Yes, I could explain the method, but I don't want to ruin the fun and the mystery. Just enjoy the magic of the prediction for what it is, since that's how it's meant to be enjoyed.
Ever since I started this blog, I've been waiting for this day. I started Grey Matters on 3/14/05, specifically with the goal of having its 10th blogiversary on the ultimate Pi Day: 3/14/15!
Yes, it's also Einstein's birthday, but since it's a special blogiversary for me, this post will be all about my favorite posts from over the past 10 years. Quick side note: This also happens to be my 1,000th published post on the Grey Matters blog!
Keep in mind that the web is always changing, so if you go back and find a link that no longer works, you might be able to find it by either searching for a new place, or at least copying the link and finding whether it's archived over at The Wayback Machine.
This year, I began connecting my posts with the interest of the reader, and it worked well. My series of “Visualizing” posts, Visualizing Pi, Visualizing Math, and Visualizing Scale were the biggest collectively-read posts of the year.
My own personal favorite series of posts in 2011, however, was the Iteration, Feedback, and Change series of posts: Artificial Life, Real Life, Prisoner's Dilemma, Fractals, and Chaos Theory. These posts really gave me the chance to think about an analyze some of the disparate concepts I'd learned over the years when dealing with various math concepts.
After we lost Neil Armstrong in 2012, I was inspired to add the new Moon Phase For Any Date tutorial to the Mental Gym. A completely different type of nostalgia, though, drove me to post about how to program mazes. Admittedly, this was a weird way to kick off 2013.
With 999 posts before this one, this barely even scratches the surface of what's available at this blog, so if you'd made it this far, I encourage you to explore on your own. If you find some of your own favorites, I'd love to hear what you enjoyed at this blog over the years in the comments below!
With a new calendar year, you deserve a couple of new calendar feats to go with it. In this post, you'll learn how to quickly give the day of the week AND the moon phase for any date in 2015.
Even better, both of these feats are much easier than they sound!
DAY OF THE WEEK FOR ANY DATE IN 2015: The method to do this is quite simple, and is known as the Doomsday method, originally developed by John Horton Conway.
To work out dates in only 2015, all you have to remember is that 2015's "Doomsday" is Saturday. If you think about it, you can already work out any date in February using just this knowledge.
For example, Valentine's Day, Feb. 14th, must also be a Saturday, because it's exactly 2 weeks before Feb. 28th. How about Feb. 2nd (Groundhog Day)? Well, Feb. 7th is a Saturday, and Feb. 2nd is 5 days before that. What's 5 days before a Saturday? The answer is Monday! Therefore, Groundhog Day will be on Monday in 2015.
On which day will Christmas fall in 2015? We know from the technique taught in last week's videos that December 12th is a Saturday, so 2 weeks later, December 26th, is also a Saturday. Since Christmas is one day before that, it must be on a Friday!
When is July 4th this year? It's exactly 1 week before July 11th, so it must be a Saturday, as well.
St. Patrick's Day, March 17th, is 3 days after March 14th (Pi Day, mentioned in the videos from last week), so it's 3 days after a Saturday, making it a Tuesday in 2015.
January 15th is Martin Luther King, Jr.'s birthday, but what day does it fall on in 2015? January 3rd is a Saturday this year, and so is January 17th (2 weeks later). Take back 2 days, and we get January 15th being a Thursday this year!
With the knowledge from last week's videos, and a little practice, you can quickly and easily determine the day of the week for any 2015 date. You could get practice at the Day For Any Date (Mentalist Challenge) page, changing the year to 2015, and then trying to determine the date before you click the Show button.
When you're demonstrating this ability for someone, it's nice to be able to prove that you're right about the date. I use Wolfram|Alpha and/or timeanddate.com's calendars.
MOON PHASE FOR ANY DATE IN 2015: 2 years ago, I posted a new tutorial about determining the moon phase for any date. Similar to the year calculations, focusing on a particular year, such as 2015, greatly simplifies the required calculations. Like the doomsday algorithm above, this formula was also developed by John Conway.
In fact, working out the moon phase for any date in 2015 is even simpler than working out the date! How simple is it?
(Month key number + date + 8) mod 30
It's probably best if I explain each part:
Month key number: January's key number is 3, February's key number is 4, and all other months' keys are their traditional numbers; March is 3, April is 4, May is 5, and so on up to December, which is 12.
Date: This is simply the number represented by the particular date in the month. For the 1st, add 1. For the 2nd, add 2. For the 3rd, add 3, and so on.
+ 8: The addition of 8 takes the starting point of 2015 into account, which is why this particular formula works ONLY for 2015.
The resulting number will be the approximate age of the moon in days, from 0 to 29. This formula only gives an approximation, so there's a margin of error of ±1 day.
