1. SYMMETRY MATH (SM) By Jack Kuykendall
Symmetry Math and Logic
Breaking the Broken-Symmetry (BS) Math’s
Dash (-), Cross (+) Codes

2. Why is Symmetry Math Needed?
Because the BS Rule-of-Signs, a (-)(-) = (+) is illogical and produces many incorrect answers.
The BS number line is a Broken-Symmetry number line!

3. From “What Is Mathematics” by Courant and Robbins – page 55: The Rule of Signs              (-1) (-1) = +1
Which we set up to govern the multiplication of negative integers, is a consequence of our desire to preserve the distribution law
a(b+c) = ab + ac. 
It took a long time for mathematicians to realize that the “Rule-of-signs” 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. 

4. According to Professor Philip Kanarev, there has not been a major discovery in physics or chemistry by “peer-reviewing-academia” due to THEORY since the early 1900’s.
There have been virtually no science-changing discoveries since the theories of quantum mechanics and relativity were introduced.
One of the reasons is that the math being used is BS math and it operates on Broken-Symmetry and can only provide usable answers.
BS math cannot be used to describe reality in space or time. Space is symmetrical. Space cannot depend on the direction one orientates a coordinate system.
BS mathematicians should have discovered the problem. Instead they invented symbols and definitions and bypassed the real problem, i.e., [(imaginary numbers: i2 = -1) and (absolutely values: |-X|=+X)].

5. The Mathematical Principle of Error
 Joseph A. Rybczyk 1996
Once an error enters a calculation, all calculations after that point become an extension of the error.

6. Dash sign (-) CODES: In Math, used as:
Studying the dash-cross codes of BS math has allowed me to break the codes and understand the reasons for the errors.
Dash sign (-) CODES: In Math, used as:
(-) a subtraction operator
(-) a direction in space; labeled negative (whatever that means)
(-) an exponent to mean divide
(-) the number of zeros to the right of a decimal point; 10-5=
(-) describe the negative half of a sin or cos graph
(-) describe the negative half of an “e” and “1/e” graph
(-) describe the negative side of all numbers raised to a power #x

7. In Physics: In Chemistry: (-) An Electron has been labeled as negative
(-) Anti-Particles have been labeled as negative
In Chemistry:
(-) & (+) Thermochemistry:

8. Cross sign (+) CODES In Math, used (+) an addition operator
(+) a direction in space; labeled positive (whatever that means)
(+) used to show the number of zeros to the left of a decimal point; =
In Physics and Chemistry
(+) Protons have been Labeled as positive
(+) numerous other particles have been Labeled as positive
(+) & (-) Thermochemistry

9. The same dash symbol (-) is used for the numerous different math operations.
The definitions established for the use of the dash symbol (-) do not distinguish between their different operations.
In many math operations, the dash symbol is changed to mean one of the other meanings.
It is amazing that math has proceeded to its current level of use with this illogical use of a symbol.
The same cross symbol (+) is used for numerous different math operations and produces the same illogical answers.

10. A Summary of the BS Broken-Symmetry math
Originated with broken-symmetry in the X,Y,Z plane.
Originated with mirror-broken-symmetry in the X,Z plane.
Created a Rule-of-Signs that cannot be proved.
(-)(-)=(+)
(+)(+)=(+)
(-)(+)=(-)
Created imaginary numbers to compensate for broken-symmetry.
Created absolute values to change illogical negative number answers into positive number answers.
Produces broken symmetry graphs for many functions

11. It took four years of study to discover why a (-)(-)=(+) only works in an imaginary world where space in the dash (-) direction is different from space in the cross (+) direction.
Started working on the problem in August of 2001
Solved in January of 2005
Data points created using BS math produce graphs that are not symmetrical; dash side different from cross side.
However, if a real problem's data points follow a non symmetrical graph, the graph can provide usable answers.
This is why no one discovered the problem.

