Words Versus Numbers

This weekend I read a children’s classic, The Phantom Tollbooth by Norton Juster It’s not really a children’s book. Yes, a child would enjoy the fantastical adventures of Milo the protagonist and his companions, but I think adults would greatly appreciate the meaning behind the stories. Milo enters the Kingdom of Wisdom through the Phantom Tollbooth, and discovers that the lands are not in the best of states. The king’s two sons have quarreled and heach built up their realms centered upon the cities of Dictionopolis and Digitopolis.

Azaz the Unabridged, the prince of Dictionopolis, loves words. His court is staffed by the (worthy?) wordy. Everything runs on words, and the Word trade market bustles with business. Azaz disagrees on practically everything where his brother Mathemagician, the ruler of Dictionopolis, is concerned. Numbers are everything in that realm, and the big business there is to mine numbers like ore. I don’t know if the author had the big business of ‘data mining’ in mind when he wrote The Phantom Tollbooth back in 1961, but it’s oddly prescient.

The brothers’ feud mirrors themes in The Two Cultures by C.P. Snow (1959), concerning the divide between the humanities and the sciences. The Two Cultures is constantly mentioned in discussions about a liberal arts education. Outside of academics and other ‘elites’, I’m not sure how many other people have read The Two Cultures or know of its existence. On the other hand, I’m pretty sure The Phantom Tollbooth has a much higher readership, and it’s message echoes many similarities to Snow’s thesis. The humanities are caricatured by Dictionopolis while STEM folks are the denizens of Digitopolis. The two princes represent extreme cases of taking words or numbers to the point of ridiculousness. The feud between the brothers has resulted in the banishment of Rhyme and Reason, their sisters, and Milo’s task-adventure is to bring Rhyme and Reason back to the Kingdom of Wisdom and restore the friendship of the brothers.

There is plenty of punditry in higher education circles about the ‘crisis’ in the humanities and the liberal arts in general. In recent years I have noticed more of an emphasis on the phrase ‘liberal arts and sciences’ from folks trying to remind other folks that the sciences are not in opposition to the humanities – an attempt to bridge the Two Culture gap. It’s an attempt to differentiate the sciences (and math) from being equated to professional training, the latter being seen in its narrow definition of worker-training being ‘opposed’ to the goals of a liberal arts education. It’s like the redrawing of lines to bring in more supporters into one’s camp. We would all do well to revisit Juster’s tongue-in-cheek book.

The version I have is a newer edition that includes an appreciation by Maurice Sendak (of Where The Wild Things Are fame) written in 1996. Part of the appreciation is worth quoting. Re-reading the book 35 years later, Sendak has this to say: “It provides the same shock of recognition as it did then – the same excitement and sheer delight in glorious lunatic linguistic acrobatics. It is also prophetic and scarily pertinent to late-nineties urban living. The book treats in fantastical terms, the dread problems of excessive specialization, lack of communication, conformity, cupidity, and all the alarming ills of our time.”

That was the mid ‘90s. With the current state of the U.S. and the antics of its current president, Sendak’s appreciation is prescient over 20 years later. He goes on: “Things have gone from bad to worse. The dumbing down of America is proceeding apace. Juster’s allegorical monsters have become all too real. The Demons of Ignorance, the Gross Exaggeration (whose wicked teeth were made ‘only to mangle the truth’), and the shabby Threadbare Excuse are inside the walls of the Kingdom…” With what we’ve seen in the past ten days post-inauguration of the new president, Juster’s book is sobering indeed. How Rhyme and Reason can be brought back in the present situation is a good question.

Politics aside, one demon that caught my eye was the “Terrible Trivium, demon of petty tasks and worthless jobs, ogre of wasted effort, and monster of habit.” Milo and his companions are tricked into doing worthless tasks that seem so important while they are under the demon’s spell, but the spell is eventually broken by a magic staff that makes Milo start to think and wonder. He asks the demon why one should do only unimportant things. The demon responds: “Think of all the trouble it saves… If you only do the easy and useless jobs, you’ll never have to worry about the important ones which are so difficult. You just won’t have the time. For there’s always something to do to keep you from what you really should be doing, and if not for [the staff], you’d never know how much time you were wasting.”

This made me stop to think about my Procrastination strategy, wherein I formulate a larger somewhat-nebulous grand-sounding blue-skies task, and never work on it – and instead, I am able to get all my smaller tasks done. Perhaps I need to pause to think about the grand task, make it less nebulous and more worthwhile, and then actually pursue it. In my research, I’m very good at getting the low-hanging fruit and perhaps I’m avoiding directly tackling the big questions I’m actually interested in. I have all sorts of excuses: keeping the grant money & publication virtuous cycle going (why mess with an approach that has worked well for many years?), or using the primary involvement of undergraduates (we have no graduate program) as an excuse not to dig deep because I need to keep having ‘bite-sized’ and ‘digestible’ projects for them. I’m sure I have a litany of excuses; some may be threadbare.

I’m not quite ready to overhaul everything right this minute, but The Phantom Tollbooth made me stop and think. The one who stops thinking or paying attention gets stuck in the Doldrums (as Milo does for a short stint) where essentially nothing worthwhile happens even though there’s a fair bit of ‘activity’. Now that I’m paying attention, let’s see where this thinking leads me.

Archive Copies

There was a massive computer server failure in my research lab this week. What started out as a routine hard drive swap a couple of weeks ago, which went smoothly, somehow went awry. The server was set up with a RAID 5 array. It had been stable for years, but we discovered one hard drive had failed during the move last summer when the lab was renovated. Since this was just before the Fall semester started, and everything was operational, I decided not to replace it yet. That’s the beauty of RAID. (Side note: the server is named “beauty”, replacing an old server named “beast” although beauty is more of a beast in terms of size and power). Everything still runs fine even if you lose a hard drive. So while still in winter break, a couple of weeks ago, we swapped hard drives and allowed the RAID to rebuild itself incorporating the new hard drive. Everything looked good.

This past Monday morning, I found the server completely down with orange blinking lights everywhere. It would not come back up even with the help of several systems administrators. The timing was particularly bad because it was the first week of classes, and I was also starting to train my new research students that same morning. Thankfully, I could get the workstations off NIS, create local accounts, and the students were able to proceed with learning Linux and the computational chemistry software. Most of the computations are done on clusters separate from my local lab server, so the students were able to proceed with their projects. I had moved most of my important data off the local server some time ago, so I won’t lose too much if we are not able to revive the server. The problem with RAID is that when it fails, it fails badly. This got me thinking about how one goes about making copies and archiving data, both in our world and in the magical world.

