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Distractions and amusements, with a sandwich and coffee.

And whatever I do will become forever what I've done.
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On March 14th celebrate `\pi` Day. Hug `\pi`—find a way to do it.

For those who favour `\tau=2\pi` will have to postpone celebrations until July 26th. That's what you get for thinking that `\pi` is wrong. I sympathize with this position and have `\tau` day art too!

If you're not into details, you may opt to party on July 22nd, which is `\pi` approximation day (`\pi` ≈ 22/7). It's 20% more accurate that the official `\pi` day!

Finally, if you believe that `\pi = 3`, you should read why `\pi` is not equal to 3.

Caelum non animum mutant qui trans mare currunt.

—Horace

This year: creatures that don't exist, but once did, in the skies.

And a poem.

This year's `\pi` day song is Exploration by Karminsky Experience Inc. Why? Because "you never know what you'll find on an exploration".

If you like space, you'll love my the 12,000 billion light-year map of clusters, superclusters and voids. Find the biggest nothings in Boötes and Eridanus.

Want to contribute to the mythology behind the constellations in the `\pi` in the sky? Many already have a story, but others still need one. Please submit your stories!

Here I make available all the files you need to reconstruct the chart. All files are plain text and designed to be easily parsable.

For the simplest chart, you'll need the star catalogue which already provides the longitude and latitude coordinates for each star. It'll be up to you to choose and calculate a projection.

You can then layer constellations, which are defined by a list of edges. If you like, you can draw boundaries around each constellation, which are also provided.

Star-to-constellation mapping is also given, which allows you to create labels for the stars within each constellation based on relative brightness.

Finally, you can get the species details for each constellation, including the Latin name of the species, Wikipedia URL and (for many) the mythology of the constellation.

The star catalog generated from the first 12 million digits of `\pi`.

DOWNLOAD # idx digits name x y z long lat dist mabs mapp 0 314159265358 a -1859 926 35 145.339 38.384 2077.157 3.00 14.59 1 979323846264 b 4793 -2616 126 -38.404 -39.555 5461.884 -1.00 12.69 2 338327950288 c -1617 -2205 -472 -110.162 32.164 2774.797 3.00 15.22 3 419716939937 d -803 -3307 493 -105.489 3.655 3438.620 2.00 14.68 ... 999996 601538500580 cexhk 1015 -1150 -442 -48.144 -14.704 1596.273 -5.00 6.02 999997 420478142596 cexhl -796 2814 -241 97.939 14.471 2934.330 1.00 13.34 999998 278256213419 cexhm -2218 621 -159 156.900 46.719 2308.776 4.00 15.82 999999 453839371943 cexhn -462 -1063 -306 -95.924 26.937 1198.770 -2.00 8.39

Constellations were manually defined. Each constellation has a name and abbreviation (first 3 characters unless longer is required to uniquely specify it). Shown next is the number of stars used to define the constellation and their names, as appear in the star catalogue file above. Next is the number of edges and the star pairs that define the edges of the constellation. The edges are not in any particular order and have no direction. Any spaces in names are encoded with _.

DOWNLOAD # idx n_stars n_edges name abbrev stars edges ... 2 3 3 alaotra ala blts,btosf,cbkbw btosf-cbkbw,blts-btosf,blts-cbkbw 3 4 4 alloperla all ghyr,pwkn,ssrx,ugwt pwkn-ssrx,pwkn-ghyr,ugwt-pwkn,ssrx-ghyr 4 2 1 aplonis apl cbocd,rllm rllm-cbocd ...

You can use this file to quickly search for certain shapes. For example, triangular constellations are those that have 3 stars and 3 edges.

> grep " 3 3" constellations.def.txt 2 3 3 alaotra ala blts,btosf,cbkbw btosf-cbkbw,blts-btosf,blts-cbkbw 16 3 3 camptor camp benxf,bqvh,bwqed bqvh-benxf,bwqed-bqvh,bwqed-benxf 26 3 3 desmodus des bfnqu,mork,zwzy bfnqu-mork,zwzy-bfnqu,zwzy-mork 27 3 3 ectopistes ect bopmt,cbquf,wmnw cbquf-bopmt,wmnw-cbquf,wmnw-bopmt 30 3 3 hoopoe hoo bpsop,bvmjh,tryh tryh-bvmjh,bpsop-tryh,bpsop-bvmjh 31 3 3 huia hui ccteo,xbvq,yqet xbvq-yqet,ccteo-xbvq,ccteo-yqet 39 3 3 malpaisomys mal bucqd,likq,nqn nqn-bucqd,likq-nqn,likq-bucqd 41 3 3 mariana mar gmps,jydb,pcjx pcjx-gmps,jydb-pcjx,jydb-gmps 49 3 3 palaeoaldrovanda pal bedae,oife,saz bedae-saz,oife-bedae,oife-saz 63 3 3 rhynia rhy bpviv,cenuk,hivz bpviv-hivz,cenuk-bpviv,cenuk-hivz 65 3 3 silphium sil bjesg,bmquw,bpxia bmquw-bpxia,bjesg-bmquw,bjesg-bpxia 69 3 3 tadorna tad bukqe,cbtrx,epdx cbtrx-epdx,bukqe-cbtrx,bukqe-epdx 72 3 3 traversia tra fcnw,fywb,puib fywb-fcnw,puib-fywb,puib-fcnw 80 3 3 yersinia yer colq,ibls,zgvy ibls-zgvy,colq-ibls,colq-zgvy

