In the previous post, I talked about artificial life and used it to demonstrate the amazing complexity that can develop from the simplest rules.

That kind of complexity developing from simplicity is a concept so counter-intuitive that it wasn't been part of humanity's collective mental toolbox for most of recorded history. Since it's very difficult to conceive of this, even with a feedback component involved, the only two alternative explanations left for the average person are pure chance, and the existence of deities.

If you consider the chance argument, you have to look around at the complexity of the world around you and consider that the odds of this developing by pure chance are very, very low, about 1 in a “squintillion” (a word coined by Harry Lorayne to describe any number that is so long, you have to squint to see the last numbers).

Now, consider the argument for the existence of a deity or deities. In Douglas Adams' speech, Is there an Artificial God? (originally given, interestingly, at an artificial life conference), gives a wonderful explanation in the following video of how this argument must have first developed:



Certainly, the concepts of iteration, feedback, and change were understood on a basic level, but when it came to explaining the world around us, it didn't seem possible as an explanation.

So, with a deity-created explanation, especially considering how much more satisfying it is than dumb luck, how did we go from that to start understanding the power of iteration, feedback, and change?

As so often happens in history, it began with attempts to fit the world around us into the explanation we had, and examining the problems encountered by trying to do that. In the following episode of James Burke's The Day The Universe Changed, called Fit To Rule, James Burke begins just as all that is about to fall apart. Our starting point is this wonderful introduction:

OK, Let's get the story off to a cracking start. Here's Linnaeus, the fellow who'd been up north. A really dull botanist, wandering around the really dull world they'd all made for themselves.

Not a hair out of place, so to speak: symmetrical, balanced, like their architecture. This is the type of stuff you go for if you're sure, as they were, that the world was created at 9 A.M. on October 26, 4004 B.C., and was never going to change: cool, geometrical.

They put nature in a pot in a garden because that's the way the world was for people like Linnaeus: regimented.

I'm going to take this blog in a rather unusual direction for the next few posts. I think you'll enjoy it.

Many recent experiences have brought my focus to the same three titular concepts: iteration (repetition), feedback, and change. They've provoked my thoughts in an interesting way, and I hope to bring them to you in a way that will provoke your own thinking.

These three concepts seem to work together in an almost magical way to create incredible results from even the simplest beginnings. That's easy to say, but hard to understand.

The best way to understand the impressive nature of complexity developing from simplicity is to experience it for yourself. One of the best tools for this is John Conway's Game of Life, first published back in October 1970. It's not so much a game in the traditional sense, but rather a simple simulation and/or experiment with some simple rules.

Here's John Conway himself talking about the nature of the Game of Life:





Got that? Those three simple rules, for easy reference, are as follows:

Birth: An dead (empty) square with exactly three living (filled) neighbors will give birth to a new living square in the next generation.

Death: Any living square with only 1 or 0 neighbors dies from isolation, and any living square with 4 or more neighbors dies from overcrowding.

Survival: Any living square with 2 or 3 neighbors survives to the next generation.

In the videos above, you've seen some simple examples of what can happen when these 3 rules are applied, but now I want you to play around with it for yourself.

To do this, simply go to Ian McDowell's Game of Life page and play with it. Since it's not really a game, you can win or lose, so just try various things and see what happens. Detailed instructions are on the page itself.

While you're playing around with it, ask yourself what amazes you and why. The rules don't say anything about symmetry, motion, or equilibrium, but all those concepts and more develop out of 3 simple rules.

Not only can you create a piece that moves, but also a “machine” that creates these gliders, and even a meta-machine that creates these glider guns. Go back and read those 3 rules again, and note that they say nothing about being able to do any of these things! And yet, they are still possible.

If we think of groups of pixels as “creatures”, then the creatures created in this simulation are quite fascinating and thought-provoking. As noted in the essay Get A-Life (“A-Life” being shorthand for “Artificial Life”), simulation of the Sims variety is one thing, while the type of simulation discussed here is of a completely different nature.

I highly recommended reading that full essay before continuing this discussion. In it, they discuss the Game of Life, L-Plants and Biomorphs, Core Wars and Tierra, and even evolutionary programming.

In all of these things, surprising complexity, and even seemingly-impossible simplicity arise out of just the simple combination of iteration, feedback, and change.

The notion of complexity arising out of simplicity hasn't been understood as a widespread notion for very long in human history. In my next post, we'll delve into just how that happened, and the surprising effects the spread of the notion had itself.

