Rare Earth: P and N

The idea that Planet Earth is rare and special for being able to host life has a very readable book-length argument, Rare Earth by Brownlee and Ward. Technically it argues why complex life is rare, while simpler life may be more achievable over a broader range of conditions. Given that we only have a sample size of one for life-harboring planets, who knows if life proliferates beyond our star? You can plug a range of numbers into the Drake equation to convince yourself either way.

 

The idea that Earth sits in a Goldilocks habitable zone most often refers to whether water exists as a liquid on the surface of a planet. This assumes that H₂O is crucial to life as a liquid, and that other liquids (ammonia, hydrocarbons, formamide) may not have the same versatility. It’s hard to say otherwise with a sample size of one.  We also assume that carbon-based molecules are crucial for life, which is reasonable from a chemical point of view (diversity, bond energies, or as a carrier). That takes care of carbon, hydrogen, and oxygen. What about nitrogen and phosphorus?

 

The idea that our rare Earth may be rarer than we previously thought comes from a paper published last month in Nature Astronomy (DOI: 10.1038/s41550-026-02775-z). It examines core formation of rocky planets and estimates the availability of nitrogen and phosphorus under different conditions. Things that are important are the relative redox state of the mantle. Our planet apparently sits in a zone that optimizes decent amounts of N and P (although much less abundant than C, H, O). It’s a tricky balance. If the redox situation is too reducing, availability of P plummets; too oxidizing and N might be lost to outer space by significant degassing. Simulated origin-of-life chemistry in the lab has always worked better under reducing conditions. Thus, the authors conclude: “there is a plausible case to make that only moderately oxidizing planets have both sufficient mantle P and sufficient reducing power to sustain prebiotic chemistry and then life”.

 

Why do we need N? Amino acids. Catalysts. Chemical versatility. We would not have fine-tuning of the thermodynamics and kinetics of (bio)chemical reactions without nitrogen. Why do we need P? I’m not sure. Arguments can be made for its crucial role in nucleic acids (Westheimer’s famous paper). But it’s possible some other backbone might work. Bioenergetic currency relies on phosphates today, but it’s possible that sulfur could have played the early role of energy transduction. Sulfate bacteria are also fierce competitors. I’d be very curious what is known about sulfur availability during planetary formation. We know that outgassing of volcanoes on the early Earth is a source. And I’m also clearly biased because I have a current research grant to study the role of sulfur in origins-of-life chemistry.

 

Final tidbit of the paper that I enjoyed: the authors use oxygen fugacity as their redox measure. When I teach P-Chem, I try to pepper in examples of why the math-and-models are useful. Fugacity is one of those bewildering topics to students, because the math looks like a merry-go-round and having a hypothetical reference state seems strange. Now I can point to another example why learning about fugacity is useful and interesting. The paper makes reference to Mars and other exoplanets in the search for life in the universe.

Transition Week

Final Exams for the spring semester concluded last week. I got my grading done and submitted final grades. Teaching-wise it was a much lighter semester compared to last fall when I taught biochemistry for the first time. In the spring I had two small classes: P-Chem II and the honors section of G-Chem II. With only a dozen students in each class, there was much less grading to do! I also feel that I do a better job helping students puzzle over the material in class and answering their questions when there are fewer students and my attention is not spread too widely.

 

Summer research will commence full swing starting on Monday. I had a grant funded so I will be onboarding a new crew of five undergraduates. Some of the students have just finished G-Chem, some have just finished O-Chem, none have taken P-Chem yet, and all will be new to computational research. The research students I had this past spring semester have either just graduated (this past weekend) or have other summer plans lined up. This will be the first time in a while I have had so many new students join my lab without any experienced ones present to help as guides. I’ve been updating my research guides and crib-sheets to help orient my new students. This morning I worked on detailing the training schedule for the first two days. After that students will be assigned their individual projects.

 

I am also making a software transition. This was rather annoying at first. My current software vendor essentially doubled the license renewal price; after some frustrating back-and-forth I was able to negotiate it down partially, but that was still not enough. I was particularly annoyed because I had told them the previous year what my budget would be (written into my grant) according to what I had been paying the last several years with minor increases for inflation. Thus began a hunt for new software which meant getting trial licenses and testing things out to make sure I had continuity. I found some suitable packages that will expand my research methodology options so I now see this as an opportunity. And it fit my budget.

 

The transition will still be frustrating. For most of the summer, my students will be able to get their computations done on the old software that I’m very familiar with. The very tail end is when my present licenses run out, and that’s when the group will have to make the transition. I will have a month overlap between the old and new software licenses which will give me time to write up new protocols and orientation guides. Then my pitch to the students will be that they are helping me test new protocols! And for anyone who wants to continue research with me during the semester, they’ll have to learn the new software anyway, so it’s better to do it during the summer. Once classes get started, things get busy.

 

So unlike other transition weeks in past years, this one is busier than usual. In the final two weeks of the spring semester, as finals were looming while I was busy testing out new software, it felt overwhelming. But because much of the administrative paperwork was figured out last week, this week has felt more calm. Also, I can work from home this week which saves me the commuting time! I’m no longer frazzled, and I’m working on tuning my mindset to make the most out of summer research!