The boundaries were manually defined. Shown here, for each constellation, is the constellation's area, perimeter center and boundary `(x,y)` pairs, delimited by : and represent a closed polygon that encloses the constellation's stars.

All values are longitude and latitude. The three constellations listed below are ones with smallest area.

DOWNLOAD # abbrev area perimeter centroid_xy boundary_xy_pairs ... com 74.83 34.96 -102.50,26.25 -100.00,30.00:-102.50,30.00:-105.00,30.00:-107.50,30.00:-107.50,27.50: -107.50,25.00:-107.50,22.51:-105.00,22.51:-102.50,22.51:-100.00,22.51: -97.51,22.51:-97.51,25.00:-97.51,27.50:-97.51,30.00:-100.00,30.00 pal 50.02 30.00 3.43,-40.93 5.00,-37.49:2.50,-37.49:0.00,-37.49:0.00,-40.00:0.00,-42.50:0.00,-45.00: 2.50,-45.00:5.00,-45.00:5.00,-42.50:7.49,-42.50:7.49,-40.00:7.49,-37.49:5.00,-37.49 sil 37.57 25.02 115.00,-51.25 115.00,-47.50:112.49,-47.50:112.49,-50.00:112.49,-52.49:112.49,-55.00: 115.00,-55.00:117.50,-55.00:117.50,-52.49:117.50,-50.00:117.50,-47.50:115.00,-47.50

The boundary polygons abut but do not overlap and they cover the entire sky. There is one polygon per consetllation. The total area of all constellations is `360 × 180 = 36800`.

This is a list of all the stars on the chart and their constellation membership. A star is considered to be in a constellation if it falls within the constellation boundary.

The `i` and `j` indexes give the relative brightness of the star on the map and in the constellation, respectively. If a star is used to define the constellation edges it gets a + otherwise -.

DOWNLOAD # abbreviation star i j mapp on_edge? aep bkawv 35 0 1.34 + aep gql 65 1 1.63 + aep cavix 72 2 1.71 + aep bqxvm 137 3 2.25 + aep tjow 158 4 2.31 + aep beelq 176 5 2.39 + ... yer jjlj 39365 412 7.24 - yer bgswm 39464 413 7.24 - yer ittu 39546 414 7.24 - yer wakp 39556 415 7.24 - yer bedks 39667 416 7.25 - yer gxzo 39817 417 7.25 -

To lookup the 10 brightest stars, sort on the i index. Here we see that megal (Megalodon) has the brightest star in the sky, jkxo with apparent magnitude `-2.05`. The next two brighest stars are in mam (Mammuthus) and ara (Araucaria).

> cat constellations.stars.txt | sort -n +2 -3 | head -10 megal jkxo 0 0 -2.05 + mam btsqy 1 0 -0.73 + ara ccijs 2 0 -0.38 + rap btaum 3 0 0.26 + urs bxlss 4 0 0.26 + tec bgrdk 5 0 0.43 + cop itwr 6 0 0.45 + ara mrvq 7 1 0.54 + phe loju 8 0 0.54 + mam bhlbw 9 1 0.55 +

To get a list of the brightest star in each constellation, just search for " 0 ". Below I show this list sorted by brightness.

