2e:null 2f:["$","title",null,{"children":"Hallgrímskirkja is not normal | Toph Tucker | Observable"}] 34:T8d6,# Hallgrímskirkja is not normal From time to time a photograph goes viral captioned something like “The Church of the Normal Distribution”; see _e.g._ [Reddit](https://www.reddit.com/r/funny/comments/wad1y3/behold_the_church_of_normal_distribution/), [Facebook](https://www.facebook.com/pureyoacademy/posts/church-of-normal-distribution-hallgr%C3%ADmskirkja-reykjav%C3%ADk-iceland/941048990715838/), [Twitter](https://x.com/JkayFlake/status/1743649016137572784?lang=en). It is HallgrímskirkjaHallgrímur’s Church, a Lutheran church in Reykjavík, designed by State Architect Guðjón Samúelsson (1887 – 1950), inspired by the country’s natural basalt columns. Claire and I attended a service there when we visited Iceland (and got engaged) in 2022; we went back on Thursday. It’s a beautiful church, with a beautiful organ.

But, if we are going to compare it to a probability distribution, I’d say its shape is not that of the normal distribution. Notice that its left and right wings have significant height, to house service facilities. A normal distribution would go much closer to zero much faster, like the red curve in my right hand. The church has “fat tails”, like the blue curve in my left hand. Its kurtosis is high; it is _leptokurtic_slender arching (a word I learned from replies to one of the provoking tweets). This is pedantic, but if you have a lot riding on interpreting probability curves, it’s worth looking out for. We can evaluate how “normal” the church’s curve is by overlaying a [Student’s _t_ distribution](https://en.wikipedia.org/wiki/Student%27s_t-distribution), which generalizes the normal distribution; it can vary from fat-tailed (leptokurtic) to normal (mesokurtic) as you change its “degrees of freedom”. Adjust the sliders and try to match the curve to the church: - _Scale:_ Stretch or squish the curve horizontally. - _Offset:_ Move the curve up off the baseline. - _Degrees of freedom:_ Change the kind of distribution. - At left, it has one degree, meaning fat tails. - At right, it’s approaching infinite degrees, meaning normalcy.35:T1c4a,The central steeple matches the normal distribution well, but the wings require fewer degrees of freedom. You can add a constant vertical offset to make the normal distribution match better, but that feels like cheating. You could also see it as a piecewise combination of curves (like how the distribution of human heights is normal in the middle but [abnormal in the extremes](https://www.johndcook.com/blog/2008/07/20/why-heights-are-not-normally-distributed/)). Nothing matches perfectly. It’s a church, after all, not a curve. The church was commissioned in 1937, with a mandate to surpass the height of the new Catholic church in town, LandakotskirkjaLandakot’s Church, also designed by Guðjón. (Lutheranism is the state religion, whereas there were only about 191 Catholics in the country at the time.) Work was delayed by World War II, as the British invaded and occupied the hill on which the church was to be built, and Guðjón did not live to see his final project completed. Construction began in 1945; the steeple and wings were completed in 1974; the nave was consecrated in 1986; and the current doors were added in 2010. It is named for the poet and composer Hallgrímur Pétursson. Hallgrímur was born in the north of Iceland in 1614. As a young man, he ran away from home to Copenhagen; in Glückstadt he once swore at a blacksmith in Icelandic and was overheard by a fellow Icelander, who sent Hallgrímur to seminary. His last year there, in 1637, he was paid to help re-educate other Icelanders who had just returned from ten years in slavery. Among them was Guðríður Símonardóttir, sixteen years older than Hallgrímur. She had been abducted by pirates from her home in VestmannaeyjarWestman Islands in 1627, along with her young son and almost 400 others, but without her husband; the captives were sold into slavery on the Barbary Coast. Ten years later, King Christian IV of Denmark paid the random to free 34 of them, including Guðríður but not her son, who remained behind in Algeria. Soon after meeting, Hallgrímur and Guðríður fell in love; she became pregnant; she had no idea where her husband was. They returned to Iceland to track him down, only to learn that he was dead. Hallgrímur and Guðríður wed. The church forgave Hallgrímur’s scandal and he was ordained a minister, first at Hvalsnes, then at Saurbær, where he began the six-year process of writing the PassíusgálmarPassion Hymns, or “HistoriaThe history pínunnarof the suffering ogand dauðansof the death DrottinsLord vorsour JesúJesus KristiChrist, meðwith hennarits sérlegustumost special lærdóms-learning- áminningar-admonition- ogand huggunargreinumconsolation-articles, ásamttogether with bænumprayers ogand þakkargjörðumthanksgivings, íin sálmumpsalms ogand söngvísumsongs meðwith ýmsumvarious tónumtunes samsettcompiled ogand skrifuðwritten annoyear 16591659”. Upon publication, [writes Rev. Dr. Sarah Hinlicky Wilson](https://www.sarahhinlickywilson.com/blog/2019/10/17/lutheran-saints-8-hallgrmur-ptursson), the collection of hymns became famous: >It was published in 1666 and stamped Icelandic piety forever after with its distinctive character. Most Icelanders in every generation since have learned the hymns by heart; they are the first prayers taught to small children; and the hymn “On Death’s Uncertain Hour” is sung at every funeral. Through the hymns Icelandic Christians internalized the wonder of the joyful exchange: how Christ took our place on the cross and gave us his own life and righteousness. The hymns were not sung only once a week, reserved for Sunday worship, but were part of daily life. This is due to the strong tradition of _ecclesia domestica_, the “household church,” in Iceland, that began with the Reformation and held strong through the mid-nineteenth century. Called _húslestur_ (“house reading”) in Icelandic, on this occasion the whole household would gather in the common room every Sunday and holiday—and every evening in the winter when it was dark and activities were restricted by the weather—to sing hymns, pray, and listen to readings from the Scripture and devotional books. The _húslestur_ followed the _kvöldvaka_ or evening watch, a time of entertainment or indoor chores when the head of the household would tell tales from the sagas. But all work would stop for _húslestur_. Hallgrímur’s Passion Hymns were the top choice for evening reading in Icelandic homes. The inscription over Hallgrímskirkja’s door quotes the Passíusgálmar’s 24th hymn, “UmAbout purpuraklæðiðthe purple robe ogand þyrnikórónunathorn crown”:

