Mission: Possible

If you’ve read even a smattering of the posts on this site, you know the Parallax Machine is a fan of math. The certainty of math, combined with the incredible way in which it allows us to approximate how the world around us works, makes it a powerful tool. It even makes what might seem like the impossible not just possible, but probable, as long as you follow the instructions.

Nowhere is the power of math more resoundingly demonstrated than when we safely land a robot on another world. The closest Mars ever gets to Earth is over 30 million miles away. Earth is orbiting the Sun at 67 thousand miles per hour, and Mars at 54 thousand miles per hour. And yet, in July and September of 1976, we landed two probes at different locations on the surface of Mars, almost a year after each one was launched, both of which operated for several years afterward to tell us what they found there. Mathematics allows us to do anything when we put our minds to it.

These were the Viking missions to Mars, and they actually consisted of two parts each – an orbiter and a lander – with both elements collecting multiple years of valuable data. The Viking 1 and Viking 2 landers were the first U.S. spacecraft ever to land on another planet. One of their principle activities was to collect soil samples for analysis to determine if any life existed there. This was the endgame for the century of speculation about life on Mars that preceded the Viking missions. And while Viking 1 and Viking 2 each only examined one spot on the red planet, neither one found any evidence of life.

Most people in America are familiar with the space race between the United States and the Soviet Union that ultimately landed humans on the Moon in 1969. But all during that same time period, there was a similar space race to Mars – littered with early failures. The first five attempts were all by the Soviets; four of them suffered launch failures, and the fifth lost communications before it arrived at Mars. The first U.S. attempt also failed, but in 1965, the American spacecraft Mariner 4 was the first to successfully fly by Mars – four years before Neil Armstrong’s giant leap for mankind. The Soviets were the first to successfully land on Mars, with the Mars 3 lander in 1971. Unfortunately, communications contact only lasted 14.5 seconds after that. All told, the majority of Mars missions before the Vikings were failures in one way or another, which makes the resounding success of the Viking missions that much more impressive.

Getting to Mars continued to be difficult even after the Viking missions. The next attempts were by the Soviets in 1988 with their Phobos missions (named after one of Mars’ moons), of which only one orbiter was successful. The next U.S. attempt – the Mars Observer mission of 1992 – lost communications before entering orbit. But then three U.S. missions launched in late 1996 seemed to turn the tide – at least enough to make us keep trying. Mars Global Surveyor orbited the red planet for seven years. Mars Pathfinder landed successfully on the Fourth of July in 1997 and gathered data for a couple of months afterward. And Sojourner capped it all off as the first successful rover dispatched to another planet, puttering around for 84 days before falling silent.

As if to remind us of the dangers of hubris, the next few years brought more heartache. Mars Climate Observer burned up in the Mars atmosphere – a trajectory error resulting from the use of incorrect units in the software, and a reminder that math always requires us to follow the instructions. Mars Polar Lander got there but failed to… well,… land. But in the early 2000’s we rebounded again – the U.S. and the European Union launched the very successful Mars Odyssey and Mars Express missions, respectively – both of which are expected to continue operating for several more years from *today*.

And then came two missions – Spirit and Opportunity – which may have permanently turned the tide for Mars exploration. Both of these rovers landed on Mars in January 2004, and both of them were phenomenal successes. They were only designed to last 90 days, but Spirit survived until 2010, and Opportunity sent its last signal back to Earth in 2018 – having survived 60 times longer than originally planned. In between, a number of other successful missions to Mars have been launched – but my favorite of all these was Curiosity, which was launched in November of 2011, and landed in August of 2012 – less than one and a half miles from its target, by the way. I feel lucky if either Apple or Google Maps get me that close to where I want to go.

The Curiosity rover is still operating today. But equally amazing are the NASA-named “7 minutes of terror” that accompanied its landing. NASA JPL has a terrific infographic summarizing the whole process at this link: https://www.jpl.nasa.gov/infographics/infographic.view.php?id=10776. For those of you with lazy hyperlink fingers, I’ll summarize it in words here. Curiosity approached Mars at 13,000 miles per hour (about a quarter of the speed at which Mars orbits the Sun). As it approached and entered the Martian atmosphere, Curiosity had to be decelerated to around a thousand miles an hour. It then deployed an enormous parachute while still descending at 900 miles an hour. The heat shield separated from the plummeting spacecraft while it was still traveling at 370 miles an hour. After the parachute and reverse rockets stabilized the descent down to 70 miles an hour, rocket boosters fired to slow the descent further while a sky crane lowered the rover down at 2 miles an hour. Hanging 25 feet from its mother spacecraft, the rover then touched down softly, waited a couple of seconds to confirm it was on solid ground, and then issued a command to cut the bridles. The spacecraft then fired its boosters one last time to ensure it landed (okay, crashed) sufficiently far from the rover to avoid endangering the rest of the mission. From the top of the atmosphere to the surface of Mars took seven minutes – on par with the time it takes for communications to get from Mars to Earth – and everyone had to wait until the rover sent its first signal back from the surface to find out if it worked. I was watching NASA TV and waiting right along with them (as were millions of other nerds). I actually cried a little. Best reality show *ever*.

Many more missions are in work or en route to Mars – with more nations getting involved as we go. But the tsunami of science data that started in full force with the Viking missions has revolutionized our understanding of Mars already. We’ll take a look at some of what we have found in the next post. But as with all things in life, sometimes it’s not about the destination – it’s about the journey.

Yes, we can confirm – it’s quite red. Over.

A Planet Becomes a World

For overwhelmingly most of the time we have been looking at the planets, they were nothing more than colorful points of light. That changed when Galileo began his miniature mass production of the telescope. Italy was a central location in the Renaissance, and Galileo brought some serious Renaissance game.

If you ever get to Florence, yes, you should definitely go to the Uffizi, and yes, you should definitely see Michelangelo’s David, and yes, you should definitely have some food and wine overlooking the Arno. But there’s one other thing you should definitely do: visit the Museo Galileo. There you can find Galileo’s writings and illustrations from observing the planets and the Moon. These were the first detailed recorded looks at these objects, and particularly with the planets, they began to transform these colorful points of light into worlds – real places that we might one day visit.

Galileo’s telescopes were nowhere near as powerful as those you can find for even a few hundred dollars today. In fact, a good set of binoculars today will show you the same things Galileo could see. With binoculars, you can see Jupiter’s moons lined up in orbit, incredible detail in the craters of the Moon, and at least a hint of Saturn’s rings. With Mars, you can see a blurry red disk.

Binoculars and telescopes are both just buckets for collecting light. The bigger the bucket, the more light you can collect, and the more you can see. For a telescope, that means a bigger aperture (the diameter of the end that you point at the sky). The more light you can collect, the brighter the object you are looking at will appear. You can also make that object look bigger by increasing the magnification, but that will spread the light out more and make the object look dimmer. So if you look at Mars even today with the typical consumer telescope, you might see a hint of its polar ice caps and maybe a dark patch or two, but you won’t see much more detail than that. To get a clear picture with detail, you really need a big aperture. That way you’re collecting plenty of light to offset the penalty of magnification.

Once Galileo opened the door, a number of folks built on both the technology of the telescope and the observations it enables. Few if any were better at this than Christiaan Huygens. His most well-known invention was the pendulum clock, but he was brilliant in optics and astronomy as well. Huygens discovered Saturn’s largest moon – Titan – and he also revolutionized our understanding of its rings, which he showed to be thin and flat, and nowhere touching the planet itself. Consequently, when the Cassini space probe visited Saturn in 2004, it was the Huygens lander that parachuted onto Titan the following year.

