Climate change mitigation measured in gas tanks

A lot of the discussion around what we need to do to slow down climate change is described to us in tonnes of CO2. The trouble is of course that most of us don’t know what a tonne of CO2 looks like. I thought I would try to bring this discussion into terms that most of us would understand by rephrasing it in terms of gas tanks. Keeping in mind that not all carbon emissions come from burning gasoline in a car, a gas tank is still probably a more useful visualization for most of us than a tonne of CO2. Note also that what we really care about is the total warming potential of all greenhouse gases released into the atmosphere, which is usually measured in CO2 equivalents. But since the basic unit of measure is still a tonne of CO2, the discussion below is framed in terms of CO2.

First of course we have to decide how big a tank we’re going to use. Because there’s a precedent for using a 50 L tank, that’s what I’m going to use as my standard tank. That’s the size of tank you have in a typical smaller car. At 2.3 kg of CO2 per liter of gasoline, a 50 L tank will produce 115 kg of CO2 when burned in your automobile engine. Conversely, a tonne of CO2 would be equivalent to about 8.7 tanks.

To meet its Paris accord commitments, Canada needs to cut its emissions by about 205 million tonnes of CO2 between now and 2030. (Some of you will say, “but our Paris commitments aren’t enough!” You’re right, of course, but it’s a baseline to aspire to in the short run.) As I write this, the population of Canada is about 37.6 million, so that’s 5.5 tonnes per Canadian per year. That’s about 48 gas tanks per person per year. Note that this figure includes CO2 emissions from industry and from private use, but keep in mind too that this does not include all of the carbon emissions you are responsible for through your purchases of foreign-made goods, which are accounted for in the country where these emissions are produced. So, for example, if you buy a pair of shoes made in Vietnam, those are Vietnam’s emissions, even though you are the person driving these emissions. StatsCan tried to estimate household contributions to greenhouse gas emissions (not including foreign emissions for goods imported into and consumed in Canada) a bit over a decade ago, and found that households were responsible for about 46% of Canada’s greenhouse gas emissions, either directly or indirectly. Assuming a similar ratio still holds, each of us is on the hook for about 22 gas tanks per year.

I don’t know about you, but I don’t think I fill up my gas tank 22 times per year. Remember: those are 50 L tankfuls. A lot of the times I “fill” my tank, I’m only buying 30 or 40 L of fuel. So I could stop driving completely, and that wouldn’t do it, especially when you consider that I live in a three-person household with just one car, so I can’t count on my wife and son to cut 22 fill-ups of cars they don’t have! The idea here isn’t to think in terms of literal gas tanks, but in terms of gas-tank equivalents. Between the three of us, my wife, son and myself need to cut about 66 gas-tank equivalents out of the emissions we’re responsible for.

There are plenty of web sites that will tell you what you can do to reduce your personal carbon emissions. Clearly, if I can drive less and use my bike or public transit more, that helps. Equally clearly, that alone won’t get us there. One of the things that will make a big difference that politicians don’t like to talk about is that we’re probably all going to have to just buy less stuff. I’m going to pull a few figures from Mike Berners-Lee’s excellent book How Bad Are Bananas? to make this point.

Let’s say that building the car you want to buy will produce 15 tonnes of CO2, about what it takes to build a midsize car. That’s 130 gas tanks. You could of course avoid causing those emissions by buying a used car, which won’t cause any extra emissions. But of course, eventually someone has to buy a new car (assuming we don’t all start riding public transit, but that only works for urban dwellers), and let’s suppose that you decide that you really want a new car. You could just buy a smaller car. Some cars have an emissions impact of as little as 6 tonnes of CO2, or 52 gas tanks. Even if you don’t go to the smallest car available, you could easily shave 30 or 40 gas tanks from your emissions just by buying a smaller car.

But wait! Those emissions should be amortized over the time you own the car, right? The average Canadian owns a new car for about 6 years before trading it in. So the impact of your 130-tank car over your period of ownership is about 22 gas tanks per year. Coincidentally, this is how much you need to cut out of your annual emissions, so if you can go car-free, you’ve pretty much done your part (but you might have to find other reductions if a family is sharing a car, as in our case). Going to a smaller car might save 7 gas tanks per year, which is about a third of the 22 tanks per year you need to cut out of your lifestyle. Not bad! But what if you really want that 130-tank car? If you keep it an extra two years, the impact of your new car becomes about 16 tanks per year, so you are reducing your carbon emissions by about the same amount as you would by buying a smaller car, just by keeping your car a bit longer. And obviously, this emissions reduction strategy just gets better the longer you keep the car.

And what about those Vietnamese shoes I mentioned earlier? Making the average pair of shoes and transporting it to a store near you results emissions of about 11.5 kg of CO2, or about a tenth of a tank of gas. I probably buy two to three pairs of shoes per year, so for me, this isn’t worth thinking about. But if you’re a shopaholic who loves shoes, well, I’ll let you do your own calculation…

I suspect that if you’re going to buy clothes, shoes and accessories and are actually going to wear them until they’re ready for disposal, there probably aren’t significant emissions savings to be made by changing your shopping habits. However, some of us, and you know who you are, do buy stuff we won’t wear much before putting it into the basement. Then those fractions of a gas tank really start to add up. As a general rule, buy less, and buy used if you want to cut your carbon footprint. This applies not only to clothes, but to anything else we buy on a whim and then barely use.

