Much Ado About Nothing

Why is there something rather than nothing? That’s the existential question asked by Jim Holt in his book Why Does the World Exist? Holt interviews philosophers, physicists and theologians and summarizes their positions while mixing in his own thoughts. I will admit that some parts of the book feel like a drag. Perhaps I don’t appreciate the finer points of philosophy. I find the language-wrangling tedious and wonder if the arguments all turn on sleight-of-word. The sense I get is that it might be much ado about nothing.

 

The idea of Nothing, however, is interesting. I don’t really know what nothing is. No thing, I suppose. The chemist in me thinks of atoms and the void. Without the void, you can’t differentiate things. But is the void nothing? I’m not sure. Quantum vacuum isn’t quite the colloquial use of the word nothing; the vacuum has structure. Mathematically, the empty set is still a set. I’m not sure I can imagine nothing. The closest experience I might have had was under general anaesthesia. I remember nothing.

 

I’ve heard of, or read bits and pieces from, most of the folks that Holt brings up. So I wasn’t surprised by what I read, with one exception. I had not heard of the philosopher Adolf Grunbaum, who thinks that there’s nothing surprising about existence – of our world and more. Grunbaum thinks the question of why there is something rather than nothing meaningless at best, and worse – it sucks up time and energy that could be spent pondering something more worthwhile.

 

Essentially Grunbaum thinks that just because nothingness seems simple conceptually, doesn’t mean it should be given special priority. Nor should it be assigned any significant probability. He argues that simple ideas aren’t necessarily truer than more complicated ones, and uses the example of Thales (who thought water was the fundamental element) versus Mendeleev (who brought some order to the many elements that make up the periodic table). As a chemist, I can say with some authority that the elements are idiosyncratic when you take a closer look. Yes, you can talk about broad trends and the beauty of the periodic table as an organizing principle. But when you zoom in, the elements are an unruly bunch of chameleons, adapting to different environments in different ways. That’s one of the fascinating things about chemistry. The more I learn, the more idiosyncracy I discover.

 

I’ve also been influenced by reading Robert Rosen who makes the argument that the seemingly special simple things that we scientists like to use as our models don’t match complex reality. The models are impoverished mathematically and insufficiently generic. We prioritize the simple, because that’s what we can grasp, but complexity lurks in all the side effects that materialize because our models are too simple. Since I’m partial to this idea, I’m sympathetic to Grunbaum’s argument that the question of existence might simply be much ado about nothing. The practical-bent chemist in me is more interested in what I can do with these atoms of existing matter, and it’s hard for me to see the value in caring about the concept of nothingness. So, while Holt’s book apparently garnered a top-ten in the New York Times book review, I think it might be much ado about nothing.

 

P.S. Ed Yong’s book, which made the 2022 top ten, is however well worth reading!

First Chat with GPT

The release of GPT-4, which has been hailed as a significant improvement over GPT-3 prompted me to finally create an account and see what the hoopla is all about. I haven’t stretched for a Plus upgrade, so maybe I’m still on an older not-the-latest-and-greatest version. Not sure what’s behind the curtain. But I’ll work with what I have.

 

First, I wanted to check if GPT knew anything about me so I asked if it could provide information on Hufflepuff Hippo, and whether it gets anything from my blog. GPT is very polite, and seems to have no info on me.

 

GPT: I'm sorry, but I don't have any information about a "Hufflepuff Hippo." Could you please provide more context or clarify what you're referring to so that I can better assist you?

 

You’ve likely heard about GPT getting things wrong. That’s because it’s about pattern-matching and prediction, so that’s not a surprise. Then again, isn’t part of how humans learn also through pattern-matching and then testing predictions? We don’t know exactly how that works, and it’s likely not the whole story. In any case, since I study the origin of life, I wanted to see what GPT knew about it so I asked it to give me the main theories for the origin of life and rank them. GPT assiduously avoided trying to rank them and kept repeating that there is no scientific consensus. Here’s one of several similar responses when I tried asking in different ways to coax it to give its best guess based on the available evidence.

 

GPT: As an AI language model, I cannot provide a definitive answer to which theory is the most plausible as there is no scientific consensus on the origin of life. Each theory has its strengths and limitations, and the scientific community continues to explore and test multiple hypotheses to better understand how life emerged on Earth. The origin of life is a complex and multifaceted topic that involves many interdisciplinary fields, including chemistry, biology, geology, and astronomy, and it remains an active area of research.