With his advanced telescope and eyepiece, Huygens was the first person to see a feature on another planet – a volcanic plain on Mars now known as Syrtis Major. He subsequently observed Syrtis Major over the course of several days, and in so doing was able to estimate the length of a Martian day – coming up with 24 and a half hours. Today we know a Martian day lasts 24 hours and 37 minutes. Not bad work for someone in the year 1659. It turns out the namesake of the Cassini probe wasn’t a bad astronomer either. Among many other contributions, Giovanni Domenico Cassini noted the southern polar ice cap on Mars in 1666, and refined the length of the Martian day to 24 hours and 40 minutes. Huygens viewed the other ice cap in 1672. Over the course of the next century, astronomers made more and more observations of the polar caps, and even saw some Martian dust storms along the way.

In the 1800’s, telescope design made major advances, with apertures growing past seven inches in diameter – which is comparable to what you can get for a few hundred bucks today. Astronomer Johann Heinrich Madler generated the first map of Mars in 1840. By 1877, a 26-inch aperture telescope was possible, and Asaph Hall used one to discover Mars’ two moons – Phobos and Deimos. Not everyone had access to telescopes that large, and smaller apertures fueled some active imaginations. Also in 1877, Giovanni Schiaparelli wrote down features called canali, which he saw with an 8.7-inch telescope. English-speaking folk rapidly translated and spread that to mean “canals” – however canali actually means “channels” or “grooves”. Other astronomers, most famously Percival Lowell, ran with that idea and its industrial vibe, ultimately leading to stories of Martians using canals to get water from the ice caps toward the equatorial regions, in a last ditch effort to survive their changing world. But in the early 1900’s, bigger telescopes made the perception of canals give way to clearer pictures of what is really there, shown in the picture at the bottom of this post.

The canals and associated stories of a struggling Martian civilization lent themselves to some very creative science fiction – culminating in H.G. Wells’ The War of the Worlds in the closing years of the 19th century, right on the heels of Percival Lowell’s book Mars. While bigger telescopes eventually gave us a clearer picture of Mars, the stories continued well into the 20th century. Even when a world is as close to us as Mars is, we can’t tell if life exists there without actually visiting. And in the 1970’s, we finally did just that. That’ll be the subject of the next post of course. But first, one last look at the red planet from afar.

Somebody stole the canals!


Let’s get off this confounded planet for a little while, shall we?

As discussed in a previous post, Earth sits precariously close to the edge of the Goldilocks zone in our solar system – the window of distance from our Sun that permits the formation and sustenance of life as we know it. This, among other things, gives us a sense of being something special in the universe. But our world is not even the only one in our own solar system that resides within the Goldilocks zone. Orbiting 60-ish million miles farther out is an entire other world, albeit somewhat smaller than our own, which may at one time have harbored life, and which may one day harbor us: the planet Mars.

Particularly over the last couple of centuries, Mars has fascinated us. Before that, it wasn’t viewed as any more special than the other planets we knew about. But those planets as a group were known to be something special dating back to the second millennium B.C. This new series of posts will explore Mars – from our first notions about it all the way through when we might go there, and whether we will stay. We’ll start with a broader look at the planets we’ve been seeing for a very long time, only to understand them relatively recently.

It’s quite likely that our species has been drawn to the night sky and observed its patterns for many thousands of years. That includes some attention to the fact that the planets appear to move through the sky quite differently from the stars. But the first of us to write those observations down were the Babylonian astronomers. They likely did so starting in the 17th century B.C., but the oldest surviving copy of that information is in the Venus tablet of Ammisaduqa, from the 7th century B.C. The tablet contains 21 years of observations of Venus, including its rise times and visibility.

The planets move uniquely through our night skies for two driving reasons. First, they are much closer than the stars. The nearest star is around 25 trillion miles away – over a million times farther than Mars is from Earth. So even though the planets and the stars are both moving through space at breakneck speeds, it takes a lot longer for us to notice it with the stars – so long that they appear not to move at all. Second, the planets orbit our Sun, which the stars don’t. Since Earth also orbits our Sun, the relative movements of the planets can look rather complex, almost as if the planets are just wandering through the sky (foreshadowing). The Babylonians didn’t know that the planets are orbiting the Sun, but they did track their movements. And so it was that the worlds we now know as Mercury, Venus, Mars, Jupiter, and Saturn were given distinct identities in our collective consciousness.

The word “planet” comes from the Ancient Greek asters planetai, which means “wandering stars”. The Greeks named the red planet after their god of war, Ares. The Romans, as they did after conquering the Greeks, renamed the god of war to Mars, and the planet followed suit. Mars has had many other names in other cultures, and usually those names are based on its reddish color. We now know that hue comes from the oxidizing (rusting) of the large amount of iron on its surface. So we can add iron swords and shields to the god of war imagery, if we like.

Another way the planets distinguish themselves from the stars is that they don’t twinkle. Stars are so far away that they appear as mere points of light, no matter how strong a telescope you might use. The planets in our solar system also look like points of light to the naked eye, but in a telescope, they show up as disks. The atmosphere between our eyes and a star or planet is rather turbulent, and with a single point of light, that turbulence can cause the star to “wink out” a bit, hence the twinkle. But with more rays of light traveling toward us from a planet’s disk, those twinkles get lost in the shuffle, and we just see a continuous solid light.

It is remarkable how long it took from the earliest recorded observations of Venus to having any real understanding of the planets. The Greek astronomer Aristarchus – in the third century B.C. – boldly proposed that the Sun was the center of the universe, with Earth and all other bodies revolving around it. While not completely correct, this view was much closer to the truth than the view that eventually won out and persisted for nearly two millennia – the notion that everything revolves around Earth. Four giants of science changed all of that over the course of two breathtaking centuries. Books have been written about each of these geniuses, of course, but I’ll try to sum it all up in one paragraph. And,… go.

In 1514, Nicolaus Copernicus began the first outline of the same model of the universe proposed by Aristarchus – with everything orbiting the Sun instead of Earth. This was a notion counter to the mainstream, to say the least, and Copernicus held it close until the year of his death in 1543. That year, the publication of On the Revolutions of the Celestial Spheres began a scientific revolution of its own, describing the reasons we should believe the planets orbit the Sun. Fast forward to Johannes Kepler, who in 1596 published the first defense of the Copernican view, entitled The Cosmographic Mystery. Some time after that, Kepler provided an endorsement of some observations made by this dude named Galileo Galilei, who in 1610 discovered the four largest moons of Jupiter, the observation of which clearly indicated those moons revolve around Jupiter, and not the Earth. Galileo made those observations with one of his newly designed and fabricated telescopes, which subsequently allowed him to see a full set of phases on Venus, similar to what we see with our Moon. The nature of these phases were proof that Venus, at the very least, must be orbiting the Sun – and once you open that door, why would the other planets be any different? Later, based on Galileo’s findings and many other observations, Kepler published the three volumes of Epitome of Copernican Astronomy, which described the three laws of planetary motion. These laws use mathematics to describe how the planets orbit the Sun. Finally, born in 1642 (the same year Galileo died), Isaac Newton would go on to do a few things himself, among them developing his universal theory of gravitation, which describes how the same force and physical laws governing a falling apple on Earth also govern the orbit of a planet around its star – effectively showing us why the planets orbit the Sun. Those laws are described in Newton’s Mathematical Principles of Natural Philosophy, published in 1687.


