The Speculist » Mathematics

Should I Learn Calculus?

Phil Bowermaster — Tue, 08 Feb 2011 21:27:57 +0000

I got as far as pre-Calc in high school and then never followed up, in college or elsewhere.

Is it a good idea?

I’m of the opinion that we should all be trying as best we can to continue to learn throughout our lives, to take on new challenges, and in particular to hone our understanding of science, technology, and related fields.

I bought Calculus for Dummies a while back but never got very far with it — maybe it’s just that the title is too absurd for words. I mean, what could be more ridiculous — Rocket Science for Dummies?

But yesterday over on TR I was writing about the Education Bubble and the subject of the Khan Academy came up.

I spent some time scrolling around the site. It’s amazing, the classes that are available there. And suddenly I feel that I’m out of excuses.

Actually, now I have a completely new quandary. Should I take Calculus or something else?

What is a Fractal?

Stephen Gordon — Sun, 10 May 2009 18:20:33 +0000

My latest article has been posted at Helium.com. Check it out at this link.

Here’s a sample:

Consider the most striking form of fractal: the Mandelbrot Set. Mandelbrot generated a collection of points on a graph by taking a series of complex numbers, squaring each of them, adding the original number to each, and squaring them again and again. If the number remains finite after many such iterations, it remains in the Set and is plotted on the graph.

The resulting shape is composed of successful solutions to what is truly an extraordinarily simple equation. Paradoxically or not, itâ€™s the most complex and beautiful object in mathematics. When software displays the Set in false colors, a viewer can be excused for concluding that the Set is a Set of infinities.

Software displays segments of the Set along its rich, complex edges, under greater and greater degrees of magnification. As each tiny portion is magnified, more detail emerges. Mathematicians insist that the Set holds the entire set of Julia sets in infinitely many places in its infinite numbers of levels of organization. An eternity would not be long enough to explore the Setâ€™s many hidden splendors.

Watch as â€œâ€¦its disks grow spikes of prickly thorns, spirals and filaments curl outward and around, bearing bulbous molecules that hang infinitely variegated like grapes on Godâ€™s personal vine.â€

This lovely description of the Mandelbrot Set is taken from James Gleickâ€™s book, â€œChaos,â€ which I commend to anyone interested in a more in-depth exploration of fractals and chaos theory.

Wouldn’t it be WAY COOL if our highly advanced future avatars could play in a version of Second Life loaded with n-dimensional fractals. Wheeeeee!

Making the World Computable

Stephen Gordon — Thu, 09 Apr 2009 19:53:46 +0000

Stephen Wolfram announced that his new “not a search engine,” Wolfram/Alpha, will premiere in May. This software package will enable users to query it, like Google, but instead of running a search for lists of appropriate web pages, it will calculate the answer to a query using information extracted from web pages.

I’ve written an essay giving background on Wolfram and his career. In it, I discussed the possibility that the development of Wolfram/Alpha may speed up the development of true AI. It is posted on ScribD.

Here is Wolfram’s official announcement on his blog, including his own description of Wolfram/Alpha.

Is This Right?

Phil Bowermaster — Fri, 15 Dec 2006 08:30:08 +0000

Discuss.

Stare Real Hard

Phil Bowermaster — Thu, 26 Oct 2006 09:00:10 +0000

What do you see?

Squint. Look at it sideways. Cross your eyes.

Is a pattern beginning to emerge? Or is this a trick? Maybe there’s no real image there. Maybe this is just random TV white noise.

Well, okay, it is random. But it isn’t white noise.

It’s something much more important.

Cool, eh?

Via GeekPress.