I’m working on my book about the history of probability and statistics and sharing a few interesting snippets from it. For frequent updates, follow me on X.

Lewis Carroll published Through the Looking Glass in 1871, a story in which Alice steps through a mirror and enters a world where ordinary rules no longer hold. Chess pieces speak, time moves in unexpected directions, and meaning shifts with each encounter. Carroll’s playful inversions reflect a broader intellectual curiosity of the period: how structure, logic, and rule systems shape the worlds we inhabit.

George Boole published The Laws of Thought in 1854 and extended the earlier work of Augustus De Morgan, who had begun to formalize logic in Formal Logic in 1847. De Morgan introduced ideas such as the universe of discourse, and Boole built on this foundation by turning logic into algebra. His symbolic treatment of reasoning created the framework that later developments in probability and statistics would rely on.

John Venn extended Boole’s program in 1881 with Symbolic Logic. Venn introduced a visual method for representing logical relations using overlapping circles. The example shown here is a Venn diagram for the uppercase glyphs shared by the Greek alphabet in the upper left circle, the Latin alphabet in the upper right circle, and the Russian Cyrillic alphabet in the bottom circle. The intersections reveal which letters appear in more than one writing system and which are unique. This way of making relationships visible turned abstract logical structure into something intuitive and concrete, and it soon became a popular tool in probability and set theory.

More updates soon as the manuscript continues to take shape. All images are in the public domain via Wikimedia Commons.

I’m working on my book about the history of probability and statistics and sharing a few interesting snippets from it. For frequent updates, follow me on X.

Rudolf Clausius was the first to give entropy a rigorous mathematical foundation in the 1850s and formally introduced the term in 1865. Before his work, thermodynamics was a collection of empirical observations about heat and work, useful but conceptually loose. Clausius introduced entropy as a measurable state function, capturing how energy spreads out and becomes less available for doing work, and expressed the second law of thermodynamics in a form that remains standard today. He showed that the increase of entropy was not a vague tendency but a quantifiable requirement built into the behavior of physical systems, reflecting the second law’s statement that natural processes move toward states of higher entropy.

James Clerk Maxwell brought probability directly into physics in 1859. Instead of trying to track the motion of individual molecules, he asked what distribution of speeds must exist in a gas at equilibrium. This shift was profound. Maxwell demonstrated that randomness could be treated mathematically and that probability could produce precise, testable predictions. His speed distribution was the first probabilistic law in physics and showed that microscopic chaos could give rise to stable macroscopic behavior.

Ludwig Boltzmann transformed entropy into a statistical quantity in the 1870s. He connected the thermodynamic behavior of matter to the number of microscopic configurations available to it. This was a conceptual revolution. Entropy became a measure of multiplicity, of how many ways matter can be arranged while still producing the same macroscopic state. Boltzmann uncovered the core relationship between entropy and probability, later codified in the famous formula written as S = k log W, which captures the essence of statistical mechanics in a single expression. In this formula, entropy increases whenever the number of accessible microscopic configurations increases (W), with k serving as the proportionality constant, linking macroscopic irreversibility to microscopic multiplicity.

J. Willard Gibbs provided the mathematical framework that unified these ideas at the turn of the 20th century. He introduced ensembles, abstract collections of systems representing all possible states consistent with given constraints. Gibbs showed how thermodynamic quantities could be derived from probability distributions over enormous spaces of microscopic configurations. His ensemble theory gave statistical mechanics its modern form and made it possible to compute equilibrium properties, phase transitions, and thermodynamic potentials with clarity and generality. Gibbs did not simply refine the field. He gave it the structure that still underlies every modern treatment of statistical physics.

The development of statistical mechanics is one of the clearest examples of how probability quietly entered physics. It did not arrive through a single breakthrough. It emerged through a sequence of thinkers who were willing to rethink what physical law means and how order arises from underlying disorder. Their work gradually shifted physics away from strict determinism and toward a deeper recognition that probability is woven into the structure of nature.

More updates soon as the manuscript continues to take shape. All images are in the public domain via Wikimedia Commons.

