One step of magnitude, ten times the shaking | how logarithms measure huge numbers

Magnitude seven point zero, and magnitude six point zero. The numbers differ by exactly one. But the trace on a seismograph swings **ten times as wide**. Why measure it that way at all? The swing of a small quake and a large one are about a hundred million times apart. Put that straight onto a ruler and the small ones pile up near zero, indistinguishable. The problem was never the earthquakes. It was the ruler. So we change what gets written on the ruler — not the swing itself, but *which power of ten* it is. A hundred million becomes eight. This episode follows the name that reading was given. 📍 Chapters 0:00 One step up, ten times over 0:23 Where that number came from 0:56 Written as a power of ten 1:26 That question has a name 2:34 A logarithm is the inverse of a power 3:43 Multiplying becomes adding 4:51 A three-hundred-year tool, and sound 5:58 Reading it another way 📌 What this episode covers · Why one step of magnitude means ten times — what is measured is the width of the shaking · Why an evenly spaced ruler fails: the small values pile up near zero · Writing which power of ten a number is turns a hundred million into eight · Which power of ten is fifty? No fraction reaches it — it is irrational · Push the exponent continuously and the value slides from ten to a hundred, passing fifty once · The exponent sitting at that spot has a name: the logarithm (log base ten of fifty ≈ 1.7) · On this scale, multiplying becomes adding and dividing becomes subtracting · Adding is something a ruler can do → the slide rule. Multiplication measured, not calculated · Napier and Briggs, and the people who put the scale onto a ruler — a tool that lasted 300 years · Decibels work the same way: ten times the intensity moves the scale by ten · Choosing ten as the base was *a choice, not a necessity* 🔗 Earlier episodes EP.01 One map from the counting numbers to the complex numbers EP.02 Imaginary numbers are not imagination, they are direction EP.03 Walk π along the circle and you are halfway round EP.04 A 100% grade is 45 degrees EP.05 Similarity — erase the size and the shape remains EP.06 A function is not a formula EP.07 An exponent is not how many times you multiply — Mathiter is a math learning app for international-school and study-abroad students. https://mathiter.com #math #logarithm #log10 #earthquake #richterscale #decibel #sliderule #exponents #mathconcepts