Sarah Smiles....I suppose it is logically possible to rule from afar but that is neither here nor there, the writer of that article is definitely confused and imposes the incorrect interpretation of the word while at the same time arguing against it!
isaacaustin...That's right. Of course, because of English idiom, when you translate epi you might use other words than "on, upon" (such as ep' agrou being rendered "in the fields", although of course the semantic relation is one of a person standing on the fields), but "over" in the sense of having a location above another is not part of the word's meaning -- huper is used for that. And the specific phrase epi (tés) gés "upon the earth" is such a common, widely used phrase ... it's not some obscure idiom. I just checked the NT and find that it occurs over 50 times: Matthew 6:19, 9:6, 16:19, 18:18, 19, 23:9, 35; Mark 2:10, 4:1, 26, 31, 6:47, 8:6, 9:3, 20, 14:35, 5:24, 18:8, 21:23, 25, John 17:4, Acts 2:19, 10:11, Romans 9:28, Ephesians 1:10, 6:3, Colossians 1:16, 20, 3:2, 5, Hebrews 11:13, James 5:5, 17, Revelation 3:10, 5:3, 10, 13, 6:10, 7:1, 8:13, 10:2, 5, 8, 11:10, 13:8, 14, 14:6, 16:18, 17:8, 18:14. You can look these up and see for yourself whether a location "above" is meant. In fact, often a CONTRAST with heaven is made: "I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven" (Matthew 16:19). In the Greek LXX, the phrase occurs hundreds of times in the OT. I won't bother listing them, but here are a few examples: "the Lord God had not caused it to rain upon the earth" (Genesis 2:5 LXX), "You will be a fugitive and a wanderer on the earth" (4:12 LXX), "The giants were on the earth in those days" (6:4), "I am going to bring a flood of waters on the earth" (v. 17), etc. etc.