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The Hindu
26-05-2025
- General
- The Hindu
The maths of how India's coastline lengthened without gaining new land
In December 2024, the Union Ministry of Home Affairs made an important announcement as part of its 2023-2024 annual report. It said the length of India's coastline had increased from 7,516.6 km to 11,098.8 km, and that the length is also currently under review. The 7,516.6 km figure was first recorded in the 1970s based on measurement techniques available at the time. The new revised figure wasn't prompted by any territorial expansion through new land/island annexation or geological upheaval, like tectonic activity stretching the shores. The last coastal State to join the Union of India was Goa in 1961 and the only other State that joined after — Sikkim in 1975 — is landlocked. The enclaves India exchanged with Bangladesh in 2015 also lie deep inland. So what changed? The root of the discrepancy lies in geometry, in a problem called the coastline paradox. The previous estimate from the 1970s banked on maps that displayed India's coastline at a 1:4,500,000 resolution, which is too coarse to capture intricate features like estuaries, tidal creeks, sandbars, and coastal ridges. Many island groups, particularly the Andaman & Nicobar and Lakshadweep, also hadn't been comprehensively mapped or included. The more recent updated measurement — performed by the National Hydrographic Office (NHO) and the Survey of India — used electronic navigation charts at a much finer scale of 1:250,000. Preparing these charts requires the use of technologies like geographic information systems, satellite altimetry, LIDAR-GPS, and drone-based imaging. The government has also said the coastline length will be revised every 10 years from 2024-2025, as per the report. The Survey of India used highwater lines prepared by the NHO based on 2011 data on electronic navigation charts to measure the coastline. The highwater line was used as the base reference and river mouths and creeks were closed off at a fixed threshold inland. The review also included islands exposed to low tide. But for all these advances, there is a limitation — and that comes from geometry. The coastline as puzzle What's the difference between straight lines and ragged curves? In Euclidean geometry, the length of a straight line is the shortest distance between two points at the ends of the line. Curves on the other hand are measured by their geodesic length: i.e. the length along the surface of the curve. But what happens when the curve itself is irregular, jagged, and ever-changing the way a coastline is when it's shaped by river mouths, creeks, delta formations, etc.? The problem becomes harder when one attempts to draw a boundary at a river mouth: should it be marked at the ocean opening or traced further inland? Such ambiguities add to the complexity together with constant tidal fluctuations and shifting sedimentation. This is where traditional measurement concepts break down and the choice of scale becomes decisive. The coastline paradox The British mathematician and physicist Lewis Fry Richardson first identified the coastline paradox in the early 1950s. His Polish-French peer Benoît Mandelbrot examined the problem mathematically in 1967 and also popularised it. Mandelbrot found that coastlines exhibit properties similar to fractals. In a landmark paper entitled 'How Long is the Coast of Britain?', Mandelbrot explored why the length of Britain's coast varied dramatically depending on the length of the measuring stick. Using different ruler sizes on a map, he found that Britain's coast could vary from around 2,400 km to more than 3,400 km — a striking range for a fixed landmass. Note that coastlines are not true fractals in the pure mathematical sense but display fractal-like properties. To describe fractals, scientists use the concept of fractal dimension, a number that denotes the degree of complexity a shape exhibits as one zooms into it. For example, measuring a coastline with a 200-km-long ruler would smooth over most inlets and bends — but a 50-km ruler would detect them. At 1 km, the measurement will capture every estuary, tidal flat, and creek. So the more one refines the scale of the ruler, the longer the total coast becomes. Hypothetically, using a measurement unit the size of a water molecule would result in a coastline length approaching infinity. This dependence on scale underscores the inherent paradox: a finite piece of geography yielding a seemingly infinite measurement in cartography. Implications for security, fishing The change in length is not just a mathematical curiosity or an academic pursuit. The length of India's coastline influences maritime security plans, disaster preparedness (especially for cyclones and tsunamis), and fishing rights. A longer coastline obviously means a longer length to protect but it also means a longer economic zone. India has 11 coastal States and two large island groups, faces regular cyclones, and is especially vulnerable to sea-level rise. Understanding the true extent of the national coast can thus help refine climate models, coastal zoning regulations, and disaster response strategies. In the same vein, high-school geography textbooks may need to be revised as well. The coastline paradox also reveals more than a peculiar measurement challenge: it underscores how science evolves with better tools. What once appeared to be a fixed value turns fluid when examined more closely — not because the coast moved but because our eyes sharpened. India's redefined 11,099-km coastline is a testament to this progress. C. Aravinda is an academic and public health physician. The views expressed are personal.
