Cosmos 2: One Voice in the Cosmic Fugue

by Shane L. Larson

Humanity is simultaneously blessed and cursed with one of the most ingenious creations of Nature: our imaginations.  Our brains have developed not just to run our bodies, and not just to absorb sensory data from the world. They store all the vast myriad of experiences we have and then, at a later time, recall that data for the express purpose of inventing ideas that may or may not have anything to do with reality.

An excellent example of how your brain works can be found in a simple game my daughter and I play at restaurants while we’re waiting for our food.  We call it “The Napkin Game.”  One person draws a simple line doodle, without lifting the pen, then the other person takes that doodle, looks at it from all angles, then adds more lines to turn it into a picture. When you draw a doodle for your partner, you don’t a priori know what it will be turned into.  That’s the magic of brains! Any random doodle could be Batman’s cowl, or a Wonka Bar, or a turtle. Your brain takes a little bit of visual input, maps it onto one of the trillions of neural connections in your mind, and makes something new!

An example of the Napkin Game. One person draws a simple line doodle, and the other person adds to it to make a picture.

One of the most important things your imagination does, is it extrapolates into the future.  Sometimes it makes up extrapolations out of whole cloth that likely have little bearing on reality (though they may be perfectly entertaining, if not desirable, daydreams).  I count among such extrapolations imagined futures where zombies have taken over the world, Apple Slice has made a comeback, or I am close personal friends with Queen Elsa of Arendelle.  But very often, the extrapolations are really simulations — attempts to divine a realistic future. This is the origin of wonder, of anticipation and excitement, and also of fear (particularly fear of the unknown). Imagination uses both of these extrapolations in the game we call science.

The most remarkable thing about imagination is that it knows no boundaries. T-rex flying a fighter jet? No problem. I’m really Walter Mitty, a member of MI:6 who cleans up after Bond?  Duh. Every kind of particle we have ever seen maybe has an undetected and completely made up “super-symmetric” partner particle?  Sure, that sounds cool to think about! 

Examples of imagination, possibly run amok. (L) Dinosaurs flying fighter jets [Lego model; dino added by S. Larson]. (C) The Standard model of particle physics. (R) The “SuperSymmetric” addition to particle physics, imagined by some physicists.

Unfettered by physical limitations or abstract societal rules, our imaginations can stray from the possible to the impossible, from the real to the unreal, and from the mundane to the extreme. The most powerful aspect of this ability is that it allows us to ask questions about things of which we currently are completely ignorant.

Consider the question of life in the Cosmos.  Is there life elsewhere? Are we a singular instance of life, or is there a vast froth of life-filled worlds filling the deep, deep dark of the Universe?

One lonely dish in the Very Large Array (VLA) near Socorro, NM, staring out into the Cosmos. [image by S. Larson]

It is a deep and through provoking question that has profound implications for our philosophical and cultural identities. We can ponder such questions precisely because our brains can take the question and push it to the extreme boundaries, which are:

(1) The Earth is unique. We are a singular instance of the music we call life, a lone voice shouting vainly into the vast, dark cathedral of the stars.

(2) The Cosmos is teeming with life, a vast ecosystem of atoms that have organized into patterns capable of replicating and contemplating their own existence.

Arthur C. Clarke once famously summarized these extremes, saying “Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.”  The amount we are terrified by this thought is the fault of our imaginations.  We are inherently social creatures — we thrive on contact, discussion, and shared common experience. All of us have, at some point in our lives, experienced profound loneliness — being lost, being trapped, being left out by our peers. When we imagine being alone in the Cosmos, our brain magnifies that sense of loneliness a trillion-fold.  What gets simulated is not the Earth all alone, but ourselves all alone — what if I were alone in the Cosmos, lost in the vast dark? We anthropomorphize the entire human race, mapping our own personal feelings onto 7 billion other souls.

In the opposite case, our imagination proposes a Cosmos completely contrary to the normal hubris that humanity wields.  Despite our proclaimed belief in the fundamental tenets of Copernican astronomy, where the Earth is not the Center of All That Is, we certainly don’t lead our lives that way. Humanity, as a rule, does not pretend to be anything other than the Center of Everything!  But it could be that we inhabit a Cosmos with other intelligences, some perhaps vastly greater than our own, some perhaps implacable and as unaware of us as we might be of ants or bacteria.  Such musings are disquieting because they challenge the central tenet of our perceived existence as the premiere lifeform, on planet Earth or anywhere else.

