Parshas Chukas begins with three mitzvos concerning death, impurity that ensues there from, and the purification process of sprinkling the ash of a parah adumah mixed with water after three and seven days in order to attain purification. Today, unfortunately, we do not yet have the eifer ha'parah for the sprinkling of a parah adumah.
The Torah does not explain tumas meis - the impurity that is emitted from a deceased person. Perhaps it could be explained that just as in life there are levels of holiness and sanctity, similarly in the absence of life there is a vacuum and a spiritual void commensurate with the degree of holiness that an individual had achieved. The more holiness, the greater the observance of Torah and mitzvos and the greater one's personal interaction with their fellow man, the more tumah - impurity will be created after death.
The Shelah Hakadosh (in Derech Chayim on Parshas Chukas) teaches that in the absence of the parah adumah, the learning and living of Torah serves as the purifying factor in our lives. He explains that in addition to the literal understanding of the sprinkling of the parah adumah water on the third and seventh days, the Torah was given on "day three" and enables us to attain "day seven". This comment of the Shelah is referring to the teaching of the Ramban (Bereishis, beginning of chapter 2) where he broadens our mystical horizons and demonstrates that the six days of creation correspond to the six millennia. On the third day, that is, in the third millennium of world history, we received the Torah and it enables us to attain immortality of the soul, symbolized by the seventh day of total Shabbos.
That "Torah is life" may be seen from many references in the Chumash. The Torah says, "you shall observe My decrees and My laws, which man shall carry out and by which he shall live - I am Hashem" (Vayikra 18:5). Rashi and the Targum both understand this verse to refer to life in Olam Habah. This is akin to the Talmud's (Eruvin 22a) explaining the passuk, "hayom l'asosam" (Devarim 7:11) to be teaching that today, i.e. this world, is for performing mitzvos, and tomorrow, i.e. the world to come, is for receiving reward.
The Gra (in Aderes Eliyahu) understands the verse cited above (Vayikra 18:5) to refer to this world. The Torah is therefore teaching that even though the very nature of Torah and mitzvos sustains life, one is not to perform them with a personal, physical benefit of attaining life in mind, but rather as the verse ends, "Ani Hashem - I am Hashem", do it because I commanded it. Similarly, he says given the reality highlighted by the text of every bracha recited prior to performing a mitzvah, "asher k'dishanu b'mitzvosav - Who has sanctified us with His commandments", one might be excited to perform the mitzvah to receive holiness and spirituality, therefore the text continues, "v'tzivanu - and He commanded us", instructing us to do the mitzvah for no ulterior motives, be they physical or spiritual.
In Nefesh HaChayim (book 4, chapter 29) the primary student of the Gra, Reb Chaim of Volozhin, quotes the Zohar saying that the 613 mitzvos correspond to the 613 physical components of the body (limbs, sinews, etc.). When one fulfills a mitzvah he sanctifies and invigorates that corresponding organ and part of the body. He follows in the path of his rebbe and understands "v'chai bahem" most literally.
It is interesting to note that the world as we know it is functioning in the b'dieved - second best, or plan B - mode. Initially, man was to be eternal, and the phenomenon of death was not to be in this world. Adam and Chava sinned, however, and death became part of life. We were given a second chance at Sinai, as the Gemara (Avodah Zarah 22b) teaches that at Sinai "paska zu hamasan - the impurities and negative consequences of sin were removed from them." Upon receiving the Torah the nation of Israel was, "kulach yaffa ra'ayazi u'mum ein bach - beautiful my beloved, blemish free." This is understood by Chazal to mean that all the sick were healed at Sinai and the Torah literally revitalized them. Had they not sinned with the golden calf, man could once again live eternally. Such is the power of Torah.
In addition, not only does Torah fill the void of spirituality that sets in as a result of death, thereby emulating the eifer ha'parah (the ash of the parah adumah that was to be sprinkled on the third day), but it also serves as the vehicle for future resurrection. The Gemara (Kesubos 111b) cites Isaiah (26:19), "hekitzu v'raninu shochnei afar ki tal oros talecha - awake and shout for joy you who dwell in the dust, for your dew is like the dew on fresh ground" and homiletically explains it to mean that your light, Torah, is what will resurrect you and once again give you life. The Talmud states quite unequivocally that a Jew who is not connected to Torah will not be resurrected. When the Torah says (Devarim 30:20), "for He is your life and length of your days" this is no exaggeration!
The Gemara (Brachos 61b) relates that when it was decreed by the Romans that the Jewish people should not study Torah, Rabbi Akiva defied the edict by teaching Torah publicly. He offered a parable to explain what this situation may be compared to: a fox was walking along a river saw fish gathering from place to place as if constantly fleeing. The fox asked them who they are running from to which they responded that they are fleeing the nets that people bring to capture them. The fox said that the fish should come onto dry land and be safe from the nets. The fish replied that the fox can't be the most clever of the animals, rather he is but a fool. If in the natural climate, water, that sustains a fish's life, they are afraid, then certainly they cannot live on land without water. So too, Rabbi Akiva said, we must continue to engage in Torah which is chayecha v'orech yamecha - our life and length of days, and if we desist from Torah, we would be all the more in danger.
It is no coincidence that we find in the midst of the laws of tumas meis regarding how impurity is transmitted to people, food and utensils, the statement (19:14), "zos haTorah, adam ki yamus b'ohel - this is the law regarding a man who dies in the tent." On the surface the introductory words, "zos haTorah" seem extraneous. The Gemara (Berachos 63b) learns from this a very essential point for the study of Torah: "the words of Torah are only retained by one who kills himself for it" i.e. by one who sacrifices for Torah. Torah is not to be studied casually over a cup of tea.
The Torah frames the purification process by saying, "he shall purify himself with it on the third day and on the seventh day." Torah, given on the third day-millennium purifies one and sets the stage for the seventh day of eternity of the soul. "But if he will not purify himself on the third day and on the seventh day, he will not become pure."
The parsha begins with "zos chukas haTorah" even though it really should have said "zos chukas haparah." I believe that an additional level of understanding in this passuk is that only "zos chukas haTorah" is going to keep us tahor as a people throughout the millennia.