 

So I tried a different tact and asked it about the weaknesses of each theory. GPT duly listed a number of them in general terms, which seemed reasonable. Here’s one of them:

 

GPT: It is challenging to explain how complex organic molecules could have formed under the conditions of the primitive Earth, as the atmosphere was likely reducing rather than oxidizing.

 

I followed up by asking: “Why is it challenging to explain how complex organic molecules could have formed under the conditions of the primitive Earth, as the atmosphere was likely reducing rather than oxidizing? Isn't it easier to synthesize complex organic molecules under reducing conditions?”

 

GPT: You are correct that reducing conditions can be favorable for the synthesis of organic molecules, but the challenge with explaining the origin of life under reducing conditions is that the early Earth's atmosphere was likely different from the present-day atmosphere. The primitive Earth's atmosphere was likely composed of gases such as methane, ammonia, hydrogen, and water vapor, rather than the oxygen-rich atmosphere we have today. Under these conditions, it is still unclear how complex organic molecules, such as amino acids and nucleotides, could have formed. One of the main issues is that the reducing atmosphere would not have provided the necessary oxygen to drive the formation of these molecules. Additionally, some of the most plausible mechanisms for the formation of organic molecules, such as the Miller-Urey experiment, have been challenged in recent years, suggesting that the conditions of the primitive Earth may have been more complex than previously thought.

 

The response is interesting. GPT says I’m correct. Then it provides information about the primitive atmosphere from the point of view of the Miller-Urey experiment. But then it errs by saying that “the reducing atmosphere would not have provided the necessary oxygen to drive the formation of these molecules.” That’s backward. GPT thinks that oxygen is needed to drive chemical reactions, which is true when you’re burning fuels for example, but it’s not generally true.  After more back and forth where I give it more info, I remark: “It sounds like I'm giving you the relevant information rather than the other way around. Is that what's happening here?” GPT responds very politely again about what it can do and how it will try its best to be of help.

 

I’m curious whether it can generate chemical reactions, so I ask: “Can you provide a chemical equation for this experiment that shows how amino acids were formed?” GPT demurs by saying the Miller-Urey experiment doesn’t provide this, so then I ask: “Do you provide chemical equations for any chemical reactions?” GPT is measured in its response.

 

GPT: Yes, as an AI language model, I can provide chemical equations for various chemical reactions. However, the level of detail and complexity of the equations will depend on the specific reaction and the information available. If you have a specific reaction in mind, feel free to ask me, and I will do my best to provide you with a relevant chemical equation.

 

Now let’s try it out based on info from the answers GPT had provided. I ask: “How would CH4, NH3, H2O and H2 lead to an amino acid such as glycine? Could you provide a chemical equation?” GPT provides a bunch of text that I’m not showing here that repeats things you might find from a Wikipedia page, but it also obliges with the following:

 

GPT: Here is an example of a chemical equation that shows one possible pathway for the synthesis of glycine from CH4, NH3, H2O, and H2:

·      CH4 + NH3 + 2O2 → HCN + 3H2O

·      HCN + H2O + NH3 → glycine + CO2

 

Me: “The second equation isn't balanced. Could you balance it for me?”

 

GPT: I apologize for the error in the previous equation. Here's the balanced equation for the formation of glycine from HCN, water, and ammonia: HCN + NH3 + H2O → NH2CH2COOH

 

Me: “Um, it's still not balanced. There are different numbers of atoms of different elements on each side.”

 

GPT: I apologize again for the mistake. Here's the fully balanced equation for the Strecker synthesis of glycine from HCN, water, and ammonia: HCN + NH3 + 2H2O + O2 → NH2CH2COOH + CO2

 

Notice how O2 now shows up as a reactant. And it’s still not balanced and GPT doesn’t actually understand why. But to its credit it did pull up the chemical formula of glycine. GPT can balance simpler reactions and it can tell me the predicted products for HCl or H2SO4 reacting with NaOH. How much chemistry does GPT know? I’m not sure. OpenAI claims that GPT-4 performs much better on the AP-Chemistry exam than its predecessor among other things (see graph below from OpenAI’s website touting GPT-4).

