Regular Grey Matters readers realize that I'm not just a fan of learning about new concepts and ideas, but also of finding clearer and better ways to communicate those concepts and ideas to others.

When you get that aha! moment where you truly understand a concept, or at least start to do so, there's a wonderful feeling of getting past the frustration. In today's post, we'll look at some places that encourage that moment by teaching various concepts clearly and simply.

One of the topics people have a tough time with is physics, the study of matter and how it moves through time and space. The MinutePhysics YouTube channel does a wonderful job of giving an overview of even seemingly difficult physics concepts. For example, this video explains how Einstein deduced the existence, and even the size, of atoms:



For a wider variety of topics, there's CGP Grey's YouTube channel. CGP Grey has a knack for picking topics that make you say, “I've often wondered about that, but never took the time to find out!” For example, as I write this, it's a leap year, so what exactly is the deal with leap years?



Although it's not a YouTube channel per se, the various videos of the “Charlievision” sequences from the show Numb3rs are a wonderful way of explaining complex mathematical concepts. Here's how Numb3rs summed up what is known as the knapsack problem:



Video isn't the only way to grasp new concepts, of course. I've referred to BetterExplained.com numerous times, in praise of their way of presenting insights. At the beginning of A Visual, Intuitive Guide to Imaginary Numbers, the author explains some of his secrets, which focus on analogies, relationships, and visual diagrams whenever possible.

One part of BetterExplained.com you may not be as familiar with, however, is their aha! moment section, where you can share with others the insights that worked for you. As the video below explains, it's a sort of Twitter meets Wikipedia (Twittipedia?):



One of my favorite posts there shares a handy insight from purplemath.com for remembering how to determine the proper sign when multiplying with negative numbers:

good things (+) happening to good people (+): a good thing (+)
good things (+) happening to bad people (-): a bad thing
bad things (-) happening to good people (+): a bad thing
bad things (-) happening to bad people (-): a good thing (+)

The final site in this post is a fascinating corner of reddit, called Explain Like I'm Five. There, you can post questions, and others will try and explain the concept to you as clearly and simply as possible. If you know an answer to a posted question, and can answer it in a clear and simple manner, you can post a reply yourself.

They also try and preserve the best answers given in the past, in a post they call The Five-Year-Old's Guide to the Galaxy. You'll find it's not hard to lose a lot of time finding simple answers to things you've probably wondered about frequently.

These sites may not go into every last detail needed to master the understanding of a concept, but that's OK. The general gist of all of them is to help you grasp the basics, and give you a strong foundation from which to explore each idea further.

If you have any sites where you regularly find clear and helpful insights, please share them with us in the comments!

Back in July, I posted about people who cannot forget, in which I included a 60 Minutes report on the topic.

The idea of not being able to forget has certainly captured CBS' imagination. This Tuesday, they're premiering a show about an investigator who can't forget any day of her life.

There are a couple of emotional touches, of course. Most notably, her sister was murdered when they were children, and she can't seem to remember enough details about it to figure it out.

Here's the promotional preview CBS has released:



Since Numb3rs went off the air, I've been without a show I can enjoy in my own geeky way, and this looks like a good candidate. With the perfect memory premise, you can see why I'm naturally drawn to this show. When the preview got to the point where they give her the date March 27, 1998, I'm naturally trying to get the day of the week for that date too, and I shouted “Friday!” at the screen just a split second before she said, “...Tuesday.” You can see who was right by clicking here.

While I'm not crazy about yet another New York investigative drama, Numb3rs was able to bring a fresh life to L.A. crime investigation dramas, so maybe the perfect memory premise can do the same for this show. In this behind-the-scenes look at the show, star Poppy Montgomery mentions that she sees it as as a sort of superhero story. That's a good approach, and as long as they're able to keep the premise authentic, the show should do well.

Check this show out when Unforgettable premieres on Tuesday, Sept. 20th, at 10/9c on CBS. You can learn more about the show at CBS' Unforgettable homepage.

Learning about how scams work can be a fun gateway to learning surprising things about math and psychology. But what about when you're on the go? Get out your Android and Apple iOS mobile devices for this post!

Disclaimer: As with any column on scams on Grey Matters, I don't condone using these to rip people off, and simply present the information about scams here as an educational tool. Proceed with this in mind, and at your own risk.

Before we even get to apps, don't overlook the built-in features of your mobile device(s).

With the ability to view video on YouTube and/or subscribe to podcasts, you can check out programs such as Scam School (Scam School homepage), The Real Hustler UK, The Real Hustle US, and more!

The ability to surf the internet, as always, can also bring a wealth of information. Besides learning about scams here on Grey Matters, searching around forums can be excellent resources. There's the Scam School forums, as well as the various Magic Cafe's great forums, including The Gambling Spot, Pardon me, sir..., If right you win, if wrong you lose..., Betchas, Magical equations, and Puzzle me this....

A good blog to check out is Australia's Honest Con Man: Confessions, and his previous archives at The Honest Con Man's Guide To Life.

One of the most popular mathematical scams is the game of Nim. It has already made 4 appearances on Scam School (Nim, Advanced Nim, Thirty-One, Calendar Nim).

Watching those videos is one thing, but why not use your mobile device to practice and learn more about it? It's not surprising that Nim is so readily available for mobile devices. In the early days of personal computers, it was already popular. There were basic versions, such as 23 Matches, Batnum, and Nim. Some of the versions, such as the amazing Android Nim for the PET and TRS-80, did an amazing job of presenting this classic game!

On the Android you can get NimDroid and NimSwitch, both available for free!

For iPhone/iPod Touch and even iPad users (using the iPad's "2x" mode for these apps), there's plenty of free Nim versions, including myQuickGame Free, NeonNim: The Subtraction Game, Nim Game, and PYMINIM. Update: (August 17, 2010) Another Nim game, the Race To 100 app, was originally released for 99 cents, but has been free since August 8th. This is the version of Nim taught in the 116th episode of Scam School.

