Counting letters in numbers leads to 5 or the 4-6 loop

Counting the letters of a number ends in 5 or in the 4-6 loop

«Most curious… or does it have an explanation?» With that phrase, without further development, a conversation began. The object of the intrigue is verifiable: write a number in words, count how many letters it has, and repeat the operation with the result. In the cases tested, it doesn't matter the starting point. In Spanish, CINCO has five letters, so the process bites its tail and doesn't leave there. In English, the number that locks itself in is FOUR, with four letters.

Why does five become an infinite loop?

As noted in the thread, five is the only Spanish numeral between one and ten where the number of letters matches the number itself: uno, dos, tres, cuatro, seis, siete, ocho, nueve, and diez do not fulfill the rule. That turns five into a perfect trap for the algorithm. The trick works the same with huge figures, because each step shrinks the writing: SIETE MILLONES NOVECIENTOS TREINTA MIL is written with 34 letters; TREINTA Y CUATRO, with 14; CATORCE, with 7; SIETE, with 5; and CINCO, again with 5.

The other possible ending: trapped between four and six

Not all sequences die at five. There is a second outcome, an orbit of two stations, and it appears with equally long numbers: ONCE MIL MILLONES CUATROCIENTOS TREINTA Y DOS MIL SEISCIENTOS CATORCE adds up to 59 letters; CINCUENTA Y NUEVE, 15; QUINCE, 6; SEIS, 4; CUATRO, 6. And from there it doesn't move. Two endings and only two, at least in the range that has been tested.

The objection: no mystery, just nomenclature

This is where the wonder deflates. Some argue that the phenomenon is nothing magical and that the trap is in how we call things. If we had named 10 DECIMUS, the result would change; with SEPTIMUS or OCTOPUS, the loop would end up going back and forth between 7 and 8. The underlying mechanism is that each step reduces the number of letters until the figure enters a small set of values, and there repetition is inevitable. It is the same family of problems as the Collatz conjecture. The merit of five, in the end, is having been born with five letters.

From one to a million: what percentage ends in each outcome

The video that serves as a starting point doesn't stop at pretty examples: it checks the algorithm up to one million and offers the distribution of cases between the two outcomes. Reproducing those percentages without the accompanying breakdown doesn't clarify much. What matters is that, throughout the entire range, the pattern doesn't break. And that no one has yet proven that it holds for all numbers, because numbers don't end at a million. That is precisely the crux of the matter.

From gematria to the Torah: the detour that takes over the conversation

From there, the matter changes tracks. Part of the conversation argues that studying numbers leads directly to Kabbalah and that the coincidences in the biblical text cannot be chance. Gematria is cited, Marian prayers from the 4th century such as the Sub tuum praesidium confugimus are mentioned, and verse 48 of the first chapter of Luke is traced. In parallel, much more exotic theses circulate: those of Alexandre Eleazar, who defended that Egyptian hieroglyphs are better translated with Basque, spoke of three women—María, Marta, and Margot—and placed the capital of the Beres in Cádiz. And those of Nimrod de Rosario, author of Belicena Villca, twenty years of writing and more than 5,000 books consulted, according to the accounts that accompany the work.

All this coexists on the same page without anyone having managed to close the first problem. The letter algorithm is checked up to a million and is intuited to be true; its behavior depends entirely on the language in which the figures are named. Change the language and the loop changes. Change the name of the number and everything changes. No one has explained why Spanish chose that five would have five letters, perhaps because no one chose anything.