What Infinity Means to Me

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I have a habit of reading no matter where I am or what else I am doing. I read at my computer. I read on my phone. I read while waiting at the doctor’s office. I read in the bathroom. Lately I’ve been reading a book by Stanley Fish called How to Write a Sentence: And How to Read One. Several times he makes the claim that the number of sentences one could write is infinite. This is demonstrably untrue. The number of unique sentences one could write is certainly very large, but no mathematician would ever mistake a very large number for infinity. The fact is you can’t get an infinite collection of things using only finite collections for building blocks. For example, no matter how many molecules remain to be discovered, the total number of possible molecules cannot be infinite because the number of atoms is finite, and molecules are made up of atoms. In the same way, the collection of words is finite, so the collection of sentences (which are made up of words) must also be finite, even if we place no particular limits on the length of the sentences except that they must terminate.

The concept of infinity arises in set theory. A set is a collection of things together with a rule that tells us whether a thing belongs to the set. A set can be an explicit list: {coffee, butter, flour, sugar, tomatoes, eggs}. In this case the rule is: “If the thing is on the list, it is part of the set. Otherwise it is not.” Or a set can be defined by a rule: the set of all cats in the world. To see if something is in this set, we need only answer two questions: 1) Is it a cat? 2) Is it in the world? (We might also need to decide whether “cat” refers only to “small, domestic cats” or also to “big cats” such as lions, tigers, ocelots, pumas, bobcats, cheetahs, or other animals of the cat family, but we could in principle make such a decision ahead of time and use it to determine which things belong to the set and which do not.) One question we could ask about a set is how big it is. How many members does a set have? In the case of my shopping list, we can just count the items in the list and see that there are 6. In the case of cats in the world, we could in principle count the cats, but doing so raises a number of practical considerations. For example, how do we keep from counting the same cat more than once? How do we account for cats that are born or die while we are doing the counting? There may be 600 million small cats in the world. Counting them is going to take some time. Nevertheless, we know that having counted them, the number we obtain will be a natural number. We can say whether it is larger or smaller than the number of people in the world or the number of dogs in the world. We may not know exactly what the number is, but we know that it is a number we could count to if we counted long enough.

One of the things we know about the universe is that it is finite. It’s not hard to see why. If the universe were infinite, then the number of stars would be infinite; the number of galaxies would be infinite; the gravitational pull would be infinite; the light energy produced by all those infinite stars would be infinite. The night sky would be white if by some anomaly in the physics of the universe the earth were still pretty much as it is now. All of our experience of the universe is with finite things. Nothing is infinite. Everything is enumerable—at least in principle.

Infinity is an acknowledgement that some sets have no boundary on the number of elements they can have. However, those sets are themselves ideas only; they do not represent material objects.

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The Dead Man Came Out

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Allowing or Causing

Near the end of Batman Begins, Batman (Christian Bale) confronts Ra’s al Ghul (Liam Neeson) in a speeding train. After a fierce fight, it becomes plain that Batman has won, and Ra’s al Ghul expects to be killed. “Have you finally learned to do what is necessary?” he asks Batman. “I won’t kill you,” says Batman, “but I don’t have to save you.” That distinction, between killing and failing to save, is what sets Batman apart from the criminals and from the vigilantes in the League of Shadows. As the audience, we feel the justice in the distinction: killing a man is morally different from letting him die.

Or is it?

What about a doctor who refuses to perform a life saving operation on a child because the child belongs to a hated enemy?

Good Mary, Bad Martha?

I know about Mary and Martha from Luke chapter 10. Martha complained to Jesus because Mary was not helping her with dinner. Jesus rebuked Martha for her anxiety about many things and refused to make Mary help out. “Mary has chosen what is better, and it will not be taken away from her” (Luke 10:42). I’ve heard dozens of sermons echoing Jesus’ praise for Mary, making it easy to approach the story of Lazarus’ death and resurrection with the notion that Mary is good and Martha is bad.

