Plot twist: a brief history of diagrams, the elegant messengers of mathematics

The ancients tracked points in the night sky and drew celestial patterns, creating their own versions of cosmic PowerPoint slides with clear calls to action for life on Earth.

For thousands of years, our quest to understand the world has continued. The methods and metrics we use have now become more specialized and sophisticated. They provide new levels of understanding and nuance.

For example, during the Covid-19 lockdown, seismic maps showed a completely new way of impacting our planet. Simply put: the Earth’s vibrations have halved. Between March and May 2020, when traffic, transport and industrial operations were suspended, the land itself was about 50% calmer.

Thus, quantum leaps in our methods and technologies are shedding new light on our world. If our ancestors looked to the skies for clues, we have taken to the skies to find out more: through satellite images, travelers, Mars landing missions and rovers on the Moon.

Here at home, the Indian Economic Survey 2021-22 includes a chapter titled “Tracking Development through Satellite Imagery and Mapping,” which identifies the potential cause of the pressing problem. Satellite images over Punjab showed that the kharif crop was planted about three weeks later, causing its harvest to coincide with the rabi sowing. Farmers may be burning stubble to save time due to the narrowing gap between them, contributing to Delhi’s air becoming unbreathable in November and December, a study suggests.

Every industry has charts that it uses extensively.

Consultants and MBAs adhere to 2×2 frameworks in which they encapsulate in four grid cells months of analysis and conclusions about products and behavior. Data scientists use Area Under the Curve plots to evaluate the performance of their machine learning models.

To understand new technologies, investors and businesses turn to Gartner’s Hype Cycles, a research firm that visualizes the current stage and future trajectory of new technologies.

Industries have grown around our internal need for new ways of viewing and interpreting results. The data visualization software market is now worth billions of dollars, and the pie is expanding.

For the general public, charts convey important findings without forcing them to navigate the underlying complexities and nitty-gritty details. But just as a map is not an area, a diagram is not the whole story. This is the point from which a deep dive can begin.

Take a bell curve or normal distribution chart. It contains multitudes and is perhaps the closest thing to a universal truth.

On a personal level, it has supernatural predictive powers, acting almost like a prophecy. Where one falls on the bell curve largely determines the trajectory of your life.

On the far right is the skinny tail section, symbolizing all the GOATs, the greatest of all time. “Make something of yourself” is a call to move away from the broad middle.

Move your attention to the left of the curve and you will find the strugglers and the laggards. Are the people who populate the rest of this graph the guardians of those on the left? In a nutshell, this is the social contract, and the answer to this question determines how countries and economies are governed.

A good graph tells its story in a simple, straightforward way.

To paraphrase Michelangelo, the sculptor simply cuts away excess material to free up a statue that already exists within a block of marble.

A good diagram is also wonderful. It’s a marriage of elegance and insight that creates an aha moment.

Thousands of years after we scratched our first data into stones (Click here more on that), diagrams remain our most direct way of understanding our world.

Here are nine of today’s most effective formats.

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Hockey stick chart

In 1999, climate scientist Michael Mann and his research partners created a graph of average temperatures in the northern hemisphere over six centuries (later extended to 2,000 years). The graph resembled a hockey stick, with relatively stable temperatures followed by sharp increases in the 20th century.

The graph has become a powerful form of evidence and a key visual representation of global warming and modern climate change, helping to shape public opinion around the world and influence climate policy.

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Keeling curve

More than 40 years before Mann’s hockey stick, climate science pioneer Charles Keeling developed a new technique for accurately measuring the concentration of carbon dioxide in the air. In doing so, in 1958, he also created the Keeling curve, which is the longest continuous record of atmospheric CO2.

The sharp rise in this curve was the first significant evidence of rising CO2 levels in our air. In one frame, it provided a snapshot of the impact of human activity on the planet, serving as an early indicator that we are entering the Anthropocene: the geological epoch we now find ourselves in, defined largely by human activity.

