Absence of Evidence

by Joel Marks

Sky and Telescope is an excellent magazine, and I have been a loyal subscriber for decades. However, in the introductory Spectrum column about his own fine article on planetary defense elsewhere in the June 2018 issue, Editor in Chief Peter Tyson overstates the case in his understandable eagerness to impress upon the reader the tremendous strides planetary defense has taken in mere decades since its inception.

For he writes, "NASA-funded efforts have determined that no mountain-size asteroid or comet is on a trajectory to hit Earth for at least the next 100 years." This assertion is simply false. It is not claimed in the article, and it is even contradicted by Tyson himself at the end of the very column in which it appears when he writes, "it's always possible that one of our surveys could pick up a previously unknown comet ... that might be making a beeline for Earth." One fervently hopes it does not suffer the same fate as President George W. Bush's so-called Mission Accomplished speech. 

This is a classic case of the fallacy of equating absence of evidence with conclusive evidence of absence. It is true that the odds of a large asteroid heading our way have been impressively reduced, and the odds are always low of a comet doing so. But as the article makes clear, we have at present and for the foreseeable future no way of "determining" whether or not such an object will be at our cosmic doorstep more than months or at most a few years ahead of time.

I am afraid that, next to such an impactor itself, the greatest threat to human survival today is complacency. It will be small consolation on the day one of them wipes us out because we failed to prepare for it to know that, in statistical terms, even then the probability of such an event will remain vanishingly small.

A Comet with Our Name on It?

by Joel Marks

Published in the Connecticut Post on November 25, 2013.

We have been hearing a lot about Comet ISON ever since its discovery in September of last year, when various indications raised hopes of its putting on a spectacular show by the time of its closest approach to the Sun later this month and into next year. Since then expectations have been tempered, but as of this writing nobody can say for sure one way or the other.

            I myself know the thrill of seeing a “comet of the century” – in fact two. You too may have witnessed the double-whammy of Comets Hyakutake and Hale-Bopp in 1996 and 1997, respectively. The first was noted for its magnificent tail right out of old engravings, while the second became a fixture in the night sky for months.

            But comets are not just pretty sights and photo ops. We now know from scientific inquiry what our medieval ancestors feared from superstition, namely, that a comet in the sky can be the harbinger of disaster. It may very well have been a comet that killed off the dinosaurs. The same could happen to us.

            What I find exceedingly odd is that this possibility is being uniformly downplayed or just plain ignored by experts and popular media alike. In fact this is doubly odd, given the ever-increasing attention both are paying to the threat of impact by asteroids.

            Why the relative neglect of comets? One reason is that we are indeed visited by far more asteroids than comets. Roughly a score of comets are sighted each year, whereas thousands of asteroids are being tracked even in Earth’s immediate neighborhood.

Another reason is that we are more likely to be able to mount an effective defense against an incoming asteroid than an incoming comet. This is because the greater distance comets must travel to reach Earth from their cosmic home beyond Neptune corresponds to their having greater velocities by the time they become visible to us. Hence we would have relatively little advance warning of an impending catastrophe.

In his book on Near-Earth Objects, NASA scientist Donald Yeomans estimates that we might have as little as nine months. This is hardly time to design, build, and launch a mission to deflect a comet, especially if it were large enough to threaten our very existence. This contrasts to the decades or even century we might have to prevent a predicted asteroidal collision.

Unfortunately, putting all of our eggs into the asteroidal basket rests on the assumption that no comet will threaten us until some far future time. The sad fact is, though, that comets appear at random.

            Case in point: Just this past January, Comet Siding Spring (C/2013 A1) was discovered to be on course to a near collision with Mars next October. This object could be at least as large as the one that wiped out the dinosaurs. What if it had been heading toward Earth instead?

            I for one am not pleased to be a sitting duck. So I am calling on an informed citizenry to urge policymakers to a greater sense of urgency about comets. We must have a defensive infrastructure in place not after but before we detect a comet with our name on it. In this era of budget sequesters and shutting down government, extraordinary political wisdom and courage will therefore be required to deal with this threat.