 

Why does GPT behave the way it does? I’ve read a number of articles over the last couple of months about this, and the one I like the most that’s also a quick read is Tim Harford’s “Why chatbots are bound to spout BS”. I like his point that GPT aims at sounding plausible. When pressed for details, that’s when it can deliver nonsense. Its aim is neither truth nor falsity. It says it’s trying to be helpful. Is being plausible helpful? I suppose that depends. I’ll quote the last few sentences of Harford’s article because they’re a good reminder.

 

These simple chatbots [ELIZA and others] did enough to drag the humans down to their conversational level. That should be a warning not to let the chatbots choose the rules of engagement.

 

Harry Frankfurt cautioned that the bullshitter does not oppose the truth, but “pays no attention to it at all. By virtue of this, bullshit is a greater enemy of the truth than lies are.” Be warned: when it comes to bullshit, quantity has a quality of its own.

 

That being said, I think I will go chat some more with GPT. I have some ideas of how I might be able to leverage it as a classroom tool but I’ll need to do more tests to figure out what it can do well and what it can’t. Onward!

Knowledge Base

I finished reading How to Educate a Citizen by E. D. Hirsch, a well-known voice of experience in the world of education. (I’ve read a number of his papers over the years.) This recent book echoes many themes from his earlier work. It’s a swan song reminding the American people that having a shared knowledge-based curriculum is crucial especially at the early levels of primary school. Acquiring more knowledge content then pays dividends as children go to secondary school and beyond. It’s a Matthew effect: To those who have more, they acquire even more. To those that don’t, the gap widens.

 

I’m a proponent of a knowledge-rich curriculum that spells out what students need to know and that sequences the material coherently. This is crucial in chemistry because you can only get to more advanced material if you’ve mastered the basics. There is broad agreement among chemistry educators what these basics should be. At the college level, the content knowledge and its depth are relatively uniform for general chemistry and organic chemistry from one institution to another. Yes, there are some differences, but there is often at least 80% similarity (our rule-of-thumb for deciding whether a similar course from another university will be accepted for transfer credit).

 

Hirsch stresses the importance that this knowledge be common to all students. The commonality of language and concepts allows people from different walks of life to potentially engage in meaningful conversation. There is a shared basis of knowledge that facilitates the communication. When I came to the U.S. as an international student, although I spoke English competently, I did not share similar cultural touchstones with almost everyone else. (I was the only person from my country.) So I observed, asked questions (usually timidly) and started to learn. This is probably why, when I meet people, I often ask them about their background, their family, what it was like for them growing up, and so on.

 

In my home country, I went through what Hirsch would call a Core Knowledge curriculum (that he favors). I honestly don’t recall very much of what I learned if you asked me “What did you learn that sticks out to you?” But in the flow of conversation, things that I learned a long time ago, bubble up when the appropriate context presents itself. With the appropriate triggers, I would likely be a fount of information. It helps that I enjoy learning and I read voraciously as a child. (There was no TV, and I was very blessed to have access to a wide range of reading material – something that cannot be taken for granted where I grew up.)

 

Coming to college in the U.S. was my exposure to a palette-style smorgasbord education. There wasn’t much of a common curriculum, although there were distribution requirements (pick one from Group A, pick one from Group B, etc). I’ve since experienced the pros and cons of setting up a common curriculum. One of the major advantages of the common curriculum is that it provides a shared language of discourse that can pay dividends in subsequent courses. Another advantage is that it strengthened community through that shared experience, even when it was struggling through said experience.

 

Are there things that I think an educated person should know about chemistry? I’d say some Atomic Theory and Chemical Bonding, making a connection between the microscopic and the macroscopic, the Periodic Table as an organizing principle, and what make chemical reactions “go” (i.e., the role that energy plays in chemical reactions). I think students should recognize common vocabulary: that sodium chloride (NaCl) is table salt and that its properties stem from it being an “ionic compound”. I think these basics can be covered at the secondary school level, i.e., I don’t think all students need to take chemistry in college if they’ve seen it before. Then again, the students who take college chemistry (at my institution) have mostly seen some chemistry (albeit at a more rudimentary level). Those that didn’t see any in secondary school are unlikely to take it in college. The Matthew Effect again.

