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  A1
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  ln1  L 
kt  ln1  L 
ln1  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
ln1  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