As an example, let's figure the phase of the moon on July 4, 2015. July is the 7th month, and the 4th is the date, so we work out (7 + 4 + 8) mod 30 = (11 + 8) mod 30 = 19 mod 30, which is just 19.
In that example, we estimate the age of the moon to be 19 days old.
What exactly does the age of the moon in days mean in practical terms? Here's a quick guide:
0 days = New moon (the moon is as dark as it's going to get)
0 to 7.5 days = Waxing crescent (Less than half th moon is lit, and it's getting brighter each night)
7.5 days = 1st quarter moon (Half the moon is lit, and gets brighter each night)
7.5 to 15 days = Waxing gibbous (More than half the moon is lit, and getting brighter each night)
15 days = Full moon (The moon is as bright as it's going to get, and will start getting darker each night)
15 to 22.5 days = Waning gibbous (More than half the moon is lit, and it's getting darker each night)
22.5 days = 3rd quarter moon (Half the moon is lit, and gets darker each night)
22.5 to 29 days = Waning crescent (Less than half the moon is lit, and it's getting darker each night)
So, our 19 day old moon from our example, with a plus or minus 1-day margin of error taken into account, means that the moon could actually be 18-20 days old, so it will likely appear less than fully lit, and getting darker each night. You can even verify this with Wolfram Alpha, or even timeanddate.com's calendars.
If you have any experiences or thoughts you'd like to share about memorizing the dates and moon phases for the 2015 calendar, I'd love to hear about them in the comments below!
People are often confused as to why the dates of Easter moves around so much from year to year. It moves so much much because Easter is the first Sunday after the first full moon after the first day of spring.
If this sounds confusing on its own, consider that the Roman Catholic and Eastern Orthodox churches use different calendars, which can yield different dates as a result!
Thanks to the work of John Conway, though, it is possible to work out the date of both Roman Catholic and Orthodox Easters in your head!
Some basic understanding and practice are all that's really needed to be able to calculate the Easter date in your head for any year from 1900 to 2099. In order to help make everything clearer, I've posted my new Easter Date For A Given Year tutorial over in the Mental Gym. To make it easier to learn, the tutorial is broken up into several steps:
• The introduction explains the rules for Easter calculation in detail, as well as what you need to know to get started.
• The next section explains how to calculate the date of the traditional Roman Catholic Easter. After learning how to work out the date of the Paschal full moon (the first full moon after the first day of spring in a given year), you then learn how to work out the date of Easter for that same year.
• If you want to impress others by performing this feat, there's an entire section of presentation tips that can help make this feat entertaining.
• The method for calculating the date of Orthodox Easter is covered another section, as well. Assuming you can work out Roman Catholic Easter, there are surprisingly few changes involved in working out the Orthodox Easter date.
• Finally, there's another section for those adventuresome souls who want to venture on and work out Easter dates in other centuries. Here you can find out what changes need to be made to the original calculations.
Since practice is important, I've also developed a set of interactive Easter date quizzes. Since you work through each section verbally in a step-by-step manner, the quizzes work the same way. In the first quiz, you simply work out the paschal full moon date for Roman Catholic Easter. In the next quiz, you're asked about the paschal full moon and Easter dates. The Orthodox quizzes are similar, and start with the Roman Catholic dates first, since you need that information as a starting point.
If you put in a little understanding, a little practice, and a little time, you may surprise yourself (and others) with an impressive new skill!
This month, we're going back to some favorite topics, and provide some updates and new approaches.
• Let's start the snippets with our old friend Nim. The Puzzles.com site features a few Nim-based challenges. The Classic Nim challenge shouldn't pose any difficulty for regular Grey Matters readers.
Square Nim is a bit different. At first glance, it might seem to be identical to Chocolate Nim, but there are important differences to which you need to pay attention.
Circle Nim is a bit of a double challenge. First, you may need to try and figure it out. Second, the solution is images-only. Once you realize that different pairs of images are referring to games involving odd or even number starting points, it shouldn't be too hard to understand.
• Back in July 2011, I wrote a post about hyperthymesia, a condition in which details about every day of one's life are remembered vividly. That post included a 60 Minutes report about several people with hyperthymesia, including Taxi star Marilu Henner. Earlier this year, 60 Minutes returned to the topic with a new story dubbed Memory Wizards. This updated report is definitely worth a look!
For those familiar with Doomsday algorithm, this isn't yet another variation of John Conway's fine work. Instead, I started with Durbin and Rogent's unusual and simple approach to dealing with the year, and adjusted the math so it meshed with Goddard's powerful work. The exact details and credits are given at the bottom of each section of the tutorial.
The result is a calendar creation routine that's quick and simple to learn, yet powerful enough to let you create calendar for any month and year back to 45 B.C., when the Julian calendar was first used!