Back in March, Scam School taught a card memory feat in which you apparently memorize the order of a deck of cards so well, you can identify a single moved card.

This past week, Scam School presented another card memory feat of a slightly different nature. I thought it might be fun to compare this simulated feat to the legitimate memory feat.

We'll start with the simulated version. Imagine being able to look through a deck of cards once, and then recall the missing card from the stack from memory alone.

That's what is taught in the 166th episode of Scam School:



Let's take a closer look at the method. There's an expectation that you're going to identify two cards removed from the deck, but you're really only identifying one.

Note that, with this method, you can really only identify a single card. For example, if you run through the deck and get a sum of 211 (or rather, 1), you know that the two face-down cards must total 9. Until you look, however, you can't really be sure whether the two cards are an 8 and a 1, a 7 and a 2, a 6 and a 3, or a 5 and a 4. Further, the math can't tell you which is which, and obviously can't tell you the suit.

Fortunately, the routine is set up to cover these problems in the course of the presentation. Being able to identify a single card after just a single (apparent) glance through the deck is an impressive. The fact that this method is simple and straightforward after sufficient practice is a nice bonus.

One big difference between this and the previous card memory feat taught on Scam School is that this one is not about memorizing the order. The focus is simply on memorizing which cards are in the deck, and using that information to determine the missing cards.

How does this compare to performing the same feat by legitimate memorization? Over in the Mental Gym, I teach a similar card memory feat using legitimate memorization. It does take some preparation, but the work isn't as complex as you might think.

You start by learning Bob Farmer's easy card mnemonics, and then you learn a feat where you memorize the cards in pairs. I've even developed a helpful quiz page to help you all along the way.

Before you even practice the feat, there is more work put into it than in the simulated memory feat above. However, this early work pays off in making the live work more effective, as you'll see.

As you link the cards to each other, the memorable images you create are developed and then dropped from your mind. If they're weird and creative enough, they'll come back to you with little effort. With enough practice in this legitimate memory version, recalling a single removed card won't be a problem. All you have to do is recall cards not linked to another card.

The process of discovering a missing card, however, requires that you mentally walk through each card's image (say, first all the clubs in order, then all the hearts in order, and so on) one by one to determine which one isn't linked to anything. You can even walk through this list verbally, as long as you make this interesting for your audience: “What about the Ace, 2 and 3 of clubs? I remember all those, as I do the 4...”

Even this way, it might be uninteresting to an audience. Fortunately, the legitimate memory version offers a very important feature that the simulated version can't - you can determined more than one card! You could very well recall 2 or more missing cards.

Funnily enough, since the more cards are removed, the more often you'll recognize missing cards, the legitimate memory version actually offers the added bonus of actually becoming easier and more interesting to present as more cards are removed!

You could, for example, have four 13-card bridge hands dealt out, memorize three of the hands, and recall what is in the fourth. Back in February 2009, I published Michael Frink's blackjack presentation for the card pairs in which you memorize 15 pairs of cards (30 cards total), and finish by recalling the remaining 20 cards!

So, does this mean that the legitimate memory version is better? That is actually up to you. If you're looking for a good occasional feat at the bar that you can not practice for a while, but call on when you need it, the simulated version might be the best way to go. If you're looking for a more authentic version, and you're willing to keep in practice, the legitimate version might be the way to go.

The best thing to do, either way, is to learn them both, so you know which one suits your needs better. I'd love to hear about any stories you have performing either one of these!

Admittedly, learning the Day of the Week For Any Date feat in the classical way can be quite challenging.

Not long ago, I designed the 2011 Dice Calendar iPad Cases, iPhone Cases, and iPod Touch Cases in order to simplify the feat with a hidden cheat sheet.

Now, I've gone a step farther, and I'm releasing free backgrounds with a similar design for most Android and iOS devices!

As with the cases, the basic idea of the backgrounds is to appear as a simple dice design, while secretly communicating the information you need to determine the day of the week for any date given.

You can download the .ZIP file directly from this link, and you can also download it any time by going to the Downloads page, and clicking on Dice Calendar Backgrounds.

When you unzip the file, you'll get a master directory called dice_calendar. This directory contains all the graphics for any given year. How is this possible? There are only 14 possible years, 7 leap years starting on any given day of the week, and 7 normal years starting on any given day of the week.

Let's say you want the graphic for the year 2011. You'd click on the Normal_Year_Starts folder (since 2011 isn't a leap year), and then on 6_Saturday, since 2011 starts on a Saturday.

