Day 2: Middalsbu to Litlos

My first real night in this tent is… eventful. The breeze that appeared while I was pitching the tent continued to strengthen and eventually brought along some rain. At some point in the night I’m woken by what I can only assume is the sound of a distant rockfall. Poking my head outside the tent, I’m surprised that I can see anything, and can make out the shapes of clouds ominously swirling above the mountains (where the light is coming from, I have no idea). The sight is a bit unsettling, but luckily doesn’t prevent me getting back to sleep.

When the morning comes, it is bright – the night’s dark masses replaced by white puffy cumulus. I have a quick breakfast of instant porridge, and get going. Today’s destination is Litlos – a staffed cabin, where I’ll get a bed and a hot meal. Even after only one night of camping, I’m looking forward to spending a night in a room that doesn’t move in the wind. As I pass the cabin at Middalsbu, I see lights stirring behind the windows; evidently sleeping in a tent is good for motivating early starts.

My route initially takes my round a shoulder of the mountain at the head of Valldalsvatnet. I glimpse the radio tower back at Risldal, and send a quick message home. My GPS tracker claims its batteries last over a week, but is already complaining that it’s low on charge. I hope it’s just cold, but turn it off, just in case.

As I ascend, I enter some light cloud, which doesn’t do much more than obscure the view. I also start to encounter Hardangervidda’s locals, who are very polite about sharing the path (and you can always tell when they’re nearby from the bells around their necks).

The path takes me up a shallow U-shaped valley, at whose far end, I see someone coming down towards me, but well off the trail. After a few minutes, I notice their three colleagues spread across the width of the valley, along with their sheepdogs – this must explain why I’ve seen so many sheep this morning. I try to avoid countershepherding as I pass them to reach the top of the valley, which is marked by another impressive waterfall.

For the next couple of hours, the trail follows the Northern edge of a series of lakes. The terrain varies from flat gravel beds, to gently swelling meadows, to fairly steep lakeshore, and finally scrambling around 45-degree piles of rock and talus at the water’s edge. Luckily these sections are fairly short, and I’m back on (relatively) flat ground before long.

One thing that there are quite a lot of in Hardangervidda is streams – streams that you have to cross. Most could be jumped over, but there are usually helpful stepping stones if you want to take the boring route. The wider ones sometimes take a bit of thought, as they have multiple apparent routes networking between islands of shallow gravel beds. On one of these wider crossings, I misplace my trust in a rock that looks like it won’t roll over, and receive a pair of quite wet legs in return. A change of socks doesn’t really do much for soaked shoes, so my movement for the rest of the afternoon is a bit squelchier than the morning.

Luckily for some streams and rivers, somebody has done the hard work for you and installed a wobbly bridge. This keeps crossings interesting while substantially lowering the odds of getting wet (and increasing the penalty for doing so).

Coming down from the lakes, I catch my first glimpse of Litlos and, spurred on by the thought of drying out my shoes, make good time toward it. I’m still over half an hour away when I catch the scent of diesel – apparently the air is so clean up here that the exhaust from the generator there can be smelled over a kilometre away.

Before long, I’m standing in a lovely warm reception, being told where my room is and when dinner will be served. It’s only about 16:00, so in the few hours before dinner, I read in the lounge, gaze out the windows, and make an amazing discovery: the tørkerom (drying room).

By the time dinner comes around, there are five guests at the cabin: a Norwegian couple who had come up from Hellevassbu, and a Norwegian couple who followed me from Middalsbu. The Norwegians tell us that they are hiking the length of the country in sections, and that the section they’re on now is over 40 miles long. This prompts a brief puzzled look between the Germans and myself; 40 miles is a decent distance, but won’t get you anywhere from here. The Norwegians then elaborate that in Norway (and Sweden, I think), a mil means ten kilometres; I find this a bit strange, but also kind of unsurprising.

Dinner is mushroom soup, followed by roast pork with potatoes and vegetables, with a strawberry mousse and coffee to finish – all in generous portions. Warm and well-fed, I head to my only-slightly-too-short bed.

Day 1: Røldal to (near) Middalsbu

Jondal, en route to Røldal

The bus from Bergen is busy – I’m lucky to have turned up early, as there are a few people who don’t get seats. One of the things I find amazing about Bergen is the way that the road will vanish into a tunnel, and reappear seemingly outside the city entirely. As the bus crosses from fjord to fjord, we pass some spectacular waterfalls; the driver announces that they are at a particularly high flow rate, and I wonder whether the rivers farther East will be the same. Eventually, we arrive in Odda, and the coach gets a lot less busy as about half the passengers alight outside the Trolltunga Hotel (presumably planning to hike up to the famous outcrop in the morning).

