We Make Numbers From Shapes: Hints from Neurology

As a standard disclaimer, I am not a mathematician, and you should take these as observations rather than arguments. (For example, the amount of time I would have to invest to understand even this discussion is large.) But these observations add up to an assertion that, rather than numbers and there being an abstract relationship between two separate domains, numbers are a type of geometrical entity, though they are arbitrary and do not exist separate from our nervous systems, much like pain or non-spectral colors like pink. As in that argument, again observations from neurology are central.

In Gerstmann syndrome, patients who have had a dominant (usually left) parietal lobe injury, often from a stroke, lose the ability both to distinguish left and right, and to do arithmetic. (They also lose the ability to distinguish individual fingers, suggesting how important they are for counting. Children born blind often begin counting on their fingers without being taught.)

Related, I've long been mystified why in OCD, among the more abstract obsessions patients develop, are not just symmetry, but counting, and if you have one, you're more likely to have the other than random chance would predict. In terms of evolutionary psychology, many psychiatric illnesses are easily understood as hyperactive subsystems that in their normal setting and function, would be quite adaptive. In paleolithic Africa, you need anxiety to survive, you should be afraid of heights and snakes - and you should be able to frequently and easily orient yourself. Consequently, symmetry being part of OCD makes sense. But why counting, or especially fixation or avoidance with certain numbers? Some people insist on doing things in multiples of 3 or 5, or must avoid certain numbers (7 is frequent, possibly because it's the highest single digit prime?) to the point that it impacts their life, despite knowing how irrational it is - a smart-aleck roommate calls them to say they turned their TV volume to 7 and this is so uncomfortable to the OCD patient that she has to drive home from work to adjust it even at the risk of getting fired. It's hard to explain why the number 5 (or any number) would be good, or 7 would be bad, in the Pleistocene - unless it's actually the symmetry system that's hyperactive here.

Unsurprisingly, the same brain region (the inferior parietal sulcus, Brodmann area 7) is involved in both symmetry and counting. Therefore, that a lesion to this area would result in deficits in both these abilities is completely predictable; but why would the brain have evolved so the same area was serving both purposes? As before, even proving that numbers are a geometric entity in their representations in our brains does not give us a generalizeable argument about what numbers are, and it's possible that even if this is true for humans, it's only provincially true for the way our nervous systems work - butwhen AI systems develop the same way without being directly instructed, it does increase our confidence that our nervous systems and the AIs are converging in the way they represent something because that's really what they objectively are. On that note, it was discovered that what one AI was actually doing, when it is doing arithmetic, was spontaneously turning a modeled shape and counting vertices. It "evolved" this system on its own without being instructed.

Trump is Our First Barracks Emperor: America's Crisis of the Third Century

States pass through lifecycles of 200 to 250 years. If this statement is true, then to isolate the process from other variables we should look for a a part of the world with a large fertile plain and a single ethnicity, and if left to its own devices its dynasties would last 200 to 250 years. This is in fact what we see in China, the best known example, but the pattern has been noted throughout history and throughout the world. This 200-250 year period is of obvious interest to Americans in 2025.

One mechanism for the transition from one state to the next is that the state's elites lose control of the succession process, and in this respect, history does often rhyme. Roman history provides good examples. The Roman Empire is usually divided into the Principate period lasting from the Battle of Actium in 31 BC, to the assassination of Severus Alexander by Maximinus Thrax in AD 235 that ushered in the Crisis of the Third Century. This was followed by the Dominate period, starting from Diocletian's administration in 284 to the fall of the Western Empire in 476.

