Computer Numerals for
Efficient Numeracy for Bringing up Geniuses and Eradicating Poverty, Preventing
Spread of AIDS(HIV),of Tuberculosis, and of Malaria,
and Population Crisis
You can down load PDF
file of " Becoming a Genius?" Text Book of
Computer Numerals!
Computer numerals were
developed using the concept of the binary system to form decimal numerals. This
would allow addition, subtraction, multiplication, and division to be performed
based solely on the knowledge of the 14 forms of the numerals and a few simple
rules. These numerals were taught to several developmentally challenged
individuals. After 4 days of instruction, they were able to add, subtract, and
multiply with little assistance. A Protected Computer
Numerals are proposed against forgery. An International Numeration System is
proposed based on the form of computer numerals to facilitate international
communication. A new type of abacus is proposed.
Introduction
Basic education (Literacy
and Numeracy) has been implicated by several researchers in the prevention of
the spread of infectious diseases, as well as population control, based on the
strong association between these factors and poverty and ignorance (1). The
present paper proposes the use of the abacus numeral system to improve the
efficiency of learning arithmetic. By memorizing the form of the numerals and
applying a few simple rules, the ability to perform addition, subtraction,
multiplication, and division appears to be attainable within a few months. The
form of the decimal numerals is based on the concept of the binary system.
However, knowledge of the binary system is not necessary in order to learn
these numerals. A medieval Chinese numeral system (Table 1) by which addition
and subtraction can be achieved by memorizing the form of the numerals has been
reported previously (2).
Table 1. Medieval Chinese numerals used for
calculation
However, because the Chinese
numerals were developed on the quasiquinary system,
multiplication and division can only be performed by memorizing the
multiplication table. A kind of decimal abacus (Papy's
minicomputer) based on the binary system has been reported to facilitate
addition and subtraction (3). Calculations of multiplication and division by Papy's minicomputer are possible without memorizing the
multiplication table. They are, however, difficult and necessitate much time
except for some simple cases. The abacus numeral system provides an improvement
over the Chinese numeral system and Papy's
minicomputer because multiplication and division can be performed easily
without memorizing the multiplication table. The rules guiding sformation of Computer numerals are shown in Fig. 1.
Fig.1 Rules governing
formation of computer numerals. A Order of height of
ranks of numerals from the lowest are referred to as "ma",
"mu", "mi", "ta",
"tu", "ti",
"sa". Two circles at a certain rank
correspond with a circle one rank higher. Computer numerals for a given number
are formed by putting open circles of that number at the lowest rank
"ma" and then shifting the location of the rank of the circles by the
above rule to minimize the number of circles. B Example of
creating abacus numeral for number 5. C A rule of
decimal system. One circle at rank "ta"
and another circle at rank "mu" are transformed to one circle at rank
"ma" of one higher order.
The actual forms of the
numerals are shown in Table 2 .
Table
2.Table of Computer Numerals and International Numeration System.
Examples of addition by
Computer Numerals are shown in Fig.2. The numerals to be added are joined to
yield the resultant summed numeral.
< P>
Fig.2 Examples of addition:
Resultant Computer Numerals are obtained by joining two Computer Numerals.
Actual calculations can be simplified by moving coins or stones instead of
circles (Fig.6), as is the case of a traditional abacus.
Examples of subtraction
using these numerals are shown in Fig.3.
Fig.3 Examples of
subtraction: Numerals to be subtracted are joined with filled circles or crosses.
A filled circle and an open circle at the same rank cancel each other out.
Actual calculations can be simplified by moving coins or stones instead of
circles (Fig.6) , as is the case of a traditional
abacus.
In the case of subtraction,
the numerals to be subtracted are joined by filled circles or crosses to the
subtracted numerals with open circles to yield the resultant numerals. When a
filled circle or a cross and an open circle appear at the same rank, they
cancel each other out. Multiplication is performed by reforming the numerals as
follows: Multiplication by 1 entails the addition of a given number to zero
once, resulting in the formation of the original numeral. Multiplication by 2
entails the addition of a given number to zero twice, resulting in the
formation of a numeral with two open circles in the original ranks, which
results in one open circle shifted one rank higher from the original rank [The
abacus numeral for 2 consists of single circle in rank "mu" (one rank
higher than rank "ma") and is equivalent to 2 circles in rank
"ma"](Fig.4A).
