Month: May 2020

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_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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, f_p = 0.99, n_e = 0.35, f_l = 0.75, f_i = 0.75, and f_c = 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_*, f_p, and n_e were based on a considerable number of observations, and then some logic to extrapolate them to the entire galaxy. f_l, f_i, and f_c 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)
100	35	226 billion	16,952
200,000	70,000	113 million	379
29 million	10 million	790,000	31.7
1 billion	351 million	22,507	5.35

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.

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

N = R_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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, f_p = 0.99, n_e = 0.35, f_l = 0.75, and f_i = 0.75. Now we turn our attention to f_c, 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 f_c 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?

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_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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, f_p = 0.99, n_e = 0.35, and f_l = 0.75. Now we set our sights on f_i, the fraction of developed life that becomes intelligent. In the last post, we set f_l 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 f_i 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 f_i?

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 f_i 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 f_i = 1, since we are here.

At this point, I’m going to fall back on the same kind of reasoning I used for f_l, 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 f_i = 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 × f_c × 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 f_c, 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.

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_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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, f_p = 0.99, and n_e = 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 f_l 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 f_l = 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 × f_i × f_c × 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.

In honor of social distancing, I was going to begin this post with all of the letters separated by six feet, but I figured I’d lose your attention pretty quickly. That’ll probably happen anyway. Let’s jump right to it, shall we? The Drake equation:

N = R_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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

In the first post, we decided R_* = 2 Sun-like stars added to the Milky Way galaxy per year. In the second post, we set f_p = 0.99 to reflect our understanding that nearly all stars probably have one or more planets. Now we are on n_e, the average number of planets per star that might support life. The little e stands for Earth, owing to that particular planet being the only one we know of that supports life.

We might consider ourselves very lucky to be on a world that supports life. But if you think about it, if Earth didn’t support life, we wouldn’t be here to be unlucky about it. Let that twist your noggin for a bit.

So how is Earth so conducive to life? To begin, let’s start with our distance from the Sun. Earth’s orbit is directly surrounded by the orbits of two other worlds: Mars and Venus. Mars is about 142 million miles from the Sun, Venus 67, and Earth 93. That difference alone is enough to lead, at least in part, to entirely different outcomes on these three planets. Mars is sufficiently farther away that it is much colder than Earth – and Venus is sufficiently closer that it is much hotter. In both cases, the situation has been exacerbated to an extreme. Mars has lost most of its atmosphere from being pummeled by solar radiation and particles – because in addition to being colder than Earth, it doesn’t have the protective magnetic field that Earth has. Meanwhile, Venus developed a runaway greenhouse effect (see this post for more on that phenomenon), leading to a surface temperature of well over 800 degrees Fahrenheit, and making it hotter than Mercury, the innermost planet (which doesn’t have an atmosphere at all).

To paraphrase the story of “Goldilocks and the Three Bears”, porridge on Venus is too hot, porridge on Mars is too cold, and porridge on Earth is just right. Our region of the solar system has therefore come to be known as the Goldilocks zone. Outside the zone, based on our understanding of the conditions necessary for life as we know it to develop, it can’t. So how big is this zone? The distance from Earth to the Sun (about 93 million miles) has come to be known as an Astronomical Unit (AU). Latest estimates suggest the Goldilocks zone for our Sun stretches from 0.99 AU to 1.7 AU. Had the Earth been formed in an orbit outside that range, we wouldn’t be here to lament it. And look at just how close we were to not being in the Goldilocks zone – about 1 percent closer to the Sun would have made the Earth too hot for life as we know it to survive. Also, doing the math, Mars is actually in the Goldilocks zone. And sure enough, there is still some reasonable debate over how much atmosphere and water Mars may have had in its past – and even whether it might at one point have harbored some form of life. But whatever happened there in the past, it has long since turned far too cold.

