Mathematics

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The Threat to Democracy Runs Deep, But Mathematics Could Address the Abominable State of Representation and Voting

Published by Anonymous (not verified) on Wed, 20/03/2024 - 5:30am in

In November 1990, an election took place in Bosnia, my home country, that changed the...

Understanding Humans: How Social Science Can Help Solve Our Problems – review

Published by Anonymous (not verified) on Tue, 30/01/2024 - 11:26pm in

In Understanding Humans: How Social Science Can Help Solve Our ProblemsDavid Edmonds curates a selection of interviews with social science researchers covering the breadth of human life and society, from morality, bias and identity to kinship, inequality and justice. Accessible and engaging, the research discussed in the book illuminates the crucial role of social sciences in addressing contemporary societal challenges, writes Ulviyya Khalilova.

Understanding Humans: How Social Science Can Help Solve Our Problems. David Edmonds. SAGE. 2023.

Find this book: amazon-logo

Understanding Humans_coverIn the Social Science Bites podcast series, David Edmonds, a Consultant Researcher and Senior Research Associate at the Oxford Uehiro Centre for Practical Ethics, collaborated with Nigel Warburton to explore the dynamics of modern society, interviewing eminent social and behavioural scientists on different topics. The engaging discussions that resulted led Edmonds to curate a selection of the episodes in a written format to bring the research to new audiences. The resulting book, Understanding Humans: How Social Science Can Solve Our Problems, offers valuable insights into various aspects of human life and society, covering subjects from morality, bias and identity to kinship, inequality and justice.

Understanding Humans […] offers valuable insights into various aspects of human life and society, covering subjects from morality, bias and identity to kinship, inequality and justice.

In his foreword to the book, Edmonds highlights that the selection of interviews, which translate into different chapters, reflect his own interests, though the criteria for their inclusion remains undisclosed. The book consists of eighteen chapters split between five thematic sections titled, respectively: Identity, How We Think and Learn, Human Behaviour, Making Social Change, and Explaining the Present, and Unexpected. Some topics introduced in one section can also fit into others, leading to overlaps between certain sections.

In his discussion of class, Friedman states that despite educational attainments, class privilege still significantly impacts career progression.

In the section on Identity, Sam Friedman discusses the insufficiency of education to eliminate the influence of class privilege, while Janet Carsten talks about the interconnectedness of kinship with politics, work, and gender. In his discussion of class, Friedman states that despite educational attainments, class privilege still significantly impacts career progression. The level of autonomy in the workplace, alongside one’s position and salary, could indicate whether career success correlates with social class. Friedman suggests that societal beliefs in meritocracy often overlook the inherent class-related barriers that hinder individuals’ opportunities for career development.

In the next section, Daniel Kahneman, Mahzarin Banaji, Gurminder K. Bhambra, Jonathan Haidt, Jo Boaler, and Sasika Sassen discuss various aspects of human thinking and learning. In his chapter on bias, Kahneman sheds light on biases in human thinking, discussing the dual processes of thinking: fast, associative thinking (System 1) and slower, effortful control (System 2). System 2 assists us in providing reasoning or explanations for our conclusions, essentially aiding in articulating our feelings and emotions. Education enhances System 2 and develops rational thinking, although achieving absolute rationality remains an elusive goal.

Boaler challenges the myth of innate mathematical ability, highlighting the crucial role of active engagement in developing mathematical skills.

In her chapter on the “Fear of Mathematics,” Boaler challenges the myth of innate mathematical ability, highlighting the crucial role of active engagement in developing mathematical skills. Deep thinking is crucial for developing maths skills, but it is a slow process that requires time. There is also a need for reforms in maths education, particularly addressing the issue of timed assessments that impede the brain’s capacity to develop mathematical skills effectively. Boaler states that the purpose of mathematics shouldn’t glorify speed, considering that many proficient mathematicians acknowledge working at a slower pace.

In the chapter “Before Method,” Sassen discusses how prior experiences shape research approaches, introducing the concept of “before method”, referring to both the desire for conducting research in a particular way and the actual execution of a research study. The rationale behind selecting a specific research method and topic is connected with the pre-existing experience preceding the method itself. Sassen challenges established categories by questioning whether it is possible to perceive things without initially considering categories, potentially influencing the direction of the study. She acknowledges that her awareness of prior research studies, established categories, and personal life experiences significantly shape her perception of the world as a researcher.

