Eric Roberts opens Thinking Recursively with a fundraising coordinator who must raise $1,000 in gifts of exactly $1. The iterative plan is obvious. Find 1,000 people yourself. The recursive plan is quieter. Enlist ten people to raise $100. Each of those enlists ten to raise $10. The chain stops at $1, which you can give yourself.
Most founders I sit with are running the first plan and calling it calling.
The hustle picture
The iterative picture has a holy look. One anointed person. One impossible list. One WhatsApp that never sleeps. You will visit every parish, close every sale, disciple every fellow, and still preach on Sunday. The region has a name for this and it is not faithfulness. It is hustle dressed as avodah.
AVODA has trained 543+ founders and seen 150+ start-ups launched. The pattern that keeps returning is not a lack of vision. It is a founder trying to be the whole money-tree in a single body.
Roberts writes the definition without romance:
Informally, recursion is the process of solving a large problem by reducing it to one or more subproblems which are (1) identical in structure to the original problem and (2) somewhat simpler to solve.
Identical in structure. Somewhat simpler. That is the whole method. A $100 raise is the same problem as a $1,000 raise, only smaller. One paid WhatsApp customer is the same problem as a district rollout, only smaller.
The iterative founder refuses the reduction. She treats the large problem as a different species from the small one. She will not sell one filter until the brand is ready for ten counties. She will not disciple one cell leader until the curriculum is ready for a nation. Meanwhile no dollar moves.
I will use a teaching composite here, not a named alum with invented metrics. Call her Amina. She runs a household-goods line out of Kampala, WhatsApp-first, mobile-money at the till. Her orientation plan was ten districts by Christmas and a youth-employment story a donor would love. By week six she had slept in four towns, hired two cousins, and closed almost nothing. She was trying to collect $1,000 by being all 1,000 collectors. The work looked like sacrifice. The books looked like a hole.
Roberts names the failure with a lazy volunteer. The fundraiser decides to collect the $1,000 by finding a single volunteer who will collect $1,000. If that volunteer adopts the same strategy, and every other volunteer follows, “the process will continue until we exhaust the available pool of volunteers, even though no money at all will be raised.” There is no base case. There is only the next introducer.
The African cousin is the founder who posts another strategy in the group and waits for a grant to become the missing collector. Aid-dependency is nonterminating recursion. It has no $1 case. It only has the next introducer.
Three properties as a planning liturgy
Roberts says a problem is fit for this method only if it has three properties.
- It must be possible to decompose the original problem into simpler instances of the same problem.
- Once each of these simpler subproblems has been solved, it must be possible to combine these solutions to produce a solution to the original problem.
- As the large problem is broken down into successively less complex ones, those subproblems must eventually become so simple that they can be solved without further subdivision.
Read those as liturgy, not as computer science.
Base case. What is already true, and small enough to finish this week, without a committee and without a donor. One household that pays. One cell that meets. One week of books that balance. If you cannot name that case, you do not have a plan. You have a wish with a map.
Combine rule. When the smaller instances are done, how do they become the original problem. Ten cell leaders do not become a church by sitting in the same room. They become a church when you have a rule for gathering their fruit: a shared till, a shared teaching, a shared standard for what “paid” means. Without that rule you have ten hobbies.
Stop condition. The third property is the mercy. The chain must bottom out. In Roberts’s tree, $1 “represents a simple case for the fund-raising problem, which means that it can be solved directly without further decomposition.” The volunteer does not split a dollar into dimes. She gives the gift herself. Amina’s stop condition, when she finally wrote it, was one paid 10-litre order, collected on mobile money, delivered the same day, recorded in a notebook a cousin could copy. Not a district. A gift she could give herself.
Jeff Edmonds, writing about algorithms rather than money-trees, gives the weekly test beside these three. The loop invariant is that “we have not gone wrong.” If there is a solution, at least one good solution is still consistent with the choices made so far. After this week’s hire, channel, or church partnership, can the $1 case still be finished. If the shiny step deletes every path back to the small faithful unit, you have gone wrong even if the slide looks large.
The leap of faith is not mysticism about outcomes
Roberts knows the beginner will not believe the method. The temptation is to open every nested task before you start: every supplier, every form, every village. He answers with a sentence the Church should handle carefully.
Achieving the necessary confidence often requires the programmer to adopt a strategy called the “recursive leap of faith.” As a strategy, this means that one is allowed to assume the solution to simpler problems when trying to solve a complex one.
This is not “it will work out.” This is not a prosperity claim applied to a rollout. The leap is permission to trust a smaller faithful unit while you hold the combine rule. You name the forest and the $1 case. You refuse to pretend that opening every subtree is the same as obedience.
He is blunt about the opposite error.
Even though recursion acts as a reductionistic process in the sense that each problem is reduced to a sum of its parts, writing recursive programs tends to require a holistic view of the process. It is the big picture which is important, not the details… When one cannot see the forest for the trees, it is of very little use to examine the branches, twigs, and leaves.
