Some real science

The "Slow Mo Guys" wrap a watermelon with rubber bands, about 500 of them, and the pressure forces the melon to explode. Now that's some science you can believe.  The link above has a video of the whole process, worth a few minutes to watch. Enjoy.

It's the end of the world as we know it....

I feel fine....

Yes, the world, or really the universe for that matter, is set to end in 16-billion years, and not the original 22-billion years like scientists thought.

So says two physicists from China who have analyzed dark energy and determined that this stuff that we can't see, but infer because the universe is expanding, will one day cause that self-same universe to tear itself apart. And sure they will be stars that will be ripped apart, and planets destroyed, but if we could have just 6-billion more years, well, then the universe would have collapsed on itself. It's death by separation or death by constriction, either way, it's not good.

Sometimes I wonder if anyone takes these physicists seriously, and I actually checked out their paper (link available at the link above) to see what they're thinking.

For my part, I'll just keep living as I have, without worries, at least about this.  You might want to do the same.

Book Review: An Introduction to Modern Mathematical Computing with Maple

I recently contributed a book review to the Mathematical Association of America for the new book by Jonathan Borwein and Matthew P. Skerritt.  In the past I did not post those reviews here but I thought I should try it out and see how that goes. Here's the review.

In An Introduction to Modern Mathematical Computing with Maple, Borwein and Skerritt show that computers are an excellent companion for learning mathematics. They do so not with an essay on the advantages of computers, say, less sign errors, or quicker algebraic manipulations, both of which are true. Rather, they show readers that a particular computer algebra program, for their case Maple, is so flexible and powerful that it can work alongside students to show them insights that may be otherwise difficult to see.

To that end, the authors go through many aspects of Maple such as: algebraic manipulations, graphics, matrix manipulations, integration, differentiation, sums, limits, and number theory. Their treatment of the program is thorough, well explained, and instructive. This book is a good companion to the user manual and, maybe even better than the manual on some topics because the authors' examples are succinct and clearly illustrate many facets of the program. (It is not a replacement for the user's guide, by the way.)

The theme of the book is that Maple can supplement mathematics learning and, what is more, can do much of the mathematics for the students. That is certainly true. What is missing in this book is just how will Maple, say, actually help students understand mathematics when the students are still learning the math.

Any computer algebra system can solve equations and plot functions. These operations are simple and students can type a formula (with the correct syntax) to tell the program to plot it, and presto! the graph appears. Of course, students have to trust the program that the graph is correct. Does the graph correctly show the function around a singularity? Well, to know if it does, students have to understand singularities. The program cannot tell them that.

Maple can differentiate, integrate, and simplify expressions.  Is the form that Maple provides useful? Students must know what they need and what the various forms are that meet their needs. In fairness, Borwein and Skerritt make some of these points. They say that Maple can do these tasks and note that it is up to students to know how to ask Maple to provide what they want.

Still, with Maple (and other similar programs) so readily available, one wonders if there is any incentive for students to actually work to gain an intuitive insight into mathematics. On that score, the authors are silent. I wish the authors had spent time telling us not only what Maple can do, but why students who are just learning mathematics should use it.

The temptation is tremendous for students to skip the real work to have a true understanding of mathematics. There should be more emphasis on students knowing mathematics, not just how to type an expression to see a result. This issue is not addressed in the book but it needs to be explored fully so that students know more than just how to use a program. Students, and non-students alike, should know when and why the results of the program work. Maple, for all its power, is powerless to tell them that.