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 | Sign | Used in | Significance | Name of Scheme |
| (1) | (2) | (3) | (4) | (5) | (6) |
| Sounds | |||||
| 1. | Sound of new word is like sound of referent | Bobwhite2 | 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 | Chortle4 | Spoken English; invented by Lewis Carroll, 1896 | “Chuckle” and “snort” blended | Analogical |
| 4. | Word has been used through the ages | Mother5 | 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 | 5 | English; 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 | Ʒ | International 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 | ENIAC | Abbreviations, etc. | Initial letters of a 5-word title | Alphabetic coding |
| 11. | Systematic combinations of 10 digits | 135-03-1228 | Abbreviations, 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:
| 0000 | 0001 | 0010 | 0011 |
| 0100 | 0101 | 0110 | 0111 |
| 1000 | 1001 | 1010 | 1011 |
| 1100 | 1101 | 1110 | 1111 |
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:
| 0 | 0000 | 5 | 0101 |
| 1 | 0001 | 6 | 0110 |
| 2 | 0010 | 7 | 0111 |
| 3 | 0011 | 8 | 1000 |
| 4 | 0100 | 9 | 1001 |
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.