And the general idea of buying what you need and using it applies to food, too. Food waste is a massive contributor to greenhouse gas emissions: Because food is wasted, it is necessary to overproduce food, which leads to deforestation, i.e. loss of an important carbon sink. Moreover, agriculture has a direct energy cost, so more food grown means more emissions from the agriculture sector. Then there is the transport of food that will never be eaten. And rotting food often produces methane, an even more potent greenhouse gas than carbon dioxide. A rough estimate is that household food waste (as opposed to food that is wasted somewhere in the supply chain) amounts to about a quarter tonne of CO2 per person per year in Canada, or 2.2 gas tanks. Not a huge number, but still about 10% of the emissions you need to cut per year. Roughly speaking, to reduce the amount of food you waste, you have to buy things you plan to eat, and make sure you actually do use it before it goes bad. Sounds simple, but it does take a bit of a mental adjustment to our shopping and cooking habits.

So there you have it. Climate footprint and emissions reductions conceptualized in gas-tank equivalents. Hopefully this helps you understand the size of the problem a bit better, and also puts in perspective some of the things you can do to reduce your climate impact. A lot of the advice comes down to buying less stuff and using it for longer (or using it at all in the case of food). And as an added bonus, if you spend less, you’ll have more money in your bank account for a rainy day. Win-win.

Publications in CVs

I’m currently chairing the Ph.D. program committee at the University of Lethbridge, and I just finished reading the files of the applicants who have applied to our program for admission later this year. At the UofL (and elsewhere), students applying to the Ph.D. program have to submit a CV. And of course, if you have publications, they should be in your CV. The trouble I’m having with many files I’m reading is that students don’t give full bibliographic details for their papers, which means that I sometimes have to do some additional digging if there is something I want to check on. Here are some things I sometimes find missing:

  1. A page range or article number. Yes, I know, the DOI should be enough, but if I decide to go looking for your paper for some reason, it’s often more convenient to have the first page number or article number (along with the volume number) than the DOI. Why? Because some journals make it particularly efficient to find papers with the volume and page number.
  2. The DOI. At the risk of contradicting myself, it’s sometimes easier to have a DOI. The DOI is especially useful if the journal is a bit obscure.
  3. The volume number. Well, duh!, you might say. But a surprising number of people forget to put that in.
  4. The year. Ditto.
  5. The issue number can be useful, depending on the journal, so by all means include that, too.
  6. For articles in journals that use article numbers rather than pages, the number of pages. This gives me some idea whether I’m looking at a letter-style publication or a full paper. I know it’s not foolproof, but it does help.

The point is that the more bibliographic details you include, the easier you make it to find your paper should someone wish to do so.

Finally, make sure that those bibliographic details are correct! You would be surprised at how many slightly mangled journal titles there are in people’s CVs, for example. That makes it hard to find the paper. It might cast doubt on whether the paper exists at all. Or it might just convince a person reading your CV that you don’t pay much attention to detail. Probably not the impression you want to leave.

On a related note, if you have multi-authored conference presentations in your CV, please clearly indicate if you were the presenter or not. You can use a special mark (asterisk, boldface or italics) for the presenter, or you can separate your presentations into ones you have made and ones that author people presented. Without this, long lists of multi-authored presentations are uninformative, and may be seen as padding your CV.

Before you write your thesis, read the instructions

I have a little tip today for those of you preparing to write a thesis: Before you start, read your university’s or department’s thesis guidelines. There are some things that are easy to do as you’re writing your thesis, but a pain to do after, like compiling a table of abbreviations, which is usually required. If you read the thesis guidelines before you start writing, you can make notes of the things that you will need to do, and probably save a lot of time later on. It’s quite likely that you will discover things you’re supposed to do that you wouldn’t otherwise have thought of on your own.

I would also suggest that you frequently go back to those guidelines during the writing process. If you’re wondering how you’re supposed to format figure captions, the thesis guidelines probably answer this question. If you’re not sure what is expected in a thesis abstract (it varies from school to school), or whether you need to write a longer summary in addition to the abstract (required in some places), look no further than your university’s thesis guidelines.

Every School of Graduate Studies has a person whose job is to make sure that theses meet the local requirements. This person generally doesn’t look at your thesis until you have defended it and have completed your revisions. It’s a lousy time to find out that you need to add something, or rewrite the abstract, or reformat the whole thing. A few minutes of reasonably careful reading ahead of time will save you all these headaches. It’s a smart investment of your time.

Incidentally, the same principle applies to lots of other things: Reading instructions for scholarship or grant applications, or instructions in job ads about what you are supposed to submit in your application, will generally repay handsomely the small amount of time you devote to this activity. In the case of a thesis, the worst that will happen if you mess something up is that you will be told to fix it. For a grant or job application, not following the instructions may mean that your application isn’t even considered.

So just “read the instructions, that’s how you get it right”, as the Doodlebops so eloquently put it.

SIAM Review 60th volume

This year marks the publication of the 60th volume of the venerable SIAM Review. As has become traditional when journals mark anniversaries, the editors of SIREV have compiled a list of the journal’s 10 most read articles. These lists are always interesting, both for what shows up and for what is missing (from my purely subjective point of view).

