Bios Megafauna

This weekend I revisited Bios Megafauna, another one of Phil Eklund’s games (I previously reviewed Bios Genesis on this blog and here's a session report with pictures). I played 12 games back in 2012, and then it sat in my shelf for the next 4+ years. Megafauna is set during the exciting transition from the Mesozoic to the Cenozoic eras. It was a time when dinosaurs ruled, only to be replaced by mammals as cataclysmic events caused large swings in the environment. Supercontinent Pangaea broke up giving rise to the Atlantic Ocean. In all this turmoil, plants and animals continue to evolve and adapt. Less fit species are replaced by newcomers, while other older species adapt to fend off competitors edging into their ecological niche.

The game board depicts North America in the early Mesozoic. Empty squares represent potential habitats where biomes can take root. There are two types of biomes, marine and terrestrial, that can support suitably adapted herbivores. Carnivores can find a niche in biomes where they find suitable herbivorous prey. Above is a snapshot of my most recent game in progress. You can see a lycopod meadow in the lower right, suitable for Insectivores (indicated by the capital “I” on the tile). Players represent either a dinosauran or mammalian dynasty that could potentially lead to present day fauna. In the three-player game below, red is the archosaur that led to crocodiles and birds, green is the diapsid ancestor to lizards and snakes, and white a two-tusker synapsid (now extinct).

Since this is the time of the Megafauna, creatures can grow large. Unfortunately there aren’t big dinosaur pieces. Size is tracked on the board as shown in the upper half of the picture below. Red has two different smaller species, while the white two-tuskers are quite large in the two-ton range. The cards below have two functions. They can be “purchased” by players looking to expand their DNA pool or create new genotypic progeny. In the bottom left, the Seed-Cracking Bill adaptation can provide a herbivore access to (H)usker niches. The Sculling tail in the bottom right, provides (M)arine adaptations. These letters represent DNA adaptations present in a species allowing them to eat or move in appropriate biomes. The genotype card (bottom middle) allows spawning a new species type, in this case the ancestors to perching birds or rodents.

When a card is replaced, a new card is drawn from the deck to replace it. This triggers an event. In most cases, the card reads “Draw and place 2 new Era Tiles” which provides new biomes or introduces immigrant herbivores or carnivores. However, some cards trigger a Milankovich event, while others may trigger a cataclysmic event. The lower left card is “Volcanic acid rain”. It wiped out a number of overspecialized species if they had accumulated too many adaptations. It also caused an increase in the Greenhouse gas level. Below are the two archosaur species roaming the continent when these pictures were taken. On the left is a nocturnal amphibious serpentine creature that does courtship displays and has a switchblade claw. On the right is an amphibious armored spinosaur.

In this game, a number of volcanic eruptions led to an increase in the greenhouse level. Later in the game, the CO2 level went as high as 3200 ppm (although it is 1600ppm in the photo below). If it went any higher, a Hothouse Earth would have ended the game. On the other extreme, there could be a Snowball Earth which would also have ended the game prematurely. This game was eventually won by the archosaurs although there were a fair number of extinctions throughout the game.

Like other Eklund games involving evolution, the gameplay can be brutal. Survival can be difficult, and in most games I’ve played, no one species thrives for very long. As the biomes change, a species that is unsuitably adapted dies. But accumulating the appropriate DNA to eat the flora or fauna can lead to overspecialization. The changing environment wreaks havoc in this case. Human beings, in this sense, are an amazing species. In such a short period of time we have terraformed our own planet to suit our needs, not just to survive, but in some areas to thrive. Other organisms also contributed to the changing environment, but none have done so with the speed of humans. Eklund has a game for that; it’s called Origins: How We Became Human, and was actually published before Bios Megafauna or Bios Genesis. Unlike the two latter Bios games that take 2-3 hours, Origins is more of a 4-5 hour affair.

If you’re looking to pick up a game in the Eklund series, I would recommend Bios Megafauna. Remade as a more streamlined version of its ancestor American Megafauna, it is the easiest and shortest of the three. That’s not to say it is easy. Survival can be brutal. But you get to see if a snakelike archosaur can survive and thrive over millions of years. Would having a switchblade claw help? Would being amphibious and nocturnal help? Eklund games are part-game, part-simulation. If that’s what you’re looking for, and you enjoy delving into scientific minutiae, then you will enjoy Eklund’s games. If you are looking for something lighter that incorporates herbivores, carnivores, adaptations, and climate, but plays in 45-60 minutes, then I recommend Evolution: Climate from North Star Games.

