You Do the Math(s) 5: Logarithms and Exponentials

You Do the Math(s) 5: Logarithms and Exponentials

Logarithms and Exponentials

Basic Science Clinic

Crit Think

So mathematical truth prefers simple words since the language of truth is itself simple.

Tycho Brahe

Welcome to Basic Science Clinic, this is Crit think episode 5. Today our exploration of the mathematical architecture of our most inexact of sciences brings us upon the edifice of logarithms and exponentials. Daunting as it may sound, we will try to tease out their utility and relevance to critical care medicine and even attempt to penetrate the secrets of the mysterious number e.

Logarithmic transformations permeate pharmacokinetic, biological and physiological modelling.  Exponentials are the inverse function of the logarithm, and the special properties of explosive exponential change in quantities has implications for ventilation, pharmacotherapy and beyond.

Euler’s number, e, represents the idea that all continually growing systems are scaled versions of a common rate. Describing e as a constant approximating 2.718 is like calling pi an irrational number approximating 3.141. It’s true but it totally misses the point. Pi is the ratio between the circumference and diameter of every circle. It is a fundamental ratio and therefore impacts any calculation involving circumference, area, volume and surface area for all circles, spheres and cylinders. e is not just a number it is about the fundamental relationship between all growth rates.

Thanks for listening. From The Happy Prince by Oscar Wilde: “I am so clever that sometimes I do not understand a single word of what I am saying.”

Word of the day: evanescent

Literary: soon passing out of sight, memory, or existence; quickly fading or disappearing.

Physics: denoting a field or wave which extends into a region where it cannot propagate and whose amplitude therefore decreases with distance.

For feedback, corrections and suggestions you can contact us on the twitter handles @falconzao and @sophmconnolly or post on Intensive Care Network.

Next up is the last in this Crit Think: You Do the Math(s) series and we will examine the mathematics behind clinical measurement.