“How can it be that mathematics, being after all a product
of human thought which is independent of experience, is so
admirably appropriate to the objects of reality (Einstein)?”
“How can it be that mathematics, being after all
a product of human thought which is independent of
experience, is so admirably appropriate to the objects of
reality (Einstein)?” This issue has troubled philosophers
as well as scientist since Einstein first posed it. To
answer what Einstein meant when he asked the question, a
person must understand what mathematics really is. The
physical world is very important to understand when looking
at the question. When deriving a meaning from Einstein’s
statement it is necessary to restate the quote in a
simplistic style and understand how mathematics can work
for situations dealing with the physical world. I believe
that mathematics is very useful to the understanding of
reality because we want it to be. For example, in the
movie PI, when Max Cohen, a mathematical genius, was
looking for the number 216 and he kept finding that number
everywhere he looked. All of the problems that humans
face are there because they are blocking the answer society
The Term Paper on Arabic Mathematics
Arabic Mathematics Everybody would agree that mathematics owes a great debt to the Arabs. Just as George Sarton, a famous Harvard professor of history and science wrote in his not less famous Introduction to the History of Science: From the second half of the eighth to the end of the eleventh century, Arabic was the scientific, the progressive language of mankind. When the West was sufficiently ...
or a particular human is looking for.
Mathematics is subvertly known as a group of related
subjects, including algebra, geometry, trigonometry and
calculus, concerned with the study of number, quantity,
shape, and space, and their inter-relationships, application
s, generalizations and abstractions (beckmann 102).
Mathematics is made up of concepts that are composed of
universal relationships. One example of a mathematical
concept is the number one. One does not exist but we use
this number to represent objects which exist. To understand
the quote, “How can it be that mathematics, being after all
a product of human thought which is independent of
experience, is so admirably appropriate to the objects of
reality?” it is important to realize that when Einstein
speaks of mathematics he is speaking of rationalism. A man
named Descartes, a mathematician who lived from 1596-1650,
first headed rationalism. Descartes argued that all
knowledge obtained through direct observation of nature was
suspect because it comes through the senses, and such
knowledge can notoriously be deceptive, as all kinds of
hallucinations and dreams show (Jeans 34).
Descartes has a
very good point but it is very skeptical to believe that
everything is suspect to deception. There must be some
puritanical things in the world. Two reasons why Descartes
believed that knowledge from mathematical proofs may be
deceptive were 1) mathematicians have often been wrong and
2) people can never be certain that an omnipotent God may
not have decreed that people should be deceived even in the
things people think they know the best (Jeans 35).
I agree
with him for the most part but what about people that do
not believe in God. How would number two be applicable for
them. Also, these statements would discredit the entirety
of scientific knowledge because it might be from unreliable
sources. Descartes also believed that were a number of
principles already imbedded into the brain i.e. the
existence of God. All rationalists believe that all things
can be derived through intuition. Kant, a philosopher,
The Term Paper on Human Knowledge
Anyone writes at one point or another in his lifetime to share his or her experiences, ideas, perceptions, situations, and points of view. Some write everyday in their private diaries to capture their memories. Others write to give way to the expression of their emotions, sometimes, pent up, a fond memory, thoughts, or aspirations, even frustrations. If knowledge is knowing and learning gained ...
believed so strongly that truth is obvious that he claimed
that it would be possible to construct a “pure science of
nature” (Jeans 35).
That is a very bold statement but I
think that most of the philosophers are just too black and
white. If they would just find a medium they would be able
to solve more questions. Another word for rationalism
would be a priori which means previously to, and independent
of, all actual experience of the world. Mathematics is
completely a priori and is derived from intuition.
Mathematics is very important but it is also a
necessity to understand the physical world. Physics’
purpose is to identify the most elementary building blocks
of Nature and the laws that govern them (Barrow 65).
