Danielson / ASA_Colorado
Department of English
University of British Columbia
#397 – 1873 East Mall
Vancouver, BC, Canada V6T 1Z1
Copernicus and the Tale of the Pale Blue Dot
Over the past nine years I have been having more fun than it ought to be legal for a middle-aged man to have. Since about 1994 I’ve been learning everything I possibly can, as someone without a scientific education, about the history of cosmology, and I’m pleased to say I haven’t been arrested yet.
Still, I often have to explain why a guy who’s supposed to be an English prof is dabbling in the history of science. I can give you a number of quick reasons. I’ve made part of my career as a student of the writings of the poet John Milton, who lived in the seventeenth century, the era of Kepler, Pascal, Newton, and so many others associated with the Scientific Revolution. And in his epic Paradise Lost Milton mentions by name only one of his seventeenth-century contemporaries, someone he had actually met near Florence, Italy, back in the 1630s—Galileo. Besides, one thing Jennifer didn’t tell you about me was that back in 1956, at Doncaster Elementary School, I won the first-grade science prize, so you could say I’ve been sort of returning to my roots.
I have become particularly interested in Copernicus and the first century or so of Copernicanism—partly because they are so fascinating in themselves, but also because they are so often invoked by modern-day scientists and people who comment on science. This is where I stick my oar in, because like any literary historian I’m interested in how things get interpreted, and what they mean. And so I’ve been very interested in what people think Copernicus and Copernicanism mean for the history of science, and for earth and human beings generally.
I’m sure you’re all familiar with the standard interpretation. I’ll just describe the version I was taught in school, and I’ll ask if you were taught more or less the same thing. I was taught that the Copernican Revolution entailed a humiliation or demotion or dethroning of earth, and by implication of humankind, from its previous place of cosmic centrality and importance. In other words, I was taught that the scientific smashing of geocentrism in the sixteenth and seventeenth centuries entailed a rejection of anthropocentrism. And in effect, the full stage version of this transformation features the dark forces of religion and the church locked in mortal combat with the enlightening power of science. Science has “demonstrated the insignificance of humankind in the universe overall.” And it has established—you guessed it—the centrality and importance of scientists in showing us how cosmically unimportant the earth and its inhabitants really are. Does this all sound familiar?
Now, although I’ve referred to this as a standard interpretation, it is so standard that often it is treated not as an interpretation at all, but simply as a fact of history. Nevertheless, over the past few years I’ve been on a little personal campaign to undermine this interpretation and to suggest that really it’s not the way things are at all. I’ve been calling this standard interpretation “the great Copernican cliché,” and I’ve been attacking it not only because I believe that it is false, but also because I think that its effects have been and continue to be harmful.
Let me sketch my reasons for considering the great Copernican cliché to be wrong. To start with, the cliché rests on a false idea about the cosmology that Copernicus overturned. It incorrectly presumes that earth’s cosmographic centrality in pre-Copernican thought implied earth’s privilege or specialness. In fact, to the very best of my knowledge, the overwhelmingly dominant pre-Copernican view was that the central position in the universe was one of humility. Literally, central equalled low and lowly. Physically—as in Aristotelian physics—the centre was where heavy, gross things collected. Earth was in the centre because it was heavy. And an ultimate improvement of humans’ lot would involve their rising upwards away from the centre, away from what Pico late in the fifteenth century called “the excrementary and filthy parts of the lower world.” He was referring to the earth.
By the way, in this model, people whose lot got worse rather than better ended up even closer to the centre than they were when they lived on the surface of the earth—which in geocentrism is, after all, exactly one e.r. distant from the actual centre. The actual centre, according to Dante, is the precise location of the lowest point of hell, where Satan is damned cold—frozen, in fact. It is this observation that prompted Arthur Lovejoy to quip, back in the 1930s, that the medieval universe is not anthropocentric but diabolocentric.
In any case, the simple first assertion in my argument is that for Copernicus to remove earth from that kind of central location could not possibly count as a demotion. On the contrary, as Rheticus, Copernicus’s only student, put it in the first ever published Copernican treatise, in the heliocentric theory, “the globe of the earth has risen ..., while the sun has descended to the center of the universe” (p. 151). After geocentrism, earth had nowhere to go but up. Therefore, rejecting geocentrism emphatically does not entail a demotion of earth or of humankind.