Number 1 on the list is a modern classic, The Structure and Function of Complex Networks by Mark Newman. At the time this paper appeared in 2003, network science was just getting hot. Newman’s review, which laid out all of the foundational ideas of the field in a very clear way, quickly became the standard reference for definitions and basic results about various kinds of networks. It didn’t hurt that Newman had recently made a splash in the scientific community by analyzing scientific collaboration networks: given that everyone’s favorite topic is themselves, scientists were naturally intrigued by a quantitative study of their own behavior. All kidding aside, Newman’s SIAM Review article has been hugely influential. All kinds of networks have been analyzed using these methods, ranging from social networks to protein interaction networks. As if having the number 1 paper in this list wasn’t enough, Newman is also a coauthor of the 2009 paper Power-Law Distributions in Empirical Data, which is number 6 on the list. The latter paper deals with statistical methods for determining whether or not a data set fits a power-law distribution.

Desmond Higham has the singular distinction of having two singly authored papers on this list, both of them from the Education section of SIAM Review, but both wonderful introductions to their topics for young scientists, or for old scientists who need to learn new tricks. At number 3 on the list, we have An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations, which presents the simplest introduction to stochastic differential equations I have ever had the pleasure to read. Then at number 4, we have Modeling and Simulating Chemical Reactions. In the latter, Higham walks us through three levels of description of chemical equations, as Markov chains in the space of species populations, then using the chemical Langevin equation, and finally in the bulk mass-action limit. He derives each method from the preceding one, essentially by focusing on computational methods for simulating them, and then showing that these methods simplify as various assumptions are introduced. I think that these two papers of Higham’s have been successful not only because of his exceptionally clear writing, but because he also provided Matlab code for all his examples. The interested reader can therefore go from reading these papers to doing their own calculations rather quickly. I learned a lot from these papers myself, and I’ve used both of them in a graduate course on stochastic processes. They’re just fantastic resources.

One paper that didn’t appear, and that I had guessed would be there before I looked at the list, is the classic 1978 paper Nineteen Dubious Ways to Compute the Exponential of a Matrix by Cleve Moler (original developer of Matlab, and founder of MathWorks, the company that sells Matlab) and Charles Van Loan (author with the late Gene Golub of the book Matrix Computations, known by people in numerical analysis simply as “Golub and Van Loan”). It’s possible that it didn’t make the list because an expanded version of the original was published in the SIAM Review in 2003, and that this paper’s reads are therefore split between the two versions. However, it’s still a surprise. This is one of those papers that is often mentioned, in part I’m sure because of its mischievous (if accurate) title, but also because it discusses an important problem—matrix exponentials show up all over the place—and does so with exceptional clarity.

There have been lots of papers on singular perturbation theory and the related boundary-layer problems in the SIAM Review over the years, which is perhaps not surprising given how central these methods are to a lot of applied mathematics. In fact, in 1994, the SIAM Review published an issue that contained a collection of papers on singular perturbation methods. I would have thought that at least one paper on this topic would have made the list. My all-time favorite SIREV paper is in fact Lee Segel’s Simplification and Scaling, which I routinely assign as reading to graduate students who need an introduction to the basic ideas of singular perturbation theory, followed closely by Lee Segel and Marshall Slemrod’s The Quasi-Steady-State Assumption: A Case Study In Perturbation, which derives the steady-state approximation for the Michaelis-Menten mechanism using the machinery of singular perturbation theory. The full power of these methods is made evident when they derive a more general condition for the validity of the steady-state approximation than had previously been obtained. The late Lee Segel was one of the great pioneers of mathematical biology. He worked on every important problem in the field, from oscillators to pattern formation, and left us some beautiful applied mathematics. He also left us an absolutely wonderful book, Mathematics Applied to Deterministic Problems in the Natural Sciences, coauthored with Chia-Chiao Lin, who has sadly also left us. Marshall Slemrod is, fortunately, still very much alive. Marshall is probably best known for his elegant work in fluid dynamics, but he has worked on quite a variety of problems in applied mathematics over his long and distinguished career.

It’s interesting to compare SIAM list of “most read” papers to the most cited papers from SIREV (Web of Science search, Oct. 8, 2018). Here they are:

  1. Mark Newman’s The Structure and Function of Complex Networks, cited 8333 times, more than twice as often as any other paper published in SIREV. No great surprise there.
  2. Fractional Brownian Motions, Fractional Noises and Applications by Benoit Mandelbrot and John van Ness (3554 citations). Perhaps this one should have been on my radar, although I’ll admit that I have never read it. I’ll put it on my reading list now.
  3. Power-Law Distributions in Empirical Data, Newman’s other entry on the most-read list, which interestingly comes out much higher in the most-cited ranking that in the most-read list, where it occupies the number 6 spot, with 2885 citations.
  4. Semidefinite Programming by Lieven Vandenberghe and Stephen Boyd (2086 citations)
  5. Tensor Decompositions and Applications by Tamara G. Kolda and Brett W. Bader (2042 citations, number 2 on the most-read list)
  6. Analysis of Discrete Ill-Posed Problems by Means of the L-Curve by Per Christian Hansen (1870 citations)
  7. The Mathematics of Infectious Diseases by Herbert W. Hethcote (1813 citations)
  8. Atomic Decomposition by Basis Pursuit by Scott Shaobing Chen, David L. Donoho, and Michael A. Saunders (1647 citations)
  9. On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws by Amiram Harten, Peter D. Lax, and Bram van Leer (1493 citations). This is the kind of paper we often see on most-cited lists because it discusses practical issues in the numerical solution of PDEs.
  10. Mixture Densities, Maximum Likelihood and the EM Algorithm by Richard A. Redner and Homer F. Walker (1256 citations)

It’s interesting, and perhaps a little surprising, how little overlap there is between the most-read and most-cited lists. Just three papers show up on both lists! This is another manifestation of the well-known problem of trying to use any single metric to determine the influence of a paper.