 

Having a knowledge base allows you to appreciate things that would otherwise seem opaque. I’m currently reading some short stories by William Gibson in a genre classified as cyberpunk. It’s not a genre I’m familiar with, and I don’t read much fiction in general or sci-fi in particular. Gibson throws you right into the action, and if you don’t have the vocabulary or various knowledge touchstones, you simply can’t follow the story. There’s no way I would have understood Gibson’s work when I was a teenager. (Back then, I made one attempt to read Asimov’s Foundation and understood very little.) But now, with a knowledge base or more depth and breadth, I thoroughly enjoyed Hinterlands. It’s a superb piece of storytelling that stretches the mind while it immerses you in the feeling of the main protagonist. And it helped that I knew what cargo cult meant. Being able to enjoy things outside of my domain is why I occasionally read about art or poetry. There is no way I could have known how much I could appreciate without acquiring the knowledge base.

Szilard Engine

I’m reading Quantum Steampunk by the theoretical physicist Nicole Yunger Halpern. It’s a book about the intersection of quantum mechanics, information theory, and thermodynamics. It’s also aimed at a broad audience, and couched thematically as steampunk. I have little experience with steampunk as a genre – a setting that imagines modern (seemingly magical) technology within the Victorian steam-engine era. I do have some experience with quantum mechanics and statistical thermodynamics since I teach these topics regularly. I have some but not extensive knowledge about information theory.

 

Quantum Steampunk lays the foundation of its three pillars in descriptive terms and evocative examples. You will not find a lot of equations, but you will find some beautifully illustrated figures evoking the Victorian era that Halpern utilizes to help explain the concepts. I was familiar with many of her examples, but one that jumped out at me was the quantum version of the Szilard engine.

 

We discuss Maxwell’s Demon in my statistical thermodynamics class and the possible relation between entropy and information. The Szilard engine is a thought experiment that pushes the idea behind Maxwell’s Demon a little further. Essentially you start with a box with a few gas particles zooming around. Then place a movable partition that bisects the box such that there are more particles on one side than the other, ideally with all the gas particles on one side and none in the other. (This is easier to do with fewer gas particles in the box to begin with.) If your partition is mechanically attached to something that can do work, then as the gas particles on one side push against the partition, the partition moves and you can extract work from the engine.

 

In a two-particle system, your chances of placing the partition in the middle of the box such that both particles are on one side is fifty percent. This Szilard engine can do work. The other half of the time, you’ll trap one on either side, and there is no net work done. A washout. But the quantum version is where things get interesting, and I had not pondered this until reading Halpern’s book. If your two particles are fermions, you always get the washout (Pauli Exclusion Principle!) but if your two particles are bosons, then because of indistinguishability, there’s a one-third chance you get the washout and a two-thirds chance you have a working Szilard engine. It’s an example of where quantum particles can do more thermodynamic work than classical particles. Pretty cool!

 

I enjoyed Halpern’s description of how quantum computing is different from today’s “classical” computing (which does not fundamentally use superposition). She writes in a way that makes the strange nature of quantum mechanics a little more accessible. I say a little more, because (1) no one really understands quantum mechanics, and (2) given I have some background, her writing felt accessible to me but I’m not sure if a non-scientist would agree. Halpern follows-up her Szilard engine description with the Landauer eraser and thus makes the connection to information and entropy. Or I should say entropies. Turns out there a lot of different ways to define entropy. (My students get a sense of this in my classes at a simple level, and we do briefly discuss Shannon entropy.)

 

Thus, the second thing that jumped out at me was Halpern’s discussion on what she calls “one-shot thermodynamics”. I had not heard about this before. It’s been a while since I’ve talked to a hardcore theoretical physicist so maybe that’s why I was ignorant about it. In classical thermodynamics, we rely on averages. When there are zillions (say, Avogadro’s number, applicable to the chemist) of particles in a system behaving “randomly”, then you will pretty much get the average whenever you make a measurement. That’s because that “average” is maximally probably and overshadows all other configurations. Furthermore, if we assume the system is ergodic, that gives us all sorts of other useful mileage which I won’t get into. But what if you just have a small number of particles in your system? Then things get interesting because there’s a small but practically accessible probability that you could extract thermodynamic work which you wouldn’t dream possible in a larger “classical” system. This becomes relevant in quantum systems, and is an example where quantum mechanics allows you to “bend around the Second Law of Thermodynamics” (in Halpern’s words).

