For the past several months, I've been working on a New Year's surprise for Grey Matters readers. It's almost done, and will be revealed on January 1st, 2011 (Saturday), and Sunday's post will focus on all the details.

To keep you going until then, I'm going to provide you with a few fun treats for the new year.

Since New Year's Day is coming up, you're probably working on your resolutions. Is it possible to make resolutions that have a better chance of being kept? Of course! Over at Gawker, check out How to Make Every New Year's Resolution Stick for Good. Richard Wiseman, over at his 59 Seconds blog, also has a great article called Achieve your New Year’s Resolutions!.

Don't forget to include improving your memory or math skills among your resolutions.

Enough of the serious stuff! We'll turn to some math, but nothing serious, of course. Maybe just some math doodling will fit the bill here:

How many of you got that long-awaited techno-gadget phone or tablet during the holidays which you've been waiting for?

Since you probably built it up into a magical level in your mind before you got it, how about taking it to magical levels now that you have it?

To start, go over to Andrew Mayne's iPod Tricks site. Despite the name, most of the tricks are most image- or video-based, so they're easily adaptable to any handheld mobile device. In EZ Money, you can pull real money off an image of a dollar bill, with a comedic ending. Weapon X is more of an interlude in which you x-ray your arm, to show your built-in claws, just like Wolverine.

Among the more unusual tricks on that site, there's Spirit Photo, a supernatural-themed trick done with another person's mobile-device (must have internet access for the routine). iPhone Trick works specifically only with iPhones and iPod Touches, and makes it appear that you're damaging another person's device. The final one, iPunk'd, isn't done with the phone itself. It's a cut-and-restored earphone cord, which is a nice way to update a classic for the 21st century.

If you're familiar with John Bannon's classic packet effect, Twister Sisters, there's now a way to bring it into the 21st century, as well. Go to http://superpixel.com/tsr/, and the people can make their choices using the phone. The effect remains basically the same as the original, but with the added mystery of choices on the phone affecting real playing cards. There is no explanation, as you must be familiar with Twisted Sisters to use it in the first place. The developer features a nice presentation for this version over at the Magic Cafe.

Greg Rostami's iForce is already a classic among magic tricks for mobile devices, and now it's available for both the iOS and the Android platforms! Due to its versatility, there are already many ideas on the developer's own site, as well as the Magic Cafe.

The bigger news from Greg Rostami, though, is the release of iPredict! It's a little hard to describe, so check out the video below. Note that someone else's phone is used to dial the number!

Note: The holidays are keeping me busy, so I'm reposting my 12 Days of Christmas post from 2007. Enjoy!

Since the focus of this blog is largely math and memory feats, it probably won't be a surprise to learn that my favorite Christmas carol is The 12 Days of Christmas. After all, it's got a long list and it's full of numbers!

On the extremely unlikely chance you haven't heard this song too many times already this holiday season, here's John Denver and the Muppets singing The 12 Days of Christmas:

Back when I wrote about the late Benoît Mandelbrot's fractal work, I really only covered the basics about the nature of fractals themselves.

Mathipedia recently alerted me to a documentary on fractals that gives a more complete picture.

The documentary is called Hunting the Hidden Dimension, and was an episode of NOVA back in 2008. It begins with the 19th century discovery of number sets with such unusual qualities, they were referred to as “monsters”, but regarded as little more than curiosities.

Once computers were developed, and maverick mathematicians like Mandelbrot were able to examine them, it was found that there was far more to fractals than anyone had expected. After explaining much about their nature, Hunting the Hidden Dimension examines the unexpected effects they've had on communications, medicine, entertainment, and much more. Without knowing it, you've probably taken advantage of the unique qualities of fractals without even knowing it!

Back in mid-2008, I discussed the chemical elements, mainly from the standpoint of memorizing them.

In this update, we turn our attention to understanding the elements. As always, I've tried to find the best resources that help you obtain that understanding as efficiently as possible.