The question of whether the Cosmos harbors life elsewhere is a compelling one from the perspective of our psychology, but also because there is an apparent conflict between two eminently reasonably scientific viewpoints.  The first of these viewpoints is the so called “Principle of Mediocrity.”  This is the no-holds barred manifestation of the Copernican Principle — there is nothing special about the Earth.  The Cosmos seems to be filled with planets (the latest count, as of today, 9 Dec 2013 is 1051 known planets (visit the Exoplanet Encyclopedia Catalog), with some 3000 candidates from the Kepler mission.  Our deepest probes of the Cosmos (the Hubble Extreme Deep Field) suggests there could be as many as 600 billion galaxies. If each galaxy has 300 billion stars, and every star has at least 1 planet (probably more) then there are a staggering number of possible worlds on which life could have arose. There is nothing special about Earth, so if life arose here, there should be no impediment to life arising on any of the trillions and trillions of other worlds that fill the Cosmos.

The Hubble Extreme Deep Field (XDF). [Credit: NASA; ESA; G. Illingworth, D. Magee, and P. Oesch, University of California, Santa Cruz; R. Bouwens, Leiden University; and the HUDF09 Team]

The opposing viewpoint is something called “The Fermi Paradox.”  It was originally proposed by Enrico Fermi, and can succinctly be summarized as, “Where are they?”  What Fermi wondered was why has the Earth, or any world in the solar system, not been visited by self-replicating robotic explorers of some distant alien race?  His point was that if we really want to explore the galaxy, the most efficient way to do that would be to send a robotic probe out to the nearest star.  It won’t get there in a human lifetime, but it will get there in a time substantially shorter than the age of the galaxy.  When the robot gets to a star system, it pokes around a bit, then builds 10 copies of itself using the natural resources it can find, and sends those copies out to the next 10 closest stars.  If every robot successfully makes 10 copies of itself, it only takes 11 replication cycles before there is 1 robot for every star in the galaxy.  But really, why would they stop there? They would just keep replicating until there are a whole lot of robots in the galaxy.  But we haven’t seen one yet!  Why not? One’s immediate gut reaction might be to think, “Well humans are just the first species to have such a crazy idea. The galaxy is not full of self-replicating robots because we haven’t built them yet!”  But if we apply the Copernican Principle to Earth and humanity in particular, there is no reason to believe we are the first instantiation of intelligent life; some civilization should have preceeded us, and built the fleet of galaxy filling robots.  But there are no robots, and the chance that we are the first civilization in the entire galaxy is vanishingly small.  The fact that there are no robots means that we are alone in the Cosmos. 

Why has our solar system not been visited by alien robots, sailing through to see what the galaxy is full of? This is the central tenet of the Fermi Paradox. [Model by S. Larson]

The space in between these two possibilities is a matter of intense debate among aficionados of the search for extraterrestrial life, as well as professional scientists who spend their careers thinking about this. There are as many facets of the debate as there are persons engaged in the discussion!  In the absence of true, reliable knowledge, our imaginations have free reign. We imagine every idea we can, then argue about whether the idea is plausible or even possible.  One of the most intriguing ideas in this space is that perhaps no civilization ever survives to build a self-replicating army of robots to explore the galaxy. Maybe the Cosmic fugue of life never grows beyond the initial swelling notes of the song.

The dinosaurs haven’t gone (didn’t go?) exploring the galaxy. [Image from Captain Raptor and the Moon Mystery, by O’Malley and O’Brien]

This is not an unreasonable idea. Even if we confine our considerations to the history of life on Earth, we’ve seen “civilizations” that persist for long periods of time. The dinosaurs existed on Earth for 160 Million years, and never developed a single bit of technology (so far as we know), let alone build a self-replicating robot to proclaim their existence to the Cosmos. In the end, the dinosaurs were completely obliterated, wiped off the face of the Earth by an asteroid. Today, their closest living descendants are the birds, but no chicken has reached out to explore the Cosmos either. 