Reorganizing

Not being able to find previous papers I’ve read and stored in pdf format is increasingly annoying me. I haven’t organized the files in the most logical way; rather it has evolved organically over time in what looks like a mess. When there were fewer files, and my memory was better, I could easily find what I needed. Also, prior to Covid, I separated my work-life and home-life. All my files were in a single location – on my desktop computer at work. But with a recent overseas sabbatical and then Covid (and working remotely), I now have multiple places where my files are saved.

 

My desktop contains copies of all the files from my various laptops over the years, but I haven’t made an organized effort to mesh them. No, I don’t store things on the cloud even though my university uses GoogleDrive. Instead, I have local files on various computers which I periodically back up. The inertia to change my ways – I’m not sure what to say about it, other than that I am a creature of (bad) habit. But I’m now sufficiently annoyed that I might do something about it. My current goal is to go through some of the folders every week and start to mesh everything into a single place, perhaps renaming some files so I can better search for them.

 

What I need to do is think of an overarching organizational system. I didn’t know what this would look like as a new faculty member. Also in my early pre-tenure years, I did not read as widely. Most of my papers were particular to the projects I was working on actively or grants that I was writing when considering future projects. But during my first sabbatical, I started to reach much more widely as I pondered new research directions and interests. And not just chemistry research or pedagogy. I read more widely in the sciences, history, philosophy, and psychology. My “future research project papers” folder (labelled “FutureResProjPapers” because that’s how I label folders) now has way too many files, and that’s the one that would be most practically useful as I plan ahead.

 

A starting point for reorganizing would be looking at all the subfolder names in my “Reading” folder. Actually, I have multiple such folders. There are some overlaps between the names so some can be consolidated. But I haven’t figured out what to do about papers that span multiple categories. In the past, I made copies and stuck them in different thematic folders, but I doubt I’ve done so consistently. I perhaps need a way to tag my files with an appropriate set of tags. Decisions, decisions! The whole business looms and just thinking about what I should do is giving me pangs of paralysis.

 

Are my desktops, both physical and virtual, a sign of my messy and disorganized mind? Maybe. I’m tempted to just “start fresh” with a clean slate. Are all those old papers important? Likely most of them are outdated now and less interesting. But it would take time for me to figure that out. If I could get an A.I. to read pdf files and churn out a summary, that might help. But would I trust it? I don’t know. Maybe I shouldn’t worry if I miss anything. If something is that important, it will come up again. And likely I can find the paper off the internet. So maybe I should just work on what I’m using actively (say the past one year) and just archive the rest in an “OldPapers” folder. That’s tempting.

 

What I should be doing right now is getting a move on this process. Instead I’m procrastinating by writing this blog post. Okay, I have to stop writing now and spend the next twenty minutes making some organizing headway.

Return to Conferencing

It had been a while since I went to a large conference. No thanks to the pandemic. But last week I was back at the American Chemical Society national conference. This one was in San Francisco; I’ve blogged about my usual conference activities at such a meeting. While there were a few individuals who wore masks, it mostly felt like a pre-COVID conference. There didn’t seem to be social-distancing anxiety and folks were happy to shake hands instead of just elbow-bump.

 

This was in contrast to a smaller regional conference (~100 people) I attended last October, which was my first in-person conference in almost three years. Almost everyone was masked, appropriately so since the small lecture theater barely accommodated us – the organizers were not expecting such a good turnout. I guess we were itching to get back in person. I did take off my mask when I was speaking at the podium, as did the other speakers.

 

One of the themes of the big San Francisco meeting was Artificial Intelligence applications and machine learning. I went to several high-quality talks presented by folks from both academia and industry. Some were well attended, others sparsely so. This is a field that is moving very quickly, hype notwithstanding. I’m not an expert in machine learning, although I am picking up the newest lingo, and I have some basic knowledge of how computational neural networks work.

 

Of all the talks I attended this time around, three stood out. One was a machine-learning talk on protein engineering that had underlying intriguing results to protein evolution. I don’t think the speaker had origin-of-life research in mind, but it gave me an idea of how that research could be extended. Another was a statement that a speaker made in a Q&A, essentially that living systems invert our standard thermodynamic model. In a standard G-Chem or P-Chem undergraduate course, the environment (thermal surroundings, modeled by a water bath) is considered to be a large reservoir that is relatively invariant while the chemical system is where all the “changes” are taking place. However, living systems maintain homeostasis and stay out of equilibrium while adapting to the environment changing. I liked the pithy contrast!

 

The third talk was unusual. I was in a session celebrating valence bond theory where almost all the speakers talked about research. However, one person chose to talk about how he was incorporating valence bond theory into P-Chem. This is not the (pathetically simplistic) valence bond theory of G-Chem, but the more sophisticated version that quantum chemists use. I had started incorporating bits of this into my quantum course, and I’ve been trying to slowly enlarge that share, since my expertise is in chemical bonding. This has meant cutting out some other parts (including math). Anyway, I very much enjoyed the talk and it sparked some ideas that I plan on trying.

