In the world of statistics, sufficiency plays an important role in estimation. But what about sufficiency in other aspects of our lives? What about God? What about my eternal destiny? What is sufficient, here and now, to know all that I can know about my purpose in this world and my fate when my time here is finished?
The practice of statistics generally is limited to scientists actively engaged in research—but the impact of statistics is felt by all of us whether or not we realize its benefits. Consider an automotive engineer who studies design improvements to enhance vehicle safety: experiments are conducted, data are gathered, and with the many tools of the statistical sciences, inferences are extended from a sample of experimental vehicles to the larger population they represent. The end result is a safer automobile, as attested by higher collision survival rates than fifty years ago. Farmers are more productive today than ever before largely because of improvements in precision agriculture and enhanced genetic engineering that have been developed hand-in-glove with data analysis informed by statistical theory. All of the so-called STEM (Science-Technology-Engineering-Mathematics) programs offered by schools world-wide include in their curricula introductory courses in statistics, a strong testament to the importance of the subject in training the next generation of scientists. Indeed, much of the success of the scientific enterprise, generally considered, can be attributed to contributions from the field of statistics.
At the foundation of classical statistics is the concept of inference: the idea that, based on a (usually) small but representative sample, we draw an inference that is applied to a larger population of interest. This concept, once appreciated, reflects much of our every-day experiences and informs many of our decisions. My spouse, for example, suggests an evening meal at a new restaurant. Perhaps we’ve never eaten Thai food and so we try it. And our experience—our sample of the menu items—becomes the basis for a decision about future dining choices. In particular, whereas we did not sample everything on the menu, we nevertheless use our impressions of the items we did sample to guide a future dining choice about this cuisine.
To formalize the foregoing, we first consider a population of interest, something too large to census. For example, suppose our interest lies in blood cholesterol of 65-year old men, a large population by any measure. Because it is not practical to draw a blood sample from every 65-year old man, we decide to randomly select (say) 50 subjects from this population. We measure each subject’s cholesterol, calculate an average cholesterol level, and use it to estimate the average cholesterol for the larger population.
In the process, the 50 cholesterol measurements have been condensed, summarized, and expressed in a single number, the sample average. And we use the sample average cholesterol to estimate the unknown cholesterol level for the population of 65-year olds. The sample average is called a statistic.
Now, imagine two scientists, one of whom has all 50 cholesterol measurements on hand, the other only the sample average. It turns out that the scientist who has only the sample average (a single number) can estimate the true but unknown population average just as effectively as the scientist who has the full data set of 50 sample values. That is, there is nothing, no information, in the sample of 50 cholesterol measurements that can add to, or improve, our estimate of the true but unknown population average beyond what we know from our statistic, the sample average. At first encounter, this is a startling notion. One might think, for example, that knowing the smallest and largest cholesterol measurements in our sample might add to what we know from the sample average to help us improve our estimate of the population average. But this is not true: Whatever we can know about the population average is contained in the sample average. Statisticians have a name for this property of our sample statistic—the sample average is called a sufficient statistic for the population average.
In the world of statistics, then, all we need to estimate the population average is a sample average: it is sufficient. As a concept in statistical theory and a property of certain statistics, sufficiency plays an important role in estimation. But what about sufficiency in other aspects of our lives?
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What about God? What about my eternal destiny? What is sufficient, here and now, to know all that I can know about my purpose in this world and my fate when my time here is finished?
There is an echo in this question: its answer is heard by some in the phrase sola scriptura. All we need to know is contained in the Holy Scriptures, and there is nothing that can add to Holy Scriptures: Scriptura est sufficiens.
From one perspective, of course, this is true. The Bible is the Word of God and from it we learn about God, the world He brought forth, and our place in His creation. In Jesus’ time, before the New Testament was collected and formalized, the written word of God was recorded in the canon of the Old Testament. The Old Testament was Holy Scripture. Was it sufficient? This is precisely the question that the rich young man posed to Jesus: “Teacher, what must I do to inherit eternal life? (Matt. 19:16ff). Jesus answered first by appealing to the Ten Commandments, the Word of God as recorded by Moses. When the rich young man replied that he had done all these things, since his youth, Jesus responded with what has all the appearances of asserting that Holy Scripture was not sufficient—because He added to the Old Testament commandments: “Sell all you have and come, follow Me.”
