Ebbinghaus_curve

Ebbinghaus Curve is a simple demonstration project that shows how Hermann Ebbinghaus’s forgetting theory can be implemented for spaced word repetition.

The project includes:

• a minimal PostgreSQL model
• SQL queries for calculating repetition priority
• Python examples (e.g., plotting forgetting curves)

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Installation & Setup

1. Clone the repository

git clone https://github.com/ivakorn/Ebbinghaus_curve.git
cd Ebbinghaus_curve

2. Set up the environment

Install dependencies:

pip install -r requirements.txt

3. Run PostgreSQL with Docker

The project provides a docker-compose.yml file to run PostgreSQL. Start it with:

docker-compose up -d

4. Initialize the database

After PostgreSQL is up, create the tables and populate them with test data using the script:

python update_db.py

This will create the words table and insert example English words with review dates and correct/incorrect answer statistics.

5. Run examples

• Fetch words from the database:

  python get_words.py

• Plot forgetting curves:

  python draw_graphs.py

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How it works

• The theory: the project uses Ebbinghaus’s forgetting curve formula:

$$ R(t) = \frac{100 \cdot (1.84 + S)}{1.84 + S + (\log_{10} t)^{1.25}} $$

where S is the strength coefficient (based on answer statistics).

• SQL implementation: Priority for each word is calculated directly in the query:

SELECT
    text,
    100 * (1.84 + GREATEST(correct_count * 0.8 - wrong_count * 0.5, 0))
      / (
          1.84 + GREATEST(correct_count * 0.8 - wrong_count * 0.5, 0)
          + POWER(LOG(GREATEST(EXTRACT(EPOCH FROM (NOW() - last_review)) / 60, 1)), 1.25)
      ) AS priority
FROM words
ORDER BY priority ASC
LIMIT 5;

This allows filtering and sorting words that need review directly at the database level, without extra client-side processing.

• Python implementation: Equivalent formula in Python:

memory_decay_factor = (math.log10(max(minutes_since, 1))) ** 1.25
retention = 100 * (1.84 + strength) / (1.84 + strength + memory_decay_factor)

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Use cases

This model fits any application where learning depends on repetition and retention, such as:

• language learning
• exam preparation
• memorizing texts or formulas

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Feedback

If you’d like to dive deeper into the math behind Ebbinghaus’s formula, check out my detailed article on TProger: “The Ebbinghaus Forgetting Curve in User Applications."

And if you want to see the theory in action, try my Telegram bot @Duck - Your translater. It helps you learn English words and uses these algorithms to schedule reviews.