The Math of Life and Death

1. Mathematics shapes our history and biology

Mathematics has shaped our history: through the ancestors who won evolution's numbers game and the diseases that strained and filtered our species.

Our biological foundation. Mathematics is deeply intertwined with our evolutionary history and physiological makeup. The Fibonacci sequence, for example, appears in the spiral arrangements of flowers and pinecones, while the golden ratio is found in the proportions of the human body. These mathematical patterns have influenced our aesthetic preferences and our understanding of beauty.

Cultural evolution. Mathematical concepts have co-evolved with human civilization. Ancient civilizations developed number systems based on their physical attributes, such as the Babylonians' sexagesimal system (base 60) or the Maya's vigesimal system (base 20). These systems reflected their cultural needs and understanding of the world, shaping their societies and technological advancements.

Examples of mathematics in nature:

• Fibonacci sequence in flower petals and seed arrangements
• Golden ratio in human body proportions and nautilus shells
• Fractal patterns in coastlines, trees, and blood vessels

2. Exponential growth: Powerful yet often misunderstood

Quantities that grow exponentially might appear to grow slowly at first, but they can take off quickly in a way that seems unexpected.

Deceptive beginnings. Exponential growth often starts slowly, making it easy to underestimate its potential impact. This phenomenon is seen in various contexts, from population growth to viral spread and compound interest. The initial stages may appear manageable, but the rapid acceleration can quickly lead to overwhelming numbers.

Real-world implications. Understanding exponential growth is crucial in many fields:

• Finance: Compound interest in investments and loans
• Technology: Moore's Law in computer processing power
• Biology: Population growth and viral infections
• Climate change: Accumulation of greenhouse gases

Failing to recognize exponential patterns can lead to serious miscalculations, as seen in the underestimation of COVID-19's spread in its early stages or the potential impacts of climate change.

3. False positives and negatives: The illusion of certainty in medical tests

We should remember that screens are not diagnostic tests and that their results should be taken with a pinch of salt.

Test accuracy paradox. Medical tests can be highly accurate yet still produce misleading results, especially when screening for rare conditions. This is due to the interplay between a test's sensitivity (ability to correctly identify those with the condition) and specificity (ability to correctly identify those without the condition).

Implications for healthcare. Understanding the limitations of medical tests is crucial for both healthcare providers and patients:

• False positives can lead to unnecessary anxiety and further testing
• False negatives may provide false reassurance and delay treatment
• Prevalence of the condition in the population affects the test's predictive value

Key concepts:

• Positive predictive value: Probability that a positive result is truly positive
• Negative predictive value: Probability that a negative result is truly negative
• Base rate fallacy: Neglecting the prevalence of a condition when interpreting test results

4. Statistical fallacies: Misuse of numbers in courtrooms and media

We must ensure that the person with the most shocking statistics doesn't always win the argument, by demanding an explanation of the maths behind the figures.

Manipulating perception. Statistics can be easily misused to sway public opinion or influence legal decisions. Common tactics include:

• Cherry-picking data
• Using relative vs. absolute risk
• Presenting correlation as causation
• Employing misleading graphics or scales

Critical thinking is key. To combat statistical manipulation, it's essential to:

• Question the source and methodology of presented statistics
• Look for context and comparisons
• Understand the difference between correlation and causation
• Be aware of common fallacies like the prosecutor's fallacy or ecological fallacy

Real-world examples:

• Misuse of DNA evidence in criminal trials
• Misleading health claims in advertising
• Biased reporting of scientific studies in the media

5. Number systems: From ancient civilizations to modern technology

Understanding the number systems around us, for example, gives us an insight into the history and culture of our species.

Cultural reflections. Number systems are not just mathematical constructs but reflections of the cultures that created them. The Babylonian sexagesimal system, for instance, still influences our measurement of time and angles. The Maya vigesimal system reflects their advanced astronomical knowledge.

Technological implications. Our modern decimal system and the binary system used in computers each have their strengths and weaknesses:

Decimal system:

• Intuitive for human counting (based on 10 fingers)
• Easier for mental arithmetic

Binary system:

• Efficient for electronic computation
• Basis for all digital technology

Understanding these systems helps us appreciate the evolution of human thought and the foundations of our technological world. It also highlights the importance of choosing the right system for the task at hand, as seen in the catastrophic failure of the Mars Climate Orbiter due to a unit conversion error between metric and imperial systems.

6. Algorithmic optimization: Revolutionizing everyday life

Algorithms can provide us with information that facilitates vital decisions, but in the end they are no substitute for our own subtle, biased, irrational, inscrutable, but ultimately human judgements.

Ubiquitous influence. Algorithms are reshaping numerous aspects of our lives:

• Navigation: GPS and route optimization
• E-commerce: Product recommendations and pricing
• Social media: Content curation and targeted advertising
• Healthcare: Diagnostic tools and treatment planning

Balancing efficiency and humanity. While algorithms can process vast amounts of data and optimize complex systems, they have limitations:

• Lack of contextual understanding
• Potential for bias in training data
• Difficulty in handling nuanced or ethical decisions

It's crucial to use algorithms as tools to support human decision-making rather than replacing human judgment entirely. This requires ongoing evaluation of algorithmic outcomes and maintaining human oversight in critical areas.

7. Mathematical epidemiology: Predicting and controlling disease outbreaks

Mathematical epidemiology provides a way to assess and understand these decisions. It explains why it is better for everyone if you stay away from work or school if you are ill.

Modeling disease spread. Mathematical models, such as the SIR (Susceptible, Infectious, Recovered) model, help predict the course of disease outbreaks and evaluate intervention strategies. Key concepts include:

• R0 (basic reproduction number): Average number of secondary infections caused by one infected individual
• Herd immunity threshold: Proportion of immune individuals needed to prevent sustained disease spread
• Contact networks: Patterns of interactions that facilitate disease transmission

Informing public health decisions. Epidemiological models guide crucial interventions:

• Vaccination strategies
• Quarantine and isolation measures
• Resource allocation during outbreaks

Real-world applications:

• Predicting the spread of COVID-19
• Evaluating the effectiveness of lockdown measures
• Designing optimal vaccination schedules for childhood diseases

Understanding these models empowers individuals to make informed decisions about their health and helps policymakers implement effective disease control measures.

Last updated: October 13, 2024