I am a research scientist living and working in the San Francisco Bay Area. I like to believe that I know a little bit of signal processing and applied cryptography, but experience challenges this view almost every day. I have lived in several cities, but I miss, most of all, the little town of Cambridge, Massachusetts, where I spent six lonely but productive years.

This blog started out in early 2006 as a place to collect and share thoughts on the books that I was reading outside school and work. Over time, other aspects of my life have crept in. I like to ride my bicycle, play some tennis, watch birds. I used to write about these things oftener than I do now, and I hope to return the blog to some semblance of fluidity in the coming months.

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Congrats, i saw your site listed on 9rules

Hi

Welcome to 9rules.

Best wishes

John Baker

Hi Ralph and John:

Thanks very much. I hope that this helps me to improve the way I blog and that it connects me to many more litbloggers.

I just love the name of the blog, if you eve go for a new design go woody it would be great.

Thats a charming and generous “About” page, Polaris. I suppose it’s inevitable Litlove will eventually find herself the subject of 299 words. What is this 9rules, anyway? Thank you for reaching out to me at the Reading Room!

Thanks for visiting Mirkwood, David. I found your blog recently via litlove’s comments and am very intrigued by the concept of Very Short Novels.

About 9rules: It is a community of blogs with varying subjects and interests, ranging from tech blogs to personal blogs to literary blogs. 9rules has selection rounds every few months. I was lucky to be selected into their “Writing Community” in the most recent round, and Bloglily and Litlove made it as well! You will find a lot of 9rules info on 9rules.com and on the member blogs, especially the tech blogs.

Well, then, congratulations are in order and clearly well-deserved. You set a very high standard for clear thinking and writing here, Polaris, and could scarcely be in better company than Bloglily-and-Litlove’s!

I look forward to your comments at Very Short Novels.

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hello

may i forward a query about a short story collection, Down to a Sunless Sea, which has garnered remarkable reviews of late (google my name)?

Kind Regards,

Matt Freese

Hi there,

Long time, no comment. Quick yet loaded question, for you, a professional in a relevant field:

is the rap of “applied mathematics” that it’s a drawer full of hammers, as compared to “pure mathematics” being…er, something a bit more sublime, deserved?

I won’t ramble on more, other than to say I’m pressed to decide on a pure or applied undergraduate track (yes, still, after just turning 37), and thought you might be able to provide some perspective.

Hope you’re doing well.

Daniel

Hi Daniel,

I’ll try to answer this in two parts:

Firstly, regarding the rap on applied mathematics: Some people, in both pure and applied communities think that applied mathematics is just a toolbox and something less exalted than pure mathematics. Some others, again in both fields but primarily people in industry, think that pure mathematics is so “out there” and divorced from real engineering. I think that this is a false dichotomy because I am unable to find a good distinguishing line. I use mathematics on a daily basis; sometimes I use set theory to solve problems in data compression, other times, I use Fourier analysis. At what point does set theory cease to be pure mathematics and become applied mathematics? Further, if a hitherto “pure” field suddenly finds application in a real engineering scenario, are we to say that said field has become applied and lost its purity and glamor?

One good example of a “box of hammers” is convex optimization, clearly an applied field that uses pure math concepts – geometry, convexity, set theory, linear algebra and so on. Convex optimization has reached such a stage that there are gurus who spend their entire research lives (and make a lot of money by) massaging any engineering problem into an appropriate convex optimization framework – an LP, SDP, QCQP and so on. Once they have done this, tools and software libraries to solve these standard problems may be freely used. I am unwilling to discount the effort that this requires, or even the charm involved in re-imagining the engineering problem to make it fit into an existing convex optimization framework. But, I can see why this could be frowned upon in some quarters; the effort here is directed in solving the engineering problem, the cool mathematics is merely a tool. However, there is nothing stopping a mathematician from developing an entirely new convex optimization problem framework either for its own sake, or to solve a new problem that cannot be massaged into existing frameworks. Admittedly, as the field matures, this becomes harder to do, but the reward could be worth it.

I feel the need to qualify the above statement: I do think that there is such a thing as good mathematics – good in the sense of G.H. Hardy; good in that it is not just elegant and precise, that nothing is taken for granted and everything is proved. Then, there is such a thing as bad mathematics – in the sense that some essential things might be pushed under the carpet, some things may be explained in a hand-wavy way without resorting to mathematical rigor, some approximations may be made in the interest of engineering tolerances that may not always make a mathematician happy, some tools may be co-opted for applications in which they are not suitable. It seems to me that, in most cases, the rap on applied mathematics is, in most cases, an unconscious rap on bad mathematics. I think that the struggle between pure and applied mathematics may in fact be a struggle between good and bad mathematics.

In regard to making a choice for a degree course in mathematics, I am compelled to use the first paragraph as my guide because, while studying for a mathematics degree, you are not very likely to fall a prey to bad mathematics. I wonder if the decision should depend on what you would like to do with it, i.e., would you like to look for an industrial position based on your course-work, or are you considering an advanced degree in a related field? Hedge funds seem to love students who have a background in stochastic differential equations and other difficult mathematics. From my perspective, being an engineer who often finds himself wanting in mathematics, it always seems to me that it would be easier for a mathematician to develop engineering skills if required rather than the other way round. A mathematician might think the other way round.

I don’t know how the funding situation works for pure mathematics in academia. For industry, I do know that, here in the US, whenever there is a financial crunch, fundamental research tends to be the thing that gets axed first. This is a sad thing, but it happens again and again.

I hope these thoughts are useful. I think however that, when all is said and done, one must do what one likes to do.

Good luck in your decision!

Polaris.

Hi again,

Thank you for the note. It’s more than I had reason to expect, but exactly the sort of note I was looking for. I have been balancing family, career, and undergraduate study (obviously part-, full-, and no-time) for over a decade now, so my decision weighs a bit more than might be typical. Your considerations align precisely with what I was hoping would be the case, i.e., the blind machinations that look like mathematics but which are divorced from theoretical sophistication are not necessarily a part of applied mathematics more than pure mathematics, but attend

badmathematics in any genre. Hardy’s essay is wonderful for this reflection, as you point out.Thanks again for the time and conscientiousness of your response. I’m done pwning your About comment thread. +)

Hello,

Would you be interested in reading/reviewing Garth Stein’s newest novel? He is the award-winning author of The Art of Racing in the Rain.

If you’re interested, please contact me.

Thanks!

Sarah D.