## Friday, October 03, 2014

### on fabricating data (but in a good way)

yes, it's been a while;
no, i'm no happier;
yes, I still wonder if i'm cut out for the academic life...

... but let's set aside those irreconcilable issues for now.

* * *
at the moment, i'm having far too much fun devising homework problems for my Numerical Analysis students.

one problem gives them some data points for a unknown function. their task is to show that, given a few hypotheses about the function, why the data cannot possibly come from Newton's method!

## Wednesday, July 30, 2014

### ARR, MoAR!... in which i don't know what to say ..

.. except that something has to change; this shouldn't happen in a country that calls itself a democracy.
Urban teachers have a kind of underground economy, Cohen explained. Some teachers hustle and negotiate to get books and paper and desks for their students. They spend their spare time running campaigns on fundraising sites like DonοrsChoose.org, and they keep an eye out for any materials they can nab from other schools. Philadelphia teachers spend an average of $300 to$\1,000 of their own money each year to supplement their $100 annual budget for classroom supplies, according to a Philadelphia Federation of Teachers survey. ~ from "Why Poor Schools Can’t Win at Standardized Testing" @theatlantιc ## Monday, July 28, 2014 ### ARR, MoAR!... a digital version of synesthesia? as the washingtonpost calls it: "paris with an echo" ### idle movements. ε ## Wednesday, July 23, 2014 ### ARR, MoAR!.. on the downside of passion. this article is about how programming, despite the call to arms about learning how to code, is a low-status job. when i read this post, though, it funded more like the plight of teachers: .."that we allow “passion” to be used against us. When we like our work, we let it be known. We work extremely hard. That has two negative side effects. The first is that we don’t like our work and put in a half-assed effort like everyone else, it shows. Executives generally have the political aplomb not to show whether they enjoy what they’re doing, except to people they trust with that bit of information. Programmers, on the other hand, make it too obvious how they feel about their work. This means the happy ones don’t get the raises and promotions they deserve (because they’re working so hard) because management sees no need to reward them, and that the unhappy ones stand out to aggressive management as potential “performance issues”. The second is that we allow this “passion” to be used against us. Not to be passionate is almost a crime .." ~ from "How the Other Half Works: an Adventure in the Low Status of Software Engineers" @Michael0Church. ## Tuesday, July 22, 2014 ### ARR, MoAR!.. on risk-aversion. from "Don't Send Your Kid to the Ivy League" @NewRepublic: So extreme are the admission standards now that kids who manage to get into elite colleges have, by definition, never experienced anything but success. The prospect of not being successful terrifies them, disorients them. The cost of falling short, even temporarily, becomes not merely practical, but existential. The result is a violent aversion to risk. You have no margin for error, so you avoid the possibility that you will ever make an error. Once, a student at Pomona told me that she’d love to have a chance to think about the things she’s studying, only she doesn’t have the time. I asked her if she had ever considered not trying to get an A in every class. She looked at me as if I had made an indecent suggestion. like any news article on education, one should take this report with a reasonable amount of skepticism .. .. but being a university educator myself, there's some truth in it. generally my students are uncomfortable when i ask them problems in the exam that don't match up with their textbook problems (even though they are usually combinations of the same problems). the risk of a new obstacle, of not having seen something on which they will be evaluated .. it seems to really affect them. ----- for instance, last semester i think i spooked most of my linear algebra class with one geometry problem on each exam. [1] at some point several students asked for practice geometry problems. "everyone's worried about the geometry problem," one of them admitted. i tried to point out that it was only one of at most five problems and that i generally curve the scores .. .. but (s)he didn't seem convinced. [1] e.g. "Determine, if it exists, an equation for the sphere passing through the following four points." (i even reminded them what the equation of a 2-sphere in 3-space was!) ## Friday, July 18, 2014 ### highly irrelevant, but .. .. once, at a party full of mathematicians, a friend was trying to formulate this one lemma. [1] he drew a shape and said .. .. "ok, so this is a triangle .." .. but at that point i had one too many and suddenly blurred out .. .. "no. that's just an approximation of a triangle!.." .. at which time everyone around just just burst into hysterical laughter. terrible, unrepentant mathematicians, we were .. :-) [1] yeah, we were that far in. i truly suspect maths is a language, because many drunken mathmos i know still revert to their mother tongue, after one too many .. ## Monday, July 14, 2014 ### ARR, MoAR!.. on picking-&-choosing. now i don't feel so bad about not caring about number theory problems. In one letter he even displayed contempt for the problem. His friend the German astronomer Heinrich Οlbers had written to Gaμss encouraging him to compete for a prize which had been offered by the Paris Academy for a solution to Fermαt's challenge: "It seems to me, dear Gaμss, that you should get busy about this." Two weeks later Gaμss replied, "I am very much obliged for your news concerning the Paris prize. But I confess that Fermat's Last Theorem as an isolated proposition has very little interest for me, for I could easily lay down a multitude of such propositions, which one could neither prove nor disprove." ~ from "Math's Hidden Woman" @pbs so i suppose that even the best of us should pick and choose the tasks best suited for ourselves. i wonder, though, what Gaμss thought of the Rιemann hypothesis ..? also, to explain the title of the cited article, Gaμss isn't its main subject .. but the French mathematician Marιe-Sophιe Germaιn. it's quite an account! i wonder sometimes how many women in history have kept to the academic shadows because of a lack of social tolerance and the societally-induced hardships upon them. if the best minds of their time, such as Gaμss as well as Hιlbert (in the case of Emmy Nοether) could see the potential of these scholars, then you'd think that others would be willing to listen .. \-: ## Friday, July 11, 2014 ### on an unrelated note, Ctrl-F is amazing. .. not that this is of any real importance to post about .. .. .. but i don't know what i'd do without the "find-&-replace" command that is standard on most text-editors now. ("copy-&-paste" has been indispensable for checking long chains of estimates, too.) ## Wednesday, July 09, 2014 ### the next generation, part 3*: possibilities. you know, today's meeting was pretty fun. the student, having had a few days to think about a few concrete aspects of the problem, was a lot more comfortable showing me things that he thought about, telling me claims that he suspects are lemmas .. and why he thinks so. what really helped, i think, is that it became clear to us that there was plenty we could learn, just by computing explicit configurations. the student seemed to feel both awed and excited, that