Seeing the “constructive” part of constructive criticism

Summarizing three+ years of research and talking about the significance thereof can be a daunting task. Needing to do so in a very short amount of time because one has a firm deadline, in the form of plane tickets for departure to take up a post-doctoral position makes it an interesting task. I’ve found that my reaction to this situation has varied from day to day, ranging from extreme writer’s block to highly inspired. Fortunately, when the writer’s block struck I still had other tasks to turn to such that I was still being productive with my time by gathering yet more drawings, charts, and graphs, and assembling them into ready-to print versions of the figures for thesis. Eventually, a good week later than I’d wished to do so, I completed a first draft of my final chapter, the “discussions and conclusions” part of the thesis (note: in Australia the term “thesis” is used at the PhD level, rather than “dissertation”, which is what they say in the US—I don’t know what terms are used in other countries). Oh, the joy I felt when the e-mail was sent, and I could resume working on the corrections he’d suggested to the earlier chapters.

Fortunately for me, I had reason to head into town on the next business day, and stopped in my advisor’s office that afternoon, as he was just finishing up a reply e-mail to me with his comments on the chapter. I sat and talked with him for a good hour, as he filled me in on the important points I’d not yet addressed, and why he felt that they were important. I explained that when I’d sent it to him I did feel like, perhaps, it wasn’t perfect yet, but I knew that I needed to say *something*, because it is far, far easier to edit/change text, than to write the first paragraphs on a given topic. I left that meeting feeling inspired and ready to go. As a result, when I saw his e-mail and read the comments in the chapter itself, I was ready and able to immediately work on doing the expansions he thought it needed. However, looking at the e-mail itself, I think that if I had read it before having the conversation with him, I would likely have been devastated. There is something about the thought that one’s effort isn’t deemed worthy, for whatever reason, which can either be crippling or inspiring. How easy it is to let a negative opinion on one’s work ruin one’s day, but how much better it feels when, instead, one hears the constructive, helpful suggestions one has been offered and is able to run with them, putting the suggestions to work to improve one’s efforts. This time the latter was easier to do because of the conversation. I hope that in the future, should it happen that I receive such suggestions from a mentor or colleague without such a warning conversation, I shall be able to appreciate their help and act upon their advice straight away, without any “someone doesn’t like my work” feelings standing in the way.

The tool I learned to use today, and what I discovered when I applied it

My life recently has reduced itself to not much more than working on the thesis in progress, or taking the occasional walk for exercise; I’ve even chosen to miss out on social events I would have otherwise attended in my push to “finish”. However, as I work I keep discovering new things I need to learn in the process. I once heard that the learning curve on a PhD project is exponential, and, truly, I believe it—it seems to me that I am learning ever so much more every day now in this very late stage of the project than I did in the early months of working on it (and, for the record, during those early months, I was astounded by just how very much I was learning compared to my prior rates of information acquisition).

One of this week’s new lessons was how to apply a t-test in an Excel spreadsheet. When my advisor gave me back chapter five, with comments and suggestions for improvement, one of the things he said was that the variation of some of the abundances for some of the trace elements in the monazite for the grains which grew in the Cambrian looked on the graph like they might, perhaps, vary by age of the grains. The “vary by age” we are talking here is very minor—these crystals grew ~505 Million years ago, give or take a handful of million years. How long did that growth period take? If it was fast it might have been just a couple million years, but if it was slow it could have taken tens of millions of years. In the latter case, it would be possible for there to be changes in the growing conditions (temperature/pressure) over the time period. If there were changes in the temperature and pressure during the metamorphic episode it is possible that during that period different minerals would be stable at different times during the event. It is known that how much of any given trace element is incorporated into monazite is based, in part, on what other minerals are growing or breaking down at the same time the monazite is growing. Since monazite tends to be a small mineral (generally <> 1 mm, and sometimes > 1 cm)) tend to out-compete it for any elements they are fond of if they are growing at the same time, or if the large mineral is breaking down, they tend to release trace elements, which the monazite can then incorporate into its own crystal structure.

Therefore, to test this, part of my day was spent going back to the results of my monazite analyses, sorting them by age to get all of the ones from the ~505 Million year old growing episode together, then sorting them back out into their individual samples again, then sorting each sample by first one, and then another trace element, then doing a t-test for each element to compare all of the analyses from a single sample which are high in that element with those which are low in that element. If the “t Stat” number reported is larger than the “t Critical two-tail” number then I can say that, yes, there is a statically valid difference in the ages of the two groups. However, for the samples from the first region I’ve tested, I can’t say that. Statically, the ages for those analyses high in these elements are indistinguishable from those which are low in those elements. Therefore, the factor which is more likely to effect how much of each of those trace elements wound up in the monazite is probably just a simple “how close was each grain of monazite to the other minerals which were either giving off, or taking up, those elements?”.