 

Overall a good conference, and that takes my travel tally to four in-person meetings this calendar year so far (which included going to the ESCIP and LABSIP workshops, sort of like mini-conferences). It’s refreshing to return to in-person conferencing after a lapse of several years. I’ve missed the interactions between fellow human beings without an intervening screen or device!

Paean to Learning

I’m enjoying Carlo Rovelli’s collection of essays, published in book form as There are Places in the World Where Rules are Less Important than Kindness… and Other Thoughts on Physics and the World. As my summer comes to an end, and no new flash of insight has emerged on the research project I’ve been working on, Rovelli reminds me (in the essay “Ideas Don’t Fall From the Sky”) that discovery is preceded by lots and lots of work. You don’t wake up one morning with Eureka! if you hadn’t been working hard at the problem.

 

So where do novel groundbreaking ideas come from? Rovelli writes: “They are born from a deep immersion in contemporary knowledge. From making that knowledge intensely your own, to the point where you are living immersed in it. From endlessly turning over the open questions, trying all roads to a solution, then again trying all the roads to a solution – and then trying all those roads again. Until there, where we least expected it, we discover a gap, a fissure, a way through. Something that nobody had noticed before, but that is not in contradiction with what we know; something miniscule on which to exert leverage, to scratch the smooth and unreliable edge of our unfathomable ignorance, to open a breach onto new territory.”

 

One example Rovelli provides is Copernicus’ deep astronomical knowledge of those who went before: Ptolemy, Kepler, Brahe. On top of that, Copernicus was in the rich learning environment of the University of Bologna, where Rovelli also spent time as a student. In another essay (“Copernicus and Bologna”), Rovelli reminisces on his time as a university student, while imagining what the young Copernicus might have experienced there as a student five hundred years prior. Rovelli speculates that it wasn’t just immersing oneself in specific subject knowledge, but also the rich milieu beyond one’s field and being exposed and challenged to see everything anew.

 

In our current milieu, where higher education is on the defensive, Rovelli’s final paragraph is a paean to learning: “What can the university offer us now? It can offer the same riches that Copernicus found: the accumulated knowledge of the past, together with the liberating idea that knowledge can be transformed and become transformative. This, I believe, is the true significance of a university. It is the treasure house in which human knowledge is devoutly protected, it provides the lifeblood on which everything that we know in the world depends, and everything that we want to do. But it is also the place where dreams are nurtured: where we have the youthful courage to question that very knowledge, in order to go forward, in order to change the world.”

 

This reminded me of another paean about science and the love of learning by Tom McLeish, author of Faith and Wisdom in Science. (I previously pondered his vignette on Robert Brown.) I close this post with an excerpt of his majestic first paragraph from Chapter 5, which reminds me to persevere on my building computational models for complex non-linear origin-of-life chemistry even when I feel discouraged by my lack of insight.

 

“Science runs far deeper, quirkier and at more fully human levels than we would think from stories of relentless discoveries, spectacular phenomena or the cool application of [scientific] methodology. We know better than to swallow and inadequate narrative that portrays science as simply replacing an ancient world of myth and superstition with a modern one of fact and comprehension… [This] older love of wisdom of natural things, does indeed call on a growing illumination of nature by experiment and imagination, creating understanding where there was none before and opening up the exploration of new phenomena. It maps, in increasing detail, the physical world onto patterns, often mathematical ones, in our own minds. Notably, the scope of science in both its experimental and theoretical explorations needs to capture the stochastic, the random and the chaotic as well as the regular, smooth and periodic. But science also emerges from an ancient longing, and from an older narrative of our complex relationship with the natural world. Its primary creative grammar is the question, rather than the answer. Its primary energy is imagination rather than fact. Its primary experience is more typically trial than triumph – the journey of understanding already travelled always appears to be a trivial distance compared with the mountain road ahead. But when science recognises beauty and structure it rejoices in a double reward: there is delight both in the new object of our gaze and in the wonder that our minds are able to understand it.”

Robert Brown, Investigator

I recently read an interesting vignette about Robert Brown, namesake of the phenomena known as Brownian Motion. Back in 1827, Brown noted the jittery motion of pollen grains on the surface of water, but struggled to explain his observations. We’ll get to his investigations in a moment, but what I hadn’t known until I read the vignette was that thirty years before Darwin made his famous journey on the Beagle, Brown made his own journey on the Investigator. Brown was a botanist and both collected and catalogued numerous new plant species in his trip to Australia. Brown is also famous for introducing the term nucleus – the particle in eukaryotic cells that stores genetic material.

 

Like any capable investigator, Brown tried all sorts of things. He used different particles instead of pollen. He tried different fluids. He systematically altered the ‘reaction’ conditions. As told by Tom McLeish in his book Faith & Wisdom in Science from which I read this vignette: “Beautifully designed tests of various possible causes of the motion ruled them out one by one.” Not fluid current. Not electrical effects. Not magnetic forces. Not external mechanical vibrations. Not the presence of light. “All the more tantalizing must have been his realization that the motion is universal – not depending on the particularities of particle or fluid.”