Following this, Stephen Reicher, Robert Shiller, David Halpern, and Valerie Curtis talk about various facets of human behaviour. Reicher discusses group dynamics, elucidating how physical proximity and psychological commonality foster different groups. Reicher also posits that group boundaries are loose and attributes this to the social changes, which, according to his explanation, result from a we-they dichotomy. Understanding intergroup interactions is crucial, particularly when individuals might not wish to be associated with confrontational aspects. However, belonging to a specific group often leads to labelling individuals, linking all their actions with that group, despite the distinctive nature of their involvement.

Halpern in his chapter on nudging explains that humans are not solely rational beings; their behaviour is influenced by various factors including impulses and emotions.

Halpern in his chapter on nudging explains that humans are not solely rational beings; their behaviour is influenced by various factors including impulses and emotions. He elaborates on how nudging proves beneficial for jobseekers, where incorporating specific human-related elements in emails encourages them to attend interviews. Halpern also posits that our inherent ‘groupish’ tendencies are intricately linked to human psychology. Various factors influence our proximity or distance from others, ultimately affecting societal progress, including economic development. Trust, for instance, varies significantly among different social classes. An individual from an impoverished social class facing financial challenges tends to have lower social trust. Conversely, someone from an affluent background might experience the opposite due to their social circle being influenced by their wealth.

Chenoweth’s research highlights the efficacy of nonviolent political action when contrasted with violent approaches, emphasising its higher success rates and potential to facilitate democratic transitions.

In the section on “Making Social Change” Jennifer Richeson, Erica Chenoweth, and Alison Liebling discuss how employing various approaches and research methods can drive social changes. Chenoweth’s research highlights the efficacy of nonviolent political action when contrasted with violent approaches, emphasising its higher success rates and potential to facilitate democratic transitions. Within the political sphere, an emerging trend is the digital revolution, distinct in some aspects from other revolutions. Erica Chenoweth also states that the digital revolution might foster a misleading impression by mobilising thousands to march in the streets.

In the section “Explaining the Present and the Unexpected,” Hetan Shah discusses the impacts of the Covid-19 pandemic on social and economic spheres, while Bruce Hood talks about supernatural attitudes or beliefs. Shah elucidates how the pandemic has shifted societal norms and behaviour. He also draws attention to the impact of these norms on human behaviour and the potential for fostering a fair society. Examining the pandemic from multiple angles – medical, social, and economic – deepens our understanding of human behaviour Shah emphasises that social sciences play a crucial role in unveiling how biases shape our thoughts and actions, addressing the social problems.

[Understanding Humans] provides readers with a compelling overview of exceptional research studies on how we think and act as individuals, and the social, economic, educational and political structures that we operate within.

Overall, the eclectic chapters in ‘Understanding Humans: How Social Science Can Solve Our Problems’ illuminate the profound role of social sciences in exploring and addressing social issues. This book serves as a valuable resource for a broad audience, being accessible and engaging for readers without prior knowledge or expertise in the fields drawn upon by the researchers. It provides readers with a compelling overview of exceptional research studies on how we think and act as individuals, and the social, economic, educational and political structures that we operate within.

This post gives the views of the author, and not the position of the LSE Review of Books blog, or of the London School of Economics and Political Science. The LSE RB blog may receive a small commission if you choose to make a purchase through the above Amazon affiliate link. This is entirely independent of the coverage of the book on LSE Review of Books.

Image Credit: tadamichi on Shutterstock.

Language and the Rise of the Algorithm – review

Published by Anonymous (not verified) on Tue, 16/01/2024 - 11:01pm in

In Language and the Rise of the Algorithm, Jeffrey Binder weaves together the past five centuries of mathematics, computer science and linguistic thought to examine the development of algorithmic thinking. According to Juan M. del Nido, Binder’s nuanced interdisciplinary work illuminates attempts to maintain and bridge the boundary between technical knowledge and everyday language.