The Gospel accounts don’t say what happened to the rich young man, except to add he walked away sorrowfully from the loving eyes of Jesus. But there is another poignant scene in the Gospels when Jesus showed us the way to eternal life. At Golgotha, the penitent thief turned to Jesus and asked to be remembered when He came into His Kingdom (Luke 23:42ff). And Jesus, by fiat, declared that he would be with Him that day in paradise. Whatever Jesus saw in the thief’s heart was sufficient for his soul’s salvation.
It is easy to say that the Son of God certainly can—and did—add to written scripture. His word, after all, is the Word of God. And it is also certain that the Word of God can be, and was, oral as well as written: in Old Testament times, at the time that it was spoken by Jesus, and as it was shared among his followers after His death. Jeremiah (25:7-8) and St. Paul (1 Thess. 2:13; 2 Tim. 2:2) both refer to the oral transmission of God’s Word. All of which is to say that Jesus Himself came to fulfill the Old Testament in the richest possible sense with His life, death, and resurrection.
And so (the usual argument goes), once Jesus fulfilled His earthly mission, then Scripture was settled: Holy Scripture was consummated in Christ Himself as recorded by the first generation of Christians and collected in the canon of the New Testament. St. Paul’s letter to Timothy: “All scripture, inspired by God, is profitable to teach, to reprove, to correct, to instruct…” (2 Tim. 3:16-17) often is presented as a justification of sola scriptura as codified in the New Testament.
Much has been written about the sufficiency of sola scriptura. Roman Catholics point out that nowhere in the Bible is this principle explicitly taught, and further, that some passages (e.g., John 21:25; 2 Tim. 2:2) actually tell us that what has been written is not a complete accounting of all that Christ taught. Protestants nevertheless accept sola scriptura with a counterargument that says, in effect, “Although the Trinity is not expressly taught in Scripture, Catholics accept it—and so we accept sola scriptura.”
Sola scriptura, its support and its criticisms, has a long history. The contentiousness of the claim likely will never be resolved and it is not the goal of this essay to explore its many facets and implications. Rather, the very fact that this idea has been embraced by so many believers testifies to a strong and sometimes desperate need for reassurance about what is sufficient in our lives.
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How many of us have asked “Have I done enough?”, a question that applies to so many instances in every-day life: students sitting down to a final exam in college; young professionals hoping for promotion in a career; parents watching their child leave home for the first time. These examples can be multiplied a hundred-fold during our lives. Often this is most poignantly expressed at the end of our lives. Like the scene at Calvary, it is imminent death that stirs the heart to its deepest longings and most earnest questions we can ask in this life.
Victor Hugo’s Les Misérables is the epic story of one man’s life-long attempts to rehabilitate himself, to atone for his sins. On his deathbed, Jean Valjean remembered Monseigneur Bienvenu and the candlesticks he had received from him many years earlier. He reflected: “I do not know whether he who gave them to me is satisfied with me in heaven,” a question that most of us should direct to our Father in Heaven about His countless gifts to us.
Jean Valjean answered his own question by affirming, “I have done what I could.” Christians know that this is not sufficient for salvation, else why did Christ die on the cross for our sins? And this leads to another point of difference among Christian denominations. So-called “born again” evangelicals rest in the assurance that, having accepted Jesus as their personal Lord and Savior, they are saved—that is sufficient for eternal life with God. The Catholic perspective draws a distinction between redemption and salvation, the former achieved for us by Christ on the cross and the latter conditional on our participation. St. Paul encourages us to “work to earn [our] salvation, in anxious fear” (Phil. 2:12), teaching that “All of us have a scrutiny to undergo before Christ’s judgement-seat, for each to reap what his mortal life has earned, good or ill, according to his deeds. (2 Cor. 5:10). We are told that God “…will award to every man what his acts have deserved” (Rom. 2:6).