A Crisper Story of CRISPR

The Curious Wavefunction is a science blog I follow. The author, Ash Jogalekar, is a talented writer who combines history, science and philosophy in his thoughtful contributions. This week he reviewed the book A Crack in Creation. Jennifer Doudna, one of the authors, is a co-discoverer of CRISPR technology. She might even win a Nobel prize in the near future. As an aside, Jogalekar often profiles famous scientists including many Nobel laureates – his personal take on these individuals and their accomplishments is very refreshing!

From Jogalekar’s review, A Crack in Creation sounds like a book I will enjoy reading. Except he has done such a marvelous detailed job reviewing it, that I actually feel like I’ve gotten all the major highlights of the book strung together in a coherent narrative. Oddly enough, this makes me unmotivated to go out and get the book. It’s like watching a superb movie trailer that highlights all the best parts. Most movie trailers don’t give you enough of a coherent story – they are a teaser to entice you to pay money to go watch the movie.

Since I’ve been thinking about inventing Potions based on science, the CRISPR-Cas9 system might be an excellent ingredient in a magical brew. By editing the genetic information to control transcription and downstream translation of appropriate proteins, a CRISPR-based potion could imbue a certain permanence to its effects. That’s a powerful brew. However I wonder if this would put the apothecaries and potion brewers out of business. A potion with temporary effects seems so much weaker, except that in many cases you probably only want the effects to be short-lived. It would get very annoying to be invisible all the time or looking permanently like someone else thanks to a Permanent Polyjuice Potion.

Then again, maybe there’s nothing truly permanent in a dynamic physical system. DNA mutates. Cells die and need to be replaced. Even rocks change over time, both physically on the outside and chemically on the inside. Isn’t dynamic change what constitutes life, rather than static permanence? Or should that be dynamic stability? That’s how Robert Pascal and Addy Pross would describe the bridge between chemistry and biology in the evolution of life. They argue that thermodynamically stable systems are a subset of a more general group of persistent systems. They describe the Persistence Principle as “change that takes place in the direction of increased stability/persistence”. I could attempt to summarize a crisper version of their article (“Stability and its manifestation in the chemical and biological worlds”, Chem. Commun. 2015, 51, 16160). But I don’t have Jogalekar’s skill or his persistence. Instead, I’ll stop here to keep today’s post crisp!

Abstraction

If I had read How to Bake Pi before my first college math course, I probably would have gotten a lot more out of it. Eugenia Cheng, a mathematician, gifted writer, and experimental baker, somehow makes the connection between abstract mathematics and real life. In the prologue, Cheng lists common myths about math. One that she encounters a lot: “You’re a mathematician? You must be really clever.” Here’s her written response.

“Much as I like the idea that I am very clever, this very popular myth shows that people think math is hard. The little-understood truth is that the aim of math is to make things easier. Herein lies the problem – if you need to make things easier, it gives the impression that they were hard in the first place. Math is hard, but it makes hard things easier. In fact, since math is a hard thing, it also makes math easier.”

I wish I had thought about math along those lines back in college. Having had a bunch of calculus under my belt pre-college, I was credited with two semesters of calculus and therefore placed into Real Analysis. The first half of the semester was spent on Proof and Number Theory. I had no idea what was going on. I did not understand the point of proof and the seemingly strange arguments being made for things that seemed “trivial”. Except they are not. But I only came to appreciate this later in life. Needless to say I did not take another college math course for credit. (I did sit in on Linear Algebra because I was told it was useful for a Chemistry major, although not required.)

An early chapter in How to Bake Pi is the topic of Abstraction. Cheng describes abstraction as a blueprint. By ignoring some details, one can focus on the key ingredients to bake one’s pi. How does one do that? By looking at the similarities between different things. It also acts to de-clutter one’s thought process. Cheng says it can feel uncomfortable because one is “stepping away from reality for a bit” but it pays dividends when it comes to solving real-world problems as the complexity is added back bit by bit.

Cheng gives many examples of abstraction, connecting the real world to mathematics. My favorite is Road Signs. She writes: Road signs are a form of abstraction. They don’t precisely depict what is going on in the road but represent some idealized form of it.” She shows a couple of road-signs, and you can figure out what they are even if you have not encountered them often.

