FIREPEGS is a toy and the game of challenges, which lets you play with the fundamental relations defining this world: space, time and causality. Yes, really. And it's a sequel to MAKE THEM MAD, where I was playing with the little girl called TLG and the toy pegboards.

MAKE THEM MAD began as a next-hole-finding business. I would plug a peg into a hole on my board, next to the hole, which I filled before, following some secret plan. Then I waited for TLG's neural network to fire at the matching hole on her board. Then I plugged the next peg and waited again. So I spent some 100 hours waiting, watching and thinking about a better toy revealing the pegs next to a previously revealed peg through the timing links.

Playing MAKE THEM MAD, TLG was learning elusive subjects like strategic thinking, problem solving and self control, but those were just words. Suddenly, by the age of four, she started getting symmetries in the layouts and patterns of polyominoes, and discovered the number plane, remembered as Cartesian plane. She even translated, rotated and mirrored shapes. The nationally established machine of education allows the kids of her age to learn only the linear patterns of two colors, like red-blue-red-blue. Not even a number line.

Unbeknownst to me and to her, TLG acquired the most enabling skill of procedural spatiotemporal thinking. At 4 years and 6 months she drew her first chart of additions. A year later she became an accomplished reader.

FIREPEGS can teach all this, and much more. Don't take my word. Take a look. Click on the link The Bird on the left, watch the record and read the comment.

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Welcome, touch here and look to the right!

The Bird is what I wanted FIREPEGS for: a layout and the method to build it. The pegs fire up each other and display their colors.

Click on SHOW:MORE to see through the skins. Slow down the player selecting the number of TPS (Ticks Per Second). Use STOP/GO if available, or restart the record from the link.

Every firepeg has 8 links to its neighbors. When it fires up, it spills the fire through the links. A link must have a number on it to work. The receiving peg fires up this number of ticks later. In The Bird all delays are 1 tick long.

The Bird is not the only way to decorate the layout of rotating triangles, which you saw in MAKE THEM MAD. In FIREPEGS you can also teach to build it in many ways, puzzling, challenging, surprising, teasing, deceiving and entertaining your student.

The Wires reveals the picture on the board. The pegs become transparent as they fire up. The picture could have been animated. Every peg can carry it's own picture, which can be animated too.

In The Bird firepegs are pushing fire through the links. In The Wires firepegs are pulling the fire. The numbers are on the receiving ends of the links. Every next firepeg down the track knows when a neighbor fires up, and reveals its color 1 tick later.

The Spirals introduces a new feature, which I call Ticks To Glow, or TTG. The number of TTG is currently one and the same for every firepeg on the board. It's always shown on top of the board, but you can't change it in the player. In this layout it is equal to 35 ticks.

Click on SHOW:MORE if you did not toggle it yet. Use Ticks Per Second (TPS) control to slow down the player. Restart this record from the link. Once fired up, every firepeg has 35 ticks to glow. You must be able to see them counting down and turning off as their TTGs expire. You can also use STOP/GO button to pause the player and get a better view.

Around and the following four records explain a wondrous opportunity, which TTG brought to the game. If firepegs turn off on their own, the other firepegs can turn them back on.

In Around the top left firepeg was fired up by hand. It has only one tick to glow, but in the beginning of this tick it sends the fire to the top right firepeg. The later has to wait 1 tick before firing up, so as the first peg shuts off, the second peg turns on, firing up the third peg. Skipping to the bottom left peg, which is the fourth, we see that it fires up the first peg, so they pass the fire along the loop as long as the player is running.

Around is your first FIREPEGS example of a spatiotemporal pattern. This pattern repeats itself not only in space, but in time too.

X-Blinker uses the same layout as before. but it the beginning I fired up two diagonally opposite pegs.

Designing a layout like this is very easy. You create a new board, set up the pegs' colors and the numbers on the links. Next you touch a peg or pegs to fire them up, turn on the timer and watch the pattern. TLG was 4 years and 8 months old when I showed FIREPEGS to her for the first time, and she's got it instantly. Yet soon I found the problems, which were too challenging even for her big sister.