There are other SIREV papers that I really love, even though I wouldn’t have expected them to make this list, sometimes because of their real-world applications, and sometimes just because they describe very clearly some beautiful applied mathematics.

Bryan and Leise’s The $25,000,000,000 Eigenvector: The Linear Algebra behind Google, explains the mathematics behind the Google search engine. It’s both a great educational article on large, sparse matrix eigenvector calculations, and an interesting peek into the workings of one of the most important technologies of our time.

James Keener’s article on The Perron-Frobenius Theorem and the Ranking of Football Teams is a great read, and a fun way to introduce students to the powerful Perron-Frobenius theorem. James Keener has been one of the leading figures in mathematical biology over the last several decades, and is the author, with James Sneyd, of the highly regarded textbook Mathematical Physiology.

I also really enjoyed Diaconis and Freedman’s Iterated Random Functions, which describes some lovely mathematics that connects together Markov chains and fractals, among other things. Persi Diaconis is perhaps best known for his analysis of card shuffling and other games of chance. In fact, another paper of his in the SIAM Review (with Susan Holmes and Richard Montgomery) on Dynamical Bias in the Coin Toss is also a fantastic read.

I could go on, but I think I’ll stop here.

You may have noticed some recurring themes in this post. One is that there is some great writing in the SIAM Review. In fact, I would say that this is a hallmark of SIREV. Regardless of the author or topic, the final published paper always seems to be a great piece of scientific literature. Of course, I might be a little bit biased, having published a Classroom Note in the SIAM Review myself. Another theme of this post is the number of outstanding scientists who have written for SIREV. SIREV makes room for up and comers, but it also regularly gives us the benefit of reading papers by people who have spent decades deepening their knowledge of their respective areas.

So happy birthday, SIAM Review, and many happy returns!

Using RSS to help you keep up with the literature

This is a followup to my 2014 post about “Keeping up with the literature“. I’m a strong advocate of arranging for the information to come to you rather than you having to go looking for it. I’ll look at stuff that shows up in my mailbox, or is otherwise put right in front of me, but I’m unlikely to do literature searches unless I’m looking for something fairly specific. One trick that I have perhaps not used as much as I should is RSS feeds. An RSS feed sends you a one-line summary of new content added to a web site. Some RSS feeds allow you to narrow what is sent to you according to your field of interest. Some journals provide RSS feeds. You might find this a useful alternative to receiving tables of contents by email. In some cases, RSS feeds might be useful because they will only show you content from a specific section of a journal, so you don’t get overwhelmed with lots of irrelevant stuff.

I currently subscribe to a couple of RSS feeds from the Physical Review journals. The Physical Review journals cover a huge range of topics, most of which are of no interest to me. Getting their complete tables of contents would waste a lot of my time. However, they have specialized RSS feeds broken down by area of interest. I subscribe to the Physical Review Letters Soft Matter, Biological, and Interdisciplinary Physics feed, as well as to the Physical Review E Biological Physics feed. The volume on these feeds is very manageable, and I can quickly find the few articles of interest to me.

To get started, you need to install an RSS reader application. Journals (or other web sites) with RSS feeds will display this logo:

(The logo may be quite small, and may not be colored.) If you click on this logo, you will typically end up at the actual RSS feed page. You want to copy the URL of this page, and then give it to your RSS reader application. The RSS reader will typically sit in your toolbar (or equivalent for your computer’s OS) and let you know when something new appears in your feed. And that’s it! When you see material in which you’re interested, you just have to click on it, and you will be taken to the article.

English words with Latin and Greek-derived plurals

I guess I’m on a language kick… After my recent post about the misuse of “similar to”, I’m going to tackle some Greco-latin plurals that lots of people don’t know how to use.

English is a lovely mongrel of a language, having adopted words and grammar from every invader who ever set foot on the island of Great Britain. The Romans ruled over England and Wales for about 350 years, so naturally, Latin left its mark on English. Some words were also adopted from Greek through the scholarly community. Most Latin and Greek words were eventually anglicized, and English-style pluralization rules applied, but a few retained their Greco-latin plurals. Some of these are heavily (mis)used in scientific writing. I’m going to try to sort out for you some of the ones that are most often used in the texts I read.

If you have a standard for judging something, you have a criterion. That’s right. Criterion. It’s possibly you have never seen this word and would have expected criteria instead, but criteria is the plural of criterion. It’s particularly important to get this right because English has just one definite article, “the”. Thus, “the selection criterion” and “the selection criteria” imply, respectively, one criterion and many. The meaning of the sentence is therefore altered if you use the wrong word. As another example, “a criteria”, which I see a lot, is wrong because “a” is a singular indefinite article, and “criteria” is plural. If you have one rule you use for making a decision, you have a criterion.