12. Symmetry-Math(SM) vs Broken-Symmetry(BS) Math
In SM, if we specify that the dash sign (-) means only subtraction and the cross sign (+) means only addition and an appropriate symbol is used for a direction in space, space becomes symmetrical and math becomes logical.
Math operators and directions in space are not the same and the same symbol should not be used to represent them.
Let’s start with the (dash)multiplied by a (dash)=(cross) in the BS system
Usable answers may be obtained, but it will be for illogical reasons.

13. If instead of labeling the left side of a coordinate system as a negative (-), the same as a subtraction operator, we label it with an arrow (  ) to represent the direction, then a subtraction from that arrow direction will be in the opposite direction (  ).
Symmetry-Math: The subtraction of a direction is equal to the opposite direction. The answers are correct using correct logic.
There is NO multiplication of a subtraction operator by a direction in space.
There is just the subtraction of a direction in space.

14. BS Math
A negative multiplied by a positive is equal to a negative. This is illogical.
A subtraction operator multiplied by an addition operator is equal to a subtraction operator. This is illogical.
A dash times a cross is equal to a dash. This is illogical
A direction to the left multiplied by a direction to the right is a direction to the left. This is illogical and Einstein's math error in special relativity

15. A vector moving to the left multiplied by a vector moving to the right is equal to
ONLY to a vector moving to the left that is eight orders of magnitude faster than
The speed of light

16. Symmetry Math: The subtraction of a direction is equal to the opposite direction.
There is no multiplication of a subtraction
operator times a direction in space.

17. BS Math:
What is the meaning of multiplying addition operators? Addition operators are not multiplication operators.

18. A number times a direction maintains the same direction.
Symmetry Math:
A number times a direction maintains the same direction.
The addition of a direction is in the same direction. There is no multiplication by addition operators.

19. Future math books need to eliminate the use of the cross sign (+) to represent something labeled a positive direction in space and the dash sign (-) to represent something labeled a negative direction in space. Space does not have positive and negative directions.
Symbols that are logical and have no illogical representation should be adopted. SM uses either arrows or symbols.

20. Symmetry-Math Number Line

21. Symmetry-Math Rules:
The dash sign (-) will have only one use; subtraction.
The cross sign (+) will have only one use; addition
Directions have an arrow and a number.
There is no multiplication of arrows
All observers see the same direction and magnitude.

22. Negative and Positive Directions in Space
If I asked you to point to a negative direction in space, which way would you point?
Hopefully, you will realize that there is no such thing as a negative direction in space.
If I asked you to point to a positive direction in space, which way would you point?
Again, hopefully, you will realize that there is no such thing as a positive direction in space.

23. BS math is Broken-Symmetry.
Objects on the right side of the x-axis are positive. (+)(+) = (+)
Objects on the left side of the x-axis are negative. (-)(-) = (+); negative math is different from positive math. This is illogical
Objects on the top of the y-axis are positive.
Objects on the bottom of the y-axis are negative.
Objects in the front of the z-axis are positive.
Objects in the back of the z-axis are negative.
Again, BS math of the positive direction (x; right, y; up, and z; front) is different from the BS math of the negative direction (x; left, y; down and z; back).
BS math is Broken-Symmetry.

24. Mirror image is broken symmetry in the x and z axis:
If the left & right-axis are reversed, symmetry is broken. Obs-1 math is different from obs-2.
If the front & back-axis is reversed, symmetry is broken. Obs-1 math is different from obs-2.
If the top & bottom-axis are reversed, symmetry is not broken. Obs-1 math is the same as obs-2.
Math answers cannot depend on which side of a number line an observer sit

25. Absolute values for Displacement
Even for a simple displacement of an object, BS math invented a definition and absolute values to obtain something labeled a positive number answer.
BS Math provides a usable answer without a definition or absolute values:

26. However, If an object starts at
Then, absolute values and a definition must be used.
BS Math makes up a definition that all displacements are positive. Since this example provides an answer with something labeled a negative, the positive definition must be applied and (-2) is changed to (+2). A definition is needed to arrive at a useable answer. This is Illogical.