 

The mystery wasn’t solved in Brown’s time. McLeish has some words of wisdom: “Sometimes even the deepest questions simply arise before the time to answer them has come. One of the most impressive demonstrations of self-restraint within any scientific writing must be Brown’s masterly scientific detective work, its long list of dead ends and his explanation of why he was not proposing a theory for the effect… Brown wisely guessed that satisfying the temptation to suggest various untested causes might well have set others along false trails before they had allowed imagination sufficient free reign.”

 

Interestingly, one of the popular explanations at the time, not espoused by Brown, was that the jittery motion was indication of a ‘vital force’. Apparently, the great Michael Faraday devoted much time and energy to telling the public not to jump to such conclusions. Faraday had suspected that atomic theory had legs, but back then the idea of all matter being made of seemingly occultic invisible elementary particles was far from established.

 

The solution came in 1905 in one of Einstein’s famous annus mirabilis articles. I’ve had students read it in an introductory college science class. (I annotated it heavily to help the students.) Why was Einstein able to come up with the explanation? Because he was a certified genius? Or perhaps because ‘chance favors the prepared mind’? McLeish makes the following connections: “Einstein felt discomfort with the idea of one law to govern one aspect of the world, while a different law held elsewhere… of the atomic theory – that if these particles existed then they must be in constant yet random motion… that this motion would generate the manifestation of the property we call ‘heat’ in collections of very large numbers of atoms… Brown’s pollen granules were placed among a collection of molecules in seething thermal motion… would have to pick up the random packets of energy that were jumping from particle to particle.”

 

The rest is a few lines of algebra to complete the proof. (Which is why introductory college students can appreciate it.)

 

Brown noticed something that wasn’t part of his main research interest and pursued it relentlessly. He was a botanist. I suspect that pollen moving on the surface of water was uninteresting to most botanists of his time. Brown wasn’t just curious, he was also careful. Careful in his experiments. Careful in drawing conclusions. While I’ve certainly pursued side avenues as a scientist, none were seemingly as mundane as what Brown looked at. I’m also quick to discard something that seems ‘non-promising’. One doesn’t have the luxury of squandering time and resources in this age of competitive research. But perhaps that’s part of the problem – the scientific research enterprise is skewed towards productivity and efficiency. We’re also (too) quick to trumpet success in the business. Brown’s non-conclusive efforts would be considered failure in today’s cut-throat world of scientific reputations and dollars. Maybe that’s why I found it refreshing to read about Robert Brown, the investigator.

 

P.S. I highly recommend the Introduction in McLeish's book. His parable of sonology is superb.

 

P.P.S. I found it interesting that Terrence Deacon also invokes Brownian motion to discuss how macroscopic work comes from the microscopic world.

Exact Science

Earlier this month, I blogged about The Principles of Life by Tibor Ganti (and collaborators). I was able to get my hands on a physical copy of the book (thanks to Interlibrary Loan) and I’m now in Chapter 3, “The unitary theory of life”. It begins by introducing the term “exact science”. Here’s how Ganti introduces the idea.

 

Exact sciences, such as mathematics, mechanics, the theory of electricity, thermodynamics, chemistry, etc., are characterized by the common fact that they all have specific model systems, i.e., systems which represent phenomena of the real world without disturbing factors… By using model systems the exact sciences can describe the phenomena under investigation in qualitative and quantitative respects, can formulate them mathematically.

 

I like how Ganti emphasizes the necessity of models in the physical sciences. As a chemist, we constantly use structure-based models – to represent too-small-to-see atoms and molecules. He also talks about model systems. We’re not just modeling individual structures. We’re also modeling systems and the relationships of different parts within the system. Ganti then emphasizes two things.

 

First… any one of the exact sciences models only one part of the real world and even this one only from a definite point of view, independently of the other phenomena. Second, it must be understood that it is not the real world which the exact sciences are capable of treating with an arbitrary(?) exactness, but their own model systems. Real-world phenomena are only approximated by them.

 

I’ve been thinking a lot about the modeling relation thanks to Robert Rosen’s work. I don’t quite grasp how it all works, but what I do know: When we formulate a model system (yes, with formulae!), we do so via reductionism. This is inherent in making a model. Ideally it captures the key characteristics of the system’s behavior or phenomena we’re trying to capture. But inevitably it will leave out some things. If the system is complex, and not merely complicated, probing some aspect of the system by setting some controlled test will inevitably result in surprises, somewhere down the road – they might not reveal themselves immediately depending on the underlying dynamics that we cannot capture.

 

Ganti goes on to playfully describe the absurdness of geometry (points, lines, planes) in the way it defines idealized ‘units’. Mechanics then looks ridiculous in how it uses ‘point’ masses. But the wonder is how well it works. We’ve been using Newton’s laws for over three centuries very, very fruitfully. Electricity begins with ‘point’ charges. Chemistry begins with ‘atoms’, but we have other strange hard-to-pin down elementary definitions such as the word ‘element’. But since we’re discussing Life, what is the ‘unit’ of entities that are alive? This question is tricky and Ganti spends quite a few pages discussing life, death, and the in-between – not dead, but not living – realm associated with cryptobiosis. The simple answer, the ‘cell’ isn’t quite sufficient and one has to account for different levels without privileging any one in particular – a biological relativity point of view.

