The Coastline Paradox

Abstract

How long is the coastline of the United States? While it may sound counter-intuitive, there is no objectively true answer to this question. In fact, it is impossible to precisely measure the length of any coastline.

A coastline features an endless array of bays and promontories at all scales, from hundreds of miles to fractions of an inch. Thus, the length of a coastline depends on the unit of measurement being used. The smaller the unit of measurement, the more of these bays and promontories are detected, and thus, the longer the coastline becomes. Follow this logic down to the atomic level, and the length of a coastline – any coastline – approaches infinity.

This phenomenon is known as the “coastline paradox,” and it is more than just a mathematical curiosity. Because coastlines play such a prominent role in legal frameworks, the coastline paradox presents troubling legal implications at all scales. From international maritime jurisdictions to local real estate markets, the complexities created by this phenomenon are disconcertingly understudied. In fact, the coastline paradox has never been considered as a significant source of legal problems.

This article is the first to address the legal implications of the coastline paradox. It begins with an explanation of the coastline paradox and other, similar characteristics of coastlines that defy accurate measurement. Then the legal implications for international, federal, and local legal frameworks are introduced and examined. It is apparent that awareness of the coastline paradox is low, and challenges are scarcely being addressed. While a mathematical solution to the coastline paradox may be impossible, the article concludes with a set of recommendations for coastal stakeholders.