While actual bridges and mooses/meese might not look like their stylized images, “the benefits of this system are clear. It’s much quicker to take in a symbol than read some words while you are driving. Also it’s much easier to understand.” However, if you were to encounter a more abstract sign such as the “No Entry” (shown below), would you know what it was if you hadn’t learned it beforehand? If you do know it, however recognition is simple and immediate. Also, you’ll tend to encounter these a lot, particularly in a city center with many one-way streets. The principle here: Abstracting that which is common allows you to take in other things that require some degree of complexity and cognition. Driving in a news city can be complicated.

All this reminds me about the use of symbols in chemistry. I am going to quote Cheng but substitute “math” with “chemistry” and her explanation still works well. “Once you know what they mean, the symbols are quicker to take in, and you can reserve your chemical brainpower for the more complicated parts of the chemistry you’re supposed to be focusing on. It also makes the chemistry easier to understand across different languages – it’s surprisingly easy to read a chemistry book in a language you don’t know.” Actually that last phrase isn’t as true for chemistry as it is for math, but it’s somewhat true. As an undergraduate, I had to look up a German paper for an organic synthesis procedure. I was actually able to figure out a chunk of it, and filled in the gaps on names with the help of a German-speaking friend.

In the same chapter on Abstraction, Cheng makes a very interesting point about teaching. It’s all meta. She introduces this first by suggesting the building of a machine to do something rather than doing it by yourself, especially if it is a tedious process that will need to repeated frequently. But “in order to build [such] a machine to do something… you have to understand that thing at a different level. It’s like giving someone directions. When you walk somewhere you know well, you don’t really think about exactly what streets you’re walking on… you [go] instinctively. But when you’re telling someone else how to get there, you have to analyze more carefully how you do it, in order to explain it.” That’s why all teaching is meta. I’m trying to help my students work through a process in their minds, but I can’t think for them. Somehow I have to translate the process through designing appropriate activities and exercises, to get them to see and think chemically the way that I do as an expert in the field. This is not easy. Even more so as students may have a wide range of different misconceptions they have picked up along the way before showing up in my class. It keeps my job interesting and keeps me creative!

I’m only a quarter way through the book, and I’m looking forward to more insights! Meanwhile I end this post with an excerpt from the chapter on Generalization. If this sort of writing tickles your fancy, I highly recommend How to Bake Pi. And get yourself a pi plate!

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Here are [some] “why” questions with various levels of answer. You can ask yourself whether you find each answer inadequate, satisfying, or over the top, to see what sort of level of abstraction you like.”

Question: Why does anyone use a three-legged stool?

a) Because a three-legged stool is more stable than a four-legged stool.

b) Because if you try and put four legs down on the floor, one of them might stick up a bit more than the others, leaving a gap between it and the floor, which means the stool could wobble.

c) Because given any three points in 3-dimensional space, there is a plane that goes through them all. Whereas given any four points, there might not be a plane that goes through them all.

The Hemodote Potion

I am now in the home stretch of my semester with just three more weeks of classes before Finals week. Today, in my non-majors chemistry class we discussed the details of the final project: Designing a Magical Potion. To prepare the students for the project, I had written a Prologue to the project seven weeks ago, and I make occasional references to potions in class sessions. One class was dedicated to talking about drug design, after the students had learned about protein structure and intermolecular forces.

A couple of weeks ago I wrote a full example of what a Final Project would look like. Thus, I invented the Hemodote Potion. Along with this sample, I provided detailed parameters for the project, and in class today we discussed and agreed upon the final due date, and the mechanics of what, when and how to provide me information on their projects. I had included a question on the previous problem set asking the students to list two potions they might invent with a one-paragraph of justification for each.

In class we divided into small groups and batted around some initial ideas of the science and chemistry that needs to be considered, before having a whole-class discussion. Cure for cancer and levitation potions are inherently challenging, but we came up with some ideas for camouflaging, memory-enhancement, skin anti-aging, and more. The best suggestion from a student, which I would never have thought of myself, was a potion that magically and non-toxically dissolves the skin or peel of vegetables and fruits. Just pour the potion on the desired object and moments later you are ready to eat (or cook) the food item!

Here are the required components for the project (per my instructions to the students):

Think of your project as adding an entry to a Potions textbook. Your entry must contain:

1. Name of your potion and the names of the authors contributing to the entry.

2. Background information on why this is a useful potion. Key features of the active chemical substances and how they might interact should be described here.

