What is the difference between mechanics and analog? What is the difference and the relationship between mechanics and analog/analogue? I have noticed that mechanical things are often considered analog.
Note: The difference between digital and analog is clear to me.
 A: Originally the term "analog" came from computing, where mechanical computing machines implemented systems that were analogous to the physical systems they simulated. When electronic analog computers came about, a key component was the "operational amplifier". Because they were developed to support math, it turned out that they were easier to understand through abstract circuit theory than simpler devices like triodes. That's convenient.
These days, if you want an electronic amplifier, you usually implement it as a simple analog computer, computing the desired output from the input. Opamp-based integrators and differentiators are useful building blocks of electronic signal processors. Other computation circuits like logarithmic amplifiers and multipliers are also useful.
So, as electronics processing signals understood as continuous variables evolved to resemble analog computers, "analog" came to mean "continuous", as opposed to the discrete signals a digital system processes.
A: "Mechanical" refers to the physical technology; "analog" refers to the nature of the processed signal.
As @John-Doty says in his answer, analog signals/data have continuous values, digital signals/data have descrete values. Both analog and digital computers can be (in whole or in part) electronic, mechanical, optical,
biological, ….
A: "Analog" refers to the continuous nature of a signal, as opposed to a "digital" signal which is discrete. An analog mercury thermometer, for example, can display a continuum of temperature values, while a digital thermometer can only display discrete temperature values (perhaps in 0.1 degree increments).
Mechanical systems are often considered analog because discontinuities don't truly exist in nature, so any physical machine must operate over a continuum of values. A mechanical analog watch, for example, will have the second hand sweep through an infinite continuum of positions over the course of a minute.
Electronic systems, on the other hand, are often considered digital in nature. Even though there are no true discontinuities even in an electrical system, the change involved in flipping a bit from 0 to 1 occurs so quickly it's generally viewed as a discrete change. A digital watch will count the seconds, but does not have a "smoothly" varying signal from one second to the next.
It is possible to have mechanical digital system, generally these would be systems with very fast mechanical transitions that are not viewed as continuous (imagine a mechanical cash register or a perhaps a typewriter). Conversely, non-mechanical systems can be analog, these could perhaps be electrical systems with smoothly varying values like a pulsing light. But generally, mechanical systems produce analog signals and electronic systems produce digital signals, partially as a result of how we experience the different characteristic speeds of transitions between mechanical and electronic systems.
