The God Who Draws in Curves

A Challenge Posted in 1696

In June 1696 the Swiss mathematician Johann Bernoulli printed a puzzle in the journal Acta Eruditorum and invited the best minds in Europe to solve it. Take two points, one higher than the other, and join them with a track. Let a bead slide down the track under gravity alone, with no friction to spoil the sums. What shape of track gets the bead from the top to the bottom in the least time? He gave the problem a Greek name, the brachistochrone, from words meaning shortest time.

Most people who hear it give the answer you would give. A straight line. It is the shortest distance between two points, Euclid says so, and a Lagos driver who has never opened Euclid will tell you the same. Surely the shortest road is the quickest.

It isn’t.

Galileo had half seen this already. According to the St Andrews history of the problem, he showed in 1638 that a path bent into two straight pieces can beat the straight line from the same start to the same finish. Then he overreached and decided the very quickest path must be a circular arc. He was wrong. The true answer, the one Bernoulli was fishing for, is the cycloid, the curve traced by a point on the rim of a rolling wheel.

Bernoulli had planned to give six months, and Leibniz persuaded him to allow longer, so the deadline was stretched to Easter 1697. Isaac Newton heard about the puzzle at four in the afternoon on 29 January 1697, by the usual account, and had finished by four the next morning. He sent his solution in without his name. It was printed anonymously in the Philosophical Transactions of the Royal Society, and Bernoulli is said to have known the author at once, as one knows a lion by its claw. Jakob Bernoulli, Leibniz, Ehrenfried von Tschirnhaus and the Marquis de l’Hôpital also answered, and Johann, who had set the puzzle, reportedly needed about two weeks for his own solution. That made five solutions in all.

I have lingered on the history because it is a good story, but the story is not why it matters. The Bible has been saying something very like this about roads for far longer than mathematics has.

Why the Straight Line Loses

The cycloid wins because of what happens at the start. It drops steeply at first, so the bead picks up speed early, and then it carries that speed across the flatter stretch that follows. The straight track is shorter, but the bead on it spends too long going slowly. Distance was never the only thing that counted. Speed along the way counts too, and the curve is built to buy speed early and spend it later.

Anyone who has driven from Ibadan to Lagos on a Friday evening knows a version of this. There is always a driver who leaves the expressway for a side road because it looks shorter on the map, and who is not seen again until you are home. The shortest line on the map and the quickest line through the traffic are two different lines.

I want to suggest that God knows this about the roads he sets in front of us, and that a good deal of our praying is a request for the straight line.

God Chose the Longer Road to Canaan

Look at what happens as Israel leaves Egypt. There was a direct way into Canaan. Archaeologists call it the Way of Horus, an ancient road lined with Egyptian military fortresses that connected Egypt and Canaan (Windle, 2022). Scripture’s name for it is the way of the land of the Philistines. And here is what the text says about the choice.

“When Pharaoh let the people go, God did not lead them by way of the land of the Philistines, although that was near. For God said, ‘Lest the people change their minds when they see war and return to Egypt.’ But God led the people around by the way of the wilderness toward the Red Sea.”

— Exodus 13:17 to 18 (ESV)

Notice what the verse does not say. It does not say God overlooked the near road. It says he saw it, called it near, and still turned the people away from it, because he knew what they would do at the first sign of a fight. A people who had spent centuries as slaves were not ready to meet a war on their third day of freedom, and God, who is wise as well as all knowing, preferred a road that would form them to a road that would only shorten them.

And the road he chose ran straight into the sea. The crossing of the Red Sea, in the very next chapters, was not an obstacle placed on the route. It was the route. The psalmist remembers it this way.

“Your way was through the sea, your path through the great waters; yet your footprints were unseen.”

— Psalm 77:19 (ESV)

Nobody on the shore could see a path in the water. It was there all the same.

I should be honest about the limits of the comparison. The wilderness didn’t cure Israel. When they reached the edge of Canaan a generation later, ten of the twelve scouts brought back a report of fear, and the forty years that followed are tied in the Book of Numbers to that refusal. The long road was not a guarantee that everyone on it would grow. It was a road on which growth was possible, which is a different thing, and the text offers more than one reason for the wilderness years. But the first choice, at the start, was a deliberate one. God picked the curve over the line on purpose.