3. Design Considerations: A detailed section that describes each of the important substances that will be included in the recipe. This is where you justify the proposed chemical interactions you hope to achieve, and how this might interact with the larger scale organism or object to which the potion is applied.

4. Amount Considerations: This is where you show calculations estimating how much of each active substance will be needed.

5. A Detailed Recipe as you might see in a cookbook.

6. A list of potential side-effects or cautions for your potion. This is not just a generic list but is tied to the effects of the specific potion you have proposed.

7. References

There are also certain requirements such as some number of chemical equations and structures, minimum number of active ingredients, and calculations involving masses, moles and molarity. No specialized reagents can be used directly. They must either be synthesized or extracted from a magical creature or plant. Two different font colors must be used to highlight the “creative” parts of the project and the “science-y” parts.

Hemodote is a powerful easy-to-use liquid antidote against hemoglobin poisons such as cyanide and carbon monoxide. I had sketched out my initial ideas in a previous blog post, but here is the more detailed version of the “Design Considerations” section in the full example provided to the students. I have made minor edits removing the figures, and I did not renumber the references since this text is about one page of a four-page document. I have a detailed recipe with calculations and amounts, but since I’m taking on the mantle of an alchemist, I will keep my recipe a secret for now. (My students have seen the full recipe.) Except I can’t resist telling you that I have good reason to believe that mincing and boiling the liver of the Blue Behemoth will provide one of the active ingredients. Enjoy!

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To counteract hemoglobin poisoning, there are two general approaches: (A) Introduce substances that bind cyanide or carbon monoxide more strongly compared to hemoglobin. (B) Provide an infusion of oxygen to reduce or prevent cell death due to the poison.

Two kits used to treat cyanide toxicity are Cyanokit and Nithiodote.⁶ The active agent in Cyanokit is hydroxocobalamin, a molecule closely related to hemoglobin and Vitamin B12.⁷ Hydroxocobalamin actively binds cyanide more strongly than hemoglobin, and thus can scavenge the cyanide away freeing the hemoglobin to bind to oxygen. The active center in hydroxocobalamin is a cobalt ion instead of an iron cation in hemoglobin. Cyanide displaces the hydroxide and binds strongly to the copper center. A natural source of hydroxocobalamin comes from eggs, dairy, and meat.

Nithiodote contains sodium thiosulfate (Na₂S₂O₃) as an active ingredient. This compound can be prepared from mixing sulfur with concentrated lye (or sodium hydroxide, NaOH).⁸ In the presence of Na₂S₂O₃, a natural enzyme in our bodies, rhodanese, converts cyanide into thiocyanate (SCN^-).⁹ While both kits require intravenous transmission in the Muggle world, acquiring the equivalent of hydroxocobalamin from the appropriate magical creature should suffice for an oral potion.

The treatment for carbon monoxide poisoning is to obtain an oxygen infusion.¹⁰ This will also help in cases of cyanide poisoning. Finding a hyperbaric oxygen chamber or an oxygen tank to breathe from can be challenging when the cells in your body are being rapidly depleted of oxygen. One way to quickly deliver oxygen is by using hydrogen peroxide (H₂O₂). It rapidly decomposes into H₂ and O₂ because of the weak O–O single bond in H₂O₂. However H₂O₂ cannot be consumed directly because it is a very strong oxidizing agent and will damage the cells in our body.

Recent scientific work on delivering oxygen to cells in our body is to enclose calcium peroxide (CaO₂) in a polycaprolactone polymer casing.¹¹ Calcium peroxide can be synthesized by heating slaked lime (calcium hydroxide) with hydrogen peroxide.¹²

Ca(OH)₂  +  H₂O₂  -->  CaO₂  +  2 H₂O

Caprolactones are cyclic esters and can be found naturally in flower aromas and insect pheromones.¹³ Using caprolactone as a monomer to form polycaprolactone requires catalysts that are specialty chemicals not found in nature but synthesized by chemists.¹⁴ However, extracting caprolactones from an appropriate magical insect or plant should also provide the catalysts needed to form an appropriate polycaprolactone that will encase the CaO₂ for delivery into the bloodstream.