27. In SM, absolute values and a meaningless definition of “positive” are removed. In SM, objects and directions in space are defined by the direction and magnitude of the resultant of arrows.
With SM, you get total distance traveled by the object and the final direction of the displacement.

28. Illogical and Incorrect BS math for the distributive law

31. Since there can be no negative direction from a squared term in BS math, BS math should be modified or abandoned.
The BS distributive law should be modified or abandoned.
BS math gives incorrect answers because their Rule-of-Signs allows multiplying an arrow going in one direction by an arrow going in another direction.
Clearly this is not logical.
The numbers +1,+2,+3,+4 and –1,-2,-3,-4… should be abandoned.
Arrows should be used that are specific for directions.

32. In BS math, the answer is by definition -16
unless you square -4 and then it is +16.

33. In SM, you cannot multiply arrows going in opposite directions.
The middle two terms are not logical. You cannot multiply opposite directions.
This is a MAJOR error in BS math. They multiply a dash [(-); a direction to the left] by a cross [(+); a direction to the right]. And then “by definition” label the answer dash (-). This is illogical and produces incorrect answers.

34. This is Einstein’s
math error in
Special relativity

35. Magnitude and Direction (MD): An arrow has both a magnitude and
A direction relative to a 2nd object/observer
Magnitude and velocity (MV):
relative to a 2nd object/observer.
Magnitude And acceleration (MA):
relative to a 2nd object/observer.

36. Introducing a new symbol; the “&” sign
Introducing a new symbol; the “&” sign. The “&” sign means resultant; ADD all the Arrows for each direction and then SUBTRACT to find the final resultant.

37. Does not exist: There is no multiplication of arrows
There are two arrows.
One has a magnitude of 3.
One has a magnitude of 5.
The maximum these two arrows can be is 8.
Only the resultant of arrows exist

38. There are no negative SM Arrows.
An SM arrow has a direction and a magnitude.
There are no negative SM Arrows.
There are no positive SM Arrows.
There are no ZERO SM Arrows: A zero would negate the definition of an SM Arrow; something with no magnitude and no direction cannot be the definition of an arrow that is defined as having magnitude and direction.
Arrows and magnitudes are still there even if the resultant is zero.
A resultant is the addition and subtraction of the differences in magnitude and direction arrows

39. There are only resultants when there are multiple arrows
A, B and C are the arrows
(a) A & B; exist
(b) A & B & C; exist
(c) A-B: Do Not Exist in Sm; there are no negatives or positives
(d) A+B-C; Do Not Exist in SM; there are no negatives or positives
There are only resultants when there are multiple arrows

40. SM Graphs versus BS Graphs
Numbers Raised to Powers:
When numbers are raised to powers, the negative sides of all BS math graphs are ILLOGICAL and INCORRECT.

41. In BS math, the dash sign (-) used in this example represents three different operations. They are:
• (-) Subtraction
• (-) A direction to the left
• (-) As an exponent to mean divide by
All positive numbers produce correct results and graphs.
All negative numbers produce incorrect results and graphs.
A direction of three units to the left (-3) is placed in the equation as an exponent;

42. A direction in space (3 units toward the left) changes a whole number to a fraction by using the dash (-) as an exponent rather than a direction in space.  
This is illogical and incorrect. BS math should have performed this operation as
Unfortunately, the answers to problems can come out correct because data points of a real problem fit the curve.
However, the answers will not be due to logical reasoning.
Because the equation produced a curve that real problem data points follow, it has been falsely believed that the equations and graphs are correct.

43. Incorrect BS math and graph for

46. All graphs are symmetrical with SM

47. Two BS Math Equations that Produce Incorrect Answers.

48. This incorrect result is a problem with the distributive law.
SM explains how this incorrect answer is obtained and the problem with the distributive law that allows the error.  

