Jack Kuykendall

Jack Kuykendall
Born	(1940-06-01) June 1, 1940
Residence	Phoenix, AZ, United States
Nationality	American
Known for	Math, Physics, Chemistry, Symmetry-Math
Scientific career
Fields	Science, Golf, Fitness, Military Support Foundation

Jack Kuykendall is an American physicist and independent researcher based in Phoenix, Arizona. He is known for Symmetry-Math (SM), a proposed replacement for what he calls the "Broken-Symmetry Math (BSM)" system in ordinary use — a reform that would eliminate negative and positive numbers, imaginary numbers and absolute values, and that rests on his rejection of the conventional Rule-of-Signs. He has presented this work to the Natural Philosophy Alliance and to the John Chappell Natural Philosophy Society.

Biography

Kuykendall took a BS in physics at Georgia State University and then worked for two years as an assistant research scientist at the Georgia Institute of Technology. He subsequently worked in the medical imaging industry (GE and Zonics) and in the laser industry (Coherent).

In 1986 he turned to what he describes as the discovery of an optimum method of playing golf, and in his own words "changed living to hobby and hobby to living". Alongside this he carried out some twenty-five years of independent research in mathematics and physics, publishing it through his own imprint, Symmetry Math, and the website symmetrymath.com (now offline; an archived copy survives).

Scientific contributions

Breaking the dash/cross codes

Kuykendall dates the origin of his mathematical work to January 2005, when — after four years of study — he says he "broke the dash (-) and cross (+) codes" used in ordinary arithmetic. His starting point was a passage in Courant and Robbins' What Is Mathematics, which concedes that the rule (-1)(-1) = +1 "together with all the other definitions governing negative integers and fractions cannot be proved. They were created by us in order to attain the freedom of operation while preserving the fundamental laws of arithmetic." Kuykendall takes this admission at face value: a rule that cannot be proved, and that was adopted only to preserve the distributive law a(b+c) = ab + ac, is a convention rather than a truth about the world, and in his view a convention that has quietly propagated errors through physics and chemistry ever since.

His central observation is that the same dash symbol is made to carry several incompatible jobs at once. In his analysis the dash (-) is used as a subtraction operator, as a direction in space, as a label meaning "negative", as an exponent meaning divide, as a place-holder for the number of zeros to the right of a decimal point, as the label on the electron in physics, and as a sign attached to enthalpy, entropy and Gibbs free energy in chemistry. The cross (+) is overloaded in exactly the same way — addition operator, opposite direction, "positive", the proton, and the opposite thermodynamic sign. Because the definitions never distinguish these uses, the symbol silently changes meaning in the middle of a calculation. Students, he argues, are therefore made to memorize a catalogue of special cases instead of reasoning from first principles.

Broken symmetry in the number line

Kuykendall traces the problem to the coordinate system introduced by Descartes and Fermat in 1637, which defined space as non-symmetrical: the left side of the number line is governed by different arithmetic from the right side. Since real space is symmetrical and has no preferred frame of reference, he holds that the number line itself was built with a broken symmetry, and that "once an error enters a calculation, all calculations after that point become an extension of the error."

From this he draws a series of consequences. Squaring on the right of the number line behaves one way, while on the left a quantity is squared, turned positive and moved to the right — and something said not to exist is made to exist by squaring it. Imaginary numbers, he argues, were invented only because the square root of a negative does not exist, and absolute values only as a device for turning a negative number into a positive one; both are patches over the original defect rather than discoveries. The same defect, he says, produces broken-symmetry graphs for exponential and trigonometric functions, in which the left side differs from the right, and incorrect answers in the distributive law. He also holds that it lies behind a mathematical error in Einstein's special relativity. Where data happen to follow the non-symmetrical graph the answers remain usable, which is, on his account, why the problem went unnoticed for so long.

Symmetry-Math

The proposed replacement removes negatives, positives, dashes and crosses as labels and restores a symmetrical number line. In Symmetry-Math the dash has exactly one meaning — subtract — and the cross exactly one — add. Quantities that carry orientation are written instead as arrows, each with a magnitude and a direction, and an ampersand-style resultant symbol denotes the combination of arrows by addition and subtraction. Because multiplication is repeated addition, Kuykendall argues there is no such thing as multiplying two arrows together: a number times a direction preserves the direction, and two arrows can only produce a resultant. Zero is excluded from the arrow system, since something with neither magnitude nor direction cannot satisfy the definition of an arrow; the underlying magnitudes and directions remain present even when their resultant is zero.

A claimed advantage is that Symmetry-Math returns both magnitude and direction when the Pythagorean theorem is applied, where conventional treatment returns magnitude alone. More broadly, Kuykendall's ambition is that wave equations should no longer need to be squared merely to convert a negative into a positive, that all Symmetry-Math graphs come out symmetrical, and that calculations in physics and chemistry become intelligible from first principles.

CNPS talks

He has presented in the CNPS online seminar series:

• "Flaws with Our Current Mathematical System" (27 February 2021)
• "Symmetry Math" (6 February 2021)

Abstracts

• 2012 - "Symmetry-Math (SM)" (Read in full), Proceedings of the NPA, Vol. 9, Albuquerque, NM
• 2005 - "Breaking the Dash/Cross Codes of the Rule-of-Signs"

External links

• symmetrymath.com (archived copy, 2015)
• "Symmetry Math - Jack Kuykendall" on YouTube