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whisper presents a triple isomorphism. The mental operations are the same as the symmetry operations are the same as the logical operations. Said the other way around, the logical operations are the same as the symmetry operations are the same as the mental operations. Said again in a different order, the logical operations are the same as the mental operations are the same as the symmetry operations. Here we have a prime example of cognitive ergonomics at its best. The single act of performing any one automatically performs the other two.
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262:. Serving as a system of highly abbreviated mini truth tables, Zellweger’s claim is that XLA is not only much easier to learn. It is also much easier to use. In fact, when ten-base numerals are used without the abacus and when XLA is used without written laid out rows and columns of truth tables, ordinary operations in both notations are easier to perform during the act of computational writing.
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in the deep structure of XLA has been learned, operations performed on the letter shape symbols are equivalent to logical operations acting on highly abbreviated sets of mini truth tables. Consequently, those using XLA never have the need to interrupt their calculations to check rows and columns of
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In brief, XLA is described in two steps: (1) give the 16 binary connectives the right geometry, the right shape value anatomy; and (2) add the transformational physiology, namely, apply the algebra of simple symmetry groups to the 16 iconic letter shape symbols. Change comes with a whisper. This
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relationships among all 16 binary connectives of two-valued logic, it then becomes far easier for them to perform what are normally considered to be highly abstract logical operations. Zellweger’s publications and models permit students to literally “see”, “touch”, “play with”, “work with”, and
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representing and, or, if) is a lingering, overly abstract, unsystematically selected set of symbols that was primarily developed and used by Peano, Whitehead, and
Russell, or by common acronym PWR. This already exposes the primary weakness. Dot, vee, horseshoe do not carry any information that
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Zellweger's X-stem Logic
Alphabet (XLA) shape value notation for the 16 binary logical connectives. The count of the iconographic letter shapes, 8 odd-stem (– 4 – 4 –) and 8 even-stem (1 – 6 – 1), corresponds to the fifth row of Pascal's Triangle (1 4 6 4 1). (Click Image to
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entitled “The
Simplest Mathematics” (1902). In 1989, he served the Peirce Edition Project again when he added to the proper sequencing of specific sections of Peirce’s extensive manuscripts. These multidisciplinary experiences contributed to the development, over a forty-year period, of his
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laid out truth tables. This basic and central advantage of XLA over PWR is often not fully recognized, even by practiced logicians. Nonetheless, systems of notation evolve and improve over time (e.g. Roman
Numerals to the Decimal System and Imperial Units to the Metric System).
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relations, and the isomorphic sets of interrelations inherent in logic. Conversely, the XLA symbols are iconographic and they possess a shape value. This enables complex logical operations to be performed through easy flips and rotations of the letter shape symbols themselves.
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identifies, specifies, and encodes the truth tables they represent, namely, TFFF, TTTF, and TFTT. In marked contrast, XLA is an intentionally engineered set of sixteen iconographic letter shape symbols specifically designed to improve the efficiency of learning and performing
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from 1969 to 1992. Zellweger’s lifetime achievements and academic contributions to education continue to be significant. Zellweger was probably best known for his creation of a simpler and more mentally intuitive system of logic
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materials, are extensive. A general principle expressed throughout his writings is the need for conscious and deliberate efforts that focus on the sign design and sign engineering of any and all kinds of notation (e.g.
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Each X-stem Logic
Alphabet symbol can be easily flipped or rotated, by eye-hand coordination, through a series of simple symmetry transformations. When a student can visually and manually observe the
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Zellweger’s contribution to the field of logic is best demonstrated through his development of the X-stem Logic
Alphabet (XLA). The XLA notation is a highly advanced extension of both
127:. In 1949–52, still in the era of Robert M. Hutchins and the Great Books Program, he earned his undergraduate degree at the University of Chicago. In 1975–76, he spent a year at the
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for the way we write and communicate logic. He brings to light the importance of a carefully constructed user-friendly notation that would allow students, at earlier stages of
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The Logic
Alphabet, also known as the X-stem Logic Alphabet (XLA), is a notation system that contains a unique and visually iconographic approach to learning and performing
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Whether or not the (PMZ) (XLA) system, or something similar to it, replaces the traditional PWR symbols remains to be seen. Nonetheless, for researchers and
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and its specialized systems of logical, mathematical, chemical and musical notation). Moreover, his publications primarily center on the
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are to arithmetic. Roman
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in 1966. His doctoral dissertation focused on early visual stimulation experience and its later effects on discrimination learning.
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By design, the letter shape of each X-stem Logic
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as possible, while simultaneously possessing multiple layers of rich content. The fundamental and applied principles of
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Geometric structures and symmetry relations revealed by XLA in one to four spatial dimensions. (Click Image to
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Zellweger's XLA shape value notation derived from a 2-dimensional square-framed truth table. (Click Image to Enlarge)
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and improving the structure of its symbols. Specifically, he focuses on the deliberate engineering of a
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Zellweger's evolution of a logic truth table into a four quadrant truth matrix. (Click Image to Enlarge)
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Zellweger’s background is a combination of formal education and extensive research in the fields of
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Zellweger’s teaching system, for logic, integrates the developmental and interactive approaches of
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Zellweger's evolution of a Venn Diagram into a four quadrant truth matrix. (Click Image to Enlarge)
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Dennis, Lynnclaire; McNair, Jytte Brender; Kauffman, Louis H. (2013-05-21).
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It can be said that the current PWR symbols are to logic what
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who served as Chair of the Psychology Department at the
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22:(September 7, 1925 – August 7, 2022) was an American
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Interview with Shea Zellweger by Christine Wertheim
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