DarkHorse Podcast With Pierre Kory & Bret Weinstein” by Bret Weinstein and Pierre Kory (DarkHorse) (2021) (https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5idXp6c3Byb3V0LmNvbS80MjQwNzUucnNz/episode/QnV6enNwcm91dC04NjI3ODA4?sa=X&ved=0CAUQkfYCahcKEwj4mv2KlvT6AhUAAAAAHQAAAAAQbw). Around this time, evolutionary biologists Bret Weinstein and Heather Heying (as well as physician Pierre Kory) were involved in a contentious debate as to whether Nobel-prize-winning anti-parasitic drug, Ivermectin, was an effective treatment or prophylactic against covid-19 (they believe that it is, as outlined in several DarkHorse Podcast episodes around that time). For what it's worth, my sense is that the weight of the evidence currently falsifies this hypothesis, but I do think that their opponents are generally too dismissive of sources of empirical evidence outside of the platinum-medical-standard of randomized double-blind controlled trials (in addition to engaging in ad-hominem attacks, or personal insults, and even the anti-scientific practice of censorship). For more on these topics, see the “Methodology” chapter.

XI. See The Dream Of Reason by Gottlieb (pp. 308-311, 317) for Epicurus' thoughts on the matter.

XII. See Cosmos by Sagan (pp. 96-98).

XIII. See the “Mathematics” chapter.

XIV. This is the topic of Convergence: The Idea At The Heart Of Science by Peter Watson (Simon & Schuster) (2016 / 2018) (though I have not yet finished reading this book). It was also the epistemological argument being appealed to by B. Weinstein and H. Heying in “Bret And Heather 80th DarkHorse Podcast Livestream: What Covid Reveals About Our Leaders” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://www.youtube.com/watch?v=vxTODvTNHlw) (36:46 – 1:20:43). See again footnote VIII and recognize that my focus here is on the epistemological and methodological debate, not the medical debate.

XV. See “Charles Darwin And Nomological Networks Of Cumulative Evidence” by Gad Saad (The Saad Truth) (2019) (https://www.youtube.com/watch?v=Fr4x1YWM8s8).

XVI. Look forward to the “Cosmology”, “Astronomy”, and “Physics” chapters in the “Ontology” volume.

XVII. See “In Defense Of Philosophy (Of Science)” by Gussman (https://footnotephysicist.blogspot.com/2021/05/in-defense-of-philosophy-of-science.html#FN9A).

XVIII. See the “Methodology” chapter.

XIX. For Pfizer's clinical trial results, see “Safety And Efficacy Of The BNT162b2 mRNA Covid-19 Vaccine” by Fernando P. Polack et al (NEJM) (2020) (https://www.nejm.org/doi/full/10.1056/nejmoa2034577). For Moderna's clinical trial results, see “Efficacy And Safety Of The mRNA-1273 SARS-CoV-2 Vaccine” by Lindsey R. Baden et al. (NEJM) (2020) (https://www.nejm.org/doi/full/10.1056/nejmoa2035389). For Johnson & Johnson's clinical trial results, see “Safety And Efficacy Of Single-Dose Ad26.COV2.S Vaccine Against Covid-19” by Jerald Sadoff et al. (NEJM) (2021) (https://www.nejm.org/doi/full/10.1056/NEJMoa2101544). Note that while I am not sure that I read these studies cover-to-cover, I close-read at least significant portions of them (including calculating the efficacy from their raw data myself to check their work), and continually re-referenced them on multiple occasions (so I am familiar with their findings). For on-going effectiveness observation from the U.S., see “Covid Data Tracker: Rates Of Covid-19 Cases And Deaths By Vaccination Status” (CDC) (2021 - 2022) (https://covid.cdc.gov/covid-data-tracker/#rates-by-vaccine-status). For on-going effectiveness observation from New York State, see “Covid-19 Breakthrough Data: Current Estimates Of Cases And Hospitalizations By Vaccine Status” (New York State) (2021 – 2022) (https://coronavirus.health.ny.gov/covid-19-breakthrough-data).

