Three-dimensional Minimal Axes Coordinate System

A while back, I constructed a physical model of the 3-D variety of my coordinate system, because I was unable to imagine how the space was shaped.  I thought it might have been an icosahedron, a 20-sided figure.  Imagining the 2-D variety is easy.  Even if it is not, it could be drawn.  The shape is a hexagon.  Here is a drawing of the 2-D variety.

The shapes of the areas and spaces within the 2-D and 3-D varieties of the Cartesian coordinate systems are easy to imagine as well.  The 2-D one is a square and the 3-D one is a cube.  Imagining the space within the 3-D variety of my coordinate system is not as easy.  Here are three photographs of the 3-D variety.  The four bundles of like light-colored fuzzy sticks (white, pink (which looks white), yellow and orange) can be thought of as representing the four axes of the coordinate system.  If I call the four light-colored axes-vectors a, b, c, and d, then the vectors a+b, a+c, a+d, b+c, b+d, and c+d are represented by the mixed color bundles, and then the vectors a+b+c, a+b+d, a+c+d, and b+c+d are represented by the dark-colored fuzzy stick bundles.  In the first photograph, the white axis is pointing straight up.  Note how, at certain angles, the space is outlined by a square, and, at certain angles, it is outlined by a regular hexagon (though perspective seems to distort the shape).

I have looked on the WWW for names for the shape of the space in the 3-D variety of my coordinate system, but haven't found any.  I think it might be a new shape, but I'm not certain.

First post on the Minimal Axes Coordinate System

I haven't quite gotten back to reading the book, yet, but I did work on something else.  I worked on the efficiency of the coordinate system that I invented.  I call it the Minimal Axes Coordinate System.

The idea behind the coordinate system is to use the minimal number of axes to define points on a plane, in a space, and so on.  It starts with a line.  To define a point on a line, you specify a value on one of two axes (one axis for one direction and another axis for the opposite direction).  With this, I got rid of the negatives.  Only one bit of information is necessary to pick which axis you use.

To define a point on a plane, you specify two values on each of two axes out of a possible three.  This contrasts with the Cartesian coordinate system, where you would pick two axes out of a possible of four axes.  Less information is necessary to specify which axes you use with my coordinate system.

If you use my coordinate system to store points in a circular or spherical space, you'll notice that there is some wasted space.  The same happens with the Cartesian coordinate system.  But, there is less wasted space with my coordinate system.  So, it seems like if you wanted a computer to model a space, it would be most efficient to use my coordinate system.  Assuming that all axes are of the same length and that the space that is used is circular or spherical, I calculated that 90.7% of the area with my planar coordinate system is usable, whereas 78.5% of the planar Cartesian system is usable.  Similarly, I calculated that 69.8% of the space with my spatial coordinate system is usable, and only 52.4% is usable with the corresponding Cartesian system.

One thing that I just noticed yesterday is that the number of points in my planar coordinate system is less than in the planar Cartesian system.  That was true, but not a problem.  The reason it has fewer points is that it is more efficient in using them.

The other thing that I thought yesterday was that my coordinate system was usually less efficient at specifying the regions in which points lie when modeled by a computer.  This was wrong.  The two-dimensional variety of my coordinate system has three regions, or uses two axes out of three.  The two-dimensional variety of the Cartesian coordinate system has four regions, or uses two axes out of four.  Three regions mean one base-three digit, and four regions mean one base-four digit, or two bits.  Two bits can also represent one base-three digit.  In this case, it seems apparent that there isn't much (or any?) savings of this kind by using my coordinate system. 

The three-dimensional varieties are different, though.  The three-dimensional variety of my coordinate system has four regions, which mean one base-four digit, or two bits.  The three-dimensional variety of the Cartesian system has eight regions, which mean one base-eight digit, or three bits.  Here, we start to see what may be some improvement with using my coordinate system.  I'm not certain that a reduction in the number of regions results in greater efficiency.  It seems that a coordinate system with fewer regions would have fewer points.  It should be pretty easy to figure out if my coordinate system would be more efficient in this way.  I haven't yet done it though.

Aquinas's third argument for existence of God

I'm currently reading the textbook Core Questions in Philosophy by Elliott Sober. I've had some ideas about what it discusses prior to the discussion about Thomas Aquinas's third argument for the existence of God, but I'll save that for later (if ever) and start with what I've read today.

Aquinas's third argument is about contingency. I disagree about what is contingent. According to my book, you, me, the human race and the galaxy are examples of contingent, or unnecessary things. I would say that I (or the self) am a necessary being. The universe would be empty without me. The universe is also a necessary thing. The universe is two things: the totality of all things in the present, or what is going on in my mind in the present. The latter is more true, because there may not be anything outside of my mind. If nothing was going on in my mind, I would be empty. I would be empty without the universe.

I believe that there are things to live or die for, though.

I also believe (and I jump ahead in the argument for the existence of God) that there are levels of need that God has. I think the first thing that happened that Christians believe was that the Son was begotten (not created) from the Father.  (Or maybe was among the first things, I should say.) Then God created the universe. I believe that God had varying levels of need for different things that God created (or maybe even begot). I believe that God wills some things to varying degrees, and I believe that creation can will some things to varying degrees too.

I'm going back to reading again.