Conceptual and Procedural Knowledge

“Just plugging and chugging numbers into a formula while solving a problem is NOT learning.” This is a common refrain you might hear from a teacher in a class that requires some quantitative work. Closely related to this is the oft-quoted dictum that “knowledge does not equal understanding”. We’ve been hearing this more and more in the age of the internet where knowledge seems “easy” to acquire, while understanding remains elusive. This leads to setting up a distinction between conceptual knowledge and procedural knowledge; the former being the holy grail of learning, and the latter being its mindless robotic plug-and-chug counterpart.

 

As an instructor of chemistry, I don’t think the two can be easily separated, if one desires to learn the material (at least in General Chemistry and Physical Chemistry, the two classes I teach most often). Sometimes my P-Chem students will say “I get the concept, but I get lost in the math.” I beg to differ, especially when it comes to quantum chemistry – if you don’t comprehend the math, you likely don’t have a firm grasp on the concepts. I teach the students conceptual material alongside problem-solving, weaving back-and-forth between two sides of the same coin.

 

Furthermore, a good way to check if you really understand the material is to work on a variety of problems, i.e., to make your knowledge more flexible! Conceptual material is always fuzzy when first encountered, and to sharpen both the heart of the matter and its boundaries, one needs to try and answer questions that probe the understanding in a variety of ways. Sometimes this requires a calculation. Sometimes it requires drawing a structure. Sometimes it requires comparing two calculations or two structures. Sometimes it requires making arguments and constructing explanations. I think conceptual material in chemistry isn’t intuitive, and that’s why it’s a challenging subject to learn. But it can be illuminated by practicing problem-solving.

 

There’s an interesting review article by Rittle-Johnson and colleagues titled “Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics” (Educ. Psychol. Rev. 2016, 27, 587-597). The title pretty much tells you what the story will be. There has been a trend in mathematics education in the U.S. to focus on conceptual material first before getting to the procedural parts. The article investigates whether there is evidence that the conceptual-to-procedural approach leads to superior learning outcomes. Broadly speaking, the answer is no. But that’s because setting up experiments that can compare conceptual-to-procedural versus procedural-to-conceptual are not so easy to set up without other confounding factors intruding on the experimental design.

 

The article also discusses the evidence in favor of the two-way mutual support between conceptual and procedural knowledge acquisition. It points out some problematic prevalent beliefs: (1) that “conceptual knowledge has sometimes been used to refer to knowledge that is richly connected while procedural knowledge [was] sparsely connected”, (2) that “procedural fluency seems to refer only to an end state of well-developed knowledge, while conceptual knowledge can refer to a variable amount of knowledge”, and (3) that culturally in the U.S. “practice is not believed to aid the development of understanding” while in many other countries, “practice is viewed as a route towards understanding”. In Asia for example, mathematics education often involves learning procedural knowledge first (being able to plug-and-chug efficiently) before addressing some of the trickier conceptual bits.

 

In G-Chem, there has been a shift in which topics we cover first, and we can see this by comparing textbooks from the last decade or two with earlier ones. Stoichiometry (lots of plug-and-chug) has been moved to later in the first semester. Gases (often also requiring calculations) are typically encountered at the tail end of G-Chem 1, sometimes getting short shrift. On the other hand, electronic structure of atoms and chemical bonding have been moved earlier. I don’t think that’s a necessarily bad choice overall (but do we really need orbitals at the G-Chem level?) and I’m comfortable with this move. That being said, I also do some calculational work (moles/masses, some energy calculations) earlier in the semester.

 

One potential drawback of the current sequence is that G-Chem 2 becomes much more math-heavy (thermodynamics, kinetics, equilibria). Students who are struggling with procedural fluency in doing calculations get mired down in those details and aren’t getting the conceptual material because they’re floundering in the procedural parts. I don’t think loading more conceptual knowledge upfront helps them because the conceptual material (in thermodynamics which is all about keeping quantitative track of energy) is dependent on being able to work the relevant calculations. My experience (in office hours) is that students who can work the calculations also grok the conceptual parts. Those that struggle with the calculations have little grasp of the conceptual material. Even though I always lead with some (although not a lot) of conceptual material for each subtopic in G-Chem 2.

