Michael Daniels, the webmaster behind the Mind Magician site, has just released a new PDF eBook called Speed Dating.
This eBook is his approach to one of my favorite feats, being able to name the day of the week for any given calendar date. Naturally, I couldn't resist taking a closer look.
Here are my thoughts on the bullet points from the Lybrary.com ad for Speed Dating.
* Easy calculations – The math used in this eBook is the classic approach to the day for any date feat. Most of it is simple addition. There has always been one sticking point that catches many people, but the author offers an ingenious solution to that, which I'll come back to later.
* Uses an innovative mnemonic method which is fully described – Again, if you're already familiar with the Peg/Major system (as discussed in Memory Basics), that is fully described. What is innovative here is the way the mnemonics are coded so as to bring the required key numbers to mind as quickly as possible. I do like that memorization of the year keys is emphasized here, as that's really the only way to go when speed is important.
* Simple counting technique that makes determination of the day fast and effortless – While I mentioned the one sticking point in the classic calculations, the ingenious counting method taught in Speed Dating overcomes that obstacle, and in a way that is simple to learn and use. The best part is that it overcomes the obstacle automatically. I really wish I could be more specific here, but I can't do so without giving away too much from the eBook.
* No props or gimmicks needed – This, of course, has always been one of the best things about the day of the week for any date feat, that you can do it without resorting to special props or gimmicks. Obviously, you should have some sort of perpetual calendar with you, but with the advent of mobile devices, you can usually find perpetual calendar apps without too much trouble.
* Intermediate level mentalism – Requires about two weeks’ learning and practice in order to perfect. A suggested learning schedule is included – Please pay attention to this point. If you're just beginning to learn magic, this probably isn't the best routine to learn. Once you've become more comfortable in front of an audience, and have a better idea of what to expect, this routine can be a good one. Additionally, you'll have a better idea of how to adjust for your performances and your audiences.
* Includes a browser application that enables you to practice and test your accuracy and speed (Internet connection not required) – The included HTML program is basically the same one found under step 4 of the author's online day for any date tutorial (there are a number of differences between that page and the eBook, BTW), but given its own page. The fact that it keeps your calculation time for the last question and an average is very helpful in improving your overall time.
Probably the best thing about Michael Daniels' Speed Dating eBook is the completeness. If you've thought about learning this feat, you can learn everything you need to know from this book. The counting method, the suggested learning schedule, the performance tips, and the included program are all valuable tools because of the way they aid in the learning and encouragement.
Speed Dating is available as a PDF eBook from Lybrary.com for only $10. If you practice and use the techniques in this eBook, this is a definite bargain.
Michael Daniels, the webmaster behind the Mind Magician site, has just released a new PDF eBook called Speed Dating.
Space is big. You just won't believe how vastly, hugely, mind- bogglingly big it is. I mean, you may think it's a long way down the road to the chemist's, but that's just peanuts to space.-Douglas Adams, The Hitchhiker's Guide to the Galaxy
I try to stress both memory and understanding on this blog, so I thought it might be fun to take a look at what astronomical scale really means in human terms.
Let's start in what you might term our own immediate neighborhood, with the Earth and the moon.
You might imagine that if the Earth were scaled down to, say, the size of a billiard ball. You might imagine that it would roll poorly, especially due to the mountains. Surprisingly, the Earth is actually smoother than a billiard ball, and if you don't believe me, you can click for yourself and check it out here.
Let's try a slightly larger ball. A regulation NBA basketball is 53.394 million times smaller than the earth. In other words, 1 inch on a basketball would scale up to 842.7 miles on the Earth (...or, a little less than the distance the Proclaimers would walk)!
If you scaled down the moon by the same factor, to what size ball would it be comparable? It's probably not to hard to guess that a tennis ball is about the right size. Here's a tougher question, though: If you wanted to scale down the distance from the Earth to the moon, how far away would you have to put the moon tennis ball away from the Earth basketball?
Surprised? Based on the average distance from the Earth to the moon, along with our scaling factor, the actual proper distance is about 23.66 feet, or more than two stories away. If you think that scale is big, we're about to get bigger.
Since we're talking about distances, let's try the entire solar system. Usually, when we see a picture of the solar system, it looks something like the NASA image in the upper left corner of this post, with the planets spread evenly apart. Just as with the Earth and the moon, that's not a true picture.