The Eight does have two diagonal connections. Otherwise it's just a 4-pegs loop. There is a lot behind and ahead of those simple creations. This one, for example, juggles the fire in the order, in which we Western people write, print and read. A scaled up version could blink the letters or the words one after another. Or play a music score. As always in FIREPEGS, this pattern could be supported by several different layouts of pegs and links. Finding them is much more challenging, than building the most obvious one.

The Blocks runs on the same loop, in which two links were made 0-tick long. Such link fires up the target peg immediately. The pegs connected with 0-links behave as a body.

I could spent several chapters writing about transplanting those patterns, scaling and coloring them, as well as about using them to build bigger structures, but I am going to limit myself to one example. The next one.

Complexity is that I am going to build. Suppose I use a simple 2x2 4-pegs 1-tick only loops, like in Around, and color the pegs yellow, orange, red, yellow. Now I assemble them into a 4x4 rectangle, rotating 90 degrees every time, so that the red peg is always in the corner. Next, passing from one small rectangle to another, starting from the upper left corner, I connect the 4 pegs in the loops clockwise, counterclockwise, clockwise and counterclockwise. Finally, I fire up the four yellow pegs by hand and turn on the timer. Now suppose you see the running pattern, and you were asked to build a layout, which can support it.

The Waves uses TTG to shut the pegs down, and the loop of the links to fire them up again. The loop carries the fire from the Northeast corner to Southwest and back.

Spatiotemporal patterns are very important and, to put it politely, not widely understood. Our body parts, the whole our body, our life as society members, our society, our environment up to and including our planetary system, our machinery - most of the stuff inside and around us runs in loops.

The Fireworks is another example of a simple spatiotemporal pattern. Look inside to find the loop. Remark that it goes through the gray pegs and works like a fuse. Gray pegs' color matches the color of the board. They fire up and pass the fire invisibly.

Projectile shooting is a rear example of our activity, which does not repeat itself. But then, we have repeated shooting.

Push Inchworm plays a spatiotemporal pattern, which goes back and forth. This one is rather easy. Some others can be challenging to build. There are three version of Inchworm in the records. This one is centrally operated. The central peg is the boss or the brain, telling every other peg when to fire up.

You see the delays longer than 1 tick at work, and, finally, can piece the rules together. An idle firepeg is gray and empty. A gray peg, which is counting back, is waiting to turn on. A glowing peg is counting back its Time To Glow. You can grasp the design and the status of the network at a single glance.

Pull Inchworm is the same mechanism rewired. Rewiring is very easy, and I have a little program for it. It swaps the links and tell the simulator, which I call The Time Machine, how to handle them.

To me, the transformation from push to pull instantly makes the same layout much harder to understand. Instead of bossing the leg pegs around, the central peg only sets the pace. You have to go from peg to peg and think for a bunch of them at once to figure the whole. I believe, the ability of such inverted thinking is crucial for the spider men, who can operate social media, mass marketing, win elections or battles.

Brainless inchworm is completely decentralized, yet it supports the same pattern as the first two. Four important links go outward because the board in FIREPEGS is really a torus. The border pegs are not on the border, they are connected to the other border pegs "behind" the board.

Earth is a sphere, but we draw it's surface flat. If you cross the border of the map, you do not fall off and disappear, you just emerge somewhere else.

Virtual pegboard can be very big and/or curved, and/or covered with non-rectangular pattern. Pegboarding games can be played on a sphere (tiled with pentagons), on a three-dimensional torus, on a parallelepiped, etc.

The Waltz is an example of a challenging spatiotemporal pattern operated from the gray pegs. It is supposed to demonstrate what long delays and TTG are convenient, but abundant. The visual effects of them can be achieved cascading one- and zero-tick links and one-TTG pegs. It's also an example of emergence, which I discuss in a consequent chapter in the long version of this demo. You know about the long version, do you? You are reading the brief one.

Click and wait. The pattern takes some time to emerge. The blinking red pegs indicate strong beats.

Hourglass 8x8 This and the following two records are from the long version's chapter, in which I am telling how the game of challenges has raised its scary head from the toy, which was supposed to be teaching the children to build mosaics on the pegboard.