Physics are the physical processes and phenomena of a
particular system. In this case, it would be the universe
that embodies humans and other lifeforms. The physical
world deals with empirical information and is made up of
very complex rules. To understand the quote, “How can it
be that mathematics, being after all a product of human
thought which is independent of experience, is so admirably
appropriate to the objects of reality?”, it is necessary to
understand Einstein is talking about empiricism when he say
s the objects of reality. Empiricism is derived from
experiences rather than from logical principles alone.
Empiricism is also known as a posteriori. A posteriori
means that there are sources in experience (Jeans 35).
As
I stated earlier, this black and white formula which most
intellectuals tend to work with is not the best way to
handle the issue. There should be a word in between a
priori and a posteriori. Empirical logic is strictly,
not able to be known independently of experience. This is
an epistemological property, and hence distinct from the
logical property of being synthetic (Jeans 36).
Epistemology is the study or a theory of the nature and
grounds of knowledge especially with reference to its
limits and validity. In opposition to rationalism,
empiricism is based on experience alone. The two most
The Essay on A World Without Mathematics
According to teachers for as long as any can remember, one cannot survive in this world without mathematics, yet thousands in the United States alone cannot grasp mathematics, cannot learn mathematics because of "Dyscalculia" (also called Dyscalculia). Dyscalculia is a term meaning 'specific learning disability in mathematics.' People who suffer with a poor memory for all things mathematical have ...
prominent empiricists were philosophers John Locke and
David Hume. A reason to why people were persuaded to be
empiricists was because many believed that a person could
not imagine a mathematical point, line, or triangle unless
we had first made the acquaintance of their imperfect
representations in the outer world. Locke believed that
the truths of pure mathematics were not the only issues
which were constructed through empirical views. He believed
that the existence of God and ourselves and the morality
ought to be admitted to the class of intuitive truths
(Jeans 36).
These philosopher are journeying into a very
touchy subject which has been questioned since man could
question. This qoute be the existence of God. Locke
statement about morality and truths can only be answered
to the extent that people can define morality and truth.
The truth of empiricism is what the physical world is based
on.
When Einstein said, “How can it be that mathematics,
being after all a product of human thought which is
independent of experience, is so admirably appropriate to
the objects of reality?”, he was questioning how something
as rationalistic as mathematics can explain something as
empiricalistic as the physical world. The concepts of
mathematics and the empirical physical world are so
different most people would find it difficult to be able
to comprehend that mathematics, a conceptual view, could
explain something as complex as the physical world. Some
philosopher believe the physical world is composed of
many complex equations. I believe that many of these
equations we find are simply there because we want to find
them. For example, when a person buys a new car, that
person suddenly sees his car all over the place. The
number of cars did not simply enlarge when he bought his
new car but simply the equation appeared more translucent.
In the book, Character of Physical Law, Richard Feynman
says that mathematics is related to physics by stating,
“it is perfectly natural that the mathematics will be
The Essay on St Augustine Confessions Physical World
Saint Augustine s Confessions Saint Augustine was believed to be the Christian Plato. He describes Plato with the adulation of an admirer and follower. He achieved most of his knowledge through the interpretations of the immensely popular neo-Platonists. Throughout Augustine s Confessions, he is plagued by the question of how one can know God lies in memory. He believes that memory is the ...
useful when large numbers are involved in a complex
situation i.e. the physical world (Feynman 35).
In
contradictory to that statement, Feynman also says that in
biology the action of a virus on a bacterium is
unmathematical (Feynman 35).
Feynman and many other
scientists and philosophers have tried to answer the how
mathematics can explain something so complex as the
physical world. This answer will come in time just like
the knowledge to these topics will eventually be complete.
The question concerning abstract and empirical
topics and how one can explain another is simply formed
by a biased opinion just like every other philosophical
question. Rationalism will always be prominent as long
as people believe in intuition. Empiricism will also be
just as prominent as long as there are mathematicians and
philosophers that believe that everything is a posteriori.
One explanation for the two separate ideas could be
because the Continentals loved their abstract ideas and
the British’s love for practical investigation. The
complex physical world is and always will be explained by
the a priori mathematics as long as there are people that
want it to be explained that way.
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