A new unconscious paradigm at the heart of mathematics and physics

It is already the case that philosophical foundations of mathematics and physics, need a serious critical analysis and revision of a number of generally accepted assumptions. In the future, this work may lead to a shift in the paradigm related to mathematics and physics. The article deals with the problem of the ideas of actual and potential infinity being not distinguished in the «fragmented thinking» of many mathematicians. We consider it necessary to differentiate between the concept of «representation of a number by an infinite decimal fraction» and the concept of «writing a numeral». A real number can be written in different ways, but every number must be uniquely represented using an infinite decimal fraction. First of all, we overcome the ambiguity of the representation of number 1 by assuming a potentially infinite set of signs of a periodic fraction and an actually infinite set of signs of a non-periodic fraction. This leads to the following harmonious scientific and philosophical system required by broad-minded scientists. 1. Every real number, including 0, (9) is represented by a single point of a continuous number line. 2. Every irrational number in decimal representation, unlike a rational number, does not have the last digit. 3. Real space, as well as past and future time are not mathematically equal and are referents of potentially and actually infinite, countable and uncountable sets. 4. The motion of a quantum micro-object, as a fundamental particle, is mathematically imaginary because a quantum particle has a countable set of points in time that is insufficient to move temporally and an uncountable set of points in space that is excessive for moving along the trajectory. Therefore, the motion of a quantum particle can be described as the path of a point in the plane of a complex variable.