To help you practice it more effectively, I've also developed a quiz page. The initial quizzes are simple, in order to help you master the calculation and recall required by each step, and then there's a more complete quiz, which simply has you create a calendar month for random dates. Some of you may recognize this as a modified version of my calendar quiz from Day One.
If you've never tried to do a calendar calculation before, try this out, and you might surprise yourself. If you've tried to do calendar calculations before and given up because of the difficulty of other methods, try the Quick Calendar Month Creation tutorial, and see the ease and power of this approach. Either way, I'd love to hear what you think about it in the comments!
I love it when two old friends visit and get along!
Numberphile recently took a look at one of my favorite challenges: The Knight's Tour! This is a chess-based puzzle that challenged some of the greatest minds in mathematics.
When it's a new challenge, it can seem quite difficult. Often, you get past about 50 squares, and then start having difficulty. If you want to be able to tackle this challenge, I have provided a complete Knight's Tour tutorial over in the Mental Gym. If you can understand and remember a few simple patterns, you can not only solve the Knight's Tour starting from anywhere, you can even have someone select a starting AND ending position, and still be able to solve it!
My dropbox version of the Knight's Tour offers various settings, including the ability to show a numbered path, as in the video. This version also auto-detects whether the numbered path is a semi-magic square, as discussed in the video, starting at about the 2:23 mark.
If you can learn to solve it, as in the Mental Gym tutorial, is it possible to learn to start anywhere and create a semi-magic knight's tour square? The answer is almost. Magician Harold Cataquet has done some incredible work on working out just how to do this, and it's written up in the ebook Mind Blasters, by Peter Duffie. If you're really interested in being able to the Knight's Tour AND finishing with a semi-magic square, the article is worth the price of this one book alone.
As Brady mentions in the video, there's an amazing amount of mathematical research done on the Knight's Tour. You can see many of the directions in which this challenge was taken over at Knight's Tour Notes, for a start.
Play around and enjoy the Knight's Tour. If you have any interesting discoveries you'd like to share, I'd love to hear about them in the comments!
With a new calendar year, you deserve a couple of new calendar feats to go with it. In this post, you'll learn how to quickly give the day of the week AND the moon phase for any date in 2014.
Even better, both of these feats are much easier than they sound!
DAY OF THE WEEK FOR ANY DATE IN 2014: The method to do this is quite simple, and is known as the Doomsday method, originally developed by John Horton Conway. Don't worry, learning this method for one particular year is very simple.
The "Doomsday" from which the method gets its name always refers to the last day of February, whether it's the 28th or 29th. For 2014, the "Doomsday" is Friday (Feb. 28th, since it's not a leap year). If you think about it, you can already work out any date in February using just this knowledge.
For example, Valentine's Day, Feb. 14th, must also be a Friday, because it's exactly 2 weeks before Feb. 28th. How about Feb. 2nd (Groundhog Day)? Well, Feb. 7th is a Friday, and Feb. 2nd is 5 days before that. What's 5 days before a Friday? The answer is Sunday! Therefore, Groundhog Day will be on Sunday in 2014.
It's also fairly simple to learn the even-numbered months. There's a very simple pattern to remember them: 4/4 (April 4th), 6/6 (June 6th), 8/8 (August 8th), 10/10 (October 10th), and 12/12 (December 12th) will always fall on the same day of the week as the "Doomsday" (the last day of February, remember?).
On which day will Christmas fall in 2014? We know December 12th is a Friday, so 2 weeks later, December 26th, is also a Friday. Since Christmas is one day before that, it must be on a Thursday this year!
The odd months aren't much harder, but the patter is not the same. 5/9 (May 9th) and 9/5 (September 5th) will also always fall on the Doomsday, as will 7/11 (July 11th) and 11/7 (November 7th). This is easy to remember with the following simple mnemonic: "I'm working 9 to 5 at the 7-11". It helps you remember that 9 and 5 always go together, as do 7 and 11.
When is July 4th this year? It's exactly 1 week before July 11th, so it must be a Friday, as well. If you've got all the previous dates down, you've already got the mental capability to determine the date for 10 out of the 12 months!
The easiest way to handle March is to think of Feb. 28th as also being "March 0th". Working forward from March 0th, it's easy to see that March 7th, 14th, 21st and 28th will all be Fridays. St. Patrick's Day, March 17th, is 3 days after March 14th, so it's 3 days after a Friday, making it a Monday in 2014.
In January, it's usually the 3rd day of the month that falls on the Doomsday. In a leap year, however, January 4th falls on the Doomsday. Remember it this way: "3 times out of 4, it's January 3rd. On the 4th year, it's January 4th." In 2014, since it's not a leap year, you only have to recall that January 3rd is on the Doomsday (Friday, for 2014).
