From differential to hypothesis on Gravity and Electromagnetism

This idea is first conceive when I am writing the article about the differential of the n-th power of consecutive numbers. Since if we do differentiation on them, we would eventually reach a constant and then zero. Thus the external irregularity of the pattern of the value of n-th power is itself a manifestation of hidden regularity.
Now if we apply the same line of thinking in gravity and electromagnetism, we notice that they are both decreased with the square of distance. And the reciprocal of them follow the same patterns as the 2-th power of consecutive length. Thus, in a sense, the external irregularity of their reciprocal of strength of them are themselves a manifestation of hidden regularity. Moreover, if we use the term differential space for the differential of any functions, then we notice that the differential space of the reciprocal of strength of them is linear and directly proportional to distance. Therefore, in the differential space of the reciprocal gravity and electromagnetism, they are directly related to the distance from the sources. This relationship is only distorted because the gravity and electromagnetism only lives in space of space, it has only effect on motion of motion but not motion itself. In a sense it is like force that it has only Secondary Effect on motion. I could hypothesis it is only because Space has differentiated to Secondary Space so gravity and electromagnetism has an effect.
Notice we have been talking about is the reciprocal of strength of Gravity and Electromagnetism, i.e. The lack of Gravity and Electromagnetism strength is somehow a linear phenomena directly proportional to distance. That must related to the nature of space-time itself. It is like space-time provide a mechanism to prevent the spread of Gravity and Electromagnetism field that is linear in its nature.
Assumed that Gravity and Electromagnetism strength is indeed a consequence of Differential Space, then what happen if we reverse the process of differentiation to reveal its Primary? By integrating the Gravity and Electromagnetism strength twice, we arrived at the natural logarithm. Thus we could said the irregularity of variation of strength of Gravity and Electromagnetism is a resulted from the differential Space of originally regular. So why is Gravity and Electromagnetism field strength is originally logarithmic?