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