The pages in this site have been arranged similarly to chapters of a book and cover specific topics. Each page has entries in the form of blog posts which relate to the individual concepts, or paragraphs. The reason that we’ve chosen this arrangement is that it allows us to easily maintain an edit history of the material presented here. That way, if certain materials are updated after they have been referenced and linked to, the researcher will be able to go back and find the original material that was being discussed at the time the article at the other location was written.
Figure 1.1 The Map of Physics – Image by Dominic Walliman
Direction (or orientation) is a component of space. No one seems to disagree with this arrangement. There doesn’t seem to be any authoritative source on whether direction is a property, quality, quantity, attribute, parameter, constant, or whatever. Some experts claim that it’s a thing that isn’t a thing. Additional perspective about this thing can be realized through the use of this geometric approach. It doesn’t appear to change anything that is already known regarding Euclidean 3-space, except for around the extremely remote edges where we get very near to the chasm of ignorance.
The simplest way to organize the information is to place things into two distinct piles, one which contains things that are known (proven), and another separate pile that contains speculation or theories that may or may not have merit. Since the entire topic is novel, there are no existing goalposts that can be applied in order to formulate this partition. Therefore, we can only make the logical distinction between the actual mathematics (mostly trigonometry and algebra which we know to be correct) and the speculative applications for the math with regards to physics.
We encourage readers to offer comments on the material presented here. Membership is required if you wish to comment on any of the material presented here. All comments will be reviewed before posting. If we reject your comment on technical grounds, then we will try to notify you by email. It is not our intention to try and censor any inquiry into this material, quite the contrary.
If you wish to offer assistance with this project, then please review the Participation page. We’re currently running this site as a hobby, so please give us a lot of latitude (time) when it comes to reviewing your comments.
The way that it’s mathematically expressed, space actually comprises a set of three 2D planes, arranged orthogonally. In this usage, each individual “dimension” is actually a plane, or a set of two perpendicular directions, where each direction is also called a “dimension.” The x and y dimensions combine to form the xy-plane which is perpendicular (normal) to the z axis; it is the direction of the z axis and not the location of the z axis that is the thing which is perpendicular to the x direction and the y direction. For these reasons, it would be more meaningful (less confusing or less arbitrary) to specify our mathematical treatment of space as 2D3 rather than 3D. It’s the reason why our mathematical treatment of Euclidean 3-space has octants… 2x2x2=8.
Direction is currently considered to be a ratio between lengths. This is different (mathematically and conceptually) from representing direction as a quantity. Ratios are not quantities. They are a comparison between two or more quantities, which is fundamentally different from how quantities themselves are represented.
So, what is direction, really? We can call it angular position, and we can call the change in angular position angular velocity, and we can call the change in angular velocity angular acceleration.
In case it isn’t obvious, there is a stunning symmetry with length here. We can call it linear distance, where we can call the change in linear distance speed, and the change in speed acceleration.
Even more stunning is the fact that when we add direction to length we get position, when we add direction to distance we get displacement, and when we add direction to speed we get velocity.
Still, even in light of all these facts, there seems to be a winning argument (for reasons no one can explain other than the old “we’ve always done it that way”) that direction isn’t really a base quantity, like time or length. It’s supposed to be a thing that isn’t really a thing, whereas the other two are things that really are things. This approach is rather arbitrary, especially since direction can now be quantified as a scalar value or an amount, exactly like time and length are both quantified.
Figure 2.1 – NIST Subway Diagram
So, what is direction, really?
Currently, direction is an orphan when it comes to understanding physical quantities and how they relate to one another. The basic unit that is used to define an angle, the radian, is the disconnected unit at the lower right in the NIST diagram. Why is that? And why is the unit of the solid angle, the steradian, a component of luminous flux? What’s up with that?
It’s generally understood that, when the time dimension is subtracted from spacetime, we are left with Euclidean 3-space. This is usually interpreted to mean that, once we look at spacetime without the time component, we’re left with space, or what in SI units is called volume. The SI unit for volume is which is consistent with our understanding of direction being simply a ratio between lengths. In this case, the three orthogonal lengths can be used to define an object without ever having to define orthogonality. This seems like an incomplete description of what a volume actually is.
Just as we can use a direction and a radius for identifying a position, there’s also another interesting use for combining a direction and a radius. We can use a direction and a radius to specify a volume, and this raises some other issues that have to be explained somehow.
Length in two-dimensional space (in other words, length in a plane) defines distance. If the distance is referenced from a point, then the circle is the set of all points that are this particular distance away from that point, or center. The radius is the length or measurement of the distance from the center to the perimeter. Similarly, an angle in two-dimensional space defines direction. If the direction is referenced from a line, then the direction is the difference in orientation between the two rays. This difference in orientation is expressed as an angle, which is the measurement of the orientation that separates the two directions.
Moving to three-dimensional space, the sphere defines a relative distance from the center of the sphere, with the radius of the sphere being the expression or measurement of length. Similarly, the aperture defines the relative orientation between the axis and the generatrix of the cone, with the angle being the expression or measurement of direction. In either case, the solid shape is what describes the physical property (quality, quantity, attribute, etc.)