Painter’s Paradox Reimagined

Consider the Coastline Paradox where the smaller the unit of measurement or ruler you pick out to measure the total length of the coastline of any landmass, the larger it gets. This occurs because of the fractal-like property of the coastline wherein the area bound by the curve or coastline is finite, but the perimeter or the length of the coastline approaches infinity. This is how Norway gets the second-longest coastline in the world due to its long and deep fjords placing it ahead of much bigger countries like Russia in terms of the length of coastline. In practice, the resolution of the GIS data determines the measurement of such geographical features.

Koch Snowflake

In the same manner, Gabriel’s horn, a geometry figure having infinite surface area but finite volume introduces Painter’s paradox where the horn could be filled with a finite quantity of paint and yet the paint would not be sufficient to coat its surface. To resolve the paradox there would be certain things to consider such as the limitation of a physical paint, its thickness, viscosity, flowrate etc or it can be avoided by considering a hypothetical paint for the sake of the problem.

Now let’s talk about painting the whole surface area of a country in a quest to determine the true surface area with all of its rich topographical features — mountains, hills, valleys, water bodies, and buildings. Unlike the length of coastlines, different sources providing data regarding the areas of the countries are rather consistent. The region is assumed perfectly flat and thus the area is calculated. Elevation changes are mainly disregarded in the calculation of the area as the effect of elevation difference is relatively small in the grand scheme of calculating the total area of the region. Say, for a 300 x 300 sq. km region a fairly high elevation difference of 3 km (9842 feet) i.e. 1% of the 2D stretch of the country appears to be pretty much negligible and as smooth as a baby’s bum. For the majority of the countries being relatively smaller, there is no substantial effect due to the roundness and the curvature of the earth. For mountainous countries like Switzerland or Nepal, a measurement resolution of 100 sq. m would probably only make 5% to 10 % difference in the land area.

Relief Map of the Indian subcontinent
Exaggerated Relief Map of the Indian subcontinent

However, in my little to no knowledge of geomorphometry, the actual surface area to be painted for a country, given all the mountains, troughs, buildings, and nooks and crannies — poses the same kind of paradox as the Coastline paradox does. Of course, the volume of the paint would be a finitely huge number but the painted surface area would approach an extremely unthinkable number if not infinity.

Consider this: you have a hill that is 1 km in diameter. When you measure it with a 1 sq. km resolution, it will look like 1 sq. km in area, but when you go to measure it with the 1 sq. m resolution, it will look like more than a million, because the sides of the hill have a slope to them. I believe, the economic surveys of smaller regions and the local geospatial data certainly take into account these elevation differences.

Mathematically, the shape of the terrain in a mountainous region would render a larger surface area due to its fractally rough and sloped surface and if we try to go microscopically to the atomic level taking into account all the flora, rocks, and soil particles not to mention the chaotic water bodies.

“As our circle of knowledge expands, so does the circumference of darkness surrounding it.”

— Albert Einstein

Constellations to muse

I did not pay much attention to constellations before but was always intrigued by the night sky especially when I got to my hometown up in the western Himalayas. The night sky here is almost as beautiful as the day sky. On a clear night, you can distinctly see thousands of stars sprinkled across the midnight blue fabric and the expansive Milky Way all with your naked eyes which is a lot difficult to witness in a city as opposed to the countryside because of all the light pollution and skyglow.

Star Constellation Chart (Credit: Robert Sullivan)

On one such night on the fifth of March, I spotted Canis Major — visible in the northern sky in winters with the brightest star Sirius; Orion — with the three-star belt; Taurus the Bull — with V-shaped Hyades cluster; The Pleiades star cluster, and Ursa Major (Big Dipper or Great Bear) going counterclockwise from the South. I wish to spot the Ursa Minor and the Polaris at its tail/head but could not because of the gigantic mountains towards the North.

Reminds me of a Ghalib’s sher from the ghazal sab kahan kuch laala-o-gul mein . . .

thiiñ banāt-un-nāsh-e-gardūñ din ko parde meñ nihāñ
shab ko un ke jī meñ kyā aa.ī ki uryāñ ho ga.iiñ

थीं बनात-उन-नाश-ए-गर्दुं दिन को पर्दे में निहाँ
शब को उन के जी में क्या आई कि उर्यां हो गईं
Mirza Ghalib

Here’s is an interactive night sky map to muse.

