Good book/resource/chapters on the foundations and science of accuracy, precision, and measurement? I guess measurement and accuracy is a science, and thus, I assume there's foundations and universal theory that can be learned from scratch, independently of international conventions used, just like physics is universal and does not depend on the conventions/measurements somebody uses.
This is more or less what I am looking for:

*

*Will not hide the math, nor the science. Will go ahead and say why and how.

*Will perhaps start from universal considerations of geometry, in order to teach: how to make increasingly accurate flat surfaces, or straight lines, or whatever. Or, perhaps instead, will build the basis of accuracy from universal principles.

*Will give the universal/scientific tools to judge how good is a defined measurement standard. Will show how to construct good measurement standards, perhaps arguing pros/cons of certain approaches.

*Will talk about how to make precise accurate measurements, or how to build machines/things with precision, or how to build devices that measure physical quantities accurately [how to measure distances, angles, time, weight, electric current, temperature, etc, accurately].

*Will perhaps dive into more sophisticated approaches in how to get precision, perhaps in the micrometer level, or more.

*Will allow me to understand why things are the way they are, and the principles used for ever more accurate measurements/devices.

In summary: Perhaps something like that or like that [but with math, and going deep].
All of these items is not really needed. Even if it is just a chapter of a book, I wanna know about it!  =].
This is just a vague idea of what I might be looking for, because, the truth is: I don't know metrology or these things, and I am looking for a good book to learn it.
I hope I was able to communicate accurately more or less what I'd like to find. I apologize if I weren't. I look forward to check out any recommendations you might bring, and I appreciate any pointers or any answers.
 A: I assume you mean you don't want a book about how to do specific experiments or measure specific things, since you say a few paragraphs later that you want a book about how to make precise accurate measurements and how to evaluate the quality of somebody else's measurements.
Try Experimentation: An Introduction to Measurement Theory and Experiment Design (3rd ed.) by D.C. Baird.
From the first chapter (edited for brevity):

This book provides an introduction to the study of experimenting in
general, irrespective of the area in which the experimenting is
carried out. Some students may pursue careers in physics
research; the book will serve as a suitable introduction to their
continued studies. Many others will pursue careers in completely
different areas. For our purposes, the word experimentation
means the whole process of identifying a portion of the world around
us, obtaining information from it, and interpreting that
information. This book is intended to meet the needs of all who
are either engaged themselves in any kind of study of the world around
us, or who must form a judgment on scientific statements made by
others.

The intended reader is an undergraduate physics student, however, a good high school level of physics competence is all that is required. The reader should have basic competence with multivariable calculus and statistics to get the most out of the book, but significant sections of the book require no calculus knowledge at all. High school or university freshman level statistics should be sufficient.
This is a book about experiment and measurement. It is not about engineering and manufacturing machines to a tolerance. It is not about boot-strapping increasingly perfect geometric shapes or increasingly effective measuring tools.
