A Seventeenth-Century Equation and the Man Who Already Knew the Answer

In 1696, the Swiss mathematician Johann Bernoulli issued a challenge to the greatest minds of Europe. He called it the brachistochrone problem — from the Greek brachistos, meaning “shortest,” and chronos, meaning “time.” The question, stripped of its Latin elegance, was this: if you roll a ball from point A to point B under the force of gravity alone, what shape of track will get it there the fastest?

Every sensible person gave the sensible answer. A straight line, obviously. The shortest distance between two points is a straight line. Euclid said so. Common sense confirmed it. Surely speed and directness walk hand in hand.

They do not.

The actual answer — proved independently by Leibniz, Newton, and the Bernoulli brothers themselves — is a curve. Specifically, a cycloid: the arc traced by a point on the rim of a rolling wheel. The ball released along this curve accelerates quickly in the early descent, builds velocity it would not have gathered on a flat path, and arrives at the destination faster than the ball that took the straight road. The curved path is the fastest path. Geometry, as it turns out, has a sense of humour.

I want to suggest to you that God has known this since before Bernoulli was born.

The Route God Did Not Take

The Israelites had just watched the most powerful nation on earth drown in the Red Sea. Pharaoh’s chariots, his officers, his horses gone. The water closed over them like a curtain drawn across an embarrassment. Four hundred and thirty years of bondage, ended in a night.

Canaan was waiting. It was not far. The most direct road from Egypt to the Promised Land — the coastal highway, the ancient road the Egyptians themselves called the Way of Horus — would have brought the people there in eleven days. Eleven days. You can walk it in a fortnight on tired feet.

God looked at that road and chose a different one.

“When Pharaoh let the people go, God did not lead them on the road through the Philistine country, though that was shorter. For God said, ‘If they face war, they may change their minds and return to Egypt.’ So God led the people around by the desert road toward the Red Sea.” — Exodus 13:17-18 (NIV) Read that passage slowly, because it does something uncomfortable. It does not say God was unaware of the shorter road. It says He saw it and deliberately turned away from it. He looked at the straight line and chose the curve. He looked at eleven days and chose forty years. And He explained why, with a pastoral directness that should unsettle every Christian who has ever prayed for the fast route: because the short road would have broken them.

They were not ready for what was on the straight path. The Philistines were not a footnote; they were a military power, and a people who had known nothing but slavery for four centuries were not equipped for that confrontation on day three of their freedom. God, who is not merely omniscient but wise — and there is a difference — understood that the direct path was not the fastest path to where He was actually taking them. The destination was not just Canaan. The destination was a people. And people, unlike balls on a frictionless track, require formation before they can receive what they are being formed for.

The wilderness was not the detour. The wilderness was the route.

Joseph and the Algorithm Nobody Prayed For

If you had told Joseph, at the age of seventeen, that his brachistochrone ran through the bottom of a cistern, through the slave markets of Egypt, through the house of Potiphar, through the prison of Pharaoh, and through several years of patient, unrewarded faithfulness before arriving at the throne room he would have asked you to leave. Respectfully, but firmly. He would have shown you the coat his father gave him and pointed out that this was not the attire of a man being prepared for a pit.

We know the story so well that we have lost the ability to feel it. Thirteen years. From the pit to the palace, the commentators say breezily, as though thirteen years is a comma in a sentence rather than the whole of an adolescence and the first decade of adulthood. Thirteen years of watching the straight path recede. Thirteen years of being excellent — and this is the part that really stings — and having that excellence produce, for a long time, absolutely nothing that looked like progress.

And yet.

“You intended to harm me, but God intended it for good to accomplish what is now being done, the saving of many lives.” — Genesis 50:20 (NIV) That single verse contains an entire theology of curved paths. Not: God permitted the harm. Not: God watched helplessly as bad things happened to a good man and then scrambled to make something out of the wreckage. The Hebrew word translated “intended” is the same word chashav used for both Joseph’s brothers and for God. They plotted. God also plotted. The same events, two entirely different purposes, one sovereign trajectory. What looked from inside the story like abandonment was, from above the story, architecture.

The pit was not an interruption of Joseph’s calling. The pit was the first room of it.