If you're willing to spend a little money, there's also some nice commercial versions of Nim for Apple's mobile devices. Dual Matches, Mind Nimmer, myQuickGame, and Nim.

Special mention should be made of the commercial Cannibal Muffin and Last Stone apps. Like the aforementioned 1970s Android Nim, the authors have taken extra time and care to present Nim in an extraordinary way.

Getting away from Nim, what about this interesting problem, known as the Monty Hall Problem?



Scam School also covered this, explaining how this fooled over 1,000 PhDs when it was discussed in Marilyn Vos Savant's column. Apple mobile device users use can try this counter-intuitive problem via the commercial Monty Doors or the free Monty Hall Paradox apps.

Although you can't win with this scam every time, you can win often enough that there are con men out there who use the Monty Hall Problem's counter-intuitive nature to their advantage.

While Nim and Monty Hall reign as scams from which you can learn great lessons, there are many other ways to learn about scams with your mobile device. For iPhones, iPod Touches, and iPads, Bar Tricks Free teaches you some basic scams, and its big brothers, Bar Tricks I and Bar Tricks II, both of which are paid apps, can teach you more. iDrink4Free and Gags are also available on the App Store.

Update: (August 17, 2010) The Author of the previously-mentioned Race To 100 app, also has another app called FourQuarters. From what I can tell, it's a version of the four-coin puzzle taught on the 2nd episode of Scam School.

If you're really serious about understand why these and similar scams work, Bruce Frey's book Statistics Hacks (also available in paperback) is a great, clear way to understand these often perplexing propositions. You can get a free preview of this book here, as well as the paperback link.

I'd love to hear about any insights you've developed by playing with these apps. Also, if you have any others that are relevant, I'd love to hear about them. Talk to me in the comments!

Time to geek out, and I have just the sites to help you do it!

Mental Floss: Based on the magazine of the same name, this is a must-stop for your daily dose of trivia and challenges, to help satisfy your know-it-all side. Their Twitter page and Amazing Fact Generator are great for quick drive-by knowledge.

Sporcle: Fans of my How Many Xs Can You Name In Y Minutes? post will instantly recognize this choice. It's one thing to get trivia facts into your head, but how good are you at retaining them? These quizzes will challenge your ability on even the most bizarre and obscure topics!

ThinkGeek: OK, this is a pure commercial store site. It's filled with stuff you never knew existed, but that any geek will instantly find many things to lust after!

Plus Magazine: This is a free online magazine dedicated to helping people understand all the math around them. For everything from bell-ringing to traffic jams, it's amazing to discover just where math is being used to improve life.

XKCD: For newer geeks, this comic strip is a great place to start, because it challenges you to figure out what is so funny about the topic. Naturally, geeks who have been around longer pride themselves on getting the jokes without looking anything up.

Final Answers: Granted, the table of contents here looks scary, but click around at random, and see what you discover. The complex topics are often made fun and interesting, and you're guaranteed to learn something new, even about things you thought you already knew!

Wolfram Research: The main page here is dedicated to their flagship product, Mathematica, but begin exploring over in the OUR SITES menu. Among the great places to explore are Wolfram Alpha (a natural language search engine), MathWorld, a site dedicated to demonstrations of the math used in Numb3rs, and much, much more!

Television Tropes & Idioms: You're going to get lost in this site. Even XKCD can't escape the lure of TV Tropes! This is filled with those things you keep seeing in movies and TV shows again and again. Start anywhere, and start realizing how common many aspects of your favorite entertainment really are!

BrainyQuote: Here's a 2-in-1 site for you. Besides the main quotation site, featuring quotes on just about every topic you can conceive of, there's also a history site, as well. For example, if you look at a page of quotes by Jim Carrey, you can also click on his birthday, January 17th, or the year 1962, to see what historical events happened. It's not hard to get lost in these twin sites.

Lifehacker: Here's effective advice that can be put to use to improve just about every aspect of your life. Usually, the tips and tricks you learn can often be put into immediate use, as well. While software is a favorite topic, just about anything that is handy and geeky is sure to be found here. C'mon, what internet geek wouldn't love a Lego router?

Did I forget any of your favorite sites where you like to geek out? I'd like to hear about them in the comments!

December is here, and so are this month's snippets!

• Last month, I talked about Game Theory in Popular Culture, and linked to the final scene of The Dark Knight as one example. Over at the Quantitative Peace blog, there's an excellent full analysis of this scene as it relates to game theory.

• Richard Wiseman, whom you may remember from his Quirkology work, has released a magic app called Telepath (iTunes Link). At first, it may seem like iSensor or iForce, but the fact that your spectayor picks up the iPhone instead of you will puzzle anyone who is wise to those other methods.

• The recently-mentioned Mind Your Decisions blog had a few problems lately, as noted here and here, but they seem to be fixed now. Presh has even found time to author two new game theory posts, both featuring fictional Charlies: Brown, from Peanuts, and Eppes, from Numb3rs.

• Over at Edu-tastic, they posted a list of the Top 50 Bloggers to Help You Study, Focus and Learn Better, and Grey Matters is the first blog mentioned in the Memory and Brain Training category! Grey Matters readers should definitely check out this list, as there are many great blogs you may not have known about before that you'll probably enjoy.

In my prior Game Theory post, I briefly mentioned the classic bar scene from A Beautiful Mind as one example, but there are far more examples of just about every aspect of game theory to be found in popular culture.

One common game theory scenario is known as “The Pirate Puzzle”. Here's the description, courtesy of the Mind Your Decisions blog:

Three pirates (A, B, and C) arrive from a lucrative voyage with 100 pieces of gold. They will split up the money according to an ancient code dependent on their leadership rules. The pirates are organized with a strict leadership structure—pirate A is stronger than pirate B who is stronger than pirate C.

