In this week’s astronomy lab, my students needed to make some simple calculations, mostly involving some arithmetic and a little bit of algebra to convert hours and minutes into decimal hours (for example, 1hr 30min = 1.5 hrs) and some arithmetic. Nothing too complex, but it was nevertheless a major challenge for many of my students, eliciting groans of “I suck at math”, “I’m not a math person”, etc.
I’m sympathetic, to a point. I struggled with math quite a bit as a wee lad, and even as an undergraduate astronomy major in college (don’t tell anyone). But looking back, I realize that the reason I “sucked” at math was because I told myself I sucked at math. Once I decided I no longer sucked at math, I suddenly got better at it.
I watched this happen to a student when faced with the problem of calculating the difference in time. He was struggling with some time calculations and asked me for help. It went something like this (and yes, I’m paraphrasing):
Me: Ok, so you need to figure out the time difference between 1:16 and 1:21. What is it? Student (tired, frustrated): Oh man, I’m just not sure right now. Me: No problem. Let’s imagine you and I are playing blackjack together in Atlantic City— Student: Now you’re talking my language! Me: Cool. So you’re dealt a 7 and a 9. What do you have? Student: 16, a really sucky hand. Me: And the dealer is showing an 8, what do you need to do? Student: This sucks, I have to hit. Me: Yeah, you do, but what do you have to pull in order to make 21 and guarantee you won’t get beat? Student: A 5. Me: Right, so what’s the difference between 1:16 and 1:21 again? Student: Oh geez, of course. Duh!
I got a little lucky here – I didn’t know that the student played blackjack, I just guessed. But mathematically, the problem was the same. The context of the problem seemed to make all the difference. At the blackjack table, he no longer seemed to think he sucked at math and suddenly the problem was a piece of cake.
A lot of math phobia gets swept away when you are presented with problems in a more familiar setting. That’s why I know my students don’t suck at math, or at least not nearly to the degree they think they do. After all, math is hard, but it’s a skill you can learn.
I’ll wrap this up with a video that caught my eye this morning that dispels a lot of the myths, fears, and misconceptions about math. I’m not a genius at math by any means, and I might have to stop and think a little bit more when solving a problem than others. But I don’t suck at it, and neither do you.
I realize that there are no shortageofreviews of last night’s premiere of Cosmos: A Spacetime Odyssey (including one by my good friend Mike Brotherton), but I did have a few thoughts of my own. First and foremost, I loved this show. It was beautiful and poetic, thoughtful and insightful, and firmly made the case that science is the only way to really understand the world and universe we live in. Will I love it as much as Carl Sagan’s original? Maybe, maybe not, and truthfully, I’m ok with either outcome.
Although Sagan is no longer with us, having his protege Neil deGrasse Tyson at the helm of the new Ship of the Imagination is a fitting passing of the torch. And what better way to begin the new voyage than with an homage to Sagan. I couldn’t imagine a more fitting kickoff to this series than to literally begin at the same location Carl did 34 years ago.
But in that time a new audience has grown up that is inundated with even more television channels and production values that far surpass anything Hollywood was capable of producing in 1980. Make no mistake, the production values of the original Cosmos were, in my opinion, absolutely incredible. I truly felt like I was flying through the universe with Carl on his ship. Even though there is no way they could possibly do a poor job with this new production, I was wondering if the new series might go overboard with the use of visual effects, or use them in a way that has, quite frankly, been done to death in other science programs. The answer, to be honest, was a bit of a mixed bag for me.
Cosmos sets out to orient the viewer in much the same way as it originally started out – by describing our place in both in space and in time. The space bit had Tyson and his ship zipping through the Solar System, which was fine until…
To be fair, they didn’t show the Ship zigzaging around the asteroids in hairpin tuns a-la the Millennium Falcon in Star Wars: The Empire Strikes Back; This shot was much more graceful than that, suggesting perhaps a little bit more space between the asteroids. But the truth is that asteroids are already very, very far apart from one another. I personally would have much preferred a setup where the audience thinks they’re about to play cosmic dodge ball, only to discover that the asteroid belt is wide open with nothing in sight, and Tyson actually having to set course to fly by an asteroid in order to glimpse one up close. That might not have been as visually stunning, so it looks like they went for the cool shot instead, but they also reinforced a very common misconception.
Things get much more interesting – and pretty accurate – when passing through the Jupiter system. The sequence of flying through the Great Red Spot absolutely blew me away.
Of course, you can’t do a Saturn flyby without going through the rings. I’ve heard some complaints that they didn’t get the scale right here, but the thickness of Saturn’s rings vary from as thin as 10 meters to as thick as 1 kilometer.
All things being equal, this was just too cool a shot to pass up, so I’m good with it.
Next was an all-too brief mention of the ice giants Uranus and Neptune. I know it’s an ambitious first episode show and there’s only so much time to devote to such things but I feel bad for those two worlds. To their credit, they took a moment to describe Trans-Neptunian Objects and the icy worlds of the Kuiper Belt, but once again they overcrowded the scene.
It seems that in this new sequence, we are dodging space rocks a-la the Millennium Falcon, which is unfortunate. In reality, there’s even more space between Kuiper Belt objects than there are between asteroids by virtue of the fact that the Kuiper Belt extends so much farther from the Sun than the asteroid belt. Alas, the cool shot wins out and a misconception is reinforced. Bummer.
Interestingly, as Tyson leaves the Solar System, he looks back on the Oort Cloud and notes that the objects there are as far apart from one another as Earth is from Saturn. I guess that’s why he didn’t have to dodge them on the way out. My only observation here, as with any depiction of the Oort Cloud, is that at this imagined distance, the icy comets that populate the cloud are much too small to be seen; The Oort Cloud would be no more noticeable from outside the solar system than it is from our vantage point well within it. And yet there needs to be a way to visually communicate to the viewer that they’re there, so we get a delicate sphere around the Sun.