In days of yore, there were etchings on clay, stone, bone and whatever else worked. Parchment and Paper made their debut a few thousand years ago. How was information preserved for future generations? You could etch it into your city walls or on a large imposing obelisk. The ancient equivalent of a photograph might be a carved statue. You could store scrolls in jars of clay and hide them in dry caves. Making copies was tedious. You needed human copyists. What better way to keep monks occupied or to educate the young by having them write out copies. Learning by rote was an important part of your education – you wrote out your own “textbooks” as the teacher recited the lesson.

Let’s fast forward to my lifetime. My first job as a copyist was in first grade. My teacher had a son in second-grade who came down with what I think was mumps, and therefore had to miss something like two weeks of class. (My memory is rather hazy.) Apparently I had a faster-than-average writing speed because my teacher would send me to her son’s class to copy down what was on the blackboard there halfway through the lesson. My teacher was a fierce woman, so as a seven-year old I simply did as instructed. I vaguely remember being paid ten or twenty cents per day. (I didn’t ask to be paid nor did I negotiate the salary.) I didn’t understand what I was writing, but I was good at copying. My writing must have been quite legible then, because several years later I had a teacher toss my written exercises out the window as a punishment for terrible handwriting. I attribute it to learning cursive and writing at increased speeds to finish my work as fast possible so I could go play.

My mother was also a school-teacher (at a different school) and I was drafted to help make copies. By that I mean using a typewriter to prepare a stencil. I’d like to attribute it to my relatively fast two-finger typing that was for the most part error-free. But it could have simply been one of the ways of keeping me out of trouble. I learned that the stencil would then go into a cyclostyle machine, and out would come the copies! I vaguely remember what the cyclostyle looked like – it is probably what one would call a mimeograph here in the U.S. Thankfully, when I became a teacher, we had Xerox machines. And now? I can just submit a print-and-copy job directly to the multi-function printer down the hall. At my leisure I can walk over and pick up the copies. Unless of course there’s a printer jam. Then I get irritated, especially if it was caused by the previous person’s job. (I’m sure this has happened to you too!)

Before the Wonderful World of the Wide Web, information to be learned was safely archived in physical textbooks. Since I am technically a Physical Chemist, I have a bunch of physical Physical Chemistry textbooks! Above is a snapshot of the appropriate shelf in my office. There were no e-textbooks when I started teaching, and students despaired of lugging their heavy textbooks around. When the publisher sent me a second (gratis) copy of the textbook, I put it in the student lounge with the promise from my students that it would not leave the lounge. Everyone followed this rule, and no one stole the textbook, but fat heavy P-Chem textbooks aren’t theft-worthy. More trouble than they are worth, perhaps? I’m sure some of my students thought so.

The principle of the Xerox machine for photocopying information isn’t too different from the mimeograph. You need ink, paper, and an apparatus that puts the ink in the right places on the paper per the master copy. In fact for most any physical object manufactured in bulk, you have the appropriate industrial machine that can produce these with the appropriate starting materials and molds. Robots easily do the task on an assembly line today. In biological replication (which is all biochemistry!) exquisite molecular machines work in harmony to assemble new genetic information, new proteins, new cellular materials, leading to new organisms, with an intricacy far exceeding any of our macroscopic machinery.

Today, information is increasingly stored as 1’s and 0’s on microchips. They are easy to move and easy to copy – perhaps too easy, thanks to the lightning speed of electrons. And while microchips and hard drives are physical objects that will slowly degrade over time, the digitally stored information can be cheaply, easily and quickly moved. Backup, Backup, Backup! (I almost lost most of my undergraduate thesis shortly before printing when my floppy became “corrupted”, but thankfully I had a backup on a lab computer that no one had erased yet.)

Do we even need physical books anymore? The Kindle and other modern tablets running on silicon rather than etchings on silica are starting to displace the physical book. Just think how many books you can carry on your sleek device? A library’s worth! At least for textbooks, we are starting to see increasingly better open-source materials. In one of my classes, I am only using Open Education Resources as part of a library initiative. We’ll see how the students take to my curated list. In scientific research, digital publishing of journal articles has clearly won out over print. The fight for e-advertising space and bandwidth drives billions of dollars of commerce today.

Thanks to computers, microchips and the channeling of electricity, we’ve migrated to a large extent to digital electronic storage and duplication. But in the magical world of Harry Potter, where home electronics (among other devices) interfere with magic, it seems to be old-school: paper, quills, ink and books. How are books duplicated? Is there a magical duplication spell? This is unclear. In Book 7, at the home of Xenophilius Lovegood, Harry spots a printing press described as a “wooden object covered in magically turning cogs and wheels”. The machine still seems to be required, although it is run magically. (We could replace magic with a robot in our world.) When Harry breaks into the Ministry of Magic, he sees hard-at-work employees. “They were all waving and twiddling their wands in unison, and squares of colored paper were flying in every direction… what he was watching was the creation on pamphlets – that the paper squares were pages, which, when assembled, folded, and magicked into place, fell into neat stacks…” It isn’t clear if the ministry employees use magic directly to “ink” the pamphlets, or if they were just assembling inked pages.

Do textbooks have to be printed the “old”-fashioned way? In Book 6, when Harry and Ron are without their Advanced Potions textbooks, they have to order new copies. No one attempts to magically duplicate an existing textbook. Is there a Wizarding Law that prevents duplication? To protect certain commercial interests? Or is there something inherently difficult in magicking a permanent duplication? (One could temporarily Transfigure an object to look like another, I suppose.) Can you easily copy an essay of a fellow Hogwarts student using magic? You can magically change words around as Roonil Wazlib proves. Rita Skeeter uses a Quick-Quotes Quill. Could one attach such a quill to a polygraph (magical, of course) and produce a duplicate piece of writing?

If copying information is challenging in the magical world, how about storing information? Certainly there are books and magical diaries. One could enchant ink to be permanent or make a book impervious to most types of decay and destruction. There are magical ways of extracting and storing a memory, and then viewing it in a pensieve. These memories are archive copies. Some that are deemed important (such as a significant prophecy) are stored in the ministry. What about a Horcrux? By splitting his soul, isn’t Voldemort making archive copies of himself? Or is it more than just an archive? Perhaps like a RAID array. You might destroy one Horcrux but nothing of significance is lost. Do the other Horcruxes redistribute the bits and bytes of his soul?

