Fun With Shadows on the Winter Solstice

Walking back from an errand yesterday morning, I was startled by the length of my shadow, almost 10 meters long. Yesterday, the first day of winter, marked the pinnacle of shadow-length. From today onward, as the days will begin to lengthen, as solar angles become more generous, concentrating solar radiation on less area, the march towards spring begins and shadows will shorten.

For a variety of reasons, on any day the halfway point between sunrise and sunset is most often not exactly 12 PM  (It will only be so, after adjusting for daylight savings time, for a couple of days in January and for part of July and August). The so-called solar noon yesterday occurred at 11:52 PM at our longitude and latitude in Montreal, Canada. Like most people,  I made sure I was out in the cold, standing upright on my deck with a tape measure to determine the length of my shadow.

At that time, my 75.0 inch frame, including the one inch hat, cast a shadow 196 ± 2 inches in length. (Using the actual solar angle corrected for atmospheric refraction  it should have been a bit over 194.7 inches).shadows

Using the fact that at a point directly south of us along the Tropic of Capricorn at a latitude of 23.5º South, the sun is at the zenith, so no shadow is cast. This is a situation similar to what Eratosthenes used to estimate the circumference of the Earth. But here we could also use the alternate and equal angles to derive an expression for latitude. Substituting h = 75.0″ and the measured shadow length = s = 196″, Montreal’s latitude works out to be 45.6º, pretty close to its accepted value of 45. 5º.

The nice thing about measuring the shadow at solar noon is that since the solar angle changes very slowly around midday, the shadow-length is relatively stable for several minutes. At about three in the afternoon I went out and measured my shadow, which was much longer than what was of course the shortest shadow of the day at solar noon. Fifteen minutes after 3 PM, the shadow had lengthened considerably. This not only happened because the sun does not sweep across the sky at a constant rate, but also because the tangent ratio is more sensitive to changes in smaller angles that occur shortly after sunrise and before sunset. Here is a plot to make what I just pointed out more obvious:


If you enjoy these types of experiments and calculations, and you want to verify your results, there is a great spreadsheet online with all sorts of astronomical calculations. They are set up so that you could easily adapt them for your own space and time coordinates. It is made available at no cost by the NOAA Earth System Research Laboratory.  Using their formulas, here is a graph of maximum solar angles I created for all days of the upcoming year for Montreal , Canada. As elevation angles increase, it’s not only shadows that get amplified. Ultraviolet rays also intensify, and knowing which months of the year receive the most helps us take precautions for our skin’s sake.


Life at the End of Quantum Tunnels

Recently a biochemistry student told me that her classmates looked like they had seen a ghost when their professor seemingly took a left turn from a lecture on cellular respiration and started to discuss quantum tunnelling. But this 90-year discovery keeps surfacing in different contexts, reminding us that without the tunnelling effect, there would be no life in the universe.

Part of the lecture focused on iron–sulfur clusters, which play a role in the oxidation-reduction reactions of mitochondrial electron transport. The clusters are part of four protein complexes that sequentially shuttle electrons. The latter are ultimately gained from the breakdown of food molecules and are destined for oxygen. In so doing, protons are consumed inside the mitochondrial membrane while others are pumped out, creating a potential difference that helps motor the synthesis of adenosine triphosphate (ATP). Then ATP goes on to facilitate a host of energy-requiring reactions that keep an organism alive.

Each green arrow represents an electron jump due to quantum tunnelling.

But each time an iron cluster transfers an electron, it does so against a potential energy barrier. How does it do it? Because of the wave-like properties of a tiny particle like the electron, when it’s up against a thin-enough barrier, such as the 2.2 to 3.0 angstrom gaps (0.22 to 0.30 nanometers) shown in the diagram, there is a small but non-zero probability that the electron will be in the gap, and more importantly, also beyond it.  The best way to convince yourself that quantum tunnelling is physically possible is to go through the math and physics, and if you’re interested, it’s found here.  The author does not show every tedious algebraic step, but if you get stuck, I will gladly help in the comments section. It’s great fun while the laundry is being done.