What happens if you scale down the sizes of the Sun, the planets, and their respective distances? Bill Nye demonstrates the scale with help from some models and his bicycle:
Even with a video demonstration like that, and the accurate measurement, you have to realize that they compressed the time to ride from one another to keep it interesting. To get a more immediate idea of the true distances, there's this site, which represents a 1-million-mile distance as a single pixel. This site, however, doesn't show the true relative sizes of the planets, since they're all represented by a single pixel.
If you think you can handle a site that gets both the relative sizes AND distances correct, check out phrenopolis.com's online solar system model. This model, on my screen, is about 1/7 billionth of the actual size. Even on that tiny scale, it took my browser 9 full seconds just to scroll to Mercury!
Ever seen the opening to the 1997 movie Contact? If you watch, you can easily see that either the trip through is speeding up, or that the solar system is not to scale. There's also another problem of scale in the intro, which is surprising, considering that the original story was written by Carl Sagan.
As you pass various astronomical bodies, radio sounds are playing, as if those were the most recent radio signals you could receive near those planets. By the time Saturn comes into view, we're listening to Volare, which first became a hit in 1958. So, is Saturn really just now getting 39-year-old radio signals?
Sorry, but that's not the case. Like all other types of waves in the electromagnetic spectrum, radio waves travel at the speed of light. Assuming you could exist on Saturn, and tune in Earth radio signals (while accounting for obstacles such as signal attenuation), you'd be listening with only an approximately 80-minute delay. Even Neptunian radio listeners, with a 4 hour and 10 minute delay (or so), could sing this week's musical hits, although Earth dwellers would still be more up to score on the day's Earth sports games.
If you really want an accurate and all-encompassing sense of scale, check out the classic education film, Powers of 10, keeping in mind the scale of 1 light year to 1 year ago for radio (and all other electromagnetic) waves:
The author of Mind Performance Hacks has a new book out, called Mindhacker: 60 Tips, Tricks, and Games to Take Your Mind to the Next Level.
Disclaimer: I was provided with the book by the publisher without charge, who was asked by the authors personally to provide Grey Matters with a copy. The thoughts below are purely mine as a result of going over the course on my own time for the purposed of informing Grey Matters readers.
Many regular Grey Matters readers are probably thinking, If it's being reviewed here, then it must be all about memory, math, and logic. Of the 9 chapters, only 2 involve those specific topics, but they're a good place to start.
Each chapter is broken up into 5 to 10 hacks, individual techniques that can improve your mental acuity. The great majority of these techniques are not simple re-hashes of classic ideas, rather they're either newer ideas with a solid basis, or classic ideas taken in new directions.
The Memory chapter, for example, talks about spaced repetition (which already has its own section in my Memory Tools page), but brings a new light on it by showing how this classic technique is more widely used with the advent of computers. You may have read about the classic memory palace technique, but it's brought up to date here by relocating it, into a dungeon, surprisingly (you'll have to read the book to find out how this is a modernization).
In the Math and Logic chapter, there are great hacks about topics such as how to use knowledge of common errors to your advantage, rolling mental dice, and the benefits of mixing induction and deduction with abduction.
The other chapters in the book cover learning, time management, creativity and productivity, communication, mental fitness, and clarity. With topics like these, you might expect a dry boring textbook style, but that's not the case with Mindhacker.
Sure, each hack is detailed, but never boring. As I went through it, I couldn't help but notice the emphasis on looking at old things in new ways and engaging in exercises whenever possible. Those of you who have Mind Performance Hacks might remember the occasional use of download computer programs to help in the exercises, which also happens here. There is a great sense of fun in each hack, but it never overpowers the original purpose, so as not to lose sight of a given hack's goal.
Obviously, as a non-fiction book, this isn't meant to be read from beginning to end. There are however, two basic ways to read it. Feel the need to improve, say, your mental creativity and productivity skills? Look that up in the table of contents, and find that section to learn more. Want to reread a particular hack, or look for a specific type of help for a mental challenge? Look through the second table of contents that covers both the chapters and individual hacks. This definite gives the book a more approachable feel.