 

Finally, a word about assessment. Rittle-Johnson’s article has a section titled “Evaluation Criteria”. Measuring conceptual knowledge is challenging. Measuring procedural knowledge is easier because you can check this by posing calculational problems. If the procedural task involves “near transfer”, this can actually be a good measure (albeit oblique) of conceptual knowledge. I’m not surprised by this, which is why I think exams are a good assessment tool in G-Chem and P-Chem, despite naysayers (who almost always do not teach chemistry). To some extent, the conceptual pieces of chemistry are acquired gestalt-like, and are not amenable to reductionist breaking-into-pieces. The procedural parts, on the other hand, can be atomized into pieces – and once the student gains fluency (thus moving their acquired procedural knowledge into long-term memory), they now have the bandwidth to synthesize their conceptual knowledge. But we can’t expect them to do so automatically on their own. Hence the need to teach both procedural and conceptual knowledge and keep going back-and-forth between the two. That is the road to understanding (chemistry).

Mutiverse: A Fringe Idea

The multiverse is all the rage. In the last several months I watched three blockbuster movies (thanks, local library for providing DVDs) featuring the multiverse: Spider-Man No Way Home; Doctor Strange and the Multiverse of Madness; and Everything, Everywhere, All at Once. (The last of those three, helmed by Michelle Yeoh, was the best in my opinion.) But the multiverse is not a new idea. It was called the Many Worlds Interpretation of quantum mechanics when first put forward by the physicist Hugh Everett. And although there was a lag before it gained mainstream popularity, it’s now ubiquitous in sci-fi and fantasy.

 

I just started watching the TV series Fringe. It’s old by today’s standards, having debuted in 2008, almost fifteen years ago. I started watching because I’d heard that one of the protagonists, Walter Bishop, was supposedly a biochemist or at least held an endowed chair in biochemistry at Harvard. But at the beginning of the series he’s locked up in a mental institution, and he fits the caricature of a mad scientist in many ways. There’s physics, chemistry, biology, but fitting the theme of fringe science, all sorts of weird unexplained phenomena permeate the series. Chemistry-wise, Walter has a basement lab at Harvard, and once released and working for the FBI, one often sees scenes of glassware, colored solutions, and the occasional Bunsen burner.

 

Turns out I’m not much like Walter Bishop. I don’t have the absent-minded mad professor vibe, I’m not as familiar with the range of weird physics and biology, I don’t dose myself with hallucinogens, and I don’t keep a cow in the lab. Nor do I experiment on humans or animals. (On the other hand, I do share some similarities to Walter White, protagonist of Breaking Bad.) The idea of the multiverse and being able to travel between universes doesn’t faze Walter Bishop. Season One hinted at the multiverse, but I’ve just started Season Two, the multiverse theme has become dominant. There’s a clever explanation for the feeling of déjà vu – you’ve just accessed an alternate universe for a moment – although I think the explanation provided in The Matrix movie is cleverer.

 

I just finished the fourth episode where one of the characters explains the danger of multiverses becoming accessible to each other. She takes two glass globes and smashes them together while talking about the Pauli Exclusion Principle. I’d interpret it in the following way atomistically. Imagine a probability distribution cloud of an electron (an “orbital”) with an up-spin electron. If it comes close to another orbital with a down-spin electron, they can occupy the same space. Their probability waves can have constructive interference (based on superposition of in-phase waves). There’s no problem and they can inhabit the same “space” so to speak. But if the two electrons have the same spin, the Pauli Exclusion Principle kicks in and forces the approaching waves to be out-of-phase and they must destructively interfere, i.e., they will destroy each other. Now that’s a clever fringe idea for the multiverse!

 

The multiverse is no longer considered a fringe idea, despite its prominence in Fringe. Mass media has made it mainstream. But is it true? Is it reality? The many-worlds hypothesis is challenging to test scientifically. It might be impossible to ever know if there are parallel universes adjoining our own, or whether every decision generates newborn ones. Sure, one can dream up fantastical scenarios where alternate-you shows up and tells you the “truth” of the matter. For now, I entertain the idea of a multiverse as entertainment.

ABC in XYZ

I’ve been thinking about the design of a one-semester integrated introductory chemistry and biology course that isn’t a double course. In a double course, you could get away with less integration and not have to make so many hard choices of what content to keep and what to jettison. As a chemist (who finds biology interested), I can only claim expertise in teaching introductory chemistry so I won’t address the biology portion in this post.