Leo Tolstoy’s Ivan Ilyich spent a lifetime chasing after this world’s false hopes and as he lay dying he asked himself, “What if my whole life has been wrong?” And then he answered his own question: “But if that is so… and I am leaving this life with the consciousness that I have lost all that was given me and it is impossible to rectify it—what then?” In this compelling story, Ilyich’s “what then?” was followed by his encounter with sanctifying grace through the sacraments. Yet still he endured another attack of despair because of his wasted life, and three days of screaming agony followed. Whereas Valjean rested knowing that he “had done what he could,” Ilyich knew that this was not enough, knew “that he cannot save himself.” It was only when his young son kissed his hand that Ilyich “…caught sight of the light, and it was revealed to him that though his life had not been what it should have been, this could still be rectified,” rectified by accepting his pain and by embracing his death—he had, after all, confessed his sins and partaken of Christ’s body and blood: “There was no fear because there was no death. In place of death there was light.”
Our deeds, good or ill, what we have done during our lifetime: all of this matters. For Catholics, it must be remembered, the state of our soul at our death is paramount. But there’s more to our life than its end. Msgr. Romano Guardini explained this so well in his classic The Last Things when he wrote:
Death is the last part of human life. But for everything alive it is this last part which is crucial. Our nature is patterned on a process in which the end is part of the whole… The end determines all that precedes it… But in a deeper sense, if the end comes right, it is through the concurrence of the whole, and in a good ending the whole acquires its validity… death brings man’s life to its fulfillment.
This is the source of our deathbed regrets and fears, our hopes and prayers, and ultimately, our submission to God’s mercy. Ilyich finally realized, “So that’s what it is!… What joy!” It is no wonder that the prayer that provides the foundation of the Rosary concludes with a heart-felt intercessory petition known to all Christians: “Pray for us, now and at the hour of our death.”
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We recall our statistician who was interested in understanding more about cholesterol. She asked a simple question: “Considering all 65-year old men, what is the average cholesterol level?” What she needs to know is the population average but she realizes that to know this would entail measuring the cholesterol level of every 65-year man, a daunting prospect. But she also knows that she can estimate this unknown average from a much smaller collection of men: she draws a blood sample from 50 randomly-selected men. She sits at her desk looking at all these numbers on her computer screen, realizing that although this is just a small sample from her population, still, trying to absorb all the information in this array of 50 numbers is a little overwhelming: these values vary, of course, perhaps widely, and she wonders which value might best represent her population of interest. What can she do with the 50 measurements she has collected? She can condense all 50 numbers and summarize their information into a single number, the sample average. And with her understanding of statistics, she knows that everything that she can know about the population average, her ultimate goal, is contained and expressed in this single average sample value. It is sufficient for her purpose.
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Each of us longs to be welcomed into our Father’s outstretched arms hearing, “Well done, good and faithful servant” (Matt. 25:23). The greeting itself, of course, affirms that what we have done was both done well and sufficient for our eternal salvation. But what is it that is sufficient? What is it that must be done? Is it a memory-full of Bible verses? A life-time of good works and sincere penances? We return to the rich young man and the penitent thief and a story that Msgr. Ronald Knox wrote in 1928 in which he imagined that these two Biblical characters, both of whom encountered Christ personally, were one and the same. On his journey through Judaea, Jesus counseled the rich young man to give away all he had and follow Him; and at His journey’s end at Calvary, Jesus welcomed a penitent sinner who had acknowledged who He is and had asked to be remembered. What we learn is simply this: What is needed for the salvation of our soul is complete surrender to Jesus Christ: nothing can be added to this act of submission, and nothing can take its place—it is sufficient.
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1 Victor Hugo, Les Misérables, Vol. 5, Chapter 5, p. 1258. Modern Library Edition, 1992, Random House, New York, NY.
3 Leo Tolstoy, The Death of Ivan Ilyich, Chapter 12, L. and A. Maude (trans.), The University of Adelaide Library, University of Aidelade.
8 Romano Guardini, The Last Things: Concerning Death, Purification after Death, Resurrection, Judgment and Eternity, Chapter 1, p. 12, Pantheon Books, Inc., 1954, New York, NY.
9 Leo Tolstoy, The Death of Ivan Ilyich, Chapter 12, L. and A. Maude (trans.), The University of Adelaide Library, University of Aidelade.
10 Ronald Knox, The Rich Young Man: A Fantasy, Catholic Answers Press, 2016, El Cajon, CA.
Editor’s Note: The featured image is “Justice Between the Archangels Michael and Gabriel” (1421) by Jacobello Del Fiore (1370-1439), courtesy of Wikimedia Commons.