Erosion is a natural phenomenon. It’s one of the many geological phenomena that shape our Earth. So again, you would never write “a phenomena”.

Do you grow cells in a medium, or in a media? Hopefully, you would choose the singular “a medium“, media being the plural of medium. We might prepare media (if we are preparing several different media, or possibly several batches of a particular medium), but more commonly we might prepare a medium. It’s surprising how often media is used given how rarely it’s actually the syntactically and grammatically correct choice.

We can search for minima on a potential energy surface, on the assumption that there might be more than one, but when we find one, it’s a minimum. Obviously, the same comment would apply to maximum and its plural maxima, as well as optimum/optima. Incidentally, outside of science, people tend to say minimums and maximums for the plurals of these words—a usage that is sanctioned by modern dictionaries—so perhaps it’s time for us to stop trying to sound learned by using the Latin plurals. Errors in the singular would almost certainly vanish if we did so.

But please, no “criterions”, “phenomenons”, or “mediums”. Unless, in the latter case, you want to get together a group of people who can talk to the dead.

Similar and similarly: are they similar?

As a professor, I see a lot of student writing, some good, some not so good. And I’m one of those people who think that a professor’s job includes teaching writing, regardless of the discipline one belongs to. So here is my first foray into advice on writing.

In the last couple of years, I have noticed that many students use “similar” incorrectly. I often see sentences structured like the following:

Similar to protein A, protein B binds to protein C.

So what’s the problem? To understand that, we have to ask what “Similar to protein A” modifies. What the writer is trying to say is that protein B behaves like protein A in that both bind to protein C. It’s the entire action of protein B modifying protein C that is similar to the action of protein A. Therefore, “Similar to protein A” is modifying the entire principal clause. However, “similar” is an adjective, so it should modify a noun. “Similar” therefore can’t be right.

A modifier of a clause can only be an adverb, so a correct version of the above sentence would be

Similarly to protein A, protein B binds to protein C.

“Similarly” (note the -ly ending) is an adverb, so it can modify an entire clause. Problem solved.

Of course, this isn’t the only solution. It’s always good to have more than one way to say something so you can vary the style of your text a little bit. Sometimes, the simplest way to say something is the best, so one alternative is to replace the adverb by a common preposition:

Like protein A, protein B binds to protein C.

The truth is, though, that neither of the above sentences probably says what the student who wrote it wanted to say. All these sentences really say in the end is that both A and B bind C. However, these constructions often show up in text where a student is actually trying to say that the two proteins bind C in a similar way (using similar contact surfaces, etc.). Why not just say that?

Protein B also binds protein C. B and C make similar contacts as A and C in the respective complexes.

Note that I turned one sentence into two. My meaning is now completely clear and unambiguous. This is another lesson: unless you’re strictly space limited for some reason, sometimes it’s better to use a couple of sentences and a few extra words in order to make your meaning completely clear. Similarity, for example, is a slippery complex. Saying that two things are similar really doesn’t tell us much unless we say in which ways they are similar. Similar comments apply to many other constructions. When writing, ask yourself what you want to say, and then make sure that the words you use convey your meaning without ambiguity.

What exactly do you mean by “stable”?

Stability is a highly context-dependent concept, and so it often leads to confusion among students, and sometimes among professional chemists, too.

If I say that a certain molecule is “stable”, I might mean any of a number of things:

  1. It’s possible to make it, and it won’t spontaneously fall apart.
  2. It’s possible to isolate a pure sample of the substance.
  3. It won’t react with other things. This is often qualified, for example when we say that something is “stable in air”.

The trick is to pick up which one is meant from context. A recent example arose on a test question in my Chemistry 2000 class, where I asked, in a question on molecular orbital (MO) theory, if argon hydride, ArH, is a stable molecule. In this case, the “context” was in fact a lack of context: I simply asked about the stability of this molecule, without any mention of holding it (the isolable substance definition) or of bringing it into contact with anything else. Thus, I was relying on the first definition of stability. Unexpectedly, simple pen-and-paper MO theory predicts that ArH has a bond order of ½, and so is predicted to be stable, although clearly not by much. This ought to be quite a surprise to anyone who has studied chemistry since we normally think of noble gases like argon as being quite unreactive (stable in the third sense), and so unlikely to form compounds. And when we do get compounds of noble gases, they are usually compounds with very electronegative elements such as fluorine. Moreover, ArH would violate the octet rule. Students do run across non-octet compounds from time to time, but the octet rule is deeply ingrained from high school. Finally, ArH would be a radical, and students are often taught to think that radicals are “unstable”, in the sense that they are highly reactive.

As it turns out, the simple MO theory we learned in class is sort of right: excited states of argon hydride are stable enough to be studied spectroscopically—in fact the first such study was carried out at Canada’s National Research Council by JWC Johns1—but the ground electronic state is unstable in the first sense: it dissociates into H and Ar atoms. So our chemical instinct is right about this compound, too. Welcome to the nuances of chemistry.