 

What “traditional” topics can I cut from first-semester General Chemistry? The underlying tension is that I’d want to discard topics that don’t integrate so well with the topics in introductory biology, but I wouldn’t want to leave them out if they are a crucial building block for subsequent courses. After all General Chemistry is a pre-requisite for many other courses in the sciences, for good reason in my biased opinion.

 

I’ve previously considered leaving out orbitals. But let’s push this idea further. I could leave out the photoelectric effect, wave-particle duality, quantum numbers (and their rules), orbital shapes and sizes, orbital energies (and photoelectron spectroscopy), electron configurations, hybridization, molecular orbital theory, among other things. That’s a significant chunk: I’d say that’s about 20% of our G-Chem 1 syllabus. If I leave out metallic bonding, structures of solids, and a bunch of “tricky” Lewis structures (molecules that won’t be encountered in biochemistry), most of the gases chapter, parts of stoichiometry, nuclear chemistry, that’s knocking off another 20%. I can likely “flip” another 10% of the material so that I don’t need to use class time, and that gets me to the 50% goal.

 

Things I can’t leave out: some basics of atomic structure (enough so students have some understanding of the periodic table, basics of chemical bonding, and drawing some Lewis structures), some stoichiometry (balancing chemical equations, doing some calculations, acid-base and redox reactions), a molecular view of phases of matter including aqueous solutions, and certainly intermolecular forces and their applications. I could see these topics gelling well with a number of topics in introductory biology. Also, what I’ve left in will not prevent the student from being sufficiently prepared for a standard G-Chem 2 course (thermodynamics, kinetics, equilibria, electrochemistry).

 

But having chopped a number of topics that are important for a student who wants to continue in chemistry, where would these go? I propose a follow-up course cheekily abbreviated “ABC in XYZ” or “Atoms, Bonds, Chemistry in 3-D”! It would cover many of those topics, but in more detail, i.e., I would move some material from a traditional inorganic chemistry course (symmetry, group theory, metals) to be part of ABC in XYZ. Topics such as (advanced) electron configuration and valence bond theory, metallic bonding, molecular orbital theory, solid structures, the acid-base-redox nexus, can get the treatment they deserve. And we’d be able to sink our teeth into the unity and diversity of the periodic table both as an organizing principle but also with its nitty-gritty idiosyncracies. This would set up a student very well for a quantum chemistry course in a Chem major (assuming they have the pre-requisite math) or a more advanced inorganic chemistry course that could be much more interesting than the traditional one.

 

Now I just need to go write up a syllabus. Too lazy to do so on a Friday afternoon…

Two Heads

Two Heads is a delightful “exploration of how our brains work with other brains” composed in a beautifully illustrated format. The main protagonists are cognitive science emeritus professors Uta and Chris Frith, who are also married to each other. Their son, Alex, is an established non-fiction author of books aimed at children. Not to worry if you don’t know anything about brains or neuroscience. They teach you as you read along. And each chapter is masterfully connected to the next so you just want to keep going!

 

While I was familiar with a number of the classic experiments they describe, there were more than enough new things for me to mull over. One that really caught my attention was over-imitation. Many animals learn through imitation, as do humans. Children are imitating what they see and hear all the time! Both children and adults also learn through being taught something explicitly – the basis for setting up an education system! But the interesting part is that when we first learn something, we do it through over-imitation. Instead of just copying, we try to copy exactly. I see this all the time when teaching chemistry, especially because the subject matter is often counter-intuitive.

 

Why do humans over-imitate? (Apes don’t, apparently.) The Friths argue that it’s for social reasons: “We do it because this is the way our group does things, and we want to fit in with out group.” And sometimes we do the opposite: “Deliberately not over-imitating can be a way to mark ourselves part of one group rather than another.”( Interestingly, some autistic kids tend not to over-imitate.) But there’s more. We don’t often notice that we have a tendency to imitate someone who seem more like us (the in-group) rather than someone who seems more different (the out-group). I wonder how that impacts the teaching-learning nexus. As someone who grew up in a different country but who now teaches (mostly) Americans between the ages of 18-22, and who has a noticeable accent when speaking English, I wonder if and how that affects the subconscious parts of student learning in the classroom.

