Alfonso and his savants forged Spanish into an exceptionally well-organized language with phonetic standards, making it relatively accessible for some learners. They are thought to have hewed to a policy of “castellano drecho” — straight or right Spanish — imbuing the language with a sense of purpose.

Even today, Spanish remains mutually intelligible around the world to a remarkable degree, with someone, say, from the Patagonian Steppe in Argentina able to hold a conversation with a visitor from Equatorial Guinea, one of Africa’s largest oil exporters.

Drawing on entropy, a concept from thermodynamics referring to disorder, Jean-Benoît Nadeau and Julie Barlow, the Canadian authors of a 2013 book charting the evolution of Spanish, describe the degree to which Spanish is spread out geographically over a wide array of countries.

By this measure, Mandarin ranks low on the entropy scale since most of its speakers live in the same country. English boasts greater entropy, but Spanish, the majority language in more than 20 countries, ranks first, followed by Arabic.

Rivaling Spain and parts of Latin America, the United States exemplifies how the movement of people throughout the Spanish-speaking world is taking the language in new directions.

In metropolitan Los Angeles, an area with more than 4 million Spanish speakers — more than Uruguay’s entire population — linguists say that a new dialect has coalesced as different types of Spanish come into contact with one another. And here in New Mexico, an influx of Mexican and Central American immigrants is nourishing and reshaping a variant of Spanish that has persisted since the 16th century.