For the sake of argument, suppose that ArH had a stable ground electronic state, as predicted by simple MO theory. It would fail to be stable in the second sense because the meeting of two ArH molecules would result in the energetically favorable reaction 2 ArH → 2 Ar + H2. And of course, ArH would react with a great many substances. In fact, we could think of this compound as a source of hydrogen atom radicals.

Before we move on from ArH, let’s talk about some of the reflexes that would have led us to predict it to be unstable. The fact that a material is normally unreactive doesn’t mean it won’t form a compound with something else under the right conditions. If I want to make ArH, I won’t try to react argon with hydrogen molecules because the atoms in H2 are held together by a strong bond, so it would be energetically unfavourable to swap that bond for an Ar-H bond. I will need a source of hydrogen atoms. If I do expose argon atoms to hydrogen atoms, the very reactive radical hydrogen atoms may well react with the normally unreactive argon, which is in fact what happens. But none of that is directly relevant to the question of the stability of the ArH molecule. If I ask about that, I just want to know if the thing will hold together assuming it has been made.

The octet rule is deeply embedded into the psyches of anyone who has studied chemistry. It is, indeed, an excellent rule of thumb in many, many cases, especially in organic chemistry. But students are soon exposed to non-octet compounds, so clearly the octet rule is not an absolute. And yet we often hear people talk about an octet as being a “stable electronic configuration”. There’s that word again! But what do people mean when they say that? The answer is, again, highly dependent on context. In s- and p-block atoms, an octet fills a shell, and so the next available atomic orbital is quite high in energy, and it will likely be energetically unfavourable to fill it. In molecules, the octet rule just happens to often result in electronic configurations with an excess of bonding over antibonding character, so they are stable in the first sense. And because eight is an even number, the resulting molecules often have all of their electrons paired, so they are less reactive than they might have been if they had an odd number of electrons. But you may recall that oxygen, on which more below, has two unpaired electrons, even though its Lewis structure satisfies the octet rule. We should always remember then that it’s the octet rule, and not the octet law. Arguing that something is especially stable because it has an octet is just not a very good explanation. Now having said that, the octet rule generally holds for compounds from the second period, largely because trying to add more electrons to these small atoms is energetically unfavourable. But even that is a contingent statement since it depends on where those electrons are coming from and whether they have anywhere else to go. Certainly, you can measure an electron affinity for many molecules with octet-rule structures.

As for the argument that radicals are “unstable” (which you will hear from time to time), it’s not true. Many radicals are very reactive. But a great many radicals are stable in the first and often in the second sense, too. This includes many of the nitrogen oxides, notably nitric oxide, which is stable enough to serve as a neurotransmitter, and can be stored in a gas cylinder, but is conversely reactive enough to be used as part of your body’s immune response. Again we see that stability and reactivity do not necessarily coincide, even though the word “stability” is sometimes used in the sense of “reactivity”.

Of course, ArH is an extreme, and NO is not a terribly familiar compound to most of us, even though our bodies make it. So let’s talk about a more mundane molecule. Oxygen has not one but two unpaired electrons. So despite its Lewis diagram, oxygen is a radical. Nevertheless, oxygen is certainly stable in the first and second senses. There are lots of oxygen molecules in the atmosphere, and they don’t just fall apart on their own. (They do fall apart if supplied with enough energy, for example in the form of an ultraviolet photon, but that is another question altogether.) You can store oxygen in a gas cylinder, so it is certainly isolable. But oxygen is highly reactive, in part because of its unpaired electrons, at least towards some substances and in some circumstances. It’s a fairly strong oxidizing agent for example. Many metals, if left standing in air, will become coated very quickly in a layer of their oxide. And if provided with a little heat, oxygen will react vigorously with many materials. We call these reactions of oxygen “fire”.

The very different meanings of “stable” mean that we have to think when we hear this word. Ideally, we would also banish the third meaning mentioned above in favour of more specific language, such as “reactive towards”. Conflating questions of stability and reactivity just makes it harder to think precisely about what we mean when we say that a molecule or substance is stable.

References:
1J. W. C. Johns (1970) A spectrum of neutral argon hydride. J. Mol. Spectrosc. 36, 488–510.

How Eugene Garfield (1925–2017) changed the lives of working scientists

Eugene Garfield died Feb. 26th. Ever heard of him? No? And yet, he has had a huge influence on how scientists work today. Garfield is the person who brought to life the Science Citation Index, which you may know as the Web of Science. This has allowed us to efficiently search the literature forward in time, and has also spawned a cottage industry in trying to measure the impact of scientific studies, of the journals they were published in, and of the scientists who carried them out. One way or another, if you’re a scientist, Garfield has changed your career.

Garfield started out as a chemist, but by his own account, he wasn’t very good at it. One thing led to another, and he ended up creating a citation index for science. You can read the story elsewhere. It’s interesting, but I want to talk about his impact on science and scientists.

The practical impact of the Science Citation Index and of its modern descendant, the Web of Science, has been enormous. Have you found a key paper in your field? By doing a citation search, you can find out how people followed up the original idea. If you’re not already doing citation searches regularly to find relevant material in the literature, you are living in a state of sin. If you don’t know how, run to your university library, and ask a friendly librarian to show you. This is an indispensable skill for a scientist, and one that you can learn in just a few minutes.