XX. I accused the late, great Steven Weinberg of a special case of empirical extremism, experimental-extremism (I believe his focus on particle physics led him to place too much emphasis on experimental observation as opposed to passive observation), see “In Defense Of Philosophy (Of Science)" by Gussman (https://footnotephysicist.blogspot.com/2021/05/in-defense-of-philosophy-of-science.html#FN11A) which further cites To Explain The World by Weinberg (pp. 254).

XXI. See “Bret And Heather 11th DarkHorse Podcast Livestream: Choose Your Own Black Mirror Episode” by Bret Weinstein and Heather Heying (DarkHorse) (2020) (https://www.youtube.com/watch?v=mYQJSobQgAc) (57:49 – 1:02:52); “Bret And Heather 16th DarkHorse Podcast Livestream: Meaning, Notions, & Scientific Commotions” by Bret Weinstein and Heather Heying (DarkHorse) (2020) (https://www.youtube.com/watch?v=QvljruLDhxY) (0:59 – 51:37); “Bret And Heather 61st DarkHorse Podcast Livestream: If Covid Policy Were Rational” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://www.youtube.com/watch?v=KfbBvvPVFdw) (1:36:09 - 1:37:27); “Bret And Heather 65th DarkHorse Podcast Livestream: Because Science” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://www.youtube.com/watch?v=VerirOAHgUU) (19:12 – 26:51, 1:23:03 – 1:26:32); “Bret And Heather 79th DarkHorse Podcast Livestream: #NotAllMice” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://www.youtube.com/watch?v=bU63lsHA0y0&t=74s) (47:27 – 51:04); “Bret And Heather 81st DarkHorse Podcast Livestream: Permission to Think” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://www.youtube.com/watch?v=LoaKtBMk53Y) (15:31 – 19:54); and “#84: Hey YouTube: Divide by Zero (Bret Weinstein & Heather Heying DarkHorse Livestream)” by Bret Weinstein and Heather Heying (DarkHorse) (2021) (https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5idXp6c3Byb3V0LmNvbS80MjQwNzUucnNz/episode/QnV6enNwcm91dC04NzMwNTYw?sa=X&ved=0CAUQkfYCahcKEwiY2uSX-Pn6AhUAAAAAHQAAAAAQcg) (40:38 – 1:23:45). Despite a thorough search through much of The DarkHorse Podcast, I was not able to find an example of B. Weinstein and H. Heying using the term,  “table look-up,” but I seem to remember they and I independently using this criticism of the “fact-checker” mentality.

XXII. See Cosmos by Sagan (pp. 52-65) and look forward to the “Cosmology”, “Astronomy”, and “Physics” chapters in the “Ontology” volume.

XXIII. See Cosmos by Sagan (pp. 52-65).

XXIV. See The Elegant Universe: Superstrings, Hidden Dimensions, And The Quest For The Ultimate Theory by Brian Greene (W. W. Norton & Company, Inc.) (1999 / 2003) (pp. 210-211).

XXV. See the “Sociology Of Scientists” chapter and Viral: The Search For The Origins Of Covid-19 by Alina Chan and Matt Ridley (HarperCollins) (2021) (at least pp. 1, 7, 26-28, 30, 129, 169-170, 213-214, 230-235, 239, 299-301, 305).

XXVI. There are about 2,900 athletic openings a year, see “Occupational Outlook Handbook: Athletes And Sports Competitors” (U.S. Bureau Of Labor Statistics) (accessed 2022) (https://www.bls.gov/ooh/entertainment-and-sports/athletes-and-sports-competitors.htm#tab-6). In contrast, there were about 55,283 PhDs awarded in 2020 (a number that held pretty steady for the five years beforehand (the data go back to 1958, and even then, 8,773 PhDs were awarded), see “Survey Of Earned Doctorates” (NSF / NCSES) (2021) (https://ncses.nsf.gov/pubs/nsf22300/report/u-s-doctorate-awards). Therefore, there are about 19 times as many PhDs awarded per year than professional athletes are hired.