What Our Churches Told Us Instead

There is a theology that has taken root across the Pentecostal landscape of West Africa and spread, via satellite and streaming, to diaspora churches from Peckham to Peachtree City that treats the curved path as a spiritual malfunction. It goes by several names: the anointing of acceleration, the grace of divine speed, the breaking of delays and hindrances. The vocabulary is vigorous. The promise is essentially Bernoulli’s instinct before his calculation: the straight line is fastest. Pray hard enough, sow deep enough, confess boldly enough, and God will flatten your curves.

It is a seductive theology because it is partly true. God does intervene. God does accelerate. God did, in fact, shorten some journeys and straighten some roads. The Bible is full of sudden reversals, instantaneous healings, Jericho walls that fell in a week. Miracles are real. I am not arguing against miracles.

I am arguing against the theology that makes the absence of a miracle into evidence of a deficiency in the believer. Because that theology produces a particular kind of damage: it trains people to misread their own lives. It tells them that the curve is the enemy. It makes the wilderness feel like punishment. It turns thirteen years of Joseph’s formation into thirteen years of Joseph’s failure. And it produces, eventually, people who have prayed themselves into exhaustion over a delay that was never a delay — it was the route.

A West African proverb puts it plainly: the eye of the road does not see as deeply as the inner eye. What is visible to us from inside the journey is not the whole picture. What looks like the long way around is sometimes the only way through.

The Passage Everyone Quotes and Almost Nobody Finishes Reading

“For I know the plans I have for you, declares the Lord, plans to prosper you and not to harm you, plans to give you hope and a future.” — Jeremiah 29:11 (NIV) This verse has been cross-stitched onto more cushions than any other passage in the Old Testament. It appears on mugs, on graduation cards, on the bio sections of Christian Instagram accounts. It is the theological equivalent of a warm handshake everyone loves it, nobody argues with it, and very few people read what comes immediately before it.

What comes before it is this:

“This is what the Lord says: ‘When seventy years are completed for Babylon, I will come to you and fulfil my good promise to bring you back to this place.’” — Jeremiah 29:10 (NIV) Seventy years. God’s plan to prosper them ran through seventy years of exile in a foreign empire. The hope and the future were real. The prosperity was genuine. And the path to it was long enough that most of the people who heard the original promise would not live to see its fulfilment. God was writing a brachistochrone across generations.

Jeremiah 29:11 without Jeremiah 29:10 is a fortune cookie. With it, it is a theology of perseverance.

The Fastest Road Has Always Run Through the Cross

Here is where the argument turns.

If you want the ultimate example of a God who refuses the straight path, do not go to Joseph. Do not go to Moses. Go to Golgotha.

The incarnation itself is a curve. The God who spoke existence into being from outside of time chose to enter time as an infant, in a province of the Roman Empire, to a teenage girl in a town nobody had heard of. He could have arrived differently. He could have descended in glory, suspended over Jerusalem, announcing Himself in a way that required no faith and left no room for doubt. He did not. He came small. He came curved.

And then He went to the cross. And His disciples, who had followed Him for three years, watching the lame walk and the dead rise and the bread multiply — His disciples looked at the cross and saw the same thing Bernoulli’s contemporaries saw in the curved track. They saw the wrong answer. They saw defeat. Peter had made his opinion on the subject plain: “Never, Lord! This shall never happen to you!” (Matthew 16:22, NIV). He was not being cowardly. He was being logical. This is not the path. This is not how kings take their thrones. This is the wrong road.

“For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God.” — 1 Corinthians 1:18 (NIV) The cross is the ultimate brachistochrone. It is the path that looks, to every human instinct and calculation, like the slowest and most catastrophic possible route — and it turns out to be the only route by which the sin of the whole world could be atoned for, death could be defeated, and the kingdom of God could be established on the earth. The resurrection was not a recovery from the cross. The resurrection was the destination the cross was always aimed at. Three days inside the worst thing that had ever happened was the fastest path to the best thing that has ever been offered.

God did not take a detour through the cross. The cross was always the route.

