The Mathematics of the Atonement of Jesus Christ

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by Mike Clark © 2020


Note that this article is written in accordance with my understanding of the Gospel of Jesus Christ as taught by The Church of Jesus Christ of Latter-day Saints, of which I am a member. The contents of the article are my own work, and does not necessarily represent the view of the Church.


I have not seen Mel Gibson's movie, "The Passion of the Christ," except in part. However, I have read a number of reports about it, and have heard others describing it. One LDS film director, Kieth Merrill, who has seen it, commented upon the emphasis on Christ's physical punishment at the hands of the Romans. It is clear that Gibson's Catholic background is responsible for that emphasis, and that background is clearly fixated on the image of "Christ Crucified" - as graphically portrayed in the crucifixes that adorn their churches and homes. But Gibson's vision of Jesus' suffering, and the vision of Christ crucified as seen in many Christian portrayals of that suffering, certainly pales in insignificance to the "real thing."

While I am certain that the abhorrent violence inherent in the process of crucifixion was chosen as the means of Christ's suffering for a very good reason, that is, to enable us mortals who see only the flesh to appreciate what had been done for us, Christ's real battle, his real suffering was done where we could not see it, and it was massively worse than that what we did see.

The process of crucifixion is horrendous enough, but Jesus was not at it for particularly long. On the day of his death, it took some hours for the crucifiers to begin their work, involved as Jesus was with the sham trial by the Sanhedrin and in Pilate's failed attempt to brush off the dirty work onto King Herod Antipus. We can say approximately that this shuffling around took at least until mid-morning, and by the time Pilate's executioners began the torture it may have been as late as 10 or 11 o'clock, possibly even later. How long he was scourged is impossible to say, but it is clear that he would have been in very weakened condition at its conclusion, so the walk to Golgotha carrying his cross may have consumed a fair amount of time. So, by the time he reached Golgotha and was put on the cross, it may very well have been mid-afternoon, possibly around 2 pm. Since he died before sundown, which during that time of year would have been around 6 pm, he would have been on the cross less than 4 hours. Total time for the entire ordeal of crucifixion: approximately 8 hours.

A piece of cake.

Now, I don't want to minimize his suffering on the cross. It was truly horrible. But was it unique? Not at all. Christ survived about 4 hours on the cross; but others the Romans crucified survived much longer, sometimes even days. So he suffered far less than hundreds and perhaps thousands of others who were subjected to the same method of execution. Remember that the slave revolt led by Spartacus ended with the crucifixion of nearly all those slaves who had revolted; the Via Appia in Italy was lined for miles with crosses. So, in terms of degree of suffering, Christ suffered less from crucifixion than practically anyone else in the same predicament.

But what was the crucifixion to Christ? Merely the outward physical symbol of his real suffering, which was the passion of the Atonement. Christ did not need to die on the cross to achieve the Atonement. He didn't need to be scourged, either. In fact, if Jesus had not had the slightest externally imposed physical discomfort, he could have carried out the Atonement, and it would have been 100% effective. The suffering of the crucifixion had nothing whatsoever to do with the suffering of the Atonement, except that they overlapped somewhat.

The suffering of the crucifixion was to the suffering of the Atonement as a mosquito bite was to the suffering of the crucifixion. And then some. Before Jesus had even met his cross, we read that he was already suffering:

"And being in an agony he prayed more earnestly: and his sweat was as it were great drops of blood falling down to the ground. (New Testament | Luke 22:44)

Now, some point to this as evidence that Jesus was really dreading the experience to come, and this was why he was sweating profusely. In the Doctrine and Covenants we read however that he was sweating actual blood as a result of the agony he was already bearing – the suffering of the atonement had already started:

“Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit...” (Doctrine and Covenants | Section 19:18)

In the event, late on the evening of the Passover meal, apparently after he and the Twelve (minus one) had arrived at Gethsemane, he began to suffer the pains of the Atonement, and those pains were so bad that he considered ending the process:

“...and would that I might not drink the bitter cup, and shrink...” (Doctrine and Covenants | Section 19:18)

It is interesting, that when Christ himself describes the suffering he had to endure because of the Atonement, he doesn't mention the cross at all. And as I indicated above, the qualifications to suffer crucifixion on a cross during Roman times were set quite low. In fact, anyone could do it. But who could succeed at atonement?