Former Space Shuttle astronaut Ed Lu recently said, "One-hundred years ago, if the Earth [were] hit by an asteroid ... that is bad luck. If 20 years from now we get hit again, that is not bad luck, that is stupidity." I completely agree with that statement. However I would add as a friendly amendment, “It’s the comet, stupid!”

Heaven Can Wait, But We Shouldn't

By Joel Marks

Published in the Connecticut Post on March 16, 2013, page A8

Everyone talks about the weather, but nobody does anything about it. And as with meteorology, so with meteors. While folks in New England were digging out from under record falls of the white stuff, half a world away on February 15 a charcoal black chunk of asteroid was falling from the sky and came unprecedentedly close to obliterating a city of one million people with the force of thirty Hiroshima bombs.
            But cities are laid waste from time to time, indeed, even by the weather: consider New Orleans.  What the Chelyabinsk meteor portends is something even more devastating, namely, human extinction. Why aren’t we getting our act together to spare Homo sapiens from the fate of the dinosaurs? The answer, I submit from my perspective as philosopher, is that much of the public and experts alike have fallen prey to fallacious thinking. Our species is more at risk from speciousness than from a rock from outer space.
            Nobody denies that, someday, another asteroid or comet the size of the one that did in the dinosaurs – six miles wide – will be hurtling our way. However, no sense of urgency is being felt or promulgated by most of the policymakers and spokespersons who address this issue. Instead the fear has focused on smaller but still significant calamities like the one that almost befell Chelyabinsk, which could be brought about by a football-field-size object bursting in air or impacting the ground or plunging into the sea with tsunami-inducing force.
            The reasoning behind this shift of priority is simple: There are far more Rose-Bowl-size objects out there than Everest-size ones. (Usually the word “fortunately” is uttered just prior to stating that reason.) However, this is where the fallacious inferences begin to be drawn. What you hear most often is this: “Therefore the chance of our being struck by an extinction-size object is vanishingly small.”
            That sounds like a meaningful and consoling statement. In fact it only repeats the reason in misleading terms. What we know (to a fair degree of approximation) is the relative distribution of sizes of objects in the solar system. But that is all we know. We do not know “the chance” of a mountain dropping on us. Why not? Because there is no such thing as a “chance.” That is only a way of speaking. To use it as a literal guide to action, or in this case inaction, is potentially suicidal.
            We also hear that “An object of this size falls from the sky only once every n million years.” But here again, literal-mindedness about statistics has masked the reality, for this way of putting things makes it sound like clockwork, happening on some regular and hence predictable basis. In fact these events are random.
            The risk from this misconception could not be more patent, as witness this remark by Russian Emergency Minister Vladimir Puchkov regarding the lack of preparedness for what took place in Chelyabinsk: “We thought that humanity would not have to face such an attack for another couple of thousand years, but the opposite happened and Russia was hit with a large-scale natural emergency” (as told to Kommersant daily according to RT online).
            Yet another variation on downplaying risk goes like this: “Over a one-hundred-year period, a person has about a 1 percent chance of being killed in a car crash, but only a .01 percent chance of getting hit by a 1-kilometer or larger asteroid.” Here again this seems to be saying more than it actually does. One reason is that it sidesteps the full meaning of risk, which pertains not only to the chance of something’s occurring but also to the severity of the possible outcome.
            Thus, while dying is indeed a dire outcome, annihilation of the species is incalculably more significant. This is why an actuarial approach to collision with a giant comet or asteroid makes no sense. There would be nobody left to be compensated. The very concept is difficult to comprehend. Perhaps Jonathan Schell came closest with his characterization of the “Second Death” after a global nuclear war.
            Finally, the most egregious fallacy has been to assert, “We know there are no rocks that big headed our way anytime soon, at least not for centuries.” This is just false. It violates the well-known dictum that absence of evidence is not evidence of absence. While the dictum is not universally true, it does apply here.
            February 15 was our astronomical September 11. But it was a kinder, gentler 9/11 in that, miraculously, no one was killed. For that reason will we tempt fate by continuing to assign vastly less funding to detecting and figuring out how to deflect giant asteroids and comets than to detecting and foiling terrorists, even though the former could cause incommensurably greater harm?