Galileo’s early advances with the telescope began a thread of technology that culminated a couple of centuries later in massive observatories, which would lead to an entirely new picture of Mars. We’ll talk about that in the next post. In the meantime, a toast to the wanderers in the night sky, and to the wandering minds that helped us understand them.

Um,… excuse me… I think we might have had it wrong for a couple thousand years…

The Math that Matters Most

Math and the coronavirus have one thing in common: they don’t give two poops about what you believe.

As discussions over the COVID-19 pandemic descend further into political extremism each day, math has become a weapon of choice for any viewpoint. One of the biggest targets is the mortality rate – how likely it is that an infected person will die. On the “wearing a mask makes me a freedom-despising sheep” side, the common practice is to find math that shows this new coronavirus is no different from the flu. The problem is, the lower estimates of coronavirus mortality rates generally seem to originate from that vast game of telephone that we call Facebook. A game I am admittedly playing myself with this blog post, but please carry on.

So let’s start with the flu, our affectionate name for influenza. Let’s also start with a website run by people who have been educated to, and are paid to, investigate the spread and impacts of diseases: the Centers for Disease Control (CDC). If you want to see these numbers for yourself, here is the link: https://www.cdc.gov/flu/about/burden/2018-2019.html. Summarizing the 2018-2019 flu season, the CDC estimated the mortality rate as deaths per 100,000 people in five age groups:

Age Group (years)Illness RateMortality RateMortality as Percentage of Illness (I calculated this)
Numbers and stuff

As you look at this table, one thing is clear: assigning a single number to the mortality rate hides some important information about how dramatically it varies by age group, with the elderly being most at risk as expected. But if you go ahead and count up all the infections and deaths from the 2018-2019 flu season, you get 35,500,000 ill and 34,200 deaths – leading to a mortality rate of 0.096% – or about one in a thousand.

A viral (yes I know) post on Facebook has stated the CDC “confirmed a 0.2% death rate for COVID19”. Let’s start with some more advanced math: that’s twice the rate of the 2018-2019 flu season. Let’s also look behind the number – what the CDC in fact said (in May 2020) was that their estimated mortality rate for those showing symptoms was between 0.2% and 1%, with a “best estimate” of 0.4% – or four times the mortality rate of the 2018-2019 flu. The CDC estimated (again, in May) that the mortality rate for those with and without symptoms was around 0.26% – a little over two and a half times the mortality rate of the 2018-2019 flu. In any case, every number in this paragraph says the new coronavirus is more lethal than the flu. Some people can’t even get conspiracies right.

The yearly estimates of mortality rate for the flu are usually based on the infection-fatality rate, which among other methods is explained in this National Geographic article: https://www.nationalgeographic.com/science/2020/07/coronavirus-deadlier-than-many-believed-infection-fatality-rate-cvd/. Epidemiologists (again, people who put a fair amount of effort into understanding diseases) have reviewed data from the New York City outbreak from March 1 to May 16, and their estimate of the COVID-19 mortality rate is 1.46%. That is nearly fifteen times more lethal than the most recent flu. The estimated mortality rate for those older than 75 is 13.83%. That’s about a one in seven chance of not surviving.

Despite all this conversation around mortality rates, it is my assertion that everybody is missing the point. There might be one piece of math that matters more than any other: how many people need to be hospitalized vs how many beds and respirators are available. Once the former becomes bigger than the latter, we become a society that tells some number of people we simply don’t have enough resources to keep them alive – whether they are suffering from COVID-19 or some other affliction. Think on that for a moment – and also think on what it would do to the mortality rates from just about anything.

If you go to this link: https://www.healthline.com/health-news/why-covid-19-isnt-the-flu#Hospitals-overwhelmed, you will find a comparison of hospitalization rates for the initial six weeks of the COVID-19 outbreak and the first six weeks of the 2017-2018 flu season. The overall rate for the flu was 1.3 people per 100,000. The overall rate for COVID-19 was 26.2. Both numbers go up by more than a factor of three for people 65 years and older. Just focusing on the 26.2 overall number: if you extrapolate that to the US population of around 330 million, that’s around 86,460 people requiring hospitalization, and that has typically not been a short stay for COVID-19, meaning there’s a lot of overlap. According to the American Hospital Association (https://www.aha.org/statistics/fast-facts-us-hospitals), there are 924,107 staffed beds in all US hospitals. That means at the infection rate of the first six weeks of the COVID-19 outbreak, something likely larger than 5% of the total beds in the US would have to be allocated to COVID-19 victims alone. The number of intensive care beds in community hospitals is a little over a hundred thousand, a number much more perilously close to the estimated number of people that would need hospitalization for COVID-19 – and those people tend to need fairly significant care – not just equipment, but the nurses who have to come in multiple times per hour for treatments. ICU beds, by the way, are typically configured for certain types of care (post-surgical, pediatric, etc).

Another view of available resources to combat the pandemic has been assembled by the Society of Critical Care Medicine (https://sccm.org/Blog/March-2020/United-States-Resource-Availability-for-COVID-19). There you will find a similar estimate of nearly a hundred thousand ICU beds. A smaller number of rooms are capable of negative pressure isolation, a means of containing pathogens and preventing their spread to the rest of the hospital. It is estimated that US acute care hospitals own 62,188 full-featured mechanical ventilators, with another 98,738 non-full-featured devices that can be used during a surge in need. The US Strategic National Stockpile has another 12,700 ventilators.

Let’s throw these numbers together again once more: 100,000 ICU beds, 170,000 ventilators, and 86,000 people needing hospitalization for COVID-19 alone based on data from early in the outbreak, and indications are that we are on our way up another spike in infections, with another wave expected in the fall, coincident with the new flu season, all against the backdrop of all the other reasons a person might need an ICU bed or a ventilator. This is the math that matters. This is the math that tells us how close we are to being a nation that has to choose who lives and who dies, for nothing other than lack of resources, human or otherwise. That should be the topic of a dystopian science fiction novel, not the consequence of our conscious decisions. You can refuse to wear a mask, but you can’t mask the math that goes with that decision. “Freedom” is teetering on the precipice of something far darker than masks and six feet of separation.

A photo of someone being given a chance

Raising All Kinds of Flags

The past week or so saw a firestorm of discussion about racism, and embedded within that was another firestorm of discussion about whether it’s disrespectful to kneel during the national anthem. But generally speaking, the fervor is not so much about the anthem itself, it’s about the flag, as Drew Brees so unfortunately (but in the end, maybe fortunately) stated. Of course I have a pretty firm view on this – but before we get to that, what if we take a step back and learn a little more about flags?

First, I personally had no idea how many different parts a typical flag has. The part of a flag nearest the flagpole is called the hoist, which is also the term for the height of the flag. The opposite end is called the fly, which is also the term for the length of the flag. Usually the fly is longer than the hoist, but not always (I’m looking at you, Switzerland). The largest portion of the flag itself is called the field. Quite often, there is something important in the upper corner nearest the hoist, and that is called the canton. So, on the American flag, the stripes make up the field, and the stars make up the canton. Flags are often attached to flagstaffs (that one shouldn’t have been surprising), the top of which are called trucks (that one should). The cord that keeps the flag on the flagstaff is called the halyard. Here endeth the lesson.

