The interesting thing about the Purim miracle is that nothing outside of nature occurred. It was natural for Achashveirosh to become angry at his wife, Vashti, and kill her, and it was natural that Mordechai might overhear people planning to kill Ahashveirosh, and so on. Every aspect of the megillah can be explained according to the rules of nature. But when we think about the entire episode, with all its details, we are astounded at the wondrous miracle that occurred.
The Bnei Yissaschar (Kislev 4:83) tells a mashal of an ill person who had no cure. The only remedy found was from an herb that grew in the far east, which was never imported to their country. Furthermore, even if they had the herb, they needed a doctor to prepare it so that it would have its healing abilities. But the doctor who knew how to prepare it lived far away in the west. The doctor and the herbs never came to their country.
Suddenly, they heard that a ship arrived from the east, and the herbs were on the ship. The family rejoiced. They saw that Hashem was helping them. But their doctor told them that the herbs were useless without the expertise of a doctor from the West who knew how to prepare them.
Just then, they heard that the doctor from the west arrived. They were able to heal the patient.
Each part of the story could be explained according to the rules of nature, but when one considers the chain of events, he is astounded by the hashgachah pratis, and he will recognize that this was a great miracle. This describes the miracles of Purim (and the Bnei Yissaschar adds that the miracles of Purim were far greater than this mashal portrays). The miracles were within nature; nothing miraculous occurred, but it is obvious to all that Hashem arranged it all to save Bnei Yisrael.
With this information, we understand the reason Hashem's name isn't written in the megillah. However, Hashem's name is seen in the roshei teivos and the sofei teivos of some words. For example, there aren't pasukim like 'ה אל ויצעקו, "They shouted out to Hashem," in the megillah, and the megillah doesn't say that they said, 'ה ברוך, to praise Hashem when the miracles occurred. Hashem's name isn't written in the megillah. But Hashem's name is found in the roshei teivos and the sofei teivos such as the roshei teivos of יוםה המןו מלךה באי spell ה"הוי, and the final letters of יל השו ואיננ הז וכל, spell ה"הוי.
Kedushas Levi (Kedushah Rishonah) explains that this is because Hashem was concealed when this miracle occurred. And just as Hashem was concealed in the world, Hashem's name is concealed from the megillah. But Hashem and His name are clearly seen and recognized when one looks at the series of events that occurred. Therefore, in the roshei teivos and sofei teivos, which represent a series of several events, Hashem's name is seen.
The Maharal teaches that the simple translation of the word המלך in the megillah is Hashem. When we translate it to mean Achashveirosh, it’s according to drush. But the simple and literal translation of המלך refers to Hashem.
The proof of this is in the words (Esther 6:1), המלך שנת נדדה ההוא בלילה, "That night, the king's sleep was disturbed." The Gemara (Megillah 15:) states, according to Rav Tanchum, המלך is Hashem, Who couldn't sleep because it was time to save the Jewish nation. So, we see, according to Rav Tanchum, that the simple translation of המלך is the King, Hashem.
The holy sefarim say that whenever it states the word המלך alone in the megillah (and not two words like אחשורש המלך), it refers to Hashem, the King of the world.
It seems strange to us that Hashem should be alluded to when we mention המלך in the megillah, which refers to Achashverosh. Why should Hashem be alluded to, even in a concealed manner, when we discuss this rasha? The answer is as the Maharal explained: The simple translation of המלך is Hashem.
We think that Achashverosh or others were pulling the strings and causing events to happen, but המלך is our reminder that everything is from Hashem.
Purim and Hashem's Name in Nature
The Mishnah (Megillah 1:1) states, "The megillah is read on the 11th, the 12th, the 13th, the 14th, and the 15th [of Adar]; not later and not earlier.” Bris Kehunas Olam writes that the total sum of these dates equals 65 (11 + 12 + 13 + 14 +15 = 65), the same gematriya as י"אדנ. The name י"אדנ is Hashem’s name when Hashem runs the world through the rules of nature. We read the megillah on these dates, which are gematriya י"אדנ because the purpose of the miracle is to know that even a world led through the laws of nature is directly controlled by Hashem.
The Mishnah adds, יותר ולא פחות לא, "not earlier and not later." This means we can only read the megillah on the five dates, not the day before or after. The day before is אדר 'י, and the day after is ז"ט, which together is gematriya 26 (10 + 16 = 26), the gematriya of ה"הוי, Hashem's name alluding to miracles. We can't read the megillah on these days because on Purim, we aren't celebrating the revealed miracles, which are symbolized by Hashem's name ה"הוי. On Purim, we rejoice with the realization that even when everything appears natural, we know that Hashem is with us, directing every detail.