But we don’t even have to think about lifeforms long gone. Even among our own species, entire civilizations have utterly vanished from the world.  Five thousand years ago, the Indus Valley Civilization (IVC) was comprised of 5 million persons, fully 10% of the entire world population at that time. It stretched all along the Indus River valley, in what is today the borderlands between modern India, Afghanistan and Pakistan. The preeminent civilization of the era, the IVC developed the first system of weights and measures; quantitative measure is the foundation of all technology and science.  But they did not colonize the galaxy. The civilization survived for almost two millennia, until the cities were mysteriously abandoned and the civilization collapsed, never having once cast their voice out into the Cosmos. Before they had the ability to build a robot, drought and shifting economics with other, nearby civilizations destroyed the greatest civilization the world had known to that time.

If I were to take these two examples at face value, and use my imagination to extrapolate to other worlds, I might imagine that life is common throughout the Universe, but perhaps it is far too fragile a form of matter to survive. Perhaps it is always obliterated, by the abusive hand of the Cosmos or through ignorance and self-destruction. Obliterated before it can send its seed, robotic messengers, out into the Cosmos.  That would be a depressing thought, with terrifying implications for our future on this world. But it is not inconceivable (even knowing what that word means); even in my lifetime, the spectre of the destruction of our world has constantly loomed, though it has been an evolving chorus of spectres, each sharing the lead.  As a child growing up in the 1980s, the possibility of nuclear annihilation was real and forefront in our minds, even as children. The threat is perhaps no less real today, but the end of the Cold War has reduced the threat in people’s imaginations. Today, the fragility of our climate and environment plays a more prominent role in considerations of what our future may be. Now, as in The Cold War, the conversation is driven by ideology and arguments built around emotional viewpoints rather than scientific considerations. It is not clear we will survive to build a robot army that will explore the galaxy. 

The Earth as seen from Saturn. Can you tell there might be life there from this picture?

Another possibility is that maybe it is just too hard to find other life.  Maybe it is out there, but detecting it is far more difficult than finding the proverbial needle in a haystack.  We are not even sure if there is life elsewhere in the solar system, and we live here! What would an alien robot sailing into the solar system find?  There are almost 100 known worlds in the solar system that are at least large enough to be round (say larger than 200km; list at Wikipedia). Would a robot explore all of them, or simply gaze from afar?  Consider what the Earth looks like from beyond Saturn.  Can you tell there is life here?  Look at the Earth from the Moon.  Can you tell there is life here, especially compared to a picture of Titan from roughly the same distance?  What if the probe never came in this close, landing on the first world it encountered, say Neptune’s enigmatic moon Nereid? 

The Earth (L) and Titan (R), each viewed by a spacecraft from roughly the same distance. Can you tell if either harbors life?

Despite all the difficulties, real and imagined, of searching for life elsewhere, we continue to do it, both by sifting the surfaces of worlds near Earth, as well as plumbing the depths of interstellar space looking for messages from other beings.  The idea of there being life elsewhere is one that is hard to let go of, because the alternative is far too depressing — that we truly are alone. It is a staggering thought, which we are constantly reminded of.

There is a very famous picture of Earth, taken by Michael Collins during the Apollo 11 flight.  As the ascent stage of the Lunar Module Eagle returned to dock with Collins aboard the Columbia in lunar orbit, he snapped a picture showing the Eagle (containing Aldrin and Amrstrong) hanging in front of the magnificent desolation of the Moon, with the partially illuminated Earth in the background.  Collins later remarked,  “I remember most vividly the picture of the lunar horizon and then the LEM ascent stage in the foreground with these two guys in it, and then the Earth popping up at that instant… You’ve got 3 billion people over there, two people here and that’s it.” 

A picture from Apollo 11 of every human being, alive or dead, except for Michael Collins (the photographer). [NASA Image AS11-44-6642]

It is perhaps one of the most poignant images of the lonely Cosmos ever taken — every member of the human race, alive or dead, except the photographer. If indeed we are alone in the Cosmos, then that was everything, captured in a single frame, at a single moment in time.  Every voice in the Cosmic fugue, the chorus of life.

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This post is part of an ongoing series, celebrating the forthcoming science series, Cosmos: A Spacetime Odyssey by revisiting the themes of Carl Sagan’s classic series, Cosmos: A Personal Voyage.  The introductory post of the series, with links to all other posts may be found here:  http://wp.me/p19G0g-dE

The Dwarf Planets: Water under the bridge?