Language and the Rise of the Algorithm. Jeffrey Binder. The University of Chicago Press. 2023

Find this book: amazon-logo

cover of Language and the Rise of the Algorithm by Jeffrey Binder, black background with red algebraic equations and white title fontArguably, the history of what we now call algorithmic thinking is also the history of the consolidation of algebra, mathematics, calculus and formal logic as tools for composing, enunciating, and thinking about abstractions such as “some flowers are red”. But in less obvious ways, Language and the Rise of the Algorithm shows, it is also the history of trying to compute with, and often in spite of, language, to convey a meaningful proposition about the world. In other words, it is the history of ensuring that “red” actually means red – that we are all clear on who sets what red means (for example, experts through definition or ordinary people through usage) and agree on it – and of whether agreeing about these things is what matters when we use language.

The history of what we now call algorithmic thinking []is also the history of trying to compute with, and often in spite of, language, to convey a meaningful proposition about the world.

Harking back to the 1500s, the first of the book’s five chapters examines attempts to use symbols to free writing from words at a time when vernaculars where plentiful, grammars unstable and literacy rates low. Algebra was not then considered part of mathematics proper but its rules, expressed in spoken language, were used for practical purposes like calculating taxes and inheritance. From myriad writing experiments emerged algebraic symbols: uncertain and indeterminate, they enabled computational reasoning about unknown values, a revolution that peaked when Viète first used letters in equations in 1591 (33-36).

Algebra was not [In the 1500s] considered part of mathematics proper but its rules, expressed in spoken language, were used for practical purposes like calculating taxes and inheritance

Chapter Two explores Leibniz’s attempts to produce a philosophical language made of symbols and unburdened by words, such that morals, metaphysics, and experiences are all subject to calculation. This was not an exercise in spitting out numbers, but with the aim of demonstrating the reasoning behind every step of communication: a truth-producing machine (62-64). The messiness of communication struck back: how can one ensure that all terms and their nuances are understood in the same way by different people? Leibniz argued that knowledge was divinely installed in us, waiting to be unlocked by devices such as his, but Locke’s argument that knowledge comes from sensory experience and requires an agreement over what things mean won the day (79), paving the way towards an emphasis on concepts and form.

Leibniz argued that knowledge was divinely installed in us, waiting to be unlocked [] but Locke’s argument that knowledge comes from sensory experience and requires an agreement over what things mean won the day

Leibniz also sought to resolve political differences through that language. Chapter Three argues Condorcet shared this goal and the premise that vernaculars were a hindrance, but contrary to Leibniz, he believed universal ideas needed to be taught, not uncovered. Condillac’s and Stanhope’s experiments with other logical machines – actual, material devices designed to think in logical terms through objects  – epitomised two tensions framing the century after the French Revolution: first, the matter of whether the people, and their vernacular culture, or the learned, and their enlightened culture, should govern shared meanings – that is to say, give meaning – and second, whether algebra should focus on philosophical and conceptual explanations or on formal definitions and rules (121).

The latter drive would prevail, and as Chapter Four shows, rigour came to emanate not from verbal definitions or clarity of meanings, but from axiomatic systems judged on consistency: meanings are irrelevant to the formal rules by which the system operates (148). Developing this consistency would not require the complete replacement of vernaculars Leibniz and Condorcet argued for: rather, symbolic forms would work alongside vernaculars to produce truth values, as with Boolean logic – the one powering search engines, for example. The fifth and last chapter, “Mass Produced Software Components”, rise of programming languages, in particular ALGOL, and the consolidation of regardless of specifics: intelligible, actionable results within a given amount of time (166).

Binder’s rigorous dissection of debates over language, philosophy, geometry, algebra, history and culture spanning 500 years integrates debates that most disciplines today, aside from some strands of media studies and Science and Technology Studies, tend to treat separately

This book is a tightly packed, erudite contribution to the growing concern in the Humanities with algorithms. Binder’s rigorous dissection of debates over language, philosophy, geometry, algebra, history and culture spanning 500 years integrates debates that most disciplines today, aside from some strands of media studies and Science and Technology Studies, tend to treat separately or with a poor sense of their inbuilt connections. A welcome result of this exercise is the historicisation of certain critiques of technological interventions in politics that, generally lacking this kind of integrated, long-range view, we tend to treat as novel and cutting-edge. For example, an 1818 obituary for Charles Mahon, third Earl of Stanhope and inventor of the Demonstrator, a “reasoning machine”, already claimed that technical solutions for other-than-technical problems such as his tend to replicate the biases of their creators (113), and often the very problems they intended to solve. This critique of technoidealism is now commonplace in the social sciences.