Having done all of that for this region, I next need to repeat the process for the other regions, write up the results (in less general terms!) in the thesis, and move on to the next task on the list…

There will always be just one more sample you will want to analyze, no matter how close the deadline. When this happens, just say no.

Once upon a time, before I started my PhD project, my advisor did some analysis of the mineral monazite in various samples from across Tasmania, to determine the age of the grains. When I started my project some time there after I was unable to obtain training on the use of our microprobe the first year I was here, because our microprobe operator had been hired away to Edinburgh, and it took a while to find a suitable replacement and get him the appropriate visas to start work. So, to keep me out of trouble, in addition to looking at 100+ thin sections of the various Tasmanian rocks that had been collected by previous UTAS students and faculty over the years, to determine which ones would be good candidates for detailed petrological analysis, he also put me to work writing a paper summarizing the results of the monazite dating he’d done before I arrived. For most of the samples I wrote the sample description myself, since I had the thin sections in my office. However, one of them, which had been collected in 1962 from an area which is now under a dam, wasn’t in my office, and my advisor couldn’t find it in his office. Undaunted, I searched the 1962 thesis (which didn’t have a table of contents—so I created one for it) and found the original sample description, and adapted that information for our paper.

Years elapsed. UTAS hired a new microprobe operator. I learned to use the microprobe. I engaged in my own analytical work, both my own monazite dating of other Tasmanian samples, and analysis of other minerals to do calculations as to what temperatures and pressures these minerals must have grown. Eventually, I slowed down on my data acquisition and commenced writing up my results. During this process, I noticed a familiar sample number occurring in the list of “standards” being used for each and every session of monazite dating. Yes, that missing sample from the paper has been living in the microprobe lab all this time. It gives remarkably consistent results. It has had more than 170 different analyses (some samples have had 15), and they all give more or less the same age, and have pretty much the same composition. Indeed, the graphs for its monazite composition show considerably less variation than those for the other samples.

Today it occurred to me that I should look at the sample, to see if I can relate the pattern of its composition to any other details in the sample, so I went and borrowed it from the microprobe lab. Now that I’ve seen it, I so wish I’d have seen it years ago. It is full of lovely albite porphyroblasts with inclusion trails at an angle to the foliation of the matrix minerals. There are tiny garnet grains, and biotite is present. In short, all of the minerals needed to do the pressure/temperature calculations, plus plenty of structural details visible in the sample to make for an interesting story. And here I am, with only three weeks to get my thesis finish, printed, bound, and submitted. There is just no way that I am going to be able to analyze this sample and do the calculations, since I am out of time and budget with which to do it, which is a pity, because it looks as though it would have been a lovely addition to the story.

the final push is underway

Not too long back I received an offer on a post-doctoral position in Europe. Before receiving that offer, I thought that I had already reduced my life to pretty much nothing but working on my thesis and basic “take care of myself” tasks like food, exercise, sleep, and checking in with my mother so that she knows I’m still alive. Since receiving that offer I’ve discovered that there is nothing like a solid job offer with a specific deadline when it comes to being a motivator. I did, in fact, have other places on my daily schedule that could be converted to time for “uni work”, and progress proceeds apace. Assuming that all goes well with my achieving my deadlines for submission, and with the paperwork for visas and everything else involved in such a move, July should see me in a new country, starting a new job, but there are a number of tasks yet to be completed to achieve that goal.

One word of advice for anyone else coming down to the end of a major project with a hard deadline: any time you need to take a break, be it to sleep for the night, or just to go grab a quick bite to eat, be certain you know what specific task you will be doing when you return. I find that is ever so much easier to procrastinate if I am thinking in vague terms of “lots to do”, and that it is ever so much easier to start working if I’m thinking in terms of “one specific, reasonably easy to accomplish” task to undertake next.

Being a Pet Scientist

Here in Australia there is a wonderful program to promote science to children, the Scientists in Schools program. In this program, scientists from any branch of science volunteer and are matched with a school looking for a scientist of that flavour. Sometimes the scientist is local to the school, and comes in once a week to do science with the kids. Sometimes the scientist lives a great deal away, and instead communicates with the students via e-mail. Any sort of partnership which works for the scientist, the teacher with whom they are working, and, most importantly, the students, is a good one. I recently heard about this program, and volunteered to join it, despite being busy trying to complete a PhD project (which, as most of them, has already gone on longer than I had hoped it would). I have finally been matched with a school, and met my teacher two weeks ago. We discussed having me come into the classroom early next semester, to meet the students and talk to them about how cool rocks are.