Absolute Vulnerability

by Joel Marks

Published in Philosophy Now, no. 86,September/October 2011, p. 52

I live in perpetual sadness and anxiety and frustration in the face of death. No, not my death … nor of a loved one … nor of the 7 billion currently living human beings who will, under normal circumstances, be laid to rest in a century or so inside this charnal house we call Earth … nor of the scores of billions of nonhuman animals we human beings slaughter needlessly every year, nor the scores more who succumb to loss of habitat from encroaching humanity or to predators and other natural agents of fatality. All of those things certainly have their place in my thoughts and concerns, some to an overwhelming measure. But the most immediate, the most devastating, the most far-reaching, and, ironically, the most preventable source of death for us all is our planet’s collision with a 10-kilometer rock.

            Jonathan Schell famously coined the concept of a “second death" in his 1982 book The Fate of the Earth regarding the prospect of human extinction by nuclear war. The point was that not only billions of individuals but also the entire cultural memory of humanity would be obliterated by this ultimate catastrophe. It would be the loss of hope in the worldly equivalent of immortality. That is exactly the kind of death I am talking about now but brought about by an asteroidal or cometary impact. I have written about this for my Philosophy Now readers before (issue no. 79 and below), but there I was concerned about the fallacies of thinking that make even the experts discount the risk of such an event. My claim was that, despite the rarity of extinction-level impacts in the recent history of our planet, the magnitude of the threatened consequences and the randomness of the timing combine to make the danger of the next one urgent and compelling.

But a different (albeit related) kind of thought occurs to me now. (Indeed, it struck me like a rock from outer space.) It is that we are absolutely vulnerable. I suppose you could call this an existentialist thought – not only because it is about a threat to our our species’ (and others’) existence, but also because it points to us as the masters of our destiny. The idea in plain language is that the universe could not care less about whether humanity survives to see another day. Despite the magnificence of human accomplishments (I think of Beethoven), our extraordinary ability to comprehend the universe (I think of cosmology), and countless moments of utter charm (think of your child) – and how inadequate to the task one feels when attempting to inventory the amazingness of human existence! – it could all be wiped out in the blink of an eye. Indeed, it already has been, time and time again, as history is littered with lost and even forgotten civilizations. “Nothing lasts forever but the earth and sky,” goes the song by Kansas – “and not those either,” goes cosmology.

But the inevitability of the final dissolution of Everything is not a reason to be careless about the endurance of everything we care about. In addition there is the possibility that the kind of consciousness human beings have attained on Earth is unique in the universe. So the loss would be not only like that of one’s irreplaceable child but one’s only child. Of course it would be a loss to no one if no one were left to mourn it, and hence not a loss at all, some clever reasoner might rejoin. But the sorrow I experience now is the (so to speak?) anticipatory loss of all. For apart from us – and again, this is precisely my point – the universe neither mourns nor rejoices in anything. And it certainly has no stake in our continued existence, singly or en masse or in toto. Therefore if we do not face the threats to our existence (and to our future and to our memory) with clear and rational eyes, we are that much more likely to succumb to them.

It is queerly fitting that I would be mulling this over as doomsayers fill the airwaves with Biblical prophecies. October 21 is now slated to be the end of the world, according to the Christian pastor in the United States who set the latest frenzy in motion. But that is just the sort of response – one of passive acceptance -- I wish to counter. Another is the Republican Party’s approach to catastrophic threat, such as climate change, which is that nature will sort things out without our help. And it is certainly true that nature will sort things out – one way or another. It is also true that the very logic of both biological evolution and the cosmological anthropic principle assures that we are naturally well suited to survive under prevailing conditions. However, another constant of the universe is that conditions change, which is why we are here and not dinosaurs.