The voting process is a series of proposals with a lethal twist. Here are the rules:

• The strongest pirate offers a split of the gold. An example would be: “0 to me, 10 to B, and 90 to C.”
• All of the pirates, including the proposer, vote on whether to accept the split. The proposer holds the casting vote in the case of a tie.
• If the pirates agree to the split, it happens.
• Otherwise, the pirate who proposed the plan gets thrown overboard from the ship and perishes.
• The next strongest pirate takes over and then offers a split of the money. The process is repeated until a proposal is accepted.

Pirates care first and foremost about living, then about getting gold. How does the game play out?

Most people would think that these conditions would tend toward a fair division. When it's played out, though, it's amazing how little gold the strongest pirate needs to give up. Ian Stewart's article, A Puzzle for Pirates (PDF), clearly explains why.

If this situation sounds familiar, it's because a similar situation arises in the first 5 minutes of the movie The Dark Knight, although the Joker adds his own twist:



Mind Your Decisions goes into more detail on this scene, game theory wise. For that matter, it even has a good analysis on the A Beautiful Mind bar scene I mentioned earlier.

Someone writing the script for The Dark Knight must've enjoyed studying game theory, as the movie is full of such scenarios. The later scene with the ships and detonators is also a good example of game theory.

One game theory scenario that will be familiar to most of you is the classic game of chicken, especially for those who've seen Rebel Without A Cause:



When it comes to games like chicken, the best thing to do is avoid the game altogether by changing it. If you can't get out of it, there are really only 4 basic ways to win chicken, as the crew of the USS Montana in this Dutch ad can attest.

Between the pirates, the joker's victims on their respective ships, and the USS Montana, there certainly are a lot of ships used in game theory scenarios, and we're not done with them yet. Here's a modified game of Battleship, described in an episode of Numb3rs:



When Charlie mentions game theory as studied by Rubinstein, Tversky and Heller, it's not only a funny line. It's actually a real paper, which is available online here.

There are many more examples I could give, but I figured it was best to start off with some popular references that offer clear demonstrations. If you'd like to find more examples, check out Game Theory .net's pop culture section, especially their television and movie sections. There's even a YouTube user named gametheoryclips who offers many scenes that could inspire further game theory research.

There are plenty of places you can find Pi easily on this blog, but you might be surprised as to where you can find Pi hidden, if you just look close enough. I'll start with a few of the easier places to find it.

Over on Twitter, user 3point141592653 is tweeting pi. As this writing, the tweets are only up to 290 digits, but there's more than enough material to suggest that many more entries are to come.

Back in September of 2007, I posted the following animation from Wikipedia where it seems Pi's presence would appear quite obvious. However, Pi was also ingeniously hidden in the picture itself in at least 2 ways. The ratio of the width to the length is equal to Pi to the first decimal place - 3.1 (if the picture was only 1 picture wider, it could've been accurate to 2 decimal places). Also, the final frame is held for exacty 3.14 seconds.

A calculator such as the Windows calculator is also a seemingly obvious place to find Pi, but there's even a hidden side there. Ever since Windows 98, if you copy the word pi from a document, and then paste it into the calculator, you get Pi to 32 decimal places!

Those of you who use iGoogle as your homepage, and have set it up with their custom themes, have probably noticed that the themes often change based on the time of day. What far fewer people know is that the geeks at Google, with a math-based sense of humor, have set up a special version of many of the themes that activates only at 3:14 AM, as discussed a few years ago over at DownloadSquad. Google itself has some nice screenshots of the special 3:14 AM versions of the theme.

My favorite show, Numb3rs, of course couldn't resist references to Pi when they reached their 3rd season and their 14th episode, titled “Take Out”. They even start in the first second, with the opening numbers reading:

3: Course meal
1: restaurant
4: Robberies
1592: Death squad murders

In the same episode, Charlie meets Mildred in the garden, where she's reading The Life of Pi, and Charlie explains a concept using the example of items in a refrigerator, the last example of which is pie.

Of course, the list of software with hidden Pi references, in everything from mIRC to Guitar Hero II, but it doesn't stop there. You can find them in some surprising places.

If you're a fan of the band Travis, who themselves are big fans of Pi, check out their album The Man Who. The CD lists 10 tracks, but there's a hidden one, titled Flashing Blue Light, that starts exactly 3 minutes and 14 seconds after the last track.

Probably the strangest place to find hidden examples of Pi is in subway stations. Are you having an emergency while traveling in the Buenos Aires subway system? Just dial *31416! However, an even more subtle and beautiful subway example of hidden Pi is the Downsview subway station in Toronto. There's a mural that seems to be a random blend of colors, but it's actually Pi ingeniously disguised.

Have you ever spotted hidden examples of Pi anywhere? Let me and everyone else hear about it in the comments!

7,636 Missing Persons, 2,260 Murders, 6 Unsolved Serial Killings, 100 Episodes - that's the tag that opened Numb3rs' 100th episode, which just aired this past Friday.

This episode picks up from the previous episode of Numb3rs, Fifth Man, in which Charlie's math leads to an FBI stakeout in which Don is injured by a man Charlie didn't expect via his pattern analysis. This leads Charlie to question whether he can really see beyond the math.

In Disturbed, the 100th episode, Charlie begins analyzing numerous (num3rous?) previous unsolved cases. This makes the FBI team wonder whether he's still grasping at straws after feeling responsible for Don's life, or whether he's really on to something.

If you haven't already seen the episode, here it is in full:

Need to catch up? Between Fancast's Numb3rs page and CBS' own Numb3rs videos, you should become well versed on at least the current season.

Naturally, CBS threw a 100th episode party for the stars.

Personally, I'm thrilled to see a show with such a strong math background make it this far. The nice thing is, you can delve into the mathematics of any show as deeply as you want. Redhawke's Running the Numb3rs site and Wolfram's The Math Behind Numb3rs site (and it's featured interactive demonstrations) are probably the two highest respected sites when it comes into delving into the principles discussed in the show. CBS' main Numb3rs page has even more links for Numb3rs fan, including their weekly math puzzle.

