According to the Midrash and Talmud (see chart below) each of these names means something. Their names representing various parts of the Temple service, Rabbi Moshe Meir Weiss points out, is another example of mida kineged mida, measure for measure. The advice to which the king is forced to turn brings about his queen’s eventual downfall.
Esther Rabbah 4:2 (first opinion)
In charge of king’s plants
In charge of king’s wine
In charge of king’s land measures
In charge of king’s household**Radal has “ships”
Made diced poultry for the king
Beat flour for the king
Provided food for the king
Adorned with beryls (tarshish)**According to Radal, ships traveled to Tarshish
13. And the king said to the wise men who know the times – since such is the way of the king before all those who know knowledge and justice.
According to the Talmud (Megillah 12b), the wise men whom the king approached after being insulted by his wife were none other than the Jewish Sages. The idea that they “know the times” means that our Sages are in control of the times and can have a hand in the calendar by, for instance, adding a thirteenth month (Adar Sheini) by declaring a leap year when necessary to balance the lunar months with the solar seasons (see Talmud, Sanhedrin 11b). Relevant to Tu B’Shvat this week, in the laws of orlah, a tree’s fruit cannot be eaten during the first three years of its life (Vayikra 19:23). The Sages’ ability to mandate a thirteenth month forces a farmer to wait an entire month longer for a tree to turn three years-old. We allude to this rabbinic power in our prayers. In the Musaf prayer of Shabbos (a day which cannot be set by the Sages) we say, “Blessed are You, H-Shem, Who sanctified the Shabbos,” whereas in the Musaf prayer of a Yom Tov (a day which can be set by the Sages) we say “Blessed are You, H-Shem, Who sanctified Israel and the times,” alluding to the fact that Israel can affect the calendar. Both the Ibn Ezra and Rav Dovid Feinstein add that, on a more mystical plane, the Sages were equally aware of astrology and which times have which spiritual energies (and how best to use these) as learned from Sefer Yetzira (Chapter 5).1
Rav Yehonoson Eibshutz writes that Achashverosh was hoping that the Sages, knowing these spiritual times as they do, would find that Vashti’s mazal (cosmic, spiritual influence) would allow her to live.
On a practical level, the Ben Ish Chai writes that the Sages could find ways to excuse any crime. For reasons too complex to explain here2, they were trained to do so because a unanimous decision would expatiate a perpetrator. In order to find a way to discredit a given exhibit of evidence, the Sages needed to then be completely aware of situations to best judge them.
As the Malbim writes, the Sages knew best how to apply laws to situations. The Maharal adds that a Sage, a righteous person by definition, always knows how to act under a given situation.
According to the Talmud (ibid.) the Sages found a way to not give advice because they realized that they were in a bind, a Catch-22. On the one hand, telling him to kill her as is expected of an insulted monarch may backfire and cause more Jew-hatred. On the other hand, sparing her meant subjecting Jewish women to untold humiliation under Vashti’s evil hands. To get out of having to give advice in this matter, the Sages simply pointed out that they could not judge capital cases ever since the Temple was destroyed. Rabbi Moshe Meir Weiss reminds us that one of the recurring themes of Megillas Esther is mida kineged mida, measure for measure. Here, Vashti’s halting the rebuilding of the Beis Hamikdash effectively ended her own life. Had there been a Temple, and it accompanying Sanhedrin, the Sages would have been able to pardon her.
1 My Rosh Yeshiva, Rav Yisroel Simcha Schorr, shlita, would often remind us that Pesach came before the exodus from Egypt. The time, itself, had the strength needed for an exodus. This is why Lot offered matzos to his visiting angels in Nisan (Bireishis 19:3, see Rashi there) before there was even an exodus to obligate the eating of matza. From the time of Creation, that time had the spiritual energy to be a vehicle for the Egyptian exodus.
2See Talmud (Sanhedrin 17a) for the details of this rule.