The single biggest reason that temperature determines whether a planet can support life is that temperature determines whether a planet can have liquid water – which is the substance within which life probably arose on Earth, and also the substance within which our cellular activities take place. By weight, most of your body is made of water. There are a handful of other major ingredients of life as we know it on Earth – and it seems the key to life forming here was that these other elements (carbon, nitrogen, and sulfur, as examples) were colocated with the liquid form of water, where they could dissolve and interact at their leisure over a period of many millions of years. There are two general types of planets: smaller, denser, rockier ones like Earth; and larger gas giants like Jupiter. It is much easier to get liquid water and other life-essential elements together on a rocky world like Earth than on a gas giant like Jupiter. So Earth has two things going for it: a good temperature to support liquid water and a nice rocky surface on which the magic of life can commence.

How many worlds have this good juju? Without looking any farther than our solar system, we could hazard a somewhat defensible guess that the average number of potentially habitable planets per solar system is 1. That would essentially be saying that our solar system is typical. But just how typical is it? For one thing, in our solar system, all of the denser, rockier planets ended up in the orbits closest to the Sun, increasing the likelihood that if a planet was going to be in the Goldilocks zone, it was also going to be a rocky planet. Is this common? There’s a line of thinking that denser planets with heavier elements are more likely to end up closer to a star as it forms, since gravity would tend to pull the heavier atoms closer to the star. But even a gas giant like Jupiter may have a rocky core at its center, and that core might still be bigger than Earth. And as far as we can tell, the arrangement of planets around other stars is all over the map.

For most of the exoplanets (planets orbiting other stars) that we have discovered, our most important tool has been NASA’s Kepler space telescope, which operated in orbit from 2009 to 2018. For more information on Kepler and exoplanets in general, you should definitely have a look at exoplanets.nasa.gov. Kepler confirmed over 2600 planets, and based on those observations, it is likely that 20 to 50 percent of the stars in our galaxy have rocky planets in the Goldilocks zone. Let’s split the difference and call that 35 percent, which means we are going to say that n_e = 0.35. Now, n_e was supposed to tell us how many habitable planets there are around a given star, and of course you can’t have 35 percent of a planet orbiting a star. But what this math tells us is that your chance of finding a habitable planet around a given star is 35 percent – or that a little over 1 in every 3 stars has such a world in its domain.

There’s one additional complicating factor that I didn’t take into account here. We’ve only been talking about planets that could support life. But a couple of the planets in our solar system have fairly large moons which might also be able to support life – Jupiter’s Europa and Saturn’s Titan are good examples. Europa is covered in ice, and there are indications that a vast ocean of liquid water could lie underneath. Titan looks a lot like what we think the early Earth might have. Because of its potential internal ocean, Europa looks like the stronger candidate at the moment – and if we were to make the incredible discovery of life there at some point, it would be an exception to the Goldilocks zone rule – although the fundamental reasoning behind the Goldilocks zone still applies – the formation of life is best served when liquid water can interact with other elements. Our 35 percent estimate for n_e therefore might be a bit low – but we need to learn more about Europa, and NASA is planning the Europa Clipper mission to do just that sometime later in this decade. So for now, let’s leave our estimate for n_e to be 0.35.

And thus progresses our version of the Drake equation:

N = 2 × 0.99 × 0.35 × f_l × f_i × f_c × L

In the next post, we’ll dig into f_l, the fraction of habitable worlds that actually harbor life. Up until now, we’ve had some pretty solid observations on a pretty grand scale to support our calculations. Since our world is the only one we know of where life has actually arisen, everything from here on out will be much more speculative. But taking a step back at what we’ve discussed so far, the chance for extraterrestrial life is looking pretty good – a couple of new stars a year, nearly all of which have planets, and a third of which have planets on which life could form. The early numbers are encouraging, as they say. “They” possibly being aliens.

