The maths of how India’s shoreline lengthened with out gaining new land

In December 2024, the Union Ministry of Dwelling Affairs made an vital announcement as a part of its 2023-2024 annual report. It stated the size of India’s shoreline had elevated from 7,516.6 km to 11,098.8 km, and that the size can be presently underneath assessment.

The 7,516.6 km determine was first recorded within the Nineteen Seventies primarily based on measurement methods accessible on the time. The brand new revised determine wasn’t prompted by any territorial enlargement by means of new land/island annexation or geological upheaval, like tectonic exercise stretching the shores. The final coastal State to affix the Union of India was Goa in 1961 and the one different State that joined after — Sikkim in 1975 — is landlocked. The enclaves India exchanged with Bangladesh in 2015 additionally lie deep inland.

So what modified?

The foundation of the discrepancy lies in geometry, in an issue known as the shoreline paradox. The earlier estimate from the Nineteen Seventies banked on maps that displayed India’s shoreline at a 1:4,500,000 decision, which is just too coarse to seize intricate options like estuaries, tidal creeks, sandbars, and coastal ridges. Many island teams, notably the Andaman & Nicobar and Lakshadweep, additionally hadn’t been comprehensively mapped or included.

The newer up to date measurement — carried out by the Nationwide Hydrographic Workplace (NHO) and the Survey of India — used digital navigation charts at a a lot finer scale of 1:250,000. Making ready these charts requires using applied sciences like geographic data programs, satellite tv for pc altimetry, LIDAR-GPS, and drone-based imaging. The federal government has additionally stated the shoreline size can be revised each 10 years from 2024-2025, as per the report.

The Survey of India used highwater traces ready by the NHO primarily based on 2011 information on digital navigation charts to measure the shoreline. The highwater line was used as the bottom reference and river mouths and creeks had been closed off at a set threshold inland. The assessment additionally included islands uncovered to low tide.

However for all these advances, there’s a limitation — and that comes from geometry.

The shoreline as puzzle

What’s the distinction between straight traces and ragged curves?

In Euclidean geometry, the size of a straight line is the shortest distance between two factors on the ends of the road. Curves however are measured by their geodesic size: i.e. the size alongside the floor of the curve.

However what occurs when the curve itself is irregular, jagged, and ever-changing the best way a shoreline is when it’s formed by river mouths, creeks, delta formations, and so on.?

The issue turns into more durable when one makes an attempt to attract a boundary at a river mouth: ought to or not it’s marked on the ocean opening or traced additional inland? Such ambiguities add to the complexity along with fixed tidal fluctuations and shifting sedimentation.

That is the place conventional measurement ideas break down and the selection of scale turns into decisive.

The shoreline paradox

The British mathematician and physicist Lewis Fry Richardson first recognized the shoreline paradox within the early Fifties. His Polish-French peer Benoît Mandelbrot examined the issue mathematically in 1967 and likewise popularised it. Mandelbrot discovered that coastlines exhibit properties just like fractals.

In a landmark paper entitled ‘How Lengthy is the Coast of Britain?’, Mandelbrot explored why the size of Britain’s coast assorted dramatically relying on the size of the measuring stick. Utilizing completely different ruler sizes on a map, he discovered that Britain’s coast might fluctuate from round 2,400 km to greater than 3,400 km — a hanging vary for a set landmass.

Observe that coastlines usually are not true fractals within the pure mathematical sense however show fractal-like properties. To explain fractals, scientists use the idea of fractal dimension, a quantity that denotes the diploma of complexity a form reveals as one zooms into it.

For instance, measuring a shoreline with a 200-km-long ruler would easy over most inlets and bends — however a 50-km ruler would detect them. At 1 km, the measurement will seize each estuary, tidal flat, and creek. So the extra one refines the size of the ruler, the longer the overall coast turns into.

Hypothetically, utilizing a measurement unit the scale of a water molecule would lead to a shoreline size approaching infinity. This dependence on scale underscores the inherent paradox: a finite piece of geography yielding a seemingly infinite measurement in cartography.

Implications for safety, fishing

The change in size is not only a mathematical curiosity or an instructional pursuit. The size of India’s shoreline influences maritime safety plans, catastrophe preparedness (particularly for cyclones and tsunamis), and fishing rights.

An extended shoreline clearly means an extended size to guard however it additionally means an extended financial zone. India has 11 coastal States and two giant island teams, faces common cyclones, and is very weak to sea-level rise. Understanding the true extent of the nationwide coast can thus assist refine local weather fashions, coastal zoning laws, and catastrophe response methods.

In the identical vein, high-school geography textbooks could must be revised as effectively.

The shoreline paradox additionally reveals greater than a peculiar measurement problem: it underscores how science evolves with higher instruments. What as soon as seemed to be a set worth turns fluid when examined extra intently — not as a result of the coast moved however as a result of our eyes sharpened. India’s redefined 11,099-km shoreline is a testomony to this progress.

C. Aravinda is an instructional and public well being doctor. The views expressed are private.