The next step in my argument is to show that geocentrism does not imply anthropocentrism—to move from the non-anthropocentric character of pre-Copernican geocentrism to the (figuratively speaking) anthropocentric tenor of much Copernican cosmology. Famously, Copernicus himself refers in De revolutionibus to God as the great “Architect”—who, he says, created the world “propter nos,” for our sakes. But most decisively, Galileo reads earth’s non-centrality—and its corresponding planetary status—as an exaltation. In The Starry Messenger, Galileo shows how earthshine illuminates the moon just as the moon’s light does the earth—a phenomenon proving that earth indeed shines like a star. And this account, as Galileo points out, undercuts “those who assert, principally on the grounds that it has neither motion nor light, that the earth must be excluded from the dance of the stars. For ... the earth does have motion, ... it surpasses the moon in brightness, and ... it is not the sump where the universe’s filth and ephemera collect.” Some years later, Galileo repeats essentially the same idea in the Dialogo, in which Salviati declares: “As for the earth, we seek ... to ennoble and perfect it when we strive to make it like the celestial bodies, and, as it were, place it in heaven, from whence your [Aristotelian] philosophers have banished it.”
So rather than engineering a demotion of humankind or of earth, what Copernicus made possible was our inclusion in the dance of the stars, our active participation in the harmony and polyphony of the heavenly chorus. The musical metaphor, of course, was invested in most heavily by Kepler, who favoured a highly dynamic view of our cosmic role: According to Kepler, because “man” was created for contemplation, “and adorned and equipped with eyes, he could not remain at rest in the centre. On the contrary, he must make an annual journey on this boat, which is our earth, to perform his observations. ... There is no globe nobler or more suitable for man than the earth. For it is exactly in the middle of the principal globes .... Above it are Mars, Jupiter, and Saturn. Within the embrace of its orbit run Venus and Mercury, while at the centre the sun rotates.” For Kepler, then, only with the abolition of geocentrism may we truly say that we occupy the best, most privileged place in the universe.
To summarize, then, there’s nothing much in the picture I’ve sketched so far to suggest that Copernicanism demoted humankind, nor that Copernicanism was objected to by religious parties or anybody else on the grounds that it demoted humankind. It was objected to because it ran counter to centuries of established astronomical tradition. It was objected to because it involved the absurd idea that terra firma was in motion. Galileo’s version of it was objected to because it seemed to contradict a few passages of Scripture which—if read absolutely literally, as the Council of Trent had decreed—suggested that the earth did not move. And in fact it was objected to because it seemed to entail a dethroning not of the earth but of the sun—placing it in what had been the location of greatest disrepute in the universe. This is why, by the way, Copernicus in 1.10 of De revolutionibus has to pull out all the poetic stops when he describes the location of the sun in the centre.
And behold, in the midst of all resides the sun. For who, in this most beautiful temple, would set this lamp in another or a better place, whence to illuminate all things at once? ... Truly indeed does the sun, as if seated upon a royal throne, govern his family of planets as they circle about him.
Copernicus must try to renovate the cosmic basement if it is to be a fit dwelling for the sun. And to put it in a slightly circular way, he needed to renovate the basement because the basement was in need of renovating. For as Galileo would put it, it had been the sump of the physical universe, and so for Copernicus’s purposes it needed spiffing up. This “renovative” reading is supported by the fact that, within a year of the publication of the De revolutionibus, Giovanni Tolosani in Italy was condemning Copernicus on just these grounds: Copernicus, he declares with indignation, in 1544, puts the sun in “the center of the universe, where everybody else correctly and most convincingly proves that the earth is”; Copernicus “puts the indestructible sun in a place subject to destruction” (Rosen, CSR, p. 189).
But Rheticus, Copernicus’s student and agent, had already anticipated this sort of rigorous either/or, win/lose logic. That is why, in preparing the ground for Copernicanism, he devoted much poetic and rhetorical effort to establishing a “win/win” reading of the relocation of both earth and sun. As far as earth is concerned, it is “clearer than sunlight,” Rheticus says,
that the circle which carries the earth is rightly called the great circle [Orbis Magnus]. If generals have received the surname “Great” on account of successful exploits in war or conquests of peoples, surely this circle deserves to have that august name applied to it. For almost alone it makes us share in the laws of the celestial state. (177-78)
And in Rheticus’s win/win construction, this encomium upon the greatness of earth’s location has its solar counterpart. Rheticus, anticipating Copernicus, emphasizes the sun’s royalty: it was “called by the ancients leader, governor of nature, and king.” Moreover, Rheticus continues: “[My teacher] is aware that in human affairs the emperor need not himself hurry from city to city in order to perform the duty imposed on him by God; and that the heart does not move to the head or feet or other parts of the body to sustain a living creature” (p. 138).