these were strange, interesting, yet accessible things for him. i think he realised today some scope of what was possible for him, that he started to believe in himself. this isn't to say that i didn't guide the discussion, but i felt like the back &-forth today is suggestive, and this laissez faire style might actually work. * .. and no, you didn't miss part 2; i haven't posted it yet. ## Wednesday, July 02, 2014 ### training the next generation (a first post in a potential thread) so i finally have something ready to write about [1]: i'm advising a former calculus student of mine on a summer (undergraduate) research project .. and (for me, anyway) it's a scary thing. many of my colleagues are old hands at this, i know; so if i seem naive, it's because this is the first go and i don't know any better. i worry, for good reason: he's studying a topic i know little to nothing about. in particular, it's not clear to me how easy or hard the problems i pose to him really are .. and as a result, i don't know how much frustration i'm throwing his way. it depends, of course, how much the student is willing to work. if i give him a badly-posed problem, then a good work ethick can actually be bad .. in the sense that, by working with abandon for too long a time, he burns out and gets turned off by pure maths in the future. in case it's not clear, i'm encouraging the student to make his own conjectures; of the established theorems whose proofs he can easily understand, i'm suggesting him to try his own variants. in other words .. and for better or worse .. i'm insisting that i don't give him orders; he'll have to train himself to think like a pure mathematician, but i'll be there if he needs advice or guidance. i was worried about his technical chops before .. until i realise that if his proof-writing skills require work, then this is potentially the best way that he can practice them: by working with a topic that interests him. let's hope these aren't another example of famous last words ..! [1] as you can see at the end of this post, i'll be tagging these thoughts with the handle "Σ:nextgeneration" .. and the usual disclaimer follows: unlike other maths blogs out there, i'm not out to train or educate maths-inclined people out there, at least not directly. instead, i'm going to show you, through my mistakes, what not to do. ## Friday, June 20, 2014 ### to be more creative, try becoming a more boring person? first of all, apologies to my readers for the dearth of posts in the last few weeks months and especially the lack of posts with any personal depth in them. i won't go into detail about it today, but this change in my life from a "gun-for-hire" postdoc to a "lifer" prof has bent my mind awry and i'm still learning how to cope with the job. sometimes it just feels .. crippling. more precisely, it's not the actual job that's hard, but the stress and overthinking of this faraway goal called tenure. the more i think about it, the more it feels like i'm getting my ph.d. again. all of that said, i'm going to go the lazy route again: i'll pass someone else's well-written piece to you (instead of writing my own). when i was younger and a newer hand at research, i'd make a startling insight in my work. immediately aftewards, i'd lament why it took me so long to figure it out .. especially when the outcome appeared very simple. i've become less critical of myself over the years, but the question still remains: what if there were ways to become better at solving problems? is it more than just a pipe dream to improve oneself? below are excerpts from an essay i found, through one social media engine or another. what struck me about it was how i've unconsciously kept some of these habits and gotten more insights, in the last few years. "A 2004 study published in Naturε examined the role of sleep in the process of generating insight. They found that sleep, regardless of time of day, doubled the number of subjects who came up with the insight solution to a task. (Presented graphically above.) This effect was only evident in those who had struggled with the problem, so it was the unique combination of struggling followed by sleep and not sleep alone that boosted insight. .. "There’s a good reason for this: mind-wandering fosters creativity. A 2012 study (results pictured below) found that any sort of mind-wandering will do, but the kind elicited during a low-effort task was more effective than even that of doing nothing .. This, too, is congruent with my experience. How much insight has been produced while taking a shower or mowing the lawn? Paul Dιrac, the Nobel Prize winning physicist, would take long hikes in the wood. I’d bet money that this was prime mind-wandering time." ~ from "The Science of Problem Solving" @rs.io of course, this could all just be a manifestation of confirmation bias (or if you will, the fallacy of the consequent). what i do recall, however, are periods of correlation: i was highly uncreative during those times when i was sleeping very little and had no time to exercise. lastly, the tl;dr at the end of the essay is suggestively helpful. i'd recommend newcomers to research at least to try a few of the habits listed, if only to see what works (or not) for you. ## Tuesday, June 17, 2014 ### sometimes negative signs matter ..? after browsing this article, suddenly the difference between mεasures, sιgned mεasures, and vectοr mεasures come to mind. The answer to this question takes us to the heart of quantum mechanιcs, to the part that popular explanations usually mangle. Quantum mechanιcs wasn't the first theory to introduce randomness and prοbabilities into physics. Ironically, the real novelty of quantum mechanιcs was that it replaced prοbabilities — which are defined as nonnegative real numbers — by less intuitive quantities called amplitudes, which can be positive, negative, or even complex. To find the prοbability of some event happening (say, an atom decaying, or a photon hitting a screen), quantum mechanιcs says that you need to add the amplitudes for all the possible ways that it could happen, and then take the squared absolute value of the result. If an event has positive and negative amplitudes, they can cancel each other out, so the event never happens at all. The key point is that the behavior of amplitudes seems to force prοbabilities to play a different role in quantum mechanιcs than they do in other physical theories. As long as a theory only involves prοbabilities, we can imagine that the prοbabilities merely reflect our ignorance, and that a “God’s-eye view” of the precise coοrdinates of every subatomιc particle would restore determinism. But quantum mechanιcs’ amplitudes only turn into prοbabilities on being measured — and the specific way the transformation happens depends on which measurement an observer chooses to perform. That is, nature “cooks prοbabilities to order” for us in response to the measurement choice. That being so, how can we regard the prοbabilities as reflecting ignorance of a preexisting truth? ~ via "Quantum Randomness" @ AmericanScientist ## Wednesday, June 11, 2014 ### ARR, MOAR!.. on writing. the following excerpt by s.a.pιnker isn't terribly representative of his original article about writing, but i liked it anyway and thought to share it: For example, everyone knows that scientists overuse the passive voice. It's one of the signatures of academese: "the experiment was performed" instead of "I performed the experiment." But if you follow the guideline, "Change every passive sentence into an active sentence," you don't