Thirteen Years Between the Pit and the Palace

If you had told Joseph at seventeen that his road to the throne room ran through a dry cistern, a slave market, a steward’s house and a prison, he would have asked you to leave. Politely, perhaps. He would have pointed at his father’s coat.

Genesis tells us he was seventeen when his brothers turned on him, and thirty when he stood before Pharaoh. That is thirteen years. We tell the story in a few minutes and so we feel nothing of it. Thirteen years is the whole of a young man’s twenties and the end of his teens, and for a long stretch of it the only visible result of his faithfulness was another locked door.

When the road finally arrived somewhere, Joseph read it back to his brothers in one sentence.

“As for you, you meant evil against me, but God meant it for good, to bring it about that many people should be kept alive, as they are today.”

— Genesis 50:20 (ESV)

The Hebrew behind “meant” is the same verb in both halves of the sentence. The brothers planned something and God planned something, over the same events, and the second plan was the one that stood. Joseph does not say the brothers were innocent, and he does not say the pit was pleasant. He says the pit was inside a larger design, and that he can see it now only because the road is behind him.

Seventy Years in Babylon

Most of us have met a famous sentence from the book of Jeremiah on a mug or a graduation card, the one about plans for welfare, a future and a hope. The sentence is true. It is also part of a letter written to people who had just been marched to Babylon, and the verse just before it sets the timetable.

“For thus says the Lord: When seventy years are completed for Babylon, I will visit you, and I will fulfill to you my promise and bring you back to this place.”

— Jeremiah 29:10 (ESV)

Seventy years. Many of the people who first read that letter would not live to see the end of it. God’s plan for their welfare ran through a long exile in a foreign empire, and the letter itself told them to settle in and build, which is not what anyone says to a people expecting rescue by Friday. In the next verse the promise of a future and a hope is made to people who would have to wait for it across a generation. The line from the mug is still there, but it has a long road attached to it.

What Some Churches Promise Instead

There is a stream of Pentecostal teaching in West Africa, and in the diaspora churches that watch it by satellite and stream, that treats the curved road as a malfunction. I should say what it gets right before I say what it gets wrong. Its strongest case goes like this. The Bible is full of sudden reversals. Walls fell at Jericho, the sick were healed in a moment, a widow’s jar did not run dry. People in Nigeria are tired of being told that poverty is a form of holiness, and a gospel that tells them God wants them to flourish is a relief to a person who is watching the price of garri go up. The anthropologist Daniel Jordan Smith, writing on the Nigerian prosperity churches, notes that members credit them with practical gains such as business opportunities, school admissions and housing (Smith, 2021b). That should not be waved away.

The scale of the belief is also real. Christianity Today reported in 2007 on a Pew Forum survey from 2006 in which 95 percent of Nigerian Pentecostals agreed that God will grant material prosperity to all believers who have enough faith (Christianity Today, 2007). I have not found a more recent figure that I can verify, so I leave that one as a snapshot of what was already widely believed.

My quarrel is with one inference. If God gives prosperity to people who have enough faith, then the person who is still waiting must not have enough. Delay becomes evidence against the believer. And Joseph’s thirteen years, Israel’s wilderness and Judah’s seventy years all become, by that logic, a record of people who failed to pray hard enough. Smith has described a related puzzle in his own work. These churches voice real anger at government corruption, he writes, while also offering what he calls “divine justification for the pursuit and accumulation of wealth” (Smith, 2021a). A theology that sorts people into the blessed and the insufficiently faithful will do that sorting wherever it finds them, including on the platform.

I am not arguing against miracles. God does shorten roads. What I won’t accept is a theology that reads every long road as a punishment, because it teaches people to misread their own lives. It tells the believer in her third year of waiting that something is wrong with her, when the Bible would have told her that something is being done in her.

The Cross Was the Route All Along

If you want the ultimate case of God declining the straight road, leave Joseph and Moses and go to Calvary.

The incarnation is already a curve. The one who spoke the world into being came into it as an infant, in a province of the Roman Empire, to a young woman from a town people made jokes about. He could have arrived differently, and didn’t. He chose to come small.

And then he told his disciples where it was going.

“Far be it from you, Lord! This shall never happen to you.”

— Matthew 16:22 (ESV)

That is Peter, and I do not read it as cowardice. It is logic. Kings do not take their thrones by way of a Roman execution. The cross looked to Peter exactly as the curved track looked to Bernoulli’s readers, like the wrong answer. A moment later Jesus told him, in the same passage, that he was thinking the thoughts of men rather than of God.

