{"id":89831,"date":"2019-08-30T12:52:21","date_gmt":"2019-08-30T16:52:21","guid":{"rendered":"https:\/\/valorguardians.com\/blog\/?p=89831"},"modified":"2019-08-16T20:49:31","modified_gmt":"2019-08-17T00:49:31","slug":"weekend-open-thread-introduction-to-the-4th-dimension","status":"publish","type":"post","link":"https:\/\/www.azuse.cloud\/?p=89831","title":{"rendered":"Weekend Open Thread-Introduction to the 4th Dimension"},"content":{"rendered":"
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Tesseract, a four-dimensional cube. Other names include hyper-cube and 4-cube. When the 4-D cube is rotated, the inner cube would expand and become the outer cube while the outer cube contracts and becomes the inner cube. This represents a shadow. Four-dimensional objects would leave a 3-D shadow. An actual 4-D cube is hard to visualize as we don’t see the fourth dimension. (Wikipedia User Tomruen)<\/span><\/figcaption><\/figure>\n

This post will build on something stated on my last WOT post. Take the “East-West” line (x-axis). The “north-south” line (y-axis) cuts it at 90\u00b0. The “up-and-down” line (z-axis) cuts both lines at 90\u00b0 angles. Collectively, these three lines are 90\u00b0 to each other.<\/p>\n

But, what about a line that is simultaneously 90\u00b0 to these first three lines?<\/strong><\/span><\/p>\n

A good starting point, for understanding this, would be through the Flatland story. In 1884, Seeley & Co. published a book written by Edwin A. Abbott: Flatland: A Romance of Many Dimensions<\/em>.<\/p>\n

This is a fictional story involving a square living in a two-dimensional world. This world is nothing but a flat plane. The inhabitants are two-dimensional geometric shapes. The main character is a square named, “A Square.”<\/p>\n

Each generation is born with an extra side. So, the children of “A Square” happen to be pentagons. The women are just “lines”. There appears to be a social and economic progression as new generations are born. Circles tend to be in leadership positions.<\/p>\n

Workers, soldiers, guards, etc. are “triangles”. The more sides a shape has, the more likely it’ll do “brain” work. Women, having limited rights compared to men, were naturally represented as “lines” in the story.<\/p>\n

The author intended to highlight social division, hierarchy, etc., that existed during his time. However, he helped bring the concept of “dimensions” to the public.<\/p>\n

A sphere enters Flatland, a square in Flatland sees it as a size-changing circle.<\/strong><\/span><\/p>\n

In one scene, “A Square” meets a sphere from the third dimension. This character is from “space land”. When this spherical character enters flatland, “A Square” only sees a cross-section of who he is. He doesn’t see a sphere. Instead, he sees the part of the sphere in the second dimension… A circle.<\/p>\n

When the spear first touches Flatland, the square sees a point. That point grows as a circle, stops growing, then shrinks. The circle shrinks to a dot, then disappears. The sphere is completely on the other side of Flatland.<\/p>\n

Now, putting us in “A Square’s” place, we could face a similar experience if visited by a fourth-dimensional sphere, a 4-Sphere\/hypersphere.<\/p>\n

We could project the “sphere through Flatland” scene up one dimension. This time, a 3-dimensional being, us, watch a hypersphere cut through the third dimension. If a hypersphere were to transit from the fourth dimension through our three-dimensional world, we wouldn’t see it in its entirety. We would only see its spherical cross-sections.<\/p>\n

As this hypersphere moved into our three-dimensional realm, it would start as a point. That point would expand as a sphere. It would stop expanding, then it would start shrinking. It would shrink down to a point and then it would disappear.<\/p>\n

The following videos help capture this concept. The first two videos are short. They provide visualizations of what I talked about above… And more.<\/p>\n

Flatland, an introduction:<\/span><\/p>\n