One problem with Voldy’s approach is that his Horcruxes are localized, thus leading to his destruction in a massive failure of Horcruxes. What if you could upload your essence into the “cloud”? A distributed array of supercomputers houses Will Caster in the movie Transendence; it is much, much more difficult to kill such a being. It just keeps coming back to life, like Skynet in Terminator sequels. Somehow though, the heroes are always able to find the link causing the system to fail and fail badly; perhaps never to recover. We’ll see if that happens to my system. I’d like to be able to bring it up temporarily just to get some data off. Thinking that this was just a simple hard drive swap, I forgot my own rule of Backup, Backup, Backup! I admit feeling a moment of dread that parts of my life are at the mercy of metal boxes with wires and chips, and a desire to “get off the grid”. Then reality struck back, and I decided to write this blog post. Hmmm… I wonder where my blog is archived.

Ursuppe: Amoebae in the Primordial Soup

This past winter break I have been revisiting older boardgames in my collection. Maybe it’s the scientist in me, but I have amassed a decent set of evolution-themed boardgames. I’ve always been interested in puzzles and games, but I only started growing my collection in the late 1990s when introduced to games coming out of Germany. These combine strategy, luck, shorter rule-books, and shorter playing times compared to the “wargame” beasts of yesteryear.  One of the early games I acquired, back when you could still find really good deals on eBay (now crowded by commercial sellers), harks back to the beginning of life on Earth. That game is Ursuppe by Doris & Frank.

Ursuppe was published in 1997, twenty years ago. It was re-released for the English-speaking market as Primordial Soup in 2004. I have the older German version, with English rules included. Since this was a used copy, the owner had already assembled the amoebae, requiring the hammering of a stick into a wooden base. One amoeba was cracked by this process but the owner had glued it back together and even provided a new replacement in case I did not like the glue job (which was fine). I’m glad I didn’t have to assemble the amoebae myself. Those were the days when games had some assembly required!

I looked back at my games log and was shocked to see that between 2003 and 2006, I had only played five games of Ursuppe, and that it hadn’t been played in the last ten years! I did play it more often prior to 2003 (before logging plays) when I had a smaller collection of games. But as the collection grew, god but older games got less love – a rather sad situation. My goal is to try and remedy that situation by bringing out some old favourites. So without further ado, here’s what Ursuppe is about accompanied by a couple of pictures from my one game (so far) in January 2017.

In Ursuppe, each player manages a family of amoebae*. The goal is to grow the family both in numbers and in evolutionary traits. Each turn, players score points for the number of amoebae they have on the board and how many evolutionary traits their family possesses. Players start the game with two amoebae in the soup. Each “sector” of soup also contains two food cubes of each colour (red, blue, yellow, green). A game turn has six phases; the first is “Movement and Feeding”. An amoeba may drift in the soup or attempt to move against the drift. The direction of drift changes each turn according to the environment card in the middle of the board. To move an amoeba against the drift, a player must pay one biological point (BP), rolls a die, and moves in the direction indicated. (Rolling a six allows the player to choose the direction.)

A key part of the game is keeping your amoebae alive. They must eat to survive. After movement or drift, each of your amoebae eats one food cube of every other colour, and then “poops” two food cubes of its own colour. So if you are the blue family, your amoebae eat red, yellow and green cubes, while pooping blue cubes. (One amoeba’s poop is another’s food!) Thus, the distribution of food cubes changes as the game progresses leading to all sorts of different strategies to stay alive and possibly even thrive! Amoebae unable to feed suffer damage. (A grey sphere is threaded through the stick.) After two damage points, an amoeba dies. Unless it has the evolutionary trait Life Expectancy, in which case it only dies after accumulating three damage points. The picture above shows the game board after several turns. You can see the different distributions of food in each sector, and several of the amoebae have taken one grey damage sphere. When amoebae die, they are converted to food cubes of each colour thus replenishing the food supply.

Biological Points (BPs) are the currency of the game. Among other things, they can be used to attempt active moments in the soup, to acquire new evolutionary traits, and to increase your family size by binary fission! The picture below shows the blue player with three evolutionary traits: Spores, Struggle for Survival, and Intelligence. The cost of each card is indicated under Price. The number in the square (Mutation Points) indicates how susceptible these traits are to mutation due to ultraviolet damage from the environment. In this example, the Environment card indicates the number 8. The blue player has 4+4+3 = 11. During the Environment phase, the player can choose to either lose one of these traits (so that the mutation point total is 8 or below) or pay 3 BPs to make up the difference between 8 and 11. Thus, it becomes costly to accumulate too many evolutionary traits, and these are gained and lost as players try to adapt to the changing situation. Their amoebae evolve!

Let’s take a look at what the cards do. As the blue player, Spores allows me to place a new amoeba anywhere on the board not already occupied by one of my own amoeba in the Cell Division phase. Otherwise, I would have to place it in a sector adjacent to one that has an existing blue amoeba. Chances are there isn’t much remaining food of the needed colours near my other amoeba; that’s why Spores is useful. Struggle for Survival allows my amoeba that is unable to eat the needed food the opportunity to chomp on another amoeba in the same sector. It costs one BP to make an attack. It is successful unless the other player’s amoeba has Escape, Defense or Armour evolutionary traits. Intelligence is “completely useless” as these are amoebae and it makes for a fun joke. However it is the cheapest card, and having evolutionary traits increases your victory points acquired each turn!

There are many other fun and interesting traits and the cards interact well with one another and with the changing environment. There is a UV protection trait that reduces the sum of mutation points on your cards so you can have more of them. A Tentacle trait allows you to pull food cubes as your amoeba moves or drifts. A Movement card allows you to roll two dice instead of one when moving against the drift (you choose one of the dice as your final movement). Frugality allows you to eat one colour less but one cube more at Feeding time. Defense allows you to fend off an attacker in a struggle for survival. In Ursuppe, the cards are double-sided. The side with English text is black and white, but if you read German, the other side is coloured! There are no other language-dependent components. (In the Environment card, east is the letter “O” for “Osten”, the German word for East. The other directions have the same first letter: N, W, S)

A full game of Ursuppe typically takes 1.5–2 hours. The game accommodates three or four players, but not two. There is an expansion allowing up to six players, and also features new gene cards, but I have no plans to acquire it. In this day and age, it is no longer as easy to find other folks willing to spend more than two hours to play a boardgame (and the expansion will almost surely extend the playing time). I personally enjoy playing Ursuppe, both for the theme and because the game is fluid (pun-intended) with the ever-changing environment and the evolution of traits. Twenty years ago, when the choice of games was more limited, this would have been played more often. But today there are many games streamlined to play in the sweet spot of 40-60 minutes, while still containing a good dose of strategy and luck, and able to accommodate 2-5 players. This limits Ursuppe to a niche crowd.

