"KNOWING" = eidos of oida in Greek, a second perfect active participle, emphasizing the full consciousness of Christ -- seeing clearly, not stumbling in the dark with limited light or knowledge. Same verb of vs.1, therefore, as plainly as He knows it is now His Hour, He equally knows:

a.	His Authority is OF GOD,
b.	His Ancestry is IN GOD, and
c.	His Ascension is BACK TO GOD.

Here is another proleptic statement of John to Jesus that Jesus makes clear a short time later (without proverb). He knows and declares His Deity. (This is to refute the Gnostic's teaching.)

This is a very important point John makes, for he now contrasts Jesus condescending His lofty Heavenly Heritage to that of the lowliest servant. (Seen in removing His Jewish tallith as a sign of divesting His rightful position in Glory, to wear only the attire [tunic] of an attending slave on Earth, thus demonstrating one's duty to another.)

This is done to counter their earlier quarrel over position. He does what pride had previously prevented any from performing, as hospitable custom of that day required, generally done by the servant of the house. Clearly, then, we see in His teaching that pride is a barrier to one's service for another. Love can never be all that it can be, unless one is willing to do, without grudging, that most lowliest of deeds for the other, whatever it may be! To turn one's head away with an uplifted nose at that "everything but THAT" duty, is to deny the equality of your relationship and define the limitations of your love. Christ's love is limitless, so ours should be He pleads!
Therefore, limiting your love in service for another is not loving as He loved us, consequently, a clear violation of His commandment is seen. And, as we shall see later, when this is the case, the abiding relationship is seriously broken.

TRUTH:
JESUS TAUGHT MORE HEAVENLY LESSONS BY HIS ACTIONS THAN EVER BY HIS WORDS. (Had He never uttered a word in His life, His life was so lived there still would have been no question as to His identity, purpose, and Plan for the Ages.)

It is said of John in his later frail years that after being carried into Church services in the arms of others, he would weakly utter a one sentence sermon:  "Little children, love one another."
One weary soul is said to have asked why the same sermon repeatedly, to which he replied, "It is the Lord's command, and if this alone be done, it is enough!"

The disciples likely had fully bathed in the a.m. and all that was necessary here was the partial cleansing (as was customary) of their feet, dusty from the day's contact with the dirt of their travels. And so it is today with our own daily contact with the world after having received His full cleansing, a daily washing of that which has adhered to us from the world. Jesus then, and still today, comes to us for this cleansing, if we will accept. But know this: someday He will come as Judge for an accounting, too late for His cleansing mercy then.

Peter was a man of extremes, full of pride and impulsive ambition. His courage knew no bounds; his humility is pretense, however, and goes from refusing His Master's humble act, to requiring more of Him than Jesus deemed necessary. Remember the Baptist's earlier refusal to baptize Jesus? In both cases, Jesus is seen correcting man's misconceived sense of his own humility. This must be accomplished to render one fit for genuine service in God's Kingdom. Peter will later be overheard to say in essence: All that I am and all that I own, I owe to Christ, and that is all I have to give to any needy man, and so I give of whom I have, In Jesus' name... ( Mt.3:14, Mt.3:15, Acts 3:6)

Whereas the Synoptists record the event of the Lord's Supper, John chooses to stress its prerequisites:

With Judas present, it must be assumed that our Lord did not exclude him from this washing. This is an important point with many implications. Not only was He attempting to purge all of their pride, as earlier stated, but I see now a personal attempt to purge the leaven of the Pharisee (Hametz) from Judas' heart that He had previously warned them all of. This act is a barrier breaker between believers' hearts, causing old walls built upon years of pride to melt in this moment. In my youth, I myself have witnessed this scene played out in fellowship, and saw and heard long-standing, at-odds saints, reconciled in total by His Spirit. It was moving! Try as He might, Jesus was unable to melt this Judas' heart. They both knew there was enmity between them, risen from the leaven in Judas' own heart.

If Jesus is to be called Master, each one's heart must be clean and that life committed to others in genuine service, as Christ is seen here serving: nothing too lowly for one to do for another. His joy is only guaranteed to this one.