50. JK: definitely a surprise; the answer was incorrect and illogical
Page 148 –149 Barry Mazur – Imagining Numbers
Gerhard Gade University Professor doing math at Harvard University.
Solve this equation using the distributive law:
Do the computation carefully, on paper, using the rules we agreed to. Then ponder your answer, which should be something of a surprise to you, don’t stop there. Think of what your answer might possibly mean or might imply.
JK: definitely a surprise; the answer was
incorrect and illogical

51. Here is the BS math answer that Barry Mazur* calculated.
When the distributive law is used with the BS Rule-of-Signs and one of the signs is a (-) dash sign, the middle two terms always cancel each other. This leads to the incorrect answer of (-1) in the above equation.

52. Barry Mazur did not go back and check his answer with the original equation. If he had, he would have known that the answer was incorrect:

53. BS Illogical and Incorrect Numbers Raised to Powers:
In BS math, only a positive number can have an answer if “n” is an even number (2,4,6,---)
All negative numbers have no solutions.

54. With SM, just add a direction arrow and any number gives the correct answer. 
Since a negative number has no square root answer in BS math, BS mathematicians invented imaginary numbers
i2=-1

55. These equations are easily solved without the use of imaginary numbers with SM math.

56. The 360-degree circle is a 4400 years old , extremely outdated system based on a year of 12 months of 30 days each, that is, 360 days.
SM will use a more logical system that will have a circle of o.

61. In SM math, Pythagoras’ theorem provides both magnitude and direction.
In BS math, Pythagoras’ theorem provides magnitude only.
In SM math, Pythagoras’ theorem provides both
magnitude and direction.

62. In BS math, this is an equation for a traveling wave
must use a square term in order to make the curve symmetric.
This is a major fault in BS math.
In SM math, when t is set to “0”,
; NO SQUARE TERM IS NECESSARY

63. x
f(x) -4
0.019 -3
0.033 -2
0.073 -1
0.273
3.000 1 2 3 4

64. In SM, NO squared terms are needed
< to >
f(<,>)
< -4
0.073 -3
0.097 -2
0.143 -1
0.273
origin
3.000
> 1 2 3 4

66. SPRING

72. In December of 2006, I discovered the mathematical error in Einstein’s Special Relativity.
Einstein used BS math and that math only works in an imaginary world.
It cannot describe real symmetrical space.
Einstein’s Special Relativity should be abandoned and a theory of real space using SM should be used to replace it.
Numerous articles on the Internet show Einstein’s theory to be incorrect, but no one in academia is willing to publish the information.

73. Einstein’s Math Error in Special Relativity Transformation of Velocity
(From Eisenberg- Fundamentals of Modern Physics; pages 27-29)
Consider the particle shown in figure (1-10), moving with velocity v as seen in a frame of reference O,
Figure A moving particle observed from two frames of
reference in uniform translation.

74. We would like to evaluate the velocity v' of the particle, as seen in the frame of reference 0' which is itself moving relative to 0 with velocity v. Measured in the 0 frame, the velocity vector of the particle has com­ponents
The same velocity vector, as measured in the 0' frame,
has components

75. Now from equations (1-13) we know that the relation between the
primed and the unprimed coordinates and times is

76. Take the differential of these equations, remembering that v is a constant. This gives

77. Page 28: Fundamentals of Modern Physics
(1-16)

78. According to Einstein, this equation tells you how to transform
the observed velocity from one frame of reference to another
frame of reference. First we note that, as V/c and v/c approach
zero, the equation approaches those which would be derived
from the Galilean transformation.
Another property of this equation is that it is impossible to
choose V and v such that V’, the magnitude of the velocity
which is seen in the new frame, is greater than c.

79. A confusing INCORRECT and ILLOGICAL answer!
Example: As seen by O, particle 1 has velocity 0.9c in the direction of positive x, and particle 2 has velocity 0.9c in the negative x direction
JK: LOGIC will observe the particles separating at 1.8c.
Einstein equation, however, predicts: To evaluate the velocity of particle 1 with respect to particle 2 we transform from the O frame to the O’ frame moving in the negative x direction with velocity v = -0.9c, using equation We obtain:
A confusing INCORRECT and ILLOGICAL answer!