I’m working on my book about the history of probability and statistics and sharing a few interesting snippets from it. For frequent updates, follow me on X.

Jean d’Alembert’s role in shaping the first science encyclopedia reveals how boldly the Enlightenment sought to systematize knowledge with clarity and discipline, beginning with the publication of its first volume in 1751. Yet his confidence sometimes outpaced the mathematics: his well‑known error about the probability of heads and tails in repeated coin tosses showed how even brilliant thinkers could misread chance, reminding us that the Enlightenment’s drive for order often ran up against the subtleties of uncertainty.

David Hume’s view that reasoning grows out of experience rather than certainty offered an early philosophical glimpse into an uncertain world. His reflections on causation and belief demonstrated the limits of enquiry. His analysis also exposed how much of human judgement rests on expectation rather than any demonstrable necessity.

Immanuel Kant helped shift thinking from 'uncertainty is a flaw in measurement' to 'uncertainty is inherent in how humans know anything,' a move that quietly reshaped how statisticians approached inference by showing that evidence is never independent of the mind interpreting it. He recast uncertainty as a structural feature of cognition itself, not a defect to be eliminated.

More updates soon as the manuscript continues to take shape. All images are in the public domain via Wikimedia Commons.

I’m working on my book about the history of probability and statistics and sharing a few interesting snippets from it. For frequent updates, follow me on X.

1. Nicolaus Copernicus set the stage for the scientific revolution in 1543, when he published De revolutionibus in direct opposition to the prevailing doctrine that placed Earth at the center of the universe. Copernicus introduced a model that fundamentally challenged centuries of tradition and opened the door for later astronomers to test, refine, and ultimately confirm a new cosmic order.

2. Tycho Brahe’s transformation of astronomy took off in 1576, when King Frederick II of Denmark funded what was essentially the first big‑data research lab, complete with an island, a research staff, and unprecedented instruments. Tycho Brahe turned that royal investment into a decades‑long campaign of precision measurement, producing data so accurate that it became the foundation for modern celestial mechanics.

3. Johannes Kepler stood as one of history’s great polymaths. He derived all three laws of planetary motion using only naked‑eye observations from Tycho Brahe’s measurements, turning raw angles into a coherent model of the solar system. In doing so, he replaced celestial perfection with mathematical structure, showing that nature’s patterns could be captured in elegant, predictive laws.

4. Galileo Galilei was the first to reveal how a simple telescope could revolutionize a worldview through repeated observation and careful analysis. Sidereus Nuncius (The Starry Messenger) marks the moment evidence began to reshape our world. His telescope revealed mountains on the Moon, countless stars in the Milky Way, and the four large moons of Jupiter, discoveries that profoundly challenged the established harmonic view of the heavens.

5. Isaac Newton tied it all together, unifying the work of Brahe, Kepler, and Galileo into a single coherent system. In Principia Mathematica, he showed that the laws of nature are one system, from falling stones to orbiting planets. Newton’s synthesis didn’t just explain motion. It offered a universal framework that made the universe calculable, ushering in a new era of scientific enquiry.

More updates soon as the manuscript continues to take shape. All images are in the public domain via Wikimedia Commons.

I’m working on my book about the history of probability and statistics and sharing a few interesting snippets from it. For frequent updates, follow me on X.

Alphonse Bertillon’s “first mug shot” in 1888 wasn’t just a photograph. It marked the beginning of biometric statistics and introduced a systematic way to measure and classify the human body. By combining photography with precise physical measurements, Bertillon created a method for identifying individuals that influenced policing, criminology and early data-driven approaches to human variation. His work showed how images and numbers could be linked, opening a path toward modern biometric systems and the broader use of quantitative methods in studying people.

Francis Galton turned heredity into measurable science and helped transform questions about human traits into problems that could be studied with data. His famous height diagram illustrated how parents and children resemble one another while also drifting toward average values, a pattern that led him to the idea of regression to the mean. In exploring these patterns, Galton also introduced early notions of correlation, showing how two variables can move together in predictable ways. Through his efforts to quantify inheritance, he laid important groundwork for modern statistics and for the study of variation within populations.