 

This leads to an interesting discussion of stability. Ganti exhorts us to be careful because we have to describe narrow scientific ‘model’ terms using everyday language, much like how Bohr argues about the nature of reality using his ‘complementarity’ view given the strangeness of quantum mechanics. Ganti distinguishes equilibrium from stability. He then considers the stationary (or steady) state, which he will differentiate from homeostasis.

 

The stationary state is, by definition, a state of open systems with an equal rate of inward and outward movement of matter. However, living systems are fundamentally growing (accumulating) systems, in which more matter enters than leaves… [it] cannot be in a stationary state, and hence attempts to reduce the stability of living systems to the irreversible thermodynamics of open systems in the steady state are… doomed to failure.

 

The nub of my research studying proto-metabolic systems is how to move from thermodynamic (and kinetic) systems where equilibrium reigns starting, into the arena of non-equilibrium systems that exhibit some measure of stability (such as stationary states), and somehow layered hierarchies of control on top of all this. I’ve barely begun to learn how to deal with non-equilibrium thermodynamics, and already the looming field of control theory (of which I am mostly ignorant) already looms. I have a long, long way to go. Ganti does provide some direction – his idea of “constrained paths” embodied in the wetworks of cyclic chemistry. Autocatalytic networked cyclic chemistry, to be more specific.

 

This measure of control allows the living system to maintain a ‘stable’ internal environment (the idea of homeostasis) against what is going on external to it. This requires sampling some parameters of the external environment, and then responding to it in some way. An element of prediction or anticipation must be involved. The system needs to formulate a model that is sufficiently reduced to guess what might happen next – akin to running a quick simulation in a short timeframe before deciding how to respond. I find myself forced to use such anthropomorphic expressions: guessing and deciding seem to tread on consciousness and free-will. Indeed, there is a long way to go. But the way forward seems to be starting with ‘exact science’, recognizing its limitations, and continuing to refine better and better models.

Trial and Error

Sometimes I enjoy reading math. Or I should say I enjoy reading about math when it’s aimed at the non-specialist. Jordan Ellenberg does a great job at this, and I enjoyed reading his book How Not to Be Wrong. I had a feeling I would enjoy his latest book Shape, and so far I’ve not been disappointed. Once again, he wraps math – this time focusing on geometry and number theory – around interesting stories of people and events. Yes, there’s a chapter about Covid-19 and geometric progressions, but I won’t be discussing it today.

 

I particularly enjoyed Chapter 6, “The Mysterious Power of Trial and Error”. It’s about random walks, and features both the Drunkard’s Walk and the Gambler’s Ruin. Ellenberg begins the chapter with a question he often hears in his math class (one that I occasionally hear in my P-Chem office hours): “How do I even start this [problem]?” Ellenberg jumps at the teaching moment: “… it matters much less how you start than that you start. Try something. It might not work. If it doesn’t, try something else. Students often grow up in a world where you solve a math problem by executing a fixed algorithm...”

 

That’s a good description of how my students approach chemistry problems. In my G-Chem classes, we’re in stoichiometry tackling problems of how much of A reacts with B to form some amount of C and D. What is the limiting reactant? What if the reaction yield is less than 100%? How much leftover reactants do you have? There are systematic ways to approach these problems, and I try to model these with worked examples. But there are multiple ways to solve these problems, so I try to show the students the common approaches and their caveats. In most cases, these problems are not as open-ended, so learning algorithmic approaches is helpful.

 

Several weeks ago, we were drawing Lewis Structures in G-Chem. Trying to draw the best structures is a more open-ended problem. I tell my students that the only way to get better is to practice, practice, practice. As you draw more structures and evaluate them (using general guidelines about the octet rule, formal charges, resonance), you get better at the task. I show the students my method which is more intuitive and diagrammatic, involving some trial and error. But some of my students have learned a more algorithmic method from their high school chemistry class. I tell students that they don’t have to use my approach if they prefer something else they’ve learned. (My approach also differs from the textbook.) Students don’t like this open-endedness. They want a surefire algorithm. But real chemistry doesn’t work that way. Neither does real math, according to Ellenberg.

 

Research is a good example of trial and error. Sure, there’s intuition involved, and I’ve built up some amount of it over the years. But as I branch into areas new-to-me, I become a novice again, and so sans any better guidance, I launch in and try a few things that may or may not work. This is a challenge for students when they start working in my research group. Yes, I do tell them the first several molecules to build and calculate, and what data to extract – I’m a computational chemist – but then I try to coax them into coming up with their own ideas of what to try next. For some students, this comes more naturally. For others who resist this approach, they don’t last long in my group – because then research becomes starts to feel like a tedious chore.