Congratulations to the Numb3rs team for making it to your 100th episode! Here's hoping that the show goes on and makes 100 more!

Learning how to do math, especially mental math, can be great, but it does come with a price. It frequently changes how perceive you.

You might think that math teachers, who want you to be good at math, would be exempt from this. However, many math teachers know the area of math they're teaching and just a few other areas. To paraphrase Will Rogers, if you get them off the topic in which they were educated, they're not as knowledgeable.

In his book, Secrets of Mental Math, Arthur Benjamin tells about how he discovered how to square two-digit numbers on his own while he was still young. The method itself was previously known, but he had discovered it independently. One day, in an algebra class, his teacher was working through a problem, and finished by writing the answer as 108². Young Arthur Benjamin then blurted out that the answer was 11,664!

When he explained the method he was using, the teacher said she had never heard of that before, and young Arthur's mind quickly raced with the idea that he'd made a new discovery! He finishes by mentioning that, when he ran across the same method in a Martin Gardner book, it ruined his whole day.

With my interest in mental math and magic, I had a few similar experiences in my high school days. The first time you watch it, don't try to understand what he is explaining. Instead, imagine you're this guy's math teacher, and being boggled by what he's describing. It helped me finally understand what my math teachers must've gone through when dealing with me.

The worst part about the first time I watched this video was realizing that I could follow the techniques (largely because I'd used them myself before), and realizing how I probably sound when describing ideas like this to others.

If you want to understand the shortcuts he describes, go through the video bit-by-bit until you understand. You can find further help with my technique videos (most notably Arthur Benjamin's own Mathemagics). Sites like Curious Math, Mathpath, and BEATCALC can also help.

On a related note, TV's best known math geek, and his friends, are returning from hiatus after the writer's strike. The ad CBS used to announce the return of Numb3rs appeals to me on several levels. First, it demonstrates the perception non-mathematicians often have of people who are good at math. Second, as a Mac user, I couldn't help but appreciate that they're parodying Apple's well-known Mac vs. PC ads to grab your attention.

Certainly, you can learn enough feats from this site and its links to present yourself as a genius. Just how are geniuses presented, anyway? I thought it might be fun to look back at how TV has presented their genius characters.

To help you understand these types, many of the links below have links to one or more free full online episodes of their respective shows, which I've marked with (fe) next to their names.

* Professor: This is the classic genius caricature. Whenever the Professor is faced with a problem, his intellect is able to devise an ingenious way to solve the problem. Note that the Professor type is usually portrayed with minor emotional qualities, and is a neutral character who often helps settle disputes. As long the other characters around them understand these quirks, they get along fine with others.This category is named after the Professor from Gilligan's Island (fe), but would also include Star Trek's Mr. Spock, CSI's Gil Grissom (fe), Charlie Eppes of Numb3rs (fe), and MacGyver.

* TV Genius: The TV Genius would be the Professor type taken to extremes. Instead of simply having minor emotional qualities, they are presented as the quiet, maladjusted type. Interacting with other people is very difficult to them, even to the point of being baffling, but dealing with numerous analytical details is simple and fascinating for them, as if they were borderline autistic. They're often impossibly smart to the point that they can handle all branches of science with equal brilliance. Austin James in Probe (fe), Back To The Future's Doc Brown, and most of the cast of Frasier would fit here.

* Teen Genius: Unlike the previous types who tend to have some difficulties in dealing with people, the Teen Genius has fewer odd quirks, except for the natural problems that come with being a teenager. While Doogie Howser, M.D. (fe) is probably the first example to come to mind, there is also the four main characters of Whiz Kids (fe), Growing Pains' Carol Seaver (fe), and Willow on Buffy, The Vampire Slayer (fe).

* Insufferable Genius: This type frequently boasts of their amazing knowledge, and seems to come across as a know-it-all at first. Then, the other characters learn that this character really is as good as he says, but usually continue to regret the boasting. Many of you are probably already thinking of House (fe), but M*A*S*H's Winchester and Hercule Poirot are also classic examples of this.

* Genius Ditz: Reconciling opposites often makes for interesting characters, and applying that to geniuses gives us the Genius Ditz. These are often characters who have been originally presented as not being too bright, but are actually brilliant in one particular field. Deep Space Nine's Rom had a great talent for engineering. This type of genius is often used in kid's shows, such as the Electric Company's Fargo North, Decoder (fe).

* Genius Bruiser: The Genius Bruiser is another attempt to get away from the standard genius stereotype. When first introduced, they're thought of as a bully or a muscular brute. Later, it's discovered that they also have a brainy side, usually manifesting as some specialized geeky ability or interest. The X-Men's Dr. Henry "Beast" McCoy, and, surprisingly, B.A. Baracus of the A-Team (fe), who was occasionally shown repairing and developing electronic gadgets, are classic examples.

These, of course, aren't the only ways geniuses are portrayed on TV, only the most frequently used. Thankfully, newer approaches are being developed, too. For example, Psych (fe), features a character, Shawn Spencer, who is skilled at observation and deduction, but the police originally think this knowledge is so good, he must've been part of the crime. To keep from being prosecuted, Shawn has to keep up a facade of being psychic.

One of the best shows on TV for comparing approaches to smart characters would have to be Head of the Class (fe). This show focuses on a group of advanced placement New York high school students, and their teacher's unusual approach to education. With so many smart characters in one place, it's often interesting to see how they made the characters so different from each other, as well as the kind of challenges they faced.

Do you have any favorite geniuses from TV? I'd love to hear who it is and what you liked about their approach in the comments!

While memory feats can be amazing on their own, a reason for performing them can help make them far more interesting to your audiences. Here are a few plots I've come up with to use as starting points for memory feat presentations. I developed these on my own, and they're original as far as I know.