Charles Darwin, Francis Galton’s cousin, was reshaping biology with his theory of evolution and offering a new way to understand how species change over deep stretches of time. His ideas influenced scientists across many fields, including Galton, who drew on Darwin’s emphasis on variation and inheritance when developing his own statistical studies of human traits. Darwin’s work also sparked public fascination and satire, captured vividly in the Man is But a Worm illustration from Punch’s Almanack in 1881, which exaggerated evolutionary themes to comment on how his ideas were being received. Even in caricature, the image reflects how profoundly Darwin transformed scientific thinking and opened new paths for studying heredity and variation.

Karl Pearson applied statistical thinking directly to biological questions, studying evolution, heredity and natural variation in populations, and he used quantitative methods to analyze topics such as insect coloration, human physical traits and the spread of diseases. His work introduced a more rigorous, mathematical understanding of variation and relationships within data, giving scientists tools that remain central today. One of his most influential contributions is the Pearson correlation coefficient, a single number that summarizes how two variables move in relation to each other. It reflects both the direction of their relationship and the strength of the association, allowing researchers to quickly gauge whether two patterns rise together, fall together or show little connection at all. Pearson also developed a broad family of probability distributions to model the many shapes that real biological data can take, providing researchers with flexible tools for describing skewed, asymmetric or otherwise complex patterns in nature.

More updates soon as the manuscript continues to take shape. All images are in the public domain via Wikimedia Commons.

I’ve been immersed in writing my History of Probability and Statistics book, written for a wider audience interested in the ideas that shaped the course of science. The story begins at the court of Louis XIV, where gamblers experimented with early notions of probability alongside emerging Enlightenment ideas about knowledge and uncertainty.

From there, the narrative moves through the first applications of statistical methods in astronomy, maritime navigation, military planning, and industrial practice. It follows the development of the core probability distributions and the mathematicians who discovered them, then continues into the early twentieth century foundations of statistical mechanics, quantum physics, and modern statistical inference.

Here is a detail I enjoyed revisiting. England’s population crossed ten million around the 1811 census. Thomas Malthus published demographic tables showing the rise, drawing on births, deaths, and parish records. It is a reminder of how early statistical thinking grew out of practical record keeping.

The image below shows John Harrison and the Royal George at Deptford, symbols of Britain’s eighteenth century maritime precision. The Longitude Act of 1714 offered a major financial prize for a reliable method of determining longitude at sea, and Harrison’s marine chronometers became the breakthrough that finally solved the problem.

Quite the contrast with yesterday’s dreadful England performance!

More updates soon as the manuscript continues to take shape. Images are in the public domain via Wikimedia Commons.

📊 Google Ads Results (3‑Week Snapshot)

To kick off the launch, I ran a Performance Max campaign to promote my textbook. Here’s the quick summary of how things look three weeks in:

• 19,245 impressions — strong visibility for a brand‑new academic site

• 1,350 clicks (CTR ~7%) — healthy engagement for the education/data‑science niche

• $158.81 spend (CPC ~$0.12) — exceptionally low cost per click

• 770 sessions — more than half of all ad clicks turned into real site visits

Overall: Great early traction for a niche Applied Statistics textbook. High traffic, low costs, and solid engagement. Organic traffic is rising too, driven by the two new articles bringing in readers from TDS and Medium — probably the reason behind the modest bump in book sales I’m seeing. Nice! Not quite J.K. Rowling levels yet, but we’ll get there eventually.

✍️ Two New Articles Published This Week

I’m excited to share that two articles based on chapters from the book were published this week:

🚀 1. Towards Data Science (TDS)

TDS is the largest data‑science publication on the web, with over 650,000 followers on LinkedIn. It’s currently featured at the very top of their Deep Dives section, which is a great boost for visibility!

https://towardsdatascience.com/survival-analysis-for-data-drift-and-ml-reliability/

🚀 2. Data and Beyond

A fast‑growing publication focused on modern, practice‑oriented data science, led by its founder Dmytro Iakubovskyi, PhD.