Of these two transitions, the fall of the Western empire is better known. In AD 476, Odoacer interrupted the Western succession, or rather, he disintermediated it. As with most things in history, to contemporaries, things are either not actually so sudden, or they only seem sudden to isolated elites in denial due to normalcy bias. In this case, for a century at least, the Western emperor had largely been a figurehead for the Germanic magistri militum who held military power. When Odoacer killed the magister militum Orestes and deposed the last emperor (who was actually the magister's son), he was merely (finally) cutting out the middle man. At the time, contemporaries did not think much of the development, so naturally did it flow from the circumstances, and only later did historians begin to mark it as a major transition. But it was still the final removal of succession - even if the office was mostly ceremonial - from elite oversight, that is, from the generals who had been the de facto power in Rome during much of the Dominate.


Maximinus Thrax says Senators are cucks. "Just kill...I don't even wait." From imperiumromanum.pl
The Crisis of the Third Century is much more interesting. There were four dynasties during the Principate, but even when each of these ended, there were brief periods of at most a few years before stability returned. During the Principate, there was a tradition (if not what we would recognize as a formal institution) of future emperors being made the adopted sons of previous emperors, and then being chosen by the Senate. Earlier in the Principate dynasties, Senators frequently had military experience - they retained their connections with the legions and hence, the military's respect. But the trend during the Principate was toward less and less military experience among the elite families that produced Senators, and already by the Antonine dynasty, the military experience and connections of Senators had decreased dramatically. At its base, civilization is always backed by a threat of violence, but the more distant that threat is, the more pleasant our lives are and the more successful we could say the civilization is.

But by the time of the Severan dynasty, the emperors focused only on keeping the army happy (Alfoldy 1974), and when one side (the military) can use violence with no real threat of retaliation (from the Senate), there is clearly an unstable equilibrium. Thus, when Roman soliders assassinated the last Principate emperor Severus Alexander in 235, and then the soldiers of the legion rather than the Senate decided Maximinus Thrax was emperor, we see another example of elites losing the power to control succession. Maximinus never even came to Rome when he was "emperor" (read: general who threatened to kill others and avoided being killed for long enough for contemporaries to bother writing down his name.) Maximinus was, during his brief "reign", openly adversarial with the Senate, who rightly feared him when he did approach. This way of becoming emperor - a "barracks emperor" who had little interest in affairs in Rome or ability to govern the empire - continued until Diocletian's power-sharing arrangement in 284. The Crisis had begun.

The succession process in the United States would seem to bear little resemblance to that of the Romans. Indeed, our regular elections were set up partly with their example in mind as a warning. Though we've had leaders popular for their military record, it's not the elites’ changing relationship with the military that makes the analogy here. We choose our leaders through direct election by citizens, and since very early in the republic our choice has been constrained by two elite-controlled organizations called political parties presenting us with their candidates. It's difficult for most Americans to admit this, but this process (and until the early 2000s, the mass media oligopoly that supported it) is how the elites controlled succession - and it's even harder for us to admit that this may have been for the best. While the franchise has expanded over time, it's not obvious that each step in turn immediately changed the kinds of choices the parties were offering for national leader. Starting around 2010 the tone of politics and kind of candidates offered had, however, seemingly undergone a rapid shift, maybe not coincidentally now that everyone had a smartphone and social media.

This is how the elites have lost control of the succession process - in our case not by losing respect of and control over the military, but by a colluding media and party elite losing control of the information ecosystem and candidate selection process. The analogy here is that Trump is Maximinus Thrax, the first outsider who rose to power using a new process to circumvent the old elite-controlled pathway to leadership, with assassinations of character rather than physical bodies. This is why conventional candidates have been roadkill, like clueless, ossified Roman Senatosr during the Crisis, who might have continued maneuvering among their colleagues in Rome like their forebears did, not understanding how irrelevant such efforts had become - while generals far from Rome tried to get into position to assassinate the current one, wherever he might be encamped. If Gavin Newsom succeeds in turning Trump's social media appeal-to-the-masses approach against him, he will just be the next in a succession of social media barracks emperors - but the elites then will have lost control of the succession process, and the Crisis of the Twenty-First Century will continue.

Alföldy, G. "The Crisis of the Third Century as Seen by Contemporaries." Greek, Roman, and Byzantine Studies 15 (1974): 89–111.