Let’s face it, physics has an image problem. If we were to play a little word association game, what are the first words that comes to mind when I say “physics”?
math-y (i.e. see points 1 and 2!)
Or, if we play an image association game, what are the first things you picture when I say “physics”?
But here’s the thing – physics is so much more than cosmology and quantum computers, and you don’t have to be ‘Sheldon-Cooper smart’ to appreciate it. Fundamental physics principles help us to understand everything from how the heart pumps blood through the circulation system to why soap films form spheres when you blow air into them.
This is why I write: I love that a surprisingly small set of fundamental physical principles can explain the ‘why’ of just about any everyday phenomenon. I want to share that with anyone who will listen. The world is full of incredible examples of physics in action and you don’t need a PhD in quantum mechanics to appreciate them! And, although I feel a little late to the party in starting this blog now, I’m taking inspiration from something I saw at #SciCommTO 2020:
On an icy cold morning at the end of February, I tentatively headed down the slope behind our house, on my way out for some daily exercise. As I stepped off a retaining wall down to the walkway below, my foot went right out from under me and I crashed down, hard. The small of my back came down on the edge of the six-inch high concrete step as the rest of me landed on the lower level − I experienced the most intense pain I have ever felt. And that includes the drug-free labour and delivery of our first child.
There was no one in the house … no one to hear me scream. No matter how I tried to gingerly move, bolts of searing pain shot through me. I knew I was in trouble, so I sheepishly phoned a friend who raced over, took one look at me, and said: “I’m calling 911!” The combination of this fall and that call quite possibly saved my life because, on our way to the local hospital, the incredibly wonderful paramedic said: “I know you’re in a lot of pain and quite stressed right now, but your blood pressure is really high. You need to follow up on that!”
How high? It was consistently reading over 180/100 (mmHg) that morning. This is WAY above the normal range of 120/80, and solidly in the danger zone of risk of heart attack or stroke. According to the FDA, readings in the 180/110 range or higher are considered “hypertensive crisis” and need immediate medical attention. And here’s the truly scary part in hindsight – I had absolutely no idea. It’s not called ‘the silent killer’ for nothing.
High blood pressure (hypertension) affects almost 1 in 4 Canadian adults according to a 2015 study, with the prevalence increasing dramatically with age. We tend to think of this as a concern for our parents or grandparents, or at least I naively did, but the incidence rate in women in the 40 to 59 age range (i.e. me) is actually 21%. Of the hypertensive women in my age range, about 20% were not aware of their condition either.
Why is this an issue? Because hypertension is currently the leading risk factor for death in the world. High blood pressure means that your heart has to work harder to move blood around your body – like trying to pump air into a bike tire that is already fairly full – so the muscle of your heart thickens and is more prone to suffering a heart attack or failing. The vessels themselves can also narrow and get damaged, making blood flow more difficult. And it’s not just damage to your heart, as if that isn’t serious enough. The damage to blood vessels happens everywhere, including in the brain. Left unchecked, restricted blood flow can lead to blockages or bursts, i.e. strokes and their debilitating consequences. High blood pressure also raises the risk of developing vascular dementia, the second most common form of dementia. Reading that stopped me cold in my tracks.
For a middle-aged woman, I’m reasonably fit. Our family eats mostly home-cooked meals, avoiding the very high salt content typically found in prepared foods. I walk daily, play with my kids, row/kayak in the summers, snowshoe in the winters; 10,000 steps are pretty standard on a daily basis. But I do have a family history of concern and I should have been paying closer attention. It’s just so easy, when running a busy household and a demanding career, to de-emphasize your own health in the ever-fluctuating list of priorities. I also experienced no symptoms whatsoever, at least I didn’t think I did. It turns out that the symptoms can be pretty vague and easily chalked up to daily stresses. I mean ‘headaches’, ‘fatigue’, … who doesn’t suffer from these regularly, particularly in our current pandemic crisis?
I can guarantee you that I would not have scheduled a routine check-up with my family doctor for many months (years?) to come, given all that is going on in our lives. But my guardian-angel paramedic’s warning on my very first (and hopefully last) ambulance ride struck a chord, particularly since I lost my mother to a massive stroke when she was only 67 years old. Her premature dementia in the final years before her stroke, as well as the stroke itself, are fates I wish to avoid. Fast forward a few months and my family doc now has me on some low dose meds, I’ve amped up my exercise regime, and I have significantly reduced my alcohol intake (yes, during a pandemic, it can be done!).
To all my fellow middle-aged women, consider this a friendly nudge. It’s all too easy to dismiss little warnings as no big deal; I did, even though I should have known better, and it could have cost me my life.
 It turns out I was INCREDIBLY lucky in my fall – no broken bones, no organ damage, no slipped disks. Some deep muscle bruising and strain that took a couple of weeks of bedrest to begin to heal. More or less full mobility was back in about a month. HUGE thanks to my good friend, Cindy Johnson, for rushing to help!
 I’m using the definition of hypertension of a systolic pressure (the top number) greater than 140 mmHg OR a diastolic pressure (the bottom number) greater than 90 mmHg. This is technically Stage 2 hypertension, with Stage 1 usually considered at systolic greater than 130 mmHg or diastolic greater than 80 mmHg.
A few weeks ago during dinner there was a sudden burst of sunlight in the midst of a rain shower. Knowing that these were ideal rainbow-making conditions, we jumped up from the table and ran out to investigate. Sacrificing our meal was entirely worth it: this photo was taken just a few hundred metres down the road from our house. Once again, I am blown away by the beauty of physics in the world around me.