Once we had a citation index, it became easy to count the number of citations a paper, or a scientist’s total output, was getting. And eventually some bright spark decided that counting citations was a good way of deciding how important a scientist’s work is. Citation counting is a tricky business because citation rates are affected by a whole host of non-scientific factors, including different cultures in different disciplines. Still, used wisely, citation statistics can help round out the picture when trying to assess a scientist’s work, especially if we allow a paper to mature a bit before we start counting.

At some point, Garfield hit on the idea of trying to use citation data to measure the impact of journals, and thus was born the Journal Impact Factor. The Impact Factor is the number of citations to articles in a journal from a two-year window divided by the number of articles published in that period, so it’s essentially an average number of citations per article in a very narrow window of recent time. Although the impact factor was intended mostly as a tool for librarians to use in allocating resources, it has been widely abused as a proxy for journal quality. If you ever apply for a grant, someone is bound to look at the impact factors of the journals you have published in to try to assess how important your work is. Yes, that’s right, if you get into the right journal, you can bask in reflected glory. On the other hand, if you publish in a journal with a small impact factor or, heaven forbid!, a journal that isn’t indexed in the Web of Science and that therefore doesn’t have an impact factor, then you really have to track other measures of quality carefully because people will automatically assume the work is of lesser quality. Garfield hated this way of using impact factors, but sometimes you just can’t control the monster you created.

So whether you’re searching the literature or applying for money, you’re living in Eugene Garfield’s rather large shadow. A giant has passed. We owe him a great debt. If you want to honor his legacy, use citation searches and teach them to others, and try to make sensible use of citation statistics and impact factors.

Surviving, and maybe enjoying, your thesis defense

It’s the big day. Today, you defend your thesis. So what can you expect?

There are variations in the format of the thesis defense from university to university, and certainly from one country to another. What I’m going to say is necessarily going to apply most directly to the system we have here at the University of Lethbridge, which is similar to what you would see at most North American universities. But I think there may be elements of this post that will apply no matter where you are. With that caveat in place, I’m going to focus mainly on the questioning phase of the thesis defense.

What to bring to your defense

If your defense is to start with a presentation, make sure you have your presentation on a memory stick or two, and in your email, and maybe in some other backup place so that you’re sure to have it when you get there. It is likely that chalk or whiteboard pens will be provided, but it doesn’t hurt to have a piece of chalk or a whiteboard pen in your pocket so you can generate a quick sketch or write down an equation in the course of answering a question. If possible, check out the room first so you have some idea of what the audiovisual situation is going to be, including what kind of boards the room has.

I strongly recommend that you bring a printed copy of your thesis. The defense proper is normally conducted around some kind of table. In our case, defenses are usually conducted in classrooms, so we do our best with furniture that isn’t quite right for the purpose, but in any event you will likely be sitting for most of the defense. The examiners will invariably want to refer to specific pages of your thesis, and expect that you will have a copy on hand. I personally think that flipping through the pages of a physical copy is easier than dealing with an electronic copy, but that’s a personal choice. Either way, you need to be able to refer to a copy of your thesis during the examination. By the way, you shouldn’t count on being able to plug in a laptop in the thesis examination room. There may or may not be available outlets. Don’t take anything for granted. Charge up your device(s) or, again, bring a printed copy. You can’t go wrong with paper.

The opening presentation

Depending on the system at your university, the questioning may or may not be preceded by a presentation, which may or may not be open to the public. There are just too many variations on this theme to properly address it in a blog post. If you do have to make a presentation, tell yourself that your main audience is the examiners, who are likely to use what you say in your presentation as a springboard for questions. The same comment therefore applies to your presentation as to your thesis: Don’t say anything in your presentation that isn’t completely clear in your head.

Ready for the questions?

Because here they come! You can expect many types of questions, sometimes interspersed with comments, some of which I mentioned in my previous blog post.