improve the prose, because there's no way the passive construction could have survived in the English language for millennia if it hadn't served some purpose. The problem with any given construction, like the passive voice, isn't that people use it, but that they use it too much or in the wrong circumstances. Active and passive sentences express the same underlying content (who did what to whom) while varying the topic, focus, and linear order of the participants, all of which have cognitive ramifications. The passive is a better construction than the active when the affected entity (the thing that has moved or changed) is the topic of the preceding discourse, and should therefore come early in the sentence to connect with what came before; when the affected entity is shorter or grammatically simpler than the agent of the action, so expressing it early relieves the reader's memory load; and when the agent is irrelevant to the story, and is best omitted altogether (which the passive, but not the active, allows you to do). To give good advice on how to write, you have to understand what the passive can accomplish, and therefore you should not blue-pencil every passive sentence into an active one (as one of my copyeditors once did). (for more articles of this kind, visit edge.org.) ## Tuesday, May 27, 2014 ### are the dollar signs worth it? so i spent most of the day LaTeX'ing, which went well enough. the best thing about writing up ready results in LaTeX is that one feels smart, that maybe all those days of banging one's head against these damned technical lemmas [1] were worth it after all. .. .. on the other hand, there's something else I should write up, but i can't convince myself to do so: whenever i think about the proof, I don't feel smart. instead, it just seems .. trivial. [1] technically, the plural of lemma is "lemmata." ## Saturday, May 24, 2014 ### my younger self used to be so smart .. yesterday i printed out some research notes i wrote in february .. .. all 24 pages of them, just to prove one lemma. [1] ye gods; the ideas still make intuitive sense, but the proofs are painfully technical .. much more so than i recall. [2] they're not even a complete set of notes! for the lemma to have a complete proof, i'll have to read another set of 5 pages of notes for a sub-lemma, as well as a short 3-page section of an old preprint of mine .. no wonder why i couldn't convince myself to work hard in april. after that and then that trip to spain in march, i had little to no energy left. anyway, it's time to write up the result(s) .. .. because what currently exists are the notes, not a preprint. there's a lot of exposition and simplification before i have anything remotely readable! [1] at this point maybe i should promote it to "theorem" status. (before i thought it was .. well, obvious, and the proof would be short.) [2] one series of estimates involved 4-5 indices. i was comparing intervals at different dyadic scales, as well as the same scale, which explains two indices .. but the intervals aren't nested in one another, which requires two more indices. lastly, these estimates were "fibrewise," so an additional fifth index kept track of which fibre was which. ## Wednesday, May 14, 2014 ### ARR, MOAR!.. or: "active" = passive. one of these days i'll start posting regularly again .. and about research too. until that day comes, however, readers of this blog will have to suffer through the occasional repost about maths education, like this one: "Lectures Aren't Just Boring, They're Ineffective, Too, Study Finds" by a. bajak @science The meta-analysis, published online today in the Proceedings of the National Academy of Sciences, concluded that teaching approaches that turned students into active participants rather than passive listeners reduced failure rates and boosted scores on exams by almost one-half a standard deviation. i don't doubt that active learning causes students to retain information and to improve their understanding of the concepts of the course. my contention is that the only novelty of this teaching style is that it institutionalises what students should already be doing: studying. you see, it's been suggested that today's college students simply don't hit the books as often as previous generations. when i was an undergrad, i was told that 1 credit hour translates to 2 hours of self-study outside of the classroom, in order to keep up with the class. (by this rule, a full-time student with four 3-credit courses should be studying 24 hours per week; combined with class times, this should be close to the hours for a full-time job .. which is exactly how seriously college should be treated by college students.) to me, what active learning amounts to is .. (a) moving the act of self-study from the student's prerogative to inside of the classroom, (b) eliminating the temptation of distraction (from tv, internet, dorm buddies) by forcing the student to focus on clear goals with immediate rewards/punishments. in other words, active learning caters to the modern, distracted, undisciplined mind. they are bringing studying back into college by rebranding it as a new, structured feature of a course. to their credit, proponents of this method are being efficient. I have no doubt that this does encourage (read: force) students to study, inside and outside of the classroom .. .. but it does so, at the cost of maintaining the status-quo of short attention spans and immediate gratification, while further reducing personal responsibility. ## Friday, May 09, 2014 ### An open letter to panicked calculus students, after their final exam. [to put this in context, i had a more vicious version of this letter in mind .. but after some contemplation, it seemed wiser to be diplomatic.] Dear Student, This is to confirm receipt of your email which was sent shortly after the final exam of our course. I realise that Finals Week is a stressful time for you, as well as every other student at our University. Being that our final exam ended very recently, the final exams for our course are not fully graded. In fact, they are not even halfway done. Fair grading, especially that which rewards students for their understanding of the concepts treated in this course, necessarily warrants care, and therefore, adequate time. That said, barring a rather poor semester-long effort on your part (in which case your grade will be already close to failure) I have no idea yet what your final grade is. Based on the scores preceding this final exam, it looks likely that grades for this course will be put on a curve, and it will not be clear how the distribution will look until the final exams are fully graded. That said, it is futile for you to ask about your final grade. Either be patient or stop asking because I, your instructor and grader, simply have no answer for you yet. In fact, your (and your fellow students's) sending me these sudden emails is causing a great annoyance to me; it even affects my focus on grading exams, which further delays any outcome you would like to know. Keep in mind that if you are writing me now, then very likely other students are doing the same. All of you point to extenuating circumstances in your situation, many of which do not pertain to University guidelines for exceptions. By the very definition, exceptions are rare. Please think twice before you consider your situation a truly rare one. --- Regarding your inquiry into "extra credit" there is none available. If there were such a possibility, then it would have been properly announced on the course syllabus, as distributed