XXVII. See the “Computation” chapter.

XXVIII. For more on this argument, see the “Laws And Facts, Theories And Data” chapter.

XXIX. While I was under the impression that B. Weinstein and H. Heying, and myself, independently criticized the abuse of “empirical evidence is king” by naive empirical extremists, I have not yet found myself directly doing so, whereas I know they did in “Bret And Heather 16th DarkHorse Podcast Livestream: Meaning, Notions, & Scientific Commotions” by B. Weinstein and H. Heying) (https://www.youtube.com/watch?v=QvljruLDhxY) (0:59 – 51:37) or “#84: Hey YouTube: Divide by Zero (Bret Weinstein & Heather Heying DarkHorse Livestream)” by B. Weinstein and H. Heying (https://podcasts.google.com/feed/aHR0cHM6Ly9mZWVkcy5idXp6c3Byb3V0LmNvbS80MjQwNzUucnNz/episode/QnV6enNwcm91dC04NzMwNTYw?sa=X&ved=0CAUQkfYCahcKEwiY2uSX-Pn6AhUAAAAAHQAAAAAQcg) (40:38 – 1:23:45).

XXX. Think back to the “Logic” chapter and recognize that falsification makes an appeal to basic logical coherence: one may not claim to believe a hypothesis despite admitting its predictions are empirically untrue. For more on this topic, see the “Laws And Facts, Theories And Data” chapter.

XXXI. See “A Profusion Of Place | Part I: Of Unity And Philosophy” by Gussman (https://footnotephysicist.blogspot.com/2020/03/a-profusion-of-place-part-i-of-unity.html#FN58A) which further cites Our Mathematical Universe by Tegmark (pp. 124). One specific example are gravitational waves, a prediction of Einstein's general theory of relativity. This is currently our best theory of gravity, having many of its predictions confirmed, such as the bending of light near masses like the sun, the precession of Mercury's orbit (a post-diction for science overall, but an accidental prediction from Einstein's perspective), and the existence of black holes. As a result, most great physicists believed in gravitational waves because they were the unavoidable consequence of this mathematical theory of physics—from Feynman all the way back to Einstein himself (though he never thought they would be measured, see physicist Bruce Allen's quote in “Gravitational Waves Detected 100 Years After Einstein's Prediction”, Caltech / LIGO, 2016, https://www.ligo.caltech.edu/news/ligo20160211). Two Nobel prizes in physics have been awarded for indirect and then direct evidence of this phenomenon, since.

XXXII. See Cosmos by Sagan (pp. 11).

XXXIII. Astro-physicist Neil deGrasse Tyson has proposed this as a more proper term for the line of research typically known as “string theory” (despite its famously lacking empirical verification), see “String Theory Or 'String Hypothesis'?...” uploaded by the official StarTalk Facebook page (StarTalk) (2017) (https://www.facebook.com/watch/?v=1888251767856150) which is an excerpt from the full podcast, “Cosmic Queries: Mysterious Cosmology, With Sean Carroll” (StarTalk) (2017) (https://startalkmedia.com/show/cosmic-queries-mysterious-cosmology-sean-carroll/) (though I am not sure if I have listened to this episode). See also my August 25^th, 2019 tweet: https://twitter.com/schwinn3/status/1165490844541038597?s=20&t=9d2z2dfAVEmER76NErDV1A, and May 4^th, 2021 tweet: https://twitter.com/schwinn3/status/1389752217045975040?s=20&t=9d2z2dfAVEmER76NErDV1A on this point. B. Weinstein and H. Heying think along similar lines, see “Bret And Heather 16th DarkHorse Podcast Livestream: Meaning, Notions, & Scientific Commotions” by B. Weinstein and H. Heying (https://www.youtube.com/watch?v=QvljruLDhxY) (0:59 – 51:37). Tyson has similarly put forth that “dark matter” should really be called “dark gravity” until the cause of this signal is discovered (which may end up being explained through a new law of gravity, some other new force law, or through the discovery of a new type of matter), see “What Is Dark Matter? Neil deGrasse Tyson Tries To Explain” uploaded by the official Business Insider YouTube account (Business Insider) (2014) (https://www.youtube.com/watch?v=N4x6N0uAkTQ). The best piece of evidence that dark matter really is going to be some exotic material source of otherwise ordinary gravity (rather than a change to the known laws of physics) is that it contributes to gravitational lensing (a non-Newtonian prediction of Einstein's general theory of relativity in which the collective mass of a galaxy significantly bends the light coming from far-away galaxies behind it, reproducing multiple visual copies of it, and magnifying its apparent size), suggesting that the phenomenon really is a bending of Einsteinian space-time as only matter-energy does (incidentally, physicist Stephon Alexander proposes here that it be called “invisible matter” because it doesn't even absorb light, it ignores it), see “36: Dark Matter, Black Matters and All That Jazz” by Eric Weinstein and Stephon Alexander (The Portal) (https://omny.fm/shows/the-portal/36-dark-matter-black-matters-and-all-that-jazz) (1:16:34 – 1:25:07).