By contrast, 2012 is a leap year that starts on a Sunday, so you'd click on the Leap_Year_Starts, and then click on 0_Sunday to find the correct graphics.

Inside that folder, you'll find 6 .PNG files, each for a different device. For Android devices, there are graphics available in HVGA resolution (320 by 480), WVGA800 (480 by 800), and WVGA854 (480 by 854) resolutions. For iOS devices, there are iPhone pictures (320 by 480), iPhone Retina Display pictures (640 by 960), and iPad pictures (1024 by 1024). Choose the appropriate picture for your device.

You'll need to consult the manuals for your device for information on how to install your chosen picture. Keep in mind that these are intended only as lock screens, as the dice will be obscured by pages with apps on them. In addition, the resolution of the Android images is insufficient for use on the home screens.

For 2011, the graphic would look similar to the following one (as seen on the iPad version):



How do you use it to determine the date? The presentation I suggest is first asking for a date in the current year, then talking about how you used to get out your mobile device, turning it on (which gives you a glimpse of the dice calendar background), and looking at your built in calendar (which you never actually do). Mention that you've done this so much, that you know this year's calendar by heart, and to prove it, you give the correct day of the week (which your audience members can verify)!

How exactly is the dice calendar used to determine this? Except for only minor changes in presentation, it's done the same way as with the cases:



Of course, the cases will only be altered as the year changes. With the free backgrounds, you're ready for any year that comes along! I hope you find this simplified version fun and useful.

This week's Scam School features a classic mathematical trick I haven't thought about for a long time.

I've mentioned “old” tricks before that date as far back as the 1920s or so, but this one can be found in a book that was first published in 1633! That's right, this trick is older than the United States of America.

The best way to start off is to show you the trick. Try and think about how it could be done before you watch the method.



The principle boils down to two simple ideas. If an object is in a corner, it is counted twice, otherwise, it is only counted once. This trick is so simple, in fact, that the presentation becomes all the more important in hiding the method. One of the nicer touches in Brian's approach above is assigning everybody a different side, making it harder to determine that some coins are counted twice.

To really expand the possibilities, there are several variations of the classic version taught in the video. The first variation is to perform the routine by having objects removed instead of adding them. Instead of compensating for an added object by moving objects away from the corners, you compensate for a removed object by adding objects to the corners. Also, instead of starting with a similar number of objects in the corners (such as 4 and 3 as in the above video), you'll generally want to start with a number of objects that's farther apart, such as 4 and 1. This is because the amount of objects in each corner will get closer and closer in number as you proceed.

Another variation is to vary the shape. There's nothing special about the square shape, except for its simplicity. While you could use 5 or 6 sides, larger numbers quickly get challenging to deal with for both the audience and the performer. In Jim Steinmeyer's book Impuzzibilities, he teaches a wonderful version called “Understanding the Bermuda Triangle”, which uses little paper airplanes arranged in a triangle to demonstrate the mysteries of the Bermuda Triangle.

Peter Marucci has a nice version of the Bermuda Triangle concept called Bermuda Runes, which almost makes it seem like the result of some ancient magic ceremony!

It's quite amazing to see the variety of ways performers have adapted this principle for their presentations. Lew Brooks, best known for his Stack Attack DVD, used to have a great version for kids shows involving cookies. He'd be helped by his own kid, or sometimes the birthday kid to whom he'd explain the basics beforehand.

In this version, Lew would arrange plates in a square, and show that 13 cookies were on each side. He would then turn to face the audience, start explaining how to make good cookies, while the kid would sneak up, take a cookie, and rearrange the remaining ones. Lew would turn around and ask the kid if he took any cookies. The kid would shake his head no (since he couldn't speak with a cookie in his mouth), so Lew would count and make sure each side still had 13 cookies, which it did.

As you can imagine, after the 3rd time of a kid taking the cookie, this gets to be really puzzling. Even before the audience realizes how bizarre this is, the tension between the kid trying to hide his cookie stealing and the adult makes it really enjoyable.

Because the principle os so obvious, the more you can keep the focus on the presentation, especially by adding mystery or comedy. What shape would work best? Should you add or remove object? What objects should you use?

In his book Life Savers, Michael Weber has a presentation he calls “To Feed Many”, in which raisins are removed from bowls without seemingly affecting the remaining number, and it's presented as a Buddhist ceremony for preventing hunger. Bill Herz and Paul Harris, in the book Secrets of the Astonishing Executive, on the other hand, use paper clips from the office to demonstrate the simple yet amazing nature of brainstorming at meetings.

