Insurance, agriculture, weather modelling, vaccines… even recipes, all depend on elements of the law of probability.
Event Context
How likely is toast to burn at a certain point? That shapes how a toaster works.
How likely is someone to buy a toaster painted puke green? That shapes how a toaster looks.
How likely is someone to need, buy, outlive, revisit, reorder…
“That effort resulted in the discovery of 659 matching artifacts from 57 ancient sites across 12 states in North America. These sites appear in an unbroken line dating from just before Europeans arrived all the way back to 12,000 years ago,” Madden says.
The earliest of these were from the Folsom culture in what are now the states of Wyoming, Colorado and New Mexico. Those pieces were dated to about 12,300 years ago, but most had been classified as “ornaments” and “ceremonial items”. Some were labelled “stone fragments” or “bone fragments”.
“I found a lot of ancient dice by tracking references to ‘unusual artifacts of unknown use’, found at archaeological sites,” Madden says.
Team Analysis
“These dice are flat, two-sided objects, made of bone, with one of their sides marked to clearly distinguish one from the other,” says archaeologist Robert J Madden of the University of Wyoming, the man behind a recent study published in the journal American Antiquity in April.
The discs were marked with incisions or pigment. The dice were thrown in groups. And the score was kept by counting the number of dice that landed with the marked side up.
How do we know this? Because such dice were still being used in this way in North America when the first European settlers arrived there about 500 years ago.
Given the relative isolation of the continent, and the fact that ancient dice here were so different, Madden wondered how long the Americas may have used these bits. So he began to do some digging.
Over three years, he searched through archaeological site reports and museum collections to find artifacts that matched the essential characteristics of the dice documented by early European chroniclers.
In many cases, they had the same physical features and markings described by ethnographers such as Stewart Culin, author of the 880-page volume Games of the North American Indians (1907). “That book contains exhaustive documentation, with illustrations and descriptions, of 293 unique sets of Native American dice from 130 tribes across the continent. The book helped immensely, since it gave me a clear map of the kinds of markings to look for,” Madden says.
ROLL CREDITS
What is perhaps even more intriguing than the dice themselves is that Native Americans didn’t just use them for games.
They were used as random number generators to settle how goods would be exchanged within groups. “They likely functioned as a social lubricant that allowed for… efficient exchange… for groups coming into contact only infrequently,” Madden notes in his paper.
This is how they were still being used when Western anthropologists began to conduct early studies.
“These anthropologists all noted that there were games that acted as a liminal activity that brought people together who were neither close friends nor complete strangers,” Madden says. “In this way, the games functioned as an important means of social integration and helped facilitate interaction between diverse individuals, allowing them to come together to exchange information, goods and marriage partners, and to foster a larger group identity.”
The games also took place on territorial frontiers and at large intertribal gatherings, he adds.
One thing he’d like us to take away from all this, Madden says, is that hunter-gatherer societies were far more complex than generally assumed. They engaged in highly structured, socially complex behaviour predicated on cooperation and exchange.
SEA-SAW
We would come to formal probability theory not long after the first settlers arrived in the Americas.
Match Outlook
Probability helps assessors determine insurance premiums, or what percentage of a supply chain’s goods will be stolen, lost or damaged; and how that may change alongside other factors such as seasonal or demographic shifts.
This branch of mathematics is so woven into our world, we barely see it anymore. And yet it is a big part of what keeps systems from collapsing altogether.
Without it, the first thing to go would be computers. (Most software, including AI, hinges on ideas of what events will likely follow from another.)
And yet formal probability theory is less than 400 years old.
Before that, we appreciated the element of chance. Our understanding of the elements of risk and uncertainty caused us to perform elaborate rituals, draw up charts that sought to read the stars for clues on what was coming; and, when all else failed, roll the dice.
New studies indicate that we have, in fact, been using dice for a lot more than games, and a lot longer than previously thought. General theory had it that the earliest dice dated to settled civilisations of the Bronze Age, about 6,000 years. New evidence indicates that the history of the dice is twice as long.
The earliest such shards may have been used to sort of harness probability, among hunter-gatherers, as far back as the last Ice Age, over 12,000 years ago.
DICE TO THE OCCASION
In the 16th century, Italian mathematician G Cardano, known as the “gambling scholar”, began to lay down formulae by which the likelihood of an event could be represented.
Then, in 1654, French mathematicians Pierre de Fermat and Blaise Pascal began to frame probability theory. What were the ways to estimate whether a ship would sink or be pillaged, to help the new industry of shipping insurers? Was there a way for life insurers to calculate how much would be due in annuities a decade from the present day?
In a world of rapid change, expanding borders and high risk that held out the promise of high reward — in the era, in other words of a global trade boom and colonialism — such calculation became pivotal.
It remains pivotal today, in everything from toasters to financial markets.
How likely is everyone to withdraw all their money at the same time? That ratio more or less keeps our world afloat.