 

I’m not sure what to do with my newfound knowledge yet. Much of it is still theoretical although Halpern provides one example in chemistry related to cis-trans isomerism. I haven’t read the relevant papers. This made me think about adding a discussion of the Szilard engine to my P-Chem class and branch a little bit into information theory. I used to do a little more Shannon entropy in the early days but then I found it confused the students on exams, and I’ve since cut back on it. Maybe I should reintroduce the topic given that A.I. and quantum computing are now widespread ideas that most people have at least heard about and might be curious to learn more. So many interesting things. So little time!

Staying Curious

In the final chapter of his book, Curious, author Ian Leslie makes seven recommendations of how one can stay curious. Like most book written by journalist, each of these comes with anecdotal stories of people who exemplified the particular trait being discussed. I think I am a curious person. Do I have the traits Leslie recommends? Here’s my self-analysis.

 

1. Stay Foolish. Huh? This is how the list starts? It comes from Steve Jobs quoting Stewart Brand’s mantra: “Stay Hungry, Stay Foolish.” The gist is that one should not stay too comfortable with what has worked in the past, especially past successes. Positive anecdotal example provided are Steve Jobs and Walt Disney; the negative anecdote is the Chinese empire in the seventeenth century. Well, I’m a creature of habit. I like to do what works, but at least professionally, I also enjoy constantly tweaking my teaching and my classes and periodically I make a major overhaul. I also like being comfortable, so I rate myself low for this trait.

 

2. Build the Database. The gist is to be hungry for information, but also a connoisseur. Leslie writes: “Great ideas don’t just spring from the moment of the mental effort involved in trying to come up with one. Their roots extend back months, years, decades into their author’s life; they are products of long-formed habits of mind as much as they are of flashes of brilliance.” Well, I read a lot (at least fifty books per year) and reasonably widely. I enjoy getting lost in a good book. And I can hold my own in a conversation on most academic subjects. But I’m not so good at small talk, and I don’t follow sports or music. I’d rate myself as above average in this area with the caveat that my interests are perhaps too theoretical and narrow.

 

3. Forage like a Foxhog. What is a foxhog? It’s a cross between a fox and a hedgehog. The analogies come from Isaiah Berlin who grouped thinkers into foxes or hedgehogs. “Plato was a hedgehog, Montaigne a fox.” The hedgehog focuses on one central big idea, while the fox utilizes a varied bag of tricks. Leslie argues that “in the marketplace for talent, the people most in demand will always be those who offer an expertise few others possess. But having a breadth of knowledge is increasingly valuable, too.” Well, as an academic I do have some extensive and narrow expertise, but I can’t say that few others possess it, and I’m not sure my expertise is in high demand. I’m also poor at marketing what I’m good at. I don’t want people to know so I can go on doing what I enjoy without disturbance. But I suspect I’m more of a fox than a hedgehog. I have a wide bag of tricks for problem solving. Do I forage like a foxhog? No idea. I don’t know how to rate this, probably because I don’t have a particular foraging strategy.

 

4. Ask the Big Why. The gist is that someone needs to ask the fundamental questions to discover assumptions behind why people are saying or behaving the way they do. The anecdotal stories are about being successful negotiators and bridge-builders. Well, I’m good at asking fundamental why questions. Sometimes other people find it annoying. I can be a decent bridge-builder when I feel like it. I’m told I can be a tough negotiator. Leslie makes the useful point that people tend to substitute the harder “why” question with the easier “what” question. I agree. I also have an iconoclastic streak and so asking the big “why” is something that I practice.

 

5. Be a Thinkerer. That’s a cross between thinker and tinker. Benjamin Franklin is the anecdotal star of this story, and Leslie provides multiple examples of Franklin’s insatiable curiosity. Well, I’m a thinker. But I’m a poor tinker. This stems from a neuromuscular issue where my hands shake and I have weaker finger muscles than the average person. I’m lousy with my hands. Thankfully, as a theoretical and computational chemist, I don’t need to be good with my hands. I also don’t do many chemistry demos in class, which I expect students find disappointing, but there’s a good reason behind it. I try to make up for it with lots of enthusiasm and by bringing up the strange quirky ideas of science. My personal rating? Half at best. Probably less.