 

I’ve been educating myself about machine learning approaches for some of my research projects. Nothing hardcore yet; I’m still mostly playing in the kiddie sandpit. Hence it was fun to read Chapter 7, “Artificial Intelligence and Mountaineering”. Ellenberg introduces gradient descent, a method I’m familiar with, but then he scopes out to discuss how one approaches huge N-dimensional problems – things I will have to tackle in the large data space of chemistry. How does one navigate between underfitting and overfitting? That’s an interesting challenge and a lot of it involves trial and error as you decide how much to layer and how to assign weights to your model neural net. You get the computer to do the number-crunching for you, but you should be always cautious about the output and whether it makes sense. I’ve learned that lesson through trial and error.

 

One way you can do this is to have the algorithms play games against each other, the subject of Chapter 5. Tic-tac-toe, checkers, chess, and Go, are famous in the A.I. and machine learning literature. Tic-tac-toe can be worked out by hand. Checkers can be (almost) exhaustively decision-treed. Chess and Go have too many combinations to be checked at the speed of present processors, although quantum computing may cut the Gordian knot. But these games are all closed systems. I was interested to hear that some folks had written an A.I. for the Lord of the Rings CCG – a much trickier prospect with a random draw deck and different sorts of interactions (the A.I. was written for the cooperative version of the game). Could an A.I. learn to negotiate with players? Apparently, there are some folks working on an A.I. for Diplomacy. That is a very interesting choice for a case study: Limited movement with simple rules, but the tricky part is all about the negotiations among players.

 

Can playing games through trial and error train the machine to play the perfect game? I suppose it depends on how tractable the decision-tree might be and what the complicating factors are, but perhaps this is a less important question. Ellenberg quotes top checkers and chess players and concludes: “Perfection isn’t beauty. We have absolute proof that perfect players will never win and never lose [games that end in Draws based on finite decision trees]. Whatever interest we can have in the game is there only because human beings are imperfect. And maybe that’s not bad. Perfect play isn’t play at all… To the extent that we’re personally present in our game playing, it’s by virtue of our imperfections. We feel something when our own imperfections scrape up against the imperfections of another.”

 

That last line is perhaps the beauty in trial and error.

Sciencery

I’m now three books into Terry Pratchett’s Discworld series involving the hapless wizard-protagonist Rincewind, who once again has to save the world. Grudgingly, of course. He’s the anti-hero and prefers a non-life-threatening life, but life seems to have different ideas. This time around, the magic of wizards will be threatened by the magic of sourcerers. No, that’s not a spelling typo. Sourcerers draw their magic directly from its source, bypassing the need for learning complicated incantations and hand-motions. I wonder if they somehow break the Law of Conservation of Reality, but sadly this is not addressed in the third book, aptly titled Sourcery. 

 

However, there is a remarkable side passage that deals with what I will dub “Sciencery”, that odd practice of its acolytes, of whom I am one of many – scientists. I will quote parts of it since paraphrasing Pratchett is nigh impossible and nowhere as fun.

 

It is a well-known and established fact throughout the many-dimensional worlds of the multiverse that most really great discoveries are owed to one brief moment of inspiration. There’s a lot of spadework first, of course, but what clinches the whole thing is the sight of, say, a falling apple or boiling kettle or the water slopping over the edge of the bath. Something goes click inside the observer’s head and then everything falls into place. The shape of DNA, it is popularly said, owes its discovery to the chance sight of a spiral staircase when the scientist’s mind was just at the right receptive temperature. Had he used the lift [elevator], the whole science of genetics might have been a good deal different.

 

Coincidentally, this week I was telling one of my research students about the tedious slog that accompanies most of research, but also the ‘high’ you get when something seems to just work out in one glorious gestalt moment. Pratchett’s prose, of course, is tongue-in-cheek. One might think of adages such as “Inspiration is 99% Perspiration”, but it is interesting how one gets these ‘aha’ moments. Chemistry has its famous iconic ones such as Kekule’s telling of his serpent-eating-its-tail dream. This past Friday, I told students about Archimedes and his eureka moment, upon which we proceeded to do calculations on gold-plated crowns and discussed the practicality of measuring water displacement when submerging said crowns.

 

But Pratchett has a twist on this story, so I’ll quote what follows.

 

This is thought of as somehow wonderful. It isn’t. It is tragic. Little particles of inspiration sleet through the universe all the time, traveling through the densest matter the way that a neutrino passes through a candyfloss haystack, and most of them miss. Even worse, most of the ones that hit the exact cerebral target hit the wrong one.

 

For example, the weird dream about a lead doughnut on a mile-high gantry, which in the right mind would have the catalyst for the invention of repressed-gravitational electricity generation (a cheap and inexhaustible and totally non-polluting form of power which the world in question had been seeking for centuries, and for the lack of which it was plunged into a terrible and pointless war) was in fact had by a small and bewildered duck.

 

Oh, well. There went our chances of a workable fusion reactor. We’ll have to wait until the real Iron Man comes along and invents his new element – a subject for one of my later classes on the periodic table. In the meantime, what are my chances of being hit by an ‘inspiration particle’? I might have had one this morning in my state of hypnagogia, just as I was waking up but still having strange thoughts. At the very least I sorta think I have a new idea to analyze some data if the current simpler approach fails. Not mind-bending or profound in any way. Too bad I don’t remember the wild dream that preceded it. Now if only the inspirational particles hit when I’m conscious and ready for it.

