A blog advocating autism through my own personal experiences and insights.

Posts tagged ‘Mathematics’

The Acceptance

In my last post, I explained how I had gotten numerous rejections from various places that I had applied to begin a PhD in math. Receiving those rejections wasn’t fun and made me really wonder what I was to do this fall. I might have been able to end my master’s at the end of April, but instead I extended my master’s to the end of the summer so that I could get in more research experience.

Then just over a month ago, I received some surprising news within the department. They had decided to reconsider my application because of the original research results that I had discovered. I was incredibly pleased in hearing this news. The plan was working. Even if in the end they rejected me once again, it meant that I was at least heading in the right direction towards better my future applications. I didn’t even have to submit a new application or a new application fee. They still had my old file from the winter and with the new information that had about me this summer they added it in automatically. It was an incredibly fortunate turn of events. It was July 9 when I heard this news and they said they would get back to me by July 19. Those 10 days in between passed by too slowly as I waited in anticipation for their decision.

Then a couple of days before the big decision day, I actually heard there were positive noises coming from the committee about my application. Two days later I finally got the news. I had been accepted to start a PhD at the University of Waterloo starting this fall!

I finally had a plan in place for this fall and it felt good. I can settle down now and not have to worry about anything for the next four years (except doing math)! I’ve even picked out two courses I’m very excited about to begin my PhD with and so it looks like everything is back to normal! Let the math plough on!

Hard Solid Evidence

Two years ago I was battling perfectionism. I know I’ve elaborate in a lot of ways of how perfectionism influences my life, but something new has developed with respect to it. More specifically I’ve managed to find one large piece of evidence for why I didn’t have to be so perfectionistic back then. Of course a lot of the time simple reasoning a lot of the time tells you whether you’re being too perfectionistic or if your fears are irrational, but rational thinking often doesn’t work for overriding the emotions of perfectionism. Hard evidence is needed.

Two years ago I bought a book on perfectionism Never Good Enough by Monica Ramirez Basco that really got me thinking and changing my perfectionism. The book worked out really well and I’ve already referenced it in another blog post. But one thing I was most perfectionistic about it at this time of my life was what to do with my two interests in math and philosophy. Having decided to double major in philosophy with my math degree, I knew that I had to make choices. I only declared my philosophy major in my third year of undergrad and so had to do a lot of philosophy courses in my final year. What this amounted to though was that I needed to drop at least one math course that I was interested in taking in my final year unless I wanted to overload.

And I actually did consider doing the overload. But as a councillor at Acadia warned me after I had run to her office at the end of the fall term of that year because I didn’t feel I did well enough on a math exam to earn an A+ in that math course was that the plan was very dangerous. If my perfectionism was stressing myself out this much in taking only a normal load, imagine what would’ve happened if I had decided on the overload. And so it was for that reason that I dropped the overload option. I may have toyed with one or a couple more options here and there, but as you know if you’ve been reading this blog was that I sacrificed a math course in the end.

Before I go on, I would like to point out one error that I’ve made in a previous post. I had a terrible time last term and alluded to the fact that it was because the math program at my undergrad university Acadia didn’t prepare me well enough for the grad program here. I have since spoken to my old honours supervisor from there (who I might has always thought the best of me). He came to waterloo to give an oral exam to a PhD student there and was even nice enough to give a talk on the research on fractal geometry I did with him at Acadia, which I did my Acadia honours thesis on. Anyway, I spoke to him about Acadia’s math program and guess what? Apparently it really was the case that the one math course that I missed out on at Acadia would’ve really prepared me all that much more in doing graduate studies. I had been relying mainly on what another math student who had taken the course told me, but after talking to my honours supervisor I found out the student hadn’t remembered correctly. Anyway, so the official conclusion was that there is nothing wrong with Acadia’s math program.

But here’s the rub. This is exactly what I feared two years ago when I was trying to decide what I should take in my final year at Acadia. I feared that losing at least one math course would under prepare me for graduate school. And due to how graduate school is going, it certainly looks like those fears did come true, didn’t they?

How brilliant! How prophetic can I get!