 

There’s an interesting chapter about how the brain recognizes self from other. Apparently, you can tickle yourself if you use a double-robot arm contraption where the second robot arm has a time delay response. Weird. And sometimes the feedback self-recognition loop can break down, and we see this manifested in certain types of delusions, hearing voices, and schizophrenia. Apparently, schizophrenics can often tickle themselves. This discussion leads to the famous experiments by Benjamin Libet – before taking an action, the brain activity can be observed before one consciously recognizes the decision to take the action –  which brings up questions of free-will. The Friths think that interpreting “that your body moves, then your brain retroactively decides that the movement was deliberate” is incorrect. Instead, “your brain predicts it is going to move, then compares the final movement with the prediction. Only after the prediction has been tested does the movement get logged by your brain as a deliberate movement. It’s a quirk of biophysics that this operation takes an amount of time that can be observed and measured.”

 

I’d been thinking along those lines after reading Robert Rosen’s Anticipatory Systems. I think an interesting way to characterize life is that it’s an anticipatory system whose function cannot be cleanly separated from its genesis. Evolution of the brain is to improve anticipatory ability, particularly when it comes to social interactions – at least that’s what I gather from reading Terrence Deacon. This fits well with the overall discussion in Two Heads, and much of the book focuses on the social aspects of cognition of neuroscience. Early in the first chapter, they explicitly say that “your brain is a Bayesian prediction engine”.

 

Halfway through the book there is an interlude chapter discussing how challenging some of these psychology experiments can be with their many limitations and pitfalls. It can be so tempting to over-interpret the data towards pre-conceived notions or something that will be media-buzzworthy. There’s also an interesting section describing a collaboration with an anthropologist who studied what happens at a research institute and compares it to “a Georgian house, where this is a clear hierarchy of people, and set rooms for set tasks. The overall task of the house is to turn nature into science…”

 

Another potential take-home message from the book is that collaboration leads to better outcomes but there’s a caveat: The collaborators need to have similar levels of competency and also similar levels of confidence. There’s also some evidence that diversity improves the outcome. The experiments described are limited so I don’t know how well those conclusions extend to broader settings, but I’m certainly seeing the business world use these ideas to create buzz. I also liked how the Friths’ conclusion, as psychologists, that most people are instinctively nice (because of reputation and group dynamics) in contrast to a purely homo economicus view.  But they also acknowledge that in-group and out-group factors can complicate things.

 

Overall, if learning about the brain, cognition, and social psychology, is something you’re interested in, I recommend Two Heads. It’s an engaging book that threads the needle between giving you the details (without being overwhelming) and the big picture (with examples that you might care about). Overall two thumbs up.

Immaterial Science

As often happens while looking for one thing, I stumble across something (mostly) unrelated. Today’s edition is the Journal of Immaterial Science. Totally satirical, dorky, funny, it has something for (almost) every chemist. The articles are short, and many of them are appropriately labeled Miscommunications or Illiterature Reviews! I skimmed a few of them and here are some of my highlights.

 

Since Halloween was yesterday, I decided to read a “Proposed Detection of Ghosts with MS-SPOOKY”. The abstract: “You could shoot ghosts on a mass spec. Maybe.” The article begins by arguing that “to prove the existence of ghosts is a key value to modern society”. There’s no doubt that many folks are interested in this topic. I’ve even blogged about it (several times). And if Mary Roach has written about the afterlife, you can bet there’s interest. The SPOOKY stands for “spectral presence origin-omics kinetic yield”. Unfortunately there’s no scientific detail in the article about how SPOOKY works except for a vacuum inlet to suck up the ghosts and trap them.

 

Given my interests in astrobiology, I particularly enjoyed reading “Triphenylphosphine Oxide in the Clouds of Venus”. Various programs and telescopes have been given names and acronyms. The ALMA array is rechristened “Alien Life Molestation Array”. Haha! The article criticizes the ballyhoo about phosphine detection by discussing the problem of bias, specifically the “Cox bias, whereby the larger the telescope one uses for a study the more important it is to accompany the paper with a press-release that may be talked about by science communicators in the media.” The overall detection project is dubbed “Mission Imphossible”! When the P-31 NMR data shows a strong signal, it is assigned to “that most pernicious of impurities: triphenylphosphine oxide”. (Actual chemistry: it’s difficult to remove in a mixture via chromatography.) And if there’s some data you cannot explain, it must be attributed to Aliens!

