3
$\begingroup$

There are many examples where our senses are based off of log scales such as volume of a noise, ability to guess (i.e.) plus or minus a power of 10 with Fermi, and even when we measure pain on 1 to 10 scale most of us subconsciously do it as a log scale. There are even evolutionary advantages such as its much more for survival sake to know the log of a predator. (i.e.) it matters more if theirs 3 vs 1 lions but not if theirs 23 vs 21 lions. Are there any human senses that truly work off of a linear scale to a stimulus? This leads me to wonder the following.

Today we have a convention that is based off of linear scales based off of 1 and successors. From young we are taught linear scales and do everything in school under linear scales. Has this convention ever been reversed? It clearly was used for a time with the slide rule but that's more of a way of switching between the two.

$\endgroup$
5
$\begingroup$

According to the Weber–Fechner law in vision and hearing perception is close to proportional to the logarithm of the stimulus. This however has no direct influence on the use of scales since they are used for correlating two different observables ("stimuli"), and the preference for linear or logarithmic scale depends on the behavior of what is correllated, not on our perception of it.

For exponential laws log-linear scales are most advantageous, and for power laws log-log scales are. Since Napier's invention of logarithms in early 1600s these insights were taken advantage of, first by brute conversion as with Kepler, see How did Kepler "guess" his third law from data? Then with the slide rule, and later logarithmic graph paper invented by Lallane in 1844, and logarithmic plotting. In fact, Lallane considered far more general scales than just linear and logarithmic, and in 1880s d'Ocagne developed his ideas into a whole discipline of nomography, see When was the earliest use of log-log plots to demonstrate power-law behavior?

Today there is no need for the slide rule or logarithmic paper because we have computers and calculators, but log plotting and transformations (along with many other types of rescaling) are used in modeling and statistical analysis of data even more broadly than before. In particular, logarithmizing and other nonlinear transformations are applied to reduce non-linear dependecies to linear ones, so that the linear regression (least squares fitting) can be applied to them directly, see e.g. Exponential Regression using a Linear Model.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.