Presentation Index
1. Morris Kline’s ‘Math, dominating the
civilization’
2. Blaise Pascal
3. Mathematicians
related to probability
* Math doesn’t have grown as the math itself. It has been continuously grown
under the influence of religion, aesthetics, society, history and art and during the
growth, it sometimes made an effect on them reversely. Through the process, it
has made a great effect on not only natural science which can be thought
commonly but also studies such as religion, aesthetics, society, history and art.
Probability theory can be a representative example. Probability theory was not
just created by simple academic request from the process of creation. It was
created by the request of cultural life, ‘gambling’. Thus, probability theory started
by practical consideration accelerates the development with just pure
mathematical thought during the development. At present, probability theory is
not only used often in daily life but also applied to various fields such as
insurance company, genetics, astronomy, etc. Probability theory shows several
common characteristics during the application.
Through the common characteristics appeared in the process, appearance and
application that probability theory has been developed until now, factors which
make an effect on the development of probability theory were examined and
future’s development of probability theory was expected.
Probability started from the things related to actual life, such as coincidental
game, prophecy, drawing lots, card game, lottery, etc. In the 16th century, Europe
encountered rapid changes while changing the production of manual industry to
mass production system using machine. As the result, the trade war for selling
lots of goods made by mass production became fierce and finally, they tried to
sell products to other countries beyond the sea. On the other hand, merchants
and sailors often went and came in most of harbor cities and they sometimes
gambled in bar, etc. during their spare time. The purpose of gambling is to earn
money, so people are interested in the possibility for winner.
In about the 16th century, there were people who studied on gambling
theoretically by applying to the coincidental game, among the Italian
mathematicians. Among them, especially, Cardano was much interested in
gambling, so used math for the calculation of possibility for winning a game. In
about 1526, Cardano wrote the book related to gambling, "Liber de ludo aleae'.
Some people consider that that time is a starting point that probability concept
was theorized.
Through the common characteristics appeared in the process, appearance and
application that probability theory has been developed until now, factors which
make an effect on the development of probability theory were examined and
future’s development of probability theory was expected.
Probability started from the things related to actual life, such as coincidental
game, prophecy, drawing lots, card game, lottery, etc. In the 16th century, Europe
encountered rapid changes while changing the production of manual industry to
mass production system using machine. As the result, the trade war for selling
lots of goods made by mass production became fierce and finally, they tried to
sell products to other countries beyond the sea. On the other hand, merchants
and sailors often went and came in most of harbor cities and they sometimes
gambled in bar, etc. during their spare time. The purpose of gambling is to earn
money, so people are interested in the possibility for winner.
In about the 16th century, there were people who studied on gambling theoretically
by applying to the coincidental game, among the Italian mathematicians. Among
them, especially, Cardano was much interested in gambling, so used math for the
calculation of possibility for winning a game. In about 1526, Cardano wrote the
book related to gambling, "Liber de ludo aleae'. Some people consider that that
time is a starting point that probability concept was theorized. So, several
phenomena which will be occurred in the future will be expected accurately.
Weather prediction is still insufficient for the accurate ‘expectation’ because it
doesn’t consider regional changes sufficiently.
Those matters will be developed to the direction of more accurate ‘expectation’
by considering additional factors formed locally, such as tectonic activity, warm
current and cold current. In a movie, ‘Minority Report’ whose background is 2054,
the free crime system expects time and location of crime and even criminal
previously through the probabilistic analysis. Based on them, special policemen
of the free crime arrest future’s criminals. There is a possibility to be developed
to consider enough variables like that.
And, the development will be continued in application field rather than the study
itself. Until now, studies on probability theory and probabilistic knowledge, way to
treat the data related to probability statistically and its meaning, have been
conducted sufficiently. In the future, the study on ‘how to reduce the error of
expectation on particular problem with probability theory’, rather than
development of probability theory, will be mainly conducted. It means the study
on the method of relation for accurate expectation when lots of variables are
related to probabilistic calculation.
The study can be progressed mainly in this direction because the request of each
enterprise and each person is high. Probability theory includes the meaning of
‘expectation’ itself. One of the greatest reasons that human usually feel
uneasiness and fear is uncertainty of future and probability theory relieves it even
a little. For relieving uncertainty, studies on the application of probability theory
should be conducted, not stopped in the studies on probably theory itself. When
improving the accuracy of probability with direct application, expectation also
becomes accurate and uneasiness human feel for their future will be reduced.
2. Blaise Pascal
* French mathematician, physicist, philosopher and religious thinker. Born in
Clemont-Ferrand of Auvergne area.
People commonly say that Pascal could’ve been the greatest mathematician.
Several stories of his young period are passed down by Nui Zealvert who
became a wife of Perri. When Pascal was 3 years old, he lost his mother.
Because of his weak body, he was raised carefully by studying at home with
private teacher, without overwork. His father let him be educated by linguistic
education excluding math, so he became more curious. Because of the
curiosity, Pascal sometimes asked private teacher a question related to math.