on the first day of classes. To offer you an additional opportunity now would be unfair to other students and therefore unethical of me; being that it is Finals Week and other students will likely have arranged their schedules to best prepare for their other exams or term papers, to offer everyone a chance for extra credit would be unreasonable. In particular, I have reiterated the same consistent policy to other students in our course, earlier in the semester, and in light of this, they have chosen to withdraw from this course. So to offer you extra credit would be a disservice to those students who made the most reasonable choice with the options made available to them at the time. You are asking something unfair and unethical. I will not grant this request. --- I realise that you may be writing me not on your own rational consideration, but in the heat of panick or perhaps on the suggestion of your parents, your friends, or even your academic advisor. In that sense, it is possible that you initially did not want to send me your message in the first place. That said, please understand my position in this scenario. The grade breakdown in the syllabus has been clear from the start. Barring exceptions given in the University guidelines, every student is graded in the same way. In particular, that means I grade every student based on his/her written work, and that alone. So by writing this panicked email to me, you have an answer that you could have deduced on your own. Moreover, the time I spent writing this reply could have been more efficiently spent on actual grading of exams. This means that you have delayed the answer to your question; worse yet, it means that you have delayed a definitive answer to those other students who have the same question; in particular, you have just inconvenienced your fellow classmates. There has been no benefit to you by writing to me now. This has been a waste of your time and mine. Sincerely, Your instructor. ## Sunday, May 04, 2014 ### I'd rather students be honest, but if they're going to be efficient about it... the more i think about it, the less sense it makes: if you were a mediocre calculus student, then why wouldn't you invest in a complete solutions manual for the textbook of your course? even if you copied all the answers, the percentage of exam problems similar to textbook problems is rather high .. enough, say, for a C grade or probably a B. after all, solutions manuals are perfectly legal products to buy. the only setback I can think of is the additional cost. [scratches head] sometimes i just don't understand students. ## Tuesday, April 29, 2014 ### down, for now. more than eight years ago in a cold, snowy december I sat alone in a cafe, trying to make sense of what had happened. a little later, a fellow grad student stopped by, looked at me, and remembering, asked me how it went. "well," i said, "i didn't fail, but .." [1] i doubt i finished the sentence. we went back and forth in polarised roles, he attempting to be cheerful, me still down. i wouldn't feel "up" for a while. it would take a while of forgetting, earning small separate achievements, before i could look back at it without pain and malaise. ----- that scene from my life came to mind because right now, i have a similar mood .. only less severe. today was my last day of class .. until August, anyway. i don't feel like celebrating, though much of me feels so glad .. i don't feel mournful, but it feels like I lost something .. maybe a chance to have made a great beginning. instead at best i managed a mediocre but trouble-prone one. all I feel are regrets .. that i could have done better or more, that I put to much effort in pointless things, that i never really understood or appreciated what was really going on, under my own nose and in my own classroom .. .. that i just had no real sense of "how it all works." i feel wrong about many things that don't matter, and i don't know how I feel about the things that do. all this past academic year had taught me is doubt and stress and futility. ----- on the other hand, those were the same lessons i learned after my first year in graduate school. knowing that i'd be there a while, i worked at it and eventually it all made more sense .. not quite everything, but it got better. part of me suspects that there is no purpose in life .. in that there is no one canonical purpose. to quote the existentialists, everyone must choose for himself. i have not determined my purpose yet, but i believe there is one that suits me, in this academic life. it will take time .. but trusting on the pseudo-repetitiveness of life, it gives me a certain illusion of faith. so i'm down right now. it won't be forever. [1] it was right after my comprehensive exam, which was an oral, 1 1/2 hour friendly firing squad of questions. i distinctly remember feeling awful that i couldn't prove certain facts on the fly .. and advantageously yet unfairly, the committee never asked for them. ## Tuesday, April 22, 2014 ### another brick in the wall. the more I teach liberal arts students, the more convinced I am that my own history is .. slightly out of the ordinary. simply put.. mathematicians, let alone academic scholars, are a significant minority of the population .. even when one restricts to the college-attending sub-population of the western world only. we aren't ordinary in the sense that we are probabilistically rare. [1] i guess that's just one way of saying (read: justifying) that i'm weird and i shouldn't be surprised that my students and i don't understand one another. ----- today i taught two lectures and it felt like i was instructing two confused yet brick-made walls. it's a very isolating, unnerving experience. maybe i take too much pride in delivering clear, motivating lectures .. where "clear" means clear to me, but apparently not to anyone else. i'm not being fair, though. it's not equal footing between them and i, because i'm the one setting the agenda and I know what's coming next; to them, though, i'm speaking a foreign language and during class, it's all they can do to copy what's on the blackboard. isn't it fair, though, that after most of the semester, that they keep up with me? put otherwise, if i'm going to interact with a brick wall, why should i leave my office to do so? why should I talk about things i know well when i can explore this i don't know but that i want to? what's the damned point?!? [1] the more i think about it, the more irrationally obsessive of a student i must have been. i remember studying with friends for exams by quizzing each other, asking each other how to prove this or that statement on the spot. i remember checking out maths books from the library, reading what seemed fascinating at the time. i remember being incredibly upset that, after two years and then graduating, i couldn't solve one particular open problem that my mentor suggested to me. (as far as I know, though, even now nobody's solved it either.) ## Monday, April 14, 2014 ### i've been feeling unproductive lately; may as well make it certain. i don't regret traveling and writing through spring break. it was a pleasure to see colleagues that are soon becoming old friends, in a city becoming more familiar and pleasantly so. this isn't too say that i could live there .. odds are that I'd bend back to my hard-to-get-a-hold-of, anti-social self. put more simply, it's better that those colleagues of mine know me as a guest, not a neighbor. ----- those things said, Easter is coming and the university will be closed for chose to a week. there are so