Well, no. Not really. That isn’t the point. Let me explain. When I was reading Never Good Enough, I actually did an exercise in there that helped me keep calm and reduce my fear of making the wrong choices. And one of the choices I felt would lead to unpredictable consequences was indeed sacrificing a math course while at Acadia. Now it’s two years later. And while I must say that it did lead to undesirable effects, the effects haven’t been as bad as they could be. Okay, so I suffered a lot, and eventually had math almost become my whole life last term. But I have been fortunate enough to be put on a probationary period to take a few undergrad classes. And that seems to be going well so far not to mention the benefits I have reaped from abolishing academic perfectionism from my life and gaining a whole new drive to obtain more of a social life.

So at the end of the day, it all seems to be working out. I made my choices and the obvious disadvantages of it are resolving themselves if they haven’t done so completely already. I’m still pursuing math. I’m behind two or three terms because of it, but am still actively doing it. Of course, I’m not necessarily suggesting that we have to ignore the implications of our choices, but to not worry too much if we’re faced with a dilemma in our life.

I faced a problem. And now it’s working itself out. So I now have a solid piece of evidence in my life that suggests that worrying about choices especially in dilemmas can indeed become unnecessary.

Why I’m Making the Choices I Am Part 2

In my last post I explained the biggest transition that happened in my life: how over the course of a year my passions changed from math to fiction writing. I would now like to continue on with what I said in that post. As I explained, my passions changed at least in part because of how love searching for and obtaining truth. Mathematics in its pure form was an interest since early childhood because of this. The truth of math was readily apparent and I didn’t need to have great mathematical maturity in order to appreciate it and its beauty. Fiction writing, on the other hand, only became a great passion thus taking over math in only the last year and a half because appreciation its truth requires one (at least in my case) to have experience of the world around them.

So right after fiction writing took over, I really had to wonder what do about it all. The pursuit of fiction writing is different from the pursuit of academia. You go at it alone. And at the end of it all, the chances of making a living out of it are slim at best. So from a practical perspective at least, it seemed like no decision really had to be made. I’d continue on with academia and continue with fiction writing as something I do on the side and hope for the best. And in a way, while I have chosen to continue on with academia (at least for the time being), the reasons why have less to do with the practical perspective and more to do what I’m interested in writing.

And what am I interested in writing? Well, before fiction writing took over the math, I wanted to write mystery novels. But when fiction writing took over math that changed. It’s not as if I was thinking “I love to write fiction. I absolutely dislike academia now.” I wouldn’t have chosen to go to graduate school if I had thought like that. In truth I still liked academia. It’s just that I decided that I liked fiction writing more. Yet I wanted to keep math and philosophy in my life. (Of course, the practical perspective is rolling its eyes now and saying, “What’s your problem? That’s your day job as a writer. Almost every writer has one of those.”). So how did I want to do this? Well, when I became interested in philosophy, I thought about combining math and philosophy and going into the philosophy of math. Combining math and philosophy with fiction writing? Write novels about math and philosophy! Write science fiction novels that involve deep pure mathematics and deep ideas in philosophy. And since I also like mystery I could throw in a mystery in each novel to boot.

But here’s the catch: if I wanted to write novels about these kinds of things, I wanted to know a lot about math and philosophy in order to write them. Well, that’s easy enough, I thought. Two PhDs, one in math and one in philosophy, should do the trick.

And this is the number one reason I’m in graduate school. So I can do this kind of thing.

Now, I have both the passion and practical sides shouting how absurd this plan is. Passion: Do you really want to pursue all these years of school and then have to climb up to tenure to take over so much time in your life when you could be writing? Practical: You’ve just made your chances of success even worse. Math-phobia is pretty much widespread and to attempt to explain deep math in a novel that a reader is supposed to enjoy and at least somewhat understand in his spare time and that which a publisher is supposed to find engaging as he goes through his slush pile of manuscripts is pure insanity. Not to mention you may be overdoing your resume when you apply for a “day job” as an academic.