There is no question that the earliest flags, and most flags since then, have had some fairly strong relationship to the military. Flags likely date back to Southeast Asia (both India and China), a thousand years BC. Back then, the fall of the flag typically meant the defeat of the army carrying it. The earliest Islamic nations played a major role in the evolution of flags, which eventually made their way to major usage in Europe during the Middle Ages. Flags continued to have importance for all varieties of reasons on land, but they became particularly important at sea, as a means of communicating prior to any peaceful (or not) engagement. Perhaps the most famous is the white flag signaling surrender (or a complete lack of imagination). But a yellow flag signified someone onboard had yellow fever. And of course a red flag meant you probably shouldn’t get emotionally involved with the captain. Ok I made that one up.

National flags are relatively new to the flag scene, and they have a lot of shared history. Denmark has one of the oldest European designs – the simple cross, which has different variations across all the other Scandinavian nations. England came up with the red Cross of Saint George in the 13th century, and that is still the central element of the modern British Union Jack flag (Scotland’s Cross of Saint Andrew and Ireland’s Cross of Saint Patrick form the other elements). The Union Jack was incorporated into a lot of other flags around the globe, what with the British having been a bit imperial for quite some time. It was even, as you might expect, prominent on a number of early colonial flags in what would later become the United States.

Most Americans are somewhat familiar with the origins of the American flag, although the traditional stories are questionable at best. On June 14, 1777, the Second Continental Congress passed the Flag Resolution, which created the first version of the Stars and Stripes, and we still celebrate Flag Day on June 14 each year (although that didn’t become official until Woodrow Wilson said so in the 20th century). Even in 1777, the flag was primarily intended to declare oneself at sea. There were all kinds of variations in the original Stars and Stripes, and the legend of Betsy Ross was muddled into that nearly a century later by one of her descendants. Once it finally settled down along with our fledgling nation, the American flag began the semi-regular schedule of updates when new states were admitted (often dealing with them in groups). It did originally have thirteen stars in addition to its thirteen stripes, both signifying the thirteen original colonies which became states. Here’s an interesting tidbit: a while back we went through the Amendments to our Constitution – of which there have been 27. There have also been 27 designs to the United States flag – driven entirely by the increasing number of states (and therefore stars). In that regard, we’ve had our current flag since 1960 (the year following Hawaii’s admission to the Union), and it’s not likely to change anytime soon.

The American flag remained largely a military symbol until the Civil War, at which point it morphed into a symbol of national unity. That built momentum that ultimately culminated in the National Flag Code, which was generated on Flag Day, 1923. It became law a mere 19 years later. This code includes guidelines on how to display, fold, and dispose of the flag. Some of these guidelines are interesting in and of themselves. For example, the flag should never be carried flat or horizontally, a configuration I have regularly seen with enormous flags at football games. It should always be permitted to fall freely – however this was given an exception with the Apollo landings, since there was no lunar wind to unfurl it.

Despite the Flag Code, it is unconstitutional to prohibit desecration of the flag, however you might define that. This was determined by the Supreme Court in 1990, when the ruling on United States v. Eichman determined that such acts are an expression of free speech, protected by the First Amendment. This ironically seems to root back to when the flag was first characterized as an important symbol of our nation in the 1860’s. When the flag first became a symbol of America the nation, it also became fair game for philosophical discussion, which in our country must be permitted to run its course. As just one consequence, there is much debate over what constitutes disrespect of the flag, but that is ultimately the point: since there is no objective “right answer” on what the flag means to all of us (because it means something unique to each of us), there can be no objective “right answer” on what constitutes disrespect of it. Which makes it even more American than you had even thought.

In the last post, we talked about the Fermi Paradox. What we have here initially appears to be the Flag Paradox: the flag, among many other important things, is a symbol of our right to do whatever we want to it as an exercise in free speech. So if we kneel during the anthem, or even if we burn the flag, we are doing precisely what it represents we should do. It’s not surprising that makes some heads explode. But blind reverence of flags and symbols ultimately does little to protect freedom, as was made clear with different flags and symbols in 1930’s Germany. What deserves respect is not the cloth itself, it is the fundamental freedom and rights that cloth represents. Consider this: if every flag in the entire nation spontaneously combusted, would it change any of our laws or freedoms? While that would undoubtedly be both a literal and a figurative firestorm, I think you know the answer.

The best part is, we would always be able to sew together more flags and begin the debate anew.

It’s high time all flags be converted to circles.

Lunch with Enrico

In the middle of a pandemic, it’s fair to ask why I’ve spent the last several posts in this blog trying to calculate how many other civilizations are out there in the galaxy. One perfectly good reason is to talk about something else for a change. But now I’m going to ruin that and tie it right back to the pandemic.

COVID-19 is only the latest threat to large numbers of humans. Like some other threats, there is an element of COVID-19 we had no ability to control. But also like most other threats, we typically don’t make things better by our actions. And of course we have come up with threats entirely of our own making – like global thermonuclear warfare, for example. Not all of these threats would extinguish our species if realized, but some of them could. We’ve seen in our tour of the Drake equation that mass extinctions have happened at remarkably regular intervals on Earth – often wiping out a very high percentage of species at once. Earth has undergone its own dramatic changes to the climate, but we are the first species to consciously introduce our own changes, and we don’t know where the tipping points are. Meanwhile, at some point, another rock will hit our planet, just as one did millions of years ago to spell the dinosaurs’ doom. Depending on the size of that rock, we might survive, but we also might not.

So there is a very real question about how long we will be around on this world. Will we last long enough to venture out into deeper space? Will we get a chance to colonize Mars? And then perhaps visit other star systems? And maybe even encounter intelligent life on other worlds? What kind of imprint will humanity leave on the galaxy when all is said and done? Or will we leave nothing more than a hundred or so years of garbled radio and TV broadcasts that dissipate into thinner and indecipherable wisps as they spread into the void?

To answer those questions, it sure would be nice to know how other civilizations have fared. By the time we got to the next-to-the-last step in the Drake equation, we had estimated that once every three years in our galaxy, a star is formed that will one day see a civilization rise up on one of its worlds and send signals into space. So at least going in, it seems like there ought to be a lot of civilizations that get to that point. The last factor in the Drake equation – how long a typical civilization lasts – is the big wild card, and the one we are grappling with ourselves. Should we be worried that we haven’t heard from anyone else as yet?

Now, there is always the notion that we *have* heard – maybe even from a *lot* of them – and that aliens and/or our government(s) have covered that up. I’m not going to be arrogant enough to completely dismiss that possibility. There is a chance – however small one might choose to characterize it – that just such a thing is happening here and now. If so, there are two things we can say: 1) We were bang on with our Drake equation, and 2) There isn’t a damned thing any of us can do about it. If the governments of our world are airtight enough to have kept us from the light – and given their incompetence in many other matters, I would be rather surprised – then that is likely to continue for quite some time. If it’s the aliens themselves that are keeping us in the dark, well, basically same point, rinse and repeat.

Let’s explore the alternative instead – that we simply haven’t heard from another civilization yet, and whether that is a problem. Sometime back in the year 1950, the brilliant physicist Enrico Fermi was having lunch with a few other intellectual giants, and the conversation arrived at the question of extraterrestrial intelligent life. Depending on the account, Fermi eventually exclaimed something along the lines of “but where are they?” That question eventually came to be known as the Fermi paradox: it would seem (as we have calculated in this series of posts) that there ought to be lots of intelligent life out there, and yet despite considerable attention and effort, we have not found any – nor has it found us, as far as we can tell.