Mindhacker really is a good match to Grey Matters readers, as it is all about improving your mind, and having fun while doing so. It's approachable, educational, fun, and neither intimidating nor condescending in tone. I highly recommend Mindhacker. If you haven't already picked up Mind Performance Hacks, do your mind a favor and pick them up together.
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.
Just when I thought I'd seen every mathematical puzzle there was, along come some new ones!
In this post, we'll take a quick look around the web at some astounding new puzzles that will challenge your mathemathics skill.
I'll start off with one I have run across before in Martin Gardner's books. It's from our old friend James Grime, and concerns the best strategy for playing a simple card game:
Try and work out a good strategy for this game by yourself first. When you want to verify your strategy, or just give up and see the answer, you can watch the follow-up video.
Next up, an impressive game of lying and truth-telling from Scam School. Watch it up to the break, and see if you can work out the logic for yourself before it's explained:
Yes, the above puzzles are variations on classics, so let's turn to the more unusual ones.
From Futility Closet, we have a puzzle concerning what happens when a barge crosses a crumbling aqueduct, with some amusing and admittedly bizarre details thrown in for fun.
Also from the same source, imagine you're given a right triangle, and you draw a square on its hypotenuse. Draw a line that bisects the triangle's right angle, and extend the line all the way through the square. Can you prove whether this line will always bisect the square? As soon as most people hear the phrase square on the hypotenuse, the natural assumption is that the answer will involve working through the Pythagorean Theorem. There's a much quicker and simpler way, however.
One good source of mathe puzzles, Mind Your Decisions, has been really going like gangbusters in recent weeks, in terms of releasing mathematical puzzles. Here are my favorites:
1) You have a solid gold bar, marked into 7 equal divisions as follows:
| – | – | – | – | – | – | – |
You need to pay an employee each day for one week. He charges exactly 1 piece of the gold bar per day. You are only allowed to make 2 cuts into the bar (and this is gold so don’t even think about “folding” the bar). How can you make the cuts to pay your worker one gold piece every day?
The answer is in Monday puzzle: paying an employee in gold.
2) You are given a container that holds 24 ounces of ball bearings. You have a balance but no weights for the scale. You want to measure exactly 9 ounces. How can you do it?
The answer is in Monday puzzle: measuring ball bearings.
3) The game is played with a deck of cards numbered 1 to 100, and its rules are as follows. First, you and I each draw one card from the deck and show them face up. Then, I then draw another card from the deck. In the end, I have two cards and you have one. I win the game if either of the following happens:
–The first card I drew is higher than your card
–The second card I drew is higher than the first card I drew
Because I have two different ways to win, I agree to payout more money to compensate for the odds. I will pay you $3 when you win, and you only have to pay me $1 if I win. Are you willing to play this game?
The answer is in Probability question: would you play this card game?.
4) (This is my favorite of the recent Mind Your Decisions posts.) Two friends were getting ready to eat some small snack wraps for lunch. One had 3 wraps, and the other had 5 wraps. A hungry man came along, and convinced the two friends to share their wraps. They cut the 8 wraps into 3 equal pieces, so that everybody could have 8 pieces, and nobody felt treated unfairly.
The hungry man thanked them, and gave them 8 gold coins in payment. The friend with 3 wraps thought the fairest split would be 4 gold coins to both, since the wraps were shared equally. The other friend thought it should be split as 5 and 3, since he had 5 wraps to start, and the other friend only had 3. What is the most fair division of the 8 coins?
The answer is in A fair division storytale.
5) The final puzzle concerns the fair division of land among 4 people, but the problem comes in the fact that the land is a rather unusual shape. You can see both the problem and the answer in Puzzle: how would you divide the land equally?.
If you like this last land-splitting problem, the same blog has another challenging land-splitting puzzle back in a November 2009 column.
How did you do? Were you able to get any of the answers to these on your own?
Welcome to September's snippets! This time, it's a digital edition, with a heavy iTunes Store influence. If you like the idea of and app I mention, but don't find that you can use it on your system of choice, you can search for a similar app for your system using Quixey.
(Note: There will be no post on Sunday, as Sunday is the 10th anniversary of the September 11th attacks. I will be getting together with friends and associates, spending it in remembrance of those who died in the attacks.)
• We'll start off with memory techniques. The best place to start is with the basics. Just learning the Link System? Check out Membox Free, a free iOS game which gives you more and more objects to remember. If you like it, its ad-free big brother goes for $1.99.