 

As a theoretical chemist who often reads philosophy of science and history of science, I was amused by “Toward a Science of Dumbassery: A Theoretical Perspective”. There’s a tongue-in-cheek paragraph about philosophy of science that actually has some critical substance (of course, it’s also funny). Then the authors get down to business by trying to define dumbassery and notes that it seems to be observed where its opposite (intelligence) can be found. Cognitive neuroscience and genetics get thrown into the mix. Did I mention one of the authors is “Francis Crock… a cell biologist with an underwhelming grasp on statistics”?

 

There are lots of chemical structures and reaction schemes in many of the articles. Synthetic chemists might enjoy “Applications of Cursed Chemistry in the Total Synthesis of Impracticatechol”. Medicinal chemists might want to know about “Chemical Frenetics: Party Drugs as Organocatalysts” which provides tweetable reaction yields (see table below). And there are a bunch of pictures in “Extreme Titrations” showing folks doing titrations in extreme environments. There’s poetry and song (“an ode to triphenylphosphine oxide”). And that’s just the first edition.

 

Volume 2 was recently released. I enjoyed “The Flatom: A Novel Atomic Theory Inspired by a Flat Earth”. “The Lost Molecules of M.C. Escher” includes fractaldehydes, not to mention there’s an article on “A Total Synthesis of Tesseractane”. And John Dalton’s alter ego is profiled in “Don Jalton – A Forgotten Pioneer of Atomic Theory”. Structural biochemists will nod knowingly with “X-Ray Crystallomancy: A Practical Guide” – it’s particularly good with figures including ancient symbols and star clusters. And much, much more. It can be a black hole. I only allowed myself an hour of skimming through the articles after which I’m determined not to look at any more details. [TRIGGER Warning:] It’s a black hole of chemical proportions.

Credit for Alchemy

In the seventeenth century, there was a shortage of circulating money. One solution was to debase one’s coin, an infamous incident in the prior century being Henry VIII’s replacing the amount of gold and silver with cheaper metals. (Henry had an extravagant lifestyle and also needed to funds his wars.) A decreased influx of precious metals from the Americas and other parts of the world exacerbated the situation. One solution to the problem was to make more gold those cheaper metals via transmutation – the promise of alchemy! Thus, European courts and kings retained the services of alchemists in the hope of improving the state’s financial situation and turn the economy around.

 

I’m learning about this history after stumbling on an article with an intriguing title: “Credit-Money as the Philosopher’s Stone: Alchemy and the Coinage Problem in Seventeenth-Century England.” The author is Carl Wennelind and the citation is History of Political Economy 2003, 35, 234-261. As a chemist who’s interested in history, I’ve read a fair bit about alchemy and the philosopher’s stone. I also discuss the role of the alchemists as forerunners to the chemists and how we define chemical elements, on the first day of my introductory chemistry classes. I had never previously considered the influence it might have had on political economy.

 

Wennelind briefly describes historical landmarks in the alchemical tradition, leading to Francis Bacon and subsequently the Hartlib Circle. I’d never heard of Samuel Hartlib, but apparently his group “served as a link between Gresham College – the first systematic effort in England to apply scientific lessons to the practical affairs of the state and the demands of commercial expansion – and the Royal Society.” Robert Boyle and Benjamin Worsley were members; and the group was known as the “invisible college”, a precursor to the Royal Society’s formation.

 

The alchemists did not succeed in turning cheap metals into gold, despite the efforts of Worsley. Thus, the Hartlib circle turned to the idea of “setting up a land bank that would issue credit-money on the security of the land.” The idea was that “land is the most concrete and stable of commodities” and while you’d think “the banking sector was the most appropriate institution for the development of this kind of credit-money scheme”, Hartlib argued that such “deposit banks” were essentially pawn shops and thus limited in increasing the circulation of money. One member of the Hartlib Circle “advocated for the creation of a merchant bank that would issue promissory notes for domestic circulation” (i.e., essentially paper money in function) by making an analogy to alchemy, even referring to such credit-money as the philosopher’s stone.