80. Analyzing Einstein’s BS math Equation

81. Using SM math, a logical answer can be obtained
Cannot multiply a subtraction operator times a direction in space.
Can only subtract and change its direction.
Cannot multiply a direction to the left times a direction to the right.
Cannot multiply opposite directions in space.
Can only solve for the resultant

82. SM math predicts a logical answer using logic

83. They both use illogical BS math.
21st century scientists state, in many articles, that Einstein's General Relativity and Quantum Mechanics are incompatible.
They are not only incompatible, they are both mathematically incorrect.
They both use illogical BS math.

84. This means that Schrödinger's equations should be abandoned.
Imaginary numbers are only necessary in the current BS math system.
This means that Schrödinger's equations should be abandoned.
Any equation in quantum mechanics that uses imaginary number should be abandoned.
Any equations in math that use imaginary numbers should be abandoned.

85. Prof Kanarev has developed logical physics and chemistry
theories without the use of Quantum mechanics or relativity.
A partial list of his theories cover:
Mechanics – replaces Newton
Photon -
Electrons – Protons- Neutrons
Spectroscopy
Nucleus
Atoms & Molecules
Electrodynamics
Heat
Curvature of Space – replaces Schwarzcchild’s equation

86. Kanarev’s Hypothesis:
Electron align linearly with proton. They do NOT spin
or form clouds around the nucleus.
Neutrons are in the center of atom
Proton are outside of Neutrons
The wavelength of all particles is the experimental radius
Double slit experiment explained correctly
Heisenberg’s inequality explained correctly
is the radius of approach of the
magnetic lines around the torus of the electron

87. Why water expands when it freezes.
Why water expands when it freezes
Electron clusters form lightning
The meaning of Planck's constant is explained:
If the mr-constant describes a ring, the equations describe experiments.
If the mr-constant describes a wave, the equations do NOT describe experiments.

88. Kanarev’s 5 Equations of Mechanics
Kanarev’s 1st Equation: Acceleration
The sum of the Actions working on a moving body is never equal to zero
Kanarev’s 2nd Equation: Uniform motion
Kanarev’s 3rd Equation:
Kanarev’s 4th Equation:
Equal and opposite reaction
Kanarev’s 5th Equation:

89. Kanarev’s Photon model is a rolling ring.
His equations accurately describe known experiments with photons:
Electromagnetic radiation should be called photon radiation
Diffraction and interference are the same phenomena
Correctly explains the double slit experiment without quantum equations
Correctly explains the meaning of Heisenberg’s inequality

90. Charge
Magnetic action

91. Proton
Neutron
The intensity of the magnetic action near the geometrical center of the proton ring is so great that we theorize that it is the strong nuclear force.

94. Lithium

95. Beryllium

96. Carbon

97. Diamond

98. Graphene

99. H2O
H2O Cluster

100. free electrons in each cubic centimeter of a copper wire.
There are 8.2>22 (82,000,000,000,000,000,000,000)
free electrons in each cubic centimeter of a copper wire.
Since no protons are free, there cannot be an
Attractive charge action proton potential in a wire.

104. There are no protons present at one plate and electrons present at the other plate.

108. Temperatures between are formed with photons from the infra-red range
Temperatures between are formed with photons from the infra-red range. As the temperature increase, the radiuses of the photons decrease .

109. Temperature (felt as HEAT by humans) is formed by photon emission from electrons.

110. Kanarev’s correct equation
Schwarzschild’s (incorrect) radius equation:
Kanarev’s correct equation

123. My website: Symmetrymath.com
is my interpretation of the Author’s I have referenced.
I do not claim that any of these authors will agree with
my interpretations.
I leave it to anyone who visits my site to decide the logic
of my interpretation.