Date: 2014-12-16
To: 2D and 3D and 4D, Oh My!
Miles today: 0.0
Weather: broken clouds

The following is not a description of what I think is reality. It is a description of some things I¢ve thought about which demonstrate that I certainly don¢t know all there is to know about reality! It¢s actually a very simplified view of a possible four dimensional universe. Brainy physicists out there talk about string theory painting our universe as having 10 physical dimensions! Hopefully, this discussion will stimulate you to consider how little we really know about the universe in which we live and to consider the possibilities!OK, imagine there¢s a two dimensional world called ¢Flatland¢ with two dimensional inhabitants who have no concept of a third dimension. For now, imagine it¢s a flat plane, like the top of a table near you but with no height dimension. Imagine we pass a three dimensional object through the plane of Flatland, and consider what the inhabitants of Flatland would see. Let¢s start with a sphere. As the sphere first touches the plane of Flatland, the inhabitants first see a point suddenly appear out of nowhere in their two-dimensional universe. As we continue to lower the sphere, the Flatlanders would see the point grow to a small circle, getting larger and larger. As the sphere goes halfway through the plane, the Flatlanders would see the circle reach the sphere¢s maximum diameter and then decrease in size. As the sphere passes completely through the plane of Flatland, the Flatlanders would see the circle diminish to a point and then magically disappear.Now go ahead and jump through the plane of Flatland yourself! What would the Flatlanders see? Let¢s say you¢re wearing pants and a shirt and you jump through feet first with your arms hanging by your sides. The Flatlanders see two irregular blobs suddenly appear that are the cross sections of your feet or shoes. The blobs get smaller and more circular as your legs begin to pass through Flatland. Then two smaller blobs suddenly appear alongside the leg blobs as the tips of your hands start passing through Flatland. The two main blobs join together as one bigger blog as your hips go through, leaving a big central blob of your torso with two smaller blobs of your arms on each side. Then the two smaller blogs join the big blob as your shoulders enter Flatland. Suddenly the big blob shrinks to a much smaller and more circular blob, which then suddenly grows bigger and more oval as your neck and then your head pass through Flatland. Long hair might make it even more interesting! Finally the oval shrinks to a point and magically disappears as suddenly as it appeared!The Flatlanders have seen somewhat circular blobs suddenly appear in their universe, change shapes, and suddenly disappear. Since they have no concept of a third physical dimension, they have no way to connect the varying shapes as being simply cross sections of a single three dimensional object. They can¢t picture in their minds what a three dimensional object would look like.One more fun exercise: Imagine a pole 3 inches in diameter and six feet long, standing on end perpendicular to Flatland. Now tilt it over 30 degrees. Now cut off the top and bottom at a 30 degree angle so that the ends are flat ovals parallel to the plane of Flatland. Now move it straight down through Flatland, keeping the 30 degree tilt. What do the Flatlanders see? Suddenly a three inch wide oval appears out of nowhere in front of them. Then the oval moves across Flatland for about three feet. Then it suddenly disappears!The Flatlanders have no concept of a pole. All they can experience is an oval suddenly appearing and moving ¢sideways¢ through their universe and then disappearing. We know there wasn¢t any sideways movement of the pole. Instead, we know it moved only down, a direction the Flatlanders don¢t comprehend.Note that I¢m not considering Time like a physical dimension here. Time exists the same in Flatland as it does in our three dimensional universe. Flatlanders experience the same time for the oval to move sideways in Flatland as we experience for the pole to pass down through Flatland. I am using time in my examples to allow the Flatlanders to see multiple 2D cross sections of a 3D object, since they can¢t see it all at once.So, what would it look like for a four dimensional creature to similarly tease us three dimensional creatures? If we saw a ball suddenly appear and zoom up into the sky, zip around, and disappear, might it simply be a four dimensional ¢pole¢ that a 4D creature is stirring around in our 3D universe? Of course we can¢t conceive of what a 4D pole looks like, just like the Flatlanders can¢t conceive what a 3D pole looks like.If some part of a 4D object always intersected our 3D universe, then we wouldn¢t see it suddenly appear or disappear. There may be no "magical" appearance to it. Some 3D ¢cross section¢ of it would always be present. We can¢t tell if anything is a 3D or a 4D object.Think about you. Perhaps you¢re a 4D object! But due to our 3D limitations, at any given time we can only experience your 3D cross section intersecting our universe at that given time.When you jumped through Flatland, your 3D self was the compilation of all the 2D blobs that the Flatlanders saw over time. Perhaps your 4D self is the compilation of all the 3D persons you have been over time! Perhaps your total 4D self has always consisted of ALL the 3D slices of you since your were first conceived until you pass away - we just get to experience you one 3D slice at a time since we can¢t perceive the fourth dimension. Perhaps there's even more of you that never intersects our 3D space...Fun!Let¢s have more fun taking it a step further. The sperm and egg from which you were conceived came from your Dad and Mom and although separate from each of them in our 3D universe, they might still be part of them in the 4D universe - like all the separate blobs of you that the Flatlanders observed. That means that in the 4D universe, you might still be physically part of your Mom and Dad, and they became connected through you to each other when you were conceived! Take that several steps further and all mankind throughout all history are connected as one entity with several billion parts!Ouch! My brain hurts!Another fun aspect to consider: As we 3D creatures look down on the Flatlanders, we can see every molecule in their universe at once. We can see inside their houses and even inside their bodies. Surgery would be a lot easier for Flatland surgeons if they could go in from the 3rd dimension rather than having to stay in Flatland and cut through the outer part of the patient¢s body!Likewise, 4D creatures looking down on our universe from a 4th dimension position ¢above¢ us can see every molecule in our universe at once. They can see the internal makeup of our planet and our sun. They can see the moldy leftovers in the plastic container hiding in the back of the fridge and where you hid the jewelry in the sock drawer. They can see every aspect of our internal organs, too. They¢d be great surgeons for us!Enough! At least for today¢¦ Next will be thoughts on what it might be like if Flatland were not perfectly flat!