[6] http://emedicine.medscape.com/article/814287-treatment (Cyanide Toxicity Treatment & Management)

[7] https://en.wikipedia.org/wiki/Hydroxocobalamin

[8] https://www.youtube.com/watch?v=J_IboipV5A8 (Preparation of Sodium Thiosulfate)

[9] https://chemm.nlm.nih.gov/countermeasure_sodium-thiosulfate.htm (Reference to “Effects of thiosulfate on cyanide pharmokinetics in dogs”)

[10] http://www.mayoclinic.org/diseases-conditions/carbon-monoxide/basics/treatment/con-20025444 (Carbon Monoxide Poisoning Treatment)

[11] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3708668/ (Oxygen Releasing Biomaterials for Tissue Engineering)

[12] https://en.wikipedia.org/wiki/Calcium_peroxide

[13] https://en.wikipedia.org/wiki/Caprolactone

[14] http://pubs.rsc.org/en/Content/ArticleLanding/2009/CS/b820162p (Synthesis of polycaprolactone: A review)

Thinking in Pictures

The magazine Nautilus has a series on Consciousness this month. I was drawn to an article titled The Kekule Problem by Cormac McCarthy. The late Friedrich August Kekule was a famous organic chemist, while Cormac McCarthy is not a chemist of any sort, as far as I know. Kekule is known for his elucidations of chemical structure. He was also a pioneer in building the field known as theoretical chemistry (I’m closely related as a computational chemist). But he is best known for elucidating the structure of benzene, in a Eureka moment, by dreaming of a snake eating its own tail. At least that’s how the story goes.

Where did Language come from? That’s the root question McCarthy is attempting to answer. He has an intriguing and speculative hypothesis, rooted in how the unconscious “thinks”, not in words but in pictures. This he calls the Kekule Problem. McCarthy begins with a question: “Why the snake? That is, why is the unconscious so loathe to speak with us? Why the images, metaphors, pictures?”

We think that we think in words, but McCarthy suggests that the “actual process of thinking… is an unconscious affair.” Language is a very useful tool in posing problems and explaining them, asking questions and answering them, but it is a sign-posting tool – one that we use as a breadcrumb to mark our trail. McCarthy discusses evolutionary ideas of language, making comparisons to other biological evolutionary processes. But he still feels that nagging questions remain, perhaps even ones that cannot quite be put into words.

Could dreams be the gateway into the process? McCarthy writes: “Of the known characteristics of the unconscious its persistence is among the most notable. Everyone is familiar with repetitive dreams. Here the unconscious may well be imagined to have more than one voice: He’s not getting it, is he? No. He’s pretty thick. What do you want to do? I don’t know. Do you want to try using his mother? His mother is dead. What difference does that make?” This is, of course, a caricature personifying the unconscious speaking in a language and using words. But McCarthy is a writer, and that’s how he communicates this idea to us. Although if we were in Star Trek world, perhaps a Vulcan mind-meld may achieve the wordless communication.

As to the evolution of language: “[Language] would begin with the names of things. After that would come descriptions of these things and descriptions of what they do. The growth of languages into their present shape and form—their syntax and grammar—has a universality that suggests a common rule. The rule is that languages have followed their own requirements. The rule is that they are charged with describing the world. There is nothing else to describe.”

I’d like to ask John McWhorter what he thinks about this. Three weeks ago I read The Language Hoax, which, in my opinion, thoroughly and successfully debunks the popular and speculative versions of the Sapir-Whorf hypothesis. An example of such Whorfian thinking is that if a language has different words for the color blue, speakers of that language physically perceive blues differently. Thanks to The Arrival movie, sci-fi has run with this idea and created a masterful narrative of dreams, aliens, and the blending of the conscious and unconscious in a time-travel story. It’s very clever and very effective. McWhorter discusses why such ideas are so popular despite evidence against them, and his book was written before the movie was released. He has an even greater uphill task now.

McCarthy discusses the idea that the unconscious “thinks” or narrates in pictures. Pictures have the advantage of simplicity-in-complexity. A picture is rich in structure and content, and can potentially be recalled in their entirety much more easily than an essay of a thousand words. “The log of knowledge or information contained in the brain of the average citizen is enormous. But the form in which it resides is largely unknown. You may have read a thousand books and be able to discuss any one of them without remembering a word of the text.” The unconscious also resembles a parable, a tool for teaching and learning; it requires the conscious to chew and churn over to learn its secrets. Is this why oracles and prophets receive their knowledge in dreams?