After decapitating another mountain pass via a tunnel, we arrive in Røldal, a community of a hundred or so houses, at the head of a lake. On the three other sides, the town is hemmed in by the mountains, with the steep Southern edge of Hardangervidda rearing up just beyond the road.

Fortunately, a river (presumably with the help of a lot of ice) has cut a valley into the escarpment which offers an easier way up. Eventually, the sound of the road fades, and the soundtrack for the rest of the week begins: the white noise of wind and waterfalls. This initial section is reasonably steep, so I take multiple opportunities to stop and look back down the valley.

Looking back down to Røldalsvatnet

As I climb, the forest of stunted birch trees thins, to be succeeded by the grassy moorland of the plateau. It’s around this time that I realise that the squares on my map are 2km to a side instead of 1km. Luckily the route lengths are marked in hours, so this really means that the walking speed was faster than I’d expected from trying to (incorrectly) measure the distances myself.

After about two hours, the land levels off, and I get my first view into Hardangervidda proper. Having tried not to look at photos in advance, I’m surprised at how uneven it is. ‘Vidde’ means plateau, so I was imagining something substantially flatter. Even so, it looks far from unmanageable, so after a quick lunch of leftover takeaway pizza, I continue onward.

Apparently, there’s not always enough room for the path

A gentle descent brings me down to the level of Valldalsvatnet, along whose shore I’ll continue for the next couple of hours. The path has been replaced by a gravel road, which makes for faster, if less interesting walking. At its head, the lake is few by an impressive waterfall, where I run into the first people I’ve seen since shortly after Røldal. There are a few cabins, and a small farm at which sheep are being herded onto a livestock lorry.

Eventually, the trail peels away from the edge of the lake, and begins to climb again. The sun is well behind the mountains now, and I’m beginning to look for a place to camp. Given the slope, I don’t find anywhere suitably flat until just short of the cabin at Middalsbu. The ground seems to consist of a thick bed of moss, in which my footprints become short-lived puddles before rebounding, but it holds my tent’s stakes well and is very comfortable to lie on.

Despite the now rising wind (and it being my first pitch of this tent outside by garden), the tent goes up quickly and easily. After a quick dinner consisting of the last of the pizza, and a little cheese, chocolate and dried apricots, I call it a night at about 21:00.

Black Hole Score

Thanks to ESO/S. Brunier for use of their lovely starmap. And no, binary black holes don’t actually look like this.

About 1.5 billion years ago, a pair of black holes, each about 30 times the mass of the Sun, collided.

About 4 years ago, the spacetime ripples from this merger caused the length of a set of tunnels to change by about the diameter of a proton. This made a lot of people very excited, and is widely regarded as one of the most important observations in astronomy.

Of course, these kinds of discovery come with a surge of media attention, and this one had an extra advantage (in addition to being about black holes, which are always popular): when treated as a sound wave, the measured distortion in spacetime made a funny sound.

I’ve heard a few different representations of the chirp (as it’s called), and heard chirps from a few different gravitational wave detections, but I’ve never seen anyone try to express it using musical notation.

My self-set challenge then, was to convert this:

into something resembling sheet music.

To determine the correct note pitches, durations, and dynamics, I originally planned to extract the original LIGO data and calculate the frequency spectrum myself. Unsurprisingly, it turns out this is really hard, so I just fit functions for the frequency and amplitude to the spectrogram from the paper. I’d like to say I did something fancy here, but I just eyeballed it (using the same colour scheme helps a lot).

LIGO spectrogram compared to my fit functions – overlaid on the top, and separately on the bottom

The frequency ranges from 45 Hz initially, and is loudest at 163 Hz, which can be expressed musically as F#1 and F3, giving us the range of pitches in the final score.

Next up, I needed to work out the note durations. There was some freedom of choice here, as I could adopt a lower tempo with faster notes. The final scaling is a compromise between having enough resolution to express the note lengths, and resorting to using all quasihemidemisemiquavers (1/128 notes). I decided on using one bar to represent 0.01 seconds of time, which gives a tempo of 24000 crotchets (quarter notes) per minute. Since the spectrogram covers 0.15 seconds, the sheet music will be 15 bars long.

Finally, dynamics – this is arguably the handwaviest conversion. The amplitude of the gravitational waves is expressed as strain – the relative size of the spacetime distortion. For GW150914, this was about 10-21 (strain has no units). Plugging the strain into this formula

gives a peak amplitude of -420 dB. Then taking this table and wildly extrapolating, we can determine that at its loudest, the gravitational wave reaches a volume of ppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppppp, which I’ll express as p129. From there, I can just check my amplitude function to place the other dynamical markings.

Adding a final decoration or two gives the final piece:

pdf download

By the way, those final few notes are each 0.0003 seconds long – on a piano, the player’s hands would have to move rightward at 64 km/h.