XXXIV. To be fair to both string-theorists' critics (although this doubles as another criticism of string-theorists as well—vagueness), they never made a definite prediction of where (at what energy-level) such supersymmetric particles would arise, so it actually isn't entirely obvious the idea has been falsified just because it hasn't been found in the LHC's realm of power. But such is why the more definite the prediction, the better and more legitimate the hypothesis.

XXXV. For more on this topic, see the “Laws And Facts, Theories And Data” chapter.

XXXVI. For more on the three laws of thermodynamics, look forward to the “Physics” chapter in the "Ontology" volume.

XXXVII. See Enlightenment Now by Pinker (pp. 16-17).

XXXVIII. See “Bret And Heather 16th DarkHorse Podcast Livestream: Meaning, Notions, & Scientific Commotions” by B. Weinstein and H. Heying (https://www.youtube.com/watch?v=QvljruLDhxY) (36:35 – 37:29). For a similar argument, see my October 29^th, 2021 Twitter thread that begins with the following tweet: https://twitter.com/schwinn3/status/1454165900828061697.

XXXIX. See the “Baselines And Null Hypotheses” chapter.

XXXX. Look forward to the “Biology”, “Psychology”, and “Sociology” chapters in the “Ontology” volume.

XXXXI. See the “Knowledge As Provisional” chapter.

XXXXII. For a very similar argument, see “Bret And Heather 16th DarkHorse Podcast Livestream: Meaning, Notions, & Scientific Commotions” by B. Weinstein and H. Heying (https://www.youtube.com/watch?v=QvljruLDhxY) (38:27 – 39:45).

XXXXIII. See “Thomas Sowell: There Are No Solutions, Only Trade-Offs” uploaded by YouTube User Levan Ramishvili (Fox News) (https://www.youtube.com/watch?v=3_EtIWmja-4) (0:25 – 0:37) and A Conflict Of Visions: Ideological Origins Of Political Struggles by Thomas Sowell (Basic Books) (2007) (at least pp. 14, 17, 19).

XXXXIV. Refer back to footnote XIX.

XXXXV. See my December 4^th, 2021 tweet, here: https://twitter.com/schwinn3/status/1467213188567605253?s=20&t=X8_nwREUgyRtDpJ2MO_ozg; and my April 23^rd, 2022 tweet, here: https://twitter.com/schwinn3/status/1517899077316485121?s=20&t=X8_nwREUgyRtDpJ2MO_ozg.

XXXXVI. Many also assumed that the vaccines would confer further benefits as a pre-treatment, meaning that break-through cases would be less severe and lead to fewer hospitalizations and deaths than naive cases. I was not among them, in large part because the clinical trials did not have sample sizes large enough to detect such an effect, and because in the case of a pandemic, I thought one should be more conservative in their estimates about such things. As it turns out, the effectiveness observations (which effectively have far larger sample sizes since the vaccine was taken by O(N) = 100,000,000 Americans) do indeed show this effect, and so I changed my mind to believing that vaccines do function as pre-treatments for break-through cases in addition to their main effect (at least prior to significant effectiveness waning) of preventing cases.

