Despite being the great villain of the Israelite people, and prime enemy with the distinction of three entirely explicit mitzvot - to deal with their legacy by exterminating their seed and remembering, as well as not forgetting, what they did to us when we left Egypt - the Amalekites have quite a clear descent. Sort of. Amalek was stated to be a son of Esau, through his concubine Timna. This would have been simple, if not for the fact Timna was daughter of none other than Seir, the Horite.
While Esau’s real lineage is given to the Edomites, another critical rival nation to the Jewish people, their legitimate status as heirs to Esau’s legacy is a likely reason for the difference in treatment. Timna’s illegitimate status might also be why the Edomites are given a centralized polity just south of both Israel and Moab, while Amalek are a nomadic nation that wanders the southern Negev desert.
One of the primary reasons this group's necessary annihilation is precisely for this descent from Esau, brother of Jacob whose name is changed to “Israel” indicating that these two children’s lineages would become perpetual rivals. It is not due to the Horites that the Amalekites are important, but their bastard status among the Horites as the descendant of a concubine does give rise to their negative treatment, and their negative behavior.
A full discussion of the Amalekites will be dealt with in different books, but for our purposes, related to the war with Chedorlaomer, it is clear the Amalekites operate as a nomadic group whose troops join in the war, rather than really running any sort of official polity, or even having many cities. “Kadesh” afterall, is a generalized term for the wilderness, so it’s likely these were tent-dwellers, and it’s very possible they never really permanently inhabit any settlements.
One interesting correlation could be drawn to the various other groups listed; since Amalek are the only nation descending from a “post Abraham” lineage. The Amalekites, coming from Esau’s concubine Timna, are unlike the other groups which have some sort of pre-Israelite origin in the region, coming back to the interesting theory of seven Canaanites, and seven Rephaim
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Quick section this week since the Amalekites are dealt with in another section, but this helps relate them to the current understanding of Canaanites, and other giant groups.
Thank you once again for reading, I hope you gained some wisdom and understanding of the Torah.