Both of these positions have certainly swayed me. For example, last term was a nightmare and as a result really made me question my plans. Maybe it would just be better to read about math in my spare time. Although now that everything is better academically, I’ve still decided to stick with this plan. Besides engaging with actual professors and other students is probably the best way since I will then get a lot of guidance toward learning math and engaging in research. As well, I haven’t found very many mathematical novels. I haven’t read a lot of science fiction, but in looking at blurbs on websites and bookstores, I can really tell that it’s a very uncommon genre.

So why do I choose to stick with this plan? Because of the huge passion it generates within me. I’ve found my dream and have chosen to go along with it. That might sound a bit too simple and a bit corny and cliché, but it is true. A heavy cost with little chance of success comes with it, but so what? At least given how highly strange this path is I have the comfort of knowing how strong I am in not letting the pressures from society tempt me otherwise.

And I think that’s a skill a writer should acquire anyway.

I can choose between two attitudes. The first is to complain how I have totally unmarketable ideas and how my dream will be laughed at not only by publishers, but society at large. Or I can take the attitude the uniqueness of my ideas is what makes them special and how I’m so lucky to have such wonderful ideas. Who knows? Maybe I’ll explode the genre of mathematical fiction and increase the public’s understanding and appreciation of math.

But it’s scary. I really have no idea what the future holds in store for me. And one can only speculate so much about it. I also have fears if I fail. I worry about how much fiction writing passion will drive me and how much of other aspects of my life I will end up sacrificing for it. This is probably my biggest fear. But while I can speculate on my success until the cows come home, any aspiring writer should just sit down and write the damn book.

A post on another blog that portrays my feelings exactly is the following: Starving For More. It’s by another aspiring writer and how she describes how it’s her dream of becoming a writer and how her fate is so uncertain and if she’ll end up joining all of the starving writers and artists out there who are dying penniless. I especially love the last line.

“And maybe I’ll never be awarded my own turn, but that’s OK. As long as I’m starving, at least I know I’m hungry for something more.”

I know what I’m hungry for. The truth. And like her and every other aspiring fiction writer out there, I await my fate.

Why I’m Making the Choices I Am Part 1

As I go through life I surprise myself. I’ve surprised myself a lot, which shouldn’t come to a surprise to you if you’ve been reading this blog. But the thing about myself that I’ve been most surprised with is how radical my passions have changed in my lifetime. It was only two and a half years ago that I had a different dream than the one I had today. I was 20 going on 21 and just starting my third year of my undergrad at Acadia. From October 2009 to August 2010 was probably the biggest change that I’ve ever experienced. In September 2009, I wanted to be a mathematician. By August 2009, I wanted to be a fiction writer (regardless of how impractical this path was). And in between these two passions was a sort of ‘bridging passion’, a passion for philosophy. Philosophy, like math, is still in the realm of academia, while, like fiction writing, it is an art.

But I sometimes think about what made this take place, whether there was any possibility that could’ve happened sooner or if it could’ve happened at all. I must admit that the reasons why I started writing fiction at 16 aren’t the same as they are today. It is possible to enjoy fiction writing as a hobby, while having a job as a professor, and my reasons for choosing to write fiction back then was compatible with that plan back then. Now, however, I want fiction writing to be something more. Why did this occur?

I think first and foremost you have to go through the reasons why I chose to pursue math. The study of mathematics was a passion rooted deep in childhood. I can’t remember a time when I didn’t love math. I have a few vague memories of wanting to be a policeman when I was like four, but I’m not counting that. And even though it wasn’t until I was ten that I heard that such people as mathematicians existed for that was when I wanted to pursue a career in mathematics, I did have a passion for it throughout elementary school. Getting excited when learning about the rules of arithematic, for example, of subtraction and multiplication. Actually getting a babysitter I had to show me how to do long division (one that I like to laugh at even today).

I loved math as a child for several reasons. These were the predictability of it, the patterns that arose from it, and how it sheltered me from the highly unpredictable world. Even the most simplistic of mathematical facts such as that the cube root of 8 is 2 I found beauty in. And even though my childhood had other interests surrounding the math such as drama, playing the trumpet and piano, and writing fiction, math always remained a priority over these things to me. I even took an interest in philosophy and took a course on theory of knowledge in high school where we talked about random controversial issues.