 

Another reason why the land bank may be preferable to alchemy was that the money would not be debased if the alchemy was successful and large quantities of gold flooded the market. Land, in this sense, was more concrete than gold at least as a measure of security. Hartlib’s specific idea did not ultimately come to fruition, but by the end of the seventeenth century, the Bank of England was founded to pay for (via credit-money) the building of the British naval fleet. (The close ties between monetary-debt systems and war has been amply argued by David Graeber in his masterful treatise.) Alchemy on the other hand fell further by the wayside, no longer needed by monarchs and business titans. And with the rise of science as a distinct methodological suite, the death knell of alchemy was assured. I give alchemy credit for staying alive as long as it did.

Tallies and Ratios

Where does money come from? The familiar story is that barter comes first. I’m a fisherman. You’re a farmer. We swap some fish for some potatoes. But what if you don’t want fish or I’m tired of potatoes? How do we find the people who have what we want but who also want what we have? And when we do find them, how do you set the exchange rate? One fish for two potatoes? How big are the potatoes? How bony is the fish? There is no end to such questions.

 

The familiar story is mostly bunk, according to David Graeber in his book Debt: The First 5,000 Years. It’s a sweeping history of debt, money, credit arrangements; but it’s also an evolutionary history of trade, war, slavery, government, banking, and more. (Graeber is an anthropologist; I previously blogged about his latest book here.) Chapter Two of Debt is titled “The Myth of Barter” but it opens with a superb quote by H. L. Mencken that I’ve now memorized because we humans, so-called rational beings, prefer to be lazy and take heuristic shortcuts. Anyway, here’s the quote:

 

For every subtle and complicated question, there is a perfectly simple and straightforward answer, which is wrong.

 

The familiar (yet wrong) story imagines a stone-age village where individuals who find mutually desirable exchanges resort to barter. This proves unwieldy and so money is introduced with metal coins (for a variety of reasons), and eventually they become cumbersome to carry so we proceeded to paper money and then to credit arrangements which works especially well in our digital age. There’s little evidence for this linear story and most of it is backwards. Credit arrangements, debts, and IOUs show up first. And if some sort of monetary object shows up as a medium of exchange, it’s inevitably between strangers (for one-off transcations) and not among your fellow villagers. Then some sort of government (or tyranny) comes along and tries to capitalize on this by introducing money (coins, salt, or grain) for taxation or other purposes. This is often backed up with the threat of violence. Wars and the breakdown of society lead to urban flight, and it’s then that barter does show up in limited circumstances, but there is a reversion to credit-style arrangements. I’m not doing justice to this panoramic sweep and I highly recommend reading Debt for yourself. (Yes, it’s some 400 pages not counting the notes and index, but it’s an insightful and engaging book.)

 

Graeber divides his historical sweep into several ages, each with their dominant characteristics: “the First Agrarian Empires (3500–800 BC), dominated by virtual credit money… the Axial Age (800 BC – 600 AD) which saw the rise of coinage and a general shift to metal bullion… the Middle Ages (600–1450 AD), which saw a return to virtual credit money… the Age of Capitalist Empires, which began around 1450 with a massive planetary switch back to gold and silver bullion… ended in 1971 when Richard Nixon announced that the U.S. dollar would no longer be redeemable in gold… marked the beginning of a yet another phase of virtual money…” One thing Graeber does well is bring together insights from all over the globe. There are many similarities, but there are also significant differences between different regions.

 

So what is money? Essentially, it’s an abstraction that measures a ratio. The collective “we” (or a tyrant who rules with “might makes right”) agrees on a reference state: let’s say gold. Why gold? From my chemist point of view, it’s quite easy to purify, unlike many other metals that exist as ores (mostly oxides). It’s a relatively soft metal and it’s not hard to melt and reshape it, or even stamp a number or a symbol. You can divide it into small bits such as coins. The Islamic philosopher Ghazali would say that it’s ideal because gold (or silver) is of no use for anything else: “A thing can only be exactly linked to other things if it has no particular special form or feature of its own – for example, a mirror that has no color can reflect all colors. The same is the case with money – it has no purpose of its own, but it serves as medium for the purpose of exchanging goods.”

