The Kli Yakar on Shmos 20:13, the Aseres Hadibros, gives a fascinating explanation of the coorespondance between the dibros on the first tablet and the dibros on the second tablet. Underlying this explanation is the well-known question: Why are the dibros on two tablets? They could have been a list of ten on only one piece of stone. The implied answer to this unspoken question is that they were placed with 5 on one and 5 on the other in order to show that the dibros that were side-by-side were meant to coorespond to one another (i.e. 1 cooresponds with 6, 2 to 7, etc.).
The Kli Yakar goes through these 5 pairs of dibros and explains the coorespondance in sometimes very fascinating ways. Here we go:
- "I am Hashem." - "Don't Murder."
a) Man is created in the image of G-d. If one person kills another, then he is lessening the Presence of G-d in the world, which is a derogation of human recognition of G-d existence, which is commanded by the mitzva, “I am Hashem.”
b) Even though Hashem has no form, the Kli Yakar says that when he gives people a prophetic vision, he uses a human image in the vision. (c.f. Yechezkel 1:26 "וְעַל דְּמוּת הַכִּסֵּא דְּמוּת כְּמַרְאֵה אָדָם עָלָיו מִלְמָעְלָה.") When one kills another he shows distain for the image of man, and causes Hashem not to want to make his presence known in the world in that way any more. This idea can be seen from the verse about not disrespecting a human body in Devarim 21:22, "כִּי-קִלְלַת אֱלֹהִים תָּלוּי."
c) Yaakov Avinu choose Hashem as his portion. Eisav his brother choose to live by the sword. The fact that he killed people caused him to deny the existance of G-d (Bava Basra 16b -"וכפר בעיקר כתיב הכא (בראשית כה) למה זה לי וכתיב התם (שמות טו) זה אלי ואנוהו...") Therefore, when when commits murder, it causes him to deny G-d's existance and that is why the dibur of Anochi Hashem cooresponds with the dibur of Lo Tirtzach.
- "There Shall be no other gods before Me" - "Don't commit adultery."
Not only are Jews who worship idols compared to an unfaithful wife (see, Yechezkel 16:32- "הָאִשָּׁה הַמְּנָאָפֶת תַּחַת אִישָׁהּ תִּקַּח אֶת-זָרִים.."), but immoral relations with idol worshiping nations leads directly to actual idol worship, as we see in Devarim 7:4, which forbids intermarriage, with one reason being that it causes Jewish people to turn away from Hashem.
- "Don't take G-d's name in vain" - "Don't steal."
When one steals, he will get taken to court and will eventually have to make an oath to prove that what he is saying is true. In that false oath, he will use G-d's name in vain.
- "Remember Shabbos to keep it holy." - "Don't bear false testimony."
One must not only keep Shabbos by not doing forbidden labor, but by not even speaking about worldly, weekday concerns, as the pasuk says in Yeshaya 58:13 as interpretted in the Gemara Shabbos 113b, "שלא יהא דבורך של שבת כדבורך של חול." If a person learns to sanctify his words to the extent that he will fully keep Shabbos by only speaking about spiritual things on Shabbos, then he will certainly not come to diminish the value of his words by uttering false testimony.
- "Honor your father and your mother" - "Don't covet"
a) One who covets anothe woman besides his wife will have children who do not honor their father or mother. Why? He will think of the other woman while his child is being conceived, and since everything goes after one's intentions, it will be as if that child does not belong to his mother, and so he will disrespect her. Also, since his father did not intent to create a child, but rather to fulfill a base desire, the child will unconsciously know that his father is not really his father, since the father didn't really intend the son's creation at the time of conception. (See also, Tzidkus Hatzadik 144 on this). Therefore, he will not respect his father either. This is the reason for the coorespondance between coveting and parental honor.
b) One who desires physical things will think more about the inheritance that he will get from his parents, as they get older, than he will about his parents' actual wellbeing. Therefore, he will scrimp and be cheap when it comes to taking care of his parents in their old age, as an expression of his coveting their money. This is also how coveting leads to a derogation of the mitzva to honor one's parents.