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30 July 2006

will they wiggle for you? they wiggled for me.

Images created by Davide P. Cervone
of Union College Mathematics Department.

Okay so like we live in a 3-D world. If you want, you can call us Spacelanders. We can go right and left, forward and backwards, up and down. And that's it.

But Flatlanders are stuck in a 2-dimensional world. They can go right and left, and they can go forward and backwards. And that's it.

They're straight lines, triangles, squares, pentagons, hexagons, etc., all the way up to circles, but they have no thickness; they live their entire existence travelling around within a plane.

From time to time, a Flatlander claims to have had a weird "encounter" with a strange 2-D shape that appears first as a point, then grows into a 2-D shape like a circle, triangle, square, polygon, then it shrinks again down to a point, then vanishes again. A Flatlander who has one of these bizarre experiences runs screaming to tell the Authorities all about what he saw. The Authorities immediately lock him up in an insane asylum for life.

What's really going on in these encounters is that a Solid 3-D object "falls" from above the Flatland Plane, intersects with the Plane, and then falls below the Plane again, vanishing from Flatland altogether. But while the Solid intersects the Plane, the Flatlander sees plane slices of the descending Solid.

"Flatland" by Edwin Abbott Abbott is a wonderful story about life in Flatland, as told by a Square who had one of these weird encounters with a Solid Object, and when he tried to explain the 3rd Dimension to his neighbors, he was immediately locked in an asylum for life.

If you Leave a Comment asking what the top image is, I'll report you to Homeland Security because you're probably a terrorist. The top image is of something that can't possibly exist intersecting through another thing that can't possibly exist. Everybody knows there's no such thing as dimensions greater than 3.


Jim Olson said...

HCubes are the basis of probability projection for submarine warfare. Three dimensions, (x, y, z), or some combination of the three plus either time or speed needs to be calculated based on known data (such as sonar and radar contact info) and known tactics (historical practice). I helped refine the programming for a new tactics computer once upon a time.

Bob Merkin said...

i wouldnt mind all the tax money i've paid all these years for all those nuclear submarines if they'd just turn one of them into a tourism submarine. i can't believe they're shooting rich tourists into space before they let me take a voyage under the sea. that really sux. i want my money back.

Bob Merkin said...
This comment has been removed by a blog administrator.
Jim Olson said...

There are tourist subs in Hawaii and Florida you can catch a ride on to see coral reefs. Pretty cool. Most of the pilots are old USN sub drivers.