A second benefit of the author’s mode of writing is not explicit in the book but is arguably more consequential. From Bacon’s dismissal of words as “idols of the market” in 1623 (15) to PageRank algorithm’s developers’ goal to remove human judgement by mechanisation in the 1990s (200), the book traces attempts across the centuries to free reason and knowledge from language and rhetoric. In doing this, Language and the Rise of the Algorithm effectively serves as a highly persuasive history of the affects, ethics and aspirations of technocratic reason and rule. The book cuts across the histories of bureaucracy and expertise and the birth of governmentality to tell us how an abstraction in how we make meaning work emerged – an abstraction we are asked to trust in, and argue for, partly because it is the kind of abstraction it ended up being.

The book traces attempts across the centuries to free reason and knowledge from language and rhetoric

This is a rich and nuanced book, at times encyclopaedic in scope, and except for a slight jump in complexity and some jargon in the fifth and last chapter, it will be accessible to readers lacking prior knowledge of algorithms, mathematics or language philosophy. It will be of interest to scholars across the social sciences and humanities, from philosophy and history to sociology and anthropology, as well as readers in political science, government studies and economics for the reasons listed above. It could work as course material for very advanced students.

This post gives the views of the author, and not the position of the LSE Review of Books blog, or of the London School of Economics and Political Science. The LSE RB blog may receive a small commission if you choose to make a purchase through the above Amazon affiliate link. This is entirely independent of the coverage of the book on LSE Review of Books.

Image Credit: Lettuce. on Flickr.

More than a Glitch: Confronting Race, Gender, and Ability Bias in Tech – review

Published by Anonymous (not verified) on Thu, 28/12/2023 - 9:00pm in

In More than a Glitch: Confronting Race, Gender, and Ability Bias in Tech, Meredith Broussard scrutinises bias encoded into a range of technologies and argues that their eradication should be prioritised as governments develop AI regulation policy. Broussard’s rigorous analysis spotlights the far-reaching impacts of invisible biases on citizens globally and offers practical policy measures to tackle the problem, writes Fabian Lütz.

More than a Glitch: Confronting Race, Gender, and Ability Bias in Tech. Meredith Broussard. MIT Press. 2023. 

Find this book: amazon-logo

More than a glitch-coverAs the world witnesses advancements in the use of Artificial Intelligence (AI) and new technologies, governments around the world such as the UK and US the EU and international organisations are slowly starting to propose concrete measures, regulation and AI bodies to mitigate any potential negative effects of AI on humans. Against this background, More than a Glitch offers a timely and relevant contribution to the current AI regulatory debate. It provides a balanced look at biases and discriminatory outcomes of technologies, focusing on race, gender and ability bias, topics that tend to receive less attention in public policy discussions. The author’s academic and computer sciences background as well as her previous book Artificial Unintelligence – How Computers Misunderstand the World make her an ideal author to delve into this important societal topic. The book addresses algorithmic biases and algorithmic discrimination which not only receives increasing attention in academic circles but is of practical relevance due to its potential impacts on citizens and considering the choice of regulation in the coming months and years.

[More than a Glitch] provides a balanced look at biases and discriminatory outcomes of technologies, focusing on race, gender and ability bias, topics that tend to receive less attention in public policy discussions

The book’s cornerstone is that technology is not neutral, and therefore racism, sexism and ableism are not mere glitches, but are coded into AI systems.