The resurrection wasn’t a recovery from the cross. It was where the cross had been pointed from the beginning. Three days inside the worst thing that ever happened turned out to be the quickest way to the best thing ever offered, because there was no other road by which sin could be answered and death defeated. God did not take a detour through the cross. The cross was the road.

Living on the Curve You Are On

So you are in a season that does not look like progress. A prayer you have prayed for three years has not produced what you asked. The job that should have come has not come, and neither has the result, or the visa, or the marriage, or the healing. The thing you can see clearly at the end of the road keeps curving away from you.

I won’t tell you that nothing is wrong. Some bends in a Nigerian road are the work of providence, and some are the work of a contractor who was paid and did not finish. Not every delay is a design, and a person who treats every closed door as a divine lesson will sometimes sit in a bad situation far too long. Ask for wisdom. Ask a friend who loves you whether you are being formed or simply stuck.

But if you have asked, and nothing in the road is your own doing, then consider what James says about trials of many kinds, that the testing of faith produces steadfastness and that steadfastness has its full effect so that you may be complete. That is the destination he names, and no straight track reaches it, because the straight track does not run through the places where it is made. Paul, writing in chains, put it in a sentence I will quote only in part, because I could not honestly stretch it further. For those who love God, he wrote, “all things work together for good” (Romans 8:28, ESV). The good is real, and it is promised to a particular people, and it is promised over all things, including the bends.

The bead on Bernoulli’s curve is not lost when it drops steeply. It is gathering something it will need further down.

So here is something to try tonight. Write out the prayer you have been praying, in the words you actually use. Under it, list what this road has already put into you that the short road would not have, the skill you were forced to learn, the friend who stayed, the habit of praying when nothing was moving. Then read the page to someone who knows you. You may still want the straight road, and God doesn’t mind you asking for it. He might simply want to show you what the long one has been building while you were looking the other way.

References

Biblical References

Psalm 77:19 (ESV). The epigraph, and the picture in the body of a road through the sea that no one on the shore could see.
Exodus 13:17 to 18 (ESV). The central text: God deliberately turns Israel from the near road to the longer one, and gives his reason.
Genesis 50:20 (ESV). Joseph’s own reading of his thirteen years; the same Hebrew verb is used of the brothers’ intention and of God’s.
Jeremiah 29:10 (ESV). The timetable of seventy years that stands beside the better known promise in the next verse; the letter was sent to exiles.
Matthew 16:22 (ESV). Peter’s protest against the cross, the natural reaction to a road that looks wrong.
Romans 8:28 (ESV). Quoted in part only, as the promise to those who love God that all things work together for good.
Numbers 13 and 14; Genesis 37:2 and 41:46; James 1:2 to 4; Matthew 16:23. Referred to without direct quotation, for Israel’s refusal at the border, Joseph’s ages, the purpose of trials, and Jesus’ reply to Peter.

Other Sources

Brachistochrone curve. (n.d.). In Wikipedia. https://en.wikipedia.org/wiki/Brachistochrone_curve
Christianity Today. (2007, July). Gospel riches. https://christianitytoday.com/2007/07/gospel-riches
MacTutor History of Mathematics Archive. (n.d.). The brachistochrone problem. University of St Andrews. https://mathshistory.st-andrews.ac.uk/HistTopics/Brachistochrone
Smith, D. J. (2021a). The Pentecostal prosperity gospel in Nigeria: Paradoxes of corruption and inequality. The Journal of Modern African Studies, 59(1), 103–122. https://doi.org/10.1017/S0022278X2000066X
Smith, D. J. (2021b, May 26). Nigeria’s prosperity gospel: Pentecostal churches may reinforce inequalities and corruption. Africa at LSE. https://blogs.lse.ac.uk/africaatlse/2021/05/26/nigeria-prosperity-gospel-pentecostal-churches-may-reinforce-inequalities-corruption
Windle, B. (2022, March 8). Ancient wells discovered along the Horus Road through the Sinai. Associates for Biblical Research. https://biblearchaeology.org/ancient-wells-discovered-along-the-horus-road-through-the-sinai/

Translation Notices

Scripture quotations are from the ESV Bible (The Holy Bible, English Standard Version), copyright 2001 by Crossway, a publishing ministry of Good News Publishers. Used by permission. All rights reserved.