XXXXVII. Ironically, both extremes of the covid-vaccine debate have taken this stance. Public Health officials have taken to it, either because of incompetence, or more likely, because they somehow thought that it would increase vaccine uptake (they did not want anyone feeling protected by the fact that those around them had been vaccinated—they want almost every American to individually take these vaccines). On the other hand, those who oppose the vaccine (or at least against mandating the vaccine against one's will) espouse this view for the obvious reason that the weaker the vaccine can be shown to be, the better their case against mandates and the misbehavior of our Public Health apparatus.

XXXXVIII. As an aside, hygiene theory of immunity is that homo sapiens evolved an imprinting period during their youth (as they did for language acquisition) in which their immune system is in a particular mode almost like the training era of an AI—it is learning as much as it can about the germs in its environment so that it has built up a good general memory (or immunity) to serve the child as an adult. Why not be in this higher-powered “hygiene theory mode” all of the time, into adulthood? Because of trade-offs: childhood is about developing into an adult that is likely to successfully reproduce. Adulthood is about successfully reproducing. So it is natural to think that you would be naturally selected to spend the energy you metabolize differently at different times (an extreme case of this is pregnancy—think of all of the trade-offs a woman's body must be involved in during their gestation period versus a normal nine-month period in their life).

XXXXIX. See Our Mathematical Universe by Tegmark (pp. 240 – 241). As a specific example of this kind of process, Tegmark notes that one can derive the special theory of relativity by treating the general theory of relativity in the limit that Newton's universal gravitational constant tends to 0 (G → 0), and one can then derive classical mechanics by treating the special theory of relativity in the limit that the speed of light tends to infinity (c → ∞), see Our Mathematical Universe by Tegmark (pp. 258).

XXXXX. For more on this topic, see the “Determinism” and “Mechanical Philosophy” chapters.

XXXXXI. See the “Cosmos And Chaos” chapter and Cosmos by Sagan (pp. 180-181).

XXXXXII. See my April 28^th, 2021 twitter thread on this topic, beginning with the following tweet: https://twitter.com/schwinn3/status/1387388291247480833.

XXXXXIII. To be fair, I have seen one specific counter-view proposed, in which it is worried, what if immunity only keeps SARS-COV-2 from infecting the rest of one's body, but nevertheless, those exposed to SARS-COV-2 will end up with it replicating locally in their nose such that they may be overall-un-infected carriers capable of transmitting the disease, see “COVID-19 Vaccines May Not Prevent Nasal SARS-CoV-2 Infection And Asymptomatic Transmission” by Benjamin S. Bleier et al. (AAO-HNS) (2020 / 2021) (https://journals.sagepub.com/doi/10.1177/0194599820982633) (though I am not sure how much of this paper I read at the time, I am in possession of rather extensive thoughts on it, pertaining to its details). What I read of the paper did not convince me that this is actually likely to be the case with covid-19 because it is not thought to generally be the case with respiratory infections (or else why would we ever speak of herd immunity?); because studies which nasal-swabbed all subjects would catch this local-nose-infection as a break-through case (thereby factoring the effect into the vaccine efficacy); and because it seems perhaps unlikely that the immune system would continually be able to keep the infection in the nose over the course of the infection (as it continually “tries” to re-expose the rest of the body) versus simply removing the offensive material and nipping the situation in the bud. To me, this paper fit into a genre (I think spawned in part by publish-or-perish) wherein you pretend we know nothing about SARS-COV-2, even though we had a default model based on our knowledge of the immune system and other respiratory viruses (including coronaviruses like SARS-COV-1) from which to form an educated starting point of understanding. An early study replicated the 90% mRNA vaccine efficacy number even with a study design in which all participants were nasal swabbed to determine whether they had even an asymptomatic case of covid-19, see “Interim Estimates Of Vaccine Effectiveness Of BNT162b2 And mRNA-1273 COVID-19 Vaccines In Preventing SARS-CoV-2 Infection Among Health Care Personnel, First Responders, And Other Essential And Frontline Workers — Eight U.S. Locations, December 2020–March 2021” by Mark G. Thompson et al. (CDC / MMWR) (2021) (https://www.cdc.gov/mmwr/volumes/70/wr/mm7013e3.htm).