Rheticus published these words in 1540. And in nothing I’ve read for about the next hundred years have I been able to find any suggestion anywhere that Copernicus’s putting the earth into orbit—into what had been the sun’s place—was interpreted as locating the earth on the other side of the tracks in any depreciatory sense. Only in the mid-seventeenth-century—a hundred years after the death of Copernicus—with the preliminary glimmerings of the Enlightenment, did some French satirists such as Cyrano de Bergerac and Bouvier de Fontenelle propose the now-standard interpretation accepted by scientists and others. As Fontenelle’s character declares: “I am extremely pleased with [Copernicus] ... for having humbled the vanity of mankind, who had usurped the first and best situation in the universe.” This take on Copernicanism became the apparently unquestioned version of the Enlightenment in the eighteenth century and on into the nineteenth, as magisterially summarized by Goethe in 1808:
Perhaps no discovery or opinion ever produced a greater effect on the human spirit than did the teaching of Copernicus. No sooner was the earth recognized as being round and self-contained, than it was obliged to relinquish the colossal privilege of being the centre of the universe. (Farbenlehre, 1808)
And from Goethe and the Enlightenment to the present there has been, in more senses than one, almost no looking back.
In our own lifetimes, this now-standard interpretation of Copernicanism has had many spokespeople, perhaps none more influential than Carl Sagan (1934-1996). Sagan described Copernicanism as the first in a series of “Great Demotions ... delivered to human pride.”1 Here is one version of the scenario Sagan spins:
Our ancestors lived out of doors ... [And to them, it seemed,] the Sun, the Moon, the planets, and the stars are part of some elegantly configured cosmic clockwork ... put here for a purpose, for our benefit. Who else makes use of them? What else are they good for?
And if the lights in the sky rise and set around us, isn’t it evident that we’re at the centre of the Universe? These celestial bodies ... circle us like courtiers fawning on a king. Even if we had not already guessed, the most elementary examination of the heavens reveals that we are special. ...
This satisfying demonstration of importance, buttressed by daily observations of the heavens, made the geocentrist conceit a transcultural conceit—taught in the schools, built into the language, part and parcel of great literature and sacred scripture. Dissenters were discouraged, sometimes with torture and death. It is no wonder that for the vast bulk of human history, no one questioned it. (PBD 1994)
What I am suggesting, just to be perfectly clear, is that Sagan’s skillfully told story is mainly hokum. His tale of the “pale blue dot,” which pours scorn on the suggestion that this cosmic speck is profoundly special, is only the most prominent and famous example of the same kind of interpretation of the legacy of Copernicus. I invite you to do a Google search using the terms Copernicus and “dethroned” and see how many hits you can get that promote the same view.
But let me cite just a few examples of how I think the cliché, or its narrative form, which I’m calling “the tale of the pale blue dot,” has a bad effect on how we understand science, and perhaps the universe. As Sagan’s phrase “Demotions to human pride” suggests, he and others see the so-called demotion of earth by Copernicus as part of a larger pattern. This approach sees the earth dethroned by Copernicus; the sun and in turn the Milky Way dethroned by subsequent astronomers; the species homo sapiens dethroned by Darwin; and reason or spirit dethroned by Freud. Freud himself was very fond of citing this genealogy—because of course it meant that if you opposed his view, then you were probably disreputably medieval in your cosmology as well.