He was stimulated by teacher’s explanation of geometry and father’s objection,
so he concentrated on studying secretly in his spare time. Therefore, he
learned the characteristics of geometry and especially, realized that the sum of
triangle’s inner angles is 180° for himself within several weeks. The sum of
triangle’s inner angles was examined by folding paper like the below picture.
His father who watched him was very
surprised, so brought his son Euclid
“original copy”.
When he was 12 years old, he inferred
arranges 1-32 of Euclidian geometry
alone. And, at the age of 14,
Pascal participated in weekly meeting
of French mathematicians association
which became French academy later. At
the age of 16, he presented important
arrangements in a small thes is on conic section (Essay on Conics) that
Descartes said he couldn’t believe it was young person’s work at all
and insisted it was certainly his father’ss. This theory known as
Pascal’s theorem is that “The contact of opposite side of hexagon
inscribed by one conic section is on the same straight line and its
reverse also comes into existence.”
It became one of fundamental arrangements of projective geometry. At the age of
17, he drew 400 propositions with the theory in one thesis on conic section.
In 1640, he started to invent calculator so as to help his father who was a tac
officer (徵稅官). He was successful in 42 and the final model was completed in
1652. It was called by ‘Pascal’s calculator’. Pascal made about 50 calculators
and one of them is still kept in the museum located in Paris. While treating
father’s ankle for 46 years, he got to know Jansenist, so he and his family
participated in reform movement of Jansenism. It’s called as the first returning
mind (回心). In that year, E. Torricelli’s experiment for vacuum was additionally
conducted and it was successful. And, in 47, he presented <new experiment for
vacuum>. It overturned the traditional concept, ‘the nature hates vacuum so much’
based on the authority of Aristotle. In the next year, the experiment was
successful on the top of Puv de Dome Mountain with the help of wife’s brother
and it verified the weight of air is only one reason to stop mercury. Based on the
experiment, he presented <the story of big experiment on fluid’s balance> on Oct.
of the year and discovered <Pascal’s theory> which is the whole of hydrostatics
after widening his thought. It explains that if the pressure of one point in fluid
stopped in closed container is increased by some size, the pressure of all points
in fluid is increased by same size. “Pascal’s law” for fluid’s pressure and volume
is known to all students learning physics in high school today. (The unit of
atmospheric pressure, Pa(Pascal), is named by the Pascal’s name.)
After his father was died in 51, his younger sister, Jacqueline, entered Port Royal
Abbey. Unlike, Pascal became friendly with free thinkers such as Roanesgong (公),
Chevalier de Mere, etc, entered high society and pursued pleasure of life. Also, he
recognized the necessity of hobby judgment, spirit different from scientific spirit.
It was lately helpful to discriminate between ＜geometric spirit＞ and spirit of life
and art, ＜esprit de finesse＞. Also, Pascal established the probability theory with
Fermat. At that time, the famous problem they studied was "which way to divide
stake is the most rational way when stopping the game during the gambling?"
While studying on this problem, Pascal’s triangle was discovered. This triangle
was made by simple addition, but pattern’s development and research in this
triangle became the useful tool to explain the relationship among counting, index,
algebra, geometric form, Samkya.
*AD 1623 Born in Clermont-ferrand of France
*1626 Mother was died.
*1631 Moved Paris with family
*1635 Arranged 1-32 arrangement of Euclidian geometry for himself
*1638 His father, Etienne, participated in the protest movement for the reduction
of Paris bond’s interest rate and escaped to his hometown
*1639 Younger sister, Jacqueline, appealed for father’s pardon through the in
drama in front of a prime minister, Richelieu. Father was nominated as a
person charge of tax collection in Normandy area in autumn and
appointed to Rouen.
*1640 Published <Essay on Conics》(Pascal’s theorem) 1646 Participated in the
reform movement of Jansenism (the first returning mind). Succeeded in
additional experiment of E. Torricelli’s vacuum experiment
*1647 Returned to the old house of Paris for the treatment of disease, Presented
<new experiment for vacuum》
*1648 Presented <the story of big experiment on fluid’s balance》
*1651 Father was died.
*1654 Experienced grace light (decisively returned mind)
*1656 Published <the 1st letter> of <letter for rural friend (les Provinciales)》
*1657 Published <the 18th letter>, the last letter of <letter for rural friend
(les Provinciales)》
*1658 Wrote <questions of cycloid>, Wrote most of <Pensees》
*1659 Took a serious turn for his disease
(presumed)
*1661 Suppression for Port Royal Abbey became serious.
*1662 He was died on Aug. 19.
After Cardano was died, the studies on gambling started earnestly in
the 17th century, in France. Among the famous gamblers at that time,
Chevalier de mere obtained lots of interests through the mathematical
thought during the gambling. If there was any problem during the
gambling, he asked his genius friend, Blaise Pascal (1623～1666).
Pascal agreed to treat the problem of de mere, wrote several words of
letter to another genius mathematician, Pierre de Fermat (1601～1665).
Meanwhile, two people talked about gambling and established the
probability theory of modern form.