I’ve been thinking a lot about pictures lately. They are indispensable, in my opinion to grasping the unseen world of chemistry at the molecular level. The representations are artificial in the sense that they represent models we can see and touch to get a “feel” for how chemistry works. Videos add a dynamic layer of representation – crucial for chemistry unless you’re at zero kelvin. Even then, the atoms still “move”. It seems fitting that pictures and representations help us handle the cognitive load as we learn the “language” of chemistry. Imagine trying to learn chemistry in a purely narrative text. I’m not sure I could.

But the image of the molecule is not the thing-in-itself. It simply provides a facet, a signpost, a breadcrumb on the trail. Kekule’s idea of the ring isn’t exactly what the pi-electrons are doing in benzene. We don’t really no what the electrons are doing, but we no they are delocalized, and we can measure a ring current. In General Chemistry, we teach students how to draw Lewis structures of molecules including their resonance structures. It is difficult to describe exactly what a set of “good” resonance structures represents – the true structure is not exactly the average of the set, even though I tell the students to sort-of-think in this way, at least when we discuss properties such as bond lengths, formal charges, and dipoles.

Perhaps magical spell-casting power is mediated through pictures. I’ve speculated about this, at least in terms of chemistry. The words themselves are perhaps simply an anchoring channel. They do not need to be verbalized, but maybe a word acts as a signpost in the organization of mental-thought power. Maybe thinking in pictures should be a key curricular piece in a Hogwarts education. I recommend “Arts for the Magical Arts”! My personal challenge (likely to remain unfulfilled): Can I draw a picture to represent the thousand words in this essay?

University Admissions: Arcane Edition

Over Christmas break, I read The Name of the Wind by Patrick Rothfuss, reviewed by my sister in a blog post last month. I enjoyed the book, especially the parts that delve into how magic works. Rothfuss has a more scientific approach to magic, which follows more consistent rules compared to the world of Harry Potter.

Given the recent long Easter weekend, I was able to binge-read the second book in the series, The Wise Man’s Fear. It was long – close to a thousand pages. In much of the sequel, the main protagonist Kvothe, takes some time off from his university studies to visit faraway lands and pick up new skills. This story arc is common in fantasy literature, but I personally found it less interesting. Academic that I am, I prefer the university-related parts of the story because they are often strewn with tidbits about how magic works.

Instead of reviewing the book in today’s post, I will just concentrate on one aspect of Kvothe’s world: university admissions. The process there is very different from the universities of our world. Are there lessons we can learn? Students at Kvothe’s university are training to be arcanists. The word arcane carries the connotation of mysterious, secret, and knowledge known by only a small select group. This is fitting for a school of magic. The alchemists of old, living in an era where magic and science blended, pursued arcane knowledge and were secretive about their “discoveries”. So technically, if I was a true arcanist, I should not share any part of the university admissions process. But I’m not, so here goes.

First, Admissions is not a single event. It takes place at the beginning of every school term. The main point of Admissions is to determine your school fees (often referred to as “tuition” here in the U.S.). The decision of how much a student has to pay is supposedly dependent on the performance of an oral exam held during the Admissions period that lasts several weeks. I say “supposedly” because while prior knowledge and talent is a factor, personal rivalries, politics, and idiosyncracy also enter into the process.

Here’s how it works. First the student draws an “admissions tile” by random lottery indicating the day and time of his/her oral exam. If the student feels that (s)he needs more time to prepare for the exam, there is a bustling marketplace to trade admissions tiles for money and/or other favors. At the oral exam, the nine Masters of the university (equivalent to Professors) take turns to ask you any question(s) they desire. Ideally, they take into account your level of learning. Some do. But if you have offended a Master in some way, you are likely to be asked ridiculously difficult or impossible questions. On the other hand, a Master trying to help you out might lob some standard or relatively easy questions. A Master may even choose not to ask you any questions. After all questions have been asked, the Masters determine the school fees for that term. If you can pay it by the end of the admissions period, you continue. If not, you can take a leave of absence or even drop out. There is no negotiation by the student. It’s unclear if there is an appeal process.

In a perfect world, with wise Masters who cared about student-learning, and who didn’t stoop to politics, bitter rivalry, personal favors, or irrational idiosyncracies, one would expect that school fees would be set fairly taking into account ability to learn magic and ability to pay. My reading suggests that the decisions are not totally meritocratic and that financial need is taken into account. And the story wouldn’t be as interesting without the politics and rivalry. No mention is made of how much needs to be collected from admission fees to keep the university running. Perhaps a truly talented arcanist can turn base metals to gold, so there is no need. Or perhaps no one has successfully made a true philosopher’s stone.