Sticking with cosmology, consider Stephen Hawking’s critique, in A Brief History of Time, of something called the “strong anthropic principle” (or SAP), which is a serious proposal by serious scientific theorists in response to the astonishing fact that consciousness, apparently against all odds, has arisen in this attenuated sea of matter we call the universe. One of Hawking’s main reasons for rejecting the strong anthropic principle is as follows:
It runs against the tide of the whole history of science. We have developed from the geocentric cosmologies of Ptolemy and his forebears, through the heliocentric cosmology of Copernicus and Galileo, to the modern picture in which the earth is a medium-sized planet orbiting around an average star in the outer suburbs of an ordinary spiral galaxy, which is itself only one of about a million million galaxies in the observable universe. Yet the strong anthropic principle would claim that this whole vast construction exists simply for our sake. This is very hard to believe.2
I cite Hawking’s argument not because I’m here to defend the strong anthropic principle, but I think that ideas should be judged on the evidence and on their own merits. And what Hawking appears to be doing, unfortunately, is rejecting the SAP not because it fails on logical or evidentiary grounds, but because it is repugnant to a preestablished way of thinking—one that I’m arguing is seriously flawed. In any case, the claim that something is unacceptable because it is “hard to believe” really doesn’t stand up as a scientific argument.
I’m not, of course, objecting to Hawking’s point about cosmic geometry. At the literal level, the claim about the non-centrality of the earth is very firmly established indeed. In standard model cosmology, the non-centrality of any point in the universe is seen as a consequence or an instance of the “principle of mediocrity,” also known (misleadingly) as the “Copernican Principle.”3 Just as the surface of a sphere has no particular center, so in the universe as a whole there is no mid-point. Or, just as truly, we can say that every point in the cosmos is non-unique and is, from its own perspective, the middle—and thus, at some literal level, “mediocre.”
I generally avoid using the terms “principle of mediocrity” and especially “Copernican Principle” merely because they lend themselves so readily to the very confusion I’d like to see cleared up. It is just too easy to slide, as Hawking does, from a rigorous geometrical use of “mediocrity” to the insinuated but unproven conclusion, in the tale of the pale blue dot, that earth mustn’t be thought of as special at all.
The harmful effects of the Great Copernican Cliché also appear at a more popular level, where they impair our understanding of new scientific discoveries by forcing them into the now orthodox picture of Copernicus’s legacy. For example, in 1996 NASA announced that its scientists had discovered evidence of life in a meteorite from Mars. Nathan Myrhvold, an executive and self-styled “chief strategic daydreamer” with the Microsoft Corporation, used the occasion to issue his own denunciation of anthropocentrism:
Last week’s announcement is the biggest insult to the human species in almost 500 years, step two in a three-step process that will leave humanity totally humbled.
Ptolemy ... was the first and boldest in a long succession of spin doctors for the primacy of human beings. The whole universe, he postulated, rotated around us. ... [But then] Copernicus rudely pointed out: Sorry earthlings, we spin around the sun, not vice versa. ... Giordano Bruno, a sort of 16th-century Carl Sagan, popularized these concepts ..., saying, among other things, that “innumerable suns exist. Innumerable earths revolve around those suns. Living beings inhabit these worlds.” A soundbite like that would have gotten Bruno his 15 minutes of TV celebrity if he’d been around last week. But this was 400 years ago, so they roasted him to death instead.
Bruno’s crime, like Galileo’s, was to undermine the uniqueness of our planet, and by doing so, to threaten the intellectual security of the religious dictatorships of his time. People get cranky when you burst their bubble.4
There’s no denying the verve or the humor of Myrhvold’s account. Yet it provides a further example, in slightly exaggerated form, of the Great Copernican Cliché as repeatedly swallowed uncritically, and in the absence of good evidence, by scientists and nonscientists alike. We’ve already, in relation to Sagan, observed some of its standard features: failure to distinguish literal and figurative; fast and loose potted summary of what actually happened historically; full-blown “us-and-them” rhetoric; instruments of torture standing dramatically at the ready there on the side of the deceivers (“spin doctors”), the religious, and the cranky.
Yet the main point I’m making is merely that this sort of Punch-and-Judy depiction of the history of science detracts from the very discovery purportedly being commented on. It does nothing at all to encourage closer, open-minded examination of the evidence or its implications, because we already “know” what it means. The Great Copernican Cliché thus functions as an unreflective and, when it comes right down to it, rather uninteresting knee-jerk response to something that is actually exceptionally interesting, something that genuinely warrants careful attention. This is one of the main reasons why I think the cliché itself needs to be dispensed with.