THE DWARF PLANETS: WATER UNDER THE BRIDGE?

Shane L. Larson

ACNN (Another Crazy News Network)

 

In 2006, in a musty old hall in Prague, Czech Republic, a group of astronomers belonging to the International Astronomical Union voted on the official definition of “planet.” In one fell swoop, the former planet known as Pluto was demoted, sending millions of us who learned about the “nine planets” into paroxysms of confusion.

“This is how science works,” says Dr. Horatio Allan Tibbets, an astronomer at the Cloudy Mountain National Observatory in Utah.  “Our knowledge evolves, and we have to adapt the imperfect language that humans use to communicate with. The science hasn’t changed, Nature hasn’t changed, but how we understand Nature is changing. Our old ideas may have been perfectly good for explaining what we knew about the Cosmos; but as we see new things, we have to have new ideas that encompass the old ideas and explain the new ideas at the same time.  It’s a tough tightrope to walk.”

The “Pluto debate” is one example of the evolution of scientific understanding, Tibbets says. “We made this big decision to change our taxonomy, demoting Pluto from the lineup of planets.  But now, we’re learning some new things and it seems we should revisit this question again.”

Dr. Theo Partido of the Department of Physics and Astronomy at Greater Oklahoma Polytechnic University is a proponent of the Pluto demotion and not changing the current classification.  “The simple fact of the matter is that Pluto is different than the other planets.  It’s not like Earth; it’s not like Jupiter.  It’s been put in its proper place and it should be kept there.”

Tibbets is part of a growing number of voices in the scientific community who disagree with this.  Armed with new facts and new observational data, they are attempting to open a new dialogue that will once again change our notion of what it means to be a planet.  “The fundamental issue is that we don’t know enough about the Cosmos,” said Tibbets. “This definition of ‘planet’ has been made by looking at only one solar system — ours! We don’t know enough about what other systems might be like, and that can lead to problems.”

By the current definition, a planet is only a planet if it has cleared its orbit of other bodies, like dust and rocks and asteroids.  That is a serious flaw in the minds of many astronomers.  “Imagine a system that has a planet like Jupiter in an orbit like Pluto’s,” said Tibbets.  “In a scenario like this, Jupiter could not have cleared its orbit in the age of the solar system! It would not be considered a planet by the current definition, which is crazy! There are very few people who would argue there are cases where a world like Jupiter should not be considered a planet.”

Astronomers gathered this week at Creeping Ivy State University for a contentious meeting intended to find common ground between the two sides of this debate.  While there has been insistence from both sides that they are here to have a discussion, the debate has already become heated and contentious.  The rhetoric is vehement and the tension is palpable.

“The Plutoers are out of touch,” claims Partido.  “The sooner they accept that they are wrong, the sooner we can move on.”

Tibbets does not mince words about this philosophical battle. “They’re ideologues, and don’t behave rationally.  They call me a ‘Plutoer,’ like we’re still juveniles.  Should I turn around and call them ‘dwarfers?’  No. Someone has to be a grown up; I’m here to talk about science.”  Tibbets and a growing number of colleagues have been arguing to revisit the definition of planet in light of new information that is emerging from exoplanet studies, as well as tantalizing new data from our own solar system.  “We can’t ignore that; that’s not how science works.”

“What we’d really like to see is a dialing down of the rhetoric and less clinging to ideology for the sake of ideology,” said Tibbets.  “But that message doesn’t seem to be getting through.”

That much is evident when talking to people on the other side of the debate.  “The Plutoers seem to think there is something to argue about here, but there isn’t,” insists Partido. “We’re right, and they’re wrong. Plain and simple. It’s water under the bridge, and they should get over it.”

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NOTE: I’ve been writing long essays for this writescience experiment; I wanted to see what it would be like to be confined to a smaller space.  This is about 25-30 column inches in a newspaper, based on word count.  More than would normally be dedicated to a science story?

The Motif of Our Age

by Shane L. Larson

By the middle of the 17th century, Europe was emerging from the cloister of medieval thought, in a renaissance of human intellectualism known today as the Age of Enlightenment.  In 1784, Immanuel Kant wrote that the Age represented “Mankind’s final coming of age, the emancipation of the human consciousness from an immature state of ignorance and error.”  The methods and philosophy of science as we know it today emerged from this era; the printing of books had become common place, allowing knowledge to be recorded, preserved, and spread; exploration of the natural world and the Earth itself was encouraged for political as well as scientific reasons.

