Logarithmic Metrics


Read here about units of measurement that are logarithmic. Such units reflect an exponential world, and may be more useful to comprehending scale than linear units.

Exponential Units


Luminosity

Hipparchus stellar brightness scale is an early example of intuitive logarithmic thinking.

Early case of logarithmic scale was when the Greek astronomer Hipparchus divided the stars into six categories of brightness. Antares was first magnitude, Polaris second and so on. In radiant energy Antares is 2.5 as bright as Polaris, which is 2.5 times as bright as a third magnitude star. Today the scale is extended thirty steps in one direction to include the sun and 24 in the opposite to record the faintest object the Hubble space telescope has recorded, a brightness equal to a firefly at a distance equal to the diameter of the Earth.

Loudness

Sound is air pressure, hence it is logarithmic. It is measured in Decibels.
We intuitively experience the physical intensity of sound as logarithmic, and so the decibel unit is one of the few that is logarithmic. A normal conversation feels three times as loud as a whisper, whereas its measured intensity is 10^3 greater.

See decibel.

Musical Scale


The cent is a measure of musical scale, see musical scale.

Unit For Ratios Of Measurements


The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. It has the unit symbol Np. The unit's name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is not a unit in the International System of Units (SI), but it is accepted for use alongside the SI. The neper, an alternative logarithmic ratio unit sometimes used, uses the natural logarithm (base e).

Degrees Of Separation

6 degrees of separation is a form of exponential propagation.

Earthquake Intensity


See Richter Scale.

Entropy


A ban, sometimes called a hartley (symbol Hart) or a dit (short for decimal digit), is a logarithmic unit which measures information or entropy, based on base 10 logarithms and powers of 10, rather than the powers of 2 and base 2 logarithms which define the bit. As a bit corresponds to a binary digit, so a ban is a decimal digit. A deciban is one tenth of a ban, analogous to a decibel.
One ban corresponds to about 3.32 bits (log2(10)), or 2.30 nats (ln(10)). A deciban is about 0.33 bits.
The deciban is a particularly useful measure of information in odds-ratios or weights of evidence. 10 decibans corresponds to an odds ratio of 10:1; 20 decibans to 100:1 odds, etc. According to I. J. Good, a change in a weight of evidence of 1 deciban (i.e., a change in an odds ratio from evens to about 5:4), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis.

According to I. J. Good, a change in a weight of evidence of 1 deciban (i.e., a change in an odds ratio from evens to about 5:4), or perhaps half a deciban, is about as finely as humans can reasonably be expected to quantify their degree of belief in a hypothesis.