Both sisters make the same accusation: “Lord, if you had been here, my brother would not have died.” I think it is important that we see this statement not just as a fact (Too bad you weren’t here; you could have done something) but as an accusation (Why did you delay coming? You could have prevented our brother’s death, but you didn’t). The sisters were hoping for a healing that never came. They knew that Jesus endangered himself by coming. The Jews were seeking his life. The last time he was in Judea, the crowd had picked up stones to stone him, but he had eluded them. So Jesus had good reason for not visiting at all. John makes it clear, however, that it was not concern for his life that held him up. Jesus deliberately let Lazarus die. He tells his disciples, “[F]or your sake I am glad I was not there, so that you may believe.” His purpose in letting Lazarus die was to strengthen the faith of his followers.

If a mere man were to do such a thing, we would be appalled. We would call him callous and unfeeling for letting a good man die so he could have a teachable moment with his followers. John intends to astonish us with Jesus’ audacity. Here is a man behaving in a way that only God is allowed to behave. Only God allows good people to die young without being guilty of wrongdoing.

There is a difference, though, between Martha’s accusation and Mary’s. Martha immediately follows up with an astonishing profession of faith: “But I know that even now God will give you whatever you ask.” What tremulous hope flickers in that affirmation! Even now. You could have prevented his death, but even now you can ask God for anything—anything!—and he will give it to you. Martha believes—incompletely to be sure, and with fear and trembling—that Jesus can raise her brother from the dead.

To make sure we don’t miss it, Jesus tells her, “Your brother will rise again.”

“I know he will rise again in the resurrection at the last day.”

Martha does what we all do. She tries to take comfort in knowing that her brother will rise again at the last day. But what comfort is there in the all-too-present grief from knowing that your loved one will live again in the distant future? Doctrine is cold comfort. It is also academic. Trust in that future resurrection may bring some comfort into the present, but we can’t test it in any meaningful way. What does it matter now whether the doctrine of the resurrection is true?

Jesus will not allow Martha to take refuge in doctrine. He tells her, “I am the resurrection and the life. He who believes in me will live, even though he dies; and whoever lives and believes in me will never die.”

Then, “Do you believe this?”

Do you really believe, Martha, that God will give me whatever I ask? Do you really believe that I am the source of all life? Do you really believe that death is not the end for those whose life is entrusted to me?

“Yes, Lord, I believe that you are the Christ, the Son of God, who was to come into the world.”

Martha makes her most extraordinary profession of faith. Her trust is not in cold doctrine but in the warm presence of the living Christ who stands before her. Trust in a person is so much more complicated than trust in a doctrine. The doctrine will always behave the same way. It will not ask more of you than you think you can do. It will not make any greater demand on you than to assent to its truth. But Jesus might do anything. He has already let Lazarus die. He can raise him to life. But will he? In declaring her faith in the person of Jesus, Martha allows him to be, really to be, in control of the situation. I trust you. Whatever you do will be right.

Martha returns to her sister, her heart poised on the knife’s edge of faith. She tells Mary that Jesus is asking for her, and Mary goes to him right away. Mary makes the same accusation as her sister, but there is no accompanying profession of faith. Both sisters share an offense against Jesus. We sent for you and you did not come. If you had been here, if you had only been here, our brother would not have died. You let him die. You could have prevented it.

The Offense

Jesus makes no excuses for letting Lazarus die. Elsewhere in John, Jesus claims to do only what he sees his Father doing, so we can assume that it was God’s will and purpose for Lazarus to die. Jesus tells us why: “[I]t is for God’s glory so that God’s Son may be glorified through it.” Lazarus will die for my glory. Jesus lets Lazarus die, lets Martha and Mary experience the grief of his loss, lets them experience doubt and anger and fear and turmoil, all to bring glory to his Father and himself. What kind of God is this, who aggrandizes himself at our expense? John tells us, “Jesus loved Martha and her sister and Lazarus. Yet when he heard that Lazarus was sick, he stayed where he was two more days.” Jesus loved them, and he let them suffer.

There is an important lesson here, especially for parents. Our natural inclination is to prevent our children suffering. We want to protect them and keep them safe. No matter how old they get or how capable they become, we want to keep them from getting hurt. But growing up requires suffering. No one can become mature without experiencing pain, loss, trouble, grief, despair, discomfort, sorrow, remorse,―the list of life’s hurts is endless.

