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I read a blog post that attempts to show that the size of the territory of a country is purely random and therefore bears no major historical significance.

The argumentation (simplified a bit) is as follows:

  • If we plot sizes of countries on a logarithmic plot the distribution is linear:

enter image description here

(Each bar is a country, the Y axis is the size of countries in km2; blue bars are "large" countries, orange bars are "medium" countries and grey bars are "small" countries. Countries are labelled "large", "medium" or "small" because, according to the blogger, the exponential distribution has different arguments depending on whether the country is below or above 10000 km2, so in fact there are two distributions, as shown by the straight lines in the plot)

  • Therefore, if plot on a linear plot, the distribution will be exponential
  • Exponential distribution occurs if the events are purely random
  • If it was not random whether a country gained or lost a territory we would expect a Pareto distribution instead

This seems to make sense, but... at the same time it is very counteintuitive. Does it follow that a country competently governed is equally likely to lose a territory than a failed country? The blogger himself says this is not the case, but he claims that a country that is governed competently is likely to be governed far worse after a few generations and will start losing territory. One very profound conclusion after another...

Plus, the blogger himself claims that his findings are contrary to established knowledge.

Is it purely random if a country gains or loses a territory?

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    "Exponential distribution occurs if the events are purely random" whilst true, not all white birds are swans. There are many claims here.
    – Jiminy Cricket.
    Oct 9, 2021 at 18:17
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    Until such time as they define what they mean by “purely random”, this sounds like complete nonsense (to me, a mathematician with expertise in probability theory). It’s common to describe such claims as “not even wrong”. But this is based on your description, which I cannot verify since I can’t read the original post.
    – Dan Romik
    Oct 9, 2021 at 18:22
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    I second @DanRomik's point: "purely random" is not a thing. From your other context, what the blog is probably trying say is that land area is the product of many small independent pieces of noise? However, I'd then expect a lognormal distribution rather than exponential? Since, there are an almost unlimited number of explanations that would result in very different distributions, this whole exercise is rather pseudo-scientific. You really can't reach any general conclusions with any certainty based on this limited evidence. At best, you can say an extremely specific hypothesis is wrong.
    – Sherwin Lott
    Oct 10, 2021 at 0:08
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    (The hypothesis that it's not "purely random" is woefully underspecific not least because "purely random" is not a defined term.) Also, Enrico Fermi's quote applies here: "with four parameters I can fit an elephant, and with five I can make him wiggle his trunk."
    – Sherwin Lott
    Oct 10, 2021 at 0:11
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    @gaazkam There is no way of winning an argument with those who have fully inoculated themselves against logic and reason.
    – David Hammen
    Oct 10, 2021 at 14:12

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The conclusion of the linked blog post says (via Google Translate):

Contrary to popular belief, no "natural boundaries" exist. All borders between states, with the exception of really great countries, which occupy a large part or even the whole (Australia) of continents, are purely random.

NASA talks about this in: When Rivers are Borders

Rivers also serve as borders in several African countries: Benin, Nigeria, Senegal, Mauritania, and Niger in West Africa; the Central African Republic, the Democratic Republic of the Congo, Tanzania, and Mozambique in Central Africa; and Botswana, Zambia, Zimbabwe, and Namibia in Southern Africa. In Europe, Spain, Portugal, France, Germany, Poland, Norway, Bosnia, Romania, and Ukraine are just some of the many countries with international border rivers.

The patterns are not random. Smith explained that the continents where European powers established colonies and exerted great influence tend to have more borders defined by rivers because European explorers, cartographers, politicians, and diplomats found rivers to be a convenient way to divide territories. Asia, in contrast, has fewer river borders than other continents (16 percent) because European influence and colonialism was more limited. The exception is South Asia, where Great Britain and France remained colonial powers into the 20th century.

Which shows that the blog's assertion is nonsense.

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    The blog's assertion is wrong because NASA says something else? Umm... how do I put it... this particular blogger is pretty infamous for challenging the claims of established science. In his mind he has shown he is right, if scientists say something else scientists are wrong. I bet that this case is no different: he says in his post "Te doniosłe wydarzenia historyczne, szczegółowo opisywane i analizowane w podręcznikach szkolnych, akademickich i solennych opracowaniach naukowych, okazują się nie mieć, per saldo, absolutnie żadnego znaczenia."
    – gaazkam
    Oct 9, 2021 at 19:13
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    The author has cherry-picked a section of the graph that is roughly linear, and found arbitrary reasons to exclude the parts that are not, and dressed it up in a long ramble of supposition, backed up by a quote from the Bible.
    – Weather Vane
    Oct 9, 2021 at 19:16
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    I will point out that both NASA and the author can be correct: if the areas between rivers are randomly distributed, then the area of countries occupying those areas can also be randomly distributed. Note that I am saying "can" not "are" because the conditions are necessary, but not sufficient, to show correlation.
    – bishop
    Oct 9, 2021 at 20:51
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    @DavidHammen (and gaazkam): "Well actually... No" He splits the data into THREE parts, then removes the inconvenient outliers of Australia and larger before plotting it.
    – Oddthinking ♦
    Oct 10, 2021 at 10:20
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    @bishop you don't need to go as far as the bolded parts. The first howler is Contrary to popular belief, no "natural boundaries" exist. This is untrue, even if you disqualify the undefined 'really great countries' in the blog. Actually not undefined: the blog defines them from the data.
    – Weather Vane
    Oct 10, 2021 at 15:22

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