The bright feature in the photo labeled A is the primary bow, which is always observed with the red band on the outer edge of the arc and the violet band on the inner edge. Light coming from the Sun, behind you, scatters in all directions from the raindrops in front of you. The light doesn’t scatter equally in all directions though, as shown in the following image, modified from a 2016 paper by Alexander Haußmann. In this plot of intensity versus scatter angle, zero degrees represents light that is scattered straight back towards you, while light scattered directly away from you is at an angle of 180°.
(image from Haußmann’s 2016 paper)
We can see that the intensity is pretty steady at small angles, coming straight back towards you, then reaches a peak at 42°. This is the angle where you see the primary rainbow: 42° is the maximum angle of the cone of light that scatters straight back towards you from one bounce inside a raindrop.
At the very edge of this cone of scatter, we see the separation of the different colours of light that come from the Sun: the highest wavelength, red, scatters back at a slightly higher maximum angle (42.2°) than the lower wavelengths, like blue, which has a maximum angle of 41.2°, as we see in the sky with the red on the outside edge and violet on the inside of the primary bow.
Moving along the relative intensity graph from 42° to the next large spike at 51°, there is a region known as Alexander’s band, named after Alexander of Aphrodisias (circa 200 AD), which is marked B in my photo at the top. The band ends at 51°, which is the minimum scatter angle for light to bounce twice inside the drop and then reach our eyes as sketched here. The angle of 51° corresponds to the location of the secondary bow (C).
Alexander’s band is dark because it spans the ‘dead zone’ between the maximum angle for scattering with one bounce and the minimum angle for scattering with two bounces inside the droplet. Since light can’t bounce 1 ½ times, the intensity in this in-between range is quite low and the sky looks darker here than above the secondary bow or below the primary bow. It’s not midnight black though, because light is being scattered from clouds, other droplets, the front surface of droplets, etc.
The secondary bow, with its sharp spike at 51°, will always appear with the red band on the inside and the violet band on the outside, opposite to the order seen in the primary band. It’s not always easy to see this feature though; the intensity is less than that of the primary bow. With each bounce, some of the light continues through the droplet rather than reflecting, which means that the tertiary (and higher order) bows are rarely observed. The added challenge with seeing the tertiary bow is that it appears at about 140°, very much in the forward direction, away from the observer. To see the tertiary or quaternary bows, you have to be facing the Sun with scattering raindrops between you and the Sun, which, shining brightly, tends to wash out faint features like these weak bows. The angular spread of the colours increases with each order of bow, so this smearing out also makes them harder to see. The fifth order bow is predicted to appear just inside the secondary bow, as seen as the little spike in the intensity graph at around 50°.
We have marveled at, and tried to understand, rainbows for millennia. Way back in 1637, Descartes published a chapter in his Discours de la Méthode in which he correctly calculated the angles observed for the primary and secondary bows, although the colours were still a mystery in his day. Newton famously solved this mystery by deducing that white light is made up of all these colours. But it wasn’t until the early 1800s when Thomas Young linked the colour of light to its wavelength that physics was able to explain the observation of “supernumary arcs”, shown here in a cropped piece of my photo, marked as D.
These bands of light and dark regions just inside the primary bow are classic interference patterns caused by light scattered at the same angle but travelling different path lengths through a raindrop. Young’s theory correctly predicted the effect of drop size on this feature of the rainbow and provided further support for the wave theory of light.
Once James Clerk Maxwell figured out that light is transmitted in the form of electromagnetic (EM) waves (around 1864), a new theory emerged to understand light scattering from small objects like raindrops, known as Mie scatter after the German physicist Gustav Mie. By breaking the incoming EM wave into a series of partial waves, we then calculate how each scatters from a sphere of a particular size and electrical properties, and then add up the results. Intensive calculations with Mie theory were not possible until we had the help of computers in the latter part of the 20th century, but now millennia of wonder and delight has been explained, matching observations beautifully.
Refinements continue today, with tweaks to deal with non-spherical droplets (affectionately known as the ‘hamburger bun’ model), different sizes of droplets within the rain shower, effects of the intensity of rain in different regions of the shower, and more. Science marches on, so grab your rubber boots and let’s dash out, chasing rainbows. My little helper unicorn likes to refresh with a rainbow treat when we get back inside!
Rainbows in nature: recent advances in observation and theory by Alexander Haußmann 2016 Eur. J. Phys.37 063001
As I strode across campus to meet my second-year physics students in our Electricity and Magnetism class a few years ago, it suddenly struck me that I had the makings of a fantastic opportunity tucked under my arm. My teaching assistant had returned their last assignment of the semester to me, so I quickly formulated my plan. As I entered the room and prepped for our session, I projected a stern and serious air, quite unlike my usual smiley/jokey self. As everyone settled down, I told them that I was very disappointed to hear from our TA that there had been a considerable amount of ‘sharing’ in the assignments that had been submitted, which is completely unacceptable. I told the class that I wanted them to take out a piece of paper immediately and work through the solution to one question again, individually, right then and there.
There was much muttering and sharing of furtive looks around the room, but everyone complied as I projected the question onto the screen with the document camera. One or two students looked at me suspiciously, but I maintained my grave look and told them to get started. After a few minutes, I said to the class: “Please make sure you write your name and the date on the page …. today is April 1st.” As my students slowly looked up at me, realization dawning on their faces, I shouted: “APRIL FOOLS!” It took a good 10 minutes before we were all settled down again and ready to discuss the physics of magnetic materials, but I maintain that it was 10 minutes well spent.
