Psalm 51 is called "A prayer of repentance".

Its heading says it is a psalm of David from when Nathan the prophet reprimanded him after he had gone in unto Bathsheba. It's a cry of despair, full of deep repentance and the plea to be cleansed from the sins he has committed. The psalm shows a clear pattern through its words; by openly acknowledging the sin the speaker gets more understanding about the way of the Lord and about life. The psalm also shows a growing assurance and trust in the Lord and his acceptance of this cry.

This psalm, at a deeper level, also describes Jesus’ prayer to overcome the sins of his human nature which he took upon himself in becoming human. The Lord, unlike David, didn't give into temptations – John 8:46 has the Lord asking, “Which of you convicts me of sin?” – so His prayer is to have the strength to withstand the tendencies inherent in his human nature. The Lord was severely tempted in his humanity.

For us, this psalm is one we can relate to and feel is our own prayer when we see the ways in which our thoughts rise up out of our self-love or our proprium (our selfhood). True repentance is not remorse for some wrong we have done, although this can be part of our spiritual progress; it has far more to do with us giving our attention to thoughts and moods which suddenly rise up and plague our intention to be true to the Lord. (Divine Providence 121, 122)

This psalm mentions things which have to do with the Lord and things which have to do with us. Words like "mercy, loving kindness, just, judge, washing, presence, and good pleasure" speak about the Lord, while "transgressions, iniquities, evils, and sins" speak about us. The overall idea is that the Lord longs to give to us what is his, so that we know he is there with us and that he completely understands our human frailty. In being what we are like in ourselves, we will keep going astray. We continually need to bring ourselves before the Lord to be restored.

The Lord’s mercy is the His wish to save us and regenerate us, so that we will be drawn - and wish to be drawn - to heaven, which is where the Lord is. Mercy is not instant in its activity, but it is perpetual. (See Heaven and Hell 522)

‘Washing’ is another divine quality, but we need to be careful in understanding it. It is not the Lord washing our wrongs away as if they had never been done. Our wrongs may need to be brought back to us, not to taunt us, but to remind us of our need of the Lord and our wish to do no more wrongdoing. The true idea of washing is for us to ‘wash ourselves’ and to feel we have been washed, so that we can go forward stronger than we were. (See Divine Providence 151 and Apocalypse Explained 475.5)

‘Transgressions’ are evils we might do which come from a perverted understanding. (Arcana Caelestia 9156)

‘Iniquities’ are evils we do intentionally because we have twisted our thinking to justify doing them (Apocalypse Explained 475)

‘Evils’ are what we do because we are born with an imperfect human nature. (See The New Jerusalem and its Heavenly Doctrine 79 near the end)

‘Sins’ are evils we do intentionally because a love of evil has taken hold of us. (Arcana Caelestia 5726)

The phrase “Purge me with hyssop” means being cleansed by external truths or truths which we see and which confront us, demanding that we correlate our life to them. (Arcana Caelestia 7918)

The phrase “Let the bones which you have broken, rejoice” is describing the appearance to us that during temptation the Lord has broken us, whereas the very opposite is true, that the Lord is defending us and being our bones. So in truth, we may rejoice. ‘Bones’ spiritually mean truths because bones support the body and truths the spirit. (Arcana Caelestia 3812.8)

Overall, this is a psalm which, for us, can help us move on from seeing the number and range of our imperfections through to understanding, appreciating and acting on the truth that the Lord can and will lead us to restoration and wholeness if we go to Him.

167. And all [the churches] shall know that I am He that searcheth the reins and hearts, signifies the acknowledgment of all who are of the church, that the Lord alone knows and explores the exteriors and interiors, and the things that are of faith and love. This is evident from the signification of "searching," as being, in reference to the Lord, that He alone knows and explores; also from the signification of "reins" as being the truths of faith and their purification from falsities (of which in what follows); also from the signification of "hearts," as being the goods of love. "Heart" signifies the good of love, because there are two things that rule in man, and from these is the whole life of his body, namely the heart and the lungs. And as all things in man's body correspond to the things that are in his mind, there are two things also that rule there, namely the will and the understanding. These two kingdoms of the mind correspond to the two kingdoms of the body, namely the will to the heart and its pulse, and the understanding to the lungs and their respiration. Without this correspondence the body could not live, not even a particle of it. As the heart corresponds to the will, so it corresponds to the good of love; and as the lungs correspond to the understanding, so they also correspond to the truths of faith. It is from this correspondence that "heart" signifies love, and "soul" signifies faith. It is from this that the expression "from the heart and soul" is so often used in the Word, by which is meant from love and faith. (As this correspondence is much treated of in the Arcana Coelestia, these things may be seen more fully explained there, namely, that "heart" in the Word signifies love; and because it signifies love, it also signifies the will, n.2930, 3313, 7542, 8910, 9050, 9113, 10336. That the heart corresponds to the things that are of love with man, and the lungs to the things that are of faith with him, n. 3883-3896. That in heaven there is a pulse such as that of the heart, and a respiration such as that of the lungs, n. 3884, 3885, 3887. That the pulse of the heart there is in accordance with the state of love, and the respiration of the lungs in accord with the state of faith, n. 3886-3889. That the influx of the heart into the lungs is like the influx of good into truth, and like the influx of the will into the understanding; it is also according to the influx of love into faith, and there are like communications and conjunctions, n. 3884, 3887-3889, 9300, 9495. Of the influx of heaven into the heart and into the lungs, from experience, n. Arcana Coelestia 3884. That from this the correspondence in the Word, "from the heart and soul" signifies from love and faith, n. 2930, 9050. That the conjunction of man's spirit with his body is by means of the respiration of the lungs and the pulse of the heart, and that therefore when these cease man dies as to the body, but lives as to the spirit, see in the work on Heaven and Hell [n. 521]; and that when the pulse of the heart ceases the spirit is separated, because the heart corresponds to love, which is the vital heat, n. 447, in the same work. Many other things respecting this correspondence, see n. 95.) "Reins" signify the truths of faith, and their purification from falsities, because the purification of the blood is performed in the reins and "blood" in the Word signifies truth (as may be seen in Arcana Coelestia 4735[1-15], 9127). The like is signified by the organ that purifies; and all purification from falsities is effected by truths. From this it is clear what is signified in the Word by the expression, that Jehovah, or the Lord, "searcheth the hearts and reins," namely, that He explores the truths of faith and the goods of love, and separates them from evils and falsities.