There are different categories of dealing with this paradox. First – perhaps we were simply wrong in the Drake equation. Maybe what happened on Earth is extremely rare. Or maybe the fact that we’re so close to the edge of our Goldilocks zone – to the point where a lot of our water is vapor in the atmosphere – has made dwelling on land a possibility when it usually isn’t elsewhere. Would creatures like dolphins be able to develop space communications technology on a world completely covered by water?

Another line of thinking is that the last term in the Drake equation – how long a civilization survives – is truly constrained to a few hundred years because intelligent life always ends up destroying itself (either deliberately or by exhausting all available resources). Yet another thought is that many civilizations don’t want to communicate or be discovered. And yet another thought is that other civilizations have indeed found us, but they are more advanced and they don’t want to disturb our natural evolution toward whatever end.

There are so many different directions to go with all this. For myself, it would ultimately seem to boil down to a combination of two main things:

  1. The “lottery” of speaking and listening between civilizations: we cannot transmit deliberate signals in every direction at once and/or all the time, and we cannot listen to signals in every direction at once and/or all the time. Any other civilization is in the same boat, and each of them is at a different point in their respective history where they may or may not have the ability and/or the inclination to send a signal. So the likelihood of them transmitting at us and us listening from that exact direction at the precise moment when it arrives actually turns out to be pretty small, even if there are millions in the galaxy at any given moment.
  2. Somewhat related to (1) – the commitment. The amount of effort we have expended on the search for extraterrestrial intelligence is miniscule compared to the effort we have expended on other things. It would take orders of magnitude more effort – and commitments of life at the scale of generations by the participants – to actually go out there and visit other star systems. Meanwhile, we have only sent a handful of purposeful signals out there to reveal our own existence.

I guess what I’m saying here is that in my opinion, the Fermi paradox isn’t a paradox at all – we should expect finding another civilization to be just as difficult as it seems, even if there are millions of them in our galaxy alone. But if it’s important enough to us, perhaps we should ramp up on item (2) above – our commitment. The most famous organization exploring these questions – the Search for Extraterrestrial Intelligence (SETI) institute – receives zero funding from the Government. It is entirely financed by private donations. It would seem like this endeavor would be worthy of more systematic support than that – finding such hope from somewhere and someone else might be the most impactful thing we could do as a species to redouble our focus and work our way through the variety of crises we face today.

For now, it is my own hope that someday, we or our descendants will have a light chuckle at the idea a brilliant physicist once had to ask “but where are they?”

Finding extraterrestrial life would be even sweeter

But We Only Just Got Here

I’m not sure what is more profound – the idea of potentially thousands of extraterrestrial civilizations in our galaxy, or the idea that this is the 50th post from the Parallax Machine. One thing is certain – the equation for the extraterrestrials is more interesting. So let’s plow forward with that:

N = R* × fp × ne × fl × fi × fc × L

In this equation, 

  • N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
  • R* is the rate at which new stars are created in our galaxy
  • fp is the fraction of stars that have planets
  • ne is the average number of planets per star that might support life
  • fl is the fraction of life-supporting planets that actually develop life
  • fi is the fraction of developed life that becomes intelligent
  • fc is the the fraction of intelligent life that sends signals into space
  • L is how long a signal-sending civilization survives and sends those signals

So far, we have estimated R* = 2 per year, fp = 0.99, ne = 0.35, fl = 0.75, fi = 0.75, and fc = 0.9. Now we address the final piece of the puzzle: L, the number of years that a civilization sends signals into space.

L is probably the toughest factor to evaluate in the Drake equation. R*, fp, and ne were based on a considerable number of observations, and then some logic to extrapolate them to the entire galaxy. fl, fi, and fc were based on what we know about the origins and evolution of life on our own world, and then some more extrapolation logic. But for L, we don’t even have a data point yet to begin with. We know how long we’ve been broadcasting signals into space so far, but we don’t know how long we will be doing that into the future. So maybe if we work backwards from the extreme…

We know that in a vacuum, and based solely on the slow expansion of the Sun, Earth would probably remain habitable for up to another billion years or so, at which point the cascading effects of increased solar radiation would trigger a domino effect, with plants dying off first, and then the rest of the food chain not long after. We would effectively have exited the Goldilocks zone for good at that point. So there’s a reasonable upper limit on L: about a billion years.

Then again, there have been several mass extinctions on our world, dating back to the Cambrian explosion. They were spaced apart by 69 million, 124 million, 51 million, and 134 million years, respectively, with the last one wiping out the dinosaurs 66 million years ago, compliments of an angry rock from space. If we take the average of the intervals between major mass extinction events, we get about 95 million years. We’ve eaten up 66 million of that, meaning that on average, we should expect something to go very wrong again in another 29 million years. It’s not clear that we would die out completely from such an event, but just for argument’s sake, let’s say we do. So there’s another possible value of L: about 29 million years.

Statistically speaking, there is a small chance that something could wipe us out in the next few years. Perhaps a rogue asteroid we missed, or a sudden burst of gamma rays from deep space that we didn’t see coming. A departure that immediate, however, would be more likely to result from our own actions. For example, on Earth, our understanding of electromagnetism was closely linked to our subsequent understanding of relativity and quantum mechanics, which eventually led to the invention of nuclear weapons. So the threats come along right on the heels of the advancements, and the lower limit on L would seem to be about 100 years – at least for us. I think it’s reasonable to assume that if there are other civilizations out there with similar technology, they would also last a similar number of years before exiting stage right.

Or maybe there’s some middle ground number – say we’re halfway through our wonderful ride on Earth as the dominant species, and then take our own bow in another 200,000 years. So there’s another possible value of L. That gives us a pretty nice spread of numbers to try out in the Drake equation: 1 billion, 29 million, 200,000, and 100 years. Plugging those numbers in, we get N = 351 million, 10 million, 70,000, or 35 active, communicative civilizations, respectively. So, a couple of really big numbers, another pretty big number, and 35. To give these numbers any meaning, we need to consider how big the Milky Way galaxy is.

The Milky Way is composed of several spiral arms of stars emanating from a massive bulging center. But for the purposes of computing its total volume, we can simplify things by treating it like a disk, 100,000 light years in diameter and 1000 light years thick. When we do that, we compute a total volume of 7.9 trillion cubic light years. As another very rough approximation, we can then divide that volume by the number of star systems with active, communicative civilizations, to figure out how far apart they might be:

L (years)N (civilizations)Volume per civilization (cubic light years)Distance from one civilization to the next (light years)
10035226 billion16,952
200,00070,000113 million379
29 million10 million790,00031.7
1 billion351 million22,5075.35
So, pretty much anything is possible…

It bears repeating – these are rough approximations. But we’re just trying to get a general sense here of what certain orders of magnitude of L mean. If all communicating civilizations lasted for as long as their planets could support them, we would expect the nearest one to be a little over 5 light years away. The nearest star to our Sun is around 4 light years away. So in this scenario, the galaxy would be jam-packed with communicating civilizations, and our own signals would have reached our nearest neighbors only a few years after we first started transmitting them. If civilizations are limited more by cataclysmic events like collisions with asteroids, then we’d expect the nearest one to be about 32 light years away – still not all that far in the grand scheme of things, and still close enough that our signals would have reached them by now.