Incentivize Lecture Attendance
Study after study has demonstrated the value of a ‘flipped’ classroom, in which students engage with each other and the instructor in meaningful and deep learning activities (1,2). This little April Fools’ prank was certainly not such an activity, but it is a good example of the value of being a little silly with your students: it incentivizes lecture attendance. Step one for maximizing classroom engagement is to make your session an adventure, an event that students don’t want to miss because they never know what might happen. You care about their learning, you go to great lengths to fine-tune your pedagogy based on current physics-education research, but you need to get them out of bed and through the classroom door for all your hard work to pay off!
This is something I have struggled with during the pandemic with all my teaching done remotely. Being jokey and improvisational with my students has been incredibly difficult when only a tiny fraction of the class turns their camera and/or mic on – it is almost impossible to ‘read the room’ in Zoom. Even with these challenges, it seems more important than ever to find ways to inject some levity given the state of the world around us: I’m a firm believer in the notion that laughter truly is the best medicine. So, after grumbling about the countless ways in which technology foils my best-laid plans for an engaging virtual class, I decided to take advantage of the humour in the farcical: my students and I created a bingo game based on the myriad ways in which our sessions go sideways! (A spherical cow stress ball, pictured below, is the prize for completing a row or column.)
Break Down Barriers
In addition to incentivizing lecture attendance, injecting humour into our sessions also helps to break down barriers between my students and me. As evidenced by our bingo card, my humour tends towards the self-deprecating kind, which subtly communicates to my class that I really don’t take myself too seriously. I want my classroom to be a safe haven, where students can ask questions to each other and to me without worrying about being judged. No one, including me, has all the answers or is right all the time; mistakes are the best opportunities for learning.
So, rather than projecting an air of unassailable authority, one who, for example, would never drop a negative sign, I celebrate these moments with my students with Smarties. As we work through an example together, I want them to be trying to follow along with each step as we go, rather than just passively writing it all down to figure out later (i.e. the night before the next test). In our sessions, everyone is on high alert because the first person to catch a mistake, such as that inevitable loss of a pesky negative sign, is rewarded with a box of Smarties. Usually, in our face-to-face sessions, I have a couple of boxes in my laptop bag to hand out on the spot. With remote teaching I had to find a work-around and now I keep a running tally during the semester on my Smarties List, with payout at the end of term. This year, since I was actually keeping track, I added a personalized Smarties certificate to this special delivery, with one pictured below on proud display on the family fridge door! Students seemed to really appreciate the personalized touch so I’m keeping this new tradition going even after we are back in face-to-face sessions. (FYI, if you want to adopt this approach, definitely have extra boxes on hand if you need to teach after taking cold medication. Just saying.)
Improve Student Attitudes
I am not a stand-up comic in academic regalia. But you don’t have to be hysterical to make good use of humour in the classroom and it can have a profound effect on students’ attitudes. A recent study looked at the effect of a positive attitude towards math and the brain’s ability to learn and remember (3). The study concluded that even when they controlled for IQ, working memory, math anxiety, general anxiety and general attitude toward academics, children with poor attitudes toward math rarely performed well in the subject. And, let’s face it, in our big first-year service courses there are a lot of incoming students who do not have a positive attitude towards physics. In addition to teaching second-year Electricity & Magnetism to physics majors, a preacher to the converted, I frequently find myself in front of hundreds of first-year biology students, which is more like being an emissary to a hostile nation. In my very first lecture every year, I ask them to tell me how they are feeling about taking this course using their clickers to respond anonymously, and the breakdown invariably looks like this:
There are times when there are identically zero responses in the “excited” category. In a room full of 400 students. *sigh* Making a concerted effort to help shift our students’ attitudes towards the subject is key to opening the door for them to do well, as that positive attitude results in enhanced memory and more efficient engagement of the brain’s problem-solving capacities according to the work of the team at Stanford (3).
A Little Goes a Long Way
Whenever I can I’m injecting little scenarios to make students smile. We work through a lot of example problems in class and I try to give them a little twist. For example, in free fall calculations, we work through a problem in which “Gord is spitting (sunflower seeds) from a bridge. Just to see how far down it really is.” This precise turn of phrase won’t mean much to non-Canadian readers, but this is a line from a Tragically Hip song, a hugely popular band that appeals across generations. The delivery is important when I read the question aloud and, although not everyone will get the reference, there are plenty of smiles around the room. We have also been known to analyze the position versus time graph of someone canoeing across a lake to an island where they suddenly encounter a mumma bear and her cub, as well as determining how far across an ice floe a sweet little penguin will slide before coming to a stop. This sometimes leads to a discussion on how one would experimentally determine the coefficient of kinetic friction between a penguin’s belly and an icy surface in terms of the factors one would have to control for, but I digress.
I am always looking for opportunities for student engagement and these often take the form of multiple-choice conceptual questions to use in the peer instruction mode of delivery, originally popularized by Eric Mazur at Harvard (4). I ask a question, students vote individually and we see the results. They then chat about their choices and vote again, after which we have a discussion about the correct answer (and, often, why the incorrect answers are wrong). Throwing a ridiculous choice or fun scenario into the mix often lightens the mood, like the following question that I pose as we start talking about conservation of momentum right around Halloween:
Two physicists decide to blow up a pumpkin. When it explodes, it splits into 3 pieces of equal mass, as shown from above in the illustration here. What is the direction of the velocity of the third piece?