many things to do .. but i'm getting out of practice and growing soft. i get tired more readily. so i think i'm going to take a vacation, go up north for a day out two and go hiking as i fancied once. maybe i'll watch the latest superhero movie at the cinema. maybe I'll finally meet friends for lunch as i promised, long ago. more likely, though, i'll spend two days on a research bender, writing up a quick-&-dirty draft of a note.. /-: ## Sunday, April 13, 2014 ### an unhappy compromise. i think it accurate to say that I spent the whole day trying not to think too hard about one problem. in retrospect, i should either have worked as hard as I could have, made some small progress .. even a wrong turn would have been one more lesson in which way not go turn again .. .. or not worked at all on it; i guess I never learn. ## Monday, April 07, 2014 ### the body wanders, followed by the mind. my memory of Spain it's behind fainter and fainter. being my Nth trip there (with N > 2) i've stopped picking up souvenirs .. so the only memento i have from the trip is a LaTeX draft in dire need of revision. i haven't started counting the days until the end of the semester, but i'm getting there. the thing about having had a week off from teaching is that it skews my expectations: lately i've tried (unsuccessfully) to convince myself that a weekend is two days long and plenty of time to accomplish something small. [ to be cont'd ] ## Saturday, March 22, 2014 ### Prodigal. So in a few days I have to return to real life.. that means finally grading these exams, prepping another exam for another class, getting back to a scholarly journal, to colleagues in my department about a potential project and journal club, and so on. Why do I feel alone in my endeavors? Why do I think I'm so ineffective and inefficient? I feel refreshed.. but the sort of relief that will quickly deplete itself in a week's time and stress. My one track mind is a disadvantage in this modern society, where one had to stick to a multi-tasking schedule of barely controlled confusion.. ## Thursday, March 20, 2014 ### On what to prep. In my previous travels to attend conferences or visit colleagues,I used to bring printouts of preprints (most of them by others, not me) as well as a few books and a laptop. Experience has shown me, however, that most of this stuff is never used. These days I bring a netbook, the preprints stay in PDF form [1], and there's room for both my running shoes and climbing shoes. [1] .. and the books are digital, too.. though legal copies are harder to come by. ### Push and pull. So I lost a debate with my co-authors, but it doesn't bother me. I guess it shows that we work well together and that I can trust them to tell me when I'm wrong about something. The important thing about maths is that one remains with what is correct. Often it means that one has to be wrong on occasion, and to realise why. More and more it seems important to me to fail, if only to be aware of how far I am pushing what I knew and what I really understand. It also seems that the way American universities are structured doesn't allow for this. Sometimes I wonder how new mathematicians come out off the woodwork, and if this explains why it takes so long to get the hang of research... that is, if one ever gets the hang of it. I like Europe. I didn't realise the extent to which I missed it, how the universities work. Of course life is always more appealing as a guest.. but being in Spain reminds me of those years in Finland when I was a semi permanent resident and slowly becoming a local. I wonder often enough if I should have stayed and tried for a permanent position.. maybe teach a course or two, co-advise a student, convince my sponsoring department that I might be a good guy to keep around. Odd. I'd be scared to death of advising a Ph.d. student here in the States, but in Finland it would be more doable. ## Tuesday, March 18, 2014 ### On the bright side.. My recent posts have been rather bleak, haven't they? I guess I'm still not fully used to professorial life; sometimes I wonder if it will ever feel normal. That said, it's Spring Break and I'm away for the week, visiting my co-authors in sunny Spain. I feel life my old self again. Ideas are coming out: a few good ones, lots of bad ones too. There's a good chance we'll finish off the guts of one manuscript.. and now I'm thinking about how to start another one. So maybe I was wrong before; sometimes I can get my act together, finish what I started. ## Thursday, March 13, 2014 ### How it never ends.. but how it starts. I'm supposed to go to the airport in two days, in order to cross the ocean and to keep a promise to a few colleagues. (Being that I don't keep many of those, it's rather crucial that I do so when it counts.) Still, I'm easily exhausted. If I could say that I am exhausted right now then I would.. but the fact is that I'm not. I know that I can still work, still have enough energy to keep the collaboration going if I budget enough effort per day of the visit. I liken it to surviving on 5 1/2 hours of sleep per night: after a while it feels normal but you could swear that you used to be faster and sharper and maybe you're just "getting old" .. I also know that once I come back, then I'll spend a few days feeling exhausted and bitter at having to readjust to my old routine.. to the extent that I'll probably swear that I'll never travel mid-semester ever again. I don't feel the same anymore. It used to be easy, even natural, to be excited about getting up in the mornings and wanting to do maths right away. Yesterday I met with colleagues in the department and we talked about PDEs.. rather, they did and I was trying to decipher what the underlying mechanisms were. I am and will always be an analyst; these guys really think in terms of physical principles and what the equations are supposed to mean. I suspect that we'll keep a truce and the compromise of that truce will be geometry. Anyway, my point is that the whole time I was absolutely ambivalent: I simultaneously thought (a) this is pretty damned cool and (b) fvck: I have.. aw, fvckity fvck! [1] .. that many incomplete projects right now and I'm supposed to learn.. no, have learned.. these disparate things; how can I juggle this one too? The fact of the matter is that I don't know how long I can keep this up. It feels like a Ponzi scheme on which I can't possibly follow through. I don't know why people put up with it, with me. Whether or not I am exhausted, I feel exhausted. So let this be a lesson to you young researchers: even if your intentions are good, never promise more than you can deliver. [1] at last count, i have$5 + 3(\frac{1}{4})$collaborations and$3$solo projects; a$\frac{1}{4}$of a project means that there is a decent lemma or two, but no real theorems yet. As for the topics, they vary from geometric measure theory and PDEs to fractals, sub-Riemannian geometry, and minimal-like surfaces .. to even Banach space differentiability! On top of these, i suspect that one collaborator is trying to convince me that dynamics is interesting. ## Tuesday, March 11, 2014 ### transformation. If I could do anything right now then I'd..  taken from tours4fun ..first take a week off to go hiking, maybe rock climbing. Maybe Zion, where I'd carry a rope and harness, my own water and in doing so, suffer the weight of existence. I'd do nothing but cross sand and boulders, shoot photos, and make campfires and sit in front of them, starting into the randomness of their flames and sparks. I'd hunt the hidden moon by day, feel