Life involves a struggle against entropy made possible by a continuous energy source. For the planets and presumably moons that harbour life, the most important energy source is fusion from the sun. If you are like me in that you once assumed that the prodigious gravitational force at the core of a sun could provide hydrogen atoms with sufficient energy to overcome Coulombic repulsion and bring about fusion,

Image credit: E. Siegel

then you were also incorrect. It turns out that the kinetic energies are too small by a factor of 1000. So how does fusion take place? Like electrons in iron clusters, hydrogen atoms, although more massive, are small enough, and thanks to gravity, close enough to overcome the thousandfold barrier working against them. So quantum tunnelling is ultimately working with gravity to make stars shine.

The fact that tunnelling probability decreases steeply with lower thermal velocities extends the duration of smaller stars, those weighing less than 1.5 solar masses. This is important in that it gives life enough time to evolve in solar systems with appropriate conditions. One of the prerequisites of life, we imagine, is the presence of water on the surface of a moon or planet. Whether water is out-gassed or brought in via a comet or asteroid, it has to be first synthesized in molecular clouds according to this reaction between molecular hydrogen and hydroxyl radicals:

OH + H2  →  H + H2O

The extremely cold temperatures combined with adsorption on dust particles create boundaries small enough for quantum tunnelling to allow the production of molecular hydrogen from its atomic counterparts. There is even evidence that the hydroxyl reaction itself benefits from the same phenomenon.

From deep space back to our bodies, can tunnelling cause unwelcome changes in the DNA molecule? In the double helix or “twisted ladder” of DNA, each nucleotide of one strand of the ladder is attracted to its complement on the other strand by means of a hydrogen bond. A hydrogen bond consists of a lone pair of electrons from one nucleotide attracted to the hydrogen bonded to an oxygen or nitrogen atom of the nucleotide on the other side of the strand.

from Modelling Proton Tunnelling in the Adenine–Thymine Base Pair
A. D. Godbeer , J. S. Al-Khalili * and P. D. Stevenson

But there is a small possibility that the proton (hydrogen without electrons) can overcome the potential energy barrier and end up bonded to the hydrogen-less atom on the other strand. If the effect would be common enough, it could lead to a mutation. It should be noted that this a very active area of research and these authors have concluded that, at least in the adenine-thymine base pair, tunnelling does not occur. Less controversial is the ideas that quantum tunnelling plays a key role in the repair of DNA from ultraviolet damage, specifically in the electron-transfer needed to undo the dimerization of pyrimidines.

If those shocked biochemistry students read this blog, I am not sure that it would erase the “seen-a-ghost” expression from their faces. As educators we don’t often empathize enough with their survival-mode of trying to focus on the “essentials” that will get them through a given course. Quantum tunnelling and quantum phenomena are central ideas, but grasping them rests on an above average foundation of mathematics, physics and chemistry concepts. Is it realistic to assume that most biochemistry freshmen have already acquired that? We have to be patient, fuel them with enthusiasm and make sure that we don’t muddy the waters of key concepts with too much content in our courses.

Other Sources:

Poor Educational Tools: memes of the smartphone and social weed-ia

With a well developed craft, imagination and proper tools, a good chef can cook a delicious meal from any palatable ingredients. While teaching I often regarded different technologies in the same light. The nature of the technology supposedly did not matter. How it was used—that was the key. But I was being naive. A meal could be tasty but not necessarily healthy–the ingredients do matter; so does the technique. Cooking over charcoal introduces carcinogens in food. Similarly, a set of educational activities based on the use of Facebook or other medium can be appealing and popular but will not necessarily help students in the long run. I also contend that social media is a risky way of keeping up with current events, not to mention that it’s a poor prosthesis for human interaction.

There are many ways of generating electricity. Although every method, when applied on a mass scale, has ecological impacts, some technologies are far less harmful than others. That’s quite obvious to most people. Yet it seems far less obvious to people that the same applies to educational tools. Some have a greater tendency to become invisible, not to become an end in themselves and not to take over the ultimate goals, including broadening the horizons of the child, so he can appreciate and add to the viewpoints of a wide variety of people from gardener to plumber, from programmer to poet, from scientist to athlete and from musician to humanist.

