The best and quite satisfying explanation is related to the Court procedure of the day and the passage in Jeremiah 17:13 ; an excellent overview of that explanation can be found at:
What Did Jesus REALLY Write in the Sand?
Enjoy reading ! (disclaimer: I'm not the author ...
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The article appears to me to being confusin or mixing Two different procedures to establish conviction.
1.) One of a jealous husband no stoning, and the other 2.) with witnesses.
So, far the only thing I can find is the "Sotah", of a jealous husband without witnesses. The ritual is: Her husband brings her to the priest, he takes her into the temple before the Lord. The ritual involves the dust of the temple floor, mixed with water called "bitter water" that causes the curse if guilty. The water also blots out the writing. The priest first uncovers here head, and charges here with oath . He then writes the curse of the oath in a book, or is translated "evidence" / bill etc. is sometimes used instead. The priest then tells her what will happen if she is guilty, she responds amen. The husband is innocent in this ritual.
The rabbinic Idea his conscience concerning her is abated by the ritual.
I also found the Rabbi's did modify what was considered sufficient evidence to bring a woman. If he had warned her concerning a suspected man. it was sufficient for Adultery to be charged. Note a "suspected man". What strictures were placed upon her concerning him by here husband? Talking? Laughing? eating with? I do not know. He is merely a "suspect", with regard to his wife.
So, yes, the Rabbis did modify things. There was no need to bring the man in this case, as it was motivated by the husbands jealousy. And the Priest bringing her before the Lord to witness for conviction of guilt. Her belly swell and thigh to rot.
It is interesting that the Greek translates bitter water as water of conviction.
with witnesses to be stoned.....
With witnesses. (2)
As we can see Jesus warned those who would be witnesses. There were not any lawful witnesses. They were unwilling to cast the first stone, as the witnesses doing so first was to kill the person. The rest just piled on symbolically. It was a trap.
This was by design since if the witnesses lied, they themselves were guilty of the same punishment they inflicted.