I like to couple our peer-instruction discussions with demonstrations, trying to include student helpers whenever possible. I always structure these as Predict-Observe-Explain, where students vote on what they think will happen, the demonstration/experiment is conducted, and then we discuss what happened and why. A popular one we do when talking about resistors in series and in parallel is the smoothie race – a head-to-head student battle with two straws in series vs. two straws in parallel to see which “battery” generates the greater current. This is a fun way to visualize currents/batteries/resistors as well as another good opportunity to discuss experimental design. But just as importantly, there is lots of cheering and laughter; a spoonful of sugar to help the physics go down!
Every teacher develops their own style with practice and guidance, and I had the good fortune to be mentored by exceptional educators as I began to shape mine at the University of Guelph almost 20 years ago. I learned from some of the best in the business that humour is a powerful tool in the lecture hall for incentivizing class attendance, creating a welcoming environment, and improving student attitudes. To my mind, there is always room for a little tomfoolery in teaching physics!
F Finkenberg and T Trefzger 2019 Flipped classroom in secondary school physics education J. Phys.: Conf. Ser.1286 012015
David C.D. van Alten, Chris Phielix, Jeroen Janssen, Liesbeth Kester 2019 Effects of flipping the classroom on learning outcomes and satisfaction: A meta-analysis Educational Research Review28 100281 https://doi.org/10.1016/j.edurev.2019.05.003
Chen L, Bae SR, Battista C, et al. Positive Attitude Toward Math Supports Early Academic Success: Behavioral Evidence and Neurocognitive Mechanisms. Psychological Science. 2018;29(3):390-402. doi:10.1177/0956797617735528
Despite legions of campers swearing to the contrary, campfire smoke does NOT actually follow you around like your friend’s labrador retriever who really, really, really wants that wiener you just roasted. Of course, if there was no wind, if there were no complex air currents generated by the mixing of hot and cold air, and if you were the only person near the fire, then perhaps you could claim otherwise. But, in any realistic campfire scenario, the airflow is dictated by a large number of variables and where you happen to be sitting is likely the least important factor of them all.
For argument’s sake, let’s assume that we had the perfect evening. There is no wind and the air is moving in the simplified path shown in the sketch below. Denser cool air is drawn in towards the fire at ground level as the warmer, less dense air moves upward in a process called convection. In this scenario, the smoke travels directly upward with the heated air, unless there is a local disruption to these convection currents.
Now, if we add in just one person near the campfire, this could create a local obstruction at ground level:
The camper blocks cool air from flowing in toward the base of the fire at that point in the circle. Like a large boulder in a quickly moving stream, this person is an obstruction to the flow. The disrupted airflow could lead to the smoke swirling around in the region between the fire and the camper, like eddy currents or vortices downstream from the boulder. If she moves to another spot around the circle, the same disrupted airflow and eddies go with her, hence the feeling that the smoke is following her.
This is the same principle by which obstructions are diagnosed in blood vessels with Doppler ultrasound: regular blood flow becomes turbulent with vortices and eddies behind obstructions. The resulting colour Doppler image clearly shows these regions of anomalous flow.
But for the effect of these eddies and vortices to be so pronounced with smoke, there would have to be no other people around the campfire and no wind. You would likely need to be relatively close to the fire as well. So, in reality, campfire smoke doesn’t really follow you around, it just seems like it does. This is a classic example of confirmation basis, a phenomenon observed as long ago as the time of Sir Francis Bacon (1561 – 1626), who said:
It does make sense. After all, it is super annoying when it swirls in your face and makes your eyes water, so we remember these instances vividly. We don’t, however, tend to notice or remember all the times that the smoke was swirling in the face of your friend with the moochy labrador retriever.
To prevent smoke from swirling in front of you at the campfire, several survivalist references suggest that you build your fire with a large object nearby, such as a rock, a pile of sand, or firewood. This object will create a bigger disruption in airflow and, in theory, the smoke will swirl in front of the wood pile rather than your face. Again, however, this effect will only be observable with very specific circumstances. Let’s just call me skeptical on this one. Rather than going to great lengths to ensure there is a smoke-attracting decoy near the fire in case you have the perfect evening, why not look at it as an opportunity to do some fun experiments on confirmation bias instead?
Back in 1611, Johannes Kepler, court mathematician to the Holy Roman Emperor Rudolf II, found himself flat broke in the lead-up to the holiday season. (Apparently Rudolf didn’t pay his court all that regularly.) As he wandered across the Charles Bridge in Prague, he noticed a delicate snowflake attached to the lapel of his coat and marvelled at its geometric beauty. Why does the snowflake always appear ‘six cornered’?, he wondered. Never five or eight or twelve. The theory he then developed became the foundation of the field of crystallography, proposing that the geometric shapes of crystals is determined by the most efficient way for molecules to arrange themselves.
Stop and think about that for a second …. Kepler came up with a theory about how molecules arrange themselves almost 200 years before the notion of atoms forming molecules was even formulated! He wrote his musings down in the 24-page booklet “De nive sexangula”, which he presented to his friend Johannes Matthäus Wackher von Wackenfels as a New Year’s gift. (Anyone feeling strapped for cash right now? Now that’s a priceless homemade gift!)
The crux of Kepler’s argument was that the six-sided hexagonal shape arises because of how the ‘smallest natural units of a liquid like water’ (i.e. molecules before we called them that) arrange themselves to fill the space most efficiently. This idea of how molecules arrange themselves in close-packed configurations was inspired by earlier work from an English mathematician Thomas Harriot, who had advised Raleigh on how to stack cannonballs on the ship’s deck in the most efficient manner: hexagonal, like the snowflakes.