The idea of tying admissions each term to satisfactory progress isn’t a bad idea. But it’s not novel. Most universities have some rule where a student finishing a term below some GPA cutoff goes on academic probation. A failure to get grades back up may result in the student being asked to leave. I like the idea of oral exams that include my fellow examiners for a more holistic approach, but this could only work if the number of students was relatively small. A small rich exclusive college could potentially do this. Tying school fees to performance is trickier, but not unheard of. Merit-based scholarships do a similar thing. Need-based scholarships help to offset the costs for capable students with only modest financial support otherwise.

Having an oligarchy of “experts” decide on the fees? I don’t know what qualifies the Masters to do this – they could certainly test for academic competency in their subject area, but how does one weigh this against the financial need of the student and the economic needs of running the university? This looks crazy today, but one to two hundred years ago when many small colleges were first started, there were a small number of faculty-administrators who taught the classes but also ran the institution. The increasing size and complexity of tertiary institutions has forced a division of labor, perhaps for reasons of efficiency. Perhaps there isn’t really anything arcane about admissions to the Arcane University. It mirrors what we might have done in a different era although it looks strange today.

Revisiting Johnstone's Triangle

In an earlier post discussing the heavy cognitive load imposed in learning chemistry, I described the ways in which practicing “expert” chemists fluidly move among the macroscopic phenomena, microscopic atomistic models, and chemical symbols. On the other hand, the “novice” student attempting to wrap his or her brain around all this three-legged stool of chemistry is a monumentally difficult task. This “iron triangle” problem was articulated by Alex Johnstone many years ago in a series of articles. Chemical educators often refer to it as Johnstone’s Triangle.

Participating in events with a science education expert in March led me to revisit Johnstone’s triangle. In today’s post I will highlight two papers, one is a reflection by Johnstone with a provocative title: “Teaching of Chemistry – Logical or Psychological?” that kicked off a new journal (Chem. Educ. Res. Pract. 2001, 1, 9-15). The other by Keith Taber revisits the Johnstone Triangle with some new insights that usefully refine the model (Chem. Educ. Res. Pract. 2013, 14, 156-158).

First, let’s look at Johnstone’s article. It’s hard to beat the opening line of the introduction: “I should like to begin by recording a number of depressing facts about chemical education in the last forty years…” I won’t do justice paraphrasing, so here’s a snapshot of his “unpleasant observations”.

Point #1 is interesting. Were students almost everywhere opting out of chemistry back in the 1990s? Possibly, although my particular department has the opposite problem – we have too many interested students. In chatting with my colleagues from other parts of the country who are mostly at small liberal arts colleges, we are seeing stable numbers or growth.

Point #3 is depressing. Have chemistry educators “solved almost none of the problems in chemistry teaching”? I admit that students still have misconceptions with the mole, chemical bonding, and more – but I’d like to think I’m getting better at teaching these concepts and I’m seeing fewer problems. But maybe I’m deluding myself with anecdotal selective memory.

Point #6 is similarly depressing. “For normal daily living most people believe that they need no knowledge of chemistry, and maybe they are right.” In my Chemistry and Society class, I am constantly making reference to where chemistry shows up in the everyday lives of my students, but maybe I’m not really making any impact in changing that belief. Perhaps the students just humor me because I’m the instructor who “controls” their grade. Maybe subconsciously I know this, and perhaps I’m trying to sell the importance of knowing chemistry to a fictional magical community!

I have personally experienced Point #7 multiple times. “I was never any good at chemistry” and “I never understood [fill in the blank with some chemistry-related word]” come up all the time. I’d like to say I was never good at English Literature or Business Accounting or whatever else the other person might be good at, but I’m not sure what purpose this serves. In fact I’ve done this on several occasions, only for the conversation to drag into why chemistry is clearly more difficult than [insert other subject here]. But maybe my new acquaintance is on to something. Maybe chemistry really is more difficult conceptually than all these other subject areas. Maybe Johnstone’s Triangle is a cognitive killer.