 

6. Question Your Teaspoons. Wha-a-a-t? There is no spoon. Turns out the anecdotal story to this trait is one I was ignorant about: The Boring Conference. It’s actually interesting how what bores some people (perhaps most) is particularly interesting to a few individuals. Paper clips. Cash registers. How to make “hotel toast”. Leslie also mentions some psych studies I was less familiar with and this piqued my curiosity, particularly the contrast between goal-setting and describing one’s experience doing an activity. Do I see that anything can be interesting if you look at it long enough and hard enough? I don’t know. Do I have obscure hobbies where I’ve become a resident expert? Not anymore. I’ve become boring, and perhaps not in a good way. But I still feel curious about all manner of things. Rating unclear.

 

7. Turn Puzzles into Mysteries. I like puzzles. I do a New York Times crossword puzzle every day, among other things. Leslie writes: “A puzzle is something that commands our curiosity until we have solved it. A mystery, by contrast, never stops inviting inquiry… When we come across a puzzle of any kind, we should always be alert to the mystery that lies behind it, because it might be a mystery that will occupy and entertain us long after the puzzle is solved.” Perhaps that’s why I pivoted to study origin-of-life chemistry as my overarching research interest. It’s a topic that will keep me interested and engaged long after I retire professionally. But do I turn puzzles into mysteries? Sometimes. My imagination leads me to delve down rabbit-holes on a regular basis, and I enjoy thinking fox-like about many things even if I’m not a thinkerer.

 

Do I possess traits for staying curious? According to this list, partially. But I don’t really care about lists in general, so I’m not putting too much stock into this one. I do ask strange questions such as whether dementors get cold feet. I think I’m curious enough. And for me, that is enough.

 

P.S. For previous blog posts on this book, here are part one and part two.

Ungrading Yet Again

Every few years, I think about de-emphasizing grades. (Here’s my previous blog post on it with links to discussion about grades.) I’ve tried several different things, some of which worked well, some of which did not. In upper-division elective courses where we mostly read the primary literature and discuss it, de-emphasizing grades has been relatively easy. There are no exams. I’m looking for engagement. And in a small discussion-based class with students who are interested in the topic and do the reading (also because they know I will call on them), it’s not hard for the students to be engaged. But in more “standard” courses such as G-Chem and P-Chem, this has not been so easy.

 

Why am I thinking about this again? Because I’m reading Ungrading (edited by Susan Blum), a collection of essays from instructors who discuss their varied approaches to de-emphasizing grades and reflect on the process. The opening essays preached the gospel of ungrading. I can summarize, tongue-in-cheek, that there were two main thrusts: a story of spiritual uplift from burden, and a demonizing of “traditional” approaches to grading. I’ve heard many of these arguments before and I’m partly sympathetic (I agree with some of the points) and partly unimpressed (by arguments I deem simplistic). After getting past the opening philosophical zealotry, I settled in to read the practices and reflections. These are interesting and quite varied – different folks have tried different things.

 

While science/math folks constituted a minority of the contributors, one that I read through slowly was by an instructor of organic chemistry, Clarissa Sorensen-Unruh. She provides excerpts from her O-Chem II syllabus on the “grade” breakdown. Students are required to do some writing and reflection, take some quizzes, and take exams. Her quizzes had a simple ternary scale like mine except she provided written feedback and allowed group work and resubmission. The final exam, like mine, is a summative assessment. The interesting part comes from the three midterm exams (worth 45% of the total class grade) where she incorporates a multi-tiered ungrading approach. Here’s how it works.

 

Sorensen-Unruh looks through the exams and provides written feedback only to the student. On the back-end she does record a score that the student would have earned if all that mattered was a score. The student then looks at the feedback and suggests an exam score (they’ll need to figure out how right or wrong they were on their answers). If the student’s predicted score is lower than the instructor score, the instructor score is used. If not, then the final score is an average of the two values. Bonus points are given if the student predicted score is within one standard deviation of the instructor’s. Points are subtracted if the standard deviation is larger than three.  Sorensen-Unruh also takes the time to explain why she’s doing what she’s doing. (This was important feature of all the essays – to get student buy-in when you’re swimming against the “traditional” current.) I liked her first-day-of-class approach that had the students think about their goals, but also think about what employers think are important skills.