Ursuppe is easy to learn and fun to play, in my opinion, but it simply takes more time, and there can be a bit of analysis-paralysis for new players trying to choose what new evolutionary traits to acquire. The 2014 game Evolution allows for 2-6 players, plays in half the time, and does a great job simulating evolution and adaptation. If one were hosting a boardgame night, Evolution would probably be picked over Ursuppe the majority of the time. (I will feature Evolution in a future post.) At the other end of things, Bios Genesis is fantastic thematically but takes a good 3-4 hours and much more patience to learn a set of complex rules. Shorter and more streamlined games often have to sacrifice some thematic elements for streamlined game-play (and rules explanation). Evolution is essentially a card game. You don’t move creatures around to eat food and/or other creatures; unlike in Ursuppe where you have the tactile feel of moving wooden pieces on a game board. (Many of the games from that era coming out of Germany, Settlers of Catan being the most widely known example.)

I’m not sure when I will play Ursuppe again, but I’m glad I was able to revisit it and be reminded of why I like the game and why it will likely stay in my collection even with limited play. Primordial Soup!

*Technically, the first organisms that would demonstrate what we think of as “alive” would be prokaryotes, bacteria or archaea. The amoeba is a eukaryote, significantly more complex than a prokaryote. But since the game refers to “amoeba” that’s what I will call them in this post.

Designing Questions to Probe Learning

If you ask me today what is the best book to read about teaching, I will say Embedded Formative Assessment by Dylan Wiliam. After the many good books that I’ve read the past five years, I don’t know why I didn’t come across this gem earlier. No doubt I will encounter better books in the future, but this one really gave me that kick-in-the-pants encouragement to make larger inroads into improving my teaching, which would hopefully improve student learning. Why “hopefully”? That’s because Wiliam is very realistic about the centrality of assessment in the learning process. This is not Assessment of the generate-more-paperwork administrative mandate pervading our institutions. It is the assessment we should all be doing as teachers embedded in our lesson plans.

In chapter two, where the author makes the case for formative assessment, there is a section titled “Assessment: The Bridge Between Teaching and Learning”. I will quote several sentences. “Assessment occupies such a central position in good teaching because we cannot predict what students will learn, no matter how we design our teaching… Students do not [necessarily] learn what we teach. If they did, we would not need to keep gradebooks. We could, instead, simply record what we have taught. But anyone who has spent any time in a classroom knows that what students learn as a result of our instruction is unpredictable. We teach what we think are good lessons, but after we collect our students’ [work], we wonder how they could have misinterpreted what we said so completely.”

Before I elaborate on the author’s suggestions, let me first describe how I presently assess student learning. Outside of occasional project work and writing assignments, I generally grade four types of content-based assessments: worksheets, quizzes, homework (or problem sets) and exams. One might call these summative assessments, although they partly function as formative assessments – at least in the standard lingo. (It’s not the grading that makes something formative or summative in my opinion.) I don’t always collect worksheets or homework, i.e., sometimes the work is ungraded, so to speak. While a significant portion of my class time is spent systematically going through worked examples (one of the best ways to learn many chemical concepts), students also have opportunities to “work problems” and get feedback from me in class. In addition I get feedback from them as I observe what difficulties they run into.

In each of the four “graded” items mentioned above, I get information on different scales. Worksheets tell me immediately which students understood the lesson material of the day, who didn’t understand it, and who helped whom. (My classes are small enough that I can circulate through all groups at least once, often more.) Quizzes tell me if students individually understood one key thing from the previous class period. (My quizzes are taken in the first five minutes of class.) Problem Sets tell me if students learned a chunk of material usually over the course of 3-4 class meetings, and in particular whether they were able to apply the concepts to different but related problems (not identical to ones worked in class). Sometimes solving the problems requires integrating multiple concepts. Exams assess individual student learning over a larger chunk, usually about a month; the final exam is cumulative Students can work together on problem sets and worksheets. Quizzes and exams are individual assessments.

What feedback do the students get? On worksheets and problem sets, the students get their graded work back along with a detailed answer key. If there is a particularly egregious common error, I discuss it briefly the next class meeting. For quizzes, I provide the answer immediately in class before I’ve seen the student responses. I grade a stack of 3x5 index cards after class. Rarely do I look through the responses in class. For graded exams, the students can see what they got right and wrong accompanied by a detailed answer key, but I don’t discuss it in class. In rare instances, when I observe a widely common error, I would mention this in class. I attribute the rarity of such an occurence to students having to work individually on exams. When they work in groups with other students, the same error tends to propagate widely – often traced to one of the more capable and confident students who first made the error.

While I think I am mostly asking the right questions on exams from a summative assessment perspective, I’m not sure I’m doing well in the earlier stages. My questions focus on what I think the students should know, but don’t necessarily reveal how they think or where a misconception may lie. Of course when I discover a common misconception when grading, I make it a point to relay this to the students. But my in-class questions might not being do the best or even the right job from a formative assessment point of view. Wiliam writes: “Questions that provide a window into students’ thinking are not easy to generate, but they are crucially important if we are to improve the quality of students’ learning.”

I think that’s the really hard part: constructing excellent questions at the formative stage. These should be questions that expose previous learning and probe for potential misconceptions. Given the brevity of his book (a good thing overall), Wiliam provides just a handful of examples of standard questions, and then builds on these with much better constructed questions. While his examples are mainly in middle school math (his training is as a math teacher), one gets the gist of the type of question that really gets at the nub of learning. I need to ask much better questions but haven’t taken the time to do so. Lest, I use this as an excuse, Wiliam addresses the matter head-on.

