"We will relate the power of this day's holiness, for it is awesome and terrible.... On Rosh HaShanah it is written, and on the day of the Fast of Atonement it is sealed: how many will pass away, and how many will be created; who will live, and who will die; who at the end of his allotted time, and who not at the end of his allotted time; who by water and who by fire, who by the sword and who by wild beast, who by starvation and who by thirst, who by storm and who by plague, who by strangulation and who by stoning; who will have rest and who will wander, who will have quietude and who will be savaged, who will have peace and who will suffer, who will become impoverished and who will become wealthy, who will be humiliated and who will be aggrandized. And repentance and prayer and charity reverse the evil of the decree." (from the Unetanneh Tokef prayer in the repetition of the Mussaf of Rosh HaShanah and Yom HaKippurim)
We can understand how God is influenced by our tears of repentance, our heartfelt prayers, and the charity we give: by these actions we show that we have put our sins behind us - or at the very least, that we are genuinely
What efficacy can there be in prayer during the rest of the year?
trying to put our sins behind us - and get closer to Him. But if, as we declare in this prayer, all that happens in the coming year is written on Rosh HaShanah and sealed on Yom HaKippurim, then what efficacy can there be in prayer during the rest of the year? The implication is that there is a mere ten-day opportunity for beseeching God for His benefits throughout the year.
The precise wording of the final sentence is all-important: "And repentance and prayer and charity reverse the evil of the decree." Note that they do not reverse the decree itself: that, indeed, is fixed and unalterable from Yom HaKippurim to Rosh HaShanah a year later. But they can - and do! - "reverse the evil of the decree".
An outstanding example is in the Book of Jonah - the Haftarah for the afternoon of Yom Kippur. The prophet Jonah entered Nineveh and proclaimed his unequivocal message: "Another forty days, and Nineveh will be overturned!" (Jonah 3:4) No ifs, buts and unlesses. There seems to be no way out for the Ninevehites to be spared.
And yet, "the people of Nineveh believed in God, and they declared a fast... and the matter reached the king of Nineveh, who rose from his throne and removed his royal robe, donned sack-cloth, and sat on ashes.... And God saw their actions, that they repented of their evil way; so God relented of the evil that He had said He would do to them, and did not do it." (ibid. 5-10)
In fact, Nineveh was overturned - from evil to good: the overturning was spiritual rather than physical. Once the decree had been made, it was not to be rescinded; but the Ninevehites' repentance reversed the evil of the decree. The self-same decree was reversed from evil to good.
And this brings us to the mitzvah of sounding the shofar on Rosh HaShanah. The Hebrew word for the shofar-blast is t'ru'ah, from the root reish-vav-ayin (the Torah in Numbers 29:1 calls Rosh HaShanah Yom T'ru'ah). This same root is a cognate both of ra'ah ("evil") and of rei'a ("friend", "beloved"). The piercing, wordless blast of the shofar gives us the power of repentance to transform ra'ah into rei'a.
Another of the shofar's notes is the sh'varim - those three broken, whimpering cries, from the word shever ("breaking"). This is from the three-letter root shin-bet-reish: in the kal (also called pa'al) form, this root means "break"; yet in the hif'il form, the same root gives us the word hishbir - to supply sustenance - like Joseph whom the Torah (Genesis 42:6) describes as the mashbir, the supplier of sustenance for all Egypt (like the chain of supermarkets in Israel today called HaMashbir). Again, we have these two very different, almost contradictory, concepts - breaking and supplying sustenance - expressed by the same Hebrew root.
It seems astounding that the same Hebrew root should mean both "evil" and "friend", and that the same Hebrew root should mean both "break" and "supply sustenance" - diametrically opposing concepts in the same word. But this is far from unique in Hebrew.