 

Another interesting aspect of her midterm exams is that next to each question she provided a box with three emojis (see above) for the students to rate their confidence in their answer. In addition, she made it a point in her comments to provide thoughtful feedback, both positive and negative. But what really struck me was the following reflection she had while doing so: “I assumed my students would thoughtfully consider the points I’d taken off each question as a stand-in for feedback. I made this assumption mainly because I thoughtfully took off those points, weighing exactly how much of the question had been missed and why it was necessary to take off the points. My major ungrading realization was that students did not get this message. At all. My students did not even recognize this kind of grading was something we regularly agonized over until they had to do it themselves. It was only when they graded their own papers for the first time that they realized taking off points had reasoning behind it and that the process of grading was muddy and difficult.”

 

I introduced annotated self-grading of some exams (I called them self-tests) in my G-Chem class several years ago and I’ve been tweaking my approach. However, in those self-grades, I wanted to take the pressure off and essentially gave full-credit regardless of how the student actually performed. I pitched the self-annotated grading as a tool for them to study on the graded-exams. Some students took this task seriously and benefited from the exercise. Others did not. My setup was different from Sorensen-Unruh’s and I can see how her approach worked better than mine. Not that she didn’t have hiccups, which she details in her essay. She also reported student feedback, and it was interesting for me to read about students finding the confidence-level check useful. I’ve not done that before on an exam so I’m potentially intrigued to try it.

 

Overall the ungrading that Sorensen-Unruh and two other contributors (one computer science, one math) employed was not as “drastic” as their fellow essayists in the humanities. I think that’s helpful to me as a chemist who thinks that grades, while they have their drawbacks, also have some value. A long discussion or argument could ensue about how to evaluate that value, but that’s not the purpose of today’s blog post. One other thing I appreciated from reading Ungrading was the heartfelt final essay by John Warner (who taught writing as part of his career) where he imagines himself like Wile E. Coyote in the never-ending quest to catch the Roadrunner. Warner’s sentiments moved me more towards ungrading approaches than the previous preaching in the early chapters. So while I overall give the book a mixed grade, there were some enlightening gems worth my reading and thinking time!

System States and Parameters

I’m having an epiphany! While lying down in bed. It helps to have had more sleep the night before. It helps that I’m having a lighter teaching semester with two small classes. It helps that I spent part of yesterday in interdisciplinary conversations with colleagues. It helps that I’m sitting in on a biochemistry course this semester (in preparation to teach it in the future) right after teaching my G-Chem II course where we’re now covering some applications of thermodynamics to solutions and mixtures. And now onward to the nerdy epiphany.

 

In the first week of class, one of my students stopped by office hours to ask me about state functions. I had just introduced the tripartite model of the thermodynamic universe consisting of the chemical system, the thermal surroundings (modeled by an insulated water bath), and the mechanical surroundings (modeled by a piston and shaft) – see the picture below. What we care about is measuring the energy changes in the system that result from a chemical process which typically involves making and breaking chemical bonds.

 

The internal energy of the system is a state function. It only depends on the chemical ‘state’ of the system – which atoms are bonded to each other. The system is thermodynamically closed, i.e., it is cleanly separated from the environment in that no atoms can enter or leave the system (although energy can be transferred between system and surroundings). The word tripping up this student was ‘function’ because it made him immediately think of functions in a math class. Since this is G-Chem and not P-Chem (where we delve into the mathematical functions), I convinced him to substitute the word ‘function’ with ‘property’ and he was satisfied. I didn’t spend time thinking about other appropriate words because the student had other questions for us to discuss. Should these instead be called state ‘variables’ or state ‘parameters’?

 

In thermodynamics, language and terminology can be tricky. For example, ‘heat’ is not a noun. And ‘work’ (in the piston and shaft model) is of a specific type (PV-work) that confuses students later when we introduce the definition of free energy. The word ‘function’ is often used in biochemistry in the context of structure-function relationships that relate (but don’t exactly map) to the seeming genotype-phenotype divide in biology. So for this post, let’s stick to the word ‘variable’ for now to describe system states. Most students would associate this word with an algebraic quantity that can change, and at the G-Chem level this works just fine. Thus, the internal energy of a chemical system is a state variable.