“One common objection […] is that teachers do not have time to develop such questions, not least because they are too busy grading, but this just shows how ineffective many of our standard classroom routines are. Every teacher has had the experience of writing the same thing on [multiple student] notebooks because the students were allowed to leave the classroom before the teacher discovered that the students had failed to understand some crucial point. So the important issue is this: does the teacher only discover this once he looks at the students’ notebooks? Viewed from tis perspective, grading can be seen as the punishment given to teachers for failing to find out that they did not achieve the intended learning when the students were in front of them.”

I consider myself appropriately schooled. What I really need to do is build up a stock of excellent questions for formative assessment, particularly at the introductory level. I have enough teaching experience to know where the tricky parts are in my courses. I should also work with others who are teaching the same sections to pool and share knowledge; we have many of these at the introductory levels. One thing I am going to do this semester is to devote some time to coming up with good in-class probing questions. And perhaps, I can do less grading which seems like a more-than-reasonable trade-off.

Although a short book, Embedded Formative Assessment is chock full of great practical examples. The author does a fantastic job getting straight to the point, providing the necessary theory and scaffolding, chooses good representative examples to make his point, and keeps moving things forward. All these are marks of an excellent teacher. His experience shows. On the other hand, as I went through the book I was partly self-berating myself for not reading this book sooner, and thinking about how I’d potentially let down hundreds of students in the course of my teaching while floundering around repeating the same mistakes. (On average I teach 100-150 students per year.) I could have built up a set of really good formative assessment questions by now. As it is, I have plenty of great summative assessment questions (that I do reuse) but a limited set of great formative assessment questions. The author anticipates my despair! Here’s what he says in the epilogue.

“The problem with being provided with so many techniques is that […] too much choice can be paralyzing and dangerous. When teachers try to change more than two or three things about their teaching at the same time, the typical result is that their teaching deteriorates and they go back to doing what they were doing before. My advice is that each teacher chooses one or two of the techniques, […] tries them out […] If they appear to be effective […] practice them until they become second nature. If they are [not] … try another technique or [modify a previous one].”

I’ve decided to pick two things to work on this semester. The first is to come up with some great formative assessment questions in class. For a start, I’ll set myself the goal of one insightful one each week that I will build into my classes. The second is one I had mentioned in a blog post last summer during an assessment exercise. I came up with a great suggestion: having students critique written answers from students in a previous year. Of course, these would be carefully curated for maximum learning to take place. (Wiliam recommends this in his book!) I got so busy this past Fall that I did not do this at all. Shame on me! This semester, I will remedy things. I dug up final exams from the equivalent class last year, and I plan to make appropriate selections when the corresponding topic is covered in class. I should also commit on blogging about my trials and errors – for accountability!

I end this post with a final quote from the author. He exhorts teachers to “accept the need to improve practice, not because [we] are not good enough, but because [we] can be even better, and focus on the things that make the biggest difference to [our] students”. What great advice! His book receives my highest recommendation.

Tales of Grimm

For the first half of 2017, I am going to inject something new into my blog series for some variation - one Guest post each month! The first essay is by one of my sisters who is halfway through the first season of Grimm. Enjoy!

Grimm Season 1 – a different interpretation of fairy tales

The TV series Grimm asks the question—what if the fairy tales we know are in fact a distillation of a larger (fantastic) reality? And what if the protagonist is more feared than loved?

Set in the Pacific Northwest, already famous as the home of vampires and werewolves, Grimm has a surprisingly light touch when it comes to both its source material as well as any expectations of ‘grimness’ or darkness in the series.

Each episode starts with a quote from a fairy tale—familiar-sounding yet oblique enough that it may take you awhile to place it, at least until confirmed by other events. The series is conceived as a police procedural—crime drama, with Portland detective Burkhardt as the titular Grimm. While there is the usual murder, partner, lieutenant, and all the trappings of a police investigation, the conceit of the series is that each murder is committed by or connected to some fantasy creature who is somehow connected to a Grimm fairy tale. The creature looks human to other people, but not to a Grimm, who can “see them for what they are”.

Unlike other attempts to bring fairy tales to life, like Once Upon A Time or other reimaginations or modernizations, in Grimm, fairy tale characters are archetypes or representations of whole species of creatures. It’s difficult to illustrate this without giving spoilers, but let’s say, for example, that the Big Bad Wolf is not just a particular wolf, but he represents a whole race of wolves. Or the Bluebeard story grew from a race of creatures that likes to capture women and lock them up.

The idea, then, is similar to some fairy tale scholarship, which seeks to discover the function that traditional tales played in olden societies, passing down social mores and cultural values in the form of folk tales and children’s stories. Teaching children not to take sweets from strangers (you may find yourself in a witch’s oven!), for example, or what to do when you encounter a wolf—there are theories that Red Riding Hood had something to do with young girls reaching puberty.

Each storybook character in the Grimm TV series is thus not a ‘real’ historical person or creature, in a sense, but a distillation of a type. According to this series, the original Grimm’s fairy tales is not a collection of folk tales but a bestiary. The fairy tales are true, but not in the way you imagined. Talk about Fantastic Beasts.

In this world, Burkhardt finds out he is a Grimm—“you guys have been profiling us for centuries”, says one creature. Most creatures are afraid of Grimms—“you must hunt down and kill the bad ones”, says Aunt Marie, the librarian (that was her day job). Unlike in many coming-of-age stories, Burkhardt is an adult by the time he finds out about his special ancestry. It turns out his parents didn’t die in a car crash… oops, wrong story. (Though he does find out they didn’t die in an accident, and he gets his very own ‘Ron Weasley’, a creature who serves as a sidekick and guide through this strange new world).

What the Grimm series does well, particularly in contrast to the Harry Potter books, is that it does not take genetics as destiny. Instead of the quasi-genetic determinism which is a flaw in the otherwise excellent Potter series—notice how all Slytherins are bad, or at least nasty?—Grimm demonstrates the idea that people are not bound by their genes: there are creatures who do not necessarily act according to their traits. Not all individuals from predatory species continue to hunt, in this day and age. A genius emerges from a traditional underclass. Even the titular Grimm himself—Burkhardt—is not living up to his name and killing every creature he meets, although many clearly expect him to.

This is quite admirable, I find. After only the first few episodes of Season 1, there hasn’t been just a token ‘good guy’ out of all the evil/dark creatures. There are quite often people/creatures who transcend their ancestry. The lesson is also reinforced every time a new creature meets this strange new Grimm.