Top 20: All-Time Favourite Films From Around The World

Without going through a long rambling article, I am sharing my all-time favourite movies mostly watched multiple times over the last decade up until 2022. I do believe there are probably a lot more gems to watch which may be vying for a few places in this contentious and fiercely competitive catalogue of mine. Having said that, I just want to put it out as a disclaimer that to my little knowledge of cinema, these are the ones that piqued my interest and lingered in my mind the most after watching them. They may not be in any particular order, however, based on certain factors such as rewatch value, relevance, cinematography, and emotional finesse one could appear more engaging than the other in the listing order.

My Top 20 Films of All-Time ShySnail
My Top 20 Movies of All-Time
Sr. No.FilmYearFilm IndustryDirector
1Once Upon A Time In America1984Italian – AmericanSergio Leone
2The Good, the Bad and the Ugly1966ItalianSergio Leone
3Pulp Fiction1994AmericanQuentin Tarantino
4Harakiri (Japanese: 切腹)1962JapaneseMasaki Kobayashi
5M1931GermanFritz Lang
6Paths of Glory1957AmericanStanley Kubrick
7The Graduate1967AmericanMike Nichols
8Psycho1960AmericanAlfred Hitchcock
9A Short Film About Love
(Polish: Krótki film o miłości)
1988PolishKrzysztof Kieślowski
10Love Story1970AmericanArthur Hiller
11The Irishman2019AmericanMartin Scorsese
12Touching The Void2003BritishKevin Macdonald
13The Curious Case of Benjamin Button2008AmericanDavid Fincher
14The Hunt2012DanishThomas Vinterberg
15The Shining1984AmericanStanley Kubrick
16A Frozen Flower (Korean: 쌍화점)2008KoreanYoo Ha
17Road To Perdition2002AmericanSam Mendes
18The Man From Earth2007AmericanRichard Schenkman
19There Will Be Blood2007AmericanPaul Thomas Anderson
20In The Mood For Love2000Hong Kong – FranceWong Kar-wai
*Mughal-E-Azam1960IndianK. Asif
* honourable mention

Kullu To Manali Journey Along The Beas River

Looking back at the year it was an adventurous ride for me. In the mid of October, I planned to go on a trek to some nearby mountain pass or peak in Himachal Pradesh. It was not the best time of the year to go very high up as most of the treks above 4000 meters get closed for trekking in autumn for the rest of the year till the peak of the spring. But it was doable and I geared up for Hampta Pass (4270 m or 14000 feet) which connects Manali to Lahaul. It is only one or two months window of time between monsoon and winter for those high passes especially for amateurs like me.

I took a local bus from Rampur Bushahr, the nearest station to my hometown, to Kullu. The route NH 305 slithers through Jalori Pass or Jalori Jot at an elevation of about 3200 m and merges with NH 3, Kullu – Manali – Leh highway at the 2.6 km long and dicey Aut tunnel. The passage remains closed for four months during winters due to heavy snowfall in higher reaches. It took rather long for me on this Sainj- Luhri – Anni – Jalori – Aut route to reach the Kullu town. So I got off the bus in Bhuntar, a town just 10 km South of Kullu because of the Dussehra festival traffic.

HRTC Bus Stand Manali

So this video is the first in series of my journey to Hampta Pass Trek and it started from Bhuntar on the next day of Dussehra. Bhuntar town is situated at the confluence of the Parvati River with the River Beas. Bhuntar Airport aka Kullu Airport is one of the only 3 domestic airports in Himachal. Beas Valley, a fairly open valley, runs up North and Parvati Valley runs eastwards, through a steep-sided valley towards Kasol, Manikaran, Tosh, and Khir Ganga. You can see some processions of local deities on the way to the renowned International Mega Dussehra festival observed in Kullu. Stay tuned for the next part of the journey.

Filmi Ghazals: Repository of Ghazals in Hindi cinema aka Bollywood

As an aficionado of Ghazals, I am trying to build up a fairly comprehensive list of ghazals that are featured in Hindi cinema also known as Bollywood. I’ll keep adding to the list. Do suggest some of your favourite filmi ghazals in the comments so I can add them. Also, let me know of any mistakes in the entries.