stones at my feet, be guided by the wind at my back and the mountains that frame the land-scape. I'd imagine myself made blind by an oppressive sun, finding a path of least resistance, some kind of order amidst the entropy that is desert. Then dried by desert heat, seeking life and creation .. I'd spend a month doing nothing but writing. There are too many manuscripts to revise, ideas to shape ..good ideas to initially obscure and when the shortcomings are clear, to revise into clear, intuitive shape. In leaving Finland there were too many things left incomplete, plenty of angry impatient collaborators.. or at least, should be angry and lack any more patience. I would become strange for a while, shaped by self-imposed solitude, transforming into something less than human.. if only to create maths that I hope will transcend my mortality. if i could .. [sighs] ## Friday, March 07, 2014 ### the curse of time. i don't know what exactly i mean by the title; at best, i can only explain it by example. a month ago I was absolutely delighted to convert one of my old proofs .. which initially relied on weak star cοmpactness .. into a purely geometric argument. at the time i thought this was the coolest thing ever .. and i still think it was worth the effort .. but it's been a month and now i have to stop myself from saying .. wait: shouldn't it be obvious..? as another example: whenever i wrote an exam for one of my courses, i'd take it myself and multiply the elapsed time by 4; if the product was less than the length of the exam period, then the exam was too hard for the course. now i'm considering changing it to a factor of 5. either students today are slower or i'm getting faster .. and i'm almost sure that i'm not getting any faster. ## Monday, March 03, 2014 ### whatchamacallit (or: i'm tired) i don't know what to call it.. maybe a research bender, a maths hackathon, an intense weekend of work? all i know is that this morning i woke up from 5 hours of fitful sleep, felt like old, wrung-out towel, made coffee, and sat down and proved a lemma that bothered me all of yesterday. i sighed after i was done. it was only 9am, and there was a day of work waiting for me .. my day job, you could say. based on years of experience, i'm not one of those mathematicians who can work all the time and still wake up excited every morning. i wish i was. maybe i should take weekends off. lately i just feel tired all the time. ## Saturday, March 01, 2014 ### a picture is worth .. a few hundred backslashes! often enough it feels like i'm wilfully banging my head against a wall. in this case, it's converting visual intuition into rigorous proof. [1] i must have made this claim before .. but i'll say it again: every time i have a proof by picture, it takes 4-5 pages of$\LaTeX$to write out the details! [sighs] oh well: it is the weekend and i finally have time to hack out details for research. i shouldn't complain .. but what kind of "frustrated (over)analyst" would i be, otherwise? (: [1] for those whom are actually curious about the details, i need a suitable partition of$n$-dimensional dyadic cubes so that most of the measure lies either in subsets (a) that are convex polyhedra or (b) whose translates, under suitable unions, form convex polyhedra. ## Thursday, February 27, 2014 ### in the trenches .. or so it feels. i should probably leave the office soon, if only because .. there are students *everywhere* in the department. i hear many young voices from the few office doors that remain open. the math help room is full of people. young men and women have taken over the couches in the middle, watching a tutor intently as she's explaining demοrgan's laws on a nearby whiteboard. needless to say, 'tis the season of midterms .. and as time goes on, fewer office doors will be open. probabilistically, it's only a matter of time before someone stops by my door and asks me a maths question .. that said, i should probably get out of here before i have to say "NO" a lot to many slightly desperate faces. ## Tuesday, February 25, 2014 ### in which it is not easy to be an adult. this morning, after finalising my calculus lecture for the day, i stopped by a local cafe and started working on a proof of a statement that i had jotted down as a claim, months ago. it was frustratingly fun. i almost had the proof .. when i realised that, soon enough, i would have to reach campus and give my lectures. then i started speculating: what if i .. just didn't show up? what's the worst that could happen? .. but then i sighed and realised that, deep down inside, i respect responsible people that can be counted to show up when they need to show up, and that i want to think of myself as such a person. that said, there is only one way to get what you want .. .. and that is to put in the effort, to work hard, in order to attain that goal. i've told my students that before, and that achieving their goals is conceptually simple but emotionally nontrivial. those things said, that means that i have to do the same .. life would be so much easier if one could pick and choose one's convictions, at moment and whim. it is far harder to be consistent. it isn't easy. it takes a commitment and somehow we educators do it .. but like anything worthwhile, it shouldn't be easy .. and for me, it isn't. on a mostly unrelated note, i really enjoy visits to that cafe. the coffee is incredible. ## Friday, February 21, 2014 ### ARR, MoAR! On computers and proofs. so today i learned what a "discrepancy" is: "Adding up the numbers in a sub-sequeηce gives a figure called the discrepaηcy, which acts as a measure of the structure of the sub-sequeηce .." ~ from " Wikipedia-size maths proof too big for humans to check" @newscientist as for how this came up .. Erdös thought that for any infinite sequeηce, it would always be possible to find a finite sub-sequeηce summing to a number larger than any you choose - but couldn't prove it. It is relatively easy to show by hand that any way you arrange 12 +'s and -'s always has a sub-sequeηce whose sum exceeds 1. That means that anything longer – including any infinite sequeηce – must also have a discrepaηcy of 1 or more. But extending this method to showing that higher discrepaηcies must always exist is tough as the number of possible sub-sequeηces to test quickly balloons. Now Konev and Lisitsa have used a computer to move things on. They have shown that an infinite sequeηce will always have a discrepaηcy larger than 2. In this case the cut-off was a sequeηce of length 1161, rather than 12. Establishing this took a computer nearly 6 hours and generated a 13-gigabyte file detailing its working. ## Thursday, February 20, 2014 ### grade school, of a kind. often when meeting new people, i just tell them that i teach maths. it's a more expedient answer during those times when you don't feel like explaining your research to someone who doesn't seem particularly adept at basic algebra, simply wants to be friendly, subsequently asks about your work, and only expected a simple answer (but as to why they expected such a thing is beyond me). [1] that kind of answer gets misconstrued, if you're not specific. occasionally i'm asked if i teach junior or (senior) high school. so the next time someone asks me what grade i teach, i think i'll say: "oh, 13th through 16th, and the occasional 17th grader." (-: [1] just now i re-read that sentence and realised how long it is. did anyone get it on the first attempt? (likely the grammar is incorrect; if anything, the style is poor.) ## Monday, February 17, 2014 ### Seasonal Affective .. Re-order. odd. every february i get new ideas to struggle with.. or what i like to think as creating form out of chaos. i wonder if it's a seasonal matter, if the isolation of winter stirs deeper thinking and contemplation. when i think about it, time seemingly and magically slows down when snow is falling: i perceive it so, at least. rain doesn't fall the same way, nor do baseballs and rocks. i'm too slow to realise that the structure of snowflakes allows an exception; falling leaves, too. the alternative would be that the laws of gravity have been suddenly shut off or gone on holiday, allowing solidwater to float briefly on air. it makes me believe that improbable things can happen, urges me to try and create impossible things, if only to prove a point (via contradiction). landscapes trans-form into their mollified versions, where sharp corners of peaks and cusps are gone. in contrast, jagged edges appear from broken sheets of ice, and once clean lines along rooves are interrupted by icicles. what was rough is smooth; what was void is now full of matter, with sharp corners. this is a different world, an inverted world. ## Thursday, February 13, 2014 ### a cynical rant on .. you guessed it: teaching! i hate to say this .. but the more i think about it, the more it makes sense that good teachers slowly become negligent, if not bad, teachers. at the moment i'm grading exams. for one problem, i'm quickly realising that most of my students weren't paying attention to me when i was patiently .. doing my best .. to explain how to deal with this one particular concept. that's not the only exam problem where this phenomenon has come to pass. if the students aren't paying attention to you, then what's the point of putting in the effort to teach them carefully? coupled with the constant excuses of "i had to miss class because .." or "but my high school teacher told me .." it's enough to make you wonder how students ever learn mathematics at all, and if you were some sort of social mutation to whom maths was somehow natural .. (to their credit, students rarely (if ever) complain further, once they realise you are being fair with them .. well, in my experience, anyway.) [sighs] teaching well is as equally frustrating as doing good research .. the problem is that the former task has no real guarantee of working. it really depends on the students in your class, particularly their disposition. i've heard pundits made casual demands of educators, where ..if you're a good teacher, then you always get through to your students and they can succeed. i believe that as much as if you work hard enough, then you can become a multi-millionaire. it is surely possible, but the odds are bad and most of the time, circumstances don't favor that outcome. epilogue (as of 15 feb): on these student papers i seem to be writing "irrelevant" just as often as i write "false" or "incomplete" .. on a related note, i wish i had some mind to talk about my research .. but this new professorial life makes it all but impossible to get anything done .. ## Monday, February 10, 2014 ### on alter-egos.. all I want to do lately is have enough time to write up this one result. in fact this morning I woke up extra early to$\LaTeX$a lemma and most of its proof, before having to start my day job of being. . well.. a "professor." odd.. I didn't mean for it to come out that way, but there seems to me a sharp divide between the 'me' that teaches university maths and the me that does the research.. or tries to, anyway. it's a little like how Batman has to play at being Bruce Wayne, if only to make sure that he can be whom he thinks he should be, for at least some of the time. ## Saturday, February 01, 2014 ### "either you die a hero, or live long enough to become the villain" .. i think i give good lectures. there's enough evidence that points to this, in the form of student evaluations and comments over the years and from different universities .. and even from a few different countries. apparently i have the ability to be very clear, which is fine. what i've been struggling with is: i can give the best lectures that i can .. that i care to give. when i do, then i feel expert and in my full powers. many of my students would look up to me and i receive their esteem. simply put, it makes me feel good. it will probably impress the students, put me in a good light, and continue to give me good evaluations. it will be good for my career if i keep doing this, and only make stronger my case for tenure. the question is whether that really matters. if my students don't get anything out of the clearest, most intuitive lectures that anyone can give, then really: what's the point? some of my colleagues may argue that if the student is committed, then s/he will put in the effort to get what they can from our lectures and the course in general. i would rather say that if the student is committed, aware, and well-trained.. awareness, i believe, is not only a personality trait; with time, it can be learned. the awareness that is relevant to a student in my course is being aware of what problems are hard, why they are hard, and what steps are needed to overcome these difficulties. the point of the clarity in my lectures is so that my students can cope with the more difficult aspects of the course, by means of a few basic but useful principles. study habits are precisely their namesake: they are habits, and they can be learned too. some students never learn these habits to do well at the university level [1], which means that it is up to me and other university instructors to promote these habits. in particular, it means convincing students to change their ways, which often means that they should do things that they are not comfortable doing or simply don't want to do, like .. .. reading the textbook .. .. asking questions, answering questions .. .. "showing enough work to demonstrate understanding of the problem, the solution, and related concepts to them" [2] .. that said, commitment is a two-way street. who in their right mind would commit to responsibilities that offer no reward, tangible or otherwise? so it's not clear to me: when i'm teaching, should the lesson be so clear that the students don't realise the underlying difficulty, and fail to pay it adequate attention? if the students don't struggle with the material on their own, then will they really learn it as well as i'd like? i have played a hero before, been given a stage to strut; should i, for the greater good, play a villain instead? [1] habits form due to need and from reinforcement. i've seen plenty of students with the 'wrong' study habits, if only because they've been rewarded by their previous teachers for skills that i would not reward. high school mathematics in the united states can be taught rather formulaically, and some students have been taught to do nothing more than operate a sophisticated calculator. the point is to replace old habits with new ones .. which can be an even more daunting task for the educator! [2] i always put this policy on the cover page for my exams. sometimes i even pass out printouts of this cover page, a week or two before the exam, and explain what it means. a former colleague of mine once referred to a syllabus as a list of threats and promises; s/he's not that far off ..! on an unrelated note: since my (unexpected) fall hiatus from blogging, it's become less easy to return to the habit and have things to share with you readers. ## Tuesday, January 28, 2014 ### my teaching routine, lately. ---begin:teachingmode---$CONFUSIONPARAMETER=LOW