So why the change from October 2009 to August 2010? What I find most interesting is that the nine months right before this period, my passion for math was as strong as it ever was. In the winter of 2009, was my second semester of second year and I can certainly remember how fed up I was over that school term because the math that was being taught to me at that time, I had no interest in. I had to take a differential equations course as well as a statistics course. I wasn’t really a fan of the differential equations course and downright hated the statistics course. It wasn’t the type of math that I was interested in. Where was the pure math?

My turn to philosophy in the fall 2009, however, while unpredictable, my life did give subtle hints that the subject would really start competing with my passion for math. In my first two years I had taken philosophy as an elective every turn. And in fall 2008 I had decided to turn it into a huge minor before declaring my double major a year later.

Then the passion for fiction writing deepened, which begs the question. Why? How could someone who loved math, always thinking of it as a number one priority, from when he was practically 5 to 21, suddenly switch lanes so swiftly? As I pointed out earlier, my interest in philosophy deepened, which probably encouraged it, as philosophy and fiction writing are more linked in a lot of ways than math and fiction writing are, but even so it was a huge transition.

I won’t pretend to have a complete answer (since when is there ever one in life?). Sometimes thinks happen just because they happen or there are just so many reason and so many influences that it’s impossible to analyze the situation fully. But I do have some idea as to why this happened. I think it happened because I love looking for and studying truth. By truth I don’t mean truth in any specific context. I’m just talking about truth as simply the way things are in this world as well as in any other worlds out there.

This is why I fell in love with math at an early age. In mathematics there are patterns and it is these patterns that express the truth of math. You don’t have to study a lot of math in order to see its beauty. Just Google the term ‘fractal’ and you’ll see what I mean with what comes up. When I first saw prime numbers as a child and how chaotic they were I instantly wanted to know the truth behind their randomness. And unless I knew what all the prime numbers were, it would be impossible for me to know their pattern unless there was a pattern in their randomness. This is what attracted me to math. Its system of categorisation and patterns made its truth so precise and clear.

It is also why it took some time for my love of fiction writing to develop (of the 23 years I’ve lived, it has only surpassed my interest in math in the last year and a half). You don’t really need any experience of the empirical world to love and appreciate the truth of math. But you do (at least for me anyway) need experience to appreciate fiction I think and the kind of truth that fiction presents. I could easily grasp what pursuing the truth of the prime numbers meant when I was ten, but it would be much harder for me to at least somewhat appreciate the themes of gender and sexuality in The Handmaid’s Tale by Margaret Atwood at that age. Truth in fiction writing I think comes more slowly because we require experience of the world to appreciate its truth. Mind you, to understand math at a deep level requires great maturity with the subject, but having such a deep level is not required to appreciate the beauty and truth of the subject. For fiction writing, an appreciation of the truth involved there does require a deep level of understanding, which is why I believe my passion for writing didn’t develop until I was far older even though the potential for it was always there.

Math may have been my shelter from the wider messy world as a child, but as I grow the more I find my needs and desires requires more interaction from the external world (for example, wanting a greater social life). And thus the fiction writing passion began.

Freedom

Well, it’s been almost two months since my last posting. Sorry for not keeping up, but there was a good reason for it. It’s actually a continuation of what I described in my last posting, that is the difficulty I’ve had in adapting to the high demands of graduate school in pure math at the University of Waterloo in Waterloo, Ontario. I hope everyone had or is having a great holiday so Merry Christmas and/or Happy Holidays (whatever your celebrate) and an early Happy New Year. I’m certainly looking forward to it and I hope you are too.

As I said in my last post, I’ve had difficulty adjusting to grad school. That was early November. A lot has conspired since then, but the basic story is that the demands just got so big that I found that I couldn’t follow the conventional plan for their graduate students anymore. No, I haven’t dropped out. I’ve just made adjustments. Like making accomodations for my autism (without accommodating myself too much, of course!). Anyway, here’s the story.

