Cluster Project

How Dense Are You?

Introduction to Clusters

At first glance a person would deduct that a cluster is the same as a group. Both of the words, cluster and group, have Webster’s Dictionary definitions that state that an assembly of individuals connected by a unifying reason, is the primary characteristic of each word. Clusters however are made up of groups yet, groups are not made up of clusters. Why is this relationship not reciprocal? What characteristics beyond quantities of two or more similar objects commonly link individuals together into a cluster? Edward O. Wilson’s Biophilia Hypothesis includes the statement that humans have the “innate tendency to focus on life and lifelike processes.” As the observing scientist in this inquiry process, I will attempt to make more specific the similar characteristics of clusters by linking cross disciplinary principles. Logical deductions will help to define the progression of these characteristics that are linked to the principles of our lifelike world.


When analyzing the lifelike processes I will state the questions in the same inquiry order as I used to come to my conclusions. A range of examples from the natural, biological, man made, geologic, physical, theological, behavioral, human social, and theoretical genres will classify the realms of each example. Multiple realms exist with many of those to be stated.

In order to begin observing it is imperative to know what we are trying to observe. Thus, we will take the definition of a cluster that states, “Clusters refer to the accumulation or movement of objects or ideas to positions of proximity to one another. Such clustering may involve one or more center attractors. Clustering seems to involve some sort of attraction that brings objects together” (Bloom, 2006). The following questions were used during my discoveries to explore the key words accumulation, movement, position, centers, and attractors. The easiest example of this is the appearance and behavior of stars due to gravity.

See Appendix: "Hubbel Movie" to view clusters of stars from the human viewpoint.

+++What types of individual things can be clusters and what is at least one example of each?

Each item on the list will include the following information as shown in the example below. The information on the cluster will be derived from pictures displaying common scenes of the individuals. Every cluster should start with a broad topic that can be broken down into a more specific classification. Then, the structure can be analyzed. To analyze a cluster is to highlight a portion from the whole. This requires separating the interacting factors within the perceived set of individual items. Determining the significant context of the highlighted set of items, also known as the cluster, allows for it to be connected based on its determined, orderly purpose. Other patterns can then be seen within the existing cluster.

• General Category: Specific Example
1. Identified clusters and their structures
2. Other interacting factors
3. Contextual functions and accompanying genres
4. Other related metapatterns

See Appendix: "Example Slides 1-22"

Some of these General Categories where clusters can often be found include, but are not limited to, plants, animals, natural objects, man made objects, atomic matter, movement, ideas, affiliations, allocations, conditions, and collaborations. Specific Categories of identified clusters are chosen based on their distinct separation from the perceived base origin.

Context of the cluster is gained by further discovering the purpose of such things as a cluster of flowers or trees, specific modes of transportation, frequency rates of similar individuals in an area such as diseases or birth defects, and the concentration of populations that makes them distinctly separate from their surroundings. For example, we choose to see clusters of flowers instead of a larger cluster of dried field-brush, because colorful forms of life are regarded by our society as more beautiful, and rarer, than the arguably lesser attractive common vegetations. However, if that secondary set of individuals has a different context, such as a being fire hazard to a nearby house, we may choose to identify the dried-field brush as a dangerous cluster of vegetation; disregarding the bright flowers due to the new context. This choice of cluster leads to the next idea of clusters occurring because of the purpose they serve to the observer.

Because there are so many tangible and intangible “things” that can form into clusters the word individual will be used to refer to them, just as X refers to unknown answers in the field of algebra. Any of the previously mentioned or other possibilities for clusters may be used in place of individual at any given point in time.

Do the individual things within the cluster have to be identical?

No. The individual things within the cluster only have to be as similar as is needed to fulfill the purpose of the observer. This is what separates a cluster from a group. If the intent of pointing out a cluster of trees is to signify a forest, then the specificity of aspen versus ponderosa is a negligible difference.

When does a cluster cease to be a cluster?

1. The make-up of the individuals or the purpose for their relationship changes radically enough to exclude the individuals from one another to the point of extinction; this can only be recognized by the observer. This is commonly seen when an event such as a concert ends and a cluster of people disperse. The event is the unifying purpose as determined by the observer.
2. The density is reduced to the point that it is no longer perceived by the observer as a group due to extreme sparsity or being located outside the perceived point/field of view. This occurrence can be noted when thinking of a traffic jam. Prior and post to an accident there are not significantly more or less cars on the road as whole. The accident often causes great traffic density in one location, or a jam. At other times and locations of view the cars are merely more spread out and the field of view is larger.
3. The density has become so great that the collective of individual objects cease to maintain their sovereignty and thus merge to be classified as a solitary individual. An example of this is in the way America has treated its indigenous peoples. By placing them on solitary reservations, they ceased to have separate, unique distinctions according to our Federal Government. The concentration of these smaller clusters of unique, indigenous peoples forced them into a new, broader classification of Native Americans.