Maybe you're learning the phonetic alphabet for use in the Major/Peg System. In that case, check out NumberThink. This free iOS app both challenges you to translate between words and numbers, but also helps you look up words for numbers, as well.
• iVocAudio is a memory program that helps you remember things by having you record them in your own voice. It dropped to free yesterday (Sept. 7, 2011), and will probably only remain free for a short while, so if you like the idea, get it now. Update (Sep. 9, 2011): It's just gone back up to $1.99.
• If you want to learn to memorize a shuffled deck of cards quickly, check out the free How to memorize a deck of cards app. It uses the PAO (Person-Action-Object) system, as popularized in the book Moonwalking With Einstein.
• Speaking of books, there are a couple of app-based books on memory available for free. Check out How to Memorize Anything and the game/book combination The Best Memory Game & Memory Technique Most Effective.
• One of the more unusual apps is The Date Game, where you race through the calendar to be the first person to land on Dec. 31st. It's free, with a 99-cent charge for a clue on how to win. However, regular Grey Matters readers and Scam School viewers will already know not only how to win this version, but how to win while going backwards, too!
• Since I mentioned Scam School (iTunes Link), it's time to turn our attention to podcasts. Brian Brushwood's Pi Day and Pi Day 2 cohort, James Grime now has his own podcast on iTunes U, courtesy of the University of Cambridge! It's called Quite Easy Done (or QED for short). It's planned to contain not only his classic videos from YouTube, but new original content, as well.
• To round up this app-based column, I should update you on my progress with the new app version of Train Your Brain and Entertain. I've got all the quizzes from the original version working! My focus now is on developing the animated help system, where an arrow takes you through how to use each part of the interface. When that's done, I'll be creating in-app slideshows teaching the techniques themselves. After a little user-based testing, I'll be releasing it for sale! It shouldn't be too long now.
It's often joked that lotteries are a tax on people who are bad at math.
Being good at math can't always help you win, but it can help prepare you for that rare moment when that good opportunity comes along.
Probably the single most famous example of this is Edward O. Thorp. Like many others before him, he knew that the odds of blackjack changed as the cards were dealt. However, thanks to the use of computers, he was the first to work out how to take advantage of this fact. In this British documentary (story continues in part 2), here's a brief history about the invention of card counting:
On a somewhat smaller scale, Mohan Srivastava, a geological statistician from Canada, took advantage of the type of math he used at work everyday to find a flaw in a Canadian scratch-off game. The game had a tic-tac-toe theme, and the ticket featured exposed numbers, apparently placed in a random manner, arranged on several tic-tac-toe boards. You would then scratch off the hidden part of the ticket, and if any 3 of the numbers appeared in a winning tic-tac-toe arrangement on the board, that ticket was a winner.
Knowing that computers generated these tickets, and that computers have great difficulty with generating true random numbers, he was able to find the hidden flaw in this game. Due to the $50,000 limit of the game, he also realized that holding on to this secret himself wouldn't make him rich. He played a few games to verify his theory, and then turned his findings over to the Ontario Lottery Commission, who promptly pulled the game.
Sometimes, all it takes to get an advantage in a gambling game is to see a big enough disparity between the jackpot, the cost of playing, and the odds of winning.
When the city of Paris had to default on its municipal bonds, and offered a lottery as an alternative way for bondholders to at least hope to get their money back, a group of people including no less than Charles Marie de La Condamine and Voltaire realized that the combined cost of the tickets was much less than the jackpot being offered.
To take advantage of this, they put together a syndicate that bought up all the bondholder's tickets each month. This made the bondholders happy, because they were at least recouping the cost of their bonds. It made the syndicate happy, because they were guaranteeing themselves a generous profit each month. After 6 months, the government confronted them caught on and confronted the two about this. However, since what they had done was not a crime, there wasn't much the government could do.
This same principle still works today. An elderly couple in Massachusetts has taken advantage of that state's Cash WinFall game, which occasionally offers large jackpots to what is a relatively small number of players, to clear more than $1 million in winnings.
This type of principle has been used by many to gain an advantage in gambling games over the years. However, even with it's mathematical basis, even using this approach isn't always a sure thing.
