I still remember, back in 1978, flipping through the channels by getting up and going over to the TV set and turning an actual knob to one of 13 different channels we received at the time, and running across a show on PBS teaching history in an unusual manner. Instead of teaching history in the straightforward way we all learned it, such as "first the telegraph was developed, then the telephone...", the host was showing how history happened in a zig-zag manner, with influences coming from many directions, just like today. History, for the first time, was coming alive for me!

I was hooked.

The host was James Burke, and the series was called Connections. Beyond just enjoying the series itself, it was the first time I realized that learning could be fun! I also remember talking with adults about history, and seeing their reactions to my ability to intelligently discuss the subject. The mixture of fun, technical knowledge and ability to amaze came together in my brain. The geek bug had bitten me.

It wasn't until two years after the initial airing that I was first able to see the whole series in order. By the time I got my first VCR, the series wasn't easy to find on TV, and impossible to find in any video store. I always regretted not having that series available for easy reference, hoping to see it again some day.

Thanks to YouTube and Google Video, my wait is finally over! If you have seen this series before, here's your chance to see it for the first time in what may have been a long time. If you haven't seen it, I highly recommend checking this series out. Either way, you may also wish to download and save it to see again and again.

Over at Google Video, the BBC has made episodes 1, 2, 3 and 4 available.

All 10 episodes are already up over at YouTube. Since each episode is about 50 minutes long, and YouTube doesn't allow videos longer than 10 minutes, each episode has been broken up into 5-6 parts. Here is a complete index for the episodes and each of their component parts over on YouTube:

[Videos deleted by YouTube]

Update (4/17/06): Although Connections is no longer available through YouTube, it and its sister series The Day The Universe Changed are available as free podcasts. See this post for more details.

Mathematicians are used to working with knots, but now they're discovering knits, as well.

When you think of mathematical visualizations, computer graphics instantly spring to mind. However, even with the best 3D math, you're still viewing the graphics on a 2D surface which doesn't allow you to truly feel the object. According to Science News, mathematicians are discovering that knitting mathematical shapes and concepts helps researchers, teachers and students get a better sense of the surface qualities of the more unusual shapes.

If I talk about the mathematics of a plane, I can simply show you a piece of paper. For spherical geometry, I can use a baseball, basketball or a globe as an example. When I talk about hyperbolic geometry, in which surfaces grow exponentially as they extend out, what can I show you? For 2D hyperbolic geometry, I could show you Escher's Circle Limit III, but what about 3D?

This is why knitted models are so effective. They can be held in the hand and explored, and the surfaces can be colored to get across various concepts. If I were to hand you the model of a hyperbolic surface that is shown in the upper left corner of this post, and ask you which shade of purple used the most yarn to create, you would probably say that the darkest shade required the most yarn. Actually, due to the nature of this unusual surface, each shade uses the exact same amount of yarn!

Hyperbolic geometry isn't the only thing you can visualize with knitting, either. Various concepts such as the mathematics of toruses (doughnuts) and the Lorenz manifold, a concept from chaos theory, have been knitted. As a matter of fact, a recent competition concerning the crocheting of the Lorenz manifold attracted interest from numerous magazines and TV stations!

Interestingly, according to the article, there is even a book being planned for a spring 2007 release, called Making Mathematics with Needlework. While I might go for the knitted Moebius strip, I'm not so sure about the Klein bottle hat.

Through December 26th, Magic Roadshow is generously offering its book Advanced Memory Techniques for Magicians & Mentalists for free! The link is available here (you will need to scroll down). Normally it is available for US$5, but now is your chance to get it at no charge!

It's been quite a year here at Grey Matters. As everyone settles in for the holidays, and the year draws to a close, I thought it would be fun to take a look back at the changes.

Courtesy of the Internet Archive's Wayback Machine, we can start by seeing how the site looked at the beginning of this year. It looks so different now, doesn't it?

It's also important to remember that at this time, the Grey Matters blog was the only part of Grey Matters. It was only during the past year that the store (opened February 9th), the Mental Gym (opened February 19th), the video section (opened May 11th) and the presentation section (opened June 4th) were added!

The search feature, while not new, certainly has been improved with help from Google.

Actually, Google has helped improve this site in several ways over the past year. If you haven't already done so, check out the Grey Matters Google Homepage Gadgets that were introduced back on June 29th.

The first post of the year concerned the addition of categories to Grey Matters. Thanks to Google's blogspot update, you may notice that these have now been replaced by "labels" at the bottom of each post. Instead of having category links that take you to another site, each of the labels are now clickable links that will bring up past posts with the same label! For example, clicking the fun label at the bottom of this post will bring up the past posts that are also labeled fun.

Next year is already looking to be a better one for this blog, as well. I can't say too much at this point, but rest assured that there is still plenty of steam in the Grey Matters engine!

As some of you may have guessed from the video in my Monty Hall Dilemma post, I'm a fan of the TV show Numb3rs. If you're not familiar with the show, CBS has a description of the basics of the show, which is already in its 3rd season.

To get a feel for the show, CBS has posted several clips of Charlie Eppes (David Krumholtz) explaining various concepts over on YouTube:

Tracking A Sex Offender Killer
A Big Problem
Math and Shoeless Joe
Betting On The Horses
A Discussion of Randomness

There are many clips posted by fans. My favorites include the previously-mentioned Monty Hall Dilemma clip, as well as Game Theory. Shuzak's Numb3rs clip collection is also very impressive.