January 15th is Martin Luther King, Jr.'s birthday, but what day does it fall on in 2014? January 3rd is a Friday this year, and so is January 17th (2 weeks later). Take back 2 days, and we get January 15th being a Wednesday this year!
With the above knowledge, and a little practice, you can quickly and easily determine the day of the week for any 2014 date. You could get practice at the Day For Any Date (Mentalist Challenge) page, changing the year to 2014, and then trying to determine the date before you click the Show button.
When you're demonstrating this ability for someone, it's nice to be able to prove that you're right about the date. I use QuickCal on my iPod Touch (similar calendar are available for many portable devices).
MOON PHASE FOR ANY DATE IN 2014: 1 year ago, I posted a new tutorial about determining the moon phase for any date. Similar to the year calculations, focusing on a particular year like 2014 greatly simplifies the required calculations. Like the doomsday algorithm above, this formula was also developed by John Conway.
In fact, working out the moon phase for any date in 2014 is even simpler than working out the date! How simple is it?
(Month key number + date - 3) mod 30
It's probably best if I explain each part:
Month key number: January's key number is 3, February's key number is 4, and all other months' keys are their traditional numbers; March is 3, April is 4, May is 5, and so on up to December, which is 12.
Date: This is simply the number represented by the particular date in the month. For the 1st, add 1. For the 2nd, add 2. For the 3rd, add 3, and so on.
- 3: The subtracting of 3 takes the starting point of 2014 into account, which is why this particular formula works ONLY for 2014.
The resulting number will be the approximate age of the moon in days, from 0 to 29. This formula only gives an approximation, so there's a margin of error of ±1 day.
As an example, let's figure the phase of the moon on July 4, 2014. July is the 7th month, and the 4th is the date, so we work out (7 + 4 - 3) mod 30 = (11 - 3) mod 30 = 8 mod 30, which is just 8.
In that example, we estimate the age of the moon to be 8 days old.
What exactly does the age of the moon in days mean in practical terms? Here's a quick guide:
0 days = New moon (the moon is as dark as it's going to get)
0 to 7.5 days = Waxing crescent (Less than half th moon is lit, and it's getting brighter each night)
7.5 days = 1st quarter moon (Half the moon is lit, and gets brighter each night)
7.5 to 15 days = Waxing gibbous (More than half the moon is lit, and getting brighter each night)
15 days = Full moon (The moon is as bright as it's going to get, and will start getting darker each night)
15 to 22.5 days = Waning gibbous (More than half the moon is lit, and it's getting darker each night)
22.5 days = 3rd quarter moon (Half the moon is lit, and gets darker each night)
22.5 to 29 days = Waning crescent (Less than half the moon is lit, and it's getting darker each night)
So, our 8 day old moon from our example, with a plus or minus 1-day margin of error taken into account, means that the moon could actually be 7-9 days old, so it will likely appear as close to half lit, and getting brighter each night. You can even verify this with Wolfram Alpha.
If you have any experiences or thoughts you'd like to share about memorizing the dates and moon phases for the 2014 calendar, I'd love to hear about them in the comments below!
From the videos, I gather the producer is a teacher, and tends to make these videos in the fall, presumably for the students. Personally, I enjoy these videos and the creativity used in developing these mnemonics. I'll definitely be keeping an eye on eveRide's channel, and bring you more as they become available.
The advice in Mental Floss' star navigation post is good as far as it goes. Yes, there are really only a few constellations you need to know to find your way around the sky, but the column stops short of practical teaching.
A website called quietbay.net used to feature a great tutorial on finding the important constellations, but that site has vanished from the internet. Fortunately, the Internet Wayback Machine has come to the rescue!
Here is the archived version of quietbay's clear, visual, and interactive constellation tutorial. It only takes about 15-20 minutes for the full tutorial. Being an archived version, there are a few images missing here and there, and only once or twice are those missing images are essential to finding the stars in the tutorial, but overall, it's still quite workable, and will quickly teach you how to located Polaris, Betelgeuse, Orion, the Big Dipper, Cassiopeia, and even Jupiter, if it's in the sky.
You should also note that it's a northern hemisphere-based tutorial, so the constellation Crux isn't included. Unless you're viewing from the southern hemisphere or the northern tropics, you won't be able to see Crux. If you can see it, Crux is one of the easier constellations to locate.
Try out the tutorial, read the Wikipedia article on Crux, and practice with the real night sky, and you'll be amazed how quickly you can get a good, basic knowledge of the night sky!
Logarithms are percieved to be very difficult, or even mysterious. If you take the time to understand them, however, they're not mysterious or difficult, and they can even make some things easier for you! Let's get right to the basics.