Daily Record
02-05-2025
- Daily Record
Football fan breached court order and ended up with jail term
Thomas Park was arrested as he wasn't supposed to have any contact with the woman after he was convicted of assaulting her. A domestic abuser who planned to watch an Old Firm cup final with his partner landed a nine-month jail sentence instead. Thomas Park was arrested as he wasn't supposed to have any contact with the woman after he was convicted of assaulting her. When officers spotted them together on December 15 they discovered he was the subject of a one-year non-harassment order. Park, 43, formerly of Loch Assynt, East Kilbride, admitted breaching the order and separate bail conditions simply by being in Ms Frame's company. Hamilton Sheriff Court heard the couple were seen chatting at a bus stop in Union Street, Hamilton, around lunchtime. They were planning to watch the Celtic-Rangers League Cup final on TV in Glasgow. Danielle McDonald, prosecuting, said: "On seeing the police, the woman made efforts to walk away, but she and Park were stopped. Checks revealed he was in breach of a non-harassment order and bail conditions." Defence lawyer Andy Thomson said the one-year NHO has now expired, adding: "The woman was never supportive of it. "She has mental health and addiction issues. She sees Thomas Park as the only person who can give her the support she needs. "There had been an attempt in court to have the NHO removed, but a sheriff refused this. "On the day in question there was a football cup final in Glasgow and they had decided to go to the city to watch the match. "My client has paid a heavy price for that as he has been in custody since his arrest in December. "They don't have their troubles to seek." Park was jailed for nine months, backdated to December 16, but Sheriff Colin Dunipace decided not to impose a fresh NHO. *Don't miss the latest headlines from around Lanarkshire. Sign up to our newsletters here. And did you know Lanarkshire Live had its own app? Download yours for free here.
Glasgow Times
24-04-2025
- Glasgow Times
OAP, 80, kept tabs on 27-year-old woman in Glasgow
Dennis Hislop, 80, spent time behind bars after he kept tabs on the then 27-year-old in Glasgow's Parkhead and Dalmarnock. Hislop tailed her several times a day as she walked her dog. READ NEXT: Three jailed after 'large cannabis farm' found in Greenock READ NEXT: Manhunt after killer with links to Glasgow escapes prison The retired metal worker told police that he hid in bushes with binoculars looking in the direction of her house. Hislop also concealed himself in bushes at Celtic Park to leer at her and fled after being pointed out to the police. Hislop was convicted of stalking between February 2020 and June 2022 at Glasgow Sheriff Court. Hislop was released from prison after trial and put on a tag for 12 months and ordered to stay 200 metres from the woman and not to enter her street. However, Hislop was back in the dock for breaching his non-harassment order (NHO) against the woman. He was also convicted of a further charge of behaving in a threatening or abusive manner against a teenage girl and a man. Jurors heard Hislop first flouted the NHO and a court undertaking in September 2023. Prosecutor Danielle McGuinness put to Hislop: "Why did she see you a couple of months after the NHO was put in place in bushes at the bottom of her street?" He replied: "She has an iPhone. I pass her regularly walking her dog in my car - she watches me go up to Bridgeton where I stay. "Why did she not take a picture if she saw me there?" The trial earlier heard from an 18-year-old girl who also came across Hislop in the area in 2023. She first became aware of him amid claims he put a note on her mum's windscreen at the Emirates Arena when she came to pick up her daughter. The girl stated: "The note said she was a paedo and that I felt unsafe around my mum and that I came to him and told him this." An allegation that he put a note on the car was found not proven by the jury. The girl denied ever speaking to Hislop and claimed that he was a stranger to her. She also recalled times Hislop confronted her and her boyfriend in the streets around Parkhead. The girl stated that Hislop told them that he was "quite famous" with "young boys" in the area as he managed to get them a signed Rangers football. His previous trial heard Hislop claimed he had a contact at Rangers who got him a signed ball from ex-player Ryan Kent for a boy he knew. The girl stated that Hislop would "watch us" walk up a street in Parkhead while he was pulled up in his car. The witness recalled a time when she saw Hislop knelt down in bushes near the Emirates Arena. She said: "He got caught up in twigs...I was quite shocked. I honestly didn't think he was waiting on me and I think he was shocked that someone had noticed him." The girl stated in another encounter that Hislop told her boyfriend that she was "not to be scared" of him. She added that she would see Hislop driving round the street three times a day at the time. Hislop was also convicted of repeatedly following a John Carletto in his car which included following him home. Mr Carletto told the court that Hislop "made my life a misery" and he had to sell his car because of him.
