It is mathematically true that they don't have to move together, but there are lines of evidence that for PIE they did. For example, there are lots of divinity related words and root words found in the PIE language that then carried forward in various derived languages in distinct geographical regions of Indo-Europe. This is not nothing.
There are even be stories that similarly exist in common. There is the story of slaying the serpent. There is another story of the divine twins. These stories are found everywhere that the PIE culture went.
The third line of evidence is PIE poetic formulas and poetic traditions. These again show up in multiple post-PIE cultures. The local writings show the same mythic structure across cultures. These things are too difficult to explain without a common ancestor culture/religion.
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It is mathematically true that they don't have to move together, but there are lines of evidence that for PIE they did. For example, there are lots of divinity related words and root words found in the PIE language that then carried forward in various derived languages in distinct geographical regions of Indo-Europe. This is not nothing.
There are even be stories that similarly exist in common. There is the story of slaying the serpent. There is another story of the divine twins. These stories are found everywhere that the PIE culture went.
The third line of evidence is PIE poetic formulas and poetic traditions. These again show up in multiple post-PIE cultures. The local writings show the same mythic structure across cultures. These things are too difficult to explain without a common ancestor culture/religion.