~ The Study of Threes ~
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During this 20th installment of the Mathematics Perspective series I want to explore the impression of Mathematics as a symbolic reference to a type of anatomical description. For example, the usage of a base 10 and the correlation to ten fingers or ten toes, whereas a base 20 would appear to be more appropriate, but may signal a cognitive orientation of the originator(s). And though it is understood that parts of the body were once used as a means by which a primitive person counts (as do some children when counting fingers), I want to look at the old body/number correlation by suggesting that the use of such a method is a reference to the presence of a sentience involving biological develop in terms of an emergent property.
For example, it is thought by some that the emergence of consciousness is due to an accumulation of a certain type and quantity of mental activity associated with a given brain structure, whereby the same amount (quantity) of brain activity occurring with a different insect or animal would not create the emergence of a human type of consciousness, but may nonetheless give rise to a life form-specific consciousness, whereby there are different kinds of consciousness which can be expressed according to the types of biologically-based tools a life form has. If this is the case for humans, then Mathematics might well be viewed in terms of a type of consciousness which has been allowed to and encouraged to and provided with support to develop further.
One might also say that a given aggregate of cells and cell activity have enabled the emergence for different life forms, and are thus an expressed form of consciousness with respect to cellular activity. But perhaps the usage of the word "consciousness" in not your word of choice, because you prefer to restrict it to human-only activity. Be that as it may, the idea of emergence may nonetheless understood, though you disagree with how I am describing it in the present context related to the activity of Mathematics.
The idea of one or more "emergent" properties can well be related to all things. For example, one might say the Universe is an emergent property developed as a result of aggregated atomic nuclei (such as particles) and that each part-icle is itself the emergent property of that which we can only guess at, the concept of a "god" notwithstanding. Similarly, one might say that putting together certain designs of metal and precious stones creates the emergence of a property we call jewelry. From this perspective one might say that the solution to an equation is the emergent property of the equation's parts (symbols, numbers) set in a given order. While for some the idea of Mathematics being an emergent property of an evolved (and evolving) intellect might not receive too much disagreement as a general statement, they might take exception with the idea that Mathematics symbolically represents an appendage of thought processing whose underlying blueprint takes its cue from already existing designs which humanity attempts to label and configure into models which do not resemble some underlying biological theme.
For example, while they might agree that a base 10 can be related to ten fingers, ten toes or five of each, they could interject the view that no such appendage or collection thereof is readily transferred to a base 12 or base 60. (For a refresher of bases, see: History of Bases Used in Ancient Civilizations. Also see: Body-part counting system, and: 12 Mind Blowing Number Systems From Other Languages by Arika Okrent, Dec 12, 2012). Clearly they would argue that not all math systems can easily be viewed as extensions of the human body, or some other body structure of a different life form. And though it is true that some non-biological form can be used as a foundation for a Mathematical system, the fact that in some cases the obverse is true; should bring to mind the idea that at least some math-related patterns do in fact resemble a body form (real or imagined), instead of some other more abstract configurement. Yet, it is not typical for a person looking at mathematics to say that one or another math pattern is related to a body structure, and which are not. Hence, the idea that the recurrence of using patterns-of-two may not cross the mind of someone interested in the deep history of math to consider it to be an extension of the bipedal gait. Indeed, the insistent use of a Binomial Nomenclature, Yin and Yang Duality, and the Binary Computing System, might well be described by some as resulting from something other than a repetitious binary gait that was possibly preceded by a binary swing of the arms (Brachiation) taking place in a jungle, zoo, or other artficialized "monkey bars" characteristic of many schoolyards.
No less, we can find repetitious patterns-of-two in the division of cells whose multiplications can be seen in the numerical quantities being used in computer technology such as 4gb ram, 6 or 8 cores, etc., which are multiples of the "2" pattern also described in the pairing of amino acids (see for example the brief remark: Amino acid pairing by Robert ScottRoot-Bernstein; even though Nature decided to build on the pattern-of-two (transcend) by using a triplet association (for example see: Nucleic Acids to Amino Acids: DNA Specifies Protein by Ann P. Smith, PhD.).
While patterns-of-two are substantial in some instances, and that in others we see it displaced or at least complemented with a pattern-of-three, but that in the case of Mathematics, the transition can be said to be muted though there are examples such as Trigonometry, the Pythagorean theorem, and as a basic equation where one number added, subtracted, multiplied or divided by another number results in a third number. However, the occasions for using a pattern-of-three do not appear to be as substantial for a recurring use of dualities. Much like an organism stuck in a two-appendage stage of development and not representative 3-digits emerging as we see in fingers. For example with respect to anatomy, while we can reference multiple patterns-of-two such as Anterior/Posterior, mouth/anus, bilateral symmetry, proximal/distal, etc., (Anatomical terminology) we can also cite multiple patterns-of-three (List of Three's in Anatomy by Dr. McNulty and Associates).
