The five books that taught me most about leadership are

**On Grand Strategy**by John Lewis Gaddis**War and Peace**by Leo Tolstoy**The Open Society and its Enemies**by Karl Popper**Talleyrand**by Duff Cooper**Middlemarch**by George Eliot

By leadership, I mean the act of forging and articulating a vision and then engaging and motivating individuals in its execution. …

The prevailing paradigm of data analysis is buried deep in the arid soil of a philosophical school called Logical Positivism. The framework is characterized by three mythical tenets derived from Positivism

- Data are the only natural point of departure for all analysis
- We ensure objectivity in our models by gathering data impartially
- Data “speak”. That is, they guide our minds in the construction of models.

As I discuss in my article “Myths of Modelling: Data Speak”, Positivism — and, by association, its mythical beliefs — had been pretty thoroughly discredited by the 1960s. Unfortunately, as if often the case…

Thank you so much for your thoughtful and thought-provoking commentary.

It was absolutely not my intention to dismiss attempts to refute theories, only that we shouldn't (and don't) *only* try to refute theories, that confirmation - and other criteria - can have a place in an open contest between rival theories, but also that refutation is harder than we might think.

I left Kuhn out, because the article was already long enough, but Kuhn is clearly essential in all this. I'd argue, though, that Kuhn, like Popper, is most persuasive in his rejection of the positivist view that science ought…

The myth of falsification has two versions

- Science progresses through repeated attempts to falsify theories, conjectures or hypotheses. This is the descriptive myth.
- Science
**ought to**progress through repeated attempts to falsify theories, conjectures or hypotheses. This is the normative myth.

The normative myth of falsification is half of a widely preached doctrine of scientific practice together with the positivist myth of the primacy and objectivity of data— the idea that data are the starting point for all analysis and that we ensure objectivity in our models by gathering data impartially and “letting the data speak”.

According to this…

The myth of speaking data has many related forms

- Data are the natural starting point for investigation and analysis, and one should approach data pure in mind and cleansed from all taint of theory
- Data are objective, or at least somehow more objective than models, which without data are just story-telling with a strong odour of opinionation.
- We ensure objectivity in our models by impartially gathering data and then letting the data “speak”.
- Data objectively guide our minds in the construction of impartial models, motivated only by “the facts”

This is the myth of the primacy and probity of…

Your business involves repeatedly predicting the outcome of a gamble — the success of acquisitions, the return from investments, the repayment of loans — and you have subjective assessments of similar gambles that you or others have made in the past in the form of some sort of score.

Mathematical modelling of uncertainty stands or falls on our ability to assess probabilities, but how do you know if your assessments are any good and what does that even mean? This article takes a pragmatic approach to answering these questions. We’ll start in the shadows of the valley of frequentism, step out on to the Bayesian foothills of subjectivism and stride on to the summits of pragmatism and an objective form of the Bayesian view.

From this standpoint, we will see what can go wrong with probabilistic assessments and discuss systematic biases. Finally, the pragmatist interpretation will bring us to…

Bayes’ theorem tells us how to update probabilities in the light of new data. When we’re assessing the probability of an event with a binary outcome — something either happens or it doesn’t — there is a particularly elegant formulation due to the high priest of Bayesianism E.T. Jaynes that richly deserves a much wider audience than it has today. It has consequences for how we look at success and failure in all branches of life.

(*The traditional practical example for introducing Bayes’ theorem is tests for medical conditions, but I figure we’re all pretty tired of talking about…*

The Monty hall problem became famous when Marilyn vos Savant published it in response to a reader’s question in her column in Parade magazine in 1990. It is as famous for the virulence with which Marilyn was mansplained as it is for the subtlety of the problem itself. Even the legendary Paul Erdos, one of the great names of 20th century mathematics was only finally convinced by a computer simulation.

This article will show how a causal framework can help elucidate the structure of the problem, which I will argue helps avoid the logical pitfalls that makes the correct answer…

Whenever a

modelappears to you as the only possible one, take this as a sign that you have neither understood themodelnor the problem which it was intended to solveKarl Popper, Philosopher (1902–1994)

If models are cheap, don’t choose. The more models the merrier. But we mustn’t waste our time on rubbish and there’s more to a good model than the accuracy of its predictions.

At catastrophic economic cost, governments across the world have imposed various levels of lockdown on the basis of results of a handful of mathematical models. …

Mathematical modelling for business and the business of mathematical modelling.