Blessed are You, Adonoy our God, Ruler of the Universe, Who sanctified us with commandments and commanded us to be engrossed in the words of Torah.
(1) Hashem spoke to Moses and Aaron, saying: (2) This is the ritual law that Hashem has commanded: Instruct the Israelite people to bring you a red cow without blemish, in which there is no defect and on which no yoke has been laid. (3) You shall give it to Eleazar the priest. It shall be taken outside the camp and slaughtered in his presence. (4) Eleazar the priest shall take some of its blood with his finger and sprinkle it seven times toward the front of the Tent of Meeting. (5) The cow shall be burned in his sight—its hide, flesh, and blood shall be burned, its dung included— (6) and the priest shall take cedar wood, hyssop, and crimson stuff, and throw them into the fire consuming the cow. (7) The priest shall wash his garments and bathe his body in water; after that the priest may reenter the camp, but he shall be unclean until evening. (8) He who performed the burning shall also wash his garments in water, bathe his body in water, and be unclean until evening. (9) A man who is clean shall gather up the ashes of the cow and deposit them outside the camp in a clean place, to be kept for water of lustration for the Israelite community. It is for cleansing. (10) He who gathers up the ashes of the cow shall also wash his clothes and be unclean until evening. This shall be a permanent law for the Israelites and for the strangers who reside among you.
. והזה הטהור על הטמא, “the ritually clean person is to sprinkle on the ritually impure person, etc.” Rabbi Akiva derived from the words על הטמא "on the ritually unclean person" instead of simply עליו, “on him,” that the extra word teaches that if the ritually impure person was sprinkled with the ash/water mixture he would be purified by it, whereas if accidentally a ritually pure person was sprinkled with the same ash/water mixture such a person would become ritually impure as a result (compare Yuma 14).
In the time of giving of the Torah, laws like that of the Red Cow made sense to people based on their traditions, customs and understanding of the world. There is no reason to assume that the Torah's first audience was more mystified by the ritual of the Red Cow than we are mystified by the pageantry of halftime at the Superbowl. On reflection, the ancient Israelites surely saw the strangeness of the law, but they accepted it as "the way we've always done it." Even if they did ask, "What is the point of this?" the answer could only have been the same one we give about the Superbowl: "That's just the way it is."
Another attempt sees in the text an important psychological insight: the complete burning of an entirely red heifer represents the burning or destruction of any notion of perfection. It teaches us that perfection is an impossibility. While we are mandated to fulfill our obligations to God, to community and to humanity, to slaughter the perfect cow is to symbolically slaughter the notion that any of us can be perfect in these enormous undertakings. This message of the burning of the Parah Adumah is that just as God doesn’t seek perfection from us, it is not perfection that any of us should seek from others, or from ourselves.
This link between the Sin of the Golden Calf and the red heifer isn’t incidental. Even though Rashi believes that this is an ordinance that has no logical reason, and that we are required to carry it out without understanding it, he also finds a link between it and the great sin that occurred moments before the Torah was given. The Golden Calf isn’t meant to provide a rationale for the commandment of the red heifer. Instead, it is there to teach us that the people sinned because they weren’t able to cope with the unknown and with things they didn’t understand, “for that man Moshe, who brought us from the land of Egypt—we do not know what has happened to him.” When the Israelites follow the commandments concerning the red heifer, they are rectifying the sin of the Golden Calf and proving to themselves and Hashem that we know how to live our lives and keep the Torah’s commandments, even when we don’t understand them.
The red heifer is what purifies us, because of the simple and unquestioned faith it exemplifies – that it personifies proximity and belonging. This is the simple, innocent faith that the spies and those who complained at the beginning of Numbers lacked. There was still hope that the people entering the land would internalize this faith, taking it into the deepest reaches of their souls. When an impure individual goes through a process of purification, he or she demonstrates faith and perfect love, which makes it possible to achieve intense proximity later, bringing entire worlds into existence.