 

Graeber follows up with the following insight: “Money is thus a unit of measure that provides a means of assessing the value of goods, but also one that operates as such only if it stays in constant motion.” It reminds me of another abstraction that we can measure but fluidly exchanges: Energy. Hard to define, but we can keep track of it. A tally of sorts. The Greek word for tally is symbolon. Graeber describes Aristotle using the same word to argue that “coins are merely social conventions”. A tally is symbolic. An abstraction that represents a ratio of exchange. (Interestingly, the Chinese word has a similar origin, which Graeber also ties to the “agreement between Heaven’s appointment and human affairs”.)

 

How does the tally work? You take the object and break it into two pieces. Each person in the agreement takes one piece. These objects could be notched sticks, rings, crockery, clay (“friendship”) tablets, or even a sheet of paper with a written agreement. Doesn’t matter what the object is because it now functions as a symbol of an agreement. These agreements were often IOUs of a sort, i.e., one person is in debt to another and one could call in that debt by presenting your piece to the holder of the other piece. It didn’t even have to be the original holder because the IOUs could move with credit swaps. Graeber, the anthropologist, argues that debt underlies social relationships. What is debt? “[The] peculiar agreement between two equals that they shall no longer be equals, until such time as they become equals once again.” But the impact takes on global and existential significance: “Inevitably, arguments about wealth and markets became arguments about debt and morality, and arguments about debt and morality became arguments about the nature of our place in the universe.”

 

As a chemist who studies the origin of life, I find an uncanny resemblance between Graeber’s evolutionary approach to debt and the chemical evolution of energy transduction. Let me be clear that there are also many differences between humans making agreements about ratios via tallies, and molecules making energy exchanges akin to a circulating currency. Today, the molecular analogy to money is ATP (adenosine triphosphate). It “releases” energy by hydrolyzing ATP (a “downhill” reaction), and this energy can be utilized by other “uphill” biochemical reactions. ATP is regenerated at a cost via other “downhill” biochemical reactions such as when molecular fuels are “burned” for energy.

 

We can keep a tally of this energy quantitatively. That’s what the science of thermodynamics is all about. But that energy is constantly moving around. ATP is not the only molecule that “stores” this energy currency. All molecules do that. Whenever there is a chemical reaction involving making and breaking bonds, there is almost inevitably a difference in energy between the reactants and the products. (One might say that debts are created or repaid in this process.) Tallies (broken objects to be rejoined) invokes the same process at the molecular level. That being said, a subset of molecules have been evolutionarily selected to act as a common currency of sorts, shuttling around and making their exchanges. Besides ATP, you may have encountered NAD, FAD, and other such acronyms, in a biology or biochemistry course.

 

ATP is a particularly interesting case because it plays double duty as a substrate in nucleic acids which function prominently for information storage and retrieval. Are nucleic acid polymers like banks or government-controlled banks? NAD is closely related to ATP in structure. So is the ubiquitous signaling molecule cAMP. But before the establishment of ATP and its close cousins as the de facto currency shuffler (among disparate parts of the cell which were previously strangers to each other), was there something akin to stone age virtual credit and IOUs among related (familial) molecules? Here’s where I think Christian De Duve’s thioester world is attractive. The core of metabolism involving a small subset of molecules containing just carbon, hydrogen, and oxygen, has closely related cousins that substitute sulfur for oxygen. Not a lot of sulfur, mind you. And since sulfur is just below oxygen in the same column of the periodic table, you might expect similar molecular structure and chemistry. The origins of metabolism could be envisioned as family and neighbors exchanging energy to do what they want to do (chemically speaking). But how did that evolve into today’s metabolism and molecular currency? Well, that’s the zillion-dollar question!

 

I’m doing my small part to figure out this conundrum, but sometimes one gets so steeped in the minutiae and forgets to look at the big picture and find inspiration from outside sources. That may be why I’ve particularly enjoyed reading Debt. The conceptual ideas of tallies and ratios, and Graeber’s evolutionary framework in telling the story, resonate with the problems I’m working on. Debt may play a key role in the inner workings of life, governed by the rules of thermodynamics, constrained by kinetics, but with plenty of room for creative interplay as energy flows through our planet from the sun to the deepness of space. New molecular systems are created to capture and harness that energy, which led to organisms doing the same thing today on an unprecedented scale. But perhaps I’m simplifying things too much. Let’s remember Mencken’s dictum.

 

For every subtle and complicated question, there is a perfectly simple and straightforward answer, which is wrong.