The motif of the age was light.  Light was the symbolic enlightenment of the freedom of thought and religion.  Light dominated the expansion of scientific thought with the discovery of the telescope and the microscope, tools that expanded the scope of human consciousness by expanding our vision into realms that had seldom been imagined or dreamed of.  Light permeated the paintings of the age, suffusing many renowned works of the day, such as Johannes Vermeer’s famous pair of paintings, “The Astronomer” and “The Geographer,” and Rembrandt van Rijn’s “The Storm on the Sea of Galilee.”

Today, as we emerge into the 21st century, the world is poised on the brink of another new age of human consciousness.  Using the tools that emerged in the 17th century, the microscope and the telescope, we have engaged in a new age of discovery that amplifies and expands the crux of the Age of Enlightenment: the Copernican Principle.  Copernicus’ rejection of an Earth centered Cosmos allowed humankind to see the world anew, to imagine and discover the inner workings of the Universe that have ultimately led to a deeper understanding of our small planet and where it came from.  The scientific revolution of the current age is no less profound: we are beginning to understand that we are not alone, and wonder if we as a species are unique.  In the last decade, improving telescope technology has led to the discovery and realization that there are other worlds like our own in the Cosmos.  The unprecedented ability to gather, categorize, store and retrieve enormous amounts of information has revealed the magnitude of our ignorance about the vast, unexplored realms on Earth that our churning scientific enterprise has yet to penetrate.  And ever so slowly, we are discovering that the human race can and does have profound impact on our small blue world.  The motif of this age, the central thread that links all these discoveries, is the ubiquitous and innocuous substance that we call water.

Water is the core element of our lives.  Water was only one of the four classic Hellenic elements, but we know today that water is special.  It is the primary mediator of climate; it is a crucial player in every niche of the Earth’s biosphere; it is one of the dominant shapers of topography and geography on the planet; human populations congregate and concentrate along the planet’s shores and waterways; it is an enormous economic resource and a focal point for political struggles large and small.  Of all of these, it is the connections to biology that make water an important player in modern scientific endeavours.  Consider the search for other, Earth-like worlds.

For the first time in history, we have the ability to detect and characterize other worlds circling other suns.  Since the mid-1990’s, we have discovered and cataloged nearly 500 other worlds, but to date we have yet to find the thing that we most desire: a world that is the size of Earth and at a proximity from its parent star such that liquid water can exist on its surface.  The search for water-bearing worlds reflects a profound bias we have: the belief that water is an essential element for any form of life we can imagine.  It is an ideal solvent for many of the essential chemicals of life, and is liquid over an enormous range of temperatures making it available for those reactions that we call “life processes.”  For hundreds of years, we had speculated that other stars harbored their own huddle of planets.  That speculation was smashed by the announcement of a planet around 51 Pegasi in 1995.  But the ecstasy of discovery passed quickly, replaced by an obsessive-compulsive search to find worlds like Earth around other suns.  Why? The desire to find other Earth-like worlds is driven by a simple and altogether human question: are we alone in the Cosmos?

Ignoring the hidden implications of the question and taking its meaning literally the answer to “are we alone in the Cosmos?” is a resounding NO!  In our zeal to look outward, it is easy to forget that we (the human species) share the planet with about 12 million other known species.  To put our not-aloneness in context, consider that there are about 6,775,000,000 people on Earth, massing around 100 million tons.  By contrast, there are 5,000,000,000,000,000,000,000,000,000,000 microbes on Earth massing about 2 billion tons (about 20x the total mass of the human race). That’s a lot of life besides humans.  Even if you ignore bacteria and fungi and microbes and viruses, the number of plant and animal species on the planet exceeds 1.5 million. Virtually all of them are dependent on water for sustaining their life processes.  As air-breathing, land-dwelling lifeforms, it is easy to be distracted by other air-breathing, land-dwelling lifeforms like kangaroos, porcupines, tapirs and angora bunnies.  But the connections between life and water are framed in rather stark terms if we confine our attention to the waters of Earth.