ÞáThen Þúyou gengurenter íinto guðshústhe Godhouse inninside

gætHeed þessit velwell,, sálsoul mínmy fróma,pious,

hæðMock þúyou þarthere ekkinot herrannthe Lord þinnof yours

meðWith hegðunbehavior líkamansof body tóma.empty.

BeygðuBend holdsinsflesh’s ogand hjartansheart’s kné,knee,

heitfervent bænprayer þínyour ástarkveðjalove- greeting sé.be.

HræsninHypocrisy munwill sístleast þéryou sóma.suit.

In 1662 Hallgrímur’s farm burned down, and he soon contracted leprosy, which he channeled into a more melancholy poetry. He succumbed and died in 1674.36:T111d,--- To learn more, see the Wikipedia pages for [Hallgrímskirkja](https://en.wikipedia.org/wiki/Hallgr%C3%ADmskirkja), [Hallgrímur Pétursson](https://en.wikipedia.org/wiki/Hallgr%C3%ADmur_P%C3%A9tursson), [Guðríður Símonardóttir](https://en.wikipedia.org/wiki/Gu%C3%B0r%C3%AD%C3%B0ur_S%C3%ADmonard%C3%B3ttir), the [Turkish Abductions](https://en.wikipedia.org/wiki/Turkish_Abductions), the [Passion Hymns](https://en.wikipedia.org/wiki/Passion_Hymns), and [Guðjón Samúelsson](https://en.wikipedia.org/wiki/Gu%C3%B0j%C3%B3n_Sam%C3%BAelsson). The vector illustration was traced from a remarkable photograph by [Rajan P. Parrikar](https://blog.parrikar.com/2012/01/14/hallgrimskirkja/), who took care to maintain the vertical lines of the church using a tilt-shift lens. The text of the inscription over the door is from [Read the Plaque](https://readtheplaque.com/plaque/entry-to-hallgrimskirkja-church#gsc.tab=0) and the official [Church relics and artwork](https://www.hallgrimskirkja.is/en-gb/kirkjumunir-og-listaverk) page. The translations are somewhat my own, advised by a combination of those sources, Google Translate, and ChatGPT, in an attempt to match literal word order while preserving intelligibility. For more information on the church’s architecture, see Aurél Benárd on [Hallgrímskirkja, Reykjavík: A Late Example of Expressionist Church Architecture](https://ybljournal.uni-obuda.hu/Archive/Volume-6-2018-Issue-1-January-2018/10.2478_jbe-2018-0006.pdf) (2018); for more on Hallgrímur’s life, see Sarah Hinlicky Wilson’s [short biography](https://www.sarahhinlickywilson.com/blog/2019/10/17/lutheran-saints-8-hallgrmur-ptursson) (2019). Adalsteinn Eythorsson has an excellent hypermedia concordance for Hallgrímur Pétursson’s [Passíusálmar](https://ordlyklar.arnastofnun.is/salmar/salmar.htm). Hear Anna Pálína sing [“On Death’s Uncertain Hour”](https://www.youtube.com/watch?v=1Nl_K5AUUk4). Finally, I want to acknowledge my debt to the supposed “wrongness” of the viral tweets calling it “The Church of the Normal Distribution”, _e.g._ from [@PhysInHistory](https://x.com/PhysInHistory/status/1863227928097558686) and [@JkayFlake](https://x.com/JkayFlake/status/1743649016137572784). There is real peril in assuming that every bell curve is the specifically normal distribution, and the façade of this church invites us to consider that peril. In that sense the church and the tweets serve the role that [Brother William of _The Name of the Rose_](https://x.com/tophtucker/status/1557339747139338240) saw served by fantastical creatures illuminating manuscripts: >‘But as the Areopagite teaches,’ William said humbly, ‘God can be named only through the most distorted things. And Hugh of St. Victor reminded us that the more the simile becomes dissimilar, the more the truth is revealed to us under the guise of horrible and indecorous figures, the less the imagination is sated in carnal enjoyment, and is thus obliged to perceive the mysteries hidden under the turpitude of the images’. That is, Hallgrímskirkja points us to the normal distribution _apophatically_, by negation, by what it’s