[a ,b , a, b, aa, ab, ba, bb] The question de mere asked Pascal is 『A
and B whose abilities are similar each other played for 32
pistol(Spanish gold coin of ancient time). In the competition, 1 score
can be obtained with one time of winning. And, person who obtained 3
scores firstly will take all of 64 pistols. If the game was stopped
because of one person’s unavoidable situation at the time A obtains 2
cores and B obtains 1 score, which way to distribute 64 pistol is fair?』
Many people tried to solve the problem actually, but there was nobody
to raise correct answer. Pascal sent the following reply after a long
thought. 『Answer: If A wins in the next game, A won 3 times, so A
can take all of the money. If B won, A won two times and B won two
times, so two people can be distributed by 32 pistol respectively.
In other words, A must take 32 pistol regardless of victory. A winner of the
next game becomes the final winner and the possibility for winning is half
because we don’t know how will win. Therefore, remained 32 pistol must be
distributed to each person by same pistol respectively. Finally, A has
32+16=48(pistol) and B has 16(pistol).』 However, Fermat thought in the
way different from Pascal’s a little. 『In this case, victory is decided by less
than 2 times. In this games, the ratio between B wins in all of two games
and A wins by obtaining 1 time at least is 1:3. Therefore, if dividing 64 pistol
under the ratio of 1:3, B will have 16 pistol and A will have 48 pistol.』Pascal
and Fermat approached same result in spite of different way.
Besides, de mere enjoyed making mathematical puzzle problem, so asked
Pascal for several questions. Among them, the famous question called as
‘de mere’s puzzle’ is『which has more possibility between 6 is appeared
more than one time while throwing dice for 4 times and all of two dices show
6 more than one time while throwing two dices for 24 times. De mere
inferred that average number of successful throwing will be same the
following two gambling.
Soviet mathematician. He graduated from Moscow University in 1925 and
was a professor of the university from 31 to 59. And then, he was installed
as a head of mathematics and dynamics laboratory in this university, became
a member of scientific academy in 39 and obtained stalin prize of 40 years
because of the study on probability study. He learned by N.N. Lusin, a
central person of Moscow Mathematical Association, and he was influenced
by him. He also made an effort to pioneer probability theory through the
succession of Moscow Mathematical Association’s tradition. Mathematical
study of probability had been started already, but the true meaning was
revealed by Moscow school and people including E. Borel in Paris at the
early stage of the 20th century. They insisted that the range and place must
be
clarified so as to consider the probability the arrow of lottery is shot which
part of target. Also, it was also problems, which range must be integrated in
integral calculus. Thus, probability and integral calculus resolved themselves
into clarifying the range, in other words, common problem, which gathering
is an object. At that time, Kolmogorov succeeded to axioatize probability
theory based on the Lebesgue’s integral. Besides the contribution for
probability theory, he greatly contributed for Fourier series, topology and its
application.
Gambling lover establishing probability theory
A famous mathematician and doctor in Italy, His father who was a
descendant of aristocrat was a jurist as a friend of Leonardo da Vinci.
Cardano’s father was died when he was 7 years old. After his father’s death,
he made a living with gambling such as card game, dice play, chess, etc.
because he didn’t be well-to-do. He was rarely defeated in games because
he can calculate probability well. However, he didn’t get rich at all. He
entered Pavia University in 1518, but he obtained the degree in Padova
because of the war. He returned to Pavia so as to obtain doctoral degree in
1525. AT that time, he majored in gastrology, so obtained the degree in
medical science. After marriage, he became mathematics teacher, so he
studied on mathematics and physics and became a doctor in rural area. In
1544, he became geometry professor in Milano University.
Cardano studied mathematics, medical science, alchemy, etc. and he wrote
about 200 books related to mathematics, physics, philosophy, medical
science, religious science, acoustics, etc. For his representative books, there
are arithmetic, great technology, astronomy, etc. He showed important
achievements in various areas such as probability theory, hydromechanics,
dynamics, geology, etc. Especially, he won fame with the insistence, “There is
not permanent movement except for celestial bodies.” in the area of
dynamics. The evaluation on his personality was not good. He was badtempered and enjoyed gambling usually.
‘For the game of opportunity’ written by Cardano in 1563 was the start of
study on possibility theory. In this book, there are binomial theorem and ‘law
of considerable number’. Cardano was arrested for several months after
religious trial in 1570. After the release, Cardano went to Rome. In there, he
was warmly received unexpectedly and became a member of physics
association. Pope forgiving Cardano gave him grant. Cardano was died with
fame as a scientist. He predicted his death and killed himself for naming a
date.
An explorer and anthropologist, Galton is a leader of study on human
intelligence and concentrated on study on eugenics in the last period of
his life. In the area of statistics, he developed two theories. Firstly, the
mixture of normal distribution becomes normal distribution again.
Secondly, the concept of reversal which is called as return lately was
unfolded.
He also contributed for the areas of meteorology, anthropometry and
physical anthropology. Galton was a patient explorer and researcher of
human intelligence. Galton who was a nephew of Darwin was recognized
in various areas and the reason was believed by genetic factors. He
objected to the theory that intelligence or personality is decided by
environmental factors. He investigated racial differences and observed
mainly spiritual factors among the races. During the investigation, he used
questionnaire method for the first time. He supported the limitations by
race and blood, through that work.
Thank you
The end