When the Sheffield Owlerton Greyhound Stadium offered a record jackpot of £101,110.39 (roughly US$164,000) for correctly picking the exact winning order of 6 dogs in each of 6 races, one couple decided to run the numbers. It turned out that buying a ticket for every possible permutation would cost £46,656 (around US$75,000). Like the others above, the idea that they could guarantee themselves a big profit proved irresistible.
They made the bets, and yet still lost. How do you lose when you've covered every possibility? Two other parties held winning tickets, as well. This meant the jackpot had to be split 3 ways, giving each party £33,703.46 (over US$54,000), which was a net loss.
Even when the math is on your side, there's still no such thing as a sure thing when it comes to gambling.
Any type of math can inspire dread in a student, but algebra can cause confusion even students who have grasped all the prior math.
Why not make it fun? Try performing an algebra-based magic trick, and then having your students work through the process with algebra to see why it works. Strangely enough, Scam School is a perfect resource for this.
This week's episode of Scam School, featuring an amazing card coincidence, is a good place to start. Let's take a look:
At about 9 minutes into the video, notice that both one of the ladies and Brian Brushwood remark that they have no idea how it works (I imagine Brian probably does, but thought it was a better idea to keep everyone more at ease). The reason it works, of course, is algebra. It's time to take a closer look at the math.
The first mathematically significant step is the division of the 21 matches. All 21 matches must be divided between 2 people, and both people must have at least 1. So one person will have A amount of matches, which is at least 1 and no more than 20, and the other person has 21 - A matches.
Take a closer look at what this means. The smallest amount of matches either person can have, as already stated, is 1, with the other person having 20. What happens if we increase the number of matches from 1? With 2 matches, the other person will have 19, and so on up to 10, with the other person having 11 matches. As soon as we give the person with 10 matches 1 more match to make 11, then the other person winds up with 10!
Stated more simply, there will always be one person with a number of matches ranging from 1 to 10. We can't say who this is, but that doesn't matter any more than not being able to say how many matches each person is holding.
Naturally, at the end of the trick, you want the people to have 2 different cards, so how do you prevent them from having the same number? This is insured by the odd number of matches (21 in this video), and goes back to the old rule of an even number plus an odd number always being an odd number. If one person has an odd number of matches, then the other person must have an even number of matches for them to add up to 21. Further, since one person has an odd number of matches and the other even, they must have a different number of matches!
When this number is applied to choosing cards, that means they must be choosing cards at 2 different positions. Speaking of cards, it's time to turn our attention to them.
At this point, we know that one person is thinking of a card in position 1 through 10, and the other is thinking of a number at a position from 11 through 20. What happens when you remove those top 10 cards? Let's consider just the removal of the 10 cards first, without the reversal of the cards.
The removed packet, of course, contains one person's card, while the other person's card is still in the talon (remaining majority of the card deck). The position of the card which is still in the talon has, of course, been reduced by 10 cards. If it was the 11th card, it's now 11 - 10 = 1st card. If it's 20th, it's now the 10th card of the talon, and so on. Note that 11 through 20 is a total of 10 cards.
Let's take a look at this mathematically, defining A as the person who winds up with 1-10 matches:
So, we know A is in a packet of 10 cards somewhere, and we know B is in a different packet of 10 cards (well, 10 cards plus the remainder of the deck, but we know no selected cards are there). Thanks to the above formula, we also see that they share a definite relationship: B = 11 - A.
Think about this pattern. If one person's card is in position 1, the other person's card is at position 10 in the other pile. If one person's card is in position 2, the other person's is in position 9, and so on. In other words, wherever one person's card is, the other person's card is in the reverse position!
If either of the piles is reversed, it's not too hard to see that both cards would be in the same position in both piles! That's why exactly 10 cards need to be reversed in the trick, and why the trick itself works!
This is hardly scam school's only algebra trick, as well. If you understood the math here, try working out some of Scam School's other algebraic challenges, including Purloined Objects, Reading 5 Minds at Once (James Grime can help you work this one out), Mathemagic (I'll help you with this one), and The Trick That Fooled Einstein (this one practically GIVES you the algebraic equation!).
These are hardly the only Scam School episodes with algebra-based tricks, but they are the best places to start for getting interesting lesson ideas. Algebra is about finding patterns, even when you don't know the numbers involved. Therefore, the real trick is to get students interested in examining the pattern in the first place!