# Nugget: Vector Fields (Answers for Young People)

The following is compiled from different sources, the source links are at the end of every section.

Berners Lee:

“f = m a

says the force (a vector) on something is equal to the acceleration (how much its velocity is changing (another vector) times the mass of the thing. You can figure out how things like spaceships move in 3d space with time.

From there, you can think about values (like density, or pressure, or temperature) which have a single (non vector) value, but a different value in each place. You can think about how those values change with place. How does the pressure in a swimming pool change with depth? Why? Things which have values all over the place are called fields. Think of the pool being filled with little numbers showing the pressure at that place.

Then you can just put what you know about vectors together with what you know about fields, and think of values which are different in different places and times, and also have direction. They are vectors. Imagine a swimming pool full of little arrows, each arrow showing (by size and direction) how fast and which way the water is moving there. Imagine what happens when someone dives in. These are called vector fields. It turns out that when you do calculus with vector fields, you have really neat little results about how stuff swirls around, about how it squashes (or doesn’t), and so on. When you connect how things change with position with how they change with time, then you can show waves happen. And just as it seems that the equations are getting complicated again, then suddenly get simple. It turns out that the differentiation in space can be written as a single “vector operator”, called dell and written ∇”

What is a vector?

A study of motion will involve the introduction of a variety of quantities that are used to describe the physical world. Examples of such quantities include distance, displacement, speed, velocity, acceleration, force, mass, momentum, energy, work, power, etc. All these quantities can by divided into two categories – vectors and scalars. A vector quantity is a quantity that is fully described by both magnitude and direction. On the other hand, a scalar quantity is a quantity that is fully described by its magnitude. The emphasis of this unit is to understand some fundamentals about vectors and to apply the fundamentals in order to understand motion and forces that occur in two dimensions.  Vectors can be represented by use of a scaled vector diagram. On such a diagram, a vector arrow is drawn to represent the vector. The arrow has an obvious tail and arrowhead. The magnitude of a vector is represented by the length of the arrow. A scale is indicated (such as, 1 cm = 5 miles) and the arrow is drawn the proper length according to the chosen scale. The arrow points in the precise direction. Directions are described by the use of some convention. The most common convention is that the direction of a vector is the counterclockwise angle of rotation which that vector makes with respect to due East.

http://www.physicsclassroom.com/class/vectors/Lesson-1/Vectors-and-Direction

When all the forces that act upon an object are balanced, then the object is said to be in a state of equilibrium. The forces are considered to be balanced if the rightward forces are balanced by the leftward forces and the upward forces are balanced by the downward forces. This however does not necessarily mean that all the forces are equal to each other. Consider the two objects pictured in the force diagram shown below. Note that the two objects are at equilibrium because the forces that act upon them are balanced; however, the individual forces are not equal to each other. The 50 N force is not equal to the 30 N force.

If an object is at equilibrium, then the forces are balanced. Balanced is the key word that is used to describe equilibrium situations. Thus, the net force is zero and the acceleration is 0 m/s/s. Objects at equilibrium must have an acceleration of 0 m/s/s. This extends from Newton’s first law of motion. But having an acceleration of 0 m/s/s does not mean the object is at rest. An object at equilibrium is either …

• at rest and staying at rest, or
• in motion and continuing in motion with the same speed and direction.

This too extends from Newton’s first law of motion.

http://www.physicsclassroom.com/class/vectors/Lesson-3/Equilibrium-and-Statics

Vector Equilibrium:

R. Buckmeister Fuller

Geometry which expresses Vector Equilibrium:

Exploration of Fuller’s geometric experiements with vector equilibrium:

The Vector Equilibrium, as its name describes, is the only geometric form wherein all of the vectors are of equal length and angular relationship (60° angles throughout). This includes both from its center point out to its circumferential vertices, and the edges (vectors) connecting all of those vertices. Having the same form as a cuboctahedron, it was Buckminster Fuller who discovered the significance of the full vector symmetry in 1917 and called it the Vector Equilibrium in 1940. With all vectors being exactly the same length and angular relationship, from an energetic perspective, the VE represents the ultimate and perfect condition wherein the movement of energy comes to a state of absolute equilibrium, and therefore absolute stillness and nothingness. As Fuller states, because of this it is the zero-phase from which all other forms emerge.

The most fundamental aspect of the VE to understand is that, being a geometry of absolute equilibrium wherein all fluctuation (and therefore differential) ceases, it is conceptually the geometry of what we call the zero-point or Unified Field — also called the “vacuum” of space. In order for anything to become manifest in the universe, both physically (energy) and metaphysically (consciousness), it requires a fluctuation in the Unified Field, the result of which fluctuation and differential manifests as the Quantum and Spacetime fields that are observable and measurable. Prior to this fluctuation, though, the Unified Field exists as pure potential, and according to contemporary theory in physics it contains an infinite amount of energy (and in cosmometry, as well as spiritual philosophies, an infinite creative potential of consciousness).

Being a geometry of equal vectors and equal 60° angles, it is possible to extend this equilibrium array infinitely outward from the center point of the VE, producing what is called the Isotropic Vector Matrix (IVM). Isotropic means “all the same”, Vector means “line of energy”, and Matrix means “a pattern of lines of energy”. It is this full isotropic vector matrix that can be seen as the infinitely-present-at-all-scales-and-in-perfect-equilibrium geometry of the zero-point Unified Field. Every point in this matrix is a potential center point of a VE around which a condition of dynamic fluctuation may arise to manifest. And as has been stated and is seen in this image, this VE geometry is inherent in this matrix (the green lines comprise the VE):

The IVM also consists of a simple arrangement of alternating tetrahedron and octahedron geometries, as seen in this illustration:

In fact, the VE itself can be seen to consist of a symmetrical array of eight tetrahedons with their bases representing the triangular faces of the VE, and all pointing towards the VE’s center point. (The square faces are the bases of half-octahedron, like the form of the pyramids in Eqypt.)

Given this primary presence of tetrahedons in the VE and IVM, researcher Nassim Haramein sought to determine the most balanced symmetry of them that takes into account the positive and negative polarity of the IVM structure (i.e. “upward” and “downward” pointing tetrahedrons). He identified an arrangement of tetrahedrons in the IVM that, at a scale of complexity one level greater than the primary VE geometry, defines the most balanced array of energy structures (tetrahedons) wherein the positive and negative polarities are equal and without “gaps” in the symmetry. This arrangement consists of 32 positive and 32 negative tetrahedrons for a total 64, and looks like this (notice the underlying VE symmetry as well):