If you're familiar with exponents, such as 102, logarithms are basically just a way of rearranging the exponent problem in a different way. This video will explain that idea in a little more detail:
While that boils down what logarithms are, the only real use they describe in that video is the pH of pool water, and it doesn't delve into that much. Over at BetterExplained.com, they have a great article on Using Logarithms In The Real World that gives you a better grasp of their importance. It's a must read on the topic!
Besides showing the use of log tables, this video also introduces one of my favorite aspects of logarithms. It takes most arithmetic operations and simplifies them in an interesting way. Multiplication becomes addition, division becomes subtraction, exponents become multiplication, and roots become division. In short, logarithms can almost seem like cheating, as they turn more difficult operations into simpler ones!
Even though you see seemingly endless pages of log tables in the video above, it is possible to work out logs in your head, and with much less memorization than you might think. I be derelict in my duty at Grey Matters if I didn't show you how to do something along these lines!
You don't even need to do any mental calculation to take advantage of the power of logarithms. Go back and read my Benford's Law post. It features a quick lesson from James Grime and a Scam School video that shows you how to take advantage of Benford's Law in a very clever way.
Take some time and learn about logarithms. There's plenty to discover, learn, and enjoy about them!
As you may know from my Nim posts, I'm fond of games that can be analyzed to assure an advantage over someone.
Instead of yet another version of Nim, however, today we're going to look at another classic game, known as GHOST. It's a verbal word game, so the only item needed is some sort of resource, such as a dictionary, which will dictate which words are legal, and which words are not.
There are several variations of GHOST, but I'll only be focusing on the classic version of the game. In order to assure an advantage, I'll also only be focusing on a game with 2 players in American English.
A player is chosen at random to start the game, and begins by naming any letter of the alphabet. Players then take turns to add letters to this fragment, with the aim being to avoid completing an actual word. The player whose turn it is may - instead of adding a letter - challenge the previous player to prove that the current fragment is actually the beginning of a word. If the challenged player can name such a word, the challenger loses the round; otherwise the challenged player loses the round. If a player bluffs, or completes a word without other players noticing, then play continues. When a round ends, play generally passes to the left.
If any score is kept at all, the traditional method uses the letters of the word "Ghost" in the same fashion as the basketball game horse, with each loss giving the player the next letter of the word, and a player being eliminated when they have all five letters.
It's easy to see how Nim can be analyzed mathematically, but how is a game like this possible to analyze when we're restricted to words of a given language?
In a 2-player game, the first player can win by forcing the 2nd player to complete a word with an even number of letters. Similarly, the second player can win by forcing the 1st player to complete a word with an odd number of letters.
As I mentioned above, there must be some sort of reference book used as the standard for legitimate words. Traditionally, when playing this game, you'd carry around a dictionary. Today, it's easier to play with a reference which is accessible from a mobile device. Over in zyzzyva.net's word list page, there are several good word lists, with definitions, that will work for this. For reasons that will be explained later, I highly recommend the Official Scrabble Player's Dictionary 4 list.
Once you have a standardized list, it's possible to work out your best strategies. How? Basically, you're looking for letter combinations that limit the choices to only odd (for strategies where you're the 2nd player) or only even choices (for strategies where you're the 1st player).
This basic idea was first discussed in Word Ways in the early 1970s in a piece titled “Our Move”. It was written about again, in “Pocket Ghost”, but the most impressive work done was by Alan Frank in 1987, using the Official Scrabble Player's Dictionary (OSPD), in “Ghostbusted”.
Alan Frank's usage of the OSPD is why I recommended that particular word list link above. Do note that Mr. Frank considered words from there that only used up to 9 letters, while the linked word list included words up to 15 letters. You'll probably want to either verify that the strategies still work with the OSPD4 list and/or whittle down the list to insure your advantage. If you do the latter, you'll obviously need to store it somewhere on the web, and give it an easy-to-type and easy-to-remember link.
Once you have a set of words with which you're comfortable, how do you access them? Not surprisingly, I advocate memorizing the needed words. This sounds like plenty of work, but if you use the Link System, as taught in these videos, and memorize the words in order from shorter to longer, then the process can be more fun than you probably thought.
Challenge yourself to win, and then challenge your friends. If you've found any resources that aid in winning at GHOST, I'd love to hear about it in the comments!
If you've ever practiced determining the day of the week for any date in your head, especially if you've used one of my methods such as the version I teach in the Mental Gym or Day One, you've probably run into the fact that these methods really only work back to seemingly random dates, such as Sept. 14, 1752 or Oct. 15, 1582.
This is due to the switch from the Julian calendar to the Gregorian calendar, as well as the fact that the calendar calculation formulas are designed only to work with the latter. What if you'd like to calculate dates in the Julian calendar?