STV News
24-04-2025
- STV News
Man, 80, hid in bushes to stalk woman while she walked her dog
A pensioner convicted of stalking a woman has been jailed for 24 months after hounding her and two other people. Dennis Hislop, 80, spent time behind bars after he kept tabs on the then 27-year-old in Glasgow's Parkhead and Dalmarnock. Hislop tailed her several times a day as she walked her dog. The retired metal worker told police that he hid in bushes with binoculars looking in the direction of her house. Hislop also concealed himself in bushes at Celtic Park to leer at her and fled after being pointed out to the police. Hislop was convicted of stalking between February 2020 and June 2022 at Glasgow Sheriff Court. Hislop was released from prison after trial and put on a tag for 12 months and ordered to stay 200 metres from the woman and not to enter her street. However, Hislop was back in the dock for breaching his non-harassment order (NHO) against the woman. He was also convicted of a further charge of behaving in a threatening or abusive manner against a teenage girl and a man. Jurors heard Hislop first flouted the NHO and a court undertaking in September 2023. Prosecutor Danielle McGuinness put to Hislop: 'Why did she see you a couple of months after the NHO was put in place in bushes at the bottom of her street?' He replied: 'She has an iPhone. I pass her regularly walking her dog in my car – she watches me go up to Bridgeton where I stay. 'Why did she not take a picture if she saw me there?' The trial earlier heard from an 18-year-old girl who also came across Hislop in the area in 2023. She first became aware of him amid claims he put a note on her mum's windscreen at the Emirates Arena when she came to pick up her daughter. The girl stated: 'The note said she was a paedo and that I felt unsafe around my mum and that I came to him and told him this.' An allegation that he put a note on the car was found not proven by the jury. The girl denied ever speaking to Hislop and claimed that he was a stranger to her. She also recalled times Hislop confronted her and her boyfriend in the streets around Parkhead. The girl stated that Hislop told them that he was 'quite famous' with 'young boys' in the area as he managed to get a signed Rangers football. His previous trial heard Hislop claimed he had a contact at Rangers who got him a signed ball from ex-player Ryan Kent for a boy he knew. The girl stated that Hislop would 'watch us' walk up a street in Parkhead while he was pulled up in his car. The witness recalled a time when she saw Hislop knelt down in bushes near the Emirates Arena. She said: 'He got caught up in twigs…I was quite shocked. I honestly didn't think he was waiting on me and I think he was shocked that someone had noticed him.' The girl stated in another encounter that Hislop told her boyfriend that she was 'not to be scared' of him. She added that she would see Hislop driving round the street three times a day at the time. Hislop was also convicted of repeatedly following a man in his car which included following him home. The man told the court that Hislop 'made my life a misery' and he had to sell his car because of him. Get all the latest news from around the country Follow STV News Scan the QR code on your mobile device for all the latest news from around the country
Glasgow Times
23-04-2025
- Glasgow Times
Skye man breaches order protecting ex in Dunbartonshire
John MacInnes was convicted last summer of a charge at Portree Sheriff Court which ordered his ex be protected from any contact for 10 years. But on January, his former partner received text messages of a threatening and abusive nature. She lives in the area covered by Dumbarton Sheriff Court. On April 15, the 31-year-old appeared from custody at the court and pleaded guilty to breaching the non-harassment order (NHO). Defence solicitor Jonathan Paul said his client had an issue with alcoholism and his criminal record was on Skye. "It's clear alcohol has a grip on him," he said. "His relationship ended, he started drinking again." Mr Paul said there were bail options and that custody "would be a revolving door". Sheriff James Mulgrew said there were "difficulties" admitting him to bail considering his recent and relevant record. He told MacInnes, listed in papers as a prisoner at Low Moss: "The order was imposed in July at sheriff and jury level and the sheriff's order was for 10 years."