define class spring;
type spring.level = nonmajor;
type spring.time = 13012014;
define notes lesson;
type lesson.example = introduction;

while (spring.time != 01052014) {
lesson.example = workout(lesson.example-1);
class.print(lesson);
spring.time++;
}

---end:teachingmode---

## Wednesday, January 22, 2014

### so, if anyone asks ..

like all other working mathematicians out there, i am often asked ..
.."so what do you do all day?"
"i've been trying to build impossible geometric objects, in order to show that certain mass distributions [1] cannot possibly exist."
as you may guess, my recent obsession has to do with finishing a proof by contradiction .. which i suspect is a means of inference that most people are uncomfortable with.

if my experience in teaching basis analysis has any weight here, i think that even mathematics majors at university have trouble with this method of proof.
..
..
.. thinking about it, that kind of answer isn't terribly helpful .. that is, to me. more often than not, conversations of this kind only on go downhill after that question; either (a) i say something too complicated and the other person, not understanding, feels dumb, or (b) i make it sound too easy and the other person wonders why i bother working on that kind of problem.

more likely, the other person would probably be wondering what would drive a person to think all day about things that might not exist ..?

often i just can't win with this kind of thing.

[1] this is my colloquial expression for what's known as a measure; i think i borrowed (read: plagiarised) the term from falcοner's book, in fact. before settling on this, i tried to use the term "prοbaβility distributιon" but this usually misled my audience that my work is related to statistics of some kind ..

## Wednesday, January 15, 2014

### so it begins .. again, yet not again.

odd:
after posting a few days ago, i suddenly feel like posting again.

as i mentioned last time, yesterday was my first day of teaching for the semester. i can only say that i felt very boring.
come on: everyone knows what vector addition is!
do i really have to go over the first section of the first chapter?

surely there is a more efficient way .. maybe i should have built a worksheet, have everyone work it out in a few minutes, go over the answers, and then go on to something more interesting ..
.. thinking about it, maybe i should have done exactly that! [1]

apart from that, there's little else to say. today was the first department meeting for faculty and i learned exactly how out of the loop i am about departmental and administrative affairs.

..
it's a strange thing, being a tenure-track faculty member. it's like being suddenly thrown into the real world and realising that you have to grow up.

[1] that said, if you're reading this and will actually try this approach in your own first day of class, then let me know how it works ..!

## Monday, January 13, 2014

### what i didn't.

i don't know what happened.
tomorrow is my first day of teaching for the spring semester;
today i spent 8 hours in the office, i was busy all day ..

.. and yet i still haven't written out my lecture notes!
oh well: my classes meet in the afternoon, so i guess i'll write them tomorrow morning.

it's been a while since i've last posted in this blog. i thought i'd spend the winter break making sense of my life and all that's happened, this past fall ..

.. what with this new position at a new university and all ..

.. but things still don't make sense. most days of the week i'm making it up as i go along, just trying .. trying my best to get it all done and stay sane at the same time.

there never seems enough time to do it all: teaching, research, faculty meetings and advising and so on. more precisely, there is never enough time in the sizes and shapes that i want them [1].

if i could identify a change in my life, then i'd say that time now comes in fractured form.

so i shouldn't talk about what i did during winter break [2]. it would be more appropriate to say what i didn't do.
i didn't go to the office,
i didn't answer any student emails that i didn't have to answer.

i didn't make sense of my life,
i didn't travel out of town,
i didn't make any new goals.

for the most part, i didn't want to do anything.
i wanted to, i tried to write up notes for a research idea. there ended up being a flaw in the argument and so i thought, off-&-on about the problem ..

.. but not so deeply as to make it too much like work;
i think i got somewhere with it.

this past week i realised that, starting tomorrow, i will have to start doing things for a while: commitments, duties, promises ..

it's starting again. whether it makes sense or not, this new job and life, there are things to do, again.

[1] if you spend enough time staring at weekly schedules, such as the default format for gοogle calendar, then time stops feeling 1-dimensional and linear. instead, it becomes more and more like a very weird tetris game in 2-D, fitting commitments into rapidly dwindling empty spaces.

[2] today was also the first day of spring classes, so quite a few colleagues asked me that question anyway.