Ever since I first saw this explanation of the atom on TV, I was astounded at how simple and direct it was! It's from the original show WKRP in Cincinnati, from an episode where Venus is asked by a friend to help convince her son to return to school. To do this, Venus bets the son he can explain the basics of the atom to him in 2 minutes:

Almost all the posts on here since October have focused on mathematics. Perhaps it's time to get back to memory work.

Let's wade back into memory work with some mnemonics.

I've certainly talked enough about memorizing Pi, but what about memorizing the constant e? Robert Talbert teaches a different mnemonic approach that helps you memorize e simply by looking at a US$20 bill! Since I believe that memorization and understanding go hand-in-hand, understanding the nature of e is a big help. Also, knowing your US presidents will help here, strangely.

Speaking of memorizing USA facts, The Tutor Whisperer has some great and original mnemonics for learning the US states and their locations. The example only teaches from the Pacific coast states to the midwest states, but it wouldn't be hard to create similar mnemonics for the rest of the states.

Perhaps you only need to memorize the original 13 colonies? Then perhaps Venus, Mercury, Mars, Saturn, Neptune, and Pluto can help! No, you don't need to read your horoscope, just use this stately astro-mnemonic. This mnemonic will probably take more work than the others in this post, but it sure is handy!

As long as we're talking about outer space now, how do you go about remembering something like the speed of light? In miles per second, 186,000 isn't tough to remember, but what about in meters per second? Can we guarantee certainty, clearly referring to this light mnemonic? Not only can we, you just learned it without knowing that you did!

Ready-made mnemonics are great, but what about when there are no ready-made mnemonics for what you're studying? One solution for creating custom mnemonics I've mentioned before is JogLab. They've just made their site even more useful with a special introductory video about creating acrostic poems (It employs annotation links, so I'm not embedding it here).

Finally, those who use the Number Shape system of memory will find the following video handy. I've seen several variations of images for use with this system, but this video teaches the most distinct and easily-remembered images I've ever run across:

It's time for December snippets. Since we've been doing so many math-related posts lately, we're dedicating this edition to math goodies.

• If you like the math-related videos I've been posting lately, and still can't get your fill, check out bachelorsdegree.org's list, 20 Incredible TED Talks for Math Geeks. This list alone with keep your mind and eyes open for a while!

• If it's more math instruction videos for which you're looking, check out Math Vids, My Math Shortcuts, and Lazy Maths. Each of these sites has a good selection of instructional videos that will help you to learn how to handle various types of math problems more efficiently.

• The classic Penney Ante scam is usually done with three coin flips. If you want a real challenge, though, try doing Penney's Game with 4 coin flips, as described in this Wolfram Blog post. Unlike the Scam School video, the Wolfram Alpha Blog article doesn't provide a nice, neat system that automatically generates a better flip than a given one. Can you find such a system for 4 coin flips?

• Rounding out this edition of snippets, here's a freebie you can use for the entire next year: The 2011 “Lightning Calculation” Calendar! Each month, you'll learn new mental math skills. By the end of 2011, you'll have developed many amazing mathematical abilities! It's free as a downloadable PDF or for $17.60 as a pre-printed calendar from Lulu.com.

In the previous post, I featured James Grime's Last To Be Chosen video, where we learned about the Kruskal Count, and discussed some variations.

Today, you'll see James Grime's explanation, and learn a little bit more about how this works. I'll also discuss variations after the video explanation itself.

If you haven't watched James Grime's video from the previous post, please watch that first. Here's his explanation of the Kruskal Count:

James Grime, known to YouTube viewers as singingbanana, is back! This time, he's performing a rather interesting experiment/magic trick.

I've talked about this principle before, but I don't want to ruin it by giving the principle away before you've had a chance to enjoy it. The first 90 seconds of the following video are mainly to clarify the instructions. After that, the actual experiment begins: