Side-Vision Training
by Lothar Jost

I just visited Kate's page for the first time and wanted to go to the Puzzle Parlor. [Editor's note, 2021: Sorry, Puzzle Parlor is temporarily closed.] But its intro page is as far as I got so far. That's because the welcome/enter applet is such a great toy in itself.

The first thing you can use it for is side-vision training. Just make circular movements with your mouse around the screen so that the pieces and letters move across the screen. Then side-look at some point out of your focus and identify the letters going by there. To prevent my eyes from moving around I had to put my finger on a place on the screen to focus on and a paper clip on another place of the screen where to identify the letters/pieces. Play with it a bit to find out how it works best and then, I think, you have a nice additional way of training side-vision.

When you make really quick, circular movements all around the screen so that the letters/pieces are distributed across the screen and that it seems as if the letters don't move at all but just show up and disappear, you have letters/shapes in all corners of and all over the screen.

Then encompass the whole screen with your eyes (like in photoreading) and see how much you can identify. There's even a way to have feedback on your identification, because the letters move with the colored shape attached to them. This sounds a little silly but seems to work: intend to identify the letters first and you won't have time to consciously take in the color of the shape, so you can use its afterimage in your mind as feedback correcting your identification.

I found this last exercise (widening your gaze to encompass whole screen while moving mouse) to be really relaxing to your eyes and to somehow induce the feeling required to successfully photoread. That's because it teaches your mind to recognize letters on an area about the size of a book all over that area without relocating your eyes.

At each point on the screen, relevant information will potentially occur because your subconscious doesn't know where you'll look next. That might teach it to make this information more easily accessible. (You might even try to guess which letter last occurred on a given point; however, in this form the applet doesn't provide feedback for that.) So, altogether, this method might teach both the conscious ability to recognize letters within the scope of the photo look and the unconscious ability to make them accessible. I think I will try this.

Regarding an extended version of a brain marathon, Johnius introduced us to a great exercise to start with:

Another fun thing I've played around with is to pick any two objects in a room, hold my eyes still, and to mentally 'link' them together as a unit, with all else in the room as 'background' ... then to pick two different ones and do the same with them ... and to continue picking different pairs at faster speed ... then picking three at a time, then four ... perhaps keeping three the same and picking a new one each cycle, chaining through the room that way, while occasionally shifting eyes to keep them from habituating-blanking out the view.

The moving letters/shapes of the Puzzle Parlor's welcome page can be used as a natural extension to this idea. Just pick two or more of them and hold them together as a unit in your mind. What makes this really interesting is that the items keep moving and even change distance from each other (and if you use the M in the middle, one of the shapes rotates).

Something apparently really challenging is to dynamically find more complex systems in the moving letters/shapes. Make small, rather slow circular movements with the mouse in the middle of the screen. Then a third dimension is introduced through the fact that one item overlays the other.

Thereby, more complex systems seem to appear, for example one item rovolving around another and a third at the same time moving away from both, and such things. But since this isn't really so, the configurations on the screen can be interpreted thus for only a short period of time. Therefore, you have to be very quick to conceptualize systems. On the other hand, when your mouse movements are short and periodic (like in the circular case waiting for the completion of a whole circle (which makes for a quite too complex system)), you have stable systems to identify.

I'm really looking forward to playing the real games on your pages.

Comments? Email Lothar.

Kate replies:

Wow, Lothar, that's a really awesome analysis of what can be done with our flying pieces effect. What a great extra value besides sheer fun. You are quite right to detect multiple systems:

  1. The central rotating W (looked like M to you and is our logo) follows your mouse, at a varying speed and distance but always tracking toward the cursor, and stopping to rest on it if you stop. It comes to you like a puppy wanting to be petted.

  2. All the other pieces are in orbit around the W, each at a different rate and distance, so changing how you move the cursor will affect the motions of the W and trigger flight-path changes in the whole meta-system of individual systems.

If you enjoy playing with the flying effect, after you click on Welcome and come to the main Puzzle Parlor Menu, and after that is fully loaded, in the lower left corner a link will appear, saying "Step into the Welcome Lobby to play tag." Click on that, and the flying swarm will reappear, this time as a playable chase and without the letters. You try to click, one by one, every piece except the W (hitting it wipes you out, start over). In the meanwhile the W is chasing you, but it's harmless to you unless you click it as it gets underfoot in the heat of the pursuit. Some of the other pieces will tend to hide behind the W.

When you've caught all 15 without wiping out, you'll get a nice surprise.

I would like to give credit to Macromedia for developing the Flash technology, and to Chris Palmer for brilliantly implementing it for our Puzzle Parlor based on my vision for how it should simulate our actual products, and the irresistible idea of playing tag with the flying pieces.

Comments? Email Kate.


Games in the Classroom
by Carol Townsend

Fluxx is an excellent tool for learning to follow directions. I introduced it into our behavior mod class and saw some great things happen:

  • Forces them to read the whole card (following directions, reading for comprehension, comprehension being demonstrated concretely at all times).

  • Demonstrates active number comprehension (hand/keeper limits, draw/play numbers).

  • Is a kinesthetic form of showing the above comprehensions. Some kids learn best by doing (manipulating, handling, using) stuff than by reading or hearing it.

  • Allows the students to be in charge of when the rules change—which is a big thing for kids who have anger management problems... especially when they feel the rules have changed arbitrarily. This game allows them to be the one to change the rules, and lets them do it in a game situation, and then allows other players to learn to deal with their anger appropriately.

  • Has fostered some good debates on whether a card was a legal play or not. Students had to re-read the card, look over all the rules, and between them (the other teacher and I stood back and let them decide) figure out what was right. It later led into a discussion of the court system and politics.

  • Students see that not all rule changes are arbitrary, that there is often some real reason for that change. And it's NOT just to "screw them over"... it's to advance someone else's agenda, and often has nothing to do with them.

  • Details are important. You need to keep track of everything that is happening (as in real life), but the good news is that everything is spelled out clearly (rules are all right in front of you, which isn't what happens in real life).

  • You need to follow all the rules all the time. Yes, even the speed lim... I mean hand limit. Yes, this game has fostered discussion of what rules you need to follow outside of school, and most of these young men in the behavior room don't like following rules of any sort.

  • it's also a good role play for knowing your own limits. There was one student who KNEW that changing rules was his big trigger point, and that he would probably punch someone if they changed the rules on him mid-game, so he chose not to play the game. He sat and watched others play and enjoyed it, but it was a great example of knowing your limits and knowing when to say No.

Granted, this classroom is not your typical classroom, but it does show how a good teacher can use a simple game and make it an integral part of the curriculum, simply by knowing her own students (they weren't mine...I was there to help demo the game in another teacher's classroom) and knowing what goals she was trying to reach with them.

Comments? Email to Carol.

Editor's Note:  Carol Townsend is the educational consultant and coordinator for Looney Labs, creators of Icehouse and other great innovative games.


Some Thoughts on Puzzles
by Joe Marasco

In reading your FAQ, I was impressed by the well-thought-out rationale for doing puzzles. It all makes sense to me.

Puzzles have a rich tradition of stimulating the human mind and leading it to new areas of enquiry, as the Stomachion and Archimedes illustrate. If indeed that puzzle caused Archimedes to ponder questions combinatoric, then we have every reason to view puzzles as kind of intellectual catalysts, focusing the mind on issues and precipitating new areas of research.

So I would argue that not only do puzzles help all of us stay sharp, but they also may cause the best minds at any given time to “see deeper” or “ask unusual questions” that are not obvious to everyone. In pursuing these matters, we discover new knowledge and wisdom, sometimes going farther than we might have thought based on “just the puzzle.”

Moreover, I suspect there is a rich historical tradition of puzzle solving. It would be interesting for someone to investigate the thread of “puzzle solvers” starting in antiquity and continuing down to the present age. Of course much of natural philosophy consists of solving “nature’s puzzles,” many of which are not just mathematical in nature.

I have always been fascinated, for example, by the story of Kekulé, the chemist who was trying to figure out the structure of benzene. He is reported to have been so absorbed by the problem that he had a dream in which dancing snakes grabbed each other head-to-tail, forming a ring. The alternating single and double bonds between the carbon atoms turned out to be the solution. Mystical? Perhaps. Apocryphal? Maybe. But nonetheless, an example of a puzzle solved subconsciously. Much of organic chemistry was unleashed by Kekulé’s benzene discovery.

Of course, so much of modern science is based on “bringing order out of chaos.” Much of elementary particle research is based on symmetry and group theory, a natural extension of problem-solving. I have a theory that we have “child prodigies” in only three areas of human endeavor:  chess, mathematics, and music. Why is this? I believe the answer is that some rare children can see patterns better than all the rest of us. And seeing patterns is what makes these activities special.

Now if puzzle solving helps us recognize patterns better…

Food for thought.

Comments? Email Joe.

Editor's Note:  Joe Marasco inspired Kadon to start producing Archimedes' Square
and sponsored the historically first proof of its solution count.

One-Winner-Only Games
by Charles Titus

I'm enclosing a few paragraphs of some of my ramblings on geometric game theory for your amusement. Among other things it characterizes all games that have the "exactly one winner property." Here is an informal statement of the topological basis for the Game of Y.

Choose three points {a,b,c} in counter-clockwise order on a simple closed curve, C. These points determine three disjoint open intervals (a,b), (b,c), (c,a). Let E be the union of these intervals. Choose any number of simple curves that run from E to E or that close up; assume also that no pair of these curves intersects. This process creates a collection of open regions, R1, ... , inside the curve C.

Lemma — The closure of one and only one, exactly one of these regions intersects all three of the open intervals (a,b),(b,c),(c,a). See illustration of this lemma below, where the unique region is named R5.

Editor's Note:  Charles Titus is the inventor of The Game of Y and other mathematical games. He is a mathematician, retired from teaching at the University of Michigan in Ann Arbor.


Games... indeed!
by Stephen Tuell

Dear Stephen,
Looking about the Internet for thoughts on games, especially the psychology of human beings and the appeal of games, I came across gamepuzzles.com and began reading the articles. Great! I did especially enjoy your articles as much for the questions you posed as for the suggested answers.

I am an educator. I'm a bit "strange," some would say, because I love mathematics. Doing mathematics or physics with mathematics is for me a puzzle. I am still not sure why these particular puzzles are so motivating to me, while few popular games attract me. As an educator, I wonder what the difference is. There are so many ways in which mathematical problems are similar to puzzles (if not competitive games)...

Lately, I have moved this question from rhetorical to active. My current project is to clearly define games, to distinguish them from puzzles, to see what characteristics all games have in common and what characteristics popular (often-played games and games with a large number of players) have in common. That is the "science" side.

I hope to work out, if I can do it before the final buzzer ends the biggest game I play, how to structure game-like learning activities that will lure people into learning the moves in algebra, calculus, grammar, etc ., with the zest that they learn Bridge, Golf, Tetris or Chess. I believe that this new lexicon of skills will allow them to play the Biggest Game with more satisfaction and more wins.

Why Emphasize Zero-Sum Games?
by Nancy Van Schooenderwoert

Hi, I wonder why the focus on zero-sum games? To define my terms, I mean games where one player wins and the other loses. The first essay also emphasized two-player games. I like that type of game, especially Go, but recently I've enjoyed playing games where the players cooperate to achieve some goal.

An example is the Lord of the Rings game. Players can lose in the sense that they may be eliminated from the game before it ends, but all players can also win. I find this type of win just as enjoyable as in a two-player traditional game. In other words, winning is as much fun with or without anyone losing.

Your premiere column raised a number of interesting questions. I suppose people enjoy games as a way of getting to know others (and themselves) better. It's tempting to assume the strategies we use in games are the same ones we use in real life situations.

Comments? Email Nancy.

Editor's Note:  Nancy Van Schooenderwoert is an engineer
and the inventor of The Kites and Darts Game.

The Life of Games
No. 4  (April 2007)
©2007 Kadon Enterprises, Inc.