# Wraparound Universe

The Torus Games introduce children ages 10 and up (and adults too!) to the mind-stretching possibility of a “multiconnected universe”. While playing the games, you’ll develop an intuitive visual understanding of a model universe that is finite yet has no boundary.

The basic idea is simple. Take a sheet of paper and draw a 2‑dimensional fish on it.

If you bend the paper around and tape its left edge to its right edge, the fish’s world becomes a cylinder. When the fish swims due eastward, she goes all the way around the cylinder and returns to her starting point from the west.

If you instead bend the paper around the other way and tape its bottom edge to its top edge, the fish’s world becomes a horizontal cylinder. If the fish turns 90° and swims due northward, she’ll go all the way around the cylinder and return to her starting point from the south.

We’d like to join the paper’s left edge to its right edge, and its top edge to its bottom edge, all at the same time. But if you try this with a real sheet of paper, you’ll find that you get a crumpled mess.

Fortunately this construction is much easier in software. The Torus Games provide a square game board whose left side connects to its right side, and whose bottom connects to its top. No crumpled paper required!

Try it yourself: Go Return to the Help menu and select the Practice Board. You should see a fish. Grab the fish and push her past the top of the board – she will automatically come back from the bottom! Now push her to the right, and she will come back from the left. This sort of universe, that connects up with itself both right-to-left and top-to-bottom, is called a torus.

All the Torus Games work the same as the fish’s world. For example, if you close this help panel, press the Change Game button and select the Jigsaw Puzzle, you’ll get a jigsaw puzzle on a torus. Grab a puzzle piece and push it past the top of the board – it will automatically come back from the bottom. Now push it to the right, and it will come back from the left. Just for fun, try to assemble the whole puzzle.

For a fresh view of a game, click on the board itself (not a game piece) and drag to scroll it: drag with two fingers to scroll the board: the portions of the board that disappear off one side reappear at the other. As you play the games, this tactile, visual interaction will give you a gut-level understanding of a universe that is finite yet has no boundary.

After you’ve played all the 2D games and gotten comfortable with the “multiconnected” game board (finite but no boundary), you’ll be ready to think about a multiconnected 3D universe. Go Return to the Help menu and select How to Play — 3D.

Satellite observations hint that the real universe may be multiconnected in much the same way that the Torus Games board is multiconnected, but so far the evidence remains too weak to draw a firm conclusion.

The book The Shape of Space introduces high school students, college students and adults to multiconnected universes.

Please submit questions, comments and suggestions to the Geometry Games Contact Page for a more-or-less prompt reply.

© 2021 by Jeff Weeks