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The Journal of the Royal Institute of Thailand Vol. 27 No. 2 Apr.-Jun. 2002 °“√æ‘ Ÿ ®πå ¡‘ µ‘ ‡«≈“‡ªì πª√‘ ¡“≥‡«°‡µÕ√å ¥â «¬§≥‘ µ»“ µ√å Ù¯ Abstract Mathematic Proof of the Time Dimension as a Vector Poramest Boonsri Rajabhat Institute, Baan Somdej Chauphya, Bangkok, Thailand The purpose of this study is to prove mathematically that time is a vector, not a scalar. Real numbers on a number line are used in the data analysis. The findings indicate that time is a vector. This is due to the simultaneous solutions of both the magnitude and the resultant direction of the time values in the eight octodrants of a three-dimensional body. The investigation is divided into three steps: (1) the search for the position of the time dimension on the number line, (2) the search for the time directions in a three-dimensional body, (3) the solution of the resultant time directions is obtained. The result of the first step indicates that the positions of time values are at the same positions of the real numbers on the number line and can be found by using the two formulas, R+Rt and 0+Rt, when R is the first real number on the number line and t is the time value we wish to know its position on that number line. The zero has two characteristics, an absolute value and a relative value. If the zero is absolute, it will be a point dividing the positive from the negative numbers. If the zero numbers are relative, they will be the line dividing the positive from the negative areas. The result of the second step shows that there are n number lines in the three-dimensional body. There are also n time directions on the number lines. The y and the z axes are used in dividing the x axes into two sides. Each side has a half a sphere’s surface area. Also, the z and the x axis including the x and the y axes are used in dividing the y and the z axes respectively. In addition, every three-dimen- sional body can be divided into eight parts. Each part is called “an octodrant” having its own or- dered triple. The ordered triples of octodrant numbers 1, 2, 3, 4, 5, 6, 7, and 8 are (x, y, z), (x, y, -z), (-x, y, -z), (-x, y, z), (x, -y, z), (x, -y, -z), (-x, -y, -z), and (-x, -y, z) respectively. There are only three time directions along the principal axes in each octodrant and six time directions along the principal axes in eight octodrants. The last step concerns the solution of the resultant time directions in eight octodrants, which can be viewed as evidence to support this finding. The impact of this research has affected many concepts directly and indirectly. By overlooking the time direction, many serious misunderstandings in different fields can arise, such as incorrect analysis of micro and macroeco- nomic neoclassical theories which can be regarded as the current main concept and a big change in the fundamental concept of physics including mathematics. Key words : time dimension, vector quantity, mathematics, physics