Picture the tree from the parable you already know: a seed goes into the ground, nothing happens for
a while, and then — all at once — seven spikes, a hundred grains each. That is Qur’an 2:261’s picture of
sadaqah, and a previous paper built an entire growth model on it: a single yearly (or decade-long, depending
on the seed) harvest, one dramatic multiplication, repeat.
But three surahs later, the Qur’an describes a tree that does not work that way at all. Its fruit does not
arrive once a season — it arrives kulla hın, “every hın,” at every turn, all the time (Q. 14:25). No single
harvest day. No bare months followed by abundance. Just a tree that is always giving something.
Two trees, one Book, and — it turns out — one honest question a model of compounding sadaqah cannot
dodge: does it matter how often the return arrives, if the total for the year is the same either way?
Most people’s intuition says yes, obviously, more often is better. The mathematics in this paper says
something sharper and slightly uncomfortable: harvesting continuously buys you no extra growth at all.
What it buys you instead is protection — against the one moment, at some point during your life, when the
reckoning arrives and finds you empty-handed because your harvest hadn’t come yet. That protection turns
out to be worth almost exactly ln 700 ≈ 6.55: the natural logarithm of the very multiplier the seed parable
already promised you.
Figure 1. sketches the two trees as the paper actually treats them: not as botany, but as two different
rhythms laid over the same timeline.
Fig. 1 — Same total promise, two different rhythms. The seasonal tree (top) delivers its whole 700-fold return in two sudden bursts; the ever-fruiting tree (bottom) delivers the same yield spread continuously across the same stretch of time. The paper’s point is in what this picture cannot show: measured at the harvest marks, both trees have grown by exactly the same amount — the gain is entirely in what happens to a giver who is asked to stop at some other, unmarked point along the line.
Picture the tree from the parable you already know: a seed goes into the ground, nothing happens for
a while, and then — all at once — seven spikes, a hundred grains each. That is Qur’an 2:261’s picture of
sadaqah, and a previous paper built an entire growth model on it: a single yearly (or decade-long, depending
on the seed) harvest, one dramatic multiplication, repeat.
But three surahs later, the Qur’an describes a tree that does not work that way at all. Its fruit does not
arrive once a season — it arrives kulla hın, “every hın,” at every turn, all the time (Q. 14:25). No single
harvest day. No bare months followed by abundance. Just a tree that is always giving something.
Two trees, one Book, and — it turns out — one honest question a model of compounding sadaqah cannot
dodge: does it matter how often the return arrives, if the total for the year is the same either way?
Most people’s intuition says yes, obviously, more often is better. The mathematics in this paper says
something sharper and slightly uncomfortable: harvesting continuously buys you no extra growth at all.
What it buys you instead is protection — against the one moment, at some point during your life, when the
reckoning arrives and finds you empty-handed because your harvest hadn’t come yet. That protection turns
out to be worth almost exactly ln 700 ≈ 6.55: the natural logarithm of the very multiplier the seed parable
already promised you.
Figure 1. sketches the two trees as the paper actually treats them: not as botany, but as two different
rhythms laid over the same timeline.
📖 Read sdq_progress.pdf