It’s actually almost the opposite of that. Most European languages actually started as the same language and slowly drifted apart.
You have to remember that for thousands of years the fastest way to get around was on a horse and you had to be relatively of high station to be able to afford one so for most people it was walking. So walking 20 miles would be an entire day journey and for many people they would never leave the village they were born in.
With this in mind its quite easy to see that languages could slowly drift apart. With regional dialects evolving out of an original common language until they diverged so completely they could be classed as an entirely new language.
This is the foundation for nearly all European languages.
Only six European languages, Maltese, Basque, Estonian, Hungarian, Finnish and Sámi, aren’t from the same prehistoric root language, Indo-European.
And Basque is the super weird one as we have no idea where it came from and it is completely different to any other language. Finnish, Hungarian, Estonian and Sámi come from the Uralic language tree, while Maltese is Arabic
Latest Answers