Joosoak Kim

The construction of numbers has historically followed the process of recognizing the properties of geometry. The concept of countability is represented by natural numbers(N) on a straight line, while the completeness of real numbers(R) is derived from the continuous property of the number line. A complex number is established on a plane off the number line, and thereafter, the whole number system is completed. When the process of constructing a number with geometric features is investigated from different perspectives, it provides a new insight into the fundamental principle of a number, which leads to a novel methodology in mathematics.

Special relativity has changed the fundamental view on space and time since Einstein introduced it in 1905. It substitutes four dimensional spacetime for the absolute space and time of Newtonian mechanics. It is believed that the validity of this theory has been fully confirmed empirically for the last one hundred years, and therefore, its status is considered canonical, underpinning all physical principles. However, the spacetime metric is a geometric approach to nature when interpreting natural phenomena. A geometric flaw will be exhibited on this, and an alternative is suggested. The reasonable geometric model of space and time is a three-dimensional space that translates along the time direction. This model accurately represents the true characteristics of nature.