'Nine' may link to the PIE word for 'new' — as if it were a fresh start in counting after eight.
The cardinal number following eight and preceding ten; the square of three.
From Old English 'nigon,' from Proto-Germanic *newun, from PIE *h₁néwn̥ meaning 'nine.' The PIE form is strikingly similar to the word for 'new' (*néwos), leading some linguists to propose that 'nine' originally meant 'the new (number)' — the fresh start after completing two groups of four. This remains a speculative but widely cited etymology
November was originally the ninth month (Latin 'novem,' nine) of the Roman calendar starting in March. The possible connection between PIE *h₁néwn̥ (nine) and *néwos (new) has led linguists to speculate that nine was perceived as 'the new number' — the beginning of a fresh count after two sets of four.