As society crumbles around us, we obliviously continue our tour of the Drake equation (which ironically makes more sense if you are wearing a mask):

N = R_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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

In the last post, after much rumination and hearty chortling, we decided R_* = 2 Sun-like stars added to the Milky Way galaxy per year. Now we turn our attention to f_p, the fraction of stars that have planets.

Planets are among the most effective ways to illustrate how bull-headed the human race can be. Most people have heard of Copernicus – more completely, Nicolaus Copernicus, who in the 16th century advanced the notion that the Earth and all the other planets in our solar system revolve around the Sun. Up until that time, the prevailing view espoused by Ptolemy all the way back around the year 150 A.D. – the idea that everything revolves around the Earth. Now – first of all, of course we all happily accepted the notion that everything revolves around us. We are dumb that way. But also of course, one of the driving points of this series of blog posts is to illustrate just how ordinary we are, and it turns out the universe agrees – so the Earth and all the other planets in our solar system revolve around the Sun. It wasn’t just that we hadn’t thought of such a scenario, either. Aristarchus of Samos – in the 3rd century *B.C.* – had already figured out how things really work. But it just doesn’t stroke the human ego enough, and so yada yada yada, Roman Empire rises and falls, Dark Ages, witch burnings, and boom, Copernicus re-figured it out almost two millennia later.

Regardless of our abject confusion about what they revolve around, we’ve known since ancient times that the planets are different from all those other points of light we call stars. The stars are ridiculously far away, and so even though they are in fact traveling at breakneck speeds through space, they look like they are standing still during the extent of any human lifetime. But the planets in our solar system – even though they are many millions of miles away – are far closer than the stars, and so we can actually see them move. We are also moving, being on a planet of our own – and the end result of all that motion is that the planets appear to wander about the sky from our perspective – and in fact that is exactly what the word “planet” means – wanderer.

Five planets can be seen with the naked eye: Mercury, Venus, Mars, Jupiter, and Saturn. We have therefore been watching these little critters for quite some time. After Copernicus literally changed the world, the brilliant astronomer Galileo Galilei took the next steps – building not just on Copernican theory but also on the work of a Dutch spectacle maker Hans Lippershey who designed the first telescope. After creating his own telescope, Galileo showed us illustrations of the planets we had never seen, making them real worlds in our view for the first time. As telescopes advanced, more planets were discovered – Uranus, Neptune, and Pluto.

In the 1960’s, not long after we had first sent spacecraft into Earth orbit, we began sending them to the other planets in our solar system. In the 1970’s, we landed a couple on Mars (the Viking missions). In the 1980’s, the two Voyager probes toured the giant outer planets on their way to interstellar space. In the 1990’s, we began to detect planets around other stars – and since then, we have discovered over four thousand of them. We have quickly gone from wondering if other stars had planets to realizing that most of them probably do.

In fact we have also discovered a vast array of other small worlds that orbit our Sun. We’ve known for some time about the asteroids that orbit between Mars and Jupiter – and some of them are quite large. But there is also an unthinkably large (and sparse) cloud of little planetoids orbiting far beyond Pluto. The sum result of these findings, as well as the discovery of Pluto’s moon Charon which is not much smaller than Pluto itself, led to the demotion of Pluto to the status of “dwarf planet” in the 2000’s. This upset a lot of people, of course (and probably had no effect whatsoever on Pluto) – but the point really should be this: the solar system is simply loaded with large objects, many more of which are planet-sized than we had ever known. The discovery of thousands of planets beyond our solar system only underscores the point: worlds are probably quite common in our galaxy. So how does that come to be?