Harriot shared his cannonball-stacking analysis with Kepler, who immediately saw the connection to the symmetric crystals decorating his coat, suggesting that the six-sided structure comes about naturally since “in no other arrangement could more pellets be stuffed into the same container”. Now here is another truly mind-blowing part to this story: Kepler’s conjecture from 1611 was not formally proved until almost 400 years later by mathematician Thomas Hales and collaborators, with the formal proof eventually published by Forum of Mathematics, Pi, in 2017!
Hexagons are found just about everywhere you care to look in nature, not just in wintertime on your lapel, like honeycombs made by bees, a collection (“raft”) of bubbles on a frothy pond surface, or the compound eyes of insects. If you want to cover a flat surface as efficiently as possible with objects that all have the same shape and size, you have three options: equilateral triangles, squares, and hexagons. Hexagons often come out as the winner because they require the least amount of side length to contain a given area.
For example, let’s think about an equilateral triangle, a square, and a hexagon, each with a total area of 100 cm2. For a square, that means that each side is 10 cm long, for a total perimeter/wall length of 10 + 10 + 10 + 10 = 40 cm. For an equilateral triangle, the area is calculated as the side length squared multiplied by the square root of 3, all divided by 4. This tells us that an equilateral triangle of area 100 cm2 has a side length of 15.2 cm. The total perimeter here is then 15.2 + 15.2 + 15.2 = 45.6 cm. Lastly, the naturally-preferred hexagon. The area for such a shape is calculated as the side length squared multiplied by the factor 3/2 times the square root of 3. (This is the same thing as six-times the area of an equilateral triangle, since a hexagon is the same thing as six close-packed equilateral triangles.) For a total area of 100 cm2, the hexagon has a side length of only 6.2 cm. Adding these up for the perimeter gives us a total wall length of 37.2 cm, the smallest of these three shapes.
It takes energy to build a honeycomb structure. None other than Charles Darwin noted that the observed shape made sense from the evolutionary perspective, declaring that the hexagonal honeycomb is “absolutely perfect in economizing labor and wax.” Once again, Mother Nature, you are brilliant!
(Image of football/soccer player in the rain under stadium lights, from Shutterstock.com)
A few days ago, my football-obsessed cousin, James, commented on Twitter on a video of an incredible header by superstar athlete Cristiano Ronaldo, concluding that the “laws of physics don’t apply to [Ronaldo]”. It wasn’t intentional, but a statement like that is a bit like waving a red flag at a bull and I was definitely intrigued. So here’s the full clip and let’s just stop for a moment and admire the INCREDIBLE skill on display:
What I also love about this clip is that it shows three great examples of projectile motion:
the kick of the ball from the left wing, crossing to Ronaldo
the perfectly timed leap of Ronaldo to meet the ball in mid air
the arc of the ball from Ronaldo’s head to the back of the net, with the keeper looking on in dismay
Projectile motion is what physicists call any instance in which an object is moving through the air without any propulsion system, so my older daughter and her horse going over a jump, a dolphin leaping out of the surf, or my younger daughter diving into the pool. It does not, however, describe the motion of objects that have engines like airplanes or drones.
The common element is that the path is an arc shape – mathematically we call it a parabola. As it reaches the very top of the arc, the object is travelling horizontally for just a moment before falling back down to ground level. The eye-catching thing about Ronaldo’s jump is that he seems to travel horizontally at the top of his arc for an insane amount of time. Is he truly superhuman?
I had to find out. Using freeware called Tracker (https://tracker.physlets.org/), I can tag an object and look at its position in both horizontal and vertical directions in each frame of the video. When I tracked the motion of Ronaldo’s nose, I got this weird plot that suggests that he can defy gravity! Instead of an arc that is symmetric around the highest point, Ronaldo’s path appears to begin to drop and then miraculously rise up again before he heads the ball into the net! What????
I thought maybe Ronaldo was doing something weird with his head in preparation for contact with the ball, so I then tracked his torso (the white circle inside the P at the end of his logo, to be exact). Same thing …. how could there be two peaks in his path?? Unless he actually IS superhuman?
Nope – it’s all a trick of the eye/brain! The issue here is that the camera is moving both in the horizontal (x) and vertical (y) directions while it tracks this amazing play. There is also relative motion between the camera and Ronaldo in the forwards/backwards direction (z), and the problem is that we see the motion of Ronaldo relative to the camera instead of relative to the ground. To test my hypothesis, I tracked the “motion” of one of the metal bars at the top of the barrier at the sidelines – a stationary object that is in view most of the time. The resulting curve tells us that the camera was moving upwards as Ronaldo was moving up and then begins to move down as Ronaldo also moves down. Because the camera operator does such a great job of following Ronaldo’s motion, it appears as though he is hovering in thin air while patiently waiting for the cross to arrive. So, when I corrected Ronaldo’s tracking data for the motion of the camera, this is what I get:
The double bump has disappeared! It’s not exactly what we expect to see since it’s still a bit flat on top and not completely symmetric, but that’s because I have no way of correcting for the camera’s motion towards/away from Ronaldo. To properly track his jump, we need a video taken from a stationary camera that is always looking at Ronaldo directly from the side, like this:
Because of how we filmed this clip, we can analyze it quantitatively using the known slide height to determine the scale of our measurements. Based on her steadily increasing vertical speed, we can fit a straight line to these data and determine the slope, which tells us the rate at which Mara’s speed is increasing, or her acceleration.
The circled slope of “-10.12” tells us that Mara’s speed is increasing by ~10 m/s every second, or an acceleration of 10 m/s2, which is awfully close to 9.8 m/s2, the value we expect for acceleration due to gravity!
