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one thing that occurs to me, as I look at this, is that the cranial capacity of these giants would have been far greater than that of modern man.  Did they have larger brains, and consequently some of the preconditions for greater intelligence?

If these giants built the Egyptian pyramids, perhaps so.

Probably. But what I don't understand is how we had giants after the flood.

I actually briefly glossed over that.  There are two theories.

1) the Nephilim re-offended after the Flood
2) one or another of Noah's sons' wives had at least some Nephlim genetic material in her line

LOL ... this one causes me to chuckle due to the imagery, but one theory is that King Og survived the Flood by clinging to the ark.  Of course, that one is outlandish, appears to contradict Sacred Scripture, and ... not sure how he was able to survive a year without food.  Perhaps he'd occasionally reach in through one of the windows and snatch an animal.

There appeared to be far fewer of these giants after the Flood ... and to me that suggests that there may have been some Nephilim genetic remnants in Noah's sons' wives.  Epistle of St. Jude (verse 6) states that the Nephilim where chained up in the abyss, but it could be that some other ones that had not offended initially then later offended after the Flood, unable to resist the tempation despite having witnessed the punishment of his colleagues.

On some of the other giants threads, I've posited the theory that there was a type of angel that could also assume material bodies.

We see everything in God's creation is hierarchical, where man is thought to be the link between angels and animals, having immaterial souls like angels but also physical bodies similar to those of animals.

We also see how there's hierarchy among the angels, where the top choirs of angels simply behold the Face of God and are around His Throne, and these never interract with human beings, etc.

So, what if there was another tier of angels, a missing link between angels and human beings, where they were immaterial like angels but could assume human bodies, and not merely animate bodies, but actually take them on.  Such angels would in fact, unlike the angels above them, have an actual "sensible part of the soul", as it's known, so that this part would allow them to interface with bodies, as it were, and actually feel things though the senses, etc.

We see in the Old Testament how angels visited Abraham taking on the form of men, to the point that Abraham didn't recognize that they were not men, and these angels ate with Abraham.  So these appeared to be real bodies.  Where they just animated bodies that they controlled like puppets, or did they actually have sensible parts of their souls so they could actually interface with them?  I theorize that it's the latter.

Now, unlike men, whose essence requires both a body and soul, the essences of these angles do not, but the body can be assumed accidentally to their essential angelic nature, or not ... whichever they preferred.

We read in the Book of Enoch that this was in fact their job, to interact with a govern the material world.

So that is how they were able to mate with human women.  Now, given that they could assume bodies, perhaps they deliberately engineered bodies for themselves that had what they considered superior genetics, making their offspring gigatntic, so that they could dominate and rule over men, become their kings, etc. ... and this way their descendants would rule the world and also mankind.

I don't quite buy the theory that the "sons of God" (Nephilim) were the sons of Seth.  In the Book of Job, for instance, we see the expression "sons of God" refer very clearly to angels, not to some offspring of Seth.