In my youth, I attended exclusively houses of worship (so to speak) associated with the Reform and Conservative Jewish Religions. Orthodox Judaism frightened me, so it never entered my mind to even enter a shul. Nonetheless, I knew that we shared one prayer: their prayer for the dead that begins "yisgadal v'yiskadash". Later I learned that only the old and Orthodox say "yisgadal v'yiskadash", while the modern/enlightened say "yitgadal v'yitkadash".
Since then, of course, I've learned that yis/yit is neither good measure of religiosity nor age. I have further learned that the entire prayer -- except those first two words -- is in Aramaic. (Oh, and also except for the last line, which is a direct quote from Iyov and is added to all requests because we always want our requests and actions to increase harmony in the universe.) Of course, we all understand using Hebrew, the Holy Tongue, for our prayers. After all, the Torah was given in Hebrew; so heck, if it's good enough for the Creator, it's good enough for us. But how did Aramaic -- the Aramaic of ancient Babylonia to boot -- have the merit to be used for one of our most precious and exalted prayers?
Tosafos (Brachos 3a, dh יהא שמיה הגדול מבורך) gives two answers. Tosafos first bring the most amazing idea from the Machzor Vitry: Kaddish is so very beautiful and important praise to HaShem. It is so beautiful and inspiring that we are fearful that the ministering angels well be jealous. Therefore, says the Machzor Vitry, Kaddish is expressed in Aramaic specifically because that is the one language that the ministering angels do not understand. Since they don't understand the prayer, they will not become jealous (and interfere). Wow. Cool. Says Tosafos: Maybe, but you want to know my opinion? Really, it is just because we know that the world continues in the merit of Jews saying יהא שמיה רבא (Sotah 49a) and Kaddish is recited after Torah lectures that are largely attended by Jews who didn't go to beis yaakov schools and so don't understand Hebrew. Therefore, to allow those attendants to recite יהא שמיה רבא properly, the Kaddish is formulate in the language of the common people -- Aramaic.
Quite a disagreement, no? Either because it is so exalted and beautiful we need to sneak it past the ministering angels, or because it is so mundane that even simple, uneducated Jews need to understand it. Seems unlikely to have such a vast difference in understanding.
The gemara on the previous daf had noted that there are three watches for the ministering angels in heaven, and that we know when they are. How? Donkeys bray during the first watch, dogs bark during the second, and during the third... babies want to nurse and wives start talking with their husbands. Again... huh? What do any of those things have to do with angels in heaven. The Maharsha says on that gemara, it means what it says: those mundane activities are associated with those spiritual changing of the guard. But... there is obviously a deeper meaning. He explains that these three watches are associated with the three dimensions of the soul: נפש/self-preservation, רוח/life force, נשמה/intellect. The first watch is that time when people are coming home from a long day and need to eat and drink/refuel their bodies; they are interested in their physical needs. Donkey in Hebrew is חמור, which is the same root as חומר, physicality. During the second watch, people are sleeping and are depending on their life force to keep them alive and when they are especially susceptible to the angel of death. Dogs bark around the angel of death, as we see that the dogs were quiet in the Jewish neighborhoods of Egypt during the last plague of makkos b'choros. During the last watch of night, one is refreshed and he can direct his mind to Torah (as long as he learns, he merits Torah; just as the suckling baby receives milk) and to prayer (he can ask HaShem for all his needs, just as a wife asks her husband for all her needs.)
The mundane and the spiritual are not contradictory, they are too sides of the same coin. Every action down here has an affect upstairs, every activity upstairs in reflected in an activity down here.