The first plot is a way to get two feats for the price of one. For this, you have to know how to do the Day of the Week For Any Date feat, and any 4 by 4 magic square routine in which the spectator starts by giving you 4 numbers to use in the square. You can find routines like this in Mathematical Wizardry, Mark Farrar's How To Create A Birthday Magic Square ebook, or Chuck Hickock's Diagonal Magic Square (now out of print).

You start by asking for someone's birthday, give the day of the week for it, and have the day of the week verified via a perpetual calendar. Mention that you're often asked how you figure the day of the week so quickly. Explaining that it's not so much a particular process, you explain that you simply see the numbers come together, much like in the movie A Beautiful Mind, or the TV show Numb3rs. You bring out a board marked with a 4 by 4 grid, and say that you're going to give them an idea of what happens when you think of the dates. You ask for a new birthday from someone, and fill those in as the 4 starting numbers in the grid. For example, if they say their birthday is October 12, 1974, you write the numbers 10 (October), 12, 19 (first 2 digits of the year) and 74 (last 2 digits of the year) in different boxes, according to the particular magic square method you're using. As you're writing the numbers, you figure out the day of the week for the date, and remember that for later.

Reminding them of how the numbers come together in your mind, you quickly fill out the rest of the squares. Once you're finished, you say, "...and this is how I know that this date falls on..." and give the correct day of the week (Saturday, in our October 12, 1974 example). Once the day is verified, you explain that part of the reason you knew this date was correct was that the numbers that flash in your head allow you to verify the answer from different perspectives. To explain, you show that all the seemingly-random numbers on the grid give the same total when added horizontally, vertically, diagonally and so on.

This plot is great for giving a Rain Man type of impression. For a larger audience, you could use a pre-made grid, such as Meir Yedid's Total Destiny. However, you can make it more theatrical with the use of a transparent dry-erase board, which will build the suspense as they see the numbers written backwards, and imposed on your face. There are some great discussions on the use of transparent dry-erase boards for routines like this in the Mentalist Sanctum and the members-only section of the Magic Cafe.

The second plot is simply the idea of a book puppet, which you claim is an almanac, an atlas or whatever type of book would have the information you've memorized. The book puppet effectively acts as the source for the answers you give in your memory feat. This is a small idea with many advantages. The book can be used for a metaphor restriction violation (see vol. 1 of Wonder Words), which is the technical term for attributing powers, actions or thoughts to something, the book puppet in this case, that obviously can't possess them. The effect of this is that the audience sees through this claim, and attributes the amazing recall of facts. Since this is done both subconciously and indirectly, it's much more effective and enjoyable than directly claiming an amazing memory. In the show Dr. Wilson's Memory Elixir, a drink with apparent memory-improving qualities is used in the same way.

Also, if you need to take the time to recall the information, you can have the book apparently whisper the answer to you. You can get a brief comedic moment by seeming to forget the information, and having the book remind you. Getting into a contest where you compete against the book to see who can answer more questions from the audience correctly could be very funny.

If any of you have any great plots for memory, math or other brain-related feats you would like to share, please include them in the comments!

It's holiday time once again! If you're looking for brain straining and entertaining gift ideas, you've come to the right place! Even better, many of the links I'll share with you will allow you to compare prices, so you can get the best deal on those gifts which strike your fancy.

I live in Las Vegas, so I'm going to start close to home. Back in the late '80s and early '90s, a team of students and faculty from MIT formed a blackjack team that used mathematics, memory training, and nerve to take Las Vegas' blackjack tables for millions! The History Channel produced a documentary about the MIT blackjack team titled Breaking Vegas. One of the original team members, Ben Mezrich, has even written a detailed account of his time with the team, calling his book Bringing Down The House. We've all fantasized about winning millions in Vegas, and these true accounts show just what it takes, as well as the rewards and consequences.

Among the biggest news in entertainment this season is the return of Futurama! Among its fans, Futurama is known for including numerous examples of mathematical humor, some of it very advanced! If you know (or are) a Futurama fan, you can get caught up with the series by picking up vols. 1, 2, 3 and 4 of the series.

Once they're caught up, check out the newly-released Futurama movie, Bender's Big Score! The 90-minute movie opens, not surprisingly, with humorous references to their being canceled. After a few jabs at FOX, naked spamming aliens take control of Bender and make him travel through time to steal histories greatest treasures! Don't believe me? Check out the trailer! Among the bonuses on the DVD are a math lecture from the FuturamaMath.com team, called Bite My Shiny Metal X, a complete episode of Everybody Loves Hypnotoad, A Terrifying Message from Al Gore, and much more!

Of course, I can't mention popular math-based shows without mentioning Numb3rs! Now in its 4th season, it's proved that math can be entertaining, interesting and useful. Seasons 1, 2 and 3 are now available on DVD. The Charlievision sequences that help explain the mathematical concepts have proved especially popular with fans and educators. For those who want to learn more about the math explored in the first 3 seasons, the book Numbers behind Numb3rs: Solving Crime with Mathematics provides more details about them.

It's one thing learning about somebody else's skills in math and/or memory. Maybe you're interested in improving your own skill in these areas as part of your New Year's resolutions. But how do you go about it?

There are many fun ways to improve your memory, but as starting points, I would highly recommend the Harry Lorayne classics, The Memory Book and Super Power Memory.

For practicing the memory techniques you learn, I'm going to shamelessly self-promote my own memory training CD-ROM, Train Your Brain and Entertain (TYBE), available for both Mac OS X (view Flash demo) and Windows (view Flash demo). If you would like to try before you buy, try out the free lite version. You can download TYBELite for Mac here, and you can download TYBELite for Windows here. If you decide you like the software, but you believe it is too late to get the CD-ROM in time, it's also available for purchase as a download!

How about math? Wouldn't it be great to get better and faster at math? For improving your speed math skills, I highly recommend Secrets of Mental Math, Math Magic, Speed Mathematics and the classic Trachtenberg Speed System of Basic Mathematics.

