Let's start with a simple question: Why does Rosh HaShanah come before Yom Kippur? If you are like my granddaughter, who says her mom became good in chumash because she is now a chumash teacher, I suppose you will answer it is because Rosh HaShanah is on the first of Tishrei and Yom Kippur is on the 10th (and then you'll roll your eyes). If you are a drop more mature, you'll say it is because Rosh HaShanah mean "head of the year", so of course it is the first holiday of the year and automatically Yom Kippur has to be later (and you may still roll your eyes). To which I will answer (ignoring the eye rolling), "Yes, but Rosh HaShanah is also known as יום הדין/The Day of Judgement. Why would you only start plea bargaining (ie, Yom Kippur) after the sentencing? And while we're on the topic, why does יום הדין have to do with the new year? And also while we're at it, given that Rosh HaShana is יום הדין, why is it all about making HaShem the King? Huh? Huh? Huh?" (Yeah... maturity is not my strong suit...)
Maybe you think that יום הדין is sort of a poetic way of referring to the way we conduct ourselves on Rosh HaShanah regarding HaShem; we see him as a King ready to judge us. But, we all know -- wink/wink/nod/nod -- it's just a ceremony. In that case, I direct you you to the first halacha on the bracha of שהחיינו: if you haven't seen (heard from/email/texted/facebooked/etc) a friend in 30 days, you make a שהחיינו. If, however, it has been 12 months, then you make the bracha of מחיה המתים/who resurrects the dead. (Shulchan Aruch O. Ch. 225:1, for the interested reader) Why? The Mishna Brura explains that since you haven't seen him in a whole year, he has certainly gone through a Rosh HaShanah. If he is alive, therefore, he has been saved from a very real -- real enough to make a bracha -- possibility of getting a decree of death. In case you think, "C'mon; we're not all that bad"; I direct you to my personal rendition of "23 Dimensions to Each and Every Sin". (Not as a proof, but just sayin', Google translates יום הדין as "Doom's day"; just sayin'...)
So what's going on? As usual, it is a problem with translation/perspective. The term יום הדין is dead accurate (of course pun is intended; sheesh!). The world was born (that is, started operating) on Rosh HaShanah (as we say repeatedly in the davening). The world was, of course, built on kindness; meaning that the entire purpose of Creation is to serve as a tool for expressing the Kindness of HaShem. When Adam sinned/alternatively, when Klal Yisrael sinned with the golden calf, the situation had to be evaluated and a judgement -- an adjudication, if you will -- had to be made as to what needs to be done for the next cycle -- read "year" -- to accomplish its part in that ultimate goal. The goal of expressing the Kindness of HaShem is accomplished by putting us in a position to perfect ourselves. Hence, at the beginning of a new cycle/year, we and the entirety of Creation is judged to determine the most effective way to give each of us the greatest opportunity to perfect ourselves. It is therefore obvious that our only job on Rosh HaShana is to recognize the importance of the day and express to HaShem that we accept and, in fact, want nothing more than His Loving Sovereignty -- ה' מֶלֶךְ, ה' מָלַךְ, ה' יִמְלוֹךְ לְעוֹלָם.
A few nights ago, my grandson was heading up to bed as I was heading out to mincha. He asked me to please come up to kiss him when I returned. I said I would, but knew that he would be long asleep when I got him. (During the day he does not stop; it's exhausting just watching him! When he goes to bed, though, he is out in an instant.) Sure enough, he was fast asleep. Nonetheless, I leaned down to kiss him and adjust his covers. Apparently he wasn't completely out; I heard him mumble, "That's better" as he turned over and really fell asleep. I hope and pray that on Rosh HaShanah, this month of preparation will have been enough to rouse me from my spiritual slumber enough that HaShem can hear my faint, "That's better."