Going for a moment to the extreme case of L=100, the nearest civilization would be nearly 17,000 light years away. If we were to receive a signal tomorrow from that civilization, it would have been transmitted during our last Ice Age, and our Earth may look very different by the time they receive anything we’ve transmitted since the early 20th century. But, if L=100, that also means that civilization stopped transmitting during that same Ice Age, and by the time our signals hit their world, they would no longer be around to receive them (and neither would we). L=100 can therefore be considered the “hopeless” portion of the table.

There are other factors at work here that we haven’t considered. First, what if a civilization arises, begins to communicate, and then perishes, but it’s eventually replaced by another advanced civilization on the same planet? That would bump some of these numbers up a bit. Second, what if a civilization colonizes other systems during its lifetime? We know that, at least for ourselves, that will take longer than 100 years from our first signal. As far as we know, there is no way to travel faster than light, so even if we had the technology and the will to colonize the nearest star system, it would be a multi-decade endeavor at best between initial planning, multiple journeys, and multi-year communication delays back and forth with Earth. In other words, if L=100, then civilizations typically don’t last long enough to colonize other systems. But if L=500 – maybe that changes dramatically? Then you’d have a domino effect.

To date, and to general knowledge, we have not detected signals from another civilization. I am learning this along with you as I go, so I’m not entirely sure how to interpret that, even so far as how it effects the possible range of L. To my naive mind, this seems to suggest that either L is not in the millions or billions, or that I was too optimistic with the other factors in the equation. On the other end of the spectrum, if L=100, there isn’t much to be gained by pursuing the matter – it would mean civilizations snuff themselves out almost immediately after they are capable, and no one lasts long enough to communicate, so if there is intelligent life elsewhere, we will never know.

But assuming the values I assigned to the other factors in the equation are somewhat reasonable, what would cause a typical value of L to be in that vast wasteland between a 100 and 29 million years? Here’s another thought – maybe there is a trigger point? Species that figure out how to get sufficiently past our current adolescent stage of civilization don’t get wiped out until an asteroid comes along? So a civilization either lasts a few hundred years or tens of millions, with not much middle ground in between? In that event, looking at the table, for the majority of the potential percent mixes of those two cases, the total number of civilizations would be dominated by the more successful ones. So let’s say 10% of all civilizations figure out how to get past the phase we’re in right now, and then they last on that world until the typical extinction event comes along. That would mean a million active and communicative civilizations in the galaxy at this instant, with the closest one 100 light years away.

In the next and final post in this series, we will take a look at what’s been done to date to detect extraterrestrial civilizations, and how that meshes with the previous paragraph, as well as with the idea that we haven’t found one yet. To be complete, we’ll also consider the idea that we *have* detected one or more, but it’s been covered up. And we’ll finish with what it all means for us. For now, picture a million species like (or unlike) our own, scattered across the galaxy, and asking these same questions. If there are that many, then the vast majority figured out how to survive their youth. I would certainly like to know something like that.

How common is this image in our galaxy?…

Tap, Tap, Is This Thing On?

We are in the home stretch of our tour of the Drake equation:

N = R* × fp × ne × fl × fi × fc × L

In this equation, 

  • N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
  • R* is the rate at which new stars are created in our galaxy
  • fp is the fraction of stars that have planets
  • ne is the average number of planets per star that might support life
  • fl is the fraction of life-supporting planets that actually develop life
  • fi is the fraction of developed life that becomes intelligent
  • fc is the the fraction of intelligent life that sends signals into space
  • L is how long a signal-sending civilization survives and sends those signals

So far, we have estimated R* = 2 per year, fp = 0.99, ne = 0.35, fl = 0.75, and fi = 0.75. Now we turn our attention to fc, the the fraction of intelligent life that sends signals into space.

I’ll start with a couple of blanket assertions: it is difficult to imagine a civilization that doesn’t advance its technology over time, and it is even more difficult to imagine a civilization advancing its technology without eventually arriving at the ability to transmit signals through the air (and therefore space). On Earth, the advancement of technology is part of what led to the rise of our species – the use of tools, the discovery of fire, and so forth. Over time these activities even defined the names of the ages we now apply – the Stone Age, the Bronze Age, the Iron Age, and similar names across different cultures and locations. Even during the Dark Ages, we gradually got better at things over time, and although there was a long stretch of suppression, eventually folks like Galileo, Copernicus, Kepler, and Newton broke through with new understandings of the world and universe around us. At least on Earth, curiosity seems to go hand in hand with intelligence. Maybe I’m biased. Well of course I am. Whose blog is this, anyway?

Once a civilization heads down the path of ever advancing technology, it is bound to discover the workings of electromagnetism. The electromagnetic force is actually a great deal stronger than gravity. We just don’t notice all that much, because it is a force between oppositely charged particles, and most of the objects we deal with on a daily basis have an equal amount of positive and negative charge. But examples of the strength of electromagnetism are still fairly familiar to all of us. A magnet will pick a nail up off a table despite the entire Earth pulling from the other side. Voltages in power lines can move electric current across vast distances at breakneck speeds. And during a thunderstorm, the charge buildup in the clouds and on the ground leads to a sudden electric current (a.k.a. lightning) that momentarily makes the air hotter several times hotter than the surface of the Sun.

In the early 1860’s, the brilliant physicist James Clerk Maxwell developed a set of equations that revolutionized our understanding of the world around us. Maxwell showed us that electricity and magnetism are two aspects of the same fundamental force – electricity can generate magnetism and vice versa. He further showed that what we now call electromagnetic radiation (radio waves, X-rays, microwaves, and so on) is really just the propagation of electric and magnetic fields through space – each field generating another one like an insanely fast game of leapfrog. These particular frogs move through space at the speed of light, which leads to the final stroke of brilliance – Maxwell showed us light is just a form of electromagnetic radiation. The only fundamental difference between light and radio waves is their frequency – the same type of difference between the signals from neighboring radio stations. Give that man a scotch.

It didn’t take too long for others to seize on Maxwell’s equations – in the 1880’s we learned how to purposely transmit signals through the air, and radio broadcasts and communication took off in the early 20th century. Television followed, then satellite communications, then cell towers, and, well you get the picture. Our modern world is awash in electromagnetic signals – and for the last century or so, those signals have found their way out of our atmosphere and into space. Our ability communicate with each other over large distances has gone hand in hand with our ability to advance in so many other ways – so again, it is difficult to imagine that we wouldn’t have stumbled on this kind of technology at some point. We just needed one Scotsman to put it all together for us, and we were off and running. The price of this technology is that we have been sending these signals into space whether we wanted to or not. Since they travel at the speed of light, our signals have reached a distance of over 100 light years in virtually every direction – so there is an ever-expanding bubble of space in which another civilization could theoretically detect our existence. By the time you get to the edge of that bubble, the signal is pretty weak and probably quite garbled, but it is still there.

In moments of boldness, we have also sent some purposeful and targeted messages into space, to let any potential alien folk know we are here. One of the earliest and most famous attempts was the Arecibo message, sent in 1974 toward a distant star cluster. Its content was fairly basic information about our home and our species, but it won’t arrive at its target until around 25974. Among the other messages we have sent, the earliest arriving one will reach the planetary system Gliese 581 in 2029, 21 years after it was sent – and meaning even an immediate response would not arrive back here until 2050. Some among us, including the late Stephen Hawking, have been less than thrilled that we are revealing our presence and location to strangers. But the proverbial cat is out of the bag at this point.