There is of course only one condition: the songs should be in the ghazal format.

SrNoGhazalPoetFilmYear
1Aah Ko Chahiye Ek Umar Asar Hone TakMirza GhalibMirza Ghalib1954
2Aaj Socha To Ansoo Bhar AayeKaifi AzmiHanste Zakhm1973
3Aaye Bahar Ban Ke Lubha Kar Chale GayeHasrat JaipuriRajhath1956
4Ae Dil Mujhe Aisi Jagah Le ChalMajrooh SultanpuriAarzoo1950
5Ae Mohabbat Meri Duniya MeinShakeel BadayuniBees Saal Baad1962
6Ahl-E-Dil Yun Bhi Nibha Lete HaiNaqsh LyallpuriDard1981
7Badi Nazuk Hai Ye ManzilZameer KazmiJoggers’ Park2003
8Barbad-E-Mohabbat Ki Dua Saath Liye JaSahir LudhianviLaila Majnu1976
9Bekasi Had Se Jab Guzar JaayeJan Nisar AkhtarKalpana1960
10Bemuravat Bewafa Begana-E-Dil Aap HainJan Nisar AkhtarSushila1966
11Bhari Duniya Mein Akhir Dil KoShakeel BadayuniDo Badan1966
12Bhule Se Mohabbat Kar BaithaSahir LudhianviDil Hi To Hai1963
13Bujha Diye Hain Khud Apne HanthonSahir LudhianviShagoon1964
14Chehre Pe Khushi Chha Jaati HaiSahir LudhianviWaqt1965
15Chhalke Teri Aankhon SeHasrat JaipuriAarzoo1965
16Chhoo Lene Do Nazuk Hothon KoSahir LudhianviKaajal1965
17Chupke Chupke Raat DinHasrat MohaniNikaah1982
18Deewana Keh Ke Aaj Mujhe Phir PukariyeShakeel BadayuniMulzim1963
19Deewano Se Ye Mat PoochoQamar JalalabadiUpkar1967
20Dekha Hai Zindagi Ko Kuchh Itna Kareeb SeSahir LudhianviEk Mahal Ho Sapnon Ka1975
21Dhadakte Dil Ki Tamanna HoKaifi AzmiShama1961
22Dikhayi Diye Yun Ke Bekhud KiyaMir Taqi MirBazaar1982
23Dil Cheez Kya HaiShahryarUmrao Jaan1981
24Dil Ke Armaan Aansuon Mein Beh GayeHasan KamaalNikaah1982
25Dil-E-Nadan Tujhe Hua KyaMirza GhalibMirza Ghalib1954
26Dil-E-Nashad Ko Jeene KiM R SharmaChunaria1948
27Door Rahakar Na Karo BaatSahir LudhianviAmaanat1977
28Duniya-E-Aarzoo Mita Kar Chale GayeD N MadhokBarsat Ki Ek Raat1948
29Dushman Na Kare Dost NeIndeevarAakhir Kyon1985
30Guzre Hain Aaj Ishq Mein HamShakeel BadayuniDil Diya Dard Liya1966
31Hai Bas Ke Har Ek Unke IshareMirza GhalibMirza Ghalib1954
32Hai Isi Mein Pyar Ki AabruRaja Mehdi Ali KhanAnpadh1962
33Hai Mauj Mein Apne BegaaneArzoo LakhnaviRaat Ki Rani1949
34Hal-E-Dil Yun Unhe Sunaya GayaRajendera KrishanJahan Ara1964
35Hazaaron Khwaishein AisiMirza GhalibGhayal1951
36Hum Aapki Aankhon MeinSahir LudhianviPyaasa1957
37Hum Dard Ke Maron Ka Itna Hi Fasana HaiHasrat JaipuriDaag1952
38Hum Hain Mata-E-Koocha-O-Bazar Ki TarahRajinder Singh PuriDastak1970
39In Aankhon Ki Masti Ke MastaneShahryarUmrao Jaan1981