The surprising answer is this: anyone can do it! If that one does not take advantage of Christ, that is. We see this in accordance with these words:

“Therefore I command you to repent – repent, lest I smite you by the rod of my mouth, and by my wrath, and by my anger, and your sufferings be sore--how sore you know not, how exquisite you know not, yea, how hard to bear you know not. For behold, I, God, have suffered these things for all, that they might not suffer if they would repent; But if they would not repent they must suffer even as I” (Doctrine and Covenants | Section 19:15 - 17)

So, everyone who does not repent will suffer it.

At this point someone will inevitably object. They will say that Jesus suffered the punishment of all sinners, or at least of all sinners who would repent; meaning that the suffering of Jesus was somehow additive, according to the numbers and severity of the sins the sinners committed. So, if there were a hundred sinners who committed a total of two hundred sins, then Jesus suffered the pains associated with atoning for those two hundred sins. And if there were a million sinners with two million sins, then he suffered for those two million sins. And so on. This is what Mel Gibson understands about it. That's why Gibson's hands are the hands that appear in "The Passion of the Christ" putting the nails into Jesus's hand. Gibson considers that it is his sins (along with everyone else's) that Jesus is suffering for; that Jesus is being punished with Mel Gibson's punishment, in the place of Mel Gibson. This is a very romantic and very picturesque notion.

It is also very wrong.

For if the suffering of Jesus through the atonement were additive as I have described above, then Jesus would have to bear the suffering that every single repentant sinner would otherwise have to suffer. That seems like a lot of punishment, but it turns out that this is completely inadequate for the task. It assumes that sin is like making a purchase at a store. Say milk costs $2.00 per gallon. If you have $4.00 you can get 2 gallons of milk. Likewise, if you committed some quantity of sins, you have to suffer some equivalent suffering in return. In other words,

More sins = more suffering.

The reason why I say that an additive punishment, or an additive atonement, or this much suffering for this much sin, is completely inadequate to fulfill the requirements of justice, is simply because it is merely huge. In fact, no amount of suffering done under this regime of punishment is adequate to fulfill the requirements of justice, and allow mercy to kick in. That requires an infinite atonement.

“For it is expedient that there should be a great and last sacrifice; yea, not a sacrifice of man, neither of beast, neither of any manner of fowl; for it shall not be a human sacrifice; but it must be an infinite and eternal sacrifice.” (Book of Mormon | Alma 34:10)

There's a special import attached to the word eternal here. In that same section of the Doctrine and Covenants, the Lord gives a definition of eternal, one which applies especially to Himself and his works. See D&C 19:6-12. I won't quote these verses in their entirety, but see where the Lord uses the word eternal in the sense that pertains to Himself, in verse 11:

Eternal punishment is God’s punishment.

So when it is written in Alma that "it must be an ... eternal sacrifice", we can replace eternal with God's. In other words, the great and last sacrifice must be the sacrifice of a God. And so Christ stands in our place to receive the punishment that we would have received without His intervention and without our repentance.

Where does infinity come into this?

As modern mathematicians are aware, infinity is a very slippery concept. Most people, when talking of something that is infinite, have the notion that it is simply something that is overwhelmingly large. It is not. It is quite literally beyond imagining. Adjectives like "large," "huge," or "enormous" completely fail to get a handle on it. In fact, infinity is not a number. It is utterly impossible to count to infinity, for example, because infinity cannot be reached. However, adding punishment to punishment in order to count up to enough punishment to fit the crime, can be reached, no matter how much punishment must be added, because it is finite. Therefore, like the animal sacrifices under the Law of Moses, it has no power to free us from our sins.