+++Can the observer identify a group that is not a cluster?

No because it is impossible to be impartial after identifying or classifying something. The observer may have to change the expected perception of what it is they wish to identify but, some sort of similarity will always exist because the existence of formed matter is binary between matter and negative space. i.e. There was no longer a bright orange cluster in the sky but, there was still a cluster of colors. As soon as the observer recognizes a group it has thus taken on some semblance of meaning. To not recognize it as a cluster is to determine it extinct.

+++What does a cluster always signify?

1. The individuals must have form. The forms can co-exist or change but they will always exist even in a state of negative space.

2. Those forms, their location, purpose, stability, value, relationships, and stage-within-their-cycle will constitute their perceived status of orderly or chaotic to the observer.

3. A cluster always has some sort of value or importance. If emphasis is given to point out something that is reoccurring as opposed to mere random chance, or being unnoticed, it has acquired uniqueness, distinguishable traits and has been judged for a value of some kind. i.e. The migration trails all clustered near the river because the temperatures were cooler than the open highlands in the desert. Desired temperature is commonly significant in migration because maintaining life while seeking a suitable environment is the value of importance. Those individuals who did not follow that similar path most likely perished.

+++Why would the observer desire individual objects to exist (or not) in a clustered orientation?

Classification of individuals by characteristic is the first step in declaring the possibility of a cluster. The status of said individuals is deemed acceptably as a cluster for the purpose of comprehension or control. Orderly control is desired to allow for the observer to move or exist freely without undesired potential obstructions or uncertainties. Clusters allow for predictable navigation due to a comprehension of surroundings.

Chaos is derived from the observer failing to keep up with a system, or individual forms within that system, that which by all nature are in a process of constant change and motion. A failure to keep up with new perceptions is a failure to recognize potentially existing clusters.

Newton’s Laws of Motion are considered laws because they are lifelike processes common to all individuals. All individuals are “in a state of uniform motion that will remain in that state of motion unless an external force is applied to it” (Baker, 2007). This explains the natural desire for the most efficient route when a course of direction. Constant change of cluster density, or order, is defined by chaos which acts as an obstructing force to the individuals’ states of motion. Locus of perception, desired direction of motion and unaccepted changes in form constitute the need for control. This explains the reasoning behind identifying groups as clusters. It is a method of comprehension by controlling one’s surroundings.

+++Would an observer change their own perceiving position, and/or windows, to have individuals maintain close relative locations of distances to one another, or classifications?

• Changing perception or position is the willingness to compromise efficiency of an individual’s motion in order to maintain a course within the general direction. This creates the equation:
Goal > Desired Course of Motion = Willingness to Compromise

• If there must be an observer’s perception that identifies the total quantity of V. That perception is of V is the subjective variable. The M can then be quantified within the constraints of V. Then, D is the mathematical result of perception. If M exceeds the limitations of V either
o The individual M’s will absolve one another’s sovereignty.
o V, the perception, will be required to increase to accommodate M

• The key in this equation is the unseen factor; the observer. The locations of D, M and V can be established on a linear model based on their values. If O=observer, and is placed on that model, dramatic changes to the perceptions of “order” and “chaos” will take place when the locus of O is moved.

As it stands the total objects within the volumes boundaries are less than ½ of negative space. As you can see, if the field of perception is changed the Volume will change with it. It will affect the density or sparsity to an even greater extent.

See Appendix: "Circular Clusters Video" to view clusters through the lens of an observer changing positions and volumes.

+++Does the volume and density cycle of expanding and contracting to accommodate changes in density without changes in total matter explain the Ever Expanding Universe Theory as originally perceived by Edwin Hubble?

Somewhat; the idea that the volume forced all matter to either concede to its restricted boundaries, merge or force a greater volume in which to exist would give you a mental image similar to the Big Bang Theory (Baker, 2007). The only difference between real to life examples on earth and the purposed theory of our universes origin is in trying to think of the universe being a series of Big Bangs. This makes the universe more like an un-poppable balloon that was turned into a dry ice bomb. It would force expansion from the combustion that would stretch the balloon. Then it would reduce as everything spread and settled to create a greater balance of scarcity. This would follow Newton’s Third Law of Motion, “every action has an equal and opposite reaction. Each bang is an action undesired to the current course of motion.

+++Does an individual with a higher density tend to be more or less chaotic?

Let’s continue to use the same model as before. If another force, let’s say gravity or purposeful clustered migration, were to take effect, then the objects would become predictably chaotic and make connections to the established cluster. These are seen in other metapatterns such as holons as seen with the universe, or artistic calendars such as jazz or dance, webs such as context maps, cycles such as ocean waves, or hierarchies such as a choose your own adventure book. All are predictable as long as they have been experienced before. Yet upon initial experience they may seem random and chaotic. The forces acted upon an individual would possibly infringe on the existing selection of volume that the observer has established. This is a form of ordered chaos showing that the two concepts, order and chaos, are simply the relationship of an observer and control. Jazz music is impulsively chaotic when perception is placed on a singled out instrument but, orderly when viewed as predictable reactions to other instruments in the group as a whole.