  • There are likely to be some direct technical questions about the contents of your thesis. “What did you mean by that?” “Could you explain the logic behind this part of your thesis?” “Explain how technique A, which you used in your thesis, works and how the results are interpreted.” “Walk us through the analysis of experiment P.” And so on. As I explained previously, you almost always need to be able to answer these questions.
  • There may be criticisms disguised as questions. These pseudo-questions often sound like questions from the first category. For example, an examiner may ask a question about your use of terminology, or about an assumption you made. The examiner already knows that you will give an answer that violates some orthodoxy within which they work because of what you wrote in your thesis. They will then explain to you the error of your ways. Some examiners will dispense with the pseudo-question and just tell you outright that there is an error of some sort in your thesis. You need to be mentally prepared for these events, which are fairly common, although not typically a major component of a defense. Showing some understanding of the issues once they have been explained to you is good, provided of course you do understand the issues. Humility is absolutely required. Do not argue with the examiner if they tell you that something you wrote is wrong. Even if you don’t think it is, the examiner is at least pointing out something in your thesis that is liable to misinterpretation and that therefore needs to be clarified. Do ask questions if you do not understand the examiner’s point. Other than asking to have questions clarified, on which more below, this is the one situation where you will likely be allowed to ask questions during your defense.
  • Examiners may make suggestions about revisions to your thesis. Many students are tempted to take notes when this happens. This isn’t necessary. You will be provided with lists of suggested and required revisions from the examiners after the defense.
  • There are likely to be questions about where your thesis fits into the overall scientific enterprise. Why is your work important? How does it connect to other open questions? What new insights do we get from your work? There should already be material along these lines in your thesis, particularly in the introductory and concluding chapters. The examiners will likely want to go a bit deeper than what you wrote. You should be able to take a stab at questions like these although, on occasion, the questions will veer off into areas of science you really know nothing about.
  • Someone will almost certainly ask about what the next logical step in your research would be, were you to continue this line of research. Again, you need to be able to give some sort of answer to a question like this. Ideally, you would have answers to such questions that go beyond trivial “one more experiment” answers, and that show that you have a vision for your field of research.
  • You may be asked to revisit your work, i.e. to think about what you might have done differently, given what you know now. Usually these questions are fairly specific. “You used method B to determine property X. Are there other, possibly better ways you could have done that?” It’s great if you can answer these. You don’t have to constrain yourself to the facilities you had access to during your degree. Go ahead a propose a cool cyclotron experiment! If you really can’t think of an answer to one of these questions, an examiner may offer a suggestion and ask you to comment. Typically, an examiner would not be drawing on obscure knowledge to frame questions like these, and you should be able to provide some intelligent comment on what you would have learned (or not) from a different method.
  • On occasion, you will get an examiner who likes to steer the conversation towards their area of research. Unless the examiner’s area is very close to yours, this can get you into deep waters fairly quickly. Bonus credit if you can give a sensible answer, but it’s probably OK if you can’t answer these questions in much depth.

How to answer questions at your defense

Rule number one is: think! You don’t have to blurt something out instantly. Take a few seconds to compose your thoughts. Make sure you understood the question. If you’re not sure, ask for clarifications.

Rule number two is that answers to technical questions should be technically correct. You should understand the experiments or calculations you did thoroughly. You should know the key scientific theories, methods and observations from your field.

Rule number three is don’t overinterpret the question. Not all of the questions will be ultra-sophisticated. Remember that some of your examiners may be from a different field, and may have very simple questions. Even examiners in your own area may want to ask you a simple question, either to help you relax towards the beginning of the defense, or to set up a deeper question. Listen carefully and answer the questions that were actually asked. Don’t look for complex interpretations of simple questions. You would be surprised how often students fail to answer questions satisfactorily because they are interpreting a question in the most complicated way possible when an examiner was really asking a very simple question.

Many of the questions will invite you to speculate. Rule number four is that speculation should be based on sound science, but that it’s OK to extrapolate, even into areas you’re not comfortable with. You should however make it clear when you are doing so. “I’m not an expert on X, but I know P and Q, so I think perhaps T will hold.” Interesting conversations often evolve from such questions and answers. The examiner may give you additional information and ask you to incorporate that into your thinking. Again, give yourself a little time to think, and then tell us something interesting.

But what if I really don’t know?

Then say so. (I guess this is rule number five.) There may be questions that you genuinely don’t know anything about. Don’t try to bluff. That will end badly. Just say you don’t know. Depending on the nature of the question, any of the following may occur:

  • If the examiner knows that the question is really a stretch, they may simply move on.
  • If it’s a question the examiner thinks you should be able to answer, they may try to rephrase it, or to give you a hint about what they’re looking for. Listen carefully. Try to keep calm and to process the information provided in the question or hint. Think. Hopefully it will become clear what the examiner wants and you can proceed to answer.
  • Examiners often come to an exam with a set of related questions that build on each other. If you fail to answer a question that is part of one of these sequences, they may provide you with an answer so that they can carry on with their line of questioning.

Be aware though that you are expected to answer most of the questions. If you answer “I don’t know” more than once or twice, you’re usually in trouble. What examiners are looking for, above all, is intelligent engagement.

What happens after the examiners send you outside?

Once the questions are finished, the examiners will send you outside so they can deliberate. This can take anywhere from 10 minutes to an hour. What exactly the examiners have to decide depends on the rules at your graduate school, but typically there are two questions, whether they are evaluated separately or not:

  1. Was your thesis, on the whole, acceptable?
  2. During your oral examination, did you show an adequate grasp of your project and of your area of science?

Your thesis should have been read and extensively commented on by your supervisor before you submitted, so in most cases, it will be found acceptable, but expect to be asked to make revisions. It is very rare that the examiners don’t find at least a few passages that aren’t as clear as they could be, or some particular issue that you glossed over. In some cases, they will have more serious concerns about some parts of the thesis, and you may be asked to make major revisions.

If deliberations go on for more than 20 minutes, it’s usually because major deficiencies were identified during the defense. You either said “I don’t know” much too often, or you gave incorrect or badly incomplete answers to more than a few questions. In these cases, the examiners need to decide if they want you to do it again, possibly after revising the thesis. Deliberations that are dragging on are a sign that the examiners are having trouble agreeing. They will eventually vote, but if you had a weak defense, the discussions are much tougher and more drawn out because everyone wants to make sure they do the right thing in the end.

Of course, most of the time—and I want to end on this note—the thesis needs only minor revisions, and the defense went well enough that there is no real controversy about giving you a pass. Congratulations. You can now move on to the next stage in your life. Or at least you will be able to do so once you complete those revisions. But tonight, go out and celebrate. You can start working on the revisions tomorrow.