SYMMETRY MATH (SM) By Jack Kuykendall

1. Symmetry Math and Logic SYMMETRY MATH (SM)By Jack Kuykendall 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. 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=0.00001 • (-) 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: • (-) An Electron has been labeled as negative • (-) Anti-Particles have been labeled as negative InChemistry: • (-) & (+) 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; 10+5 = 100000 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. 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. 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. The “&” sign means resultant; ADD all the Arrows for each direction and then SUBTRACT to find the final resultant.

37. 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. An SM arrow has a direction and a magnitude. • There are no negativeSM Arrows. • There are no positiveSM Arrows. • There are no ZEROSM 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. 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. 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