Now let me be perfectly clear, this little bit of video analysis is in no way meant to detract from Cristiano Ronaldo’s incredible skills. This header was scored in the 45th minute just before half time to put his team, Juventus, ahead 2-1, and ended up being the game winner in a home match against Sampdoria back in December 2019. Ronaldo finished the season last year as the second highest goal scorer, with a pretty insane total of 31. He is arguably one of the top two players in the world, but even Ronaldo plays by the rules of physics!
Like me, you may have spent a significant amount of time around a campfire this past long weekend. Singing songs, roasting marshmallows, debating the optimal wood configuration, discussing the connection between campfire smoke and eating placenta …. No? Not the last one? Well buckle your seatbelts, kids, let’s dive right in!
Although there are many who love the lingering smell of campfire in their hair and clothing, there is plenty of science to say that prolonged exposure to campfire smoke is not good for us. Smoke from wood-burning fires contains significant quantities of known health-damaging substances, including several carcinogenic compounds. So, avoiding wood smoke is definitively a worthy goal around the campfire. But how? A study published in Nature Scientific Reports in 2015 by Adrian Bejan from Duke University concluded that a 1:1 base to height relationship is ideal. He asserts that humans of all eras have been relying on this design “unwittingly”, instinctively building fires in such a way as to generate the most heat (and least smoke) once our hominid ancestors figured out how to harness this energy source.
The use and control of fire by our ancestors is a key event in our evolution, with theories that this development influenced our social structures, our geographic expansion into cooler climates, even the way our brains evolved. While exploring the question of “why does campfire smoke follow me around?” for a friend, I stumbled upon an even more intriguing evolutionary campfire-smoke theory: the nastiness of campfire smoke may be the reason that humans are essentially the only terrestrial mammals that do not eat placenta and amniotic fluid after childbirth.
It turns out that humans are quite unusual in our rejection of the practice of ‘placentophagia’. This behaviour is regularly observed in ALL nonhuman primate species, as well as in the vast majority of more than 4000 terrestrial mammals currently in existence. So, why not in humans? (other than “eww, gross”) There are plenty of animal studies to show the benefits to the mother and the offspring for ingesting placenta and amniotic fluid (via cleaning the baby) – so why would humans not do it? Not only do we not do it now … an extensive anthropological literature search of up to 300 societies around the world turned up no evidence of the behaviour in any pre-industrial human society. Of course ‘absence of proof is not proof of absence’, but it is intriguing! Since present-day nonhuman primates exhibit the behaviour, there must have been a point in our evolution in which we stopped doing it. In 2012, Sharon Young, Daniel Benyshek, and Pierre Lienard from the University of Nevada published their theory that it may have stopped due to the unhealthy effects of a universal practice unique to humans – the habitual use of controlled fire.
The placenta is a filter to protect the baby. Hominid mums spent a lot of time around the fire – inhaled lots of smoke – filtered the bad stuff out. Bad stuff accumulates in the placenta and it becomes a health risk to eat. The costs now outweigh the benefits that other species get from eating the placenta and amniotic fluid that, in their case, is not accumulating bad stuff since they aren’t hanging around the campfire. In other words, natural selection may have eliminated the practice of placentophagia among humans or our direct human ancestors as we spent a lot more time inhaling wood smoke.
So, the next time someone around the campfire complains about getting smoke in their eyes (and lungs), you can astound them with this fascinating connection to placentophagia. Depending on your company, you might just end up with a greater share of the marshmallows as a result! You’re welcome!
Why humans build fires shaped the same way; Adrian Bejan, Scientific Reportsvolume 5, Article number: 11270 (2015)
Woodsmoke Health Effects: A Review; Luke P. Naeher, Michael Brauer, Michael Lipsett, Judith T. Zelikoff, Christopher D. Simpson, Jane Q. Koenig & Kirk R. Smith, Inhalation Toxicology: International Forum for Respiratory Research, Volume 19, Issue 1, 2007, pages 67-106
Placentophagia in Humans and Nonhuman Mammals: Causes and Consequences; Mark B. Kristal, Jean M. DiPirro, Alexis C. Thompson, Ecology of Food and Nutrition (2012) 51: 177-197
The Conspicuous Absence of Placenta Consumption in Human Postpartum Females – The Fire Hypothesis; S. M. Young, D. C. Benyshek, P. Lienard, Ecology of Food and Nutrition (2012) 51: 198-217
Fire in the Plio-Pleistocene: the functions of hominin fire use and the mechanistic, developmental and evolutionary consequences; Laura Attwell, Kris Kovarovic, Jeremy Kendal, Journal of Anthropological Sciences (2015) 93: 1-20
 It doesn’t, that’s not how air convection works. Let me know if you’re interested and I can write a separate piece on this subject!
Our younger daughter, Mara, loves to read things likeWeird But True! – filled with tons of interesting facts about the natural world. Mealtime conversations are often peppered with such declarations as “elephants drink 800 glasses of water a day!”, to which I would typically respond with something like “I’m glad I don’t have to load the dishwasher in that family!” You never know where the discussions will start or end, and mealtimes are often protracted affairs.
The other morning at breakfast, Mara suddenly blurted out: “sharks don’t blink!”. Naturally, the follow-up questions came fast and furious – can they blink but don’t need to? Do they even have eyelids? What happens when they sleep? Do they sleep? After getting myself a second cup of coffee, we started to investigate and the next thing you know, we found ourselves staring at this incredible image:
We also ooh’d and aah’d over the amazing slideshow here from National Geographic, by photographer Stephane Granzotto.