Speed math is one thing, but how do you make math in general interesting enough to inspire further exploration? As anyone who knows will tell you, the best answer are the books of Martin Gardner. A good place to start is with his book Mathematics, Magic and Mystery, which uses magic tricks to inspire interest in mathematical principles. Martin Gardner's collections of his Scientific American columns, such as Hexaflexagons and Other Mathematical Diversions, Second Scientific American Book of Mathematical Puzzles and Diversions, and The Unexpected Hanging and Other Mathematical Diversions, are great ways to dive into math.

Martin Gardner isn't the only author who can make math fun, though. If you have a daughter in middle school who is struggling with math, Danica McKellar (whom you may remember as Winnie Cooper on The Wonder Years) has written a book called Math Doesn't Suck: How to Survive Middle-School Math Without Losing Your Mind or Breaking a Nail. For the more advanced math student, Prisoner's Dilemma is a fascinating study of John von Neumann's development of game theory. I posted about the basics of the Prisoner's Dilemma back in May, but this book goes deeper into it, discussing the effect this dilemma had on everything from simple everyday human interactions all the way up to the atomic bomb and the cold war!

Reading isn't the only way to better yourself! If your loved one is into brain training, how about giving them a black and crimson Nintendo DS Lite that comes bundled with Brain Age²? They'll also be able to play the original Brain Age and Big Brain Academy on it, as well!

Let's not forget about gifts that keep on giving. You can keep your loved ones smart all year with subscriptions to magazines like GAMES, Scientific American Mind and Mental Floss (a personal favorite).

If you have a loved one who regularly read Grey Matters or similar sites, please take a look around the Grey Matters recommended products store, which allows you to compare prices on popular items, and the Grey Matters original products store, where you'll find unique gifts that aren't available anywhere else. Happy holidays!

How would you like to give clarity to your routines, so that they're easier for your audiences to understand and remember?

The trick is to make it concrete, less abstract.

When Aesop decided to record a set of morals, it would have been all too easy to simply list the moral ideals themselves. He knew that to make them easier to understand and remember, he would need to tell concrete stories. Instead of simply saying, “Misery loves company,” he gives us the story of The Fox Who Lost His Tail. Instead of Aesop's List of Moral Ideals, which probably would be long forgotten, we have Aesop's Fables, which has spanned both countries and centuries!

If you look over my memory and memory feat posts, as well as the various memory systems themselves, you'll note that the underlying technique is to find a way to make abstract concepts easier to visualize.

Numbers are the ultimate abstraction. In the Number Shape System, numbers are turned into pictures of items like a tire, a candle, or a swan that are easier to picture, and in the Number Rhyme System, they're turned into items that sound like the number, such as gun, shoe, and tree. Even in the more complex Peg/Major System, where each digit is turned into a phonetic sound, and the sounds are then combined to make words, you're advised to limit yourself to words that are nouns or verbs.

Why the limitation to nouns and verbs? What makes them, or anything else for that matter, more concrete? The answer is surprisingly simple. Something is concrete when you can experience it through at least one of your five senses (vision, hearing, touching, smelling and tasting). Our brains are specially designed to bring in information about the world through these pathways, so any concept that employs our senses can be quickly grasped.

Think about it. What is the definition of beauty? That is an abstract concept, because it is next to impossible to describe through the use of the senses. How about if I ask you the definition of, say, garden hose? That's much easier! It's a flexible tube for conveying a liquid, as water, to a desired point. You can picture the tube and the water easily. You know what flexibility feels like.

What effect can being more concrete have in magic presentations? Watch Eugene Burger perform Inquisition:

Did you notice the sensory detail in this routine? When the torture device is prepared behind the victim's back, you can imagine the beads of sweat. You can feel the torture device being pressed against your spine, and many even wince when the cards are torn, as you're hearing bones breaking! To see the difference concreteness can make, turn the sound off, and watch the video again. While you can still see some of the attitude in Eugene Burger's face, it is actually a completely different experience!

If you want to learn more about developing concrete magic presentations, the current masters of this style of presentation that first come to my mind are (There are, of course, many more current and past masters, as I will no doubt be reminded in the comments):
* Eugene Burger
* Robert Neale
* David Parr
* Docc Hilford

As a matter of fact, Docc's DVD, How to Turn Ordinary Tricks into Mind-Shaking Miracles, deserves special mention here. This DVD will show you not only how to make your own presentations more concrete, but how to use sensory detail to such great effect that you can have people remember much more happening that you actually performed! As an example, Docc performs a few simple effects with matches, yet the audience leaves with a memory of him performing a classic spook show, including decapitations, cremations, levitations and vanishes!

Lack of concreteness is also a major cause of lack of communication. What if a doctor tells a mother that her child has, say, Xeroderma pigmentosum? She (like most of us) probably wouldn't have the first idea what could be done, or what is involved. Instead, the doctor would tell the mother that, due to a rare genetic condition, her child cannot be exposed to direct sunlight, without risking skin cancer. However, putting the vivid description into the child's medical file for other doctors and nurses to read would also cause confusion. In the case of the medical records, it's much more efficient and effective to just use the phrase Xeroderma pigmentosum.

In short, abstract concepts are great when experts are talking to other experts. However, you should also remember, as Will Rogers said, “There is nothing so stupid as an educated man, if you get off the thing that he was educated in. ” Actually, it's not that non-experts are stupid, but rather that you need to make your case easier to understand and remember by getting them across in vivid sensory detail. Fans of the show Numb3rs will instantly recognize Charlievision as a great example of this idea.

If you want more of your audience to understand and remember your routines, present them in vivid detail. For more on the power of concrete ideas, check out the concreteness category of the Made To Stick blog.

See also:
Memorable Magic: Simplicity
Memorable Magic: The Unexpected

There's only one more day to go until the season premiere of Numb3rs!