Broussard argues that “social fairness and mathematical fairness are different. Computers can only calculate mathematical fairness” (2). This paves the way to understand that biases and discriminatory potential are encoded in algorithmic systems, notably by those who have the power to define the models, write the underlying code and decide which datasets to use. She argues that rather than just making technology companies more inclusive, the exclusion of some demographics in the conceptualisation and design of frameworks needs to stop. The main themes of the book, which spans eleven short chapters, are machine bias, facial recognition, fairness and justice systems, student grading by algorithms, ability bias, gender, racism, medical algorithms, the creation of public interest technology and options to “reboot” the system and society.

Biases and discriminatory potential are encoded in algorithmic systems, notably by those who have the power to define the models, write the underlying code and decide which datasets to use.

Two chapters stand out in Broussard’s attempt to make sense of the problems at hand: Chapter Two, “Understanding Machine Bias” and more specifically Chapter Seven “Gender Rights and Databases”. Both illustrate the author’s compelling storytelling skills and her ability to explain complex problems and decipher the key issues surrounding biases and discrimination.

Chapter Two describes one of the major applications of AI: machine learning which Broussard defines as to take

“..a bunch of historical data and instruct a computer to make a model. The model is a mathematical construct that allows us to predict patterns in the data based on what already exists. Because the model describes the mathematical patterns in the data, patterns that humans can’t easily see, you can use that model to predict or recommend something similar” (12).

The author distinguishes between different forms of training a model and discusses the so called “black box problem” – the fact that AI systems are very often opaque – and explainability of machine decisions. Starting from discriminatory treatment of bank loan applications, for example credit score assessment on the basis of length of employment, income or debt, the author explains with illustrative graphs how algorithms find correlations in datasets which could lead to certain discriminatory outcomes. She explains that contrary to humans, machines have the capacity to analyse huge amounts of datasets with data points which enable for example banks to make predictions on the probability of loan repayment. The mathematics underlying such predictions are based on what similar groups of people with similar variables have done in the past. The complex process often hides underlying biases and potential for discriminations. As Broussard points out,

“Black applicants are turned away more frequently than white applicants [and] are offered mortgages at higher rates than white counterparts with the same data […]” (25).

The book also demonstrates convincingly that the owners or designers of the model wield a powerful tool to shape decisions for society. Broussard sums up the chapter and provides crucial advice for AI developers when she states, advice for AI developers when she states,

“If training data is produced out of a system of inequality, don’t use it to build models that make important social decisions unless you ensure the model doesn’t perpetuate inequality” (28).

Chapter Seven looks at how databases impact gender rights, starting with the example of gender transition which is registered in Official Registers. This example illustrates the limitations of algorithmic systems as compared to humans, not only in light of the traditional binary system for assigning gender as male and female, but more generally the binary system that lies at the heart of computing. Both in the gender binary and computer binary framework, choices need to be made between one or the other leaving no flexibility. Broussard describes the binary system as follows:

“Computers are powered by electricity, and the way they work is that there is a transistor, a kind of gate, through which electricity flows. If the gate is closed, electricity flows through, and that is represented by a 1. If the gate is open, there is no electricity, and that is represented by a 0” (107).

When programmers design an algorithm, they “superimpose human social values onto a mathematical system.” Broussard urges us to ask ourselves, “Whose values are encoded in the system?” (109).

The resulting choices that need to be made within AI systems or forms used in administration often do not adequately represent reality. For people who do not feel represented by the options of male and female, such as gender non-conforming people, they are asked to make the choice in which category they fall even though this would not reflect their gender identity. Here again, Broussard reminds us of the importance of design choices and assumptions of coders which impact people’s everyday life. When programmers design an algorithm, they “superimpose human social values onto a mathematical system.” Broussard urges us to ask ourselves, “Whose values are encoded in the system?” (109). The chapter concludes with the challenge of making “technological systems more inclusive” (116) and argues that computers constitute not only mathematical but sociotechnical systems that need to be updated regularly in order to reflect societal change.

Computers constitute not only mathematical but sociotechnical systems that need to be updated regularly in order to reflect societal change.

The book successfully describes the invisible dangers and impacts of these rapidly advancing technologies in terms of race, gender and ability bias, making these ideas accessible through concrete examples. Ability bias is discussed in Chapter Seven, “Ability and Technology”, where she gives several examples, how technology companies try to provide technology to serve the disabled community in their daily jobs or lives. She gives the example of Apple shops where either sign language interpreters are available or where Apple equips employees with an iPad to communicate with customers. For consumers, she also highlights Voiceover screen reader software, auto-captioning and transcripts of audio or read-aloud functions of newspaper sites. Broussard points both to the advantages and the limitations of those technological solutions.