Thanks for asking. When we last left our fledgling star in the previous post, it had just achieved a state of zen, where gravity was causing it to collapse on itself, but nuclear fusion was generating enough energy to push back. We had been viewing the whole process as a shrinking ball of gas, but things are always a bit more complicated than that. The atoms that steady accumulate in the formation of a star aren’t all headed toward its center when they first start to get pulled in – they’re generally moving in all kinds of directions, which leads to a big swirling mess. Over time, just as gravity is pulling the star in on itself, it steadily kneads and flattens the swirl into a disk of material spinning around a single axis. You know how Saturn looks, right, with those rings spinning around a big ball? Well, most infant solar systems probably look something like that too – although the disk is spread out over a far greater distance than Saturn’s rings – so imagine huge rings spinning around a tiny ball. Eventually, just as the clumpy universe led to the star, clumps in the disk often accumulate into planets, until the planets eat up just about all of the disk, and you never knew there was a disk in the first place.

We understand this process fairly well – and now that we’ve seen thousands of worlds out there… wait a second, how do we know there are thousands of worlds out there? Well – there are a few ways to find them. In 1992, the first planet outside our solar system (also known as an exoplanet) was discovered orbiting a pulsar. Pulsars are the remnants of incredibly massive stars that ended their lives in equally massive explosions called supernovas. During those final death throes, these stars collapse at an incredible rate – and just as Carl Sagan so eloquently explained in his Cosmos series, like a figure skater pulling her arms in and spinning ever faster, these stars do the same thing, until they are spinning many times a second. As they spin, they emit pulses of radiation that we can detect on Earth – leading to their ingenious moniker “pulsar”. Pulsars spin at a constant rate, but in 1992, we noticed some subtle deviations in that rate for the pulsar affectionately named PSR B1257+12 (which I believe is also the name of Elon Musk’s next child). Aleksander Wolszczan and Dale Frail determined that the deviations were caused by one or more planets orbiting the star. It turns out this particular pulsar has three planets – and since then only four other planets have been found around pulsars. The rest have been found around relatively more “normal” stars. The dominant methods for detecting planets include the transit method – where the star’s light dims ever so slightly as a planet crosses in between the star and Earth – and the radial velocity method (or “wobble” method), where astronomer’s look for Doppler shifts in the star’s light (similar to the shift in sound that causes a train to seemingly drop pitch as it races by).

Ok – so we understand quite well how planetary systems form around stars, and we have observed thousands of them over the course of just a couple of decades. So it would seem that the piece of the equation we are after here – the fraction of stars that have planets – is probably pretty high. Multiple studies have suggested there are exoplanets around every star and/or that there is at least one planet for every star in the galaxy. So it is probably fair to say that f_p is very nearly 100% (also known as a fraction of 1). Let’s go ahead and account for those lonely stars that may pop up here and there with nary a planet to be seen – and conservatively say that f_p = 0.99. We have made yet another baby step of progress on our equation:

N = 2 × 0.99 × n_e × f_l × f_i × f_c × L

In the next post, we will take a closer look at n_e – a guess at how many of all these planets are capable of supporting life. In the mean time, a toast to all you crazy planets out there – may you never stop spinning.

Welcome to the first stop on our tour of the Drake equation, one way to estimate how many extraterrestrial civilizations might be out there and able to communicate with us. To sum up from a couple of posts ago:

N = R_* × f_p × n_e × f_l × f_i × f_c × 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
• f_p is the fraction of stars that have planets
• n_e is the average number of planets per star that might support life
• f_l is the fraction of life-supporting planets that actually develop life
• f_i is the fraction of developed life that becomes intelligent
• f_c 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

The jury is still out on whether we are intelligent, but we have managed to send detectable signals into space, so we know N is at least 1.

Today, we discuss R_*, the rate at which new stars are created in our galaxy.

Our Sun seems like a constant, and for all practical purposes, to a human being, it is. During the time between your first and last breaths, nothing that you experience of our Sun changes in any appreciable way. It’s bright, it’s hot, and it has what appears to be an immutable daily routine. But it does also have a lifetime of its own, and that includes a tumultuous birth around five billion years ago. All stars are born from a combination of gravity and nuclear fusion, and the vast majority of their lifespans consist of a delicate balance between the two. So how does it all begin?