40Is Bhari Duniya Mein Koi BhiRajendra KrishanBharosa1963
41Ishaare Ishaare Mein Duniya BanaUnattributedManmani1947
42Ishq Mujhko Nahi Wahshat Hi SahiMirza GhalibMirza Ghalib1954
43Itni Haseen Itni Jawan Raat Kya KarenSahir LudhianviAaj Aur Kal1963
44Jana Tha Humse DoorRajinder KrishanAdalat1958
45Jhuki Jhuki Si NazarKaifi AzmiArth1982
46Jurm-E-Ulfat PeSahir LudhianviTaj Mahal1964
47Justaju Jiski Thi Us ko To Na Paaya HumneShahryarUmrao Jaan1981
48Kabhi Ae Haqiqat-e-MuntazirAllama IqbalDulhan Ek Raat Ki1967
49Kabhi Khud Pe Kabhi Halat Pe RonaSahir LudhianviHum Dono1961
50Kabhi Kisiko Muqammal Jahan Nahi MiltaNida FazliAhista Ahista1981
51Kahan Meri Manzil Kahan Meri RahenMadhukar RajasthaniDiwali Ki Raat1956
52Khumar-E-Gam Hai Mahakti FizaGulzarLeela2002
53Kisi Ki Yaad Mein Duniya Ko HaiRajendera KrishanJahan Ara1964
54Kisi Nazar Ko Tera IntezarFarooq QaiserAitbaar1985
55Kisi Ne Nazar Se Nazar Jab Mila DiSahir LudhianviHumsafar1953
56Koi Fariyad Tere Dil MeinFaiz AnwarTum Bin2001
57Koi Sagar Dil Ko Bahlata NahinShakeel BadayuniDil Diya Dard Liya1966
58Lagta Nahin Hai Dil Mera Ujde Dyar MeinBahadur Shah ZafarLal Quila1960
59Layi Hayaat Aaye QaazaMohammad Ibrahim ZauqShabaab1954
60Main Teri Nazar Ka Suroor HoonRajendra KrishanJahan Ara1964
61Main Zindagi Ka Saath Nibhata Chala GayaSahir LudhianviHum Dono1961
62Mana Teri Nazar Me Tera Pyaar Hum NahiNaqsh LyallpuriAhista Ahista1981
63Mile Na Phool To Kaanton Se DostiKaifi AzmiAnokhi Raat1968
64Milti Hai Zindagi Mein MohabbatSahir LudhianviAakhen1968
65Mohabbat Hi Na Jo SamjheNoor LakhnaviParchhain1952
66Mohabbat Ki Rahon Mein ChalnaShakeel BadayuniUran Khatola1955
67Mohabbat Tark Ki Maine GarebanSahir LudhianviDo Raha1952
68Mujhe Kuch Khabar Na Ho SakiRaaz AllahabadiNon-filmi
69Mujhko Yaaron Maaf KarnaShailendraMain Nashe Mein Hoon1959
70Na Kisi Ke Aankh Ka Noor HoonBahadur Shah ZafarLal Quila1960
71Na Milta Gham Toh BarbadiShakeel BadayuniAmar1954
72Na Moonh Chhupa Ke JiyoSahir LudhianviHamraaz1967
73Na Tu Zameen Ke LiyeSahir LudhianviDastan1972
74Naghma-O-Sher Ki Saugaat Kise Pesh KarunSahir LudhianviGazal1964
75Naseeb Mein Jiske Jo Likha ThaShakeel BadayuniDo Badan1966
76Nukta Cheen Hai Gham-E-DilMirza GhalibMirza Ghalib1954
77Paon Choo Lene Do Phoolon KoSahir LudhianviTaj Mahal1963
78Parbaton Ke Pedon Par ShaamSahir LudhianviShagoon1964
79Phir Chhidi Raat Baat Phoolon Ki Raat HaiMaqdoom MohiuddinBazaar1982