We read:

"Now there is not any man that can sacrifice his own blood which will atone for the sins of another. Now, if a man murdereth, behold will our law, which is just, take the life of his brother? I say unto you, Nay.” (Book of Mormon | Alma 34:11)

In other words, no man or woman can atone for the sins of another. A man or woman can atone only for his or her own sins. But as Alma 34:10 makes clear, the Great Atonement "...shall not be a human sacrifice..." but "...an infinite and eternal sacrifice...," in other words, the sacrifice of a God. In further words, the sacrifice of the unblemished and sinless Lamb of God, the Lord Jesus Christ. Because there is no sin in him, his sacrifice can only be voluntary; it is not forced upon him. In contrast to the unrepentant soul, who must suffer.

I said that an additive sacrifice is insufficient to save anyone from their sins, because it is finite. And this is because all sins are equal, and the punishment for all sins is the same. Like atonement, sin is not additive. A person who has committed only one sin is in the same place with the person who has committed a million. Both are sinners, both fall short of the glory of God, and both can only atone for their own sin. There is only one way out of the predicament for either of them. And what will happen to both if they don't accept Christ's atonement? Let's read DC 19:15-19 once more:

“Therefore I command you to repent – repent, lest I smite you by the rod of my mouth, and by my wrath, and by my anger, and your sufferings be sore--how sore you know not, how exquisite you know not, yea, how hard to bear you know not.”

You do not know how hard to bear this suffering will be -- Christ, however, does know, because he experienced it:

“For behold, I, God, have suffered these things for all, that they might not suffer if they would repent; But if they would not repent they must suffer even as I;”

When he says "suffer even as I" he clearly does not mean that his suffering was worse than yours will be if you do not repent; he means that you get to experience precisely what he experienced, in full measure. And what was the quality of suffering that he suffered and that you would have to suffer?

“Which suffering caused myself, even God, the greatest of all, to tremble because of pain, and to bleed at every pore, and to suffer both body and spirit--and would that I might not drink the bitter cup, and shrink—"

At no time in this passage of scripture is it even remotely suggested that Christ had to suffer more than any other. What makes Christ's sacrifice, his suffering, into the Great Atonement is simply expressed by this verse:

“Nevertheless, glory be to the Father, and I partook and finished my preparations unto the children of men.”

Because there is no sin in him, his sacrifice is infinite. And no matter how large the number of those who have sinned may be, his single, infinite sacrifice is enough for all who have faith in him, repent, and sin no more. Mathematically, this might be expressed in this fashion:

Because any amount of sin, whether one single act or a lifetime of wickedness, puts you irretrievably into the status of sinner, the number 1 may be used to quantify your sin. Because the suffering that you must endure to atone for yourself is the same for all quantities of sin, the number 1 may be used to quantify your suffering.

When you divide your suffering into your sin, as in the mathematical operation of division, the formula looks like:

1 ÷ 1 = 1

In other words, your suffering covers your sin, and you are "at one". Therefore, your personal atonement covers you and no-one else. On the other hand, the amount of sin that is imputed to the Christ during his mortal lifetime was 0. But the suffering that the Christ endured in the act of atonement has the value of 1.

When you divide the Christ's suffering into the Christ's sin, the mathematical formula looks like:

1 ÷ 0 = Infinity

In arithmetic, dividing any quantity by 0 yields a result typically called "undefined", because there is no way for nothing to divide into anything. But if one were to try to divide progressively smaller and smaller values into 1, the result gets mathematically larger and larger. Since one can never progressively reach the point of zero by making the divisor smaller and smaller, you will never reach the end of the attempt. But logically, one must infer that if we could take it far enough, to zero, then the result would be infinity. Since this is mathematically meaningless, our example breaks down under close scrutiny.

But because we not dealing with mathematics, strictly speaking, the example suffices to show what it means to have an infinite atonement. It means that Christ's atonement is sufficient to cover ALL sinners who will repent, regardless of how many that is. And because the Christ's suffering was something he could have ended at any time he wished to, without personal impact upon his own status, he demonstrated love beyond measure, both for the Father's plan and for his brothers and sisters. For that he deserves all glory for ever and ever.

For further reflections upon the Atonement, see The Roles of Justice, Sacrifice and Mercy in the Atonement of Christ.