Fig.4 Examples of
multiplication： A 7x2 and 7x4 B 29x17 , 17 circles in rank "ma" become 17
in Abacus Numerals and 17 circles in A rank and B order higher from
"ma" become Computer Numerals of 17 lifted by A ranks and B orders.
The number 17 in triangle, diamond, and circle on the left hand side means 17
circles at the same rank and same order.
Multiplication by 9 is
performed by joining the numeral nine times, resulting in 9 open circles in the
original rank. That results in a numeral with each circle shifted three ranks
higher in addition to each circle in the original rank [the Computer Numerals
for 9 is equivalent to 9 circles in rank "ma" and consists of one
open circle in rank "ta" (three ranks
higher than rank "ma") and another in rank "ma"].
Multiplication by number of higher order is shown in Fig.4B. Examples of
division are shown in Fig. 5.
Fig.5 Examples of division:
Actual calculation can be simplified by moving coins or stones instead of
circles (Fig. 6), as is the case of a traditional abacus.
In the same way, abacus
numerals can be used for calculation of square roots without remembering the
multiplication table.
Mathematics instruction
using abacus numerals
The author
used Computer Numerals to instruct 5 mentally handicapped volunteers at the NiihariEn Institute with the cooperation of the president,
Mr. Kyuugo Tsukada. The
students consisted of one 23 yearold who had undergone brain surgery and had
an IQ of 61, three subjects (aged 22, 20 and 26 years) who had Down's syndrome
and had an IQ of 39, 32 and 32, respectively, and one subject (26 years old)
who was mentally deficient and had an IQ of 35. They could understand Arabic
numerals but could not perform addition with the carrying procedure nor subtraction with the borrowing procedure. They could not
perform multiplication. All students except one of the two with an IQ of 32
showed interest in the activity and after 4 days of instruction, 2 and half
hours per day, 4 of the 5 volunteers were able to add, subtract and multiply,
although with frequent errors if not assisted.
Protected Computer Numerals
In order to prevent forgery,
which can be performed easily by adding extra circles to Computer Numerals,
vacant positions are occupied by a "+" symbol to form protected
Computer Numerals (Table 3). The protected Computer Numerals can be employed
for important documents such as bonds.
Table 3. Protected Computer
Numerals against forgery.
International Numeration
System
Using Computer Numerals, an
International Numeration System can easily be developed a priori, as outlined briefly
in Table 2. The numeration to show the order can be developed from Fig. 1 by
changing the consonants, while vowels remain unchanged. In order to show the
order of magnitude from 1 to 9 or from 1 to 9, the consonants are changed
from "t" and "m" to "s" and "t". For
example, 6 E9 is changed to "miu satan" and 8 E9 as "ta satakk". To show the
order of magnitude from 10 to 90 or from 10 to 90, the consonants are changed
to "f "and "p" instead of "t" and "m".
And to show the order of magnitude from 100 to 900 or from 100 to 900, the
consonants are changed to "sh"and
"k" instead of "t" and "m". For example, 9E977 is
changed to "tama shakapiupatiutan" and 9.76
E778 to "tama nikk miuma
miu kiukapiupasakk".
The number 1998 is numerated as "ma tuan tama tun tama tan ta (in)". Thus,
the International Numeration System appears to provide a means of facilitating
international communication (4). Learning calculations including zero and
negative numbers can be represented concretely by abacus numerals, and thus
become understandable by intuition (c.f. Fig.3 C and D).
Table 4. International Numeration
System.
Abacus for Computer Numerals
A newly proposed Abacus
System is shown in Fig. 6. This abacus can be constructed simply using an iron
plate and magnets, cloth and coins, or lines on the ground and small stones,
ceramic pieces, shells or grains (5).
Fig.6 Proposed Abacus
System: Two left columns: 47+24 = 71, middle column: 8  4 = 4, two right
columns: 8 x 6 = 48.
Discussion
The use of Computer Numerals
proposed in this work appears to be able to facilitate mathematics instruction.
It seems to be beneficial not only in developing countries but also in
developed countries. Since mathematics learning is basic to any science
including higher mathematics and physics, the use of abacus numerals may
facilitate gifted children in becoming better researchers early in their
careers. The logical nature of calculation by Computer Numerals seems to
stimulate logical understanding of matters in early lives. Further, as the
sciences and technologies develop, more time seems to be required by
conventional methods of instruction for acquiring only basic knowledge for
developing research in the sciences. Therefore, for further advances in the
sciences in t he near future, innovation in instruction seems be required
especially in mathematics, reading and writing , and
in international languages. The use of an octonal
system instead of the decimal system in common practice also appears to
facilitate the application of the abacus numerals due to the simplified
carrying and borrowing procedures.
