According to the law of large numbers, in a very large universe, even an event that has little probability of occurring ends up occurring many times. But the statistical probability of two synchronous linguistic or cultural events occurring is relatively small because there are not many languages or nations in the world. Furthermore, these coincidences would occur — and do occur — between any two languages or nations. Mirroring, on the other hand, is a set of coincidences involving two countries — always the same two — in a universe where the law of large numbers does not apply. Kings of France and England ascended the throne simultaneously too many times in relation to the historical duration of these two countries, for example.
A criticism that is often made about identifying patterns where they supposedly do not exist is the so-called confirmation bias, that is, the tendency we have to only consider hits and ignore misses.
If language and society are chaotic systems, the presence of hits should remain within the probabilistic range. Even if, in any chaotic system, there are more misses than hits, the mere occurrence of hits at a level higher than statistically expected is significant.
Language and society are chaotic systems. An example of a chaotic system is sand: the more you stir it, the more it becomes the same. This means that if, after stirring it once, an identifiable figure appears in the sand (for example, a face), this may be nothing more than a mere coincidence, that is, the result of chance. But if I stir the sand again and a face appears again (or a horse, or the map of the USA), I would have to consider this a huge coincidence. However, if I stir it a third time and a familiar figure appears again, then it is no longer a coincidence; there is a law behind it.
For example, the probability of two people being born on the same day is 1/31; in the same month, it is 1/12. The probability of two people being born on the same day and month is 1/31 × 1/12 = 1/372. Assuming an average life expectancy of 75 years, the probability of two living people being born on the same day, month and year is 1/372 × 1/75 = 1/27,900. The probability that, in addition to all this, they are of the same sex and ethnicity, were born in the same city, have the same name, etc., tends to be infinitesimally small.
Although a very large number of coincidences is not mathematically impossible, cases like the Lincoln–Kennedy coincidence are embarrassing because there is no record of an intermediate gradual scale, that is, of famous people linked by one, two, three coincidences and of people linked by 20 or more, as is the case with the two American presidents.
Chaos, chance and synchronicity
Casual is the effect without a cause, perhaps only possible at the quantum level (perhaps not even at the quantum level — I am particularly suspicious of the possibility of anything happening without a cause), unpredictable to any observer, in itself.
Chaotic is the effect of a very complex set of causes, therefore unpredictable to us, but not unpredictable in itself, that is, there is some observer for whom the event is not unpredictable. For example, the result of a dice throw is only unpredictable because we have no way of calculating the mass of the dice, its initial position, the intensity and direction of the force with which it was thrown, its distance from the table, etc. If all this information were available, a mathematical equation would accurately predict which side will fall upwards.
When I choose a shirt to put on, my choice is not casual, it is chaotic, because I am not aware of the motivations for this choice (except on obvious occasions), but they exist in my unconscious.
The evolution of societies and their languages can lead to convergences and parallelisms that are not random. If they occur in greater numbers than would be statistically expected and, furthermore, follow a pattern, then there is a connexion between them, although their chaotic nature (that is, extremely complex, as it involves countless variables) does not allow us to know what law governs them.
If we compare Latins and Slavs, or Germans and Slavs, or Arabs and Jews, or Indians and Pakistanis, or Chinese and Japanese, etc., we will not reach any conclusion, except the identification of some kinship. Systematic analogies are only found in one place on the planet: in Western Europe and America, between Latin and Germanic peoples. Now, if such coincidences were fortuitous (casual or chaotic), they would not occur in such large numbers; on the other hand, if they had a natural, rationally explainable cause, they would occur regularly all over the world. This is why supersynchronicities cannot be explained as the work of chance or of “natural” phenomena (historical, social, biological, etc.) — at least not yet.
The theory of synchronicity, plus the “theory” of believing is seeing, often mentioned by self-help gurus, according to which the mind creates reality (cf. Jesus, Buddha, neurolinguistic programming, Humberto Maturana, Amit Goswami, Disney strategy, etc.), which may have an explanation at the quantum level (but I believe we have not reached that yet, since this is a field where science and pseudoscience mix very easily), may explain the phenomenon of Romania–Germania specularity. Perhaps the unconscious desire of the ancient Germans to be like the Romans made them a “clone” of the latter. But geographical symmetries lead us to believe that Europe and America were already prepared for this symmetry even before the Romans and Germans entered the scene. It would be something like the future creating the past.