Johnstone’s reflection is about how to harmonize the internal logic used by chemistry experts with insights from psychology into how novices learn, hence the title of his article. Much of what he discusses is material that I have previously read from the cognitive science literature – there’s information processing, perception, working memory, long-term memory, cognitive load, and how to make things stick. He then presents the chemistry issues illuminated by his famous triangle and its implications in teaching: the cognitive overload of working memory when all three aspects are used simultaneously at an introductory level. The learner has trouble finding a good way to properly embed this into long-term memory, at least in a way that makes conceptual chemical sense. Often the attempt results in the building of a framework riddled with misconceptions.

Johnstone makes some drastic curricular suggestions. Getting away from using hybrid orbitals to rationalize structure is one I wholeheartedly agree with, at least at the introductory level. He also suggest introducing the mole first only as an extensive property, and to make sure students really understand it, before moving to intensive properties such as concentration in solution (or molarity). Johnstone suggests starting at the macroscopic level with metals and not salts. This is one I hadn’t quite considered, but it has merit and I’m going to think about this a bit more when I rework my Fall semester General Chemistry I class sometime over the summer. (Read his article if you’re interested in his argument.)

Before I get to Taber’s paper, I’d like to quote another sobering zinger from Johnstone: “It may be that inorganic chemistry and the emphasis on acid/base titrations are historical artifacts of the time when chemistry was mostly analytical. One could be cynical and say that we keep stoichiometry in a prominent position because it is easy to set exam questions on it and easy for students to fail! A large number of practicing chemists never balance an equation or do a titration. We know this causes all kinds of trouble for students. Why do we persist with it and cause students such anguish?”

Taber revisits Johnstone’s Triangle but argues that the Symbolics corner is the triangle operates differently from the Macro and Sub-Micro. The problem with the triangle, Taber argues, is that these labels “lead to two areas of confusion: (1) confusion between two possible foci for the macroscopic: the phenomena studied in chemistry, and the conceptual frameworks developed in chemistry to formalise knowledge about those phenomena; (2) confusion over what is meant by a symbolic ‘level’ – how it fits in an ontology with ‘macroscopic’ and ‘submicroscopic’, and how it relates to notions of their being three different representational levels.”

The challenge to the student beginning to learn chemistry is that “the key macroscopic concepts only begin to make sense… in terms of the submicroscopic theoretical models… So in learning chemistry, students are indeed usually asked to coordinate learning about the subject at two very different levels: in terms of the observed phenomena reconceptualized at the macroscopic level, and in terms of the theoretical models of the structure of matter at the microscopic scale.” Taber has a very useful diagram (below) that illustrates this issue. The old Macro has two parts: events in the external world perceived as phenomena and macrosocpic level theoretical models. Both interact with the Submicro level in different ways.

Taber thinks, and I agree with him, that the Symbolics, while clearly useful and essential as a “language for communicating and representing chemical concepts”, are not on the same domain-level as the items in the diagram above. What the symbolic language does is facilitate between the macro and micro concepts through various forms of representation. Again, Taber provides a useful diagram (below).

Taber revisits the issues of information processing brought up by Johnstone with the following example. If you showed the following net chemical equation briefly to someone and then later asked for a recall, the results would vary immensely.

H₂SO_4(aq) + 2NaOH_(aq) --> Na₂SO_4(aq) + 2H₂O_(l)

This is a typical reaction you will see represented in an introductory chemistry class. In my first year of chemistry at the secondary school level, I had no idea what any of this meant. I would have a hard time recalling it if I had ten or maybe even thirty seconds to stare at it. Now, you can flash it to me for two seconds, and I can reproduce it perfectly. And this is not because I’ve used it many times as a teacher. You can pick a different acid-base reaction that I don’t commonly use and I can likely perform the same trick.

Reflecting on my own thought process, I would see an acid-base neutralization reaction to produce salt and water. My knowledge of salt solubility would allow me to figure out the states of matter. I can balance the reaction as I recall it. And I can figure out the chemical formulae of everything without explicitly memorizing what I see. In fact, all I need to know is the salt for any simple acid-base reaction (and if CO₂ gas is produced for carbonates and bicarbonates). Just seeing the “Na” and “SO₄” and recognizing the reaction type is sufficient for me to reassemble everything fluidly. My memory is hardly taxed by this activity.

Taber discusses the importance of scaffolding the material while paying close attention to the cognitive load we are demanding of our students. Effective teachers can help students build the necessary conceptual framework piece by piece by thinking carefully about how the chemistry curriculum is being “delivered” and reinforced. I won’t go into the details here but it’s an article well-worth reading, and one I should keep in mind as I continue to work on my teaching.