The root chet-tet-alef, in the kal (pa'al) form, constitutes the word chatta ("sin"). Yet, the same root in the pi'el form, gives us the word chitte ("cleanse", "purify"). Again, we have the oh-so-comforting lesson that even sins can purify us. "In the place that repentant sinners stand, even the perfectly righteous cannot stand" says the Talmud (Berakhot 34b, Sanhedrin 99a); "Reish Lakish says: Great is repentance, because it transforms deliberate sins 
Diametrically opposing concepts in the same word. But this is far from unique in Hebrew.
into accidental errors.... Great is repentance, because it transforms deliberate sins into merits.... These two statements do not contradict each other - one speaks of repentance due to love, the other of repentance due to fear." (Yoma 86b; Yalkut Shimoni, Ezekiel 342)
That is central to the message of the Ten Days of Repentance, which start with Rosh HaShanah and climax with Yom HaKippurim. No matter what decree God may have promulgated concerning us, we have the power, through our repentance and prayer and charity, to have that decree fulfilled for good. The shofar, which is the most potent symbol of Rosh HaShanah and which heralds the conclusion of Yom HaKippurim, epitomises this. The word shofar has two different cognates. The Rashba (Rabbi Shlomo ben Aderet, Spain 1235-1310), in his commentary to the Talmud (Rosh HaShanah 26a, s.v. Matnitin - kol ha-shofarot), and the Mishnah Berurah (586:7, 68) understand shofar to be from the word sh'foferet, meaning a hollow tube. But the Midrash relates shofar to the word shapper ("improve"): "In the month of Tishrei, renew your deeds with the shofar; in this month, improve (shipru) your deeds. God told Israel: If you improved (shippartem) your deeds, then I will be for you as this shofar. Just as [the sound] passes through this shofar from one end to the other, so will I arise from My Throne of Justice and sit instead on My Throne of Mercy, and thereby overturn for you the Attribute of Justice to the Attribute of Mercy." (Leviticus Rabbah 29:6; Yalkut Shimoni, Emor 645, Pinchas 782)
The Haftarah for the second day of Rosh HaShanah is one of Jeremiah's magnificent messianic prophecies (Jeremiah 31:1-19), which depicts the ingathering of the exiles at the end of days, the final eradication of the exile. The Haftarah for Yom HaKippurim is - appropriately enough - Isaiah's castigation of the nation for their insincere repentance and fasting, and his exhortation to internalise the message of fasting and repentance (Isaiah 57:14-58:14); and that Haftarah concludes with God's promise that, if we obey His mitzvot, "then you will merit to rejoice over HaShem, and I will cause you to ride over the high places of the earth, and I will sustain you with the inheritance of Jacob your father - for the mouth of HaShem has spoken". This, like the Haftarah for the second day of Rosh HaShanah, also alludes to the final ingathering of the exiles, to Shivat Zion (borrowing King David's phrase in Psalms 126:1). And the word shiva is a cognate both of shuv ("return"), per the Ibn Ezra (loc. cit.), or of shevi ("captivity"), per Metzudat Zion (loc. cit.).
"Everything is in the hands of Heaven, except for fear of Heaven." (Berachot 33b, Megillah 25a, Niddah 16b) This seems puzzling, because the individual's fear of Heaven or lack thereof determines everything else; so how can everything be in the hands of Heaven if fear of Heaven is the individual's free choice?
Perhaps we can now understand this. Heaven indeed decrees, and the individual's free choice determines if Heaven's decree be fulfilled for evil or for good. After Heaven has decreed, our repentance, prayer and charity can yet determine if the reish-ayin-heh decreed by Heaven is ra'ah ("evil") or a rei'a ("friend", "beloved"), if the chet-tet-alef is the chet ("sin") or the mechatte ("that which purifies"), if the shiva connotes "return" or "captivity".
And so it is, perhaps, no longer so surprising that the words golah ("exile") and ge'ulah ("redemption") are
The words golah ("exile") and ge'ulah ("redemption") are cognates.cognates: the ge'ulah depends on our repenting, on our transforming the chet ("sin") into the mechatte ("that which purifies"), on increasing our fear of Heaven. A contemporary gadol baTorah explains: "The only difference between golah (gimmel-vav-lammed-heh) and ge'ulah (gimmel-alef-vav-lammed-heh) is the alef, whose numerical value is 1, which alludes to God Who is One. That is to say, anyone who sits in the golah (exile), rejecting the ge'ulah (redemption) of the Land of Israel, does this only because he lacks the ‘One', the complete trust in God Who is One and Whose Name is One." (Rabbi Meir Kahane, Ohr HaRa'ayon/The Jewish Idea, end of Chapter 34)
So may these Ten Days of Repentance, starting with Rosh HaShanah and concluding with Yom HaKippurim, usher in the new year 5770 as a year of repentance and redemption, a year of transforming the bad into good, a year of forgiveness, atonement, and final Redemption for Israel and the whole world.