For precision, the sapphire clock outshines even the best atomic clocks

A real weird unit is km/l or miles per gallon, which cancels out to a unit of area.

Now, normally we do specify colors of light as frequencies in just the way you say, some number of oscillations per second (unless those frequencies are higher than about 10 GHz), but we can't do that in this case, because it would make the definition circular in just the way you say. Instead, the color of light in question is specified in terms of a quantum-physical phenomenon that produces a very precise color. The cesium-133 atom doesn't need to look at a clock to see how fast to resonate. If archaeologists from the planet Plarx land on Earth in the 37th century and are trying to figure out how our culture measured time, and this comment is all that remains from our society, well, all they need to do is build a cesium maser and hook it up to a circuit that counts to 9,192,631,770. (Actually, probably someone on Plarx has already published the spectrum of cesium, so they can just see that the oscillation period of its hyperfine transition corresponds to 0.000000038134825 of their zorps, and then they know that a "second" is 350.5594 zorps long.)

We used to do the same thing with the meter: "1650763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum." Usually we give wavelengths in terms of the meter, but in this case we're giving the meter in terms of wavelengths. That's because the wavelength is a physically existing, objective phenomenon, which can be measured by anyone. Now, instead, the meter is defined in terms of the second: a meter is defined as the distance light travels in a vacuum 299,792,458 times in a second. So the Plarxian archaeologists will have to figure out what a "second" is first, if they're working from that definition.

The primitive physical quantities are those quantities that in a theory of physics cannot be defined as functions of other previously defined quantities.

Therefore any theory of physics starts from a list of primitive physical quantities and the other quantities are defined using the primitive quantities.

Sometimes, during the evolution of physics, previously unknown relationships between quantities are discovered, which cause a previously primitive quantity to be defined now using other quantities, so in the updated theory the number of primitive quantities is reduced.

The most important examples of such cases are the discovery caused by the Oersted experiment that the magnetism is also produced by the electric charge and not by a distinct magnetic charge and the discovery as a consequence of the atomic theory and of the statistical physics that the temperature is not a primitive quantity but one that can be defined based on the distribution of the kinetic energy of an ensemble of particles.

Examples of primitive physical quantities are time, length and force.

When you establish a system of units of measurement for the physical quantities, some units are chosen arbitrary and are designated as base units. The other units are derived from them using the relationships that exist between physical quantities during various kinds of experiments.

What confuses many people, including you, is that there exists absolutely no relationship between the quantities that are primitive and the quantities whose units are chosen to be base units.

In a theory of physics, the number of primitive quantities is fixed, but the number of base units is completely arbitrary.

There might be e.g. 10 primitive quantities, but one may choose to have 0, 1, 2, 10, 20 or 50 base units.

Having too many base units makes the computations inconvenient, because in each relationship between quantities an extra base unit may introduce an extra arbitrary multiplication factor, a.k.a. "universal constant".

The systems with too few base units are disliked by many people because the units for many frequently used physical quantities become either very large or very small in comparison with the usual values, or they just become too different from the traditional units used for those quantities.

So the SI is a balance between these 2 conflicting requirements. It has much more base units than necessary but much less than the traditional systems of units that existed before SI.

The base units are chosen so that it is possible to make some devices that realize the units with high accuracy and precision.

Because of this requirement, the quantities with base units are very seldom also primitive quantities.

For a very long time, the length was both a primitive quantity and one whose unit was a base unit, because you could choose some stick or rod as the base unit for length.

Because any object has a length that is variable in time when measured with high precision, this had to be abandoned and the length does not have a base unit now (in reality it does not have a base unit, even if the SI definition attempts to preserve the illusion that the length still has a base unit).

For time, it was never possible to keep with you a certain time so the base unit has always been not for time but for the period of a periodic system or, equivalently, for its frequency. In the beginning the periodic phenomenon was the rotation of the Earth, then it was the revolution of the Earth around the Sun, then an atomic clock. The unit of time has always been derived from the unit of frequency (or of period).

The confusion for those who are not aware how the systems of units of measurement work is greatly enhanced by the definitions of the SI units, which, in an attempt to reduce the confusion (?!) define the units for the same physical quantities that were chosen to have base units at the creation of the SI, even if in fact most of them no longer have true base units.

Even at the creation of SI, the time was named as a quantity with a base unit just because it is well known as a primitive quantity, even if the actual definition defined the time unit as derived from the unit of period and later from the unit of frequency.

Today, the SI is obtained from a simpler system with much less base units by taking the derived units of various quantities, multiplying them with arbitrary factors chosen so that the new SI units match the older SI units and setting these multiplied units as the base units of the current SI.

In this case Accuracy mean the reference as in: this device reads 10C but could actual temperature could be 8 or 12. Because it drift according to multiple factors.

Precision means the linearity or if you prefer resolution (I think). Datasheet for the device says +/-0,5C meaning you can't have a reading more precise than 1C with that device. I think the term linearity apply if you try to mesure below that value: the reading may become non-linear because of fluctuaction, noise or other errors in the device.

In the precise ruler if you measure out a 1000 milimeters you will be 1 milimeter short. In the accurate ruler you will be 1/10th of a millimetre long or short.

Both are useful. If you're a carpenter measuring a space to put a cabinet in and you use the same ruler to measure the openings as to cut the cabinet you'd rather the ruler be precise than accurate. If you email those measurements to someone else you'd rather the ruler be accurate than precise.

An atomic clock is very consistent across devices as it exploits the properties of an element which is much more repeatable (just have to have a quantity of the element).

What you want is that both the average duration of a clock period is exactly a certain fraction of a second and also its variance is very small.

However, you cannot have both in the same clock device.

For atomic clocks, you know very well which is the average value, but the duration of the clock periods has a large variance.

For sapphire clocks, the variance of the duration of the clock periods is very small but the average value is known only approximately.

According to the terminology used in the article, someone who shoots accurately spreads the shots over a large area, but the center of the area is the same as the center of the shooting target.

On the other hand, someone who shoots precisely sends all the shots through the same hole in the shooting target, but that hole is far from the center of the target.

The result of the difficulty of having both high accuracy and high precision in the same clock device is that whenever you measure short times, you must use either quartz clocks for a cheaper solution or sapphire clocks for higher precision (or also hydrogen masers in the past, before the development of sapphire clocks).

Because the average frequency of the precise clock is not known, you must either measure it periodically with an atomic clock and correct digitally the measurement results or you must use a PLL loop to adjust continuously the frequency to be in a certain ratio with the average frequency of the atomic clock.