In my previous entry, I briefly referred to Charlievision, where Charlie Eppes (David Krumholtz) visualizes a mathematical approach to a problem. Wouldn't it be nice to understand these mathematical concepts in more detail?

CBS thinks so, and has teamed up with Texas Instruments to create the We All Use Math Everyday site. This site features exercises for individuals, as well as students and teachers, that directly relate to each individual episode.

If you prefer the principles organized by name, instead of by episode, check out Redhawke's All The Math section. If you wanted to find out more about, say, Pi, you would scroll down to the P section, and click Pi. Once there, you get a brief description, and links that help you learn more about the concept.

Those previous two site I've actually mentioned before. There are two great references that have just become available recently that should be required reading for any Numb3rs fan.

Back in August, the new book Numbers behind Numb3rs: Solving Crime with Mathematics became available. NPR's Math Guy, Keith Devlin, got together with Gary Lorden, who is the principal math advisor for Numb3rs, and described math used in the first 3 seasons of the show. This is a great reference to help quell your curiosity about concepts you've seen on the show, but may not have fully understood.

WARNING: If you don't want to know anything more than the commercials are telling you about the show, stop reading now! The following links may contain spoilers and/or plot details.

The newest Numb3rs reference has shown up just this week! Wolfram Research best known for their MathWorld site and their Mathematica software, has just announced their The Math Behind Numb3rs site! This is the richest resource yet for Numb3rs mathematics!

Already they have an explanation of the math used in Trust Metric, the season premiere episode. In this episode, Charlie will be using set covering deployment, the illumination problem and the Mathematics of Friendship (you'll see!). Not only are these concepts discussed on the page itself and the MathWorld site, but you can learn more about them via free interactive Wolfram Demonstration downloads.

Probably the most fun part about this site is that you may be able to learn about the math before the episode airs. Keep this site as your secret source, and you can astound your friends and family with details about the principles during the show. They'll think you're a genius!

It's almost time for the 4th season of Numb3rs! If you're not familiar with the show already, check out my original Numb3rs post, as well as the whole Numb3rs category to get a better idea of the show.

The best way to get an idea of the show, of course, is to watch it. Season 1 (13 episodes) and Season 2 (24 episodes) are already on DVD. Season 3 (24 episodes) will be released this Tuesday, along with a Three Season DVD boxed set!

If you have an iPod, you can already purchase Season 1 (by episode only), Season 2 and Season 3 from the iTunes store. Update (Oct 1): The subscription to season 4 is now available, as well. Even if you're not sure about purchasing whole seasons yet, buying just the season 3 episodes The Mole and The Janus List, a total of only $3.98, is a great way to get ready for the season premiere.

Since it's been almost 4 full months since the season-ending cliffhanger aired, and was just re-aired last Friday, I have no qualms about discussing it. In the 4th episode of season 3, The Mole, Don's (Rob Morrow) FBI team is investigating the death of a Chinese interpreter. The murderer turns out to be Dwayne Carter, who saved agent Colby Granger's (Dylan Bruno) life in Afghanistan, when they both served in the Army's Special Forces.

This doesn't seem important until the season-ending cliffhanger. In The Janus List, a list revealed by a poisoned British secret agent reveals that Colby Granger is a double agent for the Chinese government. The last thing you see in that episode is both Carter and Granger being taken away to be tried for treason.

There are other questions that will hopefully be answered this season. Will Megan (Diane Farr) decide to stay on with the FBI after her DOJ assignment? Since Larry (Peter MacNicol) has a new outlook on life after being on the space shuttle, what will happen when he sees Megan for the first time? While we've seen "Charlievision", like in this scene, the The Janus List showed us the first instance of "Donvision", when he realizes that the bombs on the bridge look like a G major scale. Will Don start understanding Charlie (David Krumholtz) better in the new season?

The new episode will air on Friday, September 28th. In this clip, director Tony Scott talks about the making of the season premiere:

So, what can we look for in the new episode? I'll let the season 4 premiere trailer speak for itself:

I'm not the only one who has been thinking about visualizing mathematical concepts!

At roughly the same time I was writing my previous post, Math Blog was posting thought-provoking mathematical videos. The videos that were chosen are very effective at making hard-to-imagine concepts easier to understand. Do you think you can understand 10 dimensions, or how to turn a sphere inside out with poking a hole in it?

The idea of making mathematical and scientific concepts easy to visualize isn't just a passing fancy, either. The National Science Foundation has hosted the Science and Engineering Visualization Challenge since 2003. Interesting past winners include Still Life: Five Glass Surfaces on a Tabletop (seen in the graphic above) and Flight Patterns.

Planetary Motion from Eudoxus to Copernicus, which only made honorable mention, is especially interesting. It's a visualization over time of how humanity pictured the universe. Planetary Motion reminds me a little of James Burke's documentaries (Connections and The Day The Universe Changed).

Speaking of TV shows, there aren't that many shows today, other than Numb3rs, that regularly feature mathematical visualizations. I remember a PBS show called Square One TV that used to teach an amazing variety of mathematical skits to hit the point home. As an example, how do you make the summation of positive and negative numbers visual? Here's Square One's approach:

You might think it would be hard to visualize would be Einstein's Theory of Relativity. If that's true, the people who created Al's Relativistic Adventures have proved that wrong. This is an interactive Flash demonstration that takes you step by step through the numerous principles involved in relativity, and even quizzes you to make sure you're following along.

It's a shame that math isn't taught to both the left brain and the right brain. As a final thought on this matter, I suggest reading If We Taught English the Way We Teach Math.

Take a close look at the tabs at the top of the page. There's something new there. It's the Recommended Products tab!

For a year and a half now, I've had the Grey Matters Online Store for my own original items, such as my Train Your Brain To Entertain CD-ROM.

However, when I recommend other commercial products, I've had to link to numerous other websites. Finally, I now have a brand new store featuring many of the items I've mentioned!