What is needed, then, is a healthy dose of fear (to allude to a theme of an anonymous advisor of mine on these matters). So long as we lull ourselves into believing that our own extinction by asteroid can’t happen any time soon, our efforts will be insufficient to avert it. And the problem is that this is always going to be the case until such time as an incoming rock is close enough for us to calculate that … we’ve run out of time to stop it! But the silver lining of the fear of which I speak is that if humanity could get it into its collective thick skull that there is no angry God directing an inevitable and irresistible Judgment upon us, nor a loving God who will perform a miracle of planetary salvation upon us, but instead we’re in a cosmic skeet-shooting contest with comets and asteroids serving for clay pigeons, we might be just scared enough to do something effective and not so traumatized that all we can do is pray.

Not with a Whimper but a Bang

By Joel Marks
Published in Philosophy Now, issue no. 79, pages 47-48, June 2010

The U.S. space program has been in a state of vacillation for decades. Although marvelous scientific missions have been mounted, the really big-ticket items have gone begging for rationales. Gone are the days when we could set a dramatic (and expensive) goal like landing human beings on the moon for the hell of it … or to beat the Russkies … or to buck up the military-industrial complex. The International Space Station never had the allure of 2001: A Space Odyssey … not even in 2001. President George W. Bush’s goal of launching people to Mars can no longer be propelled by Ray Bradbury nostalgia. And the latest manned Moon venture has just sputtered to an indifferent, even welcomed, indefinite hold by the Obama administration.

How odd this is, though, when a glaringly important and urgent mission to outer space – indeed, a flotilla of missions – has been staring us in the face for decades. I am referring to the defense of planet Earth from asteroidal or cometary impact. Why has this been ignored or sidestepped in favor of amorphous and ad hoc justifications for building rocket ships? One reason may be some fallacious reasoning. The mainstream that has been dealing with this problem has apparently bought into a complacent approach based on reassuring but misleading probabilities.

To understand this, let us begin at the beginning: How does one assess the risk of human extinction by intersection with an errant extraterrestrial rock? Start with some facts. An asteroid or comet on the order of 1 to 10 kilometers in diameter is all it would take to wipe out civilization and us, respectively. There are estimated to be about a thousand such objects whose orbits currently cross near the Earth's orbit, so-called NEOs (Near-Earth Objects). Most of these have been identified, but some remain unknown. As far as we can determine, none of those known threatens collision with our planet in the next 100 years. Other likely sources of this threat, however, are the hundreds of thousands of such-size bodies in the asteroid belt between Mars and Jupiter, the millions more in the Kuiper Belt beyond the orbit of Neptune, and the trillions more in the Oort Cloud way beyond that. At any time, one of those objects could be sent hurtling into the inner solar system where we reside due to a collision with a neighbor or the perturbation of its orbit by some passing star, or indeed may already be on its way due to such an occurrence in the past.

Counterbalancing all of the above, though, is the hugeness of space. What, then, are the chances that one of them will result in a bull’s-eye projectile? Statistically speaking, it would seem, very low indeed.

But there are two misconceptions involved in that assessment. First is that, even if unlikely, impact by a 1-kilometer-plus asteroid or comet would have practically infinite significance. For what is at stake is, essentially, everything, that is, everything human. Now the standard formula for risk assessment is to multiply the probability of the occurrence by the magnitude of the projected loss. So here we have a very small probability but a humongous loss. Ergo: high risk! Those who take solace in the low likelihood of this kind of impact, therefore, are ignoring the bump-up of risk by the magnitude of what is at stake.

