The spice merchants were already gripping their sword hilts when Al-Karaji ducked into the shaded corner of the souk. A long caravan had just rolled in, and the partnership ledger was torn right down the middle. Mental arithmetic handled quick trades just fine, but splitting months of travel, delayed shipments, and rolling profits turned simple fractions into a shouting match. A scribe scrambled to slide clay tokens across a scarred wooden board, but the pieces just clattered into a messy heap. Time-weighted investments and compound interest twisted the accounts until nobody knew who actually owned what.
Al-Karaji let the argument wash over him and looked away. Across the narrow street, a weaver pulled bright wool through a heavy wooden loom. The horizontal warp crossed the vertical weft, locking into a rigid, predictable pattern. That crossing clicked in his mind. Commercial shares could follow the exact same layout. Instead of wrestling with abstract fractions in the heat, he could pin every claim to a fixed space.
He grabbed a thick charcoal stick and smoothed a wax tablet flat. The raw numbers were already clear: each partner’s initial silver stake and the exact months that capital sat idle in the venture. He drew one straight axis for the money running left to right, and another for the time running bottom to top. Where the two lines crossed, he pressed a dot to form a square. That single intersection stood for a fixed slice of the total profit. Map the capital, count the months, and the crossing handed you the exact payout. He wasn't just patching a deal together. He was drafting a systematic table for partnership splits, replacing the messy fraction games that usually ended in duels.
He held the tablet up to the lead trader. The man leaned in, tracing the charcoal lines with a calloused thumb. He found his own marked square, counted the intersections, and the anger drained out of his posture. The others crowded around, dropped their silver markers onto the matching spots, and finally agreed. The market noise faded into focused silence as coins settled into their proper places. The grid held the chaos in check, leaving nothing to dispute.