 

Sciencery seems like a lot more work compared to Sourcery. In that sense, it’s more like the Wizardry practiced by the denizens of Unseen University in Discworld. There’s a lot of studying by the lower echelons, and then a lot of backstabbing your way into the upper echelons. Or I should say it resembles dysfunctional academia. The strong and cunning survive, and if they bide their time, one might even become the Archchancellor of Unseen University, who as Pratchett says:

 

…was the official leader of all the Wizards on the Disc. Once upon a time it had meant that he would be the most powerful in the handling of magic, but times were a lot quieter now and, to be honest, senior wizards tended to look upon actual magic as a bit beneath them. They tended to prefer administration, which was safer and nearly as much fun, and also big dinners.

 

Perhaps more Cornelius Fudge than Albus Dumbledore? But there’s always the power-hungry wizard who is also magically powerful, and who think that might makes right. But he’s also trying to avoid his date with Death – yes, Voldermort, that’s you. There’s a sort of symmetry between the antagonist in Sourcery and that of the Harry Potter series. But this stock character is true of many other stories – perhaps telling us something about human nature and the corruptibility of power. Perhaps then it’s a good thing that Sciencery is so much more difficult than Sourcery, and that the Law of Conservation of Reality kicks in when needed.

 

P.S. Here’s a reference for actual neutrinos, those ghostly particles. How do you trap ghosts anyway?

Excel Too Good

I’ve told you about Tim Harford’s new book, The Data Detective. His blog continues to be interesting, and his post on “The Tyranny of Spreadsheets” sparked a few thoughts. I recommend reading his post in full. It’s interesting and witty. The tale begins with 16,000 “missing” Covid cases, and the culprit was Microsoft Excel – or at least older file versions. You’ll learn about how spreadsheet computer programs got started, how they make our lives easier, and how they’re not the best suited thing for, say, genetics researchers.

 

I use Excel in my research. Data gets parked there and then algebraic manipulations are used to turn some numbers into other numbers. I encourage my students to use Excel and take advantage of entering in formulae for calculations, so they don’t make mistakes by hand. It also allows handy and quick analysis by some simple manipulations. Fill Down or Fill Right are wonderful inventions!

 

But I don’t solely use Excel. Particularly for larger data sets that require more advanced data manipulation. (To be clear, I use the word “manipulation” in a neutral sense and not to indicate I’m trying to fudge or twist the data.) It helps that I can write code. Most of my students can’t (since they’re mostly undergraduates majoring in chemistry or biochemistry), but a few can and I’ve recently encouraged my students to take the Intro to Computing class offered at my university when they made the switch from C to Python, and revamped the curriculum to emphasize computational thinking.

 

Data can be fumbled. And automated functions in a data processing program can mislead you and severely compound errors if you’re not careful. My students sometimes learn this the hard way, and it’s a good lesson in the importance of thinking carefully about how you’re setting up those data manipulations. I’ve had my own Excel fumbles. It helps that I’ve built up an intuition over the years so a sixth sense tingles when a number looks suspicious and I double or triple check. Too bad it only works for the narrow methodology of my expertise. Being a mediocre coder also reminds me to be extra careful. I write in little tests to check both the integrity of the data and my code. This means that sometimes things take a little longer at the initial stages, but once I’m confident everything’s working fine, the analyses proceed quickly.

 

Reading Harford’s post was an excellent reminder not to let my guard down. Also, I need to make sure I use the newer Excel file formats, since I have several old templates which are still circulating in my folders. Excel's strength - computation - the automation of mathematics, is also its greatest weakness. It is too clever by half.

The Chemistry Laboratory

This week I’m enjoying reading Chemistry: The Impure Science by Bernadette Bensaude-Vincent and John Simon. It’s about the philosophy of chemistry and the unique place that chemistry occupies within the natural sciences. Naturally, it takes a historical slant, and traces the evolution of chemical theory and practices. Today’s blog post focuses on Chapters 4 and 5 (“The Space of the Laboratory” and “Proof in the Laboratory”). 

 

What is the laboratory? You can guess that it involves hard work, evinced by the word ‘labor’. The practice of the alchemists in their labors foreshadowed what chemists today do in labs. In fact, the lab ‘practice’ of the alchemists has been adopted by all the experimental sciences. Old paintings of alchemists show dark rooms mirroring the obscure secretive practice of the alchemists. I’m glad that today we work in bright well-ventilated labs, although the chemistry lab has few windows because fume hoods take up much of wall real-estate.

 

The chemistry lab however differs from the physics or biology lab in many respects. Quoting the authors: “Material is brought into the laboratory to be manipulated and changed into something else.” The essence of chemistry is transformation, be it through synthesis or analysis, the two main operational modes in lab. (Modern instrumentation now allows for ‘non-destructive’ analysis.) The authors also make a nice connection between chemical transformation and knowledge transformation (learning!) as a result of the experiments performed.