What You Do With the Curve You Are Currently On

So you are in a season that does not look like progress. The prayer you have been praying for three years has not yet produced what you were expecting. The career that should have arrived by now has not arrived. The relationship, the healing, the breakthrough — the thing you can see clearly from a distance but cannot seem to reach — remains at the end of a road that keeps curving away from you.

I am not going to tell you that God is not with you. I am not going to tell you that the delay is simply to be endured. What I want to offer you is more uncomfortable than comfort, and ultimately more useful: the possibility that you are not delayed. The possibility that the curve you are on is precisely the curve you need to be on to arrive at the destination God has prepared, with the character and the capacity to inhabit it.

James puts it plainly, without the softening that we might prefer:

“Consider it pure joy, my brothers and sisters, whenever you face trials of many kinds, because you know that the testing of your faith produces perseverance. Let perseverance finish its work so that you may be mature and complete, not lacking anything.” — James 1:2-4 (NIV) Mature and complete. Not lacking anything. That is the destination. And it is not reached by the straight path because the straight path does not go through the trials that produce perseverance, and perseverance is not optional equipment. It is load-bearing structure.

An Igbo proverb says: he who brings kola brings life. The kola nut, before it reaches the elder’s hand, has been carried a distance. It is not the arrival that gives it meaning — it is the carrying. There is something in the journey itself that makes the offering what it is.

You are being carried. Not abandoned. Carried.

Trust the Mathematician

Bernoulli’s curve works because of a principle that is not immediately visible to the eye: the ball accelerates early, gains velocity, and uses that stored momentum to cover the remaining distance faster than the ball that took the flat road. The curve front-loads something that pays off later. What looks like the long way is actually the optimised way.

This is what Paul meant when he wrote, from inside his own brachistochrone — chains on his wrists, Roman prison around him, his missionary journeys interrupted, his plans rerouted, the straight path to the churches he loved blocked by imperial whim:

“And we know that in all things God works for the good of those who love him, who have been called according to his purpose.” — Romans 8:28 (NIV) Not some things. All things. The pit and the palace. The Philistine road not taken and the forty years of wilderness chosen instead. The exile and the prophecy that ran seventy years beyond the people who first heard it. The cross that the disciples wept over on Friday and could not explain on Saturday and only understood on Sunday.

All things.

There is a God who has been drawing in curves since before time began. He is not lost. He has not made a mistake with your life. He is not scrambling to recover something He dropped. He is the one who looked at the straight line, understood it better than you ever will, and chose the curve instead because He is not only omniscient but wise, and wisdom knows that the fastest path to who you are supposed to become does not run through the road that looks shortest from where you are standing.

The brachistochrone is His signature. The curve is His design.

Trust the Mathematician.

Biblical References

  • Psalm 77:19 — Used as the opening epigraph; God’s pathway through the sea as the archetype of the route that is invisible until it is behind you.
  • Exodus 13:17-18 — The foundational text of the article; God’s deliberate choice of the longer road for Israel to protect their formation before their confrontation.
  • Genesis 50:20 — Joseph’s summary of his own brachistochrone; the pivot verse on which the article’s theology of providence turns.
  • Jeremiah 29:10-11 — Cited in full to restore the verse most commonly used in isolation; the seventy years of exile that precede the famous promise reframe the promise entirely.
  • Matthew 16:22 — Peter’s protest against the cross as the human instinct that reads the curved path as the wrong path.
  • 1 Corinthians 1:18 — Paul on the cross as foolishness to those who cannot read the curve; the cross as the ultimate brachistochrone.
  • James 1:2-4 — The theological warrant for the formation that happens on the curved path; trials producing perseverance, perseverance producing maturity.
  • Romans 8:28 — The doxological conclusion; all things working together as the promise that the curve is not an accident but a design.

External Sources and Notes

  • Johann Bernoulli, Problema Novum (1696) — The original brachistochrone challenge, posed to European mathematicians; the historical anchor of the article’s central metaphor.
  • West African proverb: the eye of the road does not see as deeply as the inner eye. Used to ground the epistemological humility required when reading one’s own season of life.
  • Igbo proverb: he who brings kola brings life. Used to affirm the meaning carried within the journey itself, not only at its destination.