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.

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.

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.

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.

## 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.

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.

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!

## 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.

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.

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.

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.

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.

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.

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

## 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.