The second misconception is the “low probability” itself. Suppose the estimates of NEOs plus the history of major impacts on our planet suggested that a 1 km or greater NEO hits the planet once every million years on average. What would this mean? Pretty much … nothing. There are several ways to think about this. The complacent folk would argue that, therefore, in any given year the chance of a major impact is only 1:1,000,000. And suppose even that the last major impact took place exactly 1,000,000 years ago: Still, they would argue, there is hardly any imminent threat. To think otherwise would be to commit the Gambler’s Fallacy, which is to believe that, for example, since the last ten flips of a fair coin have come up tails, the chance of the next one’s being heads is much greater than 50:50. But this is not so: the chance of a fair coin coming up heads remains 50:50 no matter how many consecutive tails have preceded the flip. Just so with a major impact: even if the annual chance were 1:1,000,000 and 1,000,000 years had elapsed since the last one, the chance of another in any given year would still only be 1:1,000,000. Voilà: relaxation via mathematical prestidigitation.

But there is another way of thinking about the figures that leads to anything but relaxation. Consider again the coin-flipping: (1) sooner or later there will be a head and (2) you have no idea whether it will be sooner or later. Applied to the impact scenario, this means that another extinction-type impact is guaranteed to happen sooner or later (if we don’t prevent it), and we have no idea if that will be sooner or later.

So what follows rationally? Given again the infinite magnitude of the projected loss, I would think the answer to be obviously that we should prepare for a major impact as if we knew it were going to occur just as soon as we could possibly prepare for it.

Alas, to convince the powers-that-be of this is an uphill battle. And not so much because of the technological hurdles or even the expense, but rather the absence of public understanding and political will. What would be required to deal with this sort of threat? Nothing short of continual exhaustive monitoring of asteroids and comets, a sustained research program on methods of mitigation, and the indefinite maintenance of weapons of mass destruction, specifically nukes, along with their delivery systems. (The “mass” in this case is bodies of matter and not multitudes of people, fortunately.) But this flies in the face of current and foreseeable political realities, such as the push for denuclearization and the failure of global cooperation even to check global warming, which is already known to be in progress. How much less likely are the nations of the world, then, to marshal the resources and resolve needed to ward off a risk that is not known to be imminent? … and, indeed, due to the misunderstandings described above, is considered to be low-risk and improbable?

I am afraid, therefore, that Arthur C. Clarke got it right in this as in other predictions: If we are lucky, the wake-up call will be the destruction of “only” a major city by a relatively small impact, as happens in his 1972 science-fiction novel Rendezvous with Rama “on the morning of 11 September.”

Joel Marks is Professor Emeritus of Philosophy at the University of New Haven in West Haven, Connecticut. His thoughts about NEOs as expressed herein owe much to the National Research Council’s Defending Planet Earth: Near-Earth Object Surveys and Hazard Mitigation Strategies: Final Report (2010), available online, and the Website of the Gaiashield Group. More of his essays on astronomy can be found here.

A Planet by any other Name

An exercise in astrometaphysics
by Joel Marks
Published in Think (Royal Institute of Philosophy), winter 2007, pp. 103-106

As a philosopher I have been fascinated by the recent discussion of Pluto's planetary status. The discovery of the Kuiper Belt precipitated the current controversy; just as there is an asteroid belt between Mars and Jupiter, so, it turns out, thousands of rocks are revolving around the sun beyond the orbit of Neptune. Since some of them are large enough to be dubbed planetoids (although, I might add, not analogously to asteroids, which certainly do not approach stellar size!), the issue naturally arose as to whether Pluto is itself more properly conceived as a Kuiper Belt planetoid than as a planet proper.

What brought the question to a head was the discovery of a Kuiper Belt object that is even larger than Pluto, originally dubbed 2003 UB313 and still awaiting a permanent name. Is this new object a planet? If the answer were "Yes," then there would now be (at least) ten planets in our solar system. But if the answer were "No," then there would probably be only eight. After all, if a Kuiper Belt object that is larger than Pluto were not a planet, how then could Pluto be?

How does one decide such a question? The official answer is that the International Astronomical Union (IAU) decides (although in the aftermath of the IAU’s vote on Pluto, this has now been questioned; see for example http://skytonight.com/news/home/3805531.html). But the IAU must have criteria on which to base such a decision, while the present situation seems unique in the history of astronomy. In effect, then, the IAU has had to consider not only what 2003 UB313 and Pluto are, but also what a planet is.