Given the discussion to this point, you can probably guess that I think fc should be quite high – and I am indeed leaning toward decidedly optimistic. To leave some room for civilizations that simultaneously do not want to be found and have also developed some sort of technology to shield their signals from the rest of us, I’m going to set it at 0.9. Which brings our newly updated Drake equation to:

N = 2 × 0.99 × 0.35 × 0.75 × 0.75 × 0.9 × L

In other words, around once every three years, a star forms in our galaxy which will eventually see the beings on one of its planets send signals into outer space. In the next post, we will complete the equation with the final estimate: for how long does a typical civilization do that?

Uncomfortable silence

Upright Opposable Brains, and Fred

You’ve probably heard the phrase, “you can lead a horse to water, but you can’t make him drink.” When considering the possibility of extraterrestrial civilizations, one could alter that phrase ever so slightly: “you can generate life pretty quickly, but you can’t make it become intelligent quite so easily.” That’s not intended to be a knock on humanity (every now and then I like to take a timeout from doing that). It’s just an acknowledgement of the one data point we have on how long it takes life to become intelligent.

Mr. Drake, your equation please:

N = R* × fp × ne × fl × fi × fc × L

In this equation, 

  • N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
  • R* is the rate at which new stars are created in our galaxy
  • fp is the fraction of stars that have planets
  • ne is the average number of planets per star that might support life
  • fl is the fraction of life-supporting planets that actually develop life
  • fi is the fraction of developed life that becomes intelligent
  • fc is the the fraction of intelligent life that sends signals into space
  • L is how long a signal-sending civilization survives and sends those signals

So far, we have estimated R* = 2 per year, fp = 0.99, ne = 0.35, and fl = 0.75. Now we set our sights on fi, the fraction of developed life that becomes intelligent. In the last post, we set fl pretty high – maybe even conservatively so – because in the grand scheme of things, life on Earth developed quite quickly after the conditions were right. It took far longer to arrive at what we might call intelligent life. To understand the dramatic difference in timelines there, I’m going to steal (not for the first or last time) from Carl Sagan’s “Cosmos”, where he mapped the history of the universe to a single calendar year. Only this time, I’m going to do that only with the history of the Earth, which we will call the Earth calendar here. Or at least that’s what I’m going to call it. You can call it Fred if you like. Actually, in honor of the late Fred Willard, that is precisely what I am going to do.

If you spread the 4.54-billion-year age of Earth across a 12-month Fred-year, each month on the Fred calendar equates to about 380 million years, or alternatively each day equates to a little over 12 million years. There is a considerable amount of debate as to exactly when the oceans formed and when life originated. But one reasonable way to express it would be that if Earth was born on Fred-January 1, the oceans began to form sometime in mid-Fred-January, and they were fully formed by late Fred-February. The earliest undisputed evidence of life on Earth dates to just after mid-Fred-March, but strong evidence likely pushes that back into mid Fred-February, which means life was forming around the same time the oceans were forming. Now, again, this is a bit of speculative math – but the bottom line is, it didn’t take life long to emerge once the conditions were right.

It’s also important to note how well-organized life was even at that moment, because the earliest evidence we can find suggests these were microbes – similar to today’s bacteria – meaning life had developed beyond mere DNA and fully organized itself into cellular structures. After that, progress was painfully slow. Cells evolved their ability to “eat”, which eventually also led to the tendency to “eat” each other, and perhaps as a defense to this troubling development, they would eventually organize into loose colonies. The next revolutionary step was the evolution of sex – whose humble beginnings date to late Fred-September. At that point, DNA was able to build off the diversity of genes from two organisms instead of one, which dramatically increased the potential combinations and new features. But even after *that*, life remained largely cellular or for nearly another two Fred-months. It wasn’t until about 541 million years ago – or mid Fred-November – that life began to proliferate into the vast array we see today.. So life may have taken only a matter of Fred-days to arise, but it took another nine Fred-months to advance in any meaningful way after that.

The event that changed it all around 541 million years ago is called the Cambrian explosion. It is called Cambrian because it happened at the beginning of the Cambrian Period, which lasted until around 485 million years ago. It is called an explosion because it is when nearly all major categories of animal life that we know of today originated. There are lots of hypotheses about why this explosion occurred. It could have been a combination of any number of factors, ranging from oxygen and ozone levels to accelerating “arms races” between predators and prey to the evolution of eyes. Whatever happened, it took only a few Fred-days, after nine months of life frankly not being all that creative.

As life became more complex, it also became more dependent on specific conditions, and therefore more susceptible to major shifts in climate. Occasionally, these shifts have been quite dramatic, leading to five major (and a number of other minor) mass extinctions on the planet. They occurred 444 million years ago (Fred-November 25), 375 million years ago (Fred-December 1), 251 million years ago (Fred-December 11), 200 million years ago (Fred-December 15), and 66 million years ago (Fred-December 26). The middle one of these was the most extreme – 96% of all species went extinct. Evidence suggests this was caused by a combination of a huge volcanic eruption, a subsequent massive release of methane into the atmosphere, temperature rises in response, and acidification of the oceans. Known as the Permian-Triassic extinction event, it essentially erased the majority of the progress that had been made since the Cambrian explosion. The most recent extinction event – the Cretaceous-Paleogene event – was the one that wiped out the dinosaurs, clearing the path for mammals to rise up and eventually evolve into us. An asteroid impact probably triggered this extinction.

All while these waves of change were sweeping the planet, the brain was steadily developing as well. Its origins trace all the way back to early cellular organisms that developed the ability to transmit electrical and chemical signals – an early ancestor of the neurons that transmit signals throughout our central nervous systems and between various sections of our brains. Just as other organs developed with more specific and advanced capabilities, so did the brain. I could spend another several blog posts talking about how that all came together, but for now it’s sufficient to recognize that the brain is the seat of our intelligence, which begs another question. Since we are ultimately going to all this literary trouble to develop an estimate for fi in the Drake equation, at what threshold do we decide a species has become intelligent enough to trigger this factor?

The next factor in the equation will determine how likely a species is to start communicating signals into space, so we don’t want to restrict our definition of intelligence so far that we are double-booking (or in that case we should just be calculating one factor). But we also don’t want to be too loose with the definition of intelligence, because we are interested in the kind of intelligence that eventually leads to a civilization that can communicate with those on other worlds. There are indications the dinosaurs were fairly intelligent, but they had a couple hundred million years to develop, and as far as we can tell, they never turned into a civilization. Even the modern-day dolphin, despite possibly being the second most intelligent animal on Earth, has seemed content to remain in the ocean and not develop any kind of technology – although one must wonder how much further they would evolve if we were not around. But for the purposes of the Drake equation, let’s just state that we define intelligence to be the development of Homo sapiens – our species of human. Having done that, we can go back to the Fred calendar to see where that happened.

The beginnings of the family of species that have evolved into modern apes and humans occurred in a timeframe centered around 12 million years ago – the beginning moments of Fred-December 31. This split into two branches – one became the great apes (including gorillas and chimps), and the other led to us. The human branch began to crystallize about 4 million years ago, or 4pm on Fred-December 31. The Homo genus arrived 2 million years ago, or 8pm. The earliest fossils of our species – Homo sapiens – are from around 200,000 years ago, or a little after 11:30pm. So – after life arose sometime in Fred-February, it took the entire remainder of the Fred-year to become intelligent, and it had to endure several mass extinctions along the way. What does all of this say about fi?