What is happening?? No, these are not sharks, obviously. But our discussion of sharks and whether they sleep1 then led to other sea creatures. An important difference between sharks and marine mammals such as whales, dolphins, and seals is that the latter need to surface regularly to breathe, so resting needs to take that into account.
For many years, scientists have known that marine mammals in captivity sleep with one side of their brain shut down at a time – the fancy name for this is uni-hemispheric sleep. It allows them to swim, surface for air, maintain contact with their group, avoid dangers, but still get a little break. It is incredibly hard to study such creatures in the wild so, until recently, it was assumed that the same was true out in the deep blue sea.
However, in 2008, a team of Scottish and Japanese researchers made a stunning discovery when they literally bumped (gently, with their engines off) into a sperm whale who was part of a pod drifting vertically near the surface, seemingly fully asleep and unaware of their proximity!
These researchers tracked the movements of 59 sperm whales worldwide using devices attached by suction cups, recording a total of 562.9 hours of data. They observed that in less than 10% of the time, whales performed shallow, vertical, ‘drift dives’ with very little activity. If this is their only “sleep” time, it is tiny – the least amount of sleep observed in any other mammal studied. A subsequent study of similar behaviour in wild harbour porpoises found a similarly small percentage of drift time, although this study noted that both species are known to spend a significant amount of time floating at the surface (or “logging”), which may also provide rest. But the porpoises do NOT drift in the vertical orientation …. so why do the sperm whales?
That’s where the physics comes in! Miller and his team observed that even when the whale started a drift dive facing downwards, the tail would slowly sink until the whale had passively reoriented into an upright position. This slow-mo flip is driven by buoyancy acting differently on different parts of the whale. The tissue, which is more dense than seawater, is located more towards the back end: this part sinks. The less-dense oils inside the large spermaceti organ and the air in the respiratory system tend to be more towards the front, so this part floats. Don’t believe me? You can do the experiment yourself at home! Behold, my homemade Play-doh whales!
No doubt your whales will look INFINITELY better than mine, but here’s all you need: some Play-doh, some small Styrofoam balls (or ping pong balls), and a tank of water. Whale A was shaped with a Styrofoam ball in its head, Whale B was shaped with a Styrofoam ball near its tail, and Whale C has no Styrofoam at all. I then placed each one in a tank of water, horizontally at the surface, and watch what happened (sound on please):
So, Whale A, with the less dense head, ends up vertically upright in the water, Whale B is vertically upside down in the water, and Whale C sinks since it doesn’t have enough buoyant forces to remain afloat at all, completely consistent with the sperm-whale buoyancy theory. The harbour porpoises presumably maintain their typical swimming orientation during their resting periods because they are more uniform in their density.
Silent porpoise: potential sleeping behaviour identified in wild harbour porpoises; A. J. Wright, T. Akamatsu, K. N. Mouritsen, S. Sveegaard, R. Dietz, J. Teilmann, Animal Behaviour 2017 vol 133 pgs 211 to 222
A couple of summers ago I signed up with the Wellington Sculling Club for their Learn To Row* program. Coached by an amazing group of people, I successfully completed the course and joined as a full member, but I still have plenty to learn so I head down to the lake as often as I can.
The other morning, after putting the gear away, I stood on the dock watching a swarm of water striders skitching and sketching across the lake surface, occasionally leaping a significant height directly upwards. Their movements are so quick and directed, with sudden bursts of acceleration in one direction or another as they careen across the water. As soon as I got home, I started digging – how do they move around? How do they stay afloat? How can they leap straight up like that from a liquid surface? Imagine my surprise when I learned that these little creatures are nature’s skilled scullers!
An article in Nature in 2003, written by a team of mathematicians and engineers from MIT, studied water-strider motion through high-speed cameras and tracking software. If you look at the image at the top, there are three pairs of legs on a strider: two shorter ones at the front (under the antenna) and then two pairs of much longer legs, one at the midsection and one at the back. The pair at the midsection act as sculling oars; when the stroke is initiated, they push backwards and down, changing their angle to the bug’s body from 60⁰ to about 120⁰ before lifting out and returning to their initial positions. The bug’s legs push backwards on the water and the water pushes forward on the bug – Newton’s Action-Reaction law in action!
The group from MIT went further, showing that the leg motion creates spinning swirls of water (vortices) moving in the opposite direction to that of the bug. They even calculated that the momentum of the water moving in these vortices (approximately 1 g cm/s) nicely corresponds to the resulting momentum of the strider, but in the opposite direction. And, this is exactly what we do in our sculls (although at a much larger scale); the scoop-shaped blades are designed to create vortices of water that move opposite to the direction of the boat, as you can see in the overhead photo here. The rower is, as always, facing the back of the boat.
But water striders have six legs: what are the others doing during each stroke? An elegant study from 2018, reported in the Journal of Bionic Engineering by a group from China, coupled high-speed cameras with light sensors to analyse the forces applied by each leg. They used the “shadow method” ‒ by analysing the size and motion of the shadows cast by the strider’s legs, they could track position, velocity, acceleration, and applied force. From this they concluded that the two smaller front legs lift up during the stroke to minimize drag and then return to the water to help support the body weight as the sculling legs are lifted out after the stroke. The two rear legs act as rudders to help steer while also supporting the weight. All this revealed by watching some shadows dart across a screen in their laboratory!
Could they really tell how hard the legs were pushing just by measuring the size of each shadow? It sounds crazy, but it holds up (no pun intended) …. when they added up the supporting forces for each of the six legs, the total matched the force of gravity acting on the insect based on the mass measured by putting their subjects on a teeny, tiny electronic balance.
