Order of Magnitudes

Feb 20, 2022

Humans have a tough time comprehending exponential growth. Logarithmic scales don't really register with us the same way, no matter how many times you look at them. Here are some examples of logarithmic scales in real life.

Sun protection factor (SPF). SPF 2 blocks 50% of UV rays. SPF 4 blocks 75%. The difference between SPF 50 and SPF 100 is 1%.

Sound level (decibels). Human senses obey the Weber-Fechner law, which means that our sense perception is a logarithm of inputs – the intensity of our sensation increases as the logarithm of an increase in energy (for all senses).

Richter scale (earthquakes). The wave amplitude in a magnitude 6 earthquake is 10 times greater than a level 5 earthquake and 100 times greater than a level 4.

Acidity (pH). Every integer difference in the pH scales corresponds to a tenfold difference in acidity. Tomato juice (pH 4) is 10 times more acidic than coffee (pH 5).

Entropy. In information theory, entropy is usually measured in binary (base 2) but in physics it is usually measured by the natural log (two separate ideas).

Frequency. An octave above a musical pitch is double its frequency. For example, A has a frequency of 440 Hz and 880 Hz (an octave above).