Finally, the Grimm series also brings up another interesting idea, quite prevalent in the fantasy realm but not so much in the modern world—that people are not what they seem. If some of these creatures, who look like normal people to you and me, are living among us, who’s to know? How can you tell if your barista is actually a blut-bad or your lawyer a jaeger-bar? (The series, appropriately enough, likes Germanic names).

As C.S. Lewis said, “It is a serious thing to live in a society of possible gods and goddesses, to remember that the dullest most uninteresting person you can talk to may one day be a creature which, if you saw it now, you would be strongly tempted to worship, or else a horror and a corruption such as you now meet, if at all, only in a nightmare…” (from The Weight of Glory). 

So, as with all good fairy tales, you can read a lesson into this series. Appearances can be deceiving. Don’t take things at face value. And don’t assume you know what someone will do just based on their heritage—things may not be what they seem.

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But if you ARE in a fantasy world, do stay vigilant for those who are out to get you! There is, it turns out, a race of Reapers whose job is to go after Grimms…

P.S. If the series has one weakness, it is the lack of female leads (thus far in Season 1). Unlike other police procedurals of our time, like Bones, Mentalist, Castle, CSI, or even Criminal Minds, Portland PD seems strangely male-dominated. There are no female investigators featured, aside from the medical examiner. Even though Grimm is premised on archaic stories, it seems odd to not have a more significant female presence, in this day and age. However, girlfriend Juliet does start to play more of a role as the series goes on, and ‘Hermione’ may turn up in a later episode. So it does improve in this respect… In the meantime, the budding bromance between Burkhardt and ‘Ron’ provides the traditional banter and odd couple dynamic usually found between the male and female leads. 

Salt

After reading Paper, I decided to tackle Salt by Mark Kurlansky. Like Paper, Salt is chock full of interesting information with both breadth and depth. Appropriately, the first chapter begins in China, “A Mandate of Salt”. I learned that the earliest written record of salt production dates back to 800 B.C., but the records discuss the production and trade of salt during the Xia dynasty going back a further thousand years. I also learned the history of fermenting fish and soybeans to make what is now the ubiquitous soy sauce (although fish is no longer used in the recipe). Fermentation – it’s all chemistry! And those tasty black gelatinous century eggs? They are soaked in brine and sometimes encased in salted mud and straw

A hero in the Chinese story was the governor of what is now Sichuan province, an engineer named Li Bing. The province had long produced salt, but Li Bing figured out that the brine came from underground, and had the first brine wells drilled (in 252 B.C.) As the Chinese became more skilled at the task, the drill shafts went deeper. (Now I’ll quote two great paragraphs from Kurlansky…)

“But sometimes the people who dug the wells would inexplicably become weak, get sick, lie down and die. Occasionally, a tremendous explosion would kill an entire crew of flames spit out from the bore holes. Gradually, the salt workers and their communities realized that an evil spirit from some underworld was rising up through the holes they were digging… Once a year the governors of the respective provinces would visit these wells and make offerings.”

“By A.D. 100, the well workers, understanding that the disturbances were caused by an invisible substance, found the holes where it came out of the ground, lit them, and stated placing pots close by. They could cook with it. Soon they learned to insulate bamboo tubes with mud and brine and pipe the invisible force to boiling houses. These boiling houses were open sheds where pots of brine cooked until the water evaporated and left salt crystals.”

The passage reminded me about the kobolds of the Saxon miners, but what is particularly neat is that the workers behaved like amateur scientists and engineers. Yes, there may be evil spirits to placate, but one can make use whatever fumes may be coming from the beasts below. They essentially invented the first natural gas piping system, all in the service of salt production! Not only that, the use of bamboo piping spread to irrigation and plumbing systems. The Chinese also discovered gunpowder from mixing salt with other ingredients. And their salt taxes imposed by the government go way back, more than four millennia. The Chinese pictograph character for salt apparently “depicted the state’s control of its manufacture.” The image below is from salt.umd.edu and traces the evolution of the character.

 

As Kurlansky writes: “A substance needed by all humans for good health, even survival, would make a good tax generator. Everyone had to buy it, and so everyone would support the state through salt taxes.” The highs and lows of salt taxes are a prominent part of the book. Kurlansky trots the globe with how governments used and abused salt taxes from the pharaohs of ancient Egypt to Gandhi’s famous march in 1930 defying colonial Britain’s salt laws. He traces the important role of salt in the American Civil War, the American Revolution, and the Spanish wars with the Aztecs and the Incas. Whoever controls the salt, has the power.

History and chemistry is discussed in Chapter 18, “The Odium of Sodium”, titled after a ditty written by a British novelist.

Sir Humphry Davy

Abominated gravy.

He lived in odium

Of having discovered sodium.

In 1807, Davy isolated sodium via electrolysis. In 1810, he isolated chlorine. The former is a soft grey metal that reacts violently with water; the latter a greenish yellow gas that would gain infamy in gaseous trench warfare of the first world war. But when combined, they make sodium chloride, a white crystalline powdery substance, and the most common ingredient in what we now call table salt. The chemist thinks of salts as ionic compounds consisting of an electron donor (the metal) and an electron acceptor (the non-metal). The combinations of different metals and non-metals produces different salts with different properties. Saltpeter, a constituent of gunpowder, is potassium nitrate. Epsom salt is magnesium sulfate. Chalk is calcium carbonate. The combinations are myriad. We owe it to Davy and the many scientists who teased out the chemical theory of salts for our plethora of choices today. (Picture below from an interesting RedOrbit article about scientists studying the compression of table salt.)

Through much of history, the whiteness of salt and having uniform crystals, was highly prized. Dirtier and coarser salts were viewed as “less pure” and less valuable; perhaps related to the rise of industrial mechanization. But the tables have turned. Artisanal salt, irregular in its composition, not dazzling white because of the presence of impurities, has now become the darling of gourmet chefs and their many followers. Dirty salt, it had been called through the ages, and now it commands the higher prices.

What is our new salt today? The substance that everyone needs and can be taxed appropriately by the governments, or perhaps, the corporations of the world. The quest for the Killer App, the holy grail of the twenty-first century, is perhaps simply a short-term substitute for the position long held by salt.

Cognitive Load: Balancing Pedagogies

In my previous post, I mentioned that I’ve been thinking about how to factor in cognitive load as I design activities in my classroom. My thinking was partly motivated by having just read a monograph by A.J. Martin based on his Vernon-Wall lecture [1] in 2015. The title of his lecture: “Can educators reduce students’ cognitive load and boost motivation and engagement? Integrating explicit instruction and discovery learning through Load Reduction Instruction (LRI).”

