# Category Archives: Featured Articles

Featured articles are long and deserve more attention. They have been saved in PDF format and html formats so you may print them out. Please enjoy the rich, thoughtful and provoking articles.

# Research into the “Threes” Phenomena – Herb O. Buckland

My views of the “Threes” phenomena have changed over the years. Whereas many decades ago I began collecting various patterns-of-three examples as if they constituted some fundamental universal law, I have come to realize that many of the so-called universals exist with what may be termed an auxiliary pattern. Namely, a 3-to-1 ratio that I alternatively describe as a 3-into-1, 3-from-1, or 3-as-1, though these proportions can be turned around to read 1-into-3, 1-from-3, or 1-as-3, whether one uses numbers, letters, symbols, sounds, etc., mix or match as you will. . .

The above paragraph is only an excerpt. Herb has an amazing site. I encourage you to read more at http://threesology.org. He also has laminated poster for sale! You may contact him directly at herbobuckland@hotmail.com.

# Triplicity – Simon Kelsey

What is Triplicity?
According to the Merriam-Webster dictionary Triplicity has two meanings or definitions:

1. Triplicity is one of the groups of three signs (each distant 120 degrees from the other two) into which the signs of the zodiac are divided.
2. Triplicity is the quality or state of being triple or threefold.
3. To these I propose adding a third meaning or definition: Triplicity is the phenomenon of Threeness in life.

Why a third one?  Well let’s step back a bit and begin by defining the term “threes”.  There are three primary colors red, blue and green, and three states of matter gas, liquid and solid.  Space has three dimensions and we divide time into the past, present and future.  In other words “threes” are groups of three things that are distinct from and yet related to each other.

What is really interesting is that there are numerous “threes” in every sphere of life.  Threes are an observable phenomenon.  I considered various names for this phenomenon and eventually settled on Triplicity, and so the third meaning or definition.

The Wikipedia entry on ternary numeral systems notes:

A base-three system is used in Islam to keep track of counting Tasbih to 99 or to 100 on a single hand for counting prayers (as alternative for the Misbaha). The mnemonic benefit is that counting within this system then reduces distraction since the counter needs only to divide Tasbihs into groups of three.

use of ternary numbers conveniently to convey self-similar structures like a Sierpinski Triangle or a Cantor set. The ternary representation is useful for defining the Cantor Set and related point sets, because of the way the Cantor set is constructed.

ternary as being the integer base with the highest radix economy, followed closely by binary and quaternary. It has been used for some computing systems because of this efficiency. Rarely mentioned is the existence of ternary computers (notably defining a tryte to be 6 trits, analogous to the binary byte).

use in the representation of 3 option trees, such as phone menu systems, which allow a simple path to any branch.

Of further relevance to the pattern of argument here is the role of ternary valued logic. Such a three-valued or trivalent logic is one in which there are three truth values indicating true, false and some third value. This is contrasted with the more common bivalent logics (mentioned above) which provide only for true and false. or guilty and not-guilty. An exception occurs in the Scottish legal system providing additionally for not-proven (a distinction which would seem to be of considerable current significance with respect to many detained in Guantanamo Bay).

Conceptual form and basic ideas were initially created by Jan Lukasiewicz, C. I. Lewis and Sulski. These were then re-formulated by Grigore Moisil in an axiomatic algebraic form, and also extended to n-valued logics. In the argument here, the question is whether the pattern in the diagram above holds a meaningful relationship with a range of multi-valued logic systems.

# threesology.org (The Study of Threes)

Herb O Buckand has an enormous interest in the structure of threes and has been collecting and examining these concepts for years. He has an exciting website for his Threseology Research Journal located at http://www.threesology.org. Here he delves into concepts in threes in many different areas. He is a true generalist.

Please visit and enjoy the wealth of information provided at this site. If you wish to communicate directly with Herb, you can reach him at Herb O. Buckland (herbobuckland@hotmail.com).

Herb also has some amazing posters he created with thousands of threes! Go to http://www.threesology.org/threes-posters.php.

# Theories of Humor – Monro

Monro, D. H. “Theories of Humor.” Writing and Reading Across the Curriculum 3rd ed. Laurence Behrens and Leonard J. Rosen, eds. Glenview, IL: Scott, Foresman and Company, 1988. 349-55.

D[avid] H[ector] Monro (1911-2001 [pdf]), professor of philosophy at Monash University, Victoria, Australia, wrote The Argument of Laughter and Godwin’s Moral Philosophy. The following piece appeared in Collier’s Encyclopedia.

Humor is a term which may be used in both a wide and a narrow sense. In the wider sense, it is applied to all literature and to all informal speech or writing in which the object is to amuse, or rouse laughter in, the reader or hearer. In its narrower sense, humor is distinguished from wit, satire, and farce. It is less intellectual and more imaginative than wit, being concerned more with character and situation than with plays upon words or upon ideas; more sympathetic and less cruel than satire; more subtle than farce. On the other side, it shades into fancy and imagination, since it is concerned, as they are, with exploring the possibilities of unlikely situations or combinations of ideas, but differs from them in being concerned only with the laughable aspects of these imagined situations.

But what exactly is it about a situation that makes it laughable? We all know that some things do make us laugh; but it is very hard to say just what it is that these laughable things have in common. Theories of humor (in the wider sense) are attempts to solve this problem. They may be divided into three main types: superiority theories, incongruity theories, and relief theories. A fourth type of theory, which takes the central feature of humor to be ambivalence, a mingling of attraction and repulsion, is of minor importance.

# Number as Archetype

By Robin Robertson

### Excerpts:

• … Because human beings are capable of counting (“one, two, three…”), we imagine that is how numbers were arrived at.
• … The story seems to demonstrate that a crow (or at least the crow in the story) has a sense of “one”, “two”, “three”, and “many”.
• … In brief, one corresponds to a stage of non-differentiation; two—polarity or opposition; three—movement toward resolution, as expressed, e.g., in the Christian trinity.

This paper has been adapted from the final chapter of Jungian Archetypes: Jung, Godel and the History of Archetypes, Nicolas-Hay, 1996, with the permission of Nicolas-Hay. Copyright Nicolas-Hay Publishers.

The sequence of natural numbers turns out to be unexpectedly more than a mere stringing together of identical units: it contains the whole of mathematics and everything yet to be discovered in this field. — Carl Jung[1]

It has turned out that (under the assumption that modern mathematics is consistent) the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic; i.e., the domain of the kind of elementary indisputable evidence that may be most fittingly compared with sense perception. — Kurt Godel[2]