Jumping forward in the sequence, Tyson continues to define our cosmic address through our diminishing place in the Virgo Supercluster of galaxies. Whenever I see shots like this, I get goosebumps, despite having been familiar with the scale of the observable universe for most of my life. However, I’ll just note that if we really were as far out in between galaxies as depicted in the sequence, we wouldn’t be able to discern each individual galaxy with our own eyes. Remember, each galaxy in an image like the Hubble eXtreme Deep Field is the result of 2 million seconds of exposure time – nothing our eye would ever be able to register in a glimpse, even if we were looking through the Hubble Space Telescope itself. Still…goosebumps!
It’s when we zoom out to the large scale structure of the observable universe that we finally complete our cosmic address.
I’m not sure why they chose to represent this as purple in color, but my guess is that it was inspired by the Millennium Simulation Project, an ambitious model of the gravitational interaction of a whopping 10 billion galaxies. Here is a small piece of their result:
To tell the truth, I wish they had used this image instead of the one they created. Not only is it more realistic, but it makes the observable universe seem larger than it appeared in Cosmos.
When describing the history of the universe, we are (re)introduced to the analogy of an earth calendar. I always thought this was the best way to convey the 13.8 billion-year history of the universe, and the comparatively negligible length of time humans have been around to notice it, to a lay audience. Naturally, this has to start with the Big Bang which, unfortunately, cannot really be properly described even with the most sophisticated of visual effects.
Don’t get me wrong, it was a cool sequence. The problem is that you cannot really depict spacetime expanding into itself, which is what really happened (and is continuing to happen). That’s because there is no outside for the universe to expand into. Perhaps the most accurate way to depict a Big Bang is to show nothing on screen, then show “fire” everywhere. There was a 1991 documentary called The Astronomers that depicted the Big Bang exactly this way. But it’s hard to convey the idea of a massive explosion without showing something…well…exploding. Hmm…
Truth be told, I’d be ok with this had Tyson not made the statement that in the beginning the entire universe was compressed down to the size of an atom. If he had instead said it was the observable universe that was so compressed, it would have made all of the difference. Here’s why:
Most cosmologists generally believe that the universe is infinite. By that definition, it extends farther beyond the farthest points in space we can see. These farthest points define the observable universe, and Tyson makes a point of distinguishing the observable universe from the entire universe, which is infinite.
But here’s the catch – if the entire universe is infinite today, then it must have been infinite in the beginning as well. But how can something be both infinite and compressed down to the size of an atom? It can’t, but the part that defines today’s observable universe can, with all of the points of the infinite universe beyond compressed next to it, and so on. Here’s an illustration from Edward Wright’s excellent cosmology FAQ:
The green circle represents our observable universe, with the galaxies (dots) much closer together a billion years after the Big Bang than they are today. If we run the clock back further to the beginning, our green observable universe would be infinitesimally small, but the dots (representing the galaxies we will never see) will still go on forever.
Alas, by stating that the entire universe was compressed to the size of an atom, I think Tyson may have reinforced a major misconception.
Again, none of this is to take away from what I thought was an amazing production. And truth be told, we need Cosmos on our screens now more than ever. Carl Sagan presented Cosmos at a time of both great exploration of our solar system and of grave danger to our home planet and to humanity’s own existence. Sagan understood that our very survival depends on humankind’s knowledge of the cosmos, and of our place in it.
Today, we find ourselves once again in peril – perhaps not from nuclear annihilation but certainly from a rapidly warming planet – but now amid an ever-increasing wave of science denial. Denial of global warming, modern medicine, biotechnology, and of investments in research. If there was ever a time when we need to present Cosmos to a new generation, it’s now.
You can view the entire episode here. Enjoy the journey.
For any graduate student or postdoc, teaching is a rite of passage. Lucky for me, I got to experience teaching early on as an undergraduate at Villanova University starting in the late eighties as a teaching assistant for the core undergraduate astronomy lab.
That also happened to be the last time I actually taught astronomy lab until now. I’ve done my fair share of public outreach, informal educational activities, school partnerships, and even a weeklong cram astronomy workshop, but formally teaching for realz for a full semester at a university is something I haven’t done in over 20 years, until now.
Last night I taught the first of 12 labs for Astronomy 161 at Towson University. Now, I don’t plan on telling any war stories, but if last night is any indication, there may not be any war stories to tell anyway (I know, famous last words.)
As a subject, astronomy is one of the most counterintuitive to us. It requires to contemplate the greater universe far beyond the trappings of our day to day world. Consider these “simple” questions:
Which direction is East?
Which direction is West?
Where is the highest star in the sky?
Right off the bat, we’re faced with questions that have no bearing on our everyday experience, yet are fundamentally important to understanding our place in the cosmos.
Unsurprisingly, some people were stumped by these questions at first. But it wasn’t long before the light bulbs started going off and one by one, connections to the cosmos were made right in front of me in that lab.
It feels great to be teaching again and I’m kind of kicking myself for not thinking to do this sooner, seeing as I loved it so much going back to my undergrad days. Oh well, I’m here now at Towson and I’m looking forward to the rest of the semester.
To any of my students who might be reading this post, welcome! Feel free to grab a Astr.161 Syllabus in case you didn’t get it from the school’s Blackboard site (which is something else I’m trying to figure out – these new fangled computer internets and all…)
Oh, and feel free to leave your answers to the above questions in the comments below 🙂