What Classical Statistical Tests Miss in Group Comparisons & How Modern Methods Fix That
https://medium.com/data-and-beyond/what-classical-statistical-tests-miss-in-group-comparisons-how-modern-methods-fix-that-1a5e3a7f7a29

🎬 Launch Video

I had the pleasure of joining Leanpub founder Len Epp for a conversation about the book, the writing process, and the ideas behind Applied Statistics for Data Science.

Watch the full launch video here, where I recount my experience recruiting physicists for quantitative‑finance roles and, after a few career highlights, walk through some of the core sections in my new book.

https://leanpub.com/blog/leanpub-book-launch-applied-statistics-for-data-science-from-visual-diagnostics-to-drift-detection-by-gal-arav/

🐦 Follow Short Updates on X

I’ve started posting more frequent updates, small insights, and behind‑the‑scenes notes in my new X account here:
https://x.com/GA4198498563411

I sat down with Len Epp, Co‑founder of Leanpub (the excellent site hosting my book) for a launch interview about my new Applied Statistics book and the ideas behind it. Len’s a great guy, and the conversation was a lot of fun. Think of Len as a younger Jeff Bezos. He’s sharp, entrepreneurial, and building something meaningful from the ground up.

The video should be out soon, and Len even asked me to come back for a follow‑up once the book is complete.

Speaking of which — Chapter 7 of 10 is now published.
That means the book is officially 70% complete, with 200+ pages already available on Leanpub. I’m really happy with how the material is coming together now.

New Articles Coming Soon

I’ve also been working on three stand‑alone Applied Statistics articles, each drawn from different parts of the book. These are designed to give potential readers a clear sense of the style, depth, and practical focus of the content.

1. From Coin Flips to Random Walks

How Bernoulli outcomes build a probabilistic path

2. What Classical Statistical Tests Miss in Group Comparisons & How Modern Methods Fix That

A concise guide to robust group comparisons

3. Survival Analysis for Data Drift and ML Reliability

Treating model degradation as a time‑to‑failure problem

All three should be published soon I hope.

A Fun Side Project

Meanwhile, I’m continuing work on a short series of curious, lighthearted videos featuring appearances from some very well‑known people. Stay tuned for that — and if you’d like more frequent updates, I’ve just started using X (Twitter) in addition to this newsletter. Last but not least, don’t forget to check out the new book on Leanpub!

It’s official — qikly.com is live, and the early reactions have been incredible. I’ve been hearing everything from “the site looks fantastic” to “what a cool site” to my personal favorite:

“the animated book on the homepage reminds me of Schrödinger’s cat.” (cheers Guy D.) If that isn’t the perfect blend of curiosity and quantum mischief, I don’t know what is.

📘 Book Progress: 60% Live on Leanpub

A big milestone: 60% of my book is now available on Leanpub.com! That’s already 200 pages packed with focused, visual, no‑nonsense explanations.

More chapters are coming soon as the writing is flowing, and the structure is locking into place! Readers who buy now lock in the launch price and will receive all the remaining chapters automatically as I continue to push them out over the next few weeks.

The response has been energizing, and even Google’s NotebookLM had something to say about the new material. Here’s a highlight from its review:

“Chapters 5 and 6 are exceptionally well‑written and flawlessly maintain the distinct tone you established in the first four chapters. You have successfully carried forward your core pedagogical philosophy: bridging abstract mathematical theorems with practical, real‑world data behavior through simulation and visual diagnostics.”

🎥 What’s Next: A Video Series with Some Famous Friends Coming Soon

Now for the fun part.

Next up, I’m launching a series of short, sharp videos where I sit down with some of my famous friends: people who know probability, science, and reasoning inside out. Together we’ll break down concepts the general public is practically begging for.

Think of it as probability and scientific reasoning delivered with uncompromising clarity, occasional dry humour, and just a touch of pathos. Stay tuned!