To read the book select this link: https://kampungpadi.files.wordpress.com/2010/01/wolfgangrindlerintroductiontospecialrelativity.pdf
What this all means is that if you want to study physics, first of all you have to define what you want to investigate because generally speaking its area of interest involves its own theory or mathematics.
This raises a new question: Can you use all forms of mathematics to describe the physical world?
The answer is temporarily yes but finally no. With temporarily is meant: internal as part of a set of calculations.
For example: The final (calculated) length of an object is always positif.
For example: Temporarly you can use complex numbers, but the final answer can not contain a complex number.
What is important that most physical processes can not be described or explained by mathematics or numbers.
Generally speaking something that does not change can be measured. Something that changes is difficult to measure. That is the problem because what we want to understand is why does something change, what are the interactions involved. If we understand that, we humans can interfer and change the future in a direction we want, for the good or for the worse.
The text above related to the theory of relativity raises an issue related to frames. See: *
Consider a moving observer A in a merrygoround observing a different observer B in that same merrygoround? In that case the reference frame of observer B is in motion with respect to observer A. At the same time also the reference frame of observer A is in motion with respect to observer B. Consider also a different observer C outside the merrygoround. In that case the different reference frames of both A and B each are in motion with respect to observer C.
My concern is what is the use of all these frames why an approach based on one reference frame seems the most logical.
See for more: Reflection 2  Reference frame versus lineair frame
What is even more: Why consider multiple frames when the frames itself don't influence the physical processes which are evolving within each frame. What is even more the physical processes in each will influence each other, on a larger time scale.
See for more: Reflection 2  Reference frame versus lineair frame
Mathematics as a science follows a very rigid manner. It starts with a set of bassic axioms or laws. Using these axioms more complex axioms or laws are develloped all in the mathematical domain. (This text is on purpose kept simple).
Physics as a science is different. The leading component is the physical world, mainly based on observations. In order to describe (its behaviour) mathematics is used. Physics as a science is much less exact as mathematics because it involves uncertainties based on the physical state of the universe. The second component of physics is mathematics. Mathematics as a tool can be used to transform physical observations into single numbers, into a sequence of numbers in time.
Secondly mathematical equations can be developped which establish the relations between different parameters which inturn are an image to the physical changes which happen in the real processes studied.
But that is in principle. In reality the physical results of mathematics used should not be in conflict of what is physical possible.
For example in certain theories parameters (forces) between objects are calculated using the distance between the objects. Within the same theory objects are considered as point masses, mainly to make 'things' simpler. This can raise physical problems when these objects approach each other. From a mathematical point of view the distance between the objects can be come zero which is physical impossible.
Secondly in order to calculate the parameter (a force) involves dividing by zero which leads to infinities (singularities) which are also physical impossible. What this means is that in order to apply mathematics, certain physical constraints should be tested as part of the calculations, in order to prevent situations which are physical impossible.
Consider a second reference frame linked to the center of our Sun. From a local point of view this frame can be considered at rest, but from a global point of view this is a moving frame. You could also consider this frame as a frame with moves in a straight line. However this is an approximation because considering a longer period, this frame moves in a circle, undergoing continuous accelaration.
Forward in time the process can evolve and become more complex.
Backward in time the process becomes simpler
Considering humans the same 'problem' exists.
The purpose of this question is an introduction to a slightly different question:
The fact that certain processes are stable and can de described by mathematics is not an explanation why these processes are stable. The explanation is in the detail of the processes discussed.
Now let us discuss a certain experiment implemented with a test program.
To makes this clear the screen also contains a box, drawn with 12 white lines. The bottom plane corners are marked A,B,C and D. The top plane contains the corners are marked E,F,G and H. In mathematical notation the point A is marked as (0,0,0) and the point H as (1,1,1) The point A is considered the origin. The point H (1,1,1) is at the farthest distance from point A. However it easy to imagine that there are 7 more of thes points

GH .  .  E  F                   DC  .  . AB 
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