The biggest challenging factor to me are unexpected consequences. A beginner can easily build this hourglass-shaped looped track and run a fire along it. An attempt to scale this pattern down to 7x7 board is doomed to fail.

Hourglass 7x7. Creating the same pattern on a smaller 7x7 board may seem next to impossible because the tracks intersect and a fire passing through the central hole spreads in both directions. In fact, the layout, supporting the desired pattern, can be built, but not is a way it looks. I call this effect What You See Is Not What I Built, or WYSINWIB.

Colors. Same colors fire together, but there is no way to connect those begs without incurring unexpected consequences. We can, however, build four multicolor loops and let them synchronize themselves. Which is, of course, another example of emergence.

In Boston Museum of Science they had several computers, simulating and demonstrating emergence. Kids usually passed by without even looking, as well as their parents. Meanwhile, it's a very important concept explaining how complex behavior can appear in a mass of simple and similar participants without management and with very limited communication between them. In FIREPEGS one can play with emergence without programming.

The Rain is another simple example of WYSINWIB. The tracks here are straight, but they look diagonal. I could have named this pattern The Wind Of Time.

The Chevrons shows how the same static pattern can produce a different spatiotemporal pattern. In fact, it's a screen with a time sweep, like those found in immensely important devices called oscillographs and oscilloscopes. They have been used to visualize spatiotemporal phenomena and patterns like earthquakes, electrical signals or heartbeats. Computers replace them only to display the same graphs on their screens.

The Fish. I could not help but making a moving picture out of firepegs, even though they are not good for this yet. To move quality multicolor images I need some modifications. Currently they are experimental, and I don't have time to work on them.

In the long version's chapter, to which this record belongs, I also explain how FIREPEGS can control animations. This would be very natural to them, but not in the web browser, where they presently live. Web browsers cannot even use computer sound circuitry. They can only play prerecorded sound files. That's why there is no music in Waltz.

The Tracks and the following two records demonstrate how FIREPEGS can teach velocity. It may seem very obvious, but I realized their potential only recently, so you see my first first attempts. I need some of the proposed modifications and SOFTPEGS to get this technology right.

The record shows several different ways to reach from left to right. The possible question can be, which color is the fastest.

The Race The outer track is always much longer than the inner track. I put the stickers between the tiles on the floor and walked with TLG holding hands, until she's got it. This experience led to several interesting and useful math lessons. We'll do it again.

This record is stopped after it loads. Click on GO to watch it.

The Crossover. The traditional ingenious way to make the tracks equal. Flip SHOW:MORE and watch. Can you do it for three runners?

Nine Simple Patterns, 3x3 each, introduce entirely new way to use FIREPEGS. A heavily interconnected networks starts to oscillate if I click somewhere. Clicking again, I can change the pattern of oscillation.

Four Fancy Patterns. Well, they can get much fancier. The simplest one here goes through 4 phases. The fanciest one has 12! Morphing them to what I want is not easy. I tried. Such oscillations are one of the several bottomless sources of the static patterns for MAKE THEM MAD.

Four 4s. Firepegs are not nearly smart enough to speak, but they can handle bits and pieces of human languages in many ways. This record shows TLG's weird way to draw 4 (it's green) and her teacher's way (red), which is still weird to me. My track is blue. I learned to write using dip pen and inkwell.

HELLO WORLD. FIREPEGS turns computer into a spatiotemporal pattern machine. it can do many things, currently requiring programming, but it's not a replacement for a general purpose programming language. I would put FIREPEGS on the same shelf with the cam timers, the music boxes and the ancient automatons moving mechanical dolls. Still I could not resist using FIREPEGS to build controller, blinking HELLO WORLD in Morse code. Please check with Wikipedia if you are not sure what it means.

Please remember, FIREPEGS was never meant to be the answer to every wish. I'd like unsatisfied firepeggers to learn programming with CODEPEGS.

The records were made with an early prototype of FIREPEGS. Currently, it supports only single-level two-dimensional layouts, one color per peg, one kind of pegs and two kinds of links.

To play with FIREPEGS app, you probably need a stylus or a mouse.