There are a lot of reasonable arguments out there. The length of time it took for intelligence to take hold, combined with the fragility demonstrated by mass extinctions, combined with the fact that of all the billions of species that have existed on Earth, only one has become intelligent, suggest that fi is pretty low. On the other hand, even though it took a long time on Earth, it arose with several billion years still remaining in the planet’s lifetime. Even though there have been several mass extinctions, none of them have wiped out all the life on Earth – and even the worst one saw a relatively quick recovery in the evolution of new species. And – perhaps most importantly, we only need one civilization to become intelligent here. It doesn’t really matter how many other species on the same planet didn’t. In fact, you could make a perfectly reasonable argument that fi = 1, since we are here.

At this point, I’m going to fall back on the same kind of reasoning I used for fl, the fraction of habitable worlds that develop life. A value of 0 is absurd and also flatly contradicted by our existence. A value of 1 is likely too optimistic, as some worlds are bound to experience greater cataclysmic events than ours has to date. Even though it takes a long time, life seems to have been hell-bent on Earth toward ever-increasing complexity, which includes the development of brains and intelligence. Given enough time, I would expect the forces of natural selection (survival of the fittest) to encourage the development of intelligence on any world with life – so it’s just a matter of how many worlds are given that time. Even with massive climate shifts and the occasional rude intrusion by asteroids, Earth has come through the other side with us. So I’m going to set fi = 0.75 – again, a conservatively optimistic number, but high enough to leave us with hope that other beings are out there somewhere. Our updated Drake equation is:

N = 2 × 0.99 × 0.35 × 0.75 × 0.75 × fc × L

In other words, a little over once every three years, a star forms somewhere in our galaxy that will someday preside over an intelligent species, capable of figuring out what stars and galaxies are, and beginning to wonder if they are alone in the universe.

In the next post, we will dive into fc, the fraction of intelligent civilizations that transmit signals of their existence into space. For now, a moment of reverence for the human brain and its largely untapped potential.

There’s a lot going on in there.

Do You Copy? I Repeat, Do You Copy?

The size and apparent nature of the universe are gut punches to the human ego. There could be over a trillion galaxies, of which our Milky Way is a fairly ordinary one. Our galaxy, in turn, contains something like a hundred billion stars, of which our Sun is a fairly ordinary one. And most stars have one or more planets, of which our Earth is a fairly ordinary one, with a single glaring exception: it’s the only place we know of where life has arisen. Is it the only such place in reality? As we continue exploring the answer, we are now at the midway point on our tour of the Drake equation: 

N = R* × fp × ne × fl × fi × fc × L

In this equation, 

  • N is the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy
  • R* is the rate at which new stars are created in our galaxy
  • fp is the fraction of stars that have planets
  • ne is the average number of planets per star that might support life
  • fl is the fraction of life-supporting planets that actually develop life
  • fi is the fraction of developed life that becomes intelligent
  • fc is the the fraction of intelligent life that sends signals into space
  • L is how long a signal-sending civilization survives and sends those signals

So far, we have estimated R* = 2 per year, fp = 0.99, and ne = 0.35. Now comes the really squishy part: trying to draw conclusions about life on other planets from what we know about life on this one.

The origin of life is one of those subjects where science and religion collide rather violently. In the Western world, we seem to have a choice, for example, on the age of our Earth. The prevailing religious view suggests it is 6000 years, while the prevailing scientific view puts it at more like 4.5 billion years. I was raised Catholic, but I have also loved math and science since my earliest memories of school. The Catholic school where I was educated from 2nd through 8th grade was extremely adept at combining religion and science without ever suggesting one invalidated the other. And their library had lots of great books on science, including one entitled “Four Billion Years Ago”. One thing I have always believed since those formative years is that science and religion need not be mutually exclusive, even when we are exploring mysteries like the beginnings of Earth and life. I’m going to talk in terms of the scientific view here, but the reasoning could be applied to other views as well.

Science calls the beginning of life on Earth abiogenesis – the process by which life arises from non-living matter. We talked a bit in the last post about life forming in water. When Earth first formed 4.5 billion years ago, it was too hot to have liquid water. But it may have only taken a couple hundred million (0.2 billion) years after that to cool down to a temperature where the oceans could form. We have found evidence of microbes in Northern Quebec, in rocks that may be nearly 4.3 billion years old. There is additional evidence in other locations on Earth that life arose over 4 billion years ago. So, speaking on these vast time scales, it would appear that life began quite soon after the necessary conditions were established. We just don’t know exactly how. Scientists have conducted experiments where they place all the right material together in conditions similar to what we think prevailed back then, but thus far they have not been able to generate life from the non-living ingredients. At first that might seem disheartening, but even as “quickly” as life appears to have emerged on Earth, it still likely took tens to hundreds of millions of years after the formation of the oceans. We just don’t have that kind of time, pandemic or not.

Even though we don’t know exactly how life began on Earth, there’s a logical chain of reasoning. The fundamental molecule of life – deoxyribonucleic acid, more affectionately known as DNA – has the distinct characteristic that it can make copies of itself by unwinding and with the assistance of certain enzymes. This is how life persists and proliferates, and DNA that encodes more useful features in its parent organism will make that organism more likely to survive. Occasionally, errors will occur in the copying process, and these lead to mutations. Some become the scourge of cancer. Others have little to no effect. And still others may lead to significant new features – some of which give an advantage to the organism and its offspring. Extrapolating backwards, you can imagine that DNA has been evolving this way all the way back to the beginning over 4 billion years ago, to the very first molecule that was able to make a crude copy of itself. Once that first copy was made, you can also imagine a cascading effect – molecules that can make copies of themselves will eventually be quite plentiful compared to other types of molecules. The earliest microbes appear to be similar to those we have found in hydrothermal vents at the bottom of the ocean, so perhaps that is where this process played out as well.

If Earth is “typical” of a planet in the Goldilocks zone, then it is only a matter of time between planetary formation and the beginning of life. We also know organic (carbon-based) matter is fairly common in objects outside of Earth, and we’ve even found amino acids – the building blocks of proteins – in meteorites and comets, so it is also possible that the ingredients for life on a given planet have a head start in the rocks that come together to form that planet. On top of that, there is every indication that planets like our Earth are quite common – rocky worlds located in the habitable zone around their respective suns – and in fact we’ve already estimated such a world orbits every third star in the galaxy. Put it all together, and without any evidence that Earth is special beyond our knowledge that life exists on it, there is a compelling argument to assign a pretty high percentage to fl in the Drake equation.

Let’s drill down by the process of elimination to a good number. Assigning a value of 0 seems to make little sense given the argument above, and of course we also know 0 is impossible given that we are here to debate the matter. Assigning a value of 1 seems like overkill – surely there are habitable worlds where things just didn’t go right for one reason or another. Assigning a value of 0.5 would be a nice compromise between the extremes – but I think the 0 extreme is significantly more absurd than the 1 extreme. What if we split the difference again? That would make fl = 0.75, and that’s a number I think I could live with. No, it’s not exactly the scientific method, but let’s face it, we’re spitballing no matter what we do. And just as life evolved on Earth, thus evolves our Drake equation:

N = 2 × 0.99 × 0.35 × 0.75 × fi × fc × L

Four down, three to go. But so far, we have determined that every other year, a star that forms in our galaxy will eventually preside over life on one of its planets. In the next post, we will try to figure out how much of that life reaches a point where it decides it might as well start a blog.

Bunch of copycats