80Phir Mujhe Deeda E-Tar Yaad AayaMirza GhalibMirza Ghalib1954
81Rafta Rafta Woh Humare Dil KeQamar JalalabadiHam Kahan Jaa Rahe Hain1965
82Raha Gardishon Mein HardumShakeel BadayuniDo Badan1966
83Rahiye Ab Aisi Jaga Chal Kar Jahan Koi Na HoMirza GhalibMirza Ghalib1954
84Rahne Laga Hai Dil Mein AndheraBehzad LakhnaviRoti1942
85Rang Aur Noor Ki Baraat Kise Pesh KaroonSahir LudhianviGazal1964
86Rasm-E-Ulfat Ko NibhayeNaqsh LyallpuriDil Ki Rahen1973
87Rehte The Kabhi Jinke Dil Mein HamMajrooh SultanpuriMamta1966
88Ruke Ruke Se QadamGulzarMausam1975
89Sabaa Se Yeh Keh DoMadan MohanBank Manager1959
90Seene Mein Jalan Aankhon Mein ToofanShahryarGaman1978
91Sharma Ke Yun Na DekhSahir LudhianviNeel Kamal1968
92Tadbeer Se Bigadi Huyee TaqdeerSahir LudhianviBaazi1951
93Tang Aa Chuke HaiSahir LudhianviPyaasa1957
94Tere Pyar Ki Tamanna Gham-E-Zindagi Ke SayeHasan KamaalTawaif1985
95Tu Nahin To Zindagi MeinIftikhar Imam SiddiquiArth1982
96Tujhe Kya Sunaoon Main DilrubaMadan MohanAakhiri Daao1958
97Tum Apna Ranj-o-GhamSahir LudhianviShagoon1964
98Tum Itna Jo Muskura Rahe HoKaifi AzmiArth1982
99Tum Ko Dekha Toh Ye KhayalJaved AkhtarSaath Saath1982
100Tumhare Bulane Ko Jee Chahta HaiPrem DhawanLadli1949
101Tumhari Zulf Ke Saye Me Shaam Kar LungaKaifi AzmiNaunihal1967
102Ujdi Hui Hai Ishq Ki Duniya Tere BagairPandit PhaniRefugee1948
103Unake Kayaal Aaye To Aate Chale GayeHasrat JaipuriLal Patthar1972
104Unko Ye Shikayat Hai Ki HamRajendera KrishanAdalat1958
105Uthaye Ja Unke SitamMajrooh SultanpuriAndaz1949
106Wo Aaye Hai Dil Ko Karar Aa GayaFarooq QaiserMalika Salomi1953
107Wo Jo Hum Mein Tum Mein Qarar ThaMomin Khan MominShikaayat1948
108Ye Mulaqat Ek Bahana HaiNaqsh LyallpuriKhandaan1979
109Yeh Hawa Yeh Raat Yeh ChandniRajinder KrishanSangdil1952
110Yeh Kya Jagah HaiShahryarUmrao Jaan1981
111Yeh Na Thi Hamari QismatMirza GhalibMirza Ghalib1954
112Yeh Wadiyan Yeh FizaayeinSahir LudhianviRavi1963
113Yun Hasraton Ke Daag Mohabbat Mein Dho LiyeRajinder KrishanAdalat1958
114Zara Sun Haseena-E-NazneenShakeel BadayuniKaun Apna Kaun Paraya1963
115Zara Thehro Main Haal-e-Dil Suna DoonRaja Mehdi Ali KhanInaam1955
116Zinda Hoon Is Tarah KiBehzad LakhnaviAag1948
117Zindagi Aaj Mere Naam Se Sharmati HaiShakeel BadayuniSon of India1962
118Zindagi Jab Bhi Teri Bazm Mein Lati Hai HumainShahryarUmrao Jaan1981
119Zindagi Mein Jab Tumhare Gham Nahin TheSudarshan FaakirDooriyaan1979

