From the monthly archives:

January 2011

Mathematical landscape

by John on January 3, 2011

W. W. Sawyer makes a beautiful analogy regarding the mathematical landscape in his book Prelude to Mathematics.

Imagine farmers living in a country where no other tool was available except the wooden plough. Of necessity, the farms would have to be in those places where the earth was soft enough to be cultivated with a wooden implement. If the population grew sufficiently to occupy every suitable spot, the farms would become a map of the soft earth regions. …

It is much the same with mathematical research. At any stage of history, mathematicians possess certain resources of knowledge, experience, and imagination. These resources are sufficient to resolve some problems but not others. … Unconsciously, therefore, the map of mathematical knowledge comes to resemble the map of problems soluble by given tools.

But of course the discoveries themselves open the way for the invention of fresh tools. As the coming of the steel plough would change the map of the farmlands, so these new tools open up new regions of profitable research. But the new tools may take centuries to come, and while we wait for them, the frontier remains an impassable barrier.

Related post:

Easy to guess, hard to prove

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Educating versus credentialing

by John on January 3, 2011

“Colleges aren’t really in the education business. Colleges are in the credentialing business.” — Josh Kaufman

Of course colleges would like to educate students along the way, but ultimately they are in the business selling credentials.

Thanks to Jeff Shelton for pointing out the quote above.

Related posts:

Fairy dust on the diploma
Accelerated learning
Hidden curriculum

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The solar system in a glass of wine

by John on January 1, 2011

William Blake’s poem Auguries of Innocence opens with these famous lines:

To see a world in a grain of sand,
And a heaven in a wild flower,
Hold infinity in the palm of your hand,
And eternity in an hour.

This poem came to mind when I saw @mathematicsprof post the following on Twitter:

At your next holiday party, look straight down into your glass of wine and tilt the glass one degree. You will see the elliptic orbit of the earth.

If you tilt your glass 12 degrees you’ll see the orbit of Mercury. In general, if you tilt your glass θ degrees you’ll see an ellipse with eccentricity sin(θ).

(I’ve taken the liberty of editing the original tweets to take advantage of the extra breathing room outside of Twitter. Original tweets here and here.)

I like this for two reasons: it’s a great astronomy illustration, and it’s an example of how much information you can get into two 140-character messages.

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Two contrasting articles on minimalism

by John on January 1, 2011

This morning I ran across a couple articles on minimalism:

The former has a sense of humor; the latter does not. The former contains thoughtful criticism; the latter is a knee-jerk reaction. The former makes an interesting argument; the latter quibbles about definitions.

The former article is by Vivek Haldar. I cannot tell who wrote the latter.

Here’s an excerpt from Haldar’s article:

The zenith … is a calm geek, sitting in a bare room with a desk upon which sits only a MacBook Air, his backpack of possessions on one side, the broadband internet cable available but unplugged, fingers ready to type into the empty white screen of a minimalist editor.

I think that’s pretty funny. And I would hope that minimalists would be able to get a chuckle out of it.

But Haldar does not just lampoon hipster minimalism. He argues that you need periods of stimulation and clutter to be creative. He also argues that minimalism has its place.

Now I agree with most of the premises of the minimalists … My gripe is with the way they sell it as a way of life. It’s much more valuable as a periodic phase of life.

Minimalism cannot be a long-term strategy, but it makes an excellent short-term tactic.

The second article essentially argues that Haldar has the definition of minimalism wrong.

Minimalism, at its core, is the process of prioritizing your life and working towards concrete goals without giving in to distraction. … Like any school of thought with a certain critical mass, there is dissent and corruption among the ranks.

Who can find fault with prioritizing your life, working toward concrete goals, and avoiding distraction? And who wants to defend corruption? But this is just quibbling about definitions. By contrast, Haldar makes an argument independent of such a definition. Haldar argues that a certain set of attitudes and behaviors — however you want to label them — are not conducive to sustained creativity.

Here are some ideas I threw out a while ago on defining minimalism.

“Minimal” literally means an extreme. I appreciate moderate minimalists, though strictly speaking “moderate minimalist” is a contradiction in terms. A more accurate but unwieldy name for minimalists might be “people who are keenly aware of the indirect costs of owning stuff.”

… you could define a minimalist as someone who wants to eliminate non-essential possessions … But by that definition, Donald Trump would be a minimalist if he believes everything he owns is essential.

Generic discussions of minimalism are fluff. Haldar’s argument is more substantial because he makes a specific suggestion.

Related posts:

Maybe you only need it because you have it
Defining minimalism
Selfish minimalism

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