+++Do more objects, or points of connection, make a cluster more complex?

A few points must be considered.
a. As proven in the lottery task experiment in which drinking straws and jointed pipe cleaners were used to build a two meter structure, the more vertices or connections that existed, the higher the probability that the structural integrity will change. Too many changes to the structure will cause it to fail.

b. Conversely the more connections and facets that affiliated structures, or singularly classified clusters, have the higher the probability for uniqueness.

c. This would lead to the conclusion that the more unique an individual or classified a cluster is, the higher the probability for failure.

d. This tells us that in order for more complexly structured individuals to succeed, more conscious work is then required to ensure a higher rate of success.

e. Sparsity, or individuals moving toward solitude, may be complex in features but, are lower connections and thus lower in maintenance. This would lead one to declare them simple.
What is an instance that something becomes dense to the point of simplicity?

Revisiting the idea of the loss of sovereignty is first.
a. If the cluster which is recognized as the parts consisting of the whole eliminates the parts, or individuals, it has become solitary or sparse in nature.

The breaking of the individual’s thresholds to the point of merging concession makes a chunk out of a cluster.
a. Human brains learn most efficiently in networked clusters known as chunks; they take multiple individual information parts and merge them into one merged cluster.

b. Chunking occurs most frequently with the practiced familiarity of individual patterns.

c. Predictability of motion or momentary position is how the observer compromises with Newton’s Laws in a favorable manner of control.

d. Chunks are then in turn dense memories with no change in mass and unrelenting volumes.

e. Chunking is then a form of complex mental control, forced density, which would otherwise result in extreme perceived chaos or unfavorable compromise.

See Appendix: "On Memory Video" to view an example of clusters becoming chunks to form order and then how sparsity can create chaos with the same individual items.

+++If more chunks of dense memories are needed to make more connections for a memory that is stronger and/or easier to access, then why would we allow ourselves to strive for complex, hard to maintain machines?
Synaptic pruning takes care of much of the maintenance for us. Poor, or less strong, memories are also left behind in favor of stronger more complexly connected memories. Yet, as learners we decide whether or not to make our knowledge more or less dense based on where we choose to perceive our worlds from. The usable knowledge will only be effective if the environment, context, complexity and relativity of the observer is in a balance suitable for all individuals. The cluster of knowledge must be in an accepted order.

Some if then forms of thinking on some famous song lyrics helped to explain this: Pink Floyd’s lyric “we don’t need no thought control” is a demand for less density. The opposite of control is freedom. Kris Kristofferson wrote, “freedom is just another word for nothing left to lose.” Nothing left to lose would then allow for everything to gain. These philosophical musings beg to wonder if the desire of the brain is to fill itself or free itself. Since different answers exist it must lead back to the position of the observer.
Applications to Education and Conclusions

+++How dense is the mind of a child?

This is a fantastic philosophical question that is similar to, “if a tree falls in a forest with no one around, does it make any sound?” Ultimately importance and value play the greatest factors in establishing the child’s position for observation. Is that position assigned, guided or left to be free? How much resisting force is being applied to nature’s wild course in the education of the child? Does this explain universal knowledge as an unguided but affected course similar to that of the life cycle of a star?

This idea of clusters and chunking necessary but inundating individual pieces of knowledge allows for more freedom by the child. Large concepts taken slowly will increase the Volume for the child. Teaching data collection methods, polling, sampling, memorization and speed reading techniques, and predicting results of variable experiments are some of the lessons that can be included in cluster density studies. In math teaching students to cluster similar numbers and then add or multiple the two is a common estimation technique known as clustering strategy (Cathcart, Pothier, Vance & Bezuk, 2006).

All of these thoughts on the purpose of clusters and their respective densities are most useful in determining their value of importance. As a society, teaching children to identify clusters will help them shape their own systems of value. Learning about the traits of clusters is the primary skill in the identification and finding of patterns and metapatterns. Evidence of societies placing importance on individual things can be seen in the following examples. Having students point out the clusters and validating their choices is an assessment of comprehension either formal or informal. Using the deductive process to establish importance of the clusters they choose can be a technique used in any subject area. The following are samples of comparative clusters. Similar types of comparisons can be used in the classroom to introduce discussion and explore topics.

See Appendix: "Evidence Slides 1-21" that prove what human society and nature determine as important based on the relative cluster density of individuals as perceived by their observers. As an observer what clusters and characteristics do you see? Are those characteristics the main idea of the group?

See Appendix: "Lights from Space" to view the comparative importance of vegetation versus electricity throughout the world. It also shows a comparison to affluent human populations versus the diversity of other life forms.

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