> cat constellations.stars.txt | grep " 0 "| sort -n +4 -5 megal jkxo 0 0 -2.05 + mam btsqy 1 0 -0.73 + ara ccijs 2 0 -0.38 + rap btaum 3 0 0.26 + urs bxlss 4 0 0.26 + tec bgrdk 5 0 0.43 + cop itwr 6 0 0.45 + phe loju 8 0 0.54 + kel bnhwx 11 0 0.59 + spe rtep 13 0 0.71 + ... nes vxou 299 0 2.80 - aur bmjvf 307 0 2.81 + tra puib 318 0 2.83 + pip cecq 358 0 2.91 + pal oife 389 0 2.97 + swa gvr 463 0 3.12 + hui ccteo 485 0 3.17 + ple bzqur 506 0 3.20 + com ygrn 875 0 3.64 + car yjkn 933 0 3.68 +

For example, tec (Tecopa) has bgrdk as its brightest star, which is 6th brightest in the sky with an apparent magnitude of 0.43.

The constellation whose brightest star is dimmest of all first brightest stars is car (Caracara). Its brightest star is yjkn which is 934th brightest in the sky with an apparent magnitude of 3.68.

To get the number of stars in each constellation, just add the number of times the constellation abbreviation appears. Bron has the most stars of any constellation, more than twice as many as the next one, archaeo (Archaeopteryx). Both car (Caracara) and por (Porzana) have only 7 stars each, the fewest of all constellations.

5230 bro 2287 archaeo 2205 thy 2155 kim 1838 archaea 1789 came 1768 ard ... 20 megal 19 swa 17 mar 12 rhy 8 sil 7 por 7 car

The constellations are in no particular order in this file.

DOWNLOAD # constellation name # hemisphere (n north, s south, b both) # common name # Latin name # extinction date # URL # optional story aplonis n mysterious bird of Ulieta Aplonis ulietensis 1774-1850 https://en.wikipedia.org/wiki/Raiatea_starling desmodus n Giant Vampire Bat Desmodus draculae Pleistocene or early Holocene https://www.thoughtco.com/recently-extinct-shrews-bats-and-rodents-1092147 It is thought that each night Desmodus flies up against the dome of the sky, looking for a way to escape. ...

Discover Cantor's transfinite numbers through my music video for the Aleph 2 track of Max Cooper's Yearning for the Infinite (album page, event page).

I discuss the math behind the video and the system I built to create the video.

*Everything we see hides another thing, we always want to see what is hidden by what we see.
—Rene Magritte*

A Hidden Markov Model extends a Markov chain to have hidden states. Hidden states are used to model aspects of the system that cannot be directly observed and themselves form a Markov chain and each state may emit one or more observed values.

Hidden states in HMMs do not have to have meaning—they can be used to account for measurement errors, compress multi-modal observational data, or to detect unobservable events.

In this column, we extend the cell growth model from our Markov Chain column to include two hidden states: normal and sedentary.

We show how to calculate forward probabilities that can predict the most likely path through the HMM given an observed sequence.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Hidden Markov Models. *Nature Methods* **16**:795–796.

Altman, N. & Krzywinski, M. (2019) Points of significance: Markov Chains. *Nature Methods* **16**:663–664.

My cover design for Hola Mundo by Hannah Fry. Published by Blackie Books.

Curious how the design was created? Read the full details.

*You can look back there to explain things,
but the explanation disappears.
You'll never find it there.
Things are not explained by the past.
They're explained by what happens now.
—Alan Watts*

A Markov chain is a probabilistic model that is used to model how a system changes over time as a series of transitions between states. Each transition is assigned a probability that defines the chance of the system changing from one state to another.

Together with the states, these transitions probabilities define a stochastic model with the Markov property: transition probabilities only depend on the current stateâ€”the future is independent of the past if the present is known.

Once the transition probabilities are defined in matrix form, it is easy to predict the distribution of future states of the system. We cover concepts of aperiodicity, irreducibility, limiting and stationary distributions and absorption.

This column is the first part of a series and pairs particularly well with Alan Watts and Blond:ish.

Grewal, J., Krzywinski, M. & Altman, N. (2019) Points of significance: Markov Chains. *Nature Methods* **16**:663–664.

*Places to go and nobody to see.*

Exquisitely detailed maps of places on the Moon, comets and asteroids in the Solar System and stars, deep-sky objects and exoplanets in the northern and southern sky. All maps are zoomable.

Quantile regression explores the effect of one or more predictors on quantiles of the response. It can answer questions such as "What is the weight of 90% of individuals of a given height?"

Unlike in traditional mean regression methods, no assumptions about the distribution of the response are required, which makes it practical, robust and amenable to skewed distributions.

Quantile regression is also very useful when extremes are interesting or when the response variance varies with the predictors.

Das, K., Krzywinski, M. & Altman, N. (2019) Points of significance: Quantile regression. *Nature Methods* **16**:451–452.

Altman, N. & Krzywinski, M. (2015) Points of significance: Simple linear regression. *Nature Methods* **12**:999–1000.