The math employed in the show is legitimate, with a team of technical advisors from Caltech providing the research for the show.

Naturally, several site have sprung up to help people better understand the math needed in the show. CBS itself took the first step, and arranged a partnership with Texas Instruments to develop the We All Use Math Everyday website, which includes activities for students that are related to each episode. The name of the site, of course, comes from a quote from the show opening.

Naturally, fans have sites delving into the math of the show, as well. At redhawke, their Numb3rs section is arranged by both episodes and mathematical concepts. Over at Northeastern University, their mathematics department has an entire blog devoted solely to Numb3rs. Those who want to learn about the various concepts can find themselves getting lost in these sites for hours.

The new Guinness World Record for reciting Pi from memory is now 67890 digits! It was set by Lu Chao from China. The record was set on November 19th, 2005, but was only just recently confirmed by Guinness.

At this writing, Akira Haraguchi's attempt at 100,000 digits has neither been confirmed nor denied by Guinness, so we may see Lu Chao's record broken in the coming months.

Those of you who have read this blog for some time, know of my passion for magic squares. I've even shared several unusual magic squares, such as Werner Miller's Square Bet or the nested magic squares, from time to time.

I've recently discovered the work of George Widener, an artist who was born mildly autistic. His site features many amazing works, but I'd like to direct your attention to his calendar work. Some are simply calendars of future dates, such as New Year's Eve Bash and Birthday in 2099. The rest have more amazing and whimsical touches, however. There's Month of Sundays, which is based on the classic expression, and features dates from the 23rd century that fall on a Sunday. Similarly, TGIF spans 1500 years of Fridays.

Especially interesting though, are the mixture of calendars and magic squares. Portrait of Sarah features four birthdays of George's family members in the center of a magic square. The center four squares of the Queen Victoria magic square feature important dates from her life.

The single most astounding square, and the one featured in the upper left corner of this post, would have to be 9717TGIF. If you total the large numbers, they total 66 in every direction. If you total the years, they total 9717 in every direction. If you assign numbers to each month, with January being 1, through December, which would be 12, the months total 30 in every direction. If you're still not impressed, although I can't imagine that's the case, every date in the square falls on a Friday!

Another impressive magic square which I'd like to highlight is Lee Sallow's magic square, from the bottom of this magic square column. It's a deceptively simple 3x3 magic square that totals 45 in every direction. Going one step further, though, you can write out the numbers as English words, and the number of letters in every direction will total 21!

Unrelated note: This is the 200th Grey Matters post!

The above audio recording is agonizing to hear, and it all reduces down to a mistake in basic math made by Verizon. A Verizon customer, who used their unlimited data plan in the US, was planning a trip to Canada, and inquired about the charges he would incur while up there. He was quoted 2/1000 of a cent (.002¢) per kilobyte, but when the bill arrived, he found he was charged 2/1000 of a dollar ($.002) per kilobyte. In short, he was billed 100 times the price he was quoted.

The audio recording is 27 minutes long, but if you prefer, you can read a full transcript here, courtesy of the VerizonMath blog, which was started by the person who was incorrectly billed.

Among the most amazing twists in the story is this response by Verizon, in which they acknowledge the error, and offer to settle the matter for 50 times the quoted rate, instead of 100 times the quoted rate!

This whole episode brings to mind the story Computers Don't Argue by Gordon R. Dickson. This link is to the first of 5 pages of .GIF files, but the story is well worth the read. It's another story about a customer service issue gone wrong, told only through the correspondence that occurs as a result of a bookclub error. Thankfully, the Dickson story is fictional.

To offer your support, or to simply follow the story of this as it develops, check into the VerizonMath blog regularly.

I'm in the process of adding some new features to Grey Matters.

Over at the Mental Gym, I've changed the instructions for the Serial Number Feat over to a slideshow format, with help from KeyNote and SlideShare. Do you find that this way better, or do you prefer the older text-based instruction? Should both be an option? I'd greatly appreciate your feedback on this change.

The other change is easier to find. It's right below this post, as a matter of fact. For some time now, every post has been easily bookmarked to Del.icio.us with one click. Now, I've added one-click icons for Digg, Furl, Reddit, Technorati, Yahoo, Ma.gnolia, StumbleUpon and Google, too! To bookmark to any post here on Grey Matters, as well as Grey Matters Videos, simply create a free account at your chosen service or services, and log on. Then, the next time you find a post you enjoy here, simply click the corresponding icon to bookmark the post!

I hope you enjoy these new features, and find them useful.

If you enjoyed the book Mind Performance Hacks, you will most likely enjoy the article 22 Ways To Overclock Your Brain, from the self-improvement site Ririan Project.

There are several approaches recommended in the list of which you should be critical, most notably the Mozart Effect, but overall, the list is very good.

Among the most valuable pieces of advice would have to be #22:

Surround yourself with inspiring people from a wide variety of fields who encourage you and stimulate your creativity. Read magazines from a wide variety of fields. Make connections between people, places and things, to discover new opportunities, and to find solutions to your problems.

Read the whole thing, including my new favorite quote that opens the article.

On 20/20 this week, they featured human calculator Mike Byster, who teaches kids in the Chicago how to improve their math abilities. The story linked above includes some great footage of the amazing feats being performed by his students, and is well worth checking out.

On Mike's own site, you can find further footage of him in action, in Windows Media, RealPlayer or Quicktime formats.