One of the best things about this new store is that, instead of having a single set price for the items, the items will be listed from various sources so that you can compare prices! For example, take a look at the Numb3rs Second Season DVD. At this writing, there are prices listed ranging from $31.08 to $48.33!

Currently, there are 8 sections with over 80 products! Check out the DVDs, books, puzzles, games, brain training, magazines, kids & family and presentation sections.

Many of the items in the store I've mentioned or used specifically on here, such as Every Good Boy Deserves Fudge, which I just reviewed last Thursday.

There are also items I think would be useful to the Brain Gang, such as Days, Months and Years: A Perpetual Calendar for the Past, Present and Future, which has obvious use for those of you who've learned the Day of the Week For Any Date Feat.

All the items, just as with the store of my original products, are guaranteed to fit in with the Grey Matters philosophy of helping you have fun while challenging and improving your mind! Please take a look around, explore the new store, compare prices, and maybe even help out Grey Matters by making a purchase.

Also, if you have any products to suggest, or other comments or questions about the store, please let me know in the comments, or via the Contact Me tab at the top.

Numb3rs has just wrapped up its third season with some big surprises and puzzling character questions (WARNING: This link contains spoilers!).

Numb3rs' season 3 DVD is tentatively set for a US release on September 18, 2007, and CBS has renewed the show for a 4th season, so now seems like a good time to go over the series.

There are a few things that I haven't covered in my previous Numb3rs posts.

Popular Science Magazine covers one thing I've puzzled over in the past few years, and that is just when prime-time TV went from bathing suits to lab coats.

Eric Weisstein, whose Mathworld site I've written about numerous times, and covers The Math(ematica)Behind Numb3rs. This is an especially good article, bothe because of the links that allow you to dig further into the math used in the show, and because Eric himself is part of the mathematical research team for the show!

Until the Season 3 DVD is released, I suggest the summer re-runs, and perhaps the upcoming August release of The Numbers Behind NUMB3RS: Solving Crime with Mathematics.

Imagine you and another person are arrested by the police. The police don't have sufficient evidence for a conviction, so the police split you and this other person up into different rooms. They offer you and the other person the same deal. If both you and the other person stay silent, both of you will wind up spending 6 months in jail (the police have enough evidence for a lesser charge). If both you and the other person agree to testify against each other, you will both spend the next 2 years in jail. If one agrees to testify for the prosecution, and the other person remains silent, the one who testifies will go free, while the one who remains silent will go to jail for 10 years.

Considering that you can't know what choice the other person is going to make, what is the best choice you can make to minimize your jail time?

This is a classic puzzle known as the Prisoner's Dilemma. The version stated as above has a very simple solution. If you stay silent, you'll either serve 6 months or 10 years. If you testify against the other person, you'll either serve 2 years or go free. Obviously, the better choice is to testify against the other person.

This seems fairly obvious, and doesn't seem like much of a puzzle. Perhaps it needs one more aspect to make it more interesting.

Imagine this is done not just once, but repeated numerous times (perhaps both you and the other person have been charged with numerous crimes). Only after you have made your choice each time, and before the next round, are you told the other person's choice. Now, what is your best strategy?

This makes it a bit more difficult, doesn't it? This variation is known as the iterated prisoner's dilemma. Before we discuss the best strategy for this version, try some online simulations to see if you can work it out for yourself. You can try out a version using the reward of gold coins. If this doesn't help, and you have Java installed, try another version that allows you to control the other person's strategy.

If the Monte Carlo method gives you trouble, perhaps applying the Nash equilibrium might help. True, the article might be a bit long, but here is the basic idea of the Nash equilibrium, from the movie A Beautiful Mind.

Have you figured it out yet? If not, I'll let Charlie Eppes (David Krumholtz) explain the optimum strategy, from the The Art of Reckoning episode of Numb3rs, with a great rock-climbing analogy:

Yes, Tit For Tat is the best overall strategy. However, there is one strategy that beat it out in the Prisoner's Dilemma competition. A team from Southampton University created the programs that did just that.

How is this possible? The Southampton strategy was to submit 60 programs. Each of the programs was able to recognize the others by the sequence of the first 5-10 choices made. If a Southampton program recognized another Southampton program, one of the programs would always choose to cooperate with the police, while the other one would always choose to remain silent. If a Southampton program realized it was playing a non-Southampton program, it would always choose to cooperate with the police, thereby minimizing the score of the competing program. This strategy took the top three places in the competition when it was applied, not to mention numerous places at the bottom for the programs that would consistently stay silent.

So why do people still claim Tit For Tat is the best? In the classic iterated problem, it is assumed that you only have control of your own actions, and have not pre-arranged a code with the other person (as you were separated before the offer was first made).

To wind up this post, I'd like to point you to Bill Whittle's site, in which he discusses the philosophical implications of the prisoner's dilemma. If you haven't visited this site before, I also suggest you explore the previous entries, too. His essays and even his simple posts are always clear and thought-provoking.

Just how does our society think of mathematicians? One of the best ways to find out is to look at their portrayal in movies and TV.

The question is, just where do you find such portrayals? Oliver Knill's Mathematics and Movies page (Flash required) is an excellent place to start. It can be surprising how much math has appeared in your favorite movies and TV shows.

Once you realize the quantity of math out in popular media, how is the quality? Just because you hear the Pythagorean theorem stated doesn't mean that time was put into researching it. Thankfully, Alex Kasman comes to the rescue with his Mathematical Fiction page, in which the stories are rated not only for the quality of the story, but the accuracy of the mathematical principles, as well.

Of course, some shows have already established their reputation for mathematical accuracy among their fans. Numb3rs quickly comes to mind. Futurama and the Simpsons (surprised?) are also great sources of high quality mathematical principles, and even mathematical humor! As noted on Bender Bending Rodriguez' Mathematical Curiosities page, even jokes in the background of Futurama are well researched.

If you like math humor like this, you'll be see more like this when new Futurama episodes arrive in 2008!