In today's post, you'll learn how to handle Julian dates all the way back to the 200s!
The first official switch from the Julian to the Gregorian calendar happened in 1582, as noted in the video below. October 4, 1582 was not followed by October 5, but by October 15, 1582, effectively skipping 10 days.
Since the switch was made due to the inaccuracy of the Julian calendar, the question becomes one of how to compensate for the change? As mentioned above, the change in the 1500s was only 10 days, yet in the 1700s it was an 11-day change.
To start, take the given year, and drop the last (rightmost) 2 digits. For example, 1491 becomes 14, an 943 becomes 9. This century number, which we'll call x, can be used to find the number of days that need to be added to the Julian date, in order to get the corresponding Gregorian date.
UPDATE (June 3, 2013):I've run across a much easier formula for determining the days needed to go from the Julian to the Gregorian calendar. I'll post the updated method here, and keep the method from the original post below the line.
Once you've got the century digits as x, multiply it by 3. If 3x isn't already a multiple of 4, round it up to the next multiple of 4. Once you've done that, divide the number by 4, subtract 2, and you've got your answer!
For example, let's find the adjustment needed for the 1200s. In this case x = 12, and 12 × 3 = 36. 36 is already a multiple of 4, so there's no adjustment at this point. Finally, we divide by 4 and then subtract 2, so 36 ÷ 4 = 9, and 9 - 2 = 7. This means we add 7 days to Julian dates in the 1200s to get the corresponding Gregorian dates.
What about the 900s? 9 × 3 = 27, which isn't evenly divisible by 4, so we round it up to the next multiple of 4, which is 28. 28 ÷ 4 = 7, and 7 - 2 = 5, so we would add 5 days to any Julian date in the 900s to get the corrresponding Gregorian date.
Naturally, once you have the correct Gregorian date, you can use standard calendar formulas to get the day of the week for the given date.
Since I posted this on May 30, 2013, let's try the Julian date of May 30, 1013. What would the corresponding date be in the Gregorian calendar? 10 × 3 = 30, and we round 30 up to the next multiple of 4, which is 32. 32 ÷ 4 = 8, and 8 - 2 = 6. Now we add 6 days to May 30 to get May 36, or more accurately, June 5th (36 - 31 days in May = 5). If we double check with Wolfram|Alpha, we see that May 30th, 1013 in the Julian calendar is indeed June 5th, 1013 in the Gregorian calendar.
Once you have a Gregorian date, you can treat it as you would any other date in your system. With practice, you can now go back as far as the 200s, since the adjustment for the 200s is 0. You can actually go farther back, but the calculations have additional things you have to deal with, such as negative adjustments, and compensation for date with BC or BCE before them.
In performance, and with a little practice, you can buy yourself the extra time needed for this extra calculation by performing the calculation while explaining briefly about the Julian and Gregorian calendars. Practice with Julian dates, and you'll surprise yourself with a wider range on your calendar calculation abilities!
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ORINGAL POST:
It's done with the following formula:
Those funny-looking brackets with an upside-down L-shape simply mean to round any fractional answer you get upwards. Mathematicians and programmers know this as the ceiling function.
As a simple first example, let's assume we're working with a date in the 1200s. For any such date, we drop the last 2 digits, leaving us with x = 12. First, subtract x from 16: 16 - 12 = 4. Next, divide that result by 4: 4 ÷ 4 = 1. Finally add that result to x again, and subtract 6: 1 + 12 - 6 = 13 - 6 = 7.
Naturally, once you have the correct Gregorian date, you can use standard calendar formulas to get the day of the week for the given date.
That 1200s example worked out nicely because 4 divided by 4 comes out even. What about when we're dealing with a century that doesn't work out so neatly? Let's try a date in the 900s.
For the 900s, of course, x = 9, so let's start going through the formula again. The first step is 16 - 9 = 7. Next, we have to work out 7 ÷ 4. The exact mathematical answer is 1.75, but since the next step is to round up any fractional answers (remember the upside-down L-shaped brackets?) up, all you really need to know is that 7 ÷ 4 = “1 and some extra”. When you round this up, you get 2.
Since I posted this on May 30, 2013, let's try the Julian date of May 30, 1013. What would the corresponding date be in the Gregorian calendar? We know x = 10, so 16 - 10 = 6. Next, 6 ÷ 4 = 1 and some more, which rounds up to 2. 2 + 10 - 6 = 12 - 6 = 6, so we need to add 6 days to get the Gregorian date. May 30th + 6 days = May 36, or more accurately, June 5th.
I just ran across a new Bill of Rights mnemonic video recently. Instead of using the whole body, this one uses various hand arrangements involving 1 to 10 fingers for each of the corresponding amendments:
Some of the hand arrangements need some further explanation.