She also introduces the idea of tackling biases and discrimination with the help of audit systems

Readers are invited to reflect on concrete policy proposals and suggestions, on the basis of some ideas sketched out in last chapter, “Potential Reboot” where she shows her enthusiasm for the EU’s proposed AI Act and the US Algorithmic Accountability Act. She also introduces the idea of tackling biases and discrimination with the help of audit systems and presents a project for one such system based on the regulatory sandbox idea, which is a “safe space for testing algorithms or policies before unleashing them on the world” (175). The reader might wish that Broussard‘s knowledge of technology and awareness of discrimination issues could have informed the ongoing policy debate even further.

In sum, the book will be of interest and use to a wide range of readers, from students, specialised academics, policy makers and AI experts to those new to the field who want to learn more about the impacts of AI on society.

This post gives the views of the author, and not the position of the LSE Review of Books blog, or of the London School of Economics and Political Science. The LSE RB blog may receive a small commission if you choose to make a purchase through the above Amazon affiliate link. This is entirely independent of the coverage of the book on LSE Review of Books.

Image Credit: Vintage Tone on Shutterstock.

Further maths from Sunak is still a fail | David Mitchell

Published by Anonymous (not verified) on Sun, 23/04/2023 - 7:00pm in

The PM banging on – again – about numeracy doesn’t look likely to provoke the conflict he’s hoping for

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Careful with that thing – you could kill someone

Published by Anonymous (not verified) on Tue, 27/07/2021 - 9:06pm in

It’s been a while, but guest author Mark Lauer is returning to the Mule. While in COVID-induced lockdown, the mind naturally turns to armchair epidemiology, but here Mark goes beyond mere amateur probability to add a sprinkling of ethics.

So, you’re in lockdown during a COVID-19 outbreak in your city. And you’re wondering, now that most of the elderly are vaccinated, if all the fuss is really justified. After all, only a tiny proportion of the city has caught COVID so far, and even if you get it, statistically speaking it is unlikely to harm you. The number of people dying is a small fraction of the population, especially now that effective vaccines are being rolled out. So just how dangerous would it be if you popped down to see that friend you’ve been missing?

It turns out, if you happen to have COVID, it could be rather dangerous indeed.  It may not be too risky for you, or your friend, but let’s do some simple mathematics to see what the consequences might be for others if you do pass on the virus.

In what follows, I’ll focus on the current outbreak here in Sydney, which began on June 16. It’s unusual at this stage of the global pandemic, since the population has lived largely unrestricted for over a year and perhaps some have become complacent about dealing with the virus, despite the carnage and sacrifices of freedom seen overseas. But the general gist applies anywhere that has significant case counts which aren’t falling dramatically.

Please note though, I am not an epidemiologist. There are many more qualified people, building far more sophisticated models. Listen to them and follow their advice.

One obvious factor to consider is how likely it is that you’re infected.  This will vary depending on the number of cases in the outbreak, how many cases are near you, and how often you go shopping or meet others.  But remember it takes several days for testing to reveal where cases are, during which time the outbreak can spread far across the city.  Also many people with COVID are asymptomatic, or at least asymptomatic for a period while they are infectious. None of the people who’ve passed on the virus so far have thought they had it at the time.  And it seems the Delta strain may take as little as a few seconds of contact to transmit.  But let’s set that question aside, and look at what happens if you do transmit it.

So suppose you unknowingly have the virus, and choose between two courses of action, one that passes it on to another person, and the other that avoids doing so.  From an ethical stand point, just how bad is it if you opt for the former?

To start, let’s consider the average risk of death for the person you infect. Case fatality rates for COVID-19 are in the range of 1-3% in most countries, but of course these will vary depending on many factors: the standard and capacity of health facilities, who in the population is getting the disease, how many of those are vaccinated, and the virulence of the prevalent strain.

