The importance of precision *or* Why are mathematicians so picky?

11 January 2010

The following joke is very old (the following version comes from wikipedia).

An astronomer, a physicist and a mathematician are on a train in Scotland. The astronomer looks out of the window, sees a black sheep standing in a field, and remarks, “How odd. Scottish sheep are black.” “No, no, no!” says the physicist. “Only some Scottish sheep are black.” The mathematician rolls his eyes at his companions’ muddled thinking and says, “In Scotland, there is at least one sheep, at least one side of which looks black.”

One skill that mathematicians are encouraged to develop is the ability to precisely formulate ideas, questions, etc., sometimes overly precisely.  We have lots of vocabulary and syntax conventions that helps us to draw very fine distinctions.

This is a common point of contention between mathematicians and non-mathematicians when discussing mathematical ideas.  Such as, let me think, teachers and students in a math classroom.

Read the rest of this entry »


Rubik’s Hypercubes

10 January 2010

Tired of your mundane three-dimensional Rubik’s cube? Want a hands-on activity to help you make sense of the fourth dimension? Download Magic Cube 4D. The interface is really quite intuitive (and that’s saying something considering how un-intuitive the fourth dimension is).

Oh, and if you consider 4-dimensional Rubik’s Cubes too easy to be worth your time, perhaps you’d prefer Magic Cube 5D.

Happy New Year!

9 January 2010

It’s 2010, and your friendly neighborhood Cap is back from his holiday hiatus.  Back with a non-default wordpress theme, back with some links in the sidebar, back with a sackful of ideas for making this blog better.

Whether you’ve been here since the beginning or checking things out for the first time, welcome, welcome.  Thanks for looking in on me in the new year.

During my hiatus I’ve received a number of very encouraging emails from well-wishing readers; for those I thank you.  It’s good to learn that so many of you are finding my words meaningful.

If you’re new here, the “About the Blog” link above will give you some idea of what we’re all about here.  And if you’re wondering about the seemingly inexplicable title of this blog, the “What’s in a blog name?” link should help.

The holidays have given me a chance to reflect on Not About Apples so far, and I have plenty of ideas about what I think has worked and what I can make better.  I have high hopes for this year; stay tuned.

In particular, notice that the sidebar has some interesting links now, and more will be added (as I’ve said elsewhere, I have very little patience for the wordpress link manager).  There’s some good stuff over there, so pick one and give it a click!  Have a favorite blog that you think belongs there?  Have a blog of your own that I should know about?  Please let me know; the blogosphere is a big place, getting bigger every day, and I’ll never find everything worth finding without a lot of help.

Expect new articles on Monday mornings and recommended links on Fridays, plus whatever minor posts my whimsy may send you at other times.