population map of Scotland

(Source: *Wikipedia*)

Posts tagged with **geography**

* What is Eastern Europe?* How did places like Gepidia, Nitra, Great Moravia, the Avar Khaganate, Habsburgia, Pannonia, Thrace, Dacia, Moesia, nomadic Göktürks under the Rouran Khaganate, Dalmatia, Cimmeria, Anatolia, the Great Seljuq Empire, Corinth, Onoghuria, Scythia, Syrmia, Vojvodina, Bulgaria, Carpathia, Illyria, Hamangia, Bosnia, Budim, Egri, Sigetvar, Temeşvar, Pomorje, Serbia, Arduba, Daorson, Ošanićia, Sarmatia, Čapljina, Ardea, Neretva, and Ossetia, in the middle of a continent that became socially dominated in the later half of the 2nd millennium A.D. by residents of its western islands and peninsulas, come to be seen as a “unified group” so that when an American visits Bratislava he expects something similar to Bucharest?

Anne Applebaum’s answer is that the present categorisation was essentially shaped by the USSR, a political powerhouse in Eurasia during the 20th century.

**bonus:** from Wikipedia, here are some notable biomes in the middle of the Eurasian supercontinent.

**the steppe:**

The Pannonian plain is divided into two parts along the Transdanubian Mountains (Hungarian: *Dunántúli-középhegység*). The northwestern part…and the southeastern part…comprise the following sections:

- Western Pannonian Plain (province):
- Eastern Pannonian Plain (province):
- Great Hungarian Plain
- Pannonian Island Mountains (Serbian: Panonske ostrvske planine)
- Transdanubian Mountains (Hungarian:
*Dunántúli-középhegység*) - Drava–Mura lowlands

Note: The Transylvanian Plateau and the Lučenec-Košice Depression (both parts of the Carpathians) and some other lowlands are sometimes also considered part of the Pannonian Plain in non-geomorphological or older divisions.

Relatively large or distinctive areas of the plain that do not necessarily correspond to national borders include:

- Bačka/Bácska
- Banat
- Baranya/Baranja
- Burgenland (Neusiedler Basin)
- Crişana
- Jászság
- Kunság
- Little Hungarian Plain (Kisalföld/Malá dunajská kotlina)
- Mačva
- Međimurje
- Moravia
- Moslavina
- Podravina (around Drava river)
- Podunavlje (around Danube river)
- Pokuplje (around Kupa river)
- Pomoravlje around Morava river
- Pomorišje (around Mureş river)
- Posavina (around Sava river)
- Potisje (Serbia, around Tisa river)
- Prekmurje
- Semberija
- Slavonia
- Srem/Srijem
- Transdanubia
- Vienna Basin
- Vojvodina

Population distribution of the United States in units of Canadas.

(having a hard time locating the original source. if you can clue me in I’ll link to it!)

hi-res

Here’s another example of what mathematicians mean by an “ugly discontinuity”.

The Torus is the Cartesian product of circles `◯×◯`

. I.e. an abstract geometry in which concrete angular measurement **pairs** (or triples or quadruples or quintuples or …) are realised.

The Sphere is … not that.

It’s nontrivial to recognise that `◯×◯≠sphere`

. For example the people who wrote the Starfox battle mode drew the screen as a sphere but programmed the battle mode on a torus.

By the Hairy Ball Theorem we know that spheres are different to independent pairs of circles. Specifically: one circle “vanishes” at the top and bottom of the other, to make a sphere. Changing your latitude coordinate at the North Pole leaves you in the same place. In other words “two” collapses to “one” at the poles which also implies that, for consistency, latitude needs to be close to collapse around 89°N—not at all like `◯×◯`

. where the two capstans spin freely independent of one another.

(This is half of the “joke” … or, “prank”, or “not-funny joke” in my twitter location. I designate myself at `(−90,45)`

so you can imagine a person spinning around uselessly as they try to “walk in a circle” *on* the South Pole. OK … it’s only slightly funny even to me.)

This is like how globes can represent the Earth much better than maps on a flat sheet of paper. Since it’s impossible to map `R²`

onto `S²`

, flat maps can never be perfect. (The fact that the difference is merely a point—that is `R²`

does map onto `S²\{0}`

—is a distraction from how distorted real maps get. Look how different Greenland looks from the North versus the European view

Furthermore the torus can’t be deformed into a sphere, *and* it’s difficult for mathematicians to see the relationships between high-dimensional and low-dimensional spheres. (And this has something to do with the story of what Grigory Perelman achieved in solving that Clay Prize.)

The savvy way of talking about this is to say that the sphere has ugly symmetries. How can I say that when the Sphere is a Platonically perfect elementary shape?! The Sphere is so perfect that mass in outer space likes to form itself into that most balanced of balanced shapes.

Basically because when you hold the globe with two fingers and your friend spins it, the antipodes where your two fingers are holding it don’t move. (Yes, neighbourhoods around them move—but "points" in the infinitely-deep-down-continuum-set-of-measure-zero sense are singularities (erm, singularities in the `1/z`

sense, not in the “black hole” sense).)

Tomorrow: a post on a statistical application of the humble circle.