Smartphones, especially when they are used almost exclusively with social media, do not fall into that category. Far too many people access the internet exclusively through such devices which prioritise immediacy for the user. Their small screens help make long written essays and the presentation of evidence surrender to short videos, propagandistic images and “memes”. It’s ironic that the  word was originally coined to represent an idea that would survive the individual. Yet currently, to most people, a meme now means a popular “visual message” that spreads through the internet.

Facebook in conjunction with the smartphone is an optimal tool for advertising the ego and consumer items via the transmission of “memes” and other visuals. These serve little more than reinforce prejudices and either oversimplify or totally distort the truth. Twitter is no better, basically insinuating that the world is too busy to read more than 140 characters at a time, and of course it too spreads memes like a field of dandelions disseminates cloned seeds.

In a world where social issues are complex and most people are too caught up in work, child-rearing and over-consumption-cycles to get a good grasp of them, the meme tempts us like any other apparent shortcut. And various organisations are all too happy to oblige. Here is an example of a sneaky meme from ACSH (American council of Science and Health)  and RealClear Science in March 2017 that fooled many people into thinking they were receiving useful advice on which media provide the most unbiased science reporting:ACSH-RCS infographic v8

Although I have criticised Scientific American for recently increasingly relying on more articles from journalists than scientists, National Geographic, Discover, Wired and BBC are far more guilty of the practice. So by what standard is Scientific American deemed to be less reliable than the other four? Ditto for placing The TelegraphForbes and Fox News above the New York Times. It turns out that their bias against Scientific American is that they often feature environmental articles and consistently favour alternate energies, which ACSH does not support.

It was a real slap in the face of the infographic ‘s authors when Nature‘s editors, whose main publication received the highest ranking, called it “a curious exercise, and one that fails to satisfy on any level.” In fairness, I should point out that Nature’s patrons also own Scientific American, so they may have been secretly defending their own interests. But a blog by Mark Hoofnagle, a surgeon, ridicules the graphic, exposing one of its creators, the American Council for Science and  Health, as astroturf.  Such groups and think tanks pretend to be part of the consistently shrinking fraction of the internet’s reputable side. Almost invariably, they are funded by a wealthy group of individuals and industries who are out to oppose a grassroots movement . They mount their opposition surreptitiously, under the guise of a consumer information group or individuals representing everyday people. Not to be easily exposed, they usually hire individuals who hold credentials related to what they are advocating. Well-versed in the vocabulary of the field, they can report a fair deal of factual information. But they make sure to produce a filtrate that does not run counter to the often rigid economic and political viewpoint of their sponsors. Almost invariably, the writers share the convictions of their employers, and so it is not uncommon for them to object vehemently to being labelled “shills”.

ACSH is one of many groups who do not want the United States to take action against climate change, all the while claiming that in fact they are not deniers. Their real stance is made clear in the rude article by Alex Berezow “Al Gore: Still Demented After All These Years“. By design, his views invited applause from rabid climate change deniers. In the comment thread, the author and ACSH president, Hank Campbell (who, in odd contrast to just about everyone else on staff, holds no science degree), make no attempts to refute any of the readers’ unscientific responses. Yet from my own analysis of the comments on numerous other ACSH articles,  both Berezow and Campbell routinely dig deeply into the readers’ feedback to trash any views that are not consistent with their unabashed enthusiasm for fracking, nuclear power, synthetic pesticides, Haber-process-made fertilizers, drinking soda, meat consumption, GMOs, e-cigarettes, Ronald Reagan and unchecked, unregulated economic growth. They also have regular commentators who appear to support the ACSH-cause. One such person who claims to be a farmer has somehow managed to find the time to write nearly 9000 comments, suggesting that the person may be another ACSH employee in disguise. Although I have no evidence that it’s indeed the case, it’s well-known that other astroturfing groups often use fake comments and reviews to promote products.

How do memes and astroturfers survive in societies whose individuals are increasingly educated? There is no evidence that the percentage of critical thinkers has increased in recent decades. Public education at the elementary and high school levels continues to suffer as an increasing number of wealthier parents have abandoned their neighbourhood schools and have sent their children to private schools. Even the latter are not immune from what ails the former: grade inflation, subservience to trendy but unproven pedagogical approaches, and an increasing number of K-12 administrators and teachers with inadequate experience and training.

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