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Lorenz curve

Developed by economist Max Lorenz in 1905, this curve reflects income or wealth inequality in a country, showing us what percentage of total wealth is in the hands of a certain percentage of the population.

In a world where everyone had the same wealth, the graph would be a straight diagonal line. In the real world, the curve is shaped like an onion, and the more curved it is, the more unequal the distribution of wealth is.

The Gini coefficient, which is a statistical measure of economic inequality in a society, is based on the Lorenz curve.

Comparing Lorenz curves over time is a good way to measure whether the level of inequality in a society is rising or falling. Incidentally, India’s richest 1% now owns 40.1% of the country’s wealth, more than at any time since 1961.

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Laffer curve

A bell curve (or bell curve) is a graph that shows how data is distributed around a mean value. For example, if the height of a large group of adults were measured, most people would be close to average height, with only a limited number either very short or very tall.

The bell curve is the natural pattern of much of the physical world (most rocks are hard, most pillows are soft, most corn grows to a certain height over a period of time).

In other words, most things obey the 68-95-99.7 rule, which states that 68% of data points lie within 1 standard deviation (SD) of the mean, 95% lie within 2 SD, and 99.7% fall within within 3 SD from the mean. average.

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Fat-tailed distribution

In a normal distribution, there are very few data points at the extreme ends of the curve. These extreme values, or outliers, are critical in risk assessment because the likelihood of extreme events must be taken into account.

A fat-tailed distribution has a large proportion of extreme values ​​at both ends. This graph is usually seen when the natural order of things is disrupted.

The thing about a fat tail is that an unlikely event is still rare; but when it does happen, because systems were not designed to accommodate it, the consequences can be dramatic, unpredictable and long-lasting.

Consider the pandemic and the global economic downturn of 2008 as two recent examples.

Extreme weather events that were once rare are becoming more common, and it’s another fat tail we urgently need to combat.

For more on this, see former options trader Nassim Nicholas Taleb’s fascinating book, The Black Swan: The Impact of the Extremely Improbable (2007; no relation to the 2010 psychological thriller about a ballerina).

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Exponential curves

Legend has it that the king asked the man who invented the game of chess to choose a reward. He said that he needed grains of rice, starting with one grain on the first square of his chessboard, and then doubling the number on each square.

Why didn’t he ask for either land or gold? “Seems like a missed opportunity,” people said.

Well, then, as now, the human brain struggled to understand exponents. We are not used to thinking about growth in geometric proportions.

Do the math, and the chess reward would be about 18.5 quintillion grains, which is 52,000 times the rice stock in all the Food Corporation of India’s warehouses.

How can this be? Think about the million-billion comparison, which is now practically a proverb: a million seconds is about 11.5 days; A billion seconds is equal to approximately 31.7 years.

(By the way, after a billion comes a trillion, a quadrillion, then a quintillion.)

Exponential graphs are characterized by rapid growth (or decline). The rate of change is not constant, but increases (or decreases) multiplicatively. Values ​​rise slowly at first and then rise rapidly.

Consider the spike in Covid-19 cases in 2020. The investment mantra of “start early and benefit from the compounding effect” is another illustration.

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Kaplan-Meier conspiracy

This chart is used in clinical trials to analyze chances of survival and other outcomes over time. It has a step form, where each step represents an event (such as a relapse or a side effect), making it easier to determine at what intervals certain events occur.

This allows researchers to compare the effectiveness of different treatments through visual inspection. For example, in the case of survival rates, if the decline is sharp, events for that group occur faster and more frequently.

The Kaplan-Meier plot is often used in combination with other measures such as the hazard ratio (a measure of the relative risk of different treatments).

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Heat maps

A heat map is a visualization technique that uses color to represent data in a grid, with the color or hue intensity of each cell corresponding to a value.

The heat map provides a quick visual summary and is intuitive to use. They are the backbone of business reporting and are used with great success to show changes in stock basket prices, sales and distribution patterns, and even employee productivity.