Making a cubic trefoil knot from solid wood

This video follows the process of making a trefoil knot from a solid wooden cube. The object has no purpose- other than to create wonder when viewed, or to serve as a display of the wide range for possibility.
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The shape is undoubtedly complex, and so it can quickly become confusing to make one; it is difficult to recreate a shape that you do not first understand. To overcome this obstacle, I use a very simple approach: My goal is to reduce its complexity into a series of simpler constituent steps. At first, the cube consists of 343 little sub-cubes (because 7³ = 343). The task is to remove any cubes that are not part of the design.

Along each step, the cubes that can be removed are, much as a reductive artist (such as a sculptor) would do. So now if you imagine our completed trefoil as a continuous string of 48 cubes, we simply must free the 295 cubes that surround it. We only take the cubes that we are certain we can take, so that each step is a step that we understand the purpose of. Understand the parts, and you will understand the whole (at least in this case).
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With respect to its finish: I am well aware that it could be shinier and more attention-grabbing. I could have lacquered it to 'wow' viewers in the reveal, but I wanted it to look genuine. It has a few flaws, but there are no tricks; this thing was actually carved out of a solid block, and you can tell that when you look at it.
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Orthographic limitation: According to our orthographic template, after the table-saw actions were complete, the object was done. This was not the case. Additional information was still needed to proceed. The mathematical reasons for this are complex and numerous, but the simple fact is such: Orthographic maps are incomplete tools that serve only to aid in human understanding. Much is missing, but our tools must have limits in their design, because we have limits. We lack the processing power to also incorporate a wire-frame isometric model of the object into the existing (simplified) model already in our heads. I am not belittling our intelligence; I find it amazing that I am capable of rotating an imaginary colored cube in my head, and that ability has been enough for me to get by.

Here is a model that will more clearly expose orthographic limitation to you. Imagine a blueprint with views along the X,Y, and Z axes (front, side and top). The blueprint looks the same in every picture: A circle. It would be natural to conclude that the object is a sphere. But a cylinder would still look like a circle from the end, so imagine cutting out a cylinder along all three planes- the finished object would not be a ball at all. It would still have edges! Our psychology likes to fill in the gaps of what we don't know with assumptions based on our past experiences, and this usually works. But it can be tricked, so we would do well to stay aware of it. Thanks for reading this ;)
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Template:
http://postimg.cc/image/yg3ibhaqb/

Music:
"Finding Movement" Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License (creativecommons.org)

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