For the 4th amendment, prevention of unreasonable search and seizure, the 4 fingers are wrapped around the thumb just as you would if you were a police officer knocking on a door with a warrant.
The 9th amendment refers to rights not specifically mentioned in the Constitution. When you're holding 9 fingers out, one thumb is hidden, but everyone know it's still there, just like the rights that aren't mentioned.
Those of you in the US are probably spending Mother's Day honoring your mom, so I'll just sneak a wide variety of snippets in today, and you can check them out later.
• Jan Van Koningsveld, along with Robert Fountain, has released a new book that will be of interest to Grey Matters readers, titled, The Mental Calculator's Handbook (Amazon link). If you're not familiar with Jan Van Koningsveld, he was able to identify the day of the week for 78 dates in 1 minute at the World Memoriad. I haven't had a chance to read this book myself yet, but his reputation does suggest the book is worthwhile.
• Starting back in 2008, I kept track of assorted online timed quizzes, the type of quizzes that ask you how many Xs you can name in Y minutes. I found these so fun, useful, and challenging, I even developed my own timed quiz generator, and even posted several original timed quizzes created with it. However, sporcle.com, home to numerous timed quizzes (despite starting out as a sports forecasting site) has gone and outdone this. Not only can you create your own timed quizzes, you can also embed them on your own site now! Find a quiz you like, for example, this landlocked states quiz, go down to the info box below the quiz, and click on Embed Quiz. A pop-up will ask whether you want a wide or narrow window (minimum width is 580 pixels), and you will be given the proper embed code, which can be used in a manner similar to YouTube embed codes.
• For those of you who do the Fitch-Cheney card trick, as taught on Scam School or YouTube, Larry Franklin has posted a simple tutorial on using Excel to practice this routine. As long as you understand your favorite spreadsheet program well enough, it's also not hard to adapt. It will take a while to create in the first place, but once it's ready, it's fairly easy to use.
• One of the most useful card memory feats to learn is memorizing basic blackjack strategy. Over in reddit's LearnUselessTalents section, user Tommy_TSW posted an interesting approach for memorizing this using your favorite video game, movie, or TV characters. Basically, you create a battle scenario for every possible situation, and when the various cards come up, you simply recall the corresponding battle (and result). Depending on the particular variation of blackjack you're playing, basic strategy can change, so you might want to calculate the right moves using basic strategy calculators at places like Wizard of Odds or Online-Casinos.
• Fans of the game Nim will enjoy this online version, playable even on all mobile devices. It's standard Nim, meaning that the last person to remove a card is the winner. It's simple, straightforward, and a good way to practice solo.
Many of the memory feats I teach require plenty of practice.
Today's mnemonics however, are short and sweet, and so they don't require much practice. As a bonus, they're all based on something you always have handy - your hand!
This first mnemonic is probably familiar to you already. It's a way of using your knuckles to recall the lengths of each month.
Make two closed fists, and put them together so you're looking at the back of your hands, with the sides of your first fingers touching each other, as in the illustration below. As you can see, all the months located on knuckles have 31 days, and all the months located between knuckles are only 30 days long, or shorter in the case of February.
A similar, yet less well-known mnemonic, uses a piano keyboard. Starting on the F key as January, continuing with the F# (F sharp) key as February, and so on, ending with December on the E key, all the months represented by white keys will have 31 days, while all the months represented by black keys have 30 or fewer days.
Next, we move from the knuckles to the pad at the base of your thumb, which can be used, surprisingly, to tell you how a steak feels at various cooking levels. The graphic below explains this simply:
Using hands for mnemonics is hardly a new idea. In fact, many of the imperial measurements, such as inches, feet, yards, and miles, were originally based on measurements of various parts of the body. In fact, knowing the exact measurements of various parts of your own particular body (assuming you're not still growing) can be very helpful in making accurate measurements without a rule. On Quora, Peter Baskerville explains which measurements are the most useful to know.
Back in the days when few people went any further from their home in their lifetime than 7 miles, basing the measurements on one's own body was the quick and simple. As wider travel and communication became possible, this caused some confusion, as in the classic cautionary tale about the Queen's bed:
If you get stuck finding a certain person for your PAO system, here are links to lists totaling 10,000 famous people to help. No actions are objects are included, as these need to be developed based on how you imagine each of these famous people.
• For Windows users, there's a new free program available, simply titled Memorization Software. It's designed to help you remember various types of texts, such as lyrics, poems, and speeches word for word. The tutorial video below (no audio) gives you an idea of the various approaches used here.
If you like this approach, but don't have a Windows machine (or even if you do!), my web app Verbatim 2 (Video Tutorial link) is also free, works in a similar manner, and runs in any modern browser.