That’s quite a mouthful. Let’s break it down.

The goal of LRI is to optimize student learning and achievement. The trick is to match the cognitive demands required with where the students are developmentally in the learning process. In the early stages, when students are novices, a more structured approach (explicit instruction) that reduces cognitive load is required. This is because the novice mainly resorts to working memory, limited in its capacity. During this period, students gain fluency and build basic content and skills into long-term memory. This frees up working memory for further learning, and that’s when guided inquiry learning approaches can be a stepping-stone to autonomous learning. (We want students to learn how to learn!)

The focus on the article isn’t on achievement (there is a summary of previous work and an extensive citation list) but instead explores the effects of LRI on motivation and engagement. There is a Motivation and Engagement Wheel that encapsulates the main concepts of the article. It resembles a color wheel, except in the article I downloaded there was no color, just shades of grey, perhaps appropriately. I’ve also included a color version I found that uses traffic light colors from a quick Google search. Both are shown below. There is a more extensively annotated version later in the article not shown here. The monograph is dense with terminology but Martin clearly explains all the different pieces. (That’s probably why it is 35 pages long!)

 

The monograph contains a number of examples and practical suggestions included that illustrate the conceptual pillars of LRI. One section that I found quite interesting was the discussion on the southeast corner of the wheel. I had vague anecdotal notions of why my students would be anxious, and how this could result in poorer performance, but no particular conceptual framework to think about the issues involved. In a section on “Anxiety, failure avoidance, and self-handicapping”, Martin outlines the sources and downstream effects. Basically, anxiety, fear of failure, and other distractions, “may act as a source of extraneous cognitive load and tap the limited capacity of working memory”. These fears may also lead to self-defeating behavior, procrastination being one among many examples. The LRI pedagogical strategy in these cases is to reduce split-attention by carefully structuring the material to reduce the load on working memory.

A significant chunk of the article is devoted to discussing how LRI integrates both explicit instruction and inquiry-based learning, two pedagogies that are often portrayed (falsely in my opinion) as being in opposition to each other. The strawman in one corner is the “traditional lecture” and in the other corner we have “completely open-ended discovery”. These two approaches are philosophically rooted in positivist and constructivist approaches respectively. There is an extensive review of this debate in a book by Tobias and Duffy [2]. It prompted me to go back and re-read an excellent article from the book authored by Paul Kirschner [3]. I highly recommend it. The abstract is shown below.

Kirschner begins by defining epistemology and pedagogy. A scientist’s epistemology might be the “scientific method” (in its various guises). On the other hand, pedagogy refers to “strategies or styles of instruction”. Importantly, pedagogies can be (a) general, (b) domain-specific, or (c) specific to a certain approach to teaching. It is this third case that has caused the most misunderstanding as different groups tout their superior pedagogies. Three-letter acronyms are common, e.g., PBL = Problem Based Learning, TBL = Team Based Learning, and there is also LRI mentioned above. Kirschner quickly gets to the matter at hand. The most relevant section of the article to scientist-educators is appropriately titled: “Practicing Science or Learning to Practice Science?”

The movement in recent years has been towards constructivist approaches. (It’s more like the swinging back and forth of a pendulum, but discovery-based learning is what’s popular at the moment.) These voices declare that “inquiry into authentic questions generated from student experiences should be the central strategy for teaching science.” Kirschner quotes others: “The ultimate goal was to provide a learning environment in which students could feel like scientists in their own classrooms. This meant that our students would need to be involved in the acquisition of their scientific knowledge – not only reading and writing about – but actually doing science.”

As a chemist, I don’t disagree that students should be exposed to a curriculum that involves lab-based hands-on exercises. These are crucial to building important manual and observational skills, and can complement what the students are learning in the “lecture” portion of the course. However, touting the “doing science is the best way to learn science” as the primary pedagogical driving force at the introductory level is what I find questionable. The most recent PISA results would seriously question this credo, although oddly enough it hasn’t drawn much attention in the mass media. Martin somewhat alludes to this in his article, but Kirschner tackles it head on. I’m going to quote his clear prose [4].

“This focus is coupled to the assumption that to teach the process of science (i.e., the pedagogy), we can best confront learners with experiences either based on or equivalent to science procedures (i.e., the epistemology). This has led to a tenacious commitment by educators, instructional designers, and educational researchers to discovery and inquiry methods of learning which is based upon confusing teaching science as inquiry (i.e. an emphasis in the curriculum on the processes of science) with teaching science by inquiry (i.e. using the process of the science to learn science). The error here is that no distinction is made between the behaviors and methods of the scientist – who is an expert practicing her or his profession – and those of a student who is essentially a novice.”

“A student, as opposed to a scientist, is still learning about the subject area in question and, therefore, possesses neither the theoretical sophistication nor the wealth of experience of the scientist. Also, the student is learning science – as opposed to doing science – and should be aided in her/his learning through the application of an effective pedagogy and good instructional design.”

“[Discovery] presupposes a prior conceptual framework and the ability to interpret and sometimes reinterpret what has been seen or experienced in abstract terms, but there is no guarantee that it will lead to new concepts, much less correct ones. This is because, first, novices have little knowledge and experience in a domain which causes them to encode information at a surface or superficial level… Second, novices do not simply produce random guesses in the absence of knowledge, but rather as systematically off the mark in a particular way that makes sense given a particular misconception. The strangest and possibly most unfortunate aspect of this whole problem is that it is not new…”

Kirschner argues that “the lack of clarity about the difference between learning and doing science has led many educators to advocate the discovery method as the way to teach science.” This fits well with current trends. Kirschner’s article was 7-8 years ago. Constructivist pedagogies have been further on the rise since. It is unfortunate that “lecture” has been getting a bad rap. There is a place for lectures amongst the different pedagogies. Experienced educators in the trenches will utilize a variety of pedagogies. You know what works, what doesn’t, and you constantly try to hone your methods with each group of students. What worked in the past may not work in the present. The problem is when administrators or governing bodies demand a particular pedagogy be used because it is deemed a “best practice”. In tertiary education, much autonomy still rests with the professor. But in primary and secondary education, the confusion between epistemology and pedagogy could result in some poor practices. As the unbundling of education continues, however, the problems may mount. We should be watchful, thoughtful and act accordingly.