 

The lab occupies an interesting isolated artificial space that I had not quite considered until prompted by the authors: “In order to achieve this kind of control over material transformation, the laboratory has to be a closed, well-delimited space protected from the haphazard, complex circulation of materials and processes that characterize the natural world. Indeed, this is the very meaning of a laboratory, a characteristic paradox that has led to so much productive work in science studies over recent decades. The laboratory is a place deliberately isolated from the rest of the world, and so has little in common with it. Yet, it is a place intended to generate truths about the natural world… Chemists deliberately isolate themselves from natural phenomena to better understand nature.”

 

I’m a computational chemist, so my ‘lab’ exists in an even more artificial environment than the ‘wet’ labs of my experimentalist colleagues. This reductionist approach to studying nature employed by the sciences has yielded many insights, although it consistently fails when attempting to dissect complex systems. Biology, in its own right, is quite distinct from physics in its methodological approaches. Chemistry occupies an interesting interdisciplinary yet distinct space between the two, and in my biased opinion, is the most interesting of the three!

 

For chemistry, laboratory work was also the way you proved something. Lavoisier’s famous experiments in 1785 to ‘decompose’ water (an Aristotelian element) into hydrogen and oxygen (known as ‘inflammable air’ and ‘dephlogisticated air’ respectively), and then recompose them back into water, were actually quite complicated given the equipment back then and the deep-seated conviction of the audience to Aristotelian principles. How do you prove things you can’t see with the naked eye? You have to use measuring instruments and your audience has to believe that you aren’t trying to hoodwink them with other means. There’s a reason why glassware is made of transparent glass, although that’s not the only reason.

 

Lavoisier’s experiment also illustrates three important characteristics of ‘chemical proof’. Quoting the authors: “First, chemists materialize the abstract processes of analysis and synthesis in terms of chemical operations and observable phenomena, an approach that distinguishes chemistry from geometry… practical manipulations as the ultimate proof of veracity. [Second, ]… every step of Lavoisier’s demonstrated is loaded with theory… the fundamental principles such as the conservation of matter… there are no such thing as theory-independent facts… Third, the demonstration by analysis and synthesis mobilized not only theory, but also abstraction… to have the demonstration function, Lavoisier needed to insist on the purity of the raw materials he used, as well as the abstract universal nature of the products. The natural history of these elements and compounds was deemed irrelevant… [paradoxically] this very materialization of Lavoisier’s chemistry… involved a complementary idealization of the material bodies that he put in play.”

 

These ideas of abstraction and theory-laden facts are very interesting to me as an instructor. What distinguishes the novice from the expert is that the latter has a seemingly invisible scaffolding of concepts, theories, models, and other abstractions. As a chess-master easily recognizes significant positions on the chessboard, so the chemist in me quickly recognizes chemical structures and chemical equations beyond lines, letters, and symbols. How do I help my students build this scaffolding one step at a time, taking into account the invisible basis of atoms and molecules, while connecting it to macroscopic phenomena, and abstract principles represented by symbols? That’s both the challenge and joy of teaching chemistry!

 

The utility of expert ability has taken interesting turns in the history of science. Gabriel-Francois Venel, who wrote an article on “chymistry” (or perhaps it should be ‘chemystery’!) in 1753 for the Encyclopedie, “defends the chemists’ right to cultivate their own epistemological style… While the chemist’s language might well be difficult, dense and obscure, this is precisely because it reflects their unique empirical experience of the world, an experience that is drawn both from the science and the chemical arts.” Yes, chemistry is as much art as it is science, and in my opinion, sits comfortably with the liberal arts. There’s an equally strong emphasis on what you actually sense (sights and smells) to abstractions in your mind of what’s going on. I think it’s neat that our sense of smell allows us the direct detection of tiny invisible molecules! Too often we rely on sight as our primary sense.

 

I close with the authors’ discussion on “Seeing at a Glance”. This is the expert’s ability, to combine “several senses at once in the process of developing an intrinsic and non-verbal form of knowledge characteristic of the skilled artisan… this ability of seeing at a glance is not innate. Instead, it is learned through a lifetime of practical experience that breeds practical instincts or intuitions… [for example] a technician specialized in ultrasound techniques has no problem picking out the heart and legs of a foetus where the uninitiated just sees a play of light and shadows.”

 

Venel uses ‘artist’ in two senses: “as artisan… who by continued application, has trained… [in] a series of techniques that serve as tools in his trade” but also as a “creative genius”, one who cannot easily describe his or her own process of eliciting the tacit knowledge within. I can’t remember how I learned the chemistry that I understand today. I know that in my first two years of high-school chemistry, I didn’t understand anything. Somewhere along the way, something clicked, but I can’t break down that process analytically for myself. It’s likely different for different individuals. However, here’s the rub. This “seeing at a glance” expertise is increasingly supplanted by modern instrumentation in the lab. We can’t just trust our senses, we have to measure something carefully and accurately using the appropriate device to be sure. And increasingly, we are asking machines imbued with artificial intelligence to do this analysis.

 

And yet, none of the appropriate experiments can be conceived and designed without the tacit knowledge of the expert. Otherwise, Garbage In, Garbage Out. The chemical laboratory might look different today than in previous eras, but the abstract principles behind its operations are perhaps not so different.