Maths & Humans

by Steve Morgan & Sophie Connolly

"All our knowledge begins with the senses, proceeds then to the understanding, and ends with reason. There is nothing higher than reason."

Immanuel Kant

Welcome to Basic Science Clinic Crit Think. Our Raw Science series is to provide content for the new programs that you are writing for your intracranial wet-wear, Crit Think is the upgrade of your operating system. The study and understanding of the process, structure and potential pitfalls of thought, ie thinking about thinking or metacognition, helps you to integrate the knowledge you are acquiring and then apply it with scientific rigor, making you a safer, skeptical, rational bedside empiricist. Create the good habits of data seeking and analytics to emulate the best consultants, with their granular, high fidelity knowledge and their near preternatural ability of pattern recognition that leads to the right intervention just in a nick of time.

This series will include mathematics, what latin is to language, maths is to science. Without maths there is no science; and go on to cover: logic, reasoning and logical fallacies; the art of clinical decision making, heuristics, cognitive biases; educational theory; introduction to ethical principles. In the informational age, with ready available knowledge on the end of a digital swipe, there is an even greater imperative that in your nascent development as a clinician you consider these key components of the structure of your most potent, yet potentially deceptive tool, for knowledge application and making critical decisions over seconds to minutes that may be life-saving.

In this podcast we will examine the synergism between the development of mathematics and the advancement of human civilisation.

What is maths and where do we get it from?

What has been the timeline of the development of Maths?

So what about numbers themselves?

Maths & Science

by Steve Morgan & Sophie Connolly

Albert Einstein said: “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain they do not refer to reality.”

Welcome to basic science clinic Crit Think, this is the second podcast in the series on mathematics. Remember this is about stimulating insights into the machinations of your mind to assist able deployment of the knowledge you are rapidly assembling, to be a better scientist.

In this podcast we are going to examine the relationship of maths and science.

What is science and does maths qualify?

What is the scientific method?

How did the method develop and where does maths fit in?

So where does all this leave maths and science?

Mathematical Relations

by Steve Morgan & Sophie Connolly

"If you would be a real seeker after truth, you must at least once in your life doubt, as far as possible, all things."

Rene Descartes

Welcome to Basic Science Clinic, this is the 3rd Crit Think podcast on mathematics. Having examined the origin of maths and its influence on the enlightenment explosion of rationality and empiricism, we now turn our attention to extracting the ways maths turns up in our critical care practice.

Is it essential to know the maths? Thou doth protest too much methinks. Think of these relationships as the grammatical fibre to your conceptual fabric. Understanding maths as the language of science with grammatical and linguistic accuracy changes your perception of the relationships between the physiological variables that you are attempting to dial up in your practice. Go deeper, understand better, effortlessly recall.

In this pod we’ll cover:

Basic mathematical relationships

Relations Vs Functions

Classification of mathematical models

Important relations in critical care

The Calculus

by Steve Morgan & Sophie Connolly

John Maynard Keynes said: “Isaac Newton was not the first of the age of reason. He was the last of the magicians.”

It is in Isaac's Newton's iconic and seminal Principia that we see calculus used for the first time as a sophisticated tool for modeling change. Newton does not deign to truly explicate this mathematical tool and does not refer to it in its modern language or notation, but it is there permeating the equations

Calculus is all around us and is the foundational mathematical concept of modern science, with much of the scientific description of the world being based on calculus. The laws of motion, electromagnetism, sound waves, social and biological trends, efficacy of medical treatments, all of these phenomena are couched in the vocabulary of calculus.

Calculus provides the tools for measuring change and is one of the crowning intellectual achievements of humanity allowing us to successfully land a rover on the surface of mars.

In this podcasts we will cover:

The fundamental theorem of calculus

Integration

Differentiation

Applications to critical care

Logarithms & Exponentials

by Steve Morgan & Sophie Connolly

"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.

In this pod we will cover:

The discovery & applications of logarithms

Exponential relationships

Time constants, half-life, rate constants

Euler's number, e

Measurement & Calibration

"Although this may seem a paradox, all exact science is dominated by the idea of approximation."

Bertrand Russell

This is Crit Think episode 6, the final podcast in our mathematics series in which we will discuss the mathematics behind clinical measurement.

The use of ever advancing technologies is an inherent and necessary component of critical care, encompassing the most basic of measurement devices (the sphygmomanometer, the stethoscope) to the most complex methods of organ support. Such devices enable continuous monitoring and measurement of physiological variables, informing decision-making processes and underpinning management choices.

Unfortunately, the fallibilities of the clinical process extend far beyond that of human error, and increasingly so, as technological developments entail greater reliance on medical devices. Along with this, comes the tendency to overplay the perceived accuracy and precision of such devices, permitting clinical judgment to be overshadowed or misled by numerical outputs.

Accuracy and precision are terms that are colloquially interchanged, but in truth carry different meanings and different implications for specific features of the variables they are describing.  While we strive for accuracy, precision represents our chance of reliably achieving it.

In this pod we’ll cover:

Accuracy and precision

Hysteresis

Signal to noise ratio

Zero, zeroing & calibration

Pi, sine waves & Fourier analysis