Flat Like Me...

Flat like me...

Did you like being a worm? Maybe not so much? A billion worms?... ah no thanks... Before we move on, lets try a different analogy and see how that goes. Basically, to visualize the time dimension via a 3D worm, we need to loose one of our 3 dimensions. Previously, we did that by making thin slices, but there is more than one way to flatten an amoeba!

Lets do a little mental exercise to warm up! To start, either commit to a 2 hour experiment, or warm up that imagination... (Did you actually slice that carrot for my earlier post?) Now, get a brekfast bowl and a small cup. put the cup upside down in the bowl and set it somewhere warm. Now go to the freezer, get an icecube and put it on top the cup so that you can see it. Now, go away! Not too far... Every 10-15 min come back and look at your time traveler. Is it the same each time? Is it changing? It is melting you say? Well what would you expect ice to do over time!

Alright... rewind that sequence in your mind. Imagine each visit to the cube as a photo. (If you need to, consider repeating the experiment and actually taking a series of digital picutres with your cell phone.) All a photo does is capture a projection of a 3d objct onto a 2D surface, so it is an alternate way of creating a "slice". (A movie creates a series of 2D projections of 3D objetcts.) Finally, if only in your mind, print out and glue those pics to some cardboard, cut them out and stack them up like we stacked the carrot slices. Voi la, we saw a 3D icecube became a 4D time traveler, then a 3D worm! See? In order for us to visualize the 3D worm, we had to morph the icecube to a 2D surface, then grow the worm from slices. Our worm is hard and has sharp edges near the base. As we go "up" in time his edges get more round. We see him get narrower and rounder, and then eventually he disapears. Got it?

If we want to consider the liquid water too, then the worm is even more interesting. It has a fairly solid tapering core with probably some little "streams" that would be like branches ending in pools that would be sort of like leaves. Of course, over time these leaves join together into a pool... so we end up with one big leaf and no trunk, like high up in a tree. The water leaf eventually evaporates and we may get some individual pools which eventually disappear. Think about the last few pictures. We go back to some individual lobe-leaves with each one disappearing... finally only one, the tallest one, left... then gone. The whole thing might end up looking sort of like a broccoli stalk!

Now, put your hand back in front of you, but this time, just take a picture of it. Play the same print/glue/cut/stack game as with the ice cube and you end up with a different kind of you-worm. You can let this one move too, like we did with the earlier finger worms. Also, if we are cleaver, we can always take the picture from the front of the hand and glue it to the pile with a little tilt as well as a side-to-side movement. Now we have a really interesting worm!

What do you get if you wigggle your fingers? Ooey gooey...
Nois