Seneca effect
The Seneca effect, or Seneca cliff or Seneca collapse, is a mathematical model proposed by Ugo Bardi to describe situations where a system's rate of decline is much sharper than its earlier rate of growth. Description. In 2017, Bardi published a book titled "The Seneca Effect: When Growth is Slow but Collapse is Rapid", named as the Roman philosopher and writer Seneca, who wrote "Fortune is of sluggish growth, but ruin is rapid" (Lucius Anneus Seneca, "Letters to Lucilius", 91–63). Bardi's book looked at cases of rapid decline across societies (including the fall of empires, financial  crises, and major famines), in nature (including avalanches), and through man-made systems (including cracks in metal objects). Bardi concluded that rapid collapse is not a flaw, or "bug" as he terms it, but a "varied and ubiquitous phenomena" with multiple causes and resultant pathways. The collapse of a system can often clear the path for new, and better adapted, structures. In a 2019 book titled "Before the Collapse: A Guide to the Other Side of Growth", Bardi describes a "Seneca Rebound" that often takes place were new systems replace the collapsed system, and often at a rate faster than  preceding growth rates as the collapse has eliminated many of impediments or constraints from the previous system. The "Seneca effect" model is related to the "World3" model from the 1972 report "The Limits to Growth", issued by the Club of Rome. Use. One of the model's main practical applications has been to describe the resultant outcomes given the condition of a global shortage of fossil fuels. Unlike the symmetrical Hubbert curve fossil fuel model, the Seneca cliff model shows material asymmetry, where the global rate of decline in fossil fuel production is far steeper than forecasted by the Hubbert  curve. The term has also been used to describe rapid declines in businesses that had grown for decades, with the rapid post-2005 decline and resultant bancruptcy in Kodak as an quoted example. References. https://books.google.ca/books/about/The_Seneca_Effect.html?id=F14yDwAAQBAJ&printsec=frontcover&source=kp_read_button&redir_esc=y