REFERENCES
1. L.E.Brown
and H. Kane, Full House: Reassessing the Earth's Carrying
Capability,
(W.W.Norton & Co., New York, 1994), Chapter 5.
Yomiuri Shinbunsha, Shikiji (Literacy: in
Japanese), (Akashi Publishing Co., Tokyo,
1990).
United Nations
Development Program, Human Development Report
1990,
(Oxford University Press, New York, 1990), pp.128, pp144.
Preparation of
Literacy Materials for Women in Rural Areas, (Asian Cultural Center for
UNESCO, Tokyo, 1989).
H.Hirose,
Jinrui ni totte Eizu towa
Nanika (What are the implications of AIDS to
Mankind: in Japanese), ( Nihon Hoosoo Kyookai
Shuppan
Kyookai, Tokyo, 1994), Chapter 1.
P.Farmer, M.Connours and J.Simmons,
Women, poverty and AIDS,
(Common
Courage Press, Monroe, 1996).
R.M.Krause,
Science, 257, 1073(1992).
M. Yoshikawa, Saikin no Gyakushuu(Counter Attack of Microbes: in
Japanese),
(Chuuoo Kooronsha, Tokyo,
1995), Chapter 2.
2. G. Ifrah,
Histoire Universelle des Chiffres , (Seghers Ed., Paris, 1981),
Chapter
28.
3. F.Papy,
Mathematics Teaching, 50, 40(1970).
Teacher's Guide, Papy minicomputer, (Macmillan Co., New York, 1970).
4. European Phrase Book, (Berlitz Publishing Co.Ltd.,
Oxford, 1995).
East
European Phrase Book, (Berlitz Publishing Co. Ltd.,
Oxford, 1995).
Asian Culture Center for
UNESCO,ED., Talking with Asian Friends,
23 Asian Languages, ( Kaigyusha, Tokyo, 1989).
5. J.M.Pullan,
The history of the abacus, (Hutchinson & Co.Ltd., London, 1968).
6. Y.Hayakawa,
Abacus
Numerals for Literacy against AIDS and Population Crisis.
Universal
Alphabet for Literacy against AIDS and Population Crisis.
12th World Congress
of Sexology, August 13th, 1995, Yokohama.
7. Y.Hayakawa,
Abacus
Numerals for Easier Learning of Mathmatics.
Development
of Abacus for Abacus Numerals. Development of
International Numeration
System.
The first International
Commission on Mathematical Instruction East Asia Regional
Conference on Mathematics Education(ICMIEARCOME 1), August 18, 1998, Korea
National University of
Education, Kyonbuku, Republic of Korea
8.Y.Hayakawa,
Abacus Numerals for
Effective Learning of Mathematics.,
The 9th International
Congress on Mathematical Education(ICME9) ,
July 30~August 6, 2000,
Chiba, JAPAN
Acknowledgments
The author is indebted to
Mr. Kyuugo Tsukada for his
cooperation in teaching Computer (Abacus) Numerals to the mentally handicapped
youths. The author is also thankful to Dr. Nobuhiko Nohda
and Dr. Jerry P. Becker for their valuable comments.
Universal Alphabet for
Literacy against Poverty, against Spread of AIDS(HIV),
Malaria and Tuberculosis, and against Population Crisis Esperanta Hejmpagxo
·
Your Lives and Your Species(In Japanese)
o
Traffic Safety and 8 Right Methods of Budha(In Japanese)
§ Future of Human Being and
the Development of Medical Siences(In Japanese)
§ Influence of Energy Crisis
to the Society(In Japanese)
§ Pictures of Laboratory Members
§ Pictures at KoreaJapan and AsiaOceania
Congress of Medical Physics September, 2002 in Korea
Theme of Researches
§ Proton Beam Radiation
Therapy(in Japanese
§ Boron Neutron Capture Therapy(in
Japanese)
§ High Temperature Coagulation
atherapy (under construction in Japanese)
§ New CT Scanner with Reduced Xray
Dose(in Japanese
§ Radiation Biology(Under construction)
§ Universal Alphabet for Literacy(in
Japanese )
§ Abacus Numerals for Easier Lerning
of Calculation(to be created:in Japanese )
§ Email Address

Members of Hayakawa
Laboratory 