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Simple Short Term Memorization Austin Nelson, Ian Husted, Jeremy Cooper Introduction Memory: the faculty by which the mind stores and remembers information dL k 1 L dt Differential equation models simple short term memory Goal: Perform an experiment comparing the ease of memorization of words and numbers Hypothesis: It will be easier to memorize lists of words, as opposed to lists of numbers Results: People can memorize lists of words faster than they can memorize lists of numbers Experiment 3 different tests, each with 3 test subjects 3-digit numbers 5-letter words 6-letter words 1 minute study time Maximum of 10 trials Order mattered Mathematical Analysis Separation of variables dL k 1 L dt dL k dt 1 L dL k dt 1 L ln 1 L kt c e ln 1 L e kt c 1 L Ae kt L 1 Ae kt Solving for A Initial condition: L(0)=0 k 0 0 1 Ae 0 1 A1 A 1, so 0.8 0.6 0.4 0.2 L 1 e kt 2 4 6 8 10 12 14 Solving for k e 1 L kt ln e kt ln1 L kt ln1 L ln1 L k t Results 1 Memorization of 5 Letter Words (%) Time (minutes) Subject A Subject B Subject C 0 0 0 0 1 25% 40% 25% 2 25% 55% 35% 3 40% 60% 60% 4 65% 75% 70% 5 75% 90% 90% 6 85% 95% 95% 7 100% 95% 100% 8 100% 9 10 Results 2 Memorization of 6 Letter Words (%) Time (minutes) Subject A Subject B Subject C 0 0 0 0 1 30% 40% 30% 2 40% 60% 45% 3 70% 60% 20% 4 65% 85% 60% 5 95% 90% 60% 6 100% 95% 60% 7 100% 50% 8 60% 9 75% 10 90% Results 3 Memorization of 3 Digit Numbers (%) Time (minutes) Subject A Subject B Subject C 0 0% 0% 0% 1 20% 35% 10% 2 40% 45% 20% 3 50% 60% 30% 4 50% 75% 20% 5 75% 80% 45% 6 55% 90% 55% 7 65% 100% 35% 8 65% 65% 9 90% 70% 10 90% 75% Subject A's Memorization 100% 90% Percentge of Objects Memorized 80% 70% 60% 5 Letter Words 6 Letter Words 3 Digit Numbers 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Time (minutes) 6 7 8 9 10 Subject B's Memorization 100% 90% Number of Objects Memorized 80% 70% 60% 5 Letter Words 6 Letter Words 3 Digit Numbers 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Time (minutes) 6 7 8 9 10 Subject C's Memorization 100% 90% Number of Objects Memorized 80% 70% 60% 5 Letter Words 6 Letter Words 3 Digit Numbers 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Time (minutes) 6 7 8 9 10 The k Parameter lim 1 e 1 kt k -∞ e term goes to 0 At any t value, you have 100% of list memorized The more negative the k value, the faster one can memorized L = 0.25 and t = 1 ln1 L k t ln 1 .25 k 1 k = -.2877 Average k values Subject A Subject B Subject C 5 Letter Words -0.2429 -0.4214 -0.3449 6 Letter Words -0.3750 -0.4514 -0.1893 3 Digit Numbers -0.2061 -0.3479 -0.1109 OVERALL -0.4069 -0.2150 -0.2747 Solution Curves for Each Test Subject 1.0 B : L 1 e-0.4069t A : L 1 e-0.2747t 0.8 C : L 1 e -0.2150t L 1 ekt 0.6 0.4 0.2 2 4 6 8 10 12 14 Data doesn’t specifically support our k value interpretation Subject B has most negative k value, didn’t finish each test first The k value is most dependent on the number of terms memorized during the first study time period Subject B's Memorization 100% 90% Number of Objects Memorized 80% 70% 60% 5 Letter Words 6 Letter Words 3 Digit Numbers 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Time (minutes) 6 7 8 9 10 Subject A's Memorization 100% 90% Percentge of Objects Memorized 80% 70% 60% 5 Letter Words 6 Letter Words 3 Digit Numbers 50% 40% 30% 20% 10% 0% 0 1 2 3 4 5 Time (minutes) 6 7 8 9 10 Limitations To the Model Not everyone memorizes information in a strictly increasing fashion People forget Doesn’t take external factors into account Conclusions Our results support our hypothesis Reasons why the memorization of words is easier than the memorization of numbers Patterns WATC WATCH Relationships CHALK + BOARD Rhyming Usage