[2] This is signified by "reins" in the following places. In Jeremiah:

Jehovah Zebaoth, Judge of righteousness, trying the reins and the heart (Jeremiah 11:20).

In the same:

Thou hast proved ¹ them, yea, they have taken root; they grow, yea, they bring forth fruit: Thou art near in their mouth, and far from their reins. But thou, O Jehovah, Thou shalt see me, and shalt prove my heart (Jeremiah 12:2, 3).

"Near in the mouth and far from the reins" is truth in the memory only, and in some thought therefrom when man speaks, but not in the will and from that in act. Truth in the will and from that in the act is what separates and dissipates falsities. Truth in the will and from that in the act is willing and doing what a man knows and thinks to be true; such truth is what is especially meant by "reins."

[3] In the same:

I, Jehovah, search the heart, I prove the reins, even to give every man according to his ways, and according to the fruits of his works (Jeremiah 17:10).

"Searching the heart" is purifying good by separating evil from it; "proving the reins" is purifying truth by separating falsity from it; it is therefore said "to give to every man according to his ways, and according to the fruit of his works;" "ways" are the truths that are of faith, and "the fruit of works" are the goods that are of love. (That "ways" are truths that are of faith, see above, n. 97[1-2]; and that "the fruit of works" are the goods that are of love, n. 98, 109, 116.)

[4] In the same:

Jehovah Zebaoth, that provest the righteous, that seest the reins, and the heart (Jeremiah 20:12).

And in David:

Establish Thou the righteous; for Thou that provest the hearts and the reins art a righteous God (Psalms 7:9);

"the righteous" are those who love to do what is true and good, their goods and truths are purified by the Lord, which is meant by "seeing" and by "proving the reins and the hearts."

In David:

Prove me, O Jehovah, and try me, explore my reins and my heart (Psalms 26:2).

Because truths are separated from falsities and goods from evils by means of temptations, it is said, "Try me." In the same:

My heart is in a ferment, and I am pricked in my reins, but I am foolish and know not (Psalms 73:21, 22).

The infestation of good by evil and of truth by falsity is described by these words. In the same:

Behold, thou desirest truth in the reins and in the hidden part thou makest wisdom known to me (Psalms 51:6).

Here there is another word in the original for "reins," that includes the separation both of falsities from truths and of evils from goods. This shows that the "reins" signify purification and separation.

[5] In the same:

I will bless Jehovah, who hath given me counsel; also my reins chastise me in the night (Psalms 16:7).

"Night" signifies the state of man when falsities rise up; the consequent combat of truths with falsities is signified by "my reins chastise me." In the same:

Even the darkness doth not make darkness before Thee, but the night is lucid as the day; as the darkness so is the light. For thou possessest my reins, my bone was not hidden from Thee when I was made in secret (Psalms 139:12, 13, 15).

"Darkness" means falsities, and "light" truths; to "possess the reins" is to know falsities and truths with man; therefore it is said, "my bone was not hidden from Thee when I was made in secret," which signifies that no falsity that was made was hidden. (That "darkness" means falsity and "light" truth, see in the work on Heaven and Hell 126-140; and that "bone" means truth in the ultimate of order and in the contrary sense, falsity, Arcana Coelestia 3812, 5560, 5565, 6592, 8005.)

[6] As "the reins" signified truths purified from falsities, so:

In the sacrifices, the fats and reins alone were offered up (as may be seen in Exodus 29:13; Leviticus 3:4, 10, 15; 4:9 and elsewhere).

Fats and reins alone were offered upon the altar because "fats" signified the goods of love, and "reins" the truths of faith. (That "fats" or "fatnesses" signify the goods of love, see Arcana Coelestia 353, 5943, 6409, 10033. That the "reins" signify the truths of faith, examining, purifying, and rejecting from themselves falsities, is from correspondence; for each and every thing of the body corresponds, as can be seen in the work on Heaven and Hell, where this is shown in its chapter entitled, There is a Correspondence of all things of Heaven with all things of Man, n. 87-102; and on the Reins, n. 96, 97.) Unless it be known that there is such a correspondence, who could ever know why it is so often said of Jehovah or the Lord in the Word, that "He searcheth and proveth the reins and the heart?" (On the correspondence of the reins, of the ureters, and of the bladder, see further in Arcana Coelestia 5380-5386.) To "search the reins and the heart" signifies also to explore the exteriors and the interiors of man, because truth is without and good is within; and spiritual good, which in its essence is truth, and in particular is signified by the "reins," is exterior good; while celestial good which in particular is signified by the "heart," is interior good. (This can be seen more fully from what is shown respecting The Spiritual Kingdom and the Celestial Kingdom, in the work on Heaven and Hell 20-26.)

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