QUANTITY OF INFORMATION

How should we measure the quantity of information? The smallest unit of information is a “yes” or a “no,” a check mark (✓) or a cross (✕), an impulse in a nerve or no impulse, a 1 or a 0, black or white, good or bad, etc. This twofold difference is called a binary digit of information ([see Supplement 2]). It is the convenient unit of information.

SCHEMES FOR EXPRESSING MEANINGS

Example:
/——————^—————————\
No.Principle
of Scheme		SignUsed inSignificanceName of
Scheme
(1)(2)(3)(4)(5)(6)
Sounds
1.Sound of new
word is like
sound of
referent		Bobwhite[2]Spoken
English		kind of quail,
so called
from its note		Imitative;
bowwow
theory
2.An utterance
becomes a
new word		Pooh![3]Spoken
English		The speaker
expresses
disdain		Pooh-pooh
theory
3.New word is
like another
word		Chortle[4]Spoken
English;
invented by
Lewis Carroll,
1896		“Chuckle”
and
“snort”
blended		Analogical
4.Word has
been used
through
the ages		Mother[5]Spoken
English		Female
parent		Historical
Sights
5.Picture
is like
referent		Egyptian;
Ojibwa
(American
Indian)		Picture of
eye and
tears, to
mean grief		Imitative;
pictographic
6.Pattern is
symbol of
an idea		5English;
French;
German;
etc.		Five;
cinq;
fünf;
etc.		Ideographic;
mathematical;
symbolic;
numeric
Mapping of Sounds
7.Object
pictured
as the
wanted
sound		Possible
English		Picture of
a knot to
mean “not”		Rebus-
writing;
phonographic
8.Pattern is
symbol for
a large
ound unit		Ancient
Cypriote
(island of
Cyprus)		Sign for
the
syllable
mu		Syllable-
writing
9.Pattern is
symbol for
a small
sound unit		ƷInternational
Phonetic
Alphabet of
87 characters		The sound
zh, as
s in
“measure”		Phonetic
writing
alphabetic
writing;
Mapping of Sights or Symbols
10.Systematic
combinations
of 26
letters		 ENIACAbbreviations,
etc.		Initial
letters
of a
5-word
title		Alphabetic
coding
11.Systematic
combinations
of 10 digits		135-03-1228Abbreviations,
nomenclature,
etc.		Social
Security
No. of
a person		Numeric
coding
12.Systematic
combinations
of 2 marks		✓,✕,✕,✓,✓Checking
lists,
etc.		“yes,” “no,”
“no,” “yes,”
“yes,”
respectively		Binary
coding

With 2 units of information or 2 binary digits (1 or 0) we can represent 4 pieces of information:

00, 01, 10, 11

With 3 units of information we can represent 8 pieces of information:

000, 001, 010, 011, 100, 101, 110, 111

With 4 units of information we can represent 16 pieces of information:

0000000100100011
0100010101100111
1000100110101011
1100110111101111

Now 4 units of information are sufficient to represent a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and allow 6 possibilities to be left over; 3 units of information are not sufficient. For example, we may have:

0000050101
1000160110
2001070111
3001181000
4010091001

We say, therefore, that a decimal digit 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 is equivalent to 4 units of information. Thus a table containing 10,000 numbers, each of 10 decimal digits, is equivalent to 400,000 units of information.

One of the 26 letters of the alphabet is equivalent to 5 units of information, for, 5 binary digits (1 or 0) have 32 possible arrangements, and these are enough to provide for the 26 letters. Any printed information in English can be expressed in about 80 characters consisting of 10 numerals, 52 capital and small letters, and some 18 punctuation marks and other types of marks; 6 binary digits (1 or 0) have 64 possible arrangements, and 7 binary digits (1 or 0) have 128 possible arrangements. Each character in a printed book, therefore, is roughly equivalent to 7 units of information.

It can be determined that a big telephone book or a big reference dictionary stores printed information at the rate of about 1 billion units of information per cubic foot. If the 10 billion nerves in the human brain could independently be impulsed or not impulsed, then the human brain could conceivably store 10 billion units of information. The largest library in the world is the Library of Congress, containing 7 million volumes including pamphlets. It stores about 100 trillion units of information.

We can thus see the significance of a quantity of information from 1 unit to 100 trillion units. No distinction is here made between information that reports facts and information that does not. For example, a book of fiction about persons who never existed is still counted as information, and, of course, much instruction and entertainment may be found in such a source.