Holism here is not vagueness. Holism is refusing to baptise panic as diligence. The founder who opens every village file before she has one paying household is hiding from the $1 case. The details have become a refuge from faithfulness.
Amina’s correction was unglamorous. She stopped the district tour. She took the next twenty names in her own church WhatsApp and asked for one paid order each, same script, same price, same delivery promise. Eight paid. She wrote the script on a card and handed it to her cousin. The cousin closed three more. That is the leap: assume the simpler sale can be made, because you have already made it, and then combine. Revenue moved. Households that had been waiting on a “programme” paid with their own mobile money. The work became worship again, because it was small enough to do in the sight of God rather than in the sight of a gallery.
Kingdom frame: faithfulness on the $1 case
Avodah is work as worship. Worship is tested on the altar you can actually reach. The Master does not commend the servant who described a thousand cities. He commends the one who was faithful with a little. Luke 16:10 is an operating rule. Faithfulness in the least is faithfulness in much. The $1 case is the least.
Do not baptise an exponential plan that has no $1 case. A ten-country vision with no paying household is not faith. It is a money-tree with no leaf that can give a gift. A discipleship movement with no one person you will sit with this week is the volunteer who collects $1,000 by finding one more volunteer.
The triple bottom line is not a decoration we hang on a large plan. It is a test we run on the small one.
- Revenue: did the $1 case actually pay, in mobile money, in cash, in a receipt you can show.
- Social impact: did a named neighbor receive the thing, not “the community,” not “Africa.”
- Kingdom: was the work done as unto the Lord, without a bribe, without a false number, without using a church announcement as a disguise for extraction.
If the small case fails any of the three, scaling it is not growth. It is multiplying an unfaithful unit. That is the opposite of stewardship.
This is also why AVODA refuses aid-shaped plans that wait for a foreign collector to finish the tree. Self-determination is not pride. It is the $1 gift you can give yourself. A grant, if it comes, combines work that already bottoms out. It is not a substitute for the base case.
The weekly session: three lines
Every venture-design session writes three lines before anyone opens a laptop.
- Base case. What is already true, and small enough to finish this week. Name the person, the payment, the page of the book, the one WhatsApp close. If it cannot be done by Friday without a new hire and without a donor, it is not a base case.
- Inductive step. If a unit of size N is shepherded (N customers, N cell leaders, N reconciled days), what one act produces N+1 without breaking the first. The act must be copyable by someone who is not you. If only you can do it, you are still trying to be all 1,000 collectors.
- Exit. What would prove the combine rule failed. Name it before you start. Two weeks of “almost” with no paid $1 case is an exit. A partnership that forbids you from selling the small unit is an exit. A chart that can only look true if the axis starts at 80 is an exit.
Edmonds’s sentence sits under the third line: we have not gone wrong. The session is not a motivation meeting. It is a check that one faithful solution remains.
A second stewardship: tell the truth with the number
The same discipline that names the $1 case must govern how you draw the fruit. Stephanie Evergreen is plain. In a column graph the axis starts at zero, or the length of the bars sends a distorted message. A fellow’s impact slide that “pops” because the y-axis starts at 80 is a false witness, even if every count is real. The chart is a testimony. If the encoding exaggerates, the testimony is false. Faithfulness that decomposes the work and then inflates the witness has not finished the job.
The decision for the next cohort session
Do not open the nested tasks. Do not tour the twigs. Do not wait for the volunteer who will collect $1,000.
Before the next session, each fellow writes one page with four sentences.
- The large problem in one line.
- The $1 case I can finish this week without help.
- The combine rule that turns ten of those cases into the original problem.
- The exit that would prove I have gone wrong.
If any sentence is blank, the fellow does not present a scale plan. She presents the blank. The room helps her name the gift she can give herself.
The 543+ and the 150+ were not built by 1,000-collector heroes. They were built by people who learned that avodah decomposes. The Kingdom is formed by the founder who gave the $1, taught the next person to give it, and combined the gifts in the sight of God.
Name the one-dollar case. Then be faithful there.
Sources
- Eric S. Roberts, Thinking Recursively (Wiley, 1986), Ch1. Recursion as reduction to simpler instances identical in structure (p. 1). Money-tree of $1,000 in $1 gifts, iterative collector versus ten-by-ten decomposition, $1 as the simple case (pp. 1-4). Three properties of a recursive problem (p. 8). Nonterminating volunteer who collects $1,000 by finding one more volunteer, exhausting the pool with no money raised (pp. 8-9). Holism: forest, not twigs (pp. 10-11). Recursive leap of faith (p. 11).
- Jeff Edmonds, How to Think About Algorithms (Cambridge University Press, 2008), Ch16, p. 229. Loop invariant: “we have not gone wrong.”
- Stephanie D. H. Evergreen, Effective Data Visualization (SAGE, 2017), Ch1, PDF p. 25. Column axes start at zero, or bar length distorts the message.
- Luke 16:10. Faithfulness in the least is faithfulness in much.