In 2010 we completed the first decade long survey of life in the world’s oceans.  Water covers a full 70.9% of the surface area of the planet, and the Census of Marine Life revealed a startling truth: the waters of our planet harbor an astonishing and vast array of previously uncataloged lifeforms.  In October of 2010 the Census released their first Register of Marine Life, cataloging 122,500 species; the project is less than halfway done with the cataloging process.  Marine scientists estimate that once the Census is complete, around 230,000 species will have been cataloged, but that this likely only represents about one-quarter of the total species in the world’s oceans.  The waters of Earth teem with life, whether we can see it or are aware of it or not.

Looking at the world’s oceans our actions as a single species can have enormous and far-reaching effects on the other lifeforms we share this world with.  Consider the Pacific Ocean.  The waters of the Pacific (and all the world’s oceans) are in constant motion, circulating and moving water from the depths to the surface and back again, and streaming water from the tropics to the arctic and back again.  These vast currents are one of the great cogs in the climate machine that pushes weather around our small blue world.  The currents are complex and structured, driven by many physical processes such as wind, Coriolis forces, temperature gradients, and salinity gradients.  Often, circular patterns of currents form in ocean basins, known as gyres.  The North Pacific Gyre is one of the worlds five major ocean gyres.  Spanning an area of 20 million square kilometers from the equator to 50º N latitude, it is the world’s largest ecosystem.

The persistent circulation of the North Pacific Gyre traps and funnels material to its center.  Simulations in the late 1980s predicted that material could become trapped in the center of the gyre, and in 1997 Charles Moore discovered the truth while sailing through the gyre — a vast collection of human detritus, mostly plastics, has collected near the center of the North Pacific Gyre.  Dubbed the “Pacific Trash Vortex,” media reports have often suggested that the garbage patch covers an area larger than the continental United States. The little scientific voice in the back of all of our minds should immediately voice the question, “how do they know that?”  As consumers of information, we must be careful and aware of where scientific information comes from.  In 2009 the National Science Foundation funded a survey of the Pacific Trash Vortex which concluded that media reports are greatly exaggerated, and the area is much smaller than the continental United States — it is only twice as large as Texas.  Twice as large as Texas.  The Pacific Trash Vortex, only a fraction of the detritus that is spilled into the world’s oceans, covers an area of 535,000 square miles, roughly 1/250th of the total ocean surface (1/360th the total surface area of the Earth).  The plastic in the vortex degrades into small bits and pieces that mixes vertically in the water, penetrating as deep as 11 kilometers.  Human intrusion into the waters of Earth, such as the Pacific Trash Vortex, threaten the biological strata in the waters — tremendous death has been recorded in the central Pacific associated with consumption of plastic at all levels of the food chain in the pelagic zone under the Trash Vortex.

It is easy to document that the trash from our civilization is gathering in the Pacific, but despite our great scientific ability, humans are extraordinarily poor about assessing the connections and consequences associated with simple observations of the world around them.  Why should we care if some jellyfish snack on some old photodegraded pop bottles and die as a result?  Consider one on many different lines of reasoning: consumption of plastic causes the chemical infrastructure of the plastic to be metabolized and deposited in bodily tissues.  Big fish eat small fish, and the chemical elements of the plastics are metabolized by the big fish.  This continues on up the food chain.  Where does it end?  At the top of the food chain, in your dining room.  It’s easy to dismiss this, but most of us would not eat a milk jug with our steak and potatoes each night, so why should we eat pieces of milk jugs that have been incorporated into other foods?

There are other threats that like the Pacific Trash Vortex also threaten water ecosystems, such as the desalinization of seawater by ice melt and the subsequent disruption of thermohaline circulation patterns, and the increasing acidification of seawater due to the downdraw of carbon into the water cycle.  These are all issues that have their roots in human activities, have far reaching and poorly understood consequences for our race, and are almost certainly going to require human intervention to rectify.  The mysteries and predicaments we face hearken back to Rembrandt’s “The Storm on the Sea of Galilee” —  a raging apocalypse of a storm looms before us, but like the image of the sailor on the port beam of the ship (purportedly a depiction of Rembrandt himself), one must have the courage to look into the face of the storm itself, look to the light and discover the way forward.

NOTE: This essay began with “The motif of the age was light.”  A turn of phrase (and the paraphrasing of the sentence following it) were adapted from COSMOS Ch 6: “Travelers’ Tales”, by Carl Sagan.