Thanks to a recent e-mail discussion with some friends who also share an interest in memory work, we've managed to devise a simple way to find out when and how frequently "Friday the 13th" will occur in a given year.

First, you'll need to be able to perform the standard calendar feat. There are several variations in the formula, so I'll assume that you're using the version taught here. Once you've become comfortable practicing this version, you'll be ready to move on to the Friday the 13th version of the feat.

Start with the number 6. From this, subtract the code number for the year. You're done.

Yes, that's it. The resulting number will give you the month code for all months in that same year that contain a Friday the 13th.

As an example, let's figure out in which months a Friday the 13th will occur in 2006. The key number for 2006 is, interestingly, 6 (See here and here for details on how this was determined). Subtracting 6-6, we get 0.

Which months have a code number of 0? Only January and October do. Therefore, in 2006, only January and October will have a Friday the 13th. Checking the 2006 Calendar, we can verify that this correct.

Don't forget to adjust for leap years when necessary. In leap years, January is 6 and February is 2.

Why does this work? The original calendar formula has you add up numbers representing the date, month and year to get the day of the week, so it stands to reason that we can start with the day of the week, and subtract the date and year to obtain a month number.

Friday is equal to 5. Keeping in mind that we can add multiples of 7 without affecting the outcome, we'll add 14 to 5, getting 19. From this, we can subtract the date in which we're interested, the 13th, without working with negative numbers. 19 minus 13 equals 6. From 6, all we need is the key number for the year, which runs from 0 to 6. The result can only be the key number for the months containing a Friday the 13th!

Does your site have a banner?

Yes. Here it is:


This banner not only links to this site, but will continuously and automatically update to show the five most recent entries.


How to I add it to my site?

Simply copy and paste the following code into the source code of your web page, e-mail signature or discussion board profile, where you wish the banner to be displayed:
<a href="http://headinside.blogspot.com/"><img src="http://feeds.feedburner.com/cox/greymatters.gif" height="96" width="200" style="border:0" alt="Grey Matters"/></a>

In order to make this site easier to use, I have made the content available via syndication and subscription.


What is Syndication?

Without syndication, there are three basic ways to find information on this site that is interesting and relevant to you:

1) Arrive directly via a link from another site.
2) Browse through the links in the "Previous Posts", "Archives" and "Past Highlights" sections.
3) Do a search from an external site.

All of these can and do work, of course, but syndication makes the entire process easier and more direct by doing away with the frills and focusing solely on the content.

The is done with the use of files known as "RSS" and "Atom" feeds. A thorough and easy-to-understand introduction to the advantages of these standards can be found in the article Introducing RSS.

RSS and Atom feeds are read with special programs called "feed readers" or "news aggregators". Check Wikipedia's list of news aggregators, some free and some commercial, to find one for your system.


How do I read the feed for Grey Matters?

The site feed for the Grey Matters blog is available in two different ways. Simply click on your choice of link below, copy the link from the address bar, and paste it into your feed reader according to the program's directions.

XML Feed:    Summary   Full Content

The summary feed contains shorter text-only entries that work better when speed, bandwidth and/or memory is a concern. The full content feed contains the complete text and graphics of all the entries, which allows for more thorough searches.

If you don't have a feed reader yet, you can still click on the above links. Instead of a full-featured feed, you'll see a scaled-down version consisting only a list of entries with brief summaries. Only when the link is set up in your feed reader will you be able to take full advantage of the site feed.


What is Subscription?

You can also subscribe to the feed, so that you can receive notice a place you regularly visit, such as Yahoo, Blogline, or your e-mail box. This is especially handy if you either want to know immediately about new posts, or don't wish to download a feed reader.


How do I subscribe to the Grey Matters site feed?

Either click anyone of the badges under "Site Feed Subscriptions" to add it to the corresponding site of which you're a member, or enter your e-mail address into the box under e-mail, and click "Subscribe". Once you subscribe, you'll be notified everytime the site feed is updated.

If your e-mail software is unable to display links, you'll want to click the "Text-only emails" checkbox to receive a version of the feed without links. The mailing list for the Grey Matters feed is managed solely by RSSFwd, and no one associated with Grey Matters has access to the e-mail list, nor will it be sold or otherwise given to any outside party.

In each e-mail you receive, and at each site, there will be a link to unsubscribe if you wish.


Are there any other ways to read the Grey Matters site feed?

Yes, you can now add our web banner to your website, which automatically updates with the five most recent entries from Grey Matters.

Just when you think there's nothing more amazing about magic squares, someone goes and proves you wrong. I've run across some amazing magic squares, including ones that are gigantic, or work with multiplication instead of addition, or can be toured by a chess knight and so on.

Here's an 8 by 8 magic square. See if you can guess what is so unique about it:

14    56    55    54    53     7     8    13
1     24    16    45    44    43    23    64
63    15    40    26    27    37    50     2
62    48    29    35    34    32    17     3
4     47    33    31    30    36    18    61
5     19    28    38    39    25    46    60
59    42    49    20    21    22    41     6
52     9    10    11    12    58    57    51

True, it does total 260 horizontally, vertically and diagonally, and uses all the numbers from 1 to 64, but that is hardly unique among magic squares.

Here comes the truly magic part. Let's see what would happen if we removed the top and bottom rows, as well as the leftmost and rightmost columns:

24    16    45    44    43    23
15    40    26    27    37    50
48    29    35    34    32    17
47    33    31    30    36    18
19    28    38    39    25    46
42    49    20    21    22    41

Surprise! We still have a magic square! This 6 by 6 square totals 195 horizontally, vertically and diagonally.

Would you believe we can trim this magic square again, and still get yet another magic square?

40    26    27    37
29    35    34    32
33    31    30    36
28    38    39    25

This 4 by 4 magic square totals 130 in all the directions of the previous squares!

These unique constructs are referred to as nested magic squares, and it is possible to create them for any size square starting at 5 by 5.

The above examples were taken directly from the Nested Magic Squares webpage, which teaches methods for creating your own nested magic squares. For those of you who use Matlab, or an Excel-compatible spreadsheet, files are included so you can experiment with these squares yourself.

Just for fun, the author has also included some ginormous magic squares in ascii format, like the 99 by 99 nested magic square (multiple monitors may help in viewing this properly)!

No, there's no practical use for nested magic squares yet (which I consider to be one of their better qualities), but I'll take the experience of wonder wherever I can get it.

Pi will always be geekily close to my heart. That is why the very first post on this blog was about Pi, and why the blog itself was started on Pi Day.

That is why I like to see people like the ambitious blogger who runs the Desktop blog, for challenging himself to memorize 1000 digits of Pi. Why he jumped from wanting to memorize only 50 digits not that long ago, to 1000 digits, is beyond me.

What is scary is that I can both understand and relate to every one of those New Year's resolutions.

Checking around other blogs for items on memory techniques, I ran into what at first appeared to be the most incredible coincidences in blog history.

It started when MSN Encarta posted an article about four tricks for improving memory. It caught plenty of people's attention, which isn't hard to do when you're Microsoft. Plenty of people naturally includes plenty of bloggers.

Full reprints of the article can be found at:

* Let's call it a day :)
* Green Place
* blacklabel
* Sampler
* weblogkoto
* I Started A Joke
* The Tunes
* WaveLinx

It may not get the coverage of MSN Encarta, but I've found Mentat Wiki to be more in-depth when it comes to memory techniques.

Update (11/17/05): This article is still making the rounds. Add STuDeNTLiFe to the list.

Over at the Explorer blog, Koh Xuan Yang has just posted some mind-boggling 9 by 9, 10 by 10 and 12 by 12 magic squares. Check them out, and be amazed!

Mindvention began here in Las Vegas today, over at the Palace Station Casino. Mindvention is a convention dedicated solely to mentalism. As I unfortunately didn't have the time available to attend the whole convention, I spent the afternoon in the dealer's room, and I'm glad I did!

Chuck Hickok was there, with his complete line of mentalist's tools, including his brand new book, Mentalism Incorporated, Volume 2. The new book contains just about everything that Chuck has published since the original book, except for his limited edition of the Diagonal Magic Square. I picked up the Diagonal Magic Square along with the new book, and I'll be pouring over the both of them in the coming days.

Mark Strivings was demonstrating his new trick, Mnemerica. The tools themselves are a clear board with 9 pegs, and 9 black disks marked 1-9, which magnetically adhere to the pegs. In the routine, the disks are mixed up, and used to create a random equation, the answer which has been predicted. The principles behind this are similar to Predict Perfect (scroll to the bottom), which I've mentioned in an earlier entry.

These are the ones that really caught my attention, but there were many other dealers with routines to catch the eye and melt the mind. This small taste of the Mindvention did prove to be the best advertising, so I may have to set aside a little more time and money for when it comes back to Vegas next year.

Once again, over at the Magic Cafe, there's another new discussion concerning memory, this time discussing the relative merits of mnemonic stacks.

For my tastes, these threads on memory work appear far too infrequently. Fortunately, I've managed to find a solution for this. Memory Mentor.com now has a forum dedicated solely to memory techniques! They focus on both recreation techniques and real-world uses, like learning language. They also have a great section on impressive mathematical feats, referred to as "Vedic Maths". If you haven't been to Memory Mentor.com yet, check it out.

As Doug Dyment points out there are trade-offs when working with memorized decks vs. sequential and algorithmic stacks.

If you don't want to take the time to develop a memorized stack, there are many great alternatives. The classic Si Stebbins (described in the above link) has many advantages, including being easy to learn. Over at Elknase's World, there is an exhaustive guide on how to work out any card in the Si Stebbins stack, given only the knowledge of the bottom card. No, you don't need to memorize this for live work, but it is of great help when construction a particular trick with the Si Stebbins stack. One thing you should be aware of is that, despite the note that mistakenly says otherwise, "opposite suit" refers to the other suit of the same color as the bottom card.

The classic problem with the Si Stebbins deck, however, has always been the "too perfect" alternation of red-black colors. Elknase has tackled that problem, with the Elknase Card System (originally named the Dominic Card System, but changed to avoid confusion with the Dominic Memory System). Don't let the fact that the introduction page is in German scare you. The free PDF explanation is available in both German and English. I'll leave the question of whether the random appearance of the stack is worth the added work for the reader.

Just a quick note for this entry. If you didn't download the "30 second Memorized Deck" PDF from Greg Webb's Free Trick download page, which I mentioned in an earlier entry, it has now been removed, and can no longer be downloaded.

Shortly after discussing memory training software in my previous post, I ran across another excellent free memory training program for Mac OS X.

It's called Studycard Studio Lite. After just a few days of testing it and using it, I can already tell you that is even more impressive than Genius!

The biggest noticable difference is that, in Studycard Studio Lite, you can add a wide variety of multi-media to your quizzes. This can really help when memorizing something like a card stack, where you actually need to get used to associating the visual of each card with its respective name and location mnemonics. Also, since mnemonics technique in general is largely a visual technique in the first place, this can really help lock stronger visuals into your mind for whatever you wish to remember.

There is a full version, called Studycard Studio, available for US$29, with site licenses available for US$299. Even with the free version, you get a 15-day trial of the full-featured version.