I continued finding the course work for my masters incredibly difficult to complete. I raised the number of hours I worked on to try to not get behind so much. Instead of working 50 hours/week (although I ended up putting in a lot of extra hours because of the difficulty of the assignments), I bumped it up to 60 hours/week. This worked fine for about a week or two, but nearing the end of classes, I still found this not enough. I raised it high still to 70 hours. When classes were over, however, I knew something had to change. The last math assignment I was given was extraordinarily tough and what eventually happened was that I pulled an all-nighter working in an empty classroom with another student on it. While I still got it done in time (to the best of my ability), I knew something had to change. I actually felt that my joy in math was being sucked out of me.

At the end of classes, I ended up talking with a bunch of people, including the admins of the pure math dept. as well as the graduate officer. We decided that a full load of three math courses was too much for me and so in the winter term I could take only two math courses and still maintain my standing, as well as extend my masters into next fall. I also got my functional analysis exam moved until the first week of January so I wouldn’t have to concentrate so much on the few days right before the holidays.

Then the unthinkable happened. I blew my algebraic number theory exam. I had 59/60 in the course going into the exam and the exam was worth 40%, but I really blanked out on it and couldn’t answer any of the questions. I spent a lot of time preparing for the exam so it wasn’t because of lack of preparation so much as stress and high levels of anxiety that I’ve been experiencing all semester because of the workload. Thankfully, I’ve got some medicine to help with it and am planning on seeing a psychotherapist when I get back to waterloo.

I talked to Dad a lot about my problems and we agreed that there was a bit of a knowledge gap between what acadia taught me and what waterloo expects me to know. I didn’t mention this in my previous post, but I found I had to catch up on a lot of material as well, material that I was supposed to know in order to take the courses I was taking. And let me tell you. Playing catch-up isn’t fun. It’s stressful (although I’m an easily stressed out person) and tiring. It caused me to fall behind. I got uncomfortable at learning material at such an unnaturally hurried pace. And the suggestions that I got from professors of reading further textbooks and sitting in on undergraduate courses WHILE trying to stay on top of the graduate courses were of little use. I love math, but I do actually like having time of actually appreciating what I’m learning and that only happens if I can take my time with it. So after calling the pure math dept. we found what looked like a good solution. I would be put into a probationary period in my masters so that I could focus on taking a couple of undergrad courses in the winter and then a couple more in the spring with a TA in both terms. Of course, I’ve had to suspend my scholarship, but at this point, it really doesn’t matter to me. The plan is to resume everything next fall with it. And as well as the couple of undergrad courses they’re letting me take this winter, they also let me try a graduate course on top of it (the course is on logic and is one of the lower-level grad courses so I’m hoping it doesn’t cause me too much trouble not to mention I love logic!)

So what has all this come too? Right before coming home I was getting some textbooks to help with my studying for my functional analysis exam when I had an epiphany. I had never gotten closer to rock-bottom with math than this term. I failed miserably on both the one test and the one exam I had and the work was tougher that what I had ever experienced before. And one thing in particular that it has helped me with is getting rid of my perfectionism. Instead of worrying that wouldn’t get A+’s in my math courses like I did at Acadia, my worry turned to whether or not I would even get my degree. I cast aside my obsession with achieving top marks because I was past caring about them.

It also enabled me to look at myself in a more realistic way. I’m human and am prone to making mistakes in all areas of my live. Not just some areas, but all, including math. Not being the top math student anymore meant I had nothing to hide myself behind. My difficulty with math this term exposed my weaker self. I had nothing to hold onto to show how great I was. And hey if I’m allowed to be imperfect with math, then I must be allowed to be imperfect in all ways in my life. So overall, my first term in grad school didn’t just get rid of academic perfectionism, but I think it helped with my overall perfectionism in my life. I know myself a lot better as a result and am not going to pretend to be anything more than who I really am. I can easily make more free time for myself instead of simply letting math take over. I can accommodate what I’m truly interested in (while still pulling down descent marks in my courses!), such as writing fiction (a passion that has really grown).

I truly feel I was set free.