 

The internal energy of a system can change due to external variable changes such as changes in pressure and temperature of the environment. Pushing the piston down and compressing the system represents an increase in pressure. Hotter water in the thermal bath represents an increase in temperature. Assuming that the chemical system is composed of a gas (easiest for measuring changes due to P and T), we can use an equation to calculate V, the volume of the system, as P and T vary. For an ideal gas, the chemical identity of the gas does not matter; you just need to know how many gas molecules are present. Students happily use PV = nRT in their calculations.

 

Here’s part one of my epiphany. If P and T represent environmental forces that act on the system, then V is the phenotype of the system, and furthermore there is no specific genotype of the system beyond the tenets of an ideal gas: A large number of independent tiny particles moving randomly with only elastic collisions and lots of space to move in. You don’t need any other specifics if the gas behaves ideally. There is no ideal organism in biology. But there could be some abstract entity that we call ‘organism’ – a living being. We’re vague on the phenotype other than to list generic behaviors: it eats, it poops, it grows when food is plentiful, it dies for lack of food or if something else eats or injures it.

 

Here’s part two of my epiphany. In a real gas, the ‘equation of state’ PV = nRT fails to capture all the details and more complicated equations are needed. A simple one that we teach students is the van der Waals equation: (P + an²/V²)(V – nb) = nRT. This equation of state has two parameters that are dependent on the identity of the gas: a is related to the strength of the intermolecular forces and b is related to molecular size. I say ‘related’ because a and b are empirically-derived parameters from experiment and don’t exactly correspond to intermolecular forces and size respectively. In P-Chem we illuminate these relationships with mathematical models that allow us to approximate calculating a and b from first principles. But none of these models capture everything. With the van der Waals equation, you can calculate V, the system phenotype, taking into account a and b, the genotype of the system, given environmental variables P and T.

 

Here’s part three of my epiphany. There are more complicated equations that do better than the van der Waals equation in matching experimental results for the ‘behavior’ of gases, but these have more parameters. They have a larger genotype! In P-Chem my students learn the virial (not viral) equation, its advantages and disadvantages, and how to truncate the Taylor series expansion. We’re also using mathematical functions and so the language of state ‘functions’ is appropriate in P-Chem. And now for the kicker. To get everything precisely ‘correct’ mathematically requires an infinite number of parameters. So there is no largest model that truly describes the system. We truncate the model, i.e., we simplify it, for practical reasons.

 

How did this weird situation come about? Fundamentally, it comes from our sharp separation between the system and surroundings. This separation forces us to introduce parameters to ‘mediate’ (I can’t think of a better word at the moment) between the variables of the system with those of the surroundings. In biology, by trying to define what makes an organism distinct (even though it interacts with its environment), we use genotype to mediate the function (phenotypic behavior) of an organism with its environment. For practical reasons, or maybe because we’re enamored by the idea, or because it’s easier to teach students, we employ reductionism and turn genotype into genome with a focus on DNA. The blueprint of life, we call it. But we now know that that the genome is not enough. We need to account for the proteome, the metabolome, the metallome, the interactome, and likely more. (I introduced the metallome in my elective class this semester!)

 

As a chemist, I think of the state of a system primarily in terms of its structure – what chemical bonds are present, how strong they are, and what degrees of freedom the structures possess – which then determines its function, its phenotypic behavior given some environmental conditions or ‘forces’. The genotype has something to do with the idiosyncracies of each atom, but also accounts for its context dependence. The parameters I might invoke include polarizability, electronegativity, acidity, and more. But unlike the one-way structure-determines-function of the chemist, the biologist needs to employ a two-way relationship between structure and function. I don’t think this is simply practical language when discussing biology, but that it may be paradigmatic to biology that structure and function loop around each other. States and parameters in some sense cannot be cleanly separated, and we use such terms because we tried to separate system from surrounding as a starting model. I don’t see this as bad or wrong. But I do think as professors we should be more cognizant of these issues, and perhaps even expose our college-level students to these underpinnings in our fields of science.