In the Sydney outbreak we’ve had relatively few deaths. As at July 26, there have been 10 in this outbreak, whereas total case counts are now above 2000. However, that neglects the delay between cases being identified and consequent deaths. A study in the Journal of Public Health published in March finds the average lag is 8 days (even longer if a lower proportion of those infected are over 60 years old).

So a more comparable estimate of cases might be the number of locally acquired cases reported up to July 18, which is 1364. That yields a case fatality rate in this outbreak of 0.73%, which is indeed low by global standards of COVID. But while it might seem like a small number, that’s 7300 micromorts, which is equivalent to spending over 7 months as a British soldier serving in Afghanistan.

Now perhaps you and your friend are vaccinated, in which case the mortality risk to you is substantially lower. But while vaccination helps prevent your death, it is far less effective against transmitting the virus. And ethically speaking we need to consider what happens if your friend then passes the virus on further. The probability of this will vary according to the situation. If your friend is actually someone you’re  keeping locked in your cellar as a slave, then there’s no way for them to pass it on, and you can feel relieved of any moral qualms about deaths due to passing on the virus further (we can set aside other moral considerations in this scenario, since we’re talking about manslaughter here, so why worry about a minor case of enslavement).

Since normally we have little control over how others behave, even friends, let’s assume the friend is exactly like the average other Sydneysider in this outbreak. We can roughly guess the effective reproduction rate of the virus in the conditions of this outbreak by looking at case counts over time. Here is a chart of the number of new locally acquired cases by date during the outbreak so far.

Bar chart of new locally acquired cases in NSW 16.6-26.7.2021

Source: NSW Government

In the 24 days through to the imposition of city-wide stay-at-home restrictions on July 10, new cases grew exponentially to reach 103. For the purpose of this argument, I’ll assume a fixed cycle of infection lasting 3 days (this is not essential, since values below are still valid albeit with slightly different timeframes if the cycle is longer or shorter). A quick calculation yields a reproduction rate, r = 1.8.  That is, each infected person infects an average of 1.8 other people every three days.

At this level of transmission, 100 people will infect 180 people in three days, who will infect another 324 people after six days, and so on. If this continues for 15 days, the total number of resulting infections will be 4126, or 41.26 people per original infected person. If each of the 41 people infected via our friend has a 0.73% chance of dying from the virus, there is over 25% chance that at least one person will die. And that’s only counting infections in the next 15 days.  Giving the virus to one person is significantly worse than Russian roulette under these conditions.

Of course, as Sydneysiders are uncomfortably aware, the government here has been instituting successively more stringent restrictions across the city. And in the two weeks or so since July 11, the growth in case counts has happily slowed somewhat. Unfortunately, lockdown efforts so far appear to be insufficient to bring case counts down dramatically, with over 170 new cases reported on July 25.

But let’s be wildly optimistic and say that the reproduction rate is now down to 0.9. In that case, 100 people infect 90 people who infect 81 people, so that after 15 days the expected total number of resulting cases is 469. Your single transmission to your friend then leads to around 3.4% chance of at least one death as a result of infection in the next 15 days.

While that’s much better than before the citywide restrictions, it is nothing to shrug off. It’s similar to the chance of dying:

Most would agree that all these events have a “reasonable chance of killing someone”. And so too does passing on the virus under the current Sydney outbreak conditions.

So please, please be careful. Your choices can save lives.

Narrative and Proof: Two Sides of the Same Equation

Published by Anonymous (not verified) on Thu, 22/01/2015 - 8:49pm in

One of the UK's leading scientists, Marcus du Sautoy, argues that mathematical proofs are not just number-based, but also a form of narrative. Literary techniques and mathematical proofs are rarely, if ever, brought together but Marcus du Sautoy is very interested in the qualities that the narrative of proofs share with other narrative art forms. In an unusually multidisciplinary panel, he is joined by author Ben Okri, mathematician Roger Penrose, and literary scholar Laura Marcus, to consider how narrative underpins and nurtures the respective disciplines.

Somehow I don’t think solving this problem will do much...

Published by Anonymous (not verified) on Fri, 21/06/2013 - 11:47am in

Somehow I don’t think solving this problem will do much for the couple.