One of the obvious common denominators between the two days, is the lots that took place on both holidays. On Yom Kippur – the Day of Atonement, it was to choose between the two goats, and on Purim, it was the lot that the wicked Haman cast, to choose the day when he would kill all the Jews.
Sometimes, a person will prefer one choice over the other because of rational considerations. When making a raffle however, the results defy logic. On both these days, what highlights the worship of G-d is a process and a commitment to the results that are accepted as Divine Providence. Not because anyone understands, but only because that’s what G-d wants.
A person’s connection with G-d can be based on logic. He understands there must be a creator to the world and its continued existence can only be credited to Him. He therefore conscientiously decides that he will dedicate and connect himself to this source, knowing it’s for his own good. This kind of relationship is by its very nature finite and limited. It a based on a premise than can shift with the next convincing argument against the current conclusions.
Then, there is a commitment and dedication which is higher than any logical considerations. It is unconditional, depends on no rational considerations, and nothing will move the person away from this relationship because it’s not based on anything one can argue with.
On Yom Kippur, it is this deep relationship that comes into play, and therefore the worship expressed itself with lots. When a person connects with the deepest levels of a spouse, parent or friend, where the love is unconditional, how a person behaves doesn’t matter, and therefore, atonement is possible.
However, on Yom Kippur, there are physical props that bring about this deep connection. Not eating and by attending services we are like Angels, and it’s this kind of G-dly and spiritual conduct that brings out the results.
On Purim however, the concept of lots which expresses and manifests this very deep relationship we have with G-d, is revealed necessarily by drinking and eating, by being happy, and not by separating from the materialistic world. Even while connected to a physical world – and steeped into self enjoyment, we are able to connect to this unqualified and unrestricted depth of G-d.
Purim is a holiday that shows us and grants us the influence, to this the very special power in our relationship with G-d, that even while we eat and drink and it appears we are into ourselves, we can and therefore, we should be aware of, “in all your ways you should know G-d.” Purim shows us that it is possible to draw the energy of G-ds unconditional and unqualified qualities in all areas of our lives.