Besides just being a fun trick, this routine is an excellent exercise in finding your own way to present and expressing who you are. Play around and leave a comment if you develop any fun and interesting angles!
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Answers to Sunday's puzzles:

1) There are several fallacious arguments in the video. First, getting paid for the day usually means getting paid for the time you worked that day, not for a full 24 hours, so he should still be $365 at this point. The 52 Sundays bit is correct, so we subtract that to get $313. Assuming the agreement is half pay for a half day, we'll subtract $26 for the Saturdays to get $287. Subtracting $14 for a two-week unpaid vacation gives $273. The hour for lunch, assuming it is supposed to be unpaid, is already covered in the time Abbott took for not working 24 hours, so we won't subtract any amount for this. Depending on the holidays mentioned, they may or may not cross over with the Sundays on which Costello didn't work. Unfortunately, this means it is impossible to determine exactly how much Costello should receive without reference to a specific year.

2) Two invalid assumptions are made to make this argument possible. The argument made here assumes that on each living person's family tree, no ancestor appears more than once, and that the same person never appears more than once in any family tree. If a couple has 3 children, then their parents will be parents on 3 different family trees, and the grandparents will appear on 9 different family trees. As stated in the original puzzle, millions of people are counted millions of times, which is where the large amount comes in.

3) The face-down card is the 6 of Hearts. The Ace of Hearts gives the suit, and the other 3 communicate how much greater than the Ace is the face-down card. First, the cards must be considered from low to high, but this gives us 5 as the low, and two 7s which seem to be equal. The suit ranking of CHaSeD must be taken into consideration meaning that the 5 is still low, but the 7 of Clubs is considered medium and the 7 of Diamonds is considered the high. This means the cards are being shown in High/Low/Medium order, which signifies 5. Ace of Hearts plus 5 equals the 6 of Hearts.

4) When calculating the odds of a given 5-card Poker hand, we must take all 5 cards into consideration. With the 4 of a kind, we only took 4 of the 5 into consideration. With any 4 of a kind, the 5th card can be any one of the 48 remaining cards. Multiplying the 13 possible values for the 4 of a kind times the 48 possibilities for a 5th card, we get 624 possible 4 of a kind handss, not 13. The straight flush calculation is correct, so you can see why any one of the 40 straight flushes are harder to get than any one of the 624 4 of a kind hands.

It's one thing to be able to do math well, whether on paper or in your head. It's often quite another thing to be able to keep the problem in context as you work through it.

Today, Grey Matters features puzzles concerning the ability to keep your numbers in context. The answers will be posted at the end of Thursday's post. Until then, feel free to post your answers in the comments.

• I'll start off with a fairly easy one to get the ball rolling. Watch the Abbott and Costello routine below, where Costello is trying to collect his pay. It starts at $365, and gets whittled down to $1 by Abbott's fast talking. He does it so well that it does make you wonder, what is wrong with Abbott's math? Just for fun, is it possible to work out how much Costello should receive?



• This next puzzle comes from J. Newton Friend's 1954 book Numbers: Fun & Facts, by way of the Futility Closet blog:

Here is a curious problem. We may safely assume that you had two parents; each of your parents had two parents, so that you had four grandparents. Arguing along similar lines you must have had eight great grandparents and so on. Assuming an average of three generations per century the number of your ancestors since the Christian Era began must have been nearly 1 trillion–

1,000,000,000,000,000,000 or 10¹⁸

This is vastly more people than have ever lived on the Earth. What can we do about it?

Obviously, this can't be right, but where is the flaw?

• This next puzzle requires familiarity with the Fitch Cheney 5 Card Trick, as taught in the previous post. A friend of mine was using the app mentioned in that post, and was shown the arrangement you see below. He stated that the face down card was the 7 of Hearts. If you know the trick, this seems to be the right card, but he was incorrect. What is the face-down card?



• Our final puzzle also deals with cards, but in the much more familiar game of Poker. In 5-card Poker, a straight flush (5 cards of consecutive value, all of the same suit) beats 4 of a kind (4 cards of the same value).

How many straight flushes are there? A straight flush can be as low as Ace through 5, or as high as 10 through Ace, so in any given suit, there are 10 possible straight flushes. Multiplying this by the 4 suits gives us 40 possible straight flushes.