So there you have a sketch of my little campaign. In pursuing it, I have met with a number of challenging responses. Among scientists, I have discovered to my cost that a lot of people went into astronomy in the first place because they were inspired by Sagan, and these loyal folks are clearly made uncomfortably by my efforts to dethrone him. Other than that, I’ve had a pretty friendly response from scientists, short of my argument actually being accepted. After a plenary lecture to members of the American Astronomical Society two years ago, I heard many comments to the effect: “Thanks for sharing an interesting approach, but of course it can’t be right. What about Galileo?” One senior professor of astronomy took me aside afterwards and told me that, frankly, scientists would probably treat the textual evidence on which I rest my case to be, in his words, “too clever by half.” I admit I don’t know how to respond to this sort of refutation.
There is one more component of the “dethroning” business I haven’t acknowledged yet: the matter of earth’s relatively small size, cosmically speaking. If you’re an astronomer and you spend your days calculating galaxy populations per cubic gigaparsec, then you’re bound to think of earth as minuscule, to put it mildly.
Accordingly, Sagan and other proponents of his approach believe that just as the march of science has shown that we humans are not centrally located in the universe (and therefore not special), so it has demonstrated that we’re very small (and therefore not special).
It is worth pointing out here that the scientific recognition of earth’s smallness is nothing new. Ptolemy offered a number of strong observational arguments for believing that earth is “as a point” in relation to the size of the sphere of the fixed stars. But of course Copernicus said the same thing about the earth’s orbit: the Great Circle of the earth is itself “as a point” in relation to the size of the sphere of the fixed stars. So Copernicus’s universe was even more unimaginably large than Ptolemy’s already was. By my reckoning, it had to be 1.8 x 10, or almost two billion, times larger, by volume.
But if I may respond with another tautology, size is important only if size is important. In spite of what all those pesky spam emails keep telling me, it’s just not true that bigger equals better. Literal greatness (size) doesn’t imply figurative or axiological greatness (excellence or importance), and literal smallness doesn’t entail insignificance. One winter when we were in our twenties my wife and I had to live apart for two terms because we were students, she in Los Angeles and I, some hundreds of miles away, in the San Francisco Bay area. Every few weekends I’d visit her or she’d visit me. I remember, each time I’d drop her at San Jose airport, watching her plane take off and gradually recede from my vision, disappearing like a speck in the misty distance. And I’d reflect with wonder on how the most important person in the world to me could be so minuscule, a mere point in the vast expanse of the California sky.
In this and in countless other experiences like it we emphatically do not conclude, “Aha, see then how trivial and insignificant she really is.” On the contrary, we search for metaphors to express how worth may be embodied in tiny things, how love is not something merely bound by space or physical magnitude, how a jewel may dwarf in value the kingdom that contains it. And in the same way, surely a meditation on our pale blue dot requires a balancing of perspectives. Yes, it imparts a healthy humility to realize how little our planet is. But it also fills us with awe to contemplate, if we can, the inestimable riches concentrated in that small, pale, blue point of reflected light.
I want to conclude with two thought experiments that harmonize with Carl Sagan’s imaginative method but which point in the opposite direction from his conclusions. Sagan, of course, asks us, in an imaginative journey to the outer regions of the solar system to look back at our pale blue dot “and then try to convince yourself that God created the whole Universe for one of the 10 million or so species of life that inhabit that speck of dust.” By the way, Sagan doesn’t specify precisely who does make such claims. In any case, I’d like to imagine pointing the telescope in the opposite direction in search of some other planet like ours, preferably one that contains intelligent life. Before I fill in this scenario, however, let me pause and tell you parenthetically about a young boy named Jonathan Biggs, who lives in Kelowna, British Columbia. I don’t know too much about Jonathan. I know that he has Down Syndrome. I know that a few months ago he fell in love with Cinderella at Disneyworld in Florida. I know that if you ask him his name, he says something like “I am Jaw-than.”
But back to our search for ET. Suppose that one day soon some of our astronomical colleagues discover an earth-like planet somewhere out there in the galaxy. Suppose they discover that this planet contains some kind of intelligent life. And suppose, somehow, overcoming the barrier represented by the speed of light, they make radio contact with one of that planet’s inhabitants. Finally, suppose these colleagues ask that inhabitant its name, and he replies, “I am Jaw-than”—and perhaps goes on to explain, in very simple language, how he fell in love with that planet’s equivalent of Cinderella at that planet’s equivalent of Disneyworld.