To the layperson this may seem to be a strictly scientific question. There are obvious relevant scientific factors to consider, such as size, composition, and process of formation. But what intrigues me as a philosopher are two further features. First, there seems to be an element of arbitrariness. Given that the relevant considerations for planet versus planetoid look to be in a virtual dead heat, the final outcome could be the result of a virtual (or even literal!) coin toss. Perhaps a more precise description than “arbitrary” would be “extraneous to science.” In his Web site at http://www.gps.caltech.edu/~mbrown/planetlila/,
Mike Brown, the leader of the team that discovered 2003 UB313, refers to “cultural” phenomena as relevant.

Yet even more interesting, to philosopher and layperson alike, is the perennial problem of "word and object," to borrow the title of a modern classic in the field of metaphysics by the late Willard van Orman Quine. How is it that the very nature of a massive physical object can depend on a verbal decision? Aren't things what they are, regardless of what we happen to call them? After all, different words are used in different languages, but a (or un) chien is still a dog. In fact, laypersons commonly dismiss philosophical questions for precisely this reason: It seems as if we are haggling over "mere words."

The amazing fact is, however, that what something is, and hence whether something even exists, is inseparable from how we define a word. A simple case: Do unicorns (that favorite philosophical animal) exist? If the word "unicorn" means "a horse-like creature having one horn on its forehead," then the answer is probably "No." But if "unicorn" means "any mammal that has a horn on its head," then the answer is "Yes," for example, rhinos. The decision about Pluto or planets in general, or anything else, is exactly the same kind of beast.

Put it this way: There are no Platonic planets. Plato -- or perhaps Socrates -- thought that the ideal "Form" of each existing sort of thing determined its essence. So for Plato, Pluto would be a planet if Planet is a Form to which Pluto conforms. But if "planet" is just a concept that can be concocted by a committee to suit both scientific purposes and non-scientific predilections, then there is nothing essential about Pluto (or 2003 UB313) to determine what it is.

Yet another way to think about this is to contrast the controversy about the planetary status of these bodies with the concurrent quandary about 2003 UB313’s name. In part the latter issue is dependent upon the resolution of the former since the constraints on planetary names are different from those on planetoids. But without going into the details, I simply want to point out that determining that 2003 UB313 is, say, properly called a planet would be a different kind of dubbing from giving it a name, such as "Persephone." The latter is indeed a matter of "mere words," however evocative or appropriate they may be. But the former designation as "planet" would determine 2003 UB313's very nature.

I would like finally to commend Mike Brown (who also credits Gibor Basri at his Web site) for having originally come down on the side of preserving the planetary status of Pluto, and hence also by implication, 2003 UB313 (although in the aftermath of the IAU’s vote on August 24, 2006, to demote both bodies from planetary status, Brown seems reconciled to their fate). Both he and I, as it happens, have personal reasons for favoring that outcome. 2003 UB313 is his baby, and my goddaughters were born on February 18, the discovery date of Pluto. But I believe there are solid philosophical reasons for it as well.

Consider, again, that Brown’s argument was "cultural"; he thought we should be sensitive to the established usage of the notion of "planet" to designate Pluto among the planets of our solar system. This jibes nicely with a complaint I have against specialists in various fields, who appropriate a word from everyday usage and then give it a highly technical meaning. This ends up confusing everybody's thinking, sometimes even in matters of life and death.

A notorious example -- though only one of many I could cite -- emerged from a discussion I once had with a criminal justice professional about the guilt of a person who had just been convicted of murder. I made the suggestion that the person might, for all that, still be innocent of the crime. I was shocked when he denied that possibility, not because we disagreed about the weight of the evidence against the defendant, but because he maintained that "guilty" just means "convicted in a court of law." In other words, he was ruling out by definition that the person could be innocent since guilt and innocence were for him strictly legal notions. To me this is a perversion of the common meanings of "guilt" and "innocence."

