# OVER 0 (DD-284)

> Mechanical calculators divide the way people do long division: by subtracting the divisor over and over and counting the subtractions. With a divisor of zero, each subtraction takes nothing away, so the count never ends. Some machines simply keep cycling, carriage and counters spinning, until the operator stops them by hand. Others jam or trip a stop. That behavior is a physical version of why division by zero is undefined in arithmetic: no number multiplied by zero gives a nonzero result, so there's no answer to find. Desktop mechanical calculators were common office tools from the late 1800s until electronic calculators replaced them in the late 1960s and early 1970s. The footage shows a mechanical calculator's carriage and keys in motion, with a hand at the controls.

- Department: Tech (also History)
- First published: 2024-07-29
- Last updated: 2024-07-29
- Permalink: https://detailenjoyer.com/case/over-0/
- Author: Marcus Easterling (DetailEnjoyer), The Detail Department

## Quick facts

- **DD-284-F01**: Mechanical calculators divide by repeated subtraction. _(Write-up · Exhibit A (Division by subtraction))_
- **DD-284-F02**: Some keep cycling forever when asked to divide by zero. _(Write-up · Exhibit C (Endless cycling))_

## Write-up

Ask a gear to divide by zero and it never stops. Some mechanical calculators keep cranking until someone stops them by hand.

1. **Division by subtraction**: Mechanical calculators divide by repeated subtraction, counting how many times the divisor fits.
2. **Zero never runs out**: Subtracting zero never shrinks the number, so the count never ends.
3. **Endless cycling**: Some machines keep cycling until the operator stops them manually.
4. **Undefined in math**: No number times zero gives a nonzero result, so division by zero has no answer.
5. **Office staples**: Desktop mechanical calculators were common until electronic ones replaced them around 1970.

## Related case files

- [Central Limits (DD-588)](https://detailenjoyer.com/case/central-limits/): I paired it with another machine that does math with moving parts
- [Shrinking Circuits (DD-018)](https://detailenjoyer.com/case/shrinking-circuits/): I linked the electronics that replaced gear calculators

## Reel vs. record

- **Note**: 'In the 1950s mechanical calculators were widely used': right, though I'd note they were common from the late 1800s through the 1960s, not just the 1950s.
- **Note**: 'Lock up or enter an endless cycle': right. Behavior depends on the model; some cycle until stopped by hand, others jam or trip a stop.

## Video: OVER 0: Ask a Gear to Divide by Zero and It Never Stops

- Duration: 18.6 s · Published: 2024-07-29
- File: https://detailenjoyer.com/assets/videos/C-Bql5rJRwm.mp4

### Transcript

DID YOU KNOW? In the 1950s mechanical calculators were widely used for arithmetic tasks relying on gears and levers to perform operations. However, these machines could not handle division by zero as this operation is undefined in mathematics. When a division by zero was attempted the calculator would typically lock up or enter an endless cycle unable to produce a result. NOW YOU KNOW!

## Questions & answers

**Q: How do mechanical calculators divide?**  
A: They count how many times the divisor fits. _(Source: Write-up · Exhibit A (Division by subtraction) · Wikipedia: Division by zero; Wikipedia: Mechanical calculator)_

**Q: Why does dividing by zero never finish?**  
A: The count just keeps going. _(Source: Write-up · Exhibit B (Zero never runs out) · Wikipedia: Division by zero)_

**Q: What do some machines do when dividing by zero?**  
A: The operator has to stop them by hand. _(Source: Write-up · Exhibit C (Endless cycling) · Wikipedia: Division by zero; YouTube: What happens when you divide by zero on a mechanical calculator? (March 7, 2021))_

**Q: Why is division by zero undefined?**  
A: There's no answer to find. _(Source: Write-up · Exhibit D (Undefined in math) · Wikipedia: Division by zero)_

**Q: What replaced mechanical calculators?**  
A: That happened around 1970. _(Source: Write-up · Exhibit E (Office staples) · Wikipedia: Mechanical calculator)_

## Sources

- [Wikipedia: Division by zero](https://en.wikipedia.org/wiki/Division_by_zero)
- [Wikipedia: Mechanical calculator](https://en.wikipedia.org/wiki/Mechanical_calculator)
- [YouTube: What happens when you divide by zero on a mechanical calculator? (March 7, 2021)](https://www.youtube.com/watch?v=s_hbvRTGcUI)

## Cite this case file

Easterling, Marcus. "OVER 0." The Detail Department (DetailEnjoyer), case file DD-284, last updated Jul 29, 2024. https://detailenjoyer.com/case/over-0/