These little creatures are optimally tuned to living life at the boundary between air and water: small enough to be supported by surface tension, able to apply the maximum amount of force in their sculling stroke to accelerate quickly without breaking the surface, and incredibly agile when leaping straight up into the air by rotating their legs just so to dynamically match the deformation of the water surface as they push off. Incredibly coordinated actions, all occurring within fractions of a second. So, if you’re looking for me around 6 am most days during the pandemic, I’ll be out taking a few lessons from my friends, the striders.
*Rowing is the general term for the sport, which consists of boats that have two oars at each seat (sculls) or one oar at each seat (sweep boats). Sweeps come in pairs, fours, and eights. Sculls exist as singles, doubles, and quads. Our club is strictly sculling; the Guelph Rowing Club at the other end of Guelph Lake has both sculls and sweep boats.
The Hydrodynamics of Water Strider Locomotion, D. L. Hu, B. Chan, and J. W. M. Bush Nature424 663 – 666 (2003) DOI 10.1038/nature01793
Jumping on water: Surface tension–dominated jumping of water striders and robotic insect Je-Sung Koh, Eunjin Yang, et al, Science 31 Jul 2015: Vol. 349, Issue 6247, pp. 517-521 DOI: 10.1126/science.aab1637 https://science.sciencemag.org/content/349/6247/517
Propulsion Principles of Water Striders in Sculling Forward through Shadow Method, Lu, H., Zheng, Y., Yin, W. et al, J Bionic Eng15, 516–525 (2018). DOI 10.1007/s42235-018-0042-8
Science Twitter is a great place – for education and entertainment. This ‘cyanobacteria meme’ was tweeted by Jaida Elcock, also known as @soFISHtication, on June 15, 2020, and quickly racked up more than 1000 retweets and 5000 likes. As a physicist with a somewhat sketchy memory of first-year biology, I felt like I needed a bit of a refresher on the whole photosynthesis thing. Next thing I know, I’d fallen down a fascinating rabbit hole, learning a ton about some very cool research into generating electricity from biophotovoltaic cells. But, first, we need to back up a bit.
I freely admit that I fall into the naïve category of “everyone” here in thinking that trees and greenery are the suppliers of our oxygen. Or, I should say, I thought that, until this tweet led me to discover that photosynthesizing trees and land-based plants actually only provide about half of our oxygen. The other half comes from phytoplankton, an eclectic mix of (mostly) single-celled creatures that live in fresh and salt water (see illustration at the top). Cyanobacteria are just one form; collectively these organisms can be thanked for not only producing the air we breathe, but also for forming the foundation of the aquatic food chain.
Now that we are all in on @soFISHtication’s joke, you may be wondering how physics enters this story. Don’t get me wrong, I’m always happy to learn something new no matter what the subject, but my physicist tendencies draw me toward physical systems and applications. So, the papers that grabbed my eye when digging into this topic were all about the possibility of harnessing the photosynthesizing power of these teeny little organisms to generate electricity, in a nascent field called biophotovoltaics. When cyanobacteria use sunlight to form sugar and oxygen, there are steps along the way that generate electrons. The idea is to intercept some of these electrons and send them into a connected electrical circuit, thereby generating a current out of sunlight, carbon dioxide, and water. It really doesn’t get much greener than that in terms of electrical generation – microorganisms doing what microorganisms do, but providing us with a little bit of electricity as a by-product!
And when I say a little bit, I do mean a little bit. The devices that have been built so far have peak currents that are measured in microamps, which means that biophotovoltaics are not going to single-celledly solve the world’s energy problems. But, as with any young field, there are rapid developments occurring to improve both the overall efficiency as well as the total output of these systems. One paper published last month in Nano Letters by a team from South Korea coupled cyanobacteria to a nanoscopic structure consisting of gold (Au) particles and zinc-oxide (ZnO) rods. Their setup was designed to expand the range of light frequencies that could be converted to electricity, as well as to amplify the signal from the organisms.
Unlike conventional solar-powered devices, biophotovoltaics (BPVs) generate current both when the light is shining and when it isn’t, since electrons are generated during darkness from a chemical reaction involving the sugars formed by photosynthesis. And, although it almost sounds like science fiction, a British team reported in Nature Communications in 2017 that they had successfully produced a BPV using an inexpensive commercial inkjet printer to print a ‘bio-ink’ of cyanobacterial cells onto a carbon nanotube conducting surface. The device provided enough current to generate flashes in a connected LED light, suggesting that their paper-based printed BPV could work as an environmentally-friendly power supply for biosensors that only require intermittent bursts of energy. Printing BPVs is certainly a tantalizing hint that this technology could scale, with these authors suggesting the possibility of “bioenergy wallpaper” in our future.
As I said at the beginning, this particular rabbit hole has been a fascinating exploration into a world I knew nothing about. These studies really did blow my mind: fabricating devices that extract electrons from individual living cells is truly a technological marvel. I’m looking forward to following this work in the future and learning much more about the microscopic but mighty cyanobacteria. Thanks Twitter!
Electricity generation from digitally printed cyanobacteria (2017) Marin Sawa, Andrea Fantuzzi, Paolo Bombelli, Christopher J. Howe, Klaus Hellgardt & Peter J. Nixon Nature Communications volume 8, Article number: 1327 (2017) https://www.nature.com/articles/s41467-017-01084-4
Biophotovoltaics: Green Power Generation From Sunlight and Water (2019) J. Tschörtner, B. Lai, and J. O. Krömer Frontiers in Microbiology 10:866 doi: 10.3389/fmicb.2019.00866