How many 4 of a kind hands are there? They can consist of anything from 4 twos up to 4 Aces, so they can be any one of 13 different values. That means there are 13 different 4 of a kind hands.

This brings up an interesting question. If there are 40 ways to get a straight flush, but only 13 ways to get 4 of a kind, that means there are fewer ways to get 4 of a kind than a straight flush. In that case, why does a straight flush beat 4 of a kind?

As I mentioned above, answer the puzzles as best you can in the comments!

Back in 2008, I discussed the amazing Fitch Cheney Card Trick, and mentioned it again when James Grime's Pi Day Magic App was released.

As with all good Pi Day tricks, we need a Scam School episode to go with it!

Without further ado, here's Brian Brushwood teaching the Fitch Cheney Card Trick:



For convenience, you can download the free Pi Day Magic App here (iTunes Link), and use it to practice, or even perform the trick.

To learn more about this amazing trick, check out Numericana on the Fitch Cheney Card Trick and Fitch Four Glory, which is the same trick, but done with 4 cards!

Many of you watched the royal wedding at Buckingham Palace on Friday. Now that the wedding is over, the royal couple will be living in Wales while Prince William finishes his tour in the Royal Air Force.

Their Welsh home provides several excellent opportunities to challenge and improve your memory!

First, where is it? It's just off the western coast of England. Here in the US, most people only recognize the name from Prince Charles' title as Prince of Wales. Many may be surprised that, despite its proximity to England, they speak primarily Welsh.

Here's a video that shows the location of Wales, in the course of explaining the difference between Great Britain, the United Kingdom, England, and more:



While there are 22 Welsh unity authority areas (counties, boroughs, cities, etc.), thanks to the preserved counties of Wales, used largely for positions of sheriff and lord, you can get away with knowing only 8 areas.

These 8 major areas can be remembered with this poem by Peter Hobbs:

Gwent, Powys and Clwyd
(south to north) are borders 3,
next to South/Mid/West Glamorgan,
Dyfed, Gwynedd (with Anglesey).

Peter Hobbs also created another poem that helps you draw a simplified map of the Welsh preserved counties.

If you've practiced the poems and the map, it's the island of Anglesey where the royal couple is staying. As you can see from this story, the island features some beautiful scenery blended well with modern architecture.

While security cannot detail the exact location of their residence for obvious reasons, the royal couple are frequently seen in and around Llanfair PG. That's actually a shortened form of the name of the town.

It's full name is Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch, which is Welsh for “Saint Mary's Church in the hollow of the white hazel near a rapid whirlpool and the Church of St. Tysilio of the red cave”.

Locals learn to say the full name to impress tourists, but don't you think they'd be more impressed by a tourist who can properly say it?

Besides the length, there are two letter combinations that make the pronunciation of this town a little tricky. The “ch” sound isn't pronounced as in “cheese”, but rather as in “Bach” or the Scottish word “loch”. For Jeff Dunham and Achmed fans, this would be the famous “C-Phlegm” sound.

The other one is that “ll” sound, which doesn't sound at all like you'd expect. The closest thing in English is the “thl” sound, like in “athlete”. More accurately, it's a “th” sound at the end of a word or syllable (so, the Welsh word “Castell” would be pronounced “kass-teth”), and “thl” when it's starting a world (making the pronunciation of “Llan” as “thlan”).

To get the “th” inflection right, try saying the word “all”, and at the end of the word, note the position of your tongue in relation to your teeth, as well as the position of your lips. Now, keeping your tongue and lips in that same position, try and force an “sh” sound through your mouth!

The first few times you do it, you'll overemphasize it and sound like an annoyed cat. Tone down the emphasis so you can use it in a word, and you've got it. Here's more help on the Welsh “ll” sound.

So, how do you pronounce the full name? The train station sign below seems to help, but still doesn't take into account the difference between the Welsh “ll” sound and the English “ll” sound:



Fortunately, www.llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch.co.uk offers an excellent guide to pronouncing, and even understanding, each part of the name correctly. There's even a helpful sound file (.wav) consisting solely of the pronunciation of the town's name. I recommend using the Link System to help memorize the order of the sounds once you pronounce them.

Probably the most enjoyable way to learn the town's name is via Don Woods' song on iTunes, or via the following music video:



Amusingly, the actual sign used in the video had to be replaced in 2010 because it was misspelled! It was only one letter, but it's funny to think that a town that prides itself on such a long name wouldn't let something like that slip by for so long.