However, this week I received an offer on one of the post-doc positions for which I have applied, and suddenly my schedule is far, far busier than it had been. I am still aiming at the same deadline for completing my writing and submitting the final, bound, thesis to the examiners, but now it is *urgent* that it be done by then, so that I may board an airplane and go start my next adventure. As a result, after consulting with my teacher, we have decided that instead of my going into the school to meet the students in person, I would send them a letter, and invite them to e-mail me with questions. Then, in a few months, when I am settled into my new home, I can use Skype to come into the classroom and talk with them about what I am doing in my new job.

For your amusement, here is a copy of the letter I wrote for my school:

Hello, I am a Life-Long-Scholar, and I'm your pet scientist through the "Scientists in the Schools" program. My job is to be available if you have questions about science, and to share with you the fun things I do in science. My particular field is geology--I study the earth, especially the rocks which make up our planet and how they change over time. The rock cycle is an amazing process. You all know, I think, that sand is nothing more than very tiny rocks which have been broken off of bigger rocks, and you have probably seen sandstone, which is a "sedimentary" rock that is formed of sand squished or cemented back into a solid chunk again. The other parts of the rock cycle are harder to see, because they require much heat or pressure to make happen. Just as a liquidy cake batter changes when you put it into a hot oven into a solid cake, so sand and mud change if you burry them deeply enough. A kilometer is deep enough to squish them back into rock, but if you burry them really deeply (15 to 30 kilometers deep!) it gets hot enough for them to start changing. New minerals start to grow, dissolving the tiny bits of sand and mud and growing them into crystals. Left long enough, the crystals can grow to large sizes. This change is called "Metamorphism" (from the Greek word meaning "change"). Rocks that are metamorphic tend to be pretty, because, often, those crystals grow big enough for us to see them, and many minerals which like to grow at those depths tend sparkle, which makes the rock shiny. At even deeper depths than metamorphism the rocks can melt. When this happens the liquid (called magma) tends to work its way slowly back up to the surface of the earth, until it either cools back into a rock somewhere under ground (they call this "intrusive"), or until it reaches the surface and explodes out of a volcano (they call this "extrusive"). Both "intrusive" and "extrusive" rocks that cooled back into stone from liquid magma are called "igneous". The reason we call it a rock "cycle" is because all three of the main classifications of rock types: sedimentary, metamorphic, and igneous, can, under the correct conditions, and given enough time, turn into the others. A sedimentary rock is made up of broken bits of any of the three rock types and then put back together into a new rock A metamorphic rock is made up of new minerals that grew and replaced the minerals in any of the other rock types when it got buried deeply enough to change. An igneous rock is one which is cooled from liquid magma, which first melted from any of the three rock types.

All scientists first choose their general field (do you like plants? space? rocks? animals?), and then they choose more specialized things to study in the field. I am a metamorphic petrologist. This means that I study metamorphic rocks. I "read" the clues in the rocks to learn what happened to make them the way they are today. Some of the clues are physical--when rocks are deformed the minerals which happen to be long and thin (like a pencil) or thin and flat (like a piece of paper) tend to all align themselves pointing the same direction, so from this we can tell from which direction the pressure was applied. Sometimes those layers wind up folding, and those folds give us more information about the pressure which affected those rocks. Some of the clues are chemical. All minerals are made up of chemicals, arranged in a pattern. The pattern can accept more than one chemical element in certain spots, so long as they are close to the same size. Which one happens to be in that location in any given repeat of the pattern will depend on both what elements are available in the rock in the first place, and what the exact temperature and pressure is when the mineral is growing. Some minerals are buddies and like to swap elements, trading back and forth as conditions change. Iron (chemical symbol: Fe) is a little bit bigger than Magnesium (chemical symbol: Mg), but they are sort of similar in size. As a result, they tend to both show up in minerals at matching points in the pattern, but, some minerals have a pattern with more room than others. The ones with more room in the pattern will still have room for Fe when the heat and pressure increases, but the ones with a smaller slot won't. Therefore, when the heat and pressure increases, they swap, the smaller slot takes the Mg, and the bigger slot mineral takes the Fe. But, if the heat and pressure decreases, they swap back again. One of the things I do is measure how much Mg and Fe is present in certain pairs of minerals today, and from that calculate what the temperature and pressure must have been when those minerals were growing.

crushing rocks for fun and profit

There comes a time in the lives of most graduate students when the scholarship funding has run out, but the writing isn’t over yet. Fortunately for us, many geology departments have people who are busy enough with their own research that they are better off paying us students to do some easily delegate-able task than to do it themselves. As a result, this week I have been crushing rocks for fun and profit. The goal for this week is turn rocks into coarse sand so that zircons can be separated from the sand. As I mentioned in my previous post on that topic, the easy part is the first two steps. Those two steps are what I’ve been assigned this week. I've taken photos of the process to share with all of you, but most especially, for my friend in Alaska, who wanted to see the power tools with which I am playing.