[1] The Vernon-Wall lectures are part of the annual conference of the Psychology of Education Section of the British Psychological Society. The official citation for this monograph is: Martin A. J. (2016). Using Load Reduction Instruction (LRI) to boost motivation and engagement. Leicester, UK: British Psychological Society.

[2] Tobias, S. & Duffy, T. M. (Eds.) (2009). Constructivist Instruction: Success or Failure? New York, NY: Routledge.

[3] P. A. Kirschner (2009). Epistemology or Pedagogy, That is the Question.

[4] I have left out the references and a number of intervening paragraphs between the three quoted. I recommend reading the entire article.

Being in the Real World

No, today’s post is not about university professors leaving their ivory towers to encounter the real world. Nor is it about how to equip our students for the twenty-first century skills they will need to find fulfillment in the real world. If that is what you’re looking for, there’s plenty to wade through in the mass media.

Instead, I’m going to muse on what it would be like for a fictional character to suddenly take on flesh. Fictional characters coming to the real world are all the rage now. Just look at the juggernaut that is the Marvel Cinematic Universe. But there’s an important difference: the superheroes and mutants are not moving from a comic-book-fiction world into a real world. They’re just here in the real world. In the Once Upon A Time TV series, characters who come from fictional fairy tales actually travel via a portal to Planet Earth, albeit mainly constrained in the small town of Storybrooke. Do they come from a “Book” world? Or do they come from another “Physical” realm? And how would it be “adjusting” to our earthly realm?

As part of my holiday reading, I finished the sixth book in Jasper Fforde’s Thursday Next series, “One of our Thursdays is Missing”. While I feel that the overall story is less interesting than the earlier books, there is a fantastic chapter on what it might feel like for a “book” character to physically experience coming alive. The chapter is appropriately titled “Alive”. The protagonist has just made the trip through a “portal” device from BookWorld into the Real World. In her first trip, she is aided by an agent on the ground who has been stationed there for a while.

Paraphrasing Jasper Fforde would not do justice to his description. I’ve italicized the quoted sections in the book to reduce quotation marks. (The quoted sections will be punctuated with some of my musings. So really, these are Fforde’s musings.) Here goes.

I felt a pain in my chest. I didn’t know what it was until, with a sound like a tornado, a hot gush of foul air erupted from this shock, I spontaneously did the opposite and drew in an equally fast gush of air that cooled my teeth and tasted of pine needles.

“It’s called breathing,” came a voice close at hand. “It’s very simple and everyone does it. Just relax and go with the flow.”

“I used to ‘take a breath’ and ‘exhale uneasily’ at home,” I managed to say, “but this is quite different.”

“Those were merely descriptive terms intended to suggest a mood,” came the voice again… “Here you are doing it to stay alive.”

“What’s that random sensation of memories I keep getting?”

“It’s smells. They have a way of firing off recollections...”

That’s one thing we don’t see from the characters in Once Upon A Time or movies with alien invasions. Sometimes the different atmospheres are taken into account requiring some sort of spacesuit or exoskeleton. But more often than not, aliens are able to function in practically the same way. Thor, coming from Asgard, seems just fine on Earth. But maybe he has taken the trip many times and is used to the adjustment, so we don’t see him floundering. Or maybe the atmosphere on Asgard works in the same way as on Midgard. Also, hardly anyone stops to admire the view. Fforde brings to light what might be a major difference between what a book character experiences in his/her own fictional world, and how the actual physical world is much more vivid, and full of extraneous stuff – that would otherwise be distracting to the narrative.

I sat and blinked for some minutes. The view was quite astonishing, not only in range but in detail. I had been used to seeing only what was relevant within a scene. Back home, anything extra would have been unnecessary and was a pasty shade of magnolia with the texture of uncooked dough. Here there was everything, in all directions, in full color and in full detail. Several books’ worth of descriptions were just sitting there… I sat there quite numbed by the overload of sensations.

At this point, the protagonist's helper identifies himself as Agent Square from Flatland. As a two-dimensional being, he experiences three dimensions by moving through and imagining what the square slices measuring out the third spatial dimension look like when compiled. There’s also an interesting discussion about how we three-dimensional beings view time by moving through it in slices. Except that, we can’t quite control the speed and direction in which we move through this fourth dimension. In a previous post, I mused about how one as a reader of a book could move forward or backward at any pace, or jump to different parts of the story at any time in BookWorldTime. But when the BookWorld protagonist enters the real world, she is constrained by the flow of RealWorldTime.

I moved to stand up, but everything felt funny, so I sat down again. “Why does my face feel all draggy?” I asked. “The underneath of my arms too… everything feels all… weighted down.”

“That’ll be gravity,” said Square with a sigh.

“We have gravity in the BookWorld,” I said. “It’s not like this.”

“No, we just talk at though gravity existed. There’s a huge difference. In the BookWorld, gravity is simply useful. Here it is the effect of mass upon space-time. It would be manageable if it were constant, but it isn’t. Acceleration forces can give one a localized gravitational effect that is quite disconcerting…”

“If this were the BookWorld, you’d have one of those watches that counts down from [X time] to add some suspense. Believe me, the plot in this world takes a bit of getting used to. I’ve not done anything for [the boss] for six months. That’s nothing in the BookWorld, barely half a dozen words. Out here it really is six months... The boredom. There’s a limit to how much reality TV one can watch… Now, what do you want to know first?”

“Walking would be a good start.”

Gravity also turns out to be tricky. This passage reminded me of observing toddlers trying to walk for the first time. They toddle. Keeping one’s balance can be tricky, particular if you have a relatively larger head. I just take walking for granted, until I have an accident that impairs my walking ability. Then I start to notice the process of walking. It’s a good thing we can automate and thus filter out of consciousness many of our activities. It would be quite the task trying to breathe, pump blood via the heart, see and smell, all simultaneously while consciously working through the process. Cognitive Overload.

Agent Square turns out to be a good teacher, and walks his student through processes of increasing difficulty. He pushes her to try new things at appropriate times, but also gives her time to digest what she is learning and to automate the process. One of my goals this coming semester in my non-majors class is to monitor cognitive load in my students. I did not do as good a job when I taught the class last year, as I was trying other new things. However, since I’ve decided Not To Textbook the course this coming semester, I feel more freedom to rearrange the units in a way that would make sense both thematically and cognitively. In fact, I started working on this today – my first day back at work after an excellent holiday! Back in the Real World, I suppose.