Fortunately, Jesus shows us how to allow suffering. We do it with compassion, by suffering with those who suffer. The glory of God is not just in raising the dead. It is in dying with them and then raising them. It is not just in healing the sick. It is in being scourged and flayed for our healing. It is not just in delivering the prisoners. It is in descending into hell to deliver them. The glory of God is no light thing. It is weighty and majestic. God himself endures suffering to achieve his own glory. Should we be surprised if he asks us to suffer, too?

How easy it is to be offended at a God who allows suffering! How hard it is to trust him! Trusting God is work. It is not for the fainthearted. It is not for quitters. It requires persistent, unrelenting effort. But consider the rewards. “Therefore many of the Jews who had come to visit Mary, and had seen what Jesus did, put their faith in him.” Lazarus died. Martha and Mary grieved and were offended at God. But Jesus raised Lazarus from the dead, and many put their faith in him. The faith of those many was not possible without death and grief and offense.

“Did I not tell you that if you believed, you would see the glory of God?” Jesus asks Martha.

Many have become offended at God. They have buried their offenses to cover up the stench of corruption in their relationship with God. Jesus wants to call out the dead man. Allowing him to do so will be painful, but enduring that pain will result in lasting faith for ourselves and for others. In your suffering, seek God’s purpose, and allow him to glorify himself.

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Peter’s Reinstatement

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Peter was downcast after the initial joy of Jesus’ resurrection. He couldn’t forget that he had denied Jesus after boasting of his loyalty. Even though Jesus had anticipated his desertion, Peter knew he could no longer expect to be part of the new kingdom Jesus told them about. Like the other disciples, he still expected Jesus to seize power, oust the Romans, and make Israel great again. But for Peter there would no longer be a place at court on Jesus’ right or left hand. He had failed in the time of trial. He had proved disloyal and untrustworthy.

Peter still knew how to fish. So he returned to what he knew, and some of the other disciples went with him. Though not plagued with the same sense of failure, they did not know what was going to happen, and they needed to work to occupy their hands and thoughts. They spent the night fishing but caught nothing. In the morning, they saw Jesus standing on the shore of the lake, but they did not realize it was him.

Friends,” he called to them. “Don’t you have any fish.”

“No,” they answered.

He said, “Throw your net on the right side of the boat and you will find some.” When they did, they were unable to haul the net in because there were so many fish.

Then John said to Peter, “It is the Lord!” As soon as Peter heard him say, “It is the Lord,” he wrapped his outer garment around him (for he had taken it off) and jumped into the water. The other disciples followed in the boat, towing the net full of fish, for they were only about 100 yards from shore. When they landed, they saw a fire of burning coals there with fish already on it, and some bread.

Jesus said to them, “Bring some of the fish you have just caught.” So Simon Peter climbed back into the boat and dragged the net ashore. It was full of large fish, 153, but even with so many the net was not torn. Jesus said to them, “Come and have breakfast.” None of the disciples dared ask him, “Who are you?” They knew it was the Lord. Jesus came, took the bread and gave it to them, and did the same with the fish.

After they ate, Jesus took Peter aside and asked him, “Peter, do you love me more than these?”

Yes, of course, Lord,” said Peter. “You know that I love you.”

Feed my lambs,” said Jesus. Then he asked again, “Peter, do you love me?”

“Yes, Lord. You know that I love you,” Peter replied.

“Take care of my sheep,” said Jesus. Then he asked yet again, “Peter, do you like me?”

Peter was hurt that the Lord had asked the third time, “Do you like me?” He thought back on the years they had spent together, the wonders he had seen this man do, the conviction that had inexorably stolen over his heart that this man was somehow God. He said, “Lord, you know all things; you know that I like you.”

Jesus said, “Feed my sheep. Truly I tell you, when you were younger you dressed yourself and went where you wanted; but when you are old, you will feel your way, and someone else will dress you and lead you where you do not want to go.” Then he said to him in that no-nonsense tone Peter knew so well, “Follow me!”

Could it be true? Was Jesus really telling him that he still had a place for him? Wasn’t there someone else better suited to the task Jesus had in mind. He could see John obviously eavesdropping nearby. “What about him?” he asked Jesus.

If I want him to remain alive until I return, what is that to you? You must follow me.” Jesus replied.

Then Peter knew. He knew beyond doubt. Jesus had urged all the disciples to believe in him, and Peter had. His faith in Jesus had saved him, but what transformed him was Jesus’ faith in him.

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