Here is a public YouTube playlist for the same here. I’ll keep adding to the list. Till then, cheers and take care of yourself!

Filmi Ghazals: Ghazals from Hindi cinema

Kashapat: Remotest Village of Shimla | Himachal Himalayas

Kashapat is one of the remotest and unexplored villages of Shimla district in Himachal Pradesh, located at about 155 kms north-eastward of the state capital. You can never gauge the true expanse of the mountainous geography of Himalaya until you visit one of such sites.

Bhelnu Peak and Darkali Hills as seen from Shrai Koti Mata Temple

Kashapat is a cluster of villages and settlements. Most prominent are Kasha, Paat, and Kandi with an average elevation of 2500 meters or 8200 feet. The valley also hosts arguably the highest and also unclimbed peak of Shimla, Bhelnu Tibba at around 5150 meters (16700 feet). The surrounding glacial peaks are the source of Nogli river, a tributary of Sutlej.

Kasha Village

The road journey to Kashapat is filled with treacherous twists and turns as the roads are carved onto a steep rocky terrain. The giddy heights of precipitous overhangs may produce butterflies in your stomach and raise your heartbeats. The construction of this 20 kms stretch of the road undertook more than 10 years of careful rock drilling, cutting and blasting activities and it is still in the final stages of making. An entire day of knee-crushing trek is now reduced to just a few hours thanks to the rough road.

Kandi Village as seen from Jagoti Dhar

Valleys have dark forests of perennial coniferous trees like deodar (Himalayan cedar), fir, spruce, and other indigenous trees until the trees disappear beyond the treeline giving a majestic spectacle of rocky snow-capped peaks all around the year.

Winter months, December to March bring harsh sub-zero weather conditions with ample days of snowfall activities. Locals brace themselves with enough food supplies for their livestocks mainly cattle, sheep, and goats. Major occupations are animal husbandry and farming. Apple harvesting season is one of the major attractions.

Kandi Village

Like any other town of the state, education has utmost regard and kids commute long distances on foot every day — crossing water bodies and mountains to reach school just like our parents figuratively did in their childhood.

Govt. Senior Secondary School, Kashapat

As the village is situated on a rocky slope, sometimes the relationships between locals turn out to be on the rocks. Yet with all the struggle in life, they are the most innocent bunch out there.

Atal Tunnel @ 10000 feet | Rohtang Pass | Lahaul Spiti in First Snowfall 

All right, back after a long hiatus. I just happened to visit this engineering marvel in the first snowfall of the season last week.

Atal Tunnel is built on NH3 highway to provide access to Lahual-Spiti district in Himachal Pradesh throughout the year bypassing the existing Rohtang La which remains closed for more than half a year because of heavy snowfall in the high mountain pass.

Atal Tunnel South Portal


This tunnel is a little more than 9 kms in length and is the longest road tunnel above 10,000 feet in the world and reduces the travel time to Keylong and Leh by 4 to 5 hours.

Some glimpses of the journey in the video below.

A quick trip to hometown | Himachal diary

It’s always fun to watch the terrain change as you go up on the lofty country roads. Last month I had another trip to my hometown in Shimla in this rainy season. The weather offered no clemency as it continued to shower for several days and made it nearly impossible for me to venture out in the wild mountains and popular destination nearby. So many less-taken roads to inconspicuously remote locations that are untouched even by Google maps. But for the people out there it’s, as they call it, “the season time”― the season of Apples. The most cherished and primary produce of the agrarian economy of the region.

Unlike the day, some nights offered great views of the night sky ― thousands of never-seen-before points of shimmering lights in the pristine-black fabric of space laid across the edges of the alpine horizon.

We braved the weather, crossed brooks and cascades at their full might, encountered a couple landslides, some rocks even fell on our bus. During the return journey in the wee hours of the morning, our bus was confronted by the sight of a mountain leopard. Sharing some of the pictures here.

 

A short video of the journey can be seen on my YouTube channel:

it rains heavily if it rains

The clouds don’t care

for if they feel heavy

they let it all go at once

until they can’t shower anymore

it rains heavily if it rains

 

The rivers don’t care

for if they flood

they flood the entire town

and if they go dry

they go dry like a camel’s ass in Sahara

it rains heavily if it rains

 

Heart doesn’t care

for if it gets hurt, it cries

it cries like a broken faucet

it rains heavily if it rains

– BPC

 

1564323055818.jpg

Dravyavati River Project, Jaipur

Hoogli River, Howrah

Howrah Bridge, Kolkata

Sunset at Hoogli

Trip to Sikkim

Last week my friends and I had an unplanned trip to Sikkim, the hotspot state for finding mountainous valleys, monasteries, and a diverse range of flora and fauna.

As it was a really quick 3-days outing for us, we didn’t have enough time to explore the whole landscapes except the far northern region of the state, Yumthang Valley.