Numbers are hard

Numbers are hard, and randomly very scary or not scary at all to many people.

A long time ago I was paid to tutor a pupil who had difficulty with math. Those difficulties could be summarised as 'he stopped understanding math by grade 5 and doesn't take the concept of math seriously'. By bad luck one of the next chapters to tutor was set theory. Neither the boy nor his mother had any idea what set theory could possibly be good for -it's not even calculation- and he took it even less seriously. It was also nigh-impossible to justify some more hours to make him understand the chapter. Learning and understanding set theory is an almost indispensable step towards not boing a bullshit-blathering idiot as an adult.


Set theory teaches to sort thoughts and to keep apart what doesn't belong together.

Fast forward to our time, it has become painfully obvious that most humans simply cannot understand exponential functions, specifically exponential growth. Math at school didn't educate them. I looked at Covid figures in March 2020 and concluded it's going to be a huge thing while it was still tiny. I had no means of including the effects of countermeasures and whatever else leads to plague waveforms. I had the official daily case figures in a spreadsheet and told the standard software to extrapolate with an exponential function because I understood that my brain alone could not handle exponential growth and I also understood that exponential growth is a thing and the spread of a virus can be near-exponential. I ended up calculating the first million cases in Germany for a much-too early date, but I was far from failing to understand how an unchecked wave would propagate before I saw any politician showing such understanding. Almost two years later, many people are way beyond just not understanding exponential growth; about a tenth to a fifth of the population appears to have performed a 10 m high dive into total bullshit, welcoming the bullshit, becoming one with the bullshit.

'Numbers are hard' was also at work in regard to military (im-)balance in Europe. I'm the kind of guy who looks into things like IISS "Military Balance" yearbook or studies and then actually compares the figures before trying to (in a fuzzy way) take into account the not really known qualitative differences and the geographic divides.



I do hardly ever see anything of this kind in any discussion or commentary. The usual opinion appears to pretend that the Russian army is the Red Army of 1989 with some new gear while European NATO hardly has any armed forces. Military think tank types tend to avoid giving written evidence of such thinking, but their written and published conclusions are often very much compatible with such a view.

Nowadays I see press reports (now I'm not talking about subject matter experts) about threatening Russian "force concentrations" on Ukraine's border. Yet whenever they become more specific such as stating "100,000 army troops" or a map, I cannot see any Russian army concentration on the Ukraine's borders AT ALL.

The supposed Russian army forces concentrations are outnumbered by the Ukrainian army (and the Russian troops and Russian proxy troops in Donbass don't change this picture to a clear Russian numerical superiority). Those supposed Russian army concentrations are also dispersed in great depth and width, but reading the scale on maps is hard, I guess. What do these press people suppose where the Russian army should have its troops, in Siberia? Does nobody remember how awfully close to the Iron Curtain the NATO had its forces throughout the Cold War?

another illustration: nytimes.com/interactive/2022/01/07/world/europe/ukraine-maps.html

The total strength of the Russian Army in the Western and Southern Military Districts minus what's in the Kaliningrad Oblast exclave and what's indispensable near St. Petersburg and Moscow is still likely too much to bite for the Ukrainian Army, but that's not news. It's always been this way.
The press supposes we (or the Ukrainians) should be scared of "100,000 !!!!" Russians. Well, I'm not easily scared (I don't like to lean against large windows or lean over balconies and that's it), and I refuse to be scared by the alarmist news about the Russian army dispositions. The unusual thing is to move the troops out of their mildly comfortable barracks in wintertime and the really frustrating threat o the Ukraine is the vastly superior Russian air power. The actual quantity of boots on the ground near the Ukrainian border could be considered consistent with Russia positioning its troops for defence (I'm not saying this is the purpose).

So once again, a public too dumb or too lazy to pay attention to numbers and fairly simple calculations appears to misunderstand reality grossly.



  1. To a degree, consent in democracies is manufactured. The less educated people are to make informed decisions, the more their opinions are driven by influencers.

  2. 100k is not nearly enough to take Ukraine in one bite and the Ukrainian army is indeed larger than the 100-170k Russians (right now they mostly just prepositioned heavy equipment at this stage, they can fly in another 70k men in 2 weeks). Having said that, the Russians have a large (>2x) advantage in numbers of tanks, artillery, aircraft, missiles, EW systems etc. which could facilitate a short punitive campaign that uses firepower to reduce casualties and bypasses built up areas.

    That force can potentially advance to threaten Kiev with artillery bombardment, extract concessions/change the government and then withdraw.

    I am not saying that will definitely happen, but it is a scary threat even if it falls short of total occupation. Think Georgia 2008 not Barbarossa 1941.

  3. In modern warfare the number of men does not count as much as the number and the technologically level of specific equipment. At the moment the 100k russians could conquer the whole of ukraine, as the ukrainian army is still an joke in the decisive areas of modern warfare. After that the russians would met an guerilla war at least in the western part of the ukraine, and the russians forces would be not sufficient to control the country, but that is an complete different question.

    Lets take for an example the third gulf war. If you look only at the numbers, the iraqi troops were superior to the us tropps. Despite this the capital was conquered after around 20 days, despite heavy sandstorms and logistical problems. It would not be much different in a war against the ukraine.

    Despite that i doubt heavily, that the russians will attack the whole of ukraine, i think this is extreme unlikely. At worst it will become an hybrid / cyberwar / sabotage kind of war in parts of the eastern ukraine and nothing more.

    Because russia could not be that stupid to conquer the ukraine as this would harm the russian foederation extremly and would bring only disadvantages for zero benefit even in the long term.

    And despite all that, the overall theme of the thread is imo completly right: humans cannot handle numbers, as this is an common mistake in nearly every human affair.

    1. True, but off the point. The media pretends that "100k Russians concentrated!!!" is scary.
      They do not offer some nuanced analysis about Russian air power and superior Russian heavy arms and EW. Those things are constant and the audience would wonder 'why now?'.

      I doubt that the current Russian force concentrations could conquer the Ukraine, the Russian army itself is 2nd grade quality at best. They could raid through much of it, but hold little of it.

      They're not in position to clean up just the East of the Ukraine.

      The Iraq 2003 example is extremely off becuase the invaders had vastly superior morale there. In the Ukraine case it's completely uncertain who would have superior morale. The Ukrainians may fold, but they might also fight like Finns, driven by nationalism and defending their own soil.

      I suppose the whole troops deployment in a bad weather season is designed to scare the Ukraine and/or the West into concessions. It's an accumulation of illegitimate bargaining chips.

    2. Absolutly agree with your last sentence, but cannot agree with your overall assessment of the military powers of the two states in comparison. The ukrainian army is a potemkin village, their fighting power is very low and despite all rethoric also the morale is low in reality. Moreover not all ukrainians are strictly anti-russian, and ethnical russians make around 18 % of the population. They will not fight like the finns, but their propaganda show would collapse in the conventional part of the fight very fast.

      In my personal opinion russia could therefore conquer the ukraine, but conquering a country and holding it are completly different things. The following guerilla war etc would be worse than in iraq, as the russian forces were weaker than the us army then and they are not as competent in COIN, despite the image in media the russian army is very weak in COIN, nearly complete incompetent. The west would also then strengthen the ukrainian resistance movement.

      But overall i am very sure that russia will not invade the ukraine - this would suprise me very much.