| Anterior | In front of or front |
| Posterior | In behind of or behind |
| Ventral | Towards the front of the body |
| Dorsal | Towards the back of the body |
| Distal | Away or farthest away from the trunk or the point of origin of the body part |
| Proximal | Closer or towards the trunk or the point of origin of the body part |
| Median | Midline of the body |
| Medial | Towards the median |
| Lateral | Away from median |
| Superior | Towards the top of the head |
| Inferior | Towards the feet |
| Cranial | Towards the head |
| Caudal | Towards the tail |
| External | Towards the surface, superficial |
| Internal | Away from the surface, deep |
| Superficial | Nearer to the surface |
| Deep | Farther from the surface |
| Palmar | Anterior hand or palm of hand (palmar) |
| Dorsal (of hand) | Posterior surface of hand (dorsum) |
| Plantar | Inferior surface of foot (sole) |
| Dorsal (of foot) | Superior surface of foot (dorsum) |
We do not see the same quantitative developmental transition in Mathematics, and thus must consider Mathematics as either being "stuck in the muck" or it is an active "body part" (symbolic extension) that is meant for the glass case of history vestigial organs. While useful in its day, conditions come to change which relinquish a given part into a particular non-usage, or reduced usage state of activity. (Human vestigiality)
- The Appendix
- Wisdom Teeth
- Body Hair (and Arrector Pili)
- Tailbone (or Coccyx)
- Male nipples
- Third Eyelid (or Plica semilunaris)
But some readers may want to continue arguing that concepts in Mathematics are an abstract conceptualization and have no recent or distant connection to or with a body part or biological structure or physical activity. The same can be said for those who see no parallel with the concept of a double-slit experiment and the fact humans use two eyes. The contextual and connecting parallel between having two eyes with two openings involving two "particles" called pupils need not be analyzed as having any formative influence on the development and maintenance of the Double Slit Experiment used as a justification for the idea of a dual nature and single particle called the Wavicle associated with the Wave-Particle Duality.
A person can take the simple equation of 1 + 1 = 2 and claim it to be a pattern-of-three, or a pattern-of-five... and then suggest the "five" is related to the pterodactyl limb. And as we add more layers of discrimination to an equation with signs, symbols and letters, one might also say that such accumulations are like an aggregate of organelles being surrounded by a cell membrane or the skin, nerves, veins, etc., over a skeleton. However, since I am claiming that Mathematics is at a primitive state of development, one might say the basic structure of a simple equation is an exoskeleton which contains features to increase functionality. Yet, since both exoskeleton and skin are replaced and both are sometimes referred to as "thick skins"; one must wonder how it is best to think of Mathematics? Is it on the level of an insect or plant, such as a tree whose bark is replaced and provides an indication of age. Clearly the parallel of looking at the developmental structure of Mathematics over the centuries can be seen as representing different layers of accumulation. Hence, is it of value to think of Mathematics in organic terms of development and that such a development is one of a simply organism?
If we use an electro-mechanical analogy for viewing Mathematics, do we prefer to see it as a simply servo-like mechanism, or something more complex with multiple switches, albeit still using a fundamental binary language? Once we have moved beyond the usage of mathematics for everyday interactions involving basic communications between people, do we come to realize its limitations because it is centered on the existence of ideas developed in an incrementally deteriorating environment? And to an end, what then is the level of degradation that Mathematics exhibits? If it is like someone standing in the middle of a wooden raft on the ocean which is over-filled to capacity (like too many people in the world with respect to resources availability), how do those subjects which claim an elitism (such as Mathematics, Physics, and Chemistry sometimes do), see the incremental deteriorations taking place with those on the outer edges if they are labeled as "fringe" loyalists?
In an attempt to describe Mathematics as an elitist preoccupation which, (like other subjects) stands at the center of human intellectual interests which have difficulty seeing the outer rim of alternative considerations because so much of society is focused on buttressing their existence, the consequence of doing so can only remain afloat for so long before either a new craft is built with remaining resource materials, or humanity allows itself to be forced into evolving as a creature that can exist with the conditions presented along the course of deterioration.
If we view Mathematics as an Artificial Intelligence created by a biological one, just because it is not an organic one, does not mean it is incapable of further development on its own. Whereas when a new idea or different approach is generated by someone working with mathematics can not describe how the new idea or approach arose, and may not have even been recognized when first encountering it, is it truly inappropriate for us to suggest that the creation was self-generated by a process of spontaneity as an emergent property as the result of a certain type of accumulation dependent on time and place... if not a given person? And though it may not be difficult for some to say that Mathematics is the extension of a biological being, does it not also have a biologically-based origin? Though the consideration may be viewed as a philosophical conjecture since ideas are not seen as having a heart, lungs and other organs attached by veins, arteries and a motile blood source, this does not mean biological terms can not be used to describe Mathematics. Whereas Mathematics was born and lives among millions just like dolls, hammers and eye glasses, such items do not grow in the dimensional senses that one might attach to Mathematics, though make, models and social terrains of usage may give the impression that such items have grown over time. For example, stick figure dolls used in an ancient culture evolved over time to be more life-like and in some instances to have a voice, display movement, and of course wear garments. Similarly, hammers have enjoyed a development from bones, rocks and metals into implements used for specialized talents such as carpentry, sheet metal stamping, and heavy pounding. No less, eyeglasses have evolved over time as well.
Date of Origination: 11th September 2022... 4:54 AM
Date of Initial Posting: 2nd January 2023... 10:43 AM