The better course of action, I submit, is to coin special technical terms for technical concepts. A model for this might also come from criminal justice, where, for example, the notion of perjury is not the same thing as the everyday concept of lying. Suppose a person has had a criminal conviction expunged from the record, and then one day, hauled back into court, is asked on the stand whether he has ever been convicted of a crime. I could imagine that his attorney might counsel him to say "No," since even though this would be a lie, it might not constitute perjury. This is because perjury is “the willful giving of false testimony under oath or affirmation, before a competent tribunal, upon a point material to a legal inquiry” (http://dictionary.reference.com/search?q=perjury), whereas the point in question would not be properly material, I suspect, since it has been placed out of legal bounds. Nevertheless, it would still be a lie, which in common parlance is the uttering of an assertion one believes to be false for the purpose of misleading the listener.

Just so, designate Pluto and 2003 UB313 with the technical title of Kuiper Belt objects if you wish, but do not feel that we must at the same time cease to call them planets.*


* What is especially bedeviling is that the new IAU designation for Pluto and 2003 UB313 is “dwarf planet,” which makes it appear that they are still planets, albeit dwarfish ones. But in fact the new term is apparently intended as a kenning, which is a figure of speech that designates something that is not designated by its component terms, as “sail road” for the sea (http://en.wikipedia.org/wiki/Kenning). Thus, according to the IAU, dwarf planets are not planets! See also Dueling Designations.

Our Whirling World

By Joel Marks

Published in Mercury, vol. 36, no. 4, Fall 2007, pp. 28-31

Everybody knows that the earth rotates 360 degrees each day, which is why the sun comes back to the same place in the sky after 24 hours. Indeed, that is what makes a day a day. And everybody knows that the earth does this 365&1/4 times each year, which is why the sun returns to the same place in the zodiac after 365&1/4 days. Indeed, that is what makes a year a year (although we round them out to three of 365 days followed by a leap year).

Yes, everybody knows these things, but “everybody” is wrong.

No, I am not suggesting that we return to the days of a stationary earth at the center of a cosmos that revolves around us. The point is rather that the earth turns more than most people think it does.

To understand what is going on, it helps, first, to realize that we live in a whirling universe: Everything turns! Every star, every planet, every rock in space is spinning; moons revolve around planets, planets revolve around suns, suns revolve around galaxies. It’s a dizzying fact of existence.

So our little Earth not only rotates on its axis, but also orbits Old Sol, which in turn drags us in tow around the center of the Milky Way Galaxy. The latter motion normally escapes our notice because it is so slow by human standards; it takes 250 million years for the solar system to go around the galaxy once! Furthermore, what we see in the nighttime sky are the stars in our local neighborhood, so even if we were all traveling around the galactic center at breakneck speed (which, actually, we are), the naked eye would just register the relative stability of the nearby, so-called “fixed” stars.

The temporal measure of our orbit around the sun is of course well-known to us, for it constitutes the year. It is instructive to recall, however, just how counterintuitive today’s commonplace seemed at first. Copernicus (1473-1543) famously proposed that the earth revolves around the sun and not vice versa. Thus, the earth lost its place at the center of the scheme of things. But what really rattled people was a further implication, namely, that the earth moves. Commonsense rebelled at the idea that the very prototype of immobility, the ground beneath one's feet, was in fact twirling on an axis and hurtling through space. The metaphor we use to describe this revelation indicates its emotional impact: revolutionary (that is, moving in an orbit).

Thus we seem to have a neat division between the day determined by our axial rotation and the year set by our orbital revolution. But this is where the mistake lies, for these two motions are not entirely distinct. One familiar way that their interaction intrudes upon our lives is during presidential election years, otherwise known as leap years. Why do we add a day to the calendar every four years? Because the earth does not return to the same point in its orbit around the sun after exactly 365 days, but requires an additional quarter-day to complete the 360-degree circuit. Hence, adding one day every four years brings us back in synch. Of course it is only a coincidence that this correction coincides with our presidential elections, but maybe the United States should switch the date of the elections to February 29 just to press home the point!

