It states (19:2) תמימה אדמה פרה, "A perfectly red cow." Rashi explains that תמימה in this context means "It shall be perfect in its redness. Even two black hairs disqualify it." However, if it has only one black hair, the parah is kosher. It is still called תמימה, completely red.
In contrast, it states (Devarim 18:13) אלקיך 'ה עם תהיה תמים, "Be wholehearted with Hashem, your G-d." The same word is used, תמימה ,תמים, but there is a difference in the extent of temimus that is needed. The Chidushei HaRim zt'l teaches that when it comes to the temimus of the parah adumah, it can have one black hair, and it is still called tamim, entirely red. But as for temimus in our devotion to Hashem, one must be one hundred percent wholehearted with Hashem. Not even one hair of his essence should be left out.
We also add that when it comes to Torah study, one should be totally attached.
Purity of Torah Study
The Shlah (Chukas) writes, "Although we don't have the ashes of the parah adumah anymore, a person can purify himself...by studying, teaching, and keeping the Torah."
A non-kosher cooking utensil is kashered by purging it in boiling water (הגעלה). An even more thorough mode of kashering is to heat the cooking utensil in a fire (ליבון) until the utensil becomes red hot. The Or HaChaim zt’l (Rishon L’Tzion) teaches that these two approaches of kashering represent two paths people take to attain purity from their aveiros. One way is through yesurim, such as afflictions, fasting, etc. This method is compared to boiling water, which cleanses and purifies the cooking utensils from their non-kosher status. Learning Torah is a greater purifier because Torah is compared to fire. As it states (Yirmiyahu 23:19), דברי כה הלא כאש, “Behold My words are like fire.” Fire is an even greater form of cleansing and kashering.
Chazal (Brachos 63:) say, "Torah knowledge is found solely among those who are moser nefesh to know Torah, as it states in this week's parashah (19:14) באהל ימות כי אדם התורה זאת, 'Where do you find Torah? By those who die in the tents of Torah.'"
Dying for Torah means that one should study Torah with all his heart, soul, and energy. It means that he feels that his life has no purpose without Torah. If he doesn't know something, it bothers him immensely, like a part of his life is lacking.
This teaches us the attitude we should have when we study Torah. Torah should be studied with a passion to know it, and as Chazal tell us, only in this manner will we succeed in knowing Torah. This is the Torah's lesson with the words ימות כי אדם התורה זאת באהל.
But the question is, why is this essential lesson written specifically in the parashah of parah adumah? It could have been written anywhere else in the Torah!
The Rokeach explains that this tells us that studying Torah in this manner purifies a person. Just as parah adumah purifies, studying Torah as if one’s life depends on it cleanses as well.
Why is toil needed to attain purity? Why isn't it enough to study Torah nonchalantly? We can explain that it is because one needs to be immersed in Torah study. When one goes to a mikvah, he must be entirely immersed in the water. (If one’s hair is outside the water, he doesn't become pure. He must be wholly immersed in the water.) The taharah that comes from Torah study is also, ideally, when one is completely immersed in Torah study.
However, we must also know that even just a drop of connection with the Torah purifies immensely. Each line that one learns, each Mishnah, etc., purifies immensely. Perhaps a hint that even a tiny connection to Torah can purify someone is in (Yechezkel 36:25) טמאותיכם מכל וטהרתם טהורים מים עליכם וזרקתי אתכם אטהר גלוליכם ומכל, "I will sprinkle pure water upon you, and you will be clean; from all your impurities and all your abominations will I cleanse you." Even if one isn't entirely immersed in Torah but has a sprinkle of the purifying waters of Torah on him, this will purify him immensely.
Magen Avraham (580:9) writes, "It is written in kabbalah sefarim that it is proper for all Jews to cry when the Torah is burned because this causes Torah to be given over to the tumah. May Hashem return it to us quickly. Tzaddikim fast on the Friday of parashas Chukas. This is because in the year 5004 (1244 l'misparam), on Friday parashas Chukas, twenty wagons filled with sefarim were burned in France. They didn't establish the fast on the date of the month that this occurred because in a dream (shaalas chalom) it was revealed to them that the tragedy was associated with the parashah (parashas Chukas), as it states התורה חקת זאת, and Unkelus writes, אורייתא גזירת דא, 'This is the decree on the Torah.' Also, in the year ח"ת, two large communities were destroyed on this Friday, as is written in the Selichos composed by the Shach."
We don’t fast in these generations, but Friday, parashas Chukas, is a day to increase our respect and honor for the Torah. One way to do so is to toil in Torah and make plans to improve our attachment to it. One of the benefits will be the taharah that we will attain from it.