Rock dust being a nasty thing to breath, the first thing one does when entering the crushing room is turn on the ventilation system. It is recommended that in addition to that one wear a breathing mask. Once the ventilation system is functioning it is very important to clean all of the work surfaces and tools carefully, to be certain that there isn’t any remaining dust from previous samples—it is important that the zircons we collect at the end of the separation process actually came from the sample we think they did!

The hydraulic crusher, cleaned and ready to use:

A sample in the crusher, ready to crush:

A clean sheet of paper (scrap, rescued from the recycle bin upstairs) is placed under the sample to make it easier to transfer the chips to the mill in the next step. Alas, the paper does tend to get destroyed, and it requires a bit of scrubbing to remove the tiny bits of it which get squished onto the underlying metal surface, but it really does make the process easier, so is worth that extra effort.

With a push of a button, the hydraulic crusher lowers the upper head inexorably onto the sample, and, eventually, there is brittle failure of the rock.

The chips are then put into the ring mill, which had first been completely cleaned and completely dried:

the mill is taken to the milling machine, set into place, and the hydraulic clamp lowered to hold it securely. (The compressed air system in use here is essential for nearly every step of the process!)

Then the lid closed, and the machine is turned on for 3 to 5 seconds (depending on how hard this sample is).

While the machine is on the mill is shaken in such a way as to cause the internal rings to rotate and move about inside the mill, crushing the rock chips into sand.

Once the mill stops shaking one takes the sand out, pours it into a clean bag, with the sample number clearly marked upon it, and then the real work begins: scrubbing the mill, the counters, the crusher, and anything else which might have come into contact with the dust/sand from the sample. One of the challenges is cleaning the rubber collar from the hydraulic crusher, because it has many small cracks on the internal edge, from years of sometimes having been crushed along with some of the samples. It is very important to make certain that no sand remains trapped in these cracks.

Once everything is clean, and fast-dried with the compressed air gun (which will, it is hoped, blow away any tiny zircons which might have stuck to the surface during the washing process) it is time to start again on the next sample. So far I’ve turned 16 samples into sand,

with an average time of 30 minutes per sample, 3 seconds of which is the actual transformation process. There are five more samples to go on this job. One of the joys of crushing someone else's samples is that I have no idea where they come from, or what their significance is, so that I'm free to just appreciate each one on its own merit, admiring the igneous crystallization in this one, the fine banded metamorphic texture in that one, or the rich red hue of the sand of a third.

Next week I will turn rocks into powder for XRF chemical analysis. This will take much longer—the powder needs to be quite fine grained, so I will have to give it 15 seconds in the mill, instead of just 3 to 5. The cleaning process before and after each sample, however, will be unchanged. The need to avoid contamination is just as great for chemical analysis as it is for zircon separation.

One of the joys of being a scientist is that we learn skills which are applicable in other facets of our lives.

Unlike some people who were drawn to science, I am not a seriously math-oriented person. Sure, I took the algebra and calculus required to obtain my Bachelor of Science degree, but I didn’t feel the need to be doing calculations of my own on a daily basis. This was one of the reasons which drew me into Geology—it is a science, but there are many disciplines in geology wherein math isn’t needed often. For my Master’s degree the only calculations I needed to make were all done in a single afternoon. I needed to convert from feet/miles to meters/kilometers since my base map was in feet (my advisor and I both felt that metric is the more appropriate system in which to report results). This conversion is taught in pretty much all first-year geology laboratory courses in the US, and not only had I taken such a class, I was teaching that class that year, so I had the formula immediately to hand. I also needed to calculate apparent dip (what angle the tilted layer of a fold in the rock will appear to have if you happen to slice through it at some angle other than exactly perpendicular to it). This is taught in structural geology laboratory courses, and again, I happened to be teaching that class that semester, so had the necessary formulas at the ready.