PHYSICAL EQUIPMENT FOR
HANDLING INFORMATION

The first thing we want to do with information is store it. The second thing we want to do is combine it. We want equipment that makes these two processes easy and efficient. We want equipment for handling information that:

1. Costs little.

2. Holds much information in little space.

3. Is permanent, when we want to keep the information.

4. Is erasable, when we want to remove information.

5. Is versatile, holds easily any kind of information, and allows operations to be done easily.

The amount of human effort needed to handle information correctly depends very much on the properties of the physical equipment expressing the information, although the laws of correct reasoning are independent of the equipment. For example, the great difficulty with spoken sounds as physical equipment for handling information is the trouble of storing them. The technique for doing so was mastered only about 1877 when Thomas A. Edison made the first phonograph. Even with this advance, no one can glance at a soundtrack and tell quickly what sounds are stored there; only by turning back the machine and listening to a groove can we determine this. It was not possible for the men of 2000 b.c. to wait thousands of years for the storing of spoken sounds. The problem of storing information was accordingly taken to other types of physical equipment.

PHYSICAL EQUIPMENT FOR
HANDLING INFORMATION

No.Physical
Objects		Arranged
in or on		Operated or
Produced by		Low
Cost?		Little
Space?		Perma-
nent?		Eras-
able?		Vers-
atile?
(1)(2)(3)(4)(5)(6)(7)(8)(9)
Mind
1.Nerve
cells		Human
brain		Body✕✓✓✓✓✓✓
Sounds
2.SoundsAirVoice✓✓✓✓✕✕✓✓✓✓
3.Sound-
tracks		Wax
cylinders,
phonograph
records		Machines
and
motors		✓✓✓✓✕✓✓
Sights
4.MarksSandStick✓✕✓✓✓✕
5.Colored
painting
canvases,
etc.		Cave
walls,		Paintbrush
and paints		✕✕✓✕✕✕
6.Marks,
inscript-
ions		Clay,
stone		Stylus,
chisel		✕✕✓✓✓✕✕✓
7.MarksSlateChalk✓✕✓✓✓✓
8.Marks
parchment,
etc.		Paper,
and ink,
pencil		Pen✓✓✓✓✕✓✓
9.Letters,
etc.		Paper
books
etc.		Printing
press,
movable
type,
motor,
and hands		✓✓✓✓✓✓✕✕✓✓
10.Photo-
graphs		Film,
prints,
etc.		Camera✓✓✓✓✕✕✓✓
11.Letters,
etc.		Paper,
mimeograph
stencil,
etc.		Typewriter
and
fingers		✓✓✓✓✕✓✓
Body
12.GesturesSpaceBody✓✕✕✕✓✓✕✕
13.FingersHandsBody✕✕✕✕✓✓✕✕
Objects
14.PebblesSlabHands✓✓✓✓✓✕✕
15.KnotsStringHands✓✓✓✓✓✕✕
16.Tallies,
notches		StickKnife✓✓✓✓✓✕✕✕✕
17.BeadsRods in
a frame,
abacus		Hands✓✓✓✓✓✕✕
18.Ruled
lines,
pointers		Rulers,
scales,
dials		Hands,
pressure,
etc.		✓✓✓✓✓
Machines
19.Counter
wheels,
gears,
keys,
lights,
etc.		Desk
calculating
machines,
fire-control
instruments,
etc.		Motor
and
hands		✓✓✓✓✓✓
20.Punched
cards
and
paper
tape		Punch card
machinery,
teletype,
etc.		Motor
and
input
instructions		✓✓✓✓✓✕✓✓
21.RelaysDial
telephone,
other
machinery		Motor
and
input
instructions		✕✓✓✓✓✓✓
22.Elect-
ronic
tubes		MachineryMotor
and
input
instructions		✓✓✓✓✓✓✓
23.Magnetic
surfaces:
wire,
tape,
discs		MachineryMotor
and
input
instructions		✓✓✓✓✓✓✓✓✓✓
24.Delay
lines:
electric,
acoustic		MachineryMotor
and
input
instructions		✕✓✕✓✓✓✓
25.Electro-
static
storage
tubes		MachineryMotor
and
input
instructions		✕✓✓✕✓✓✓✓

What are the types of physical equipment for handling information, and which are the good ones? In the table on [pp. 16-17] is a rough list of 25 types of physical equipment for handling information. ✓✓ means “yes, very;” ✓ means “yes, adequately;” ✕ means “not generally;” ✕✕ means “not at all.”

For example, our fingers ([see No. 13]) as a device for handling information are very expensive for most cases. They take up a good deal of space. Certainly they are very temporary storage; any information they may express is very erasable; and what we can express with them alone is very limited. Yet, with a typewriter ([see No. 11]), our fingers become versatile and efficient. In fact, our fingers can make 4 strokes a second; we can select any one of about 38 keys; and, since each key is equivalent to 5 or 6 units of information, the effective speed of our fingers may be about 800 units of information a second.