Scam School's newest episode is right down the alley of many regular Grey Matters readers.
Their 265th episode teaches how to memorize a list of 20 items very quickly. This is a classic feat and a classic technique, but it's a rare treat to see it actually performed.
As you see it performed in the video above, it's a pretty bare bones technique. That's a great way to learn it, but there are other handy tips that can take it to another level.
First, as the items are called out, make sure to specifically ask for objects you can encounter in everyday life. That way, you don't get hard-to-picture images such as sickle cell anemia, as in the video. Hopefully, you don't encounter maggot-infested tacos, either, but at least it's easier to picture.
Also, ask for more details. If someone calls out a car, ask for a specific model of car, or even the color. This additional level of detail makes the feat seem more difficult, but actually makes the image more vivid, and thus easier to remember.
In the video above, you always see them calling out numbers, and having the item given in return. As long as you've formed your images effectively, there's no reason you can't have them call out the items and give the number in return, as well.
Once you've memorize the list, and they're starting to call out numbers or items, each time you recall the image, imagine your mnemonic frozen in a block of ice. If someone calls out 2, and you recall that's a unicorn, imagine the unicorn with a shoe for a horn frozen in a block of ice. Have them call out numbers or items until they've covered about 60% of the list or so. After that, you can recall the items and numbers that were never called by mentally going through the list from 1 to 20, and recall which images weren't frozen! This is a great finish!
You don't have to use rhyming pegs, of course. On my Memory Basics page, you can also learn shape-based pegs, or even the Major System, which allows you to turn any number into a vivid image.
Yes, this feat requires a little more work than most Scam School feats, but it's worth it not only for the results, but also for practical everyday uses!
When you first learn memory techniques, you also tend to apply them to a small set of standard lists, such as presidents, monarchs, countries, states, capitals, and so on.
It's not uncommon to start wondering whether there's any other type of lists to memorize, beyond just school standards. In this post, you'll find enough resources to challenge your memory skills for the rest of your life!
Not surprisingly, reddit.com can also be a good source, but there is the problem of too much information there. How do you find good sets of information to memorize there? Fortunately, reddit has done much of the work for you, with this network of subreddits, which I'll refer to as SFWP (take a look at any individual subreddit in the network, and you'll see why). Through the SFWP Network, you can easily find lots of fascinating information to challenge your memory. For example, in the map part of the network, you can see things like a map of the most common surnames in European countries in 2011, or even the most common European male and female first names in 2012. Try exploring, and you'll be amazed at the endless ideas these sections inspire.
When I originally created my free app Verbatim 2, I designed it for memorizing things like standard speeches, lyrics, and poems. However, when combined with some wordplay, memorizing AND repeating can be quite a feat. Matthew Goldman's Goonerisms Spalore site is a perfect example. The spoonerisms there range from the short and simple, such as Drain Bamage, to fully spoonerized stories, such as the many versions of Rindercella.
This month, we're going to delve into math and memory techniques you may have thought were too dificult to develop. With sufficient practice, however, they become powerful additions to your mental toolkit!
• One of the main reasons people want to improve their memory is so they can recall names and faces. This appears difficult to many people, because of the social pressure involved, and the apparent difficulty of connecting a name with the face. As USA Memory Champion Nelson Dellis will show you, it's not as difficult as you may think:
• Another memory skill that comes across as impressive is memorizing the order of a shuffled deck of cards, especially when you can do it in under 60 seconds. Over at the Four-Hour Work Week blog, they have a wonderfully vivid tutorial on memorizing the order of a shuffled deck. They use the easy-to-understand analogy of a software purchase. They start your new brain software off will a trial version they call “Bicycleshop Lite,” where you get the basic process down of memorizing shuffled cards. Once you've done that, you're ready for “Bicycleshop Pro,” which improves your speed. Need some incentive to learn this feat? They're offering $10,000 to the first person who masters it from their tutorial!
Once you develop those skills, the following video will teach how to bring them together to take any small number to any small power in your head:
• Multiplying numbers by themslves repeatedly is one thing, but how about multiplying any 2 numbers together in your head, up to, say, 7 digits? YouTube user Joesph Alexander has a series of tutorials on how to develop your mental multiplication skills to this level. He starts by teaching how to handle 2- to 4-digit numbers (presentation, explanation), then moves you up to 5-digit numbers (presentation, explanation).
When you're comfortable with doing those type of problems in your head, you're ready to move up to 7-digit numbers (presentation - shown below, explanation):
Try picking just one of these skills to develop, and you just may amaze yourself at how far you can go!
I recently ran across a number of videos I figured would be interesting to regular Grey Matters readers, so I thought I would share them.
Happy New Year!
June's snippets are ready!
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