For my PhD project, I am needing to do a fair few more calculations, on a much more regular basis. However, I don’t actually do the arithmetic myself; instead I set up Excel Spreadsheets with formulas as I need them, and then type a number into the appropriate cell, and read the answer from another cell. This is a very, very useful skill to have. It requires care to get the formulas typed in correctly, and sufficient understanding of what you want them to do and what sort of answer you should get so as to be able to tell if you’ve got it right and it is working, but once it is done correctly it can be re-used any number of times by just changing the contents of the input cell and reading the answer out of the output cell.

Today I used my spreadsheet formula building skill for something unrelated to my PhD project. For the past year I have been working on and off on making a hat by nålbinding. This has been my project which stays in my backpack in case I happen to be stuck in line somewhere, or attending a lecture, or otherwise have some time with nothing I need to be doing with my hands. A few people have asked me how long it has taken me, and while I know the date I started the project (18 May, 2008), I didn’t have a clue how much time has been spent working on it. So I set up a spreadsheet to figure it out.

I first looked up the formula to calculate the circumference of a circle (2μr) to be certain I had remembered it correctly from primary school (I had). I then told Excel to put the value for μ in cell A1 (one does this by typing “=PI()” into that cell). I then typed the headings “diameter”, “radius” and “circumference” into cells B1, C1, and D1. In the next row I set up my formulas. I measured the diameter of the hat (42 cm at the widest point thus far) and entered it into the empty cell in column B. In the adjacent cell I typed “=B2/2”, which told the computer to calculate the radius by dividing the diameter by two. In the third cell I typed “=2*$A$1*C4”, which told it to calculate the circumference by multiplying two times the value in A1 (which, as you recall, is Pi), times the radius. For the outside row of the hat this is 129.6 cm. Checking that with my tape measure confirms that this is pretty much correct (keeping in mind that the hat, being made of yarn, is able to stretch a bit, so obtaining an accurate measurement can be tricky).

(It is important to remember that in Excel, if you copy/paste a formula and the formula contains a cell name, the pasted version will instead name of the cell which is located in the same position relative to the new cell as the originally named cell is in relation to the original formula location. This is useful when you want to perform the same calculation over and over again using different starting data. However, sometimes you want the formula to point to a specific cell no matter what. In that case you add the $ symbol to the name of the cell. This is why the above formula contains both cell names with and without the $ symbol—I needed them in the name of the cell containing the value for Pi, because I wanted to use that particular value every time I calculated the circumference, but I didn’t want them in the name of cell containing the radius, because I knew that I would soon need to be calculating the circumference for lots of different radiuses.)

Having set up the first step, it was time to do the real calculations; if I want to know how long it took to make the hat, I need to know how many knots it took to make it. This hat is constructed by tying knots in a spiral pattern, starting from the center, and working outwards in what could be thought of as one continuous row, or could be thought of as a bunch of rows, each one out from the next. The latter interpretation is more useful for my purposes today, so first I counted the number of rows from the center to the outside (75). Then I measured the diameter of the innermost loop of that spiral (0.8 cm) and typed it into the 75th row of the spreadsheet in column B. I then entered “=B2-B75” into random cell out of the way of where I was working, and then (in cell F75) divided that result by 74 to get the width of a typical row (if there are 75 rows then there are only 74 spaces between them, which is why I used 74 and not 75 in that formula—if you don’t believe me, look at your hand and count the number of fingers and compare that total with the number of spaces between them). I then typed “=B2-$F$75” into cell B3, and then copied that formula into all of the rows between that cell and cell B75. This gave me the diameter of each row. I then copied the formulas for radius and circumference into all of those in between rows as well, giving me 75 rows worth of steadily decreasing circumference totals. From there it was a simple matter to add them all up (not quite 6000 cm worth of total distance for an ant to crawl if it started in the center and followed the spiral out to the edge), and multiply by the number of knots per cm (about 5), giving me a grand total of almost 27,800 knots in the hat. I then set my stopwatch running and made a few knots, and determined that if all goes well and there are no tangles in the yarn, I can do a knot in about 10 seconds, more or less. Assuming that this rate has been typical throughout the project, the computer tells me that I’ve put in about 77 hours work on this hat, which averages to about 1.7 hours a week (or less than 15 minutes a day) since I started it. (Keep in mind that some weeks it would not have been touched at all!) All in all, this sounds like a reasonable amount of time, particularly since it mostly exists as a project to keep me from being bored when I’m waiting for something.

So, the next time you hear a student complaining about their math class that they will “never need this stuff”, you can assure them for me that, yes, actually, it does come in handy, sometimes in very unexpected ways.