# Professor quantifies how 'one thing leads to another'

##### August 15, 2014 by Anne Ju

(Phys.org) —"One thing led to another," people often say. Events, discoveries and relationships are triggered by something previous. The iPhone case was designed only because the iPhone was invented first. A song became popular only after someone liked it.

Mathematicians always want to quantify things, and Steven Strogatz, Cornell's Jacob Gould Schurman Professor of Applied Mathematics, is trying to quantify the commonsense concept of "correlated novelties" – that one new thing sometimes (but not always) triggers another. He and three researchers from Italy's Sapienza University, where he spent three months on sabbatical leave, published a paper in Scientific Reports July 31 on their first crack at it.

"This concept of correlated novelties had only been phrased in verbal or conceptual terms," Strogatz said. "It seemed like a really intriguing idea, with room for creativity to make it testable."

Correlated novelties are everywhere: in economics, or perhaps most obviously, in , where traits evolve over time from a cascade of tiny events.

In this era of big data and supercomputing, going back to find patterns in outcomes is easier than ever. Strogatz and his colleagues used four data sets as test cases, each consisting of a sequence of elements ordered in time: texts, where the elements are words, and the novelty occurs when a word appears for the first time; online music, where the novelty is the first time a listener hears a song or artist; Wikipedia, where novelties are the first edit of a given wikipage; and social annotation in tagging sites, where novelties are the introduction of a new tag.

The researchers quantified the rate at which novelties occurred by focusing on the growth of distinct elements in an ordered sequence. They discovered that the rate at which novelties occur decreases over time.

They proposed a simple mathematical model that mimics the process of exploring a physical, biological or conceptual space that enlarges whenever a novelty occurs, according to the paper. The model is based on Polya's Urn, familiar to mathematicians. An urn filled with black and white balls churn like lottery balls; whenever one color is picked, more of the same color are added back. That enhances the likelihood of that original color being picked at the next turn.

The concept has an echo of the familiar, Strogatz says. For example, the urn could be considered a simplification of the "rich get richer" concept – that socioeconomic stratification isn't random, but strongly correlated with previous events.

Such insights hint at the possibility of a sophisticated building on the one proposed to address an endless list of human problems in economics, biology and epidemiology, to name a few. For example, applying the model to 100 years of influenza data, epidemiologists could perhaps learn to predict how the flu will spread going forward, Strogatz said.

Explore further: UMSL scholar examines evolution of learning

## Related Stories

#### UMSL scholar examines evolution of learning

August 14, 2014

Why do monkeys learn to be afraid of snakes and not flowers? Is this knowledge the result of evolution by natural selection? Did the monkeys that couldn't learn that association quickly die and not reproduce?

#### New model shows how often to review material for flashcard programs

January 26, 2012

(PhysOrg.com) -- A challenge for students and teachers -- and today, for designers of educational software: How often should material be reviewed for best learning? Wait too long to review and it fades away; review too soon ...

#### Going batty for jumping DNA as a cause of species diversity

April 1, 2014

The vesper bats are the largest and best-known common family of bats, with more than 400 species spread across the globe, ranking second among mammals in species diversity.

#### Researchers propose a better way to make sense of 'Big Data'

February 18, 2014

Big Data is everywhere, and we are constantly told that it holds the answers to almost any problem we want to solve. Companies collect information on how we shop, doctors and insurance companies gather our medical test results, ...

#### Mathematical model shows how groups split into factions

January 4, 2011

(PhysOrg.com) -- The school dance committee is split; one group wants an "Alice in Wonderland" theme; the other insists on "Vampire Jamboree." Mathematics could have predicted it.

#### A vexing math problem finds an elegant solution

November 14, 2013

(Phys.org) —A famous math problem that has vexed mathematicians for decades has met an elegant solution by Cornell researchers. Graduate student Yash Lodha, working with Justin Moore, professor of mathematics, has described ...

## Recommended for you

#### Experts uncover hidden layers of Jesus' tomb site

October 27, 2016

In the innermost chamber of the site said to be the tomb of Jesus, a restoration team has peeled away a marble layer for the first time in centuries in an effort to reach what it believes is the original rock surface where ...

#### Fossilized dinosaur brain tissue identified for the first time

October 27, 2016

An unassuming brown pebble, found more than a decade ago by a fossil hunter in Sussex, has been confirmed as the first example of fossilised brain tissue from a dinosaur.

#### Important ancient papyrus seized from looters in Israel

October 27, 2016

(Phys.org)—Eitan Klein, a representative of the Israel Antiquities Authority, has announced that an important papyrus document dated to 2,700 years ago has been seized from a group of Palestinian looters who reportedly ...

#### Money can buy happiness but it's costly to bank on that without measuring debt

October 26, 2016

Yes, money can lead to happiness, but how much debt one has should also be considered in the money-happiness equation, according to a new a study from Purdue University.

#### Upper Paleolithic humans may have hunted cave lions for their pelts

October 26, 2016

Upper Paleolithic humans may have hunted cave lions for their pelts, perhaps contributing to their extinction, according to a study published October 26, 2016 in the open-access journal PLOS ONE by Marián Cueto from the ...

#### Ancient parrot fossil found in Siberia

October 26, 2016

(Phys.org)—A Russian paleontologist has discovered a parrot fossil uncovered in Siberia several years ago—the first evidence of parrots living in Asia. In his paper published in Biology Letters, Nikita Zelenkov describes ...