We now come to the moral of our little tale, for there is another interaction between diurnal rotation and annual revolution, which goes largely unrecognized. Although analogous to the leap year, it is completely distinct from it. There is, again, a misalignment between two measures that has to be made up by adding something; in this case, though, what needs to be set right is the number of degrees in the daily rotation rather than the number of days in the year.

Let us consider the question: What is a day? Its normal meaning is the solar day. This is the time it takes a point on the earth's surface to return to the same place relative to the sun. For example, if we begin when the sun is due south when viewed from Boston, then exactly one day will have elapsed by the time the sun returns to that position in the sky. This is what we count as a 24-hour day. (We can ignore for the purposes of the present discussion that this is strictly speaking the mean solar day, since the eccentricity of the earth’s orbit yields solar days of slightly differing lengths during the course of a year.)

But there is also a duration known as the sidereal day. This is the time it takes a point on the earth's surface to rotate 360 degrees relative to the more distant, “fixed” stars. If you think about the physical situation, you will realize that the sidereal day must be shorter than the solar day. This is because, while the earth is rotating at a constant speed, it is also moving in its orbit around the sun, and in the same direction as the rotation (counterclockwise as seen from the north). Hence, for Boston to come all the way back around to the same place relative to the sun, it must travel more than 360 degrees.

How much more? Well, the number of days in a year, approximately 365, is almost the same as the number of degrees in a full rotation, 360. This is surely not a coincidence but a Babylonian intention. So the earth actually rotates an extra degree each day, that is, around 361 degrees daily.

Furthermore, if you carry that through the whole year, you arrive at an even more surprising conclusion, to wit: the earth rotates 366 times in a 365-day year! This turns out to be a general rule of geometry: Any planet makes one extra rotation than there are days in its year. A limiting case, which can also help you to picture why this is so, would be a planet that has no day; it would rotate one time each year. This is because the planet would always present the same face to its sun; therefore the sun would always remain in the same place in the sky, so there would be no return to the same place to constitute a day.

(The situation is similar to the moon’s motion relative to the earth. Since the moon rotates once per revolution around the earth, the earth, on the moon’s earth-facing side, simply stays put in the lunar sky all the time.)

If all that makes your head spin, it should!

Sidebars and Illustrations

What Is a Day?

The normal meaning of a day is technically the solar day. This is the time it takes a point on the earth's surface to return to the same place relative to the sun.

ILLUSTRATION

But there is also the sidereal day. This is the time it takes a point on the earth's surface to rotate 360 degrees relative to more distant stars. Because the earth is simultaneously orbiting the sun, the sidereal day is shorter than the solar day.

ILLUSTRATION

One More Rotation

A planet that always has the same face towards its sun will rotate once per year, and hence have one sidereal day per year, but no solar day at all.

ILLUSTRATION (from north of solar system)
ILLUSTRATION (of sun’s unchanging position in sky from a given location) “It’s always noon.”

A New Twist

To add to the dizzying but fascinating complexity of the spinning, orbiting Earth, consider also the recent discovery that the earth's core rotates independently from the earth's surface or mantle, since a molten layer separates them. Researchers at Columbia University and the University of Illinois have determined that the inner core rotates faster, completing an additional full rotation in roughly a millennium. So which represents the rotation of the earth?

ILLUSTRATION


Byline

Joel Marks is professor of philosophy at the University of New Haven in West Haven, Connecticut, and an amateur astronomer. He enjoys indulging in what he has dubbed "philosophical astronomy," which means arriving at new astronomical insights by reasoning about already known phenomena.

Three Websites

This is one of three websites containing short essays I have written about astronomy. The two others are:

All of the Above, which describes and explains various astronomical phenomena and events,

and

SkyMarks, a compilation of stargazing columns that appeared monthly for a couple of years in the New Haven Register.

The present site is devoted to explicitly philosophical writings about astronomy.

And here is a list of all of my publications on astronomy.

Enjoy, and clear skies! -- Joel