Now imagine the headlines the next morning in the Denver Post. Is there any doubt that they’d mention the discovery? Is there any doubt that they would treat it as one of the greatest astronomical discoveries of all time? However, do you think that the story would open by explaining, apologetically, that the intelligent life didn’t appear to have as high an IQ as Einstein? Or that the ET’s body was less than two meters in length? Or that the planet it inhabited was a paltry 8000 miles in diameter? Or that it orbited a very ordinary, garden-variety G-class yellow star situated in no particularly distinguished location on the edge of the galaxy. I don’t know exactly how the story would be told, but don’t you think it would gush with sheer astonishment at the news that the universe out there contains life that thinks and communicates and loves and has a name.
You already discern my point: if such a discovery said something momentous and significant about the nature of the universe, then our existence does too. The truth is that Jonathan Biggs does exist in this universe; and in strict consistency with the cosmological principle of mediocrity, the fact that he exists here rather than out there is really neither here nor there.
In the past when I’ve given lectures like this one, I’ve more than once been asked, “If intelligent life were discovered elsewhere in the universe, what would it do to your theology?” And having thought about it, I believe the answer is that it would do the same thing that discovering intelligent life on earth does to my theology. It fills me with awe. It drives me to ask telic questions, questions about the purpose of life. It makes me ask who or what I am in relation to other intelligent beings. It fills me with gratitude that I can live in the same world, and share a moment in time, with other such contingent creatures. It fills me with wonder that there is something rather than nothing.
The final thought experiment I want to share with you was proposed by the English poet Thomas Traherne back in the seventeenth century, about 340 years ago, in the wake of the Copernican Revolution—you know, the Revolution that supposedly dethroned earth and the human race. Traherne was a contemporary of Newton’s and also of others I have mentioned such as Fontenelle, and he illustrates the viability then of the alternative interpretation of Copernicanism that I am promoting now.
The lost manuscript of this meditation by Traherne, entitled “the Kingdom of God,” was discovered five years ago and published only within the past twelve months. It begins by sketching a scenario that partakes richly in the Copernican imagination and postulates, like Sagan, someone viewing earth from outer space. But it offers a profoundly different view of this our home and native planet, and it is the alternative and much more truly Copernican tale of the pale blue dot, that I’d like to leave you with tonight. Traherne writes:
Had a man been always in one of the stars, or confined to the body of the flaming sun, or surrounded with nothing but pure ether, at vast and prodigious distances from the Earth, acquainted with nothing but the azure sky and face of heaven, little could he dream of any treasures hidden in that azure veil afar off.
Should he be let down on a sudden and see the sea, and the effects of those influences he never dreamed of ... such strange kind of creatures, such mysteries and varieties, such never-heard of colours, such a new and lively green in the meadows, such odoriferous and fragrant flowers, such reviving and refreshing winds, it would make him cry out:
“How blessed are thy holy people, how divine, how highly exalted! Heaven itself is under their feet! The Earth seems to swell with pride that it bears them all; all its treasures laugh and sing to serve them.
“Verily this star is a nest of angels! This little star so wide and so full of mysteries! So capacious and full of territories, containing innumerable repositories of delight when we draw near! Who would have expected, and who could have hoped for, such enjoyments?”
© 2003 by Dennis Danielson
1 Carl Sagan, Pale Blue Dot (New York: Random House, 1994), p. 26. Hereafter abbreviated as PBD.
2 Stephen Hawking, A Brief History of Time (New York: Bantam, 1988), p. 126.
3 This principle, often abbreviated as “CP” and also sometimes called the Cosmological Principle, relates to the geometry of the universe, and it applies whether we’re thinking in terms of Newtonian or of Einsteinian physics. Newton believed that the “shape” of the universe followed Euclidian principles: That is, it extends in straight lines infinitely in all directions, and of course no line or plane or three-dimensional space that is infinite has a centerpoint. Thus, in such a universe, there is no middle. The same is true for Einstein’s cosmos, except here we have to think of the “four-sphere”—the four-dimensional continuum of spacetime—by analogy with a sphere like the earth itself. There is no mid-point because there is no edge or circumference from which any one point is equidistant.
4 Nathan Myrhvold, “Mars to Humanity: Get Over Yourself,” Slate, 14 August 1996; summarized in Time 148.10 (August 26, 1996): 64.