To start, our universe is clumpy. This may sound vague or even slightly insulting, but while a less clumpy universe would have been far more elegant, it would also have been far less interesting. Because the universe is clumpy, atoms will occasionally get close enough together to attract each other through a mutual pull that we call gravity. The mutual part is an important thing to remember when you’re thinking about gravity (and I know you do that all the time) – gravity is a mutual attraction between any two objects with mass (“stuff”). So you are pulling on the Earth just as surely as the Earth is pulling on you. It’s just that the Earth is a tad bit bigger, so our perception is that the Earth is doing all the pulling.

In the case of atoms in space, if gravity brings them close together, their combined mass pulls harder on everything around them, which in turn creates a larger mass, which attracts more atoms, and I presume you get the picture. It’s kind of like the way beaches were before the pandemic, or the way beaches are for idiots during the pandemic. The more there are, the more there are. Eventually, you get a huge collection of atoms pulling each other closer, and increasingly more likely to run into each other, and the resulting energy of those collisions makes them go faster, and then they run into each other some more, and that is essentially the definition of a rising temperature.

So now you’ve got this ball of gas – usually overwhelmingly composed of hydrogen, getting denser and hotter and collapsing upon itself. Gravity doesn’t stop no matter how close two objects get to each other, so if there were no other forces at play, this ball of gas would just continue shrinking upon itself until it vanished into an infinitely dense point, known in nerd circles as a singularity. And again, that would be rather elegant and simple, but also not conducive to an interesting universe.

Fortunately for us, there are other forces at play. At the heart of every atom is a nucleus – some combination of protons and neutrons. Most hydrogen atoms are composed of only a single proton, but some atoms of hydrogen and all atoms of any other substance are composed of two or more protons and/or neutrons. They are held together by what physicists call the strong force. You have to push protons and neutrons very close together to get that force to kick in, but once it does, it overpowers all other forces of nature. So, as a ball of hydrogen gas shrinks upon itself, eventually the atoms get close enough to each other that the strong nuclear force takes hold, and the protons and neutrons fuse together. When this happens, they release a tremendous amount of energy, further heating the shrinking ball of gas. At a certain point, the energy released by the fusion of atoms creates a temperature so high that it balances the force of gravity that caused the shrinking in the first place, and the ball of gas stops shrinking. Nuclear fusion also makes the ball of gas so hot that it radiates visible light, and with that, a star is born.

Now that you’re an expert on star formation, all we have left to do is figure out how frequently this happens in our modern age. I don’t know about you, but I wouldn’t know where to begin. Fortunately, there are people who do this kind of thing for a living, combining observations of the stars we can see with our maturing physical understanding of how stars are born, how long they survive, and how they eventually die. When you put it all together, the estimates seem fairly consistent: an average star like our Sun is born somewhere in our galaxy between one and three times each year.

I can’t put “between one and three” in an equation. Fortunately, there’s a thing between one and three known as two – and so we’re going to use that. R_* = 2. Anytime you can replace a letter in an equation with a number, you’ve made some progress. So let’s kick back, crack open an ice cold beverage, and take in the view of our slightly less ambiguous calculation for intelligent life in the Galaxy:

N = 2 × f_p × n_e × f_l × f_i × f_c × L

The next post will zero in on f_p – the fraction of stars that have planets. But for now, it’s kind of cool to think about the notion that a couple of times each year, a star is born somewhere in our galaxy. Combine that with our current life expectancy, and the majority of Americans can rest assured that over a hundred stars will be born during their lifetimes in our galaxy alone. The numbers become insane when you extrapolate to other galaxies, but the nearest major one of those is two million light years away, meaning any signal we might receive from there was sent long before human beings existed as a species. So it’s probably ok to keep our focus on the Milky Way for now. Even doing that – once or twice a year, somewhere in our galaxy, a star like our Sun ignites into existence, with the potential for planets, life, intelligence, technology, and blogs.

Damn, that’s a lot of blogs.