not. The Stanford Encyclopedia of Philosophy glosses the beliefs of [Pseudo-Dionysius the Areopagite](https://plato.stanford.edu/entries/pseudo-dionysius-areopagite/), whom Brother William cited above: >Even the lowest things cannot simply be despised, for even in their dissimilarity from the divine, they bear the capacity to signify the divine more appropriately than supposedly worthier images. If we say God is good, we run the risk of thinking we know entirely what we mean and consequently of closing off a thought that has to be radically open-ended, if not altogether subverted. If we liken God to a “worm”, we subvert our own comfortable tendencies by being shocked into filling the image with enquiry. So the Psalmist who uses the worm image hides the sacred from those who would defile it with a lack of understanding and yet points to the sacred in a new way. If it draws me to contemplate the normal distribution then maybe “The Church of the Normal Distribution” is a fitting moniker indeed. ---37:[{"id":"81fb493898e57de8bcd49d44b6ae05366c0cfd70af175434e95226abb6271cd13ca520b573402eaf912667549fc16bf59b3dfc409251eb50f588f607aaa42f1e","href":"https://static.observableusercontent.com/files/81fb493898e57de8bcd49d44b6ae05366c0cfd70af175434e95226abb6271cd13ca520b573402eaf912667549fc16bf59b3dfc409251eb50f588f607aaa42f1e","name":"Church.svg","type":"image/svg+xml","lastModified":1771257500085.899,"size":12928},{"id":"bf36c29e8d5d6e83ca3fa4e68755235ba15276090bdff30c9a90574d810ff69b5638cd586ad42609fb153913f69c688f6ccff63b9849cccab3ce8be6a0b66b87","href":"https://static.observableusercontent.com/files/bf36c29e8d5d6e83ca3fa4e68755235ba15276090bdff30c9a90574d810ff69b5638cd586ad42609fb153913f69c688f6ccff63b9849cccab3ce8be6a0b66b87","name":"Toph - Hallgrimskirja 2026 2.jpg","type":"image/jpeg","lastModified":1771389929049.079,"size":1723110}] 32:{"id":"9a3353c52eeaaf5c","slug":"hallgrimskirkja-is-not-normal","title":"Hallgrímskirkja is not normal","thumbnail":"078fe2e596b8584e2c76b413c59fb6db79a113b1425adce67b028c9e62219ad6","access_level":"public","create_time":"$D2026-02-16T15:39:54.857Z","update_time":"$D2026-05-15T17:24:56.448Z","view_time":null,"first_public_time":"$D2026-02-18T04:49:52.949Z","has_unpublished_edits":null,"fork":false,"stars":3,"starred":false,"owner":{"type":"team","id":"97290e936c339d8e","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":"pro_2026"},"version":633,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"0bb2842b01e0c652","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":null}],"members":[{"type":"individual","id":"0bb2842b01e0c652","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":null,"role":"editor"},{"type":"team","id":"97290e936c339d8e","login":"tophtucker","name":"Toph Tucker","avatar_url":"https://avatars-next.observableusercontent.com/3706c31a8f9c59bb716c022c04b9c073144cd1368b78ac85f49139be6c93c34e","tier":"pro_2026","role":"editor"}],"comments":[],"custom_thumbnail":true,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":null,"type":"notebook","body":{"title":"Hallgrímskirkja is not normal","cells":[{"id":0,"value":"$34","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":541,"value":"viewof parameters = Inputs.form({\n scale: SimpleRange([0.01, 1], {label: \"Scale\", step: 0.01, value: 0.3}),\n offset: SimpleRange([0, 1], {label: \"Offset\", step: 0.001, value: 0}),\n logNu: SimpleRange([0, 4], {label: \"Degrees of freedom\", step: 0.1, value: 4})\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"node = {\n const w = 640;\n const h = 798; // based on aspect ratio of tracing\n const node = htl.html`

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