From can be seen as a result. In

From the text of Science and Method, we have learnt from Poincaré about intellectual
beauty. According to Poincaré, intellectual beauty refers to the intimate
beauty that comes from the harmonious order of the nature, and it can be
grasped by pure intelligence (Poincaré 165). Simplicity and harmony are the
main characteristics of the intellectual beauty. Harmony refers to “similarities
hidden under apparent discrepancies” (Poincaré 165). Poincaré said the reason
why he studies the nature is because “he takes pleasure in it, and he takes
pleasure in it because it is beautiful” (Poincaré 165). It is believed that the
intellectual beauty has been revealed in our understanding of the nature. In my
opinion, intellectual beauty has been shown in our understanding of the nature
in not only science but also mathematics. Different ways of showing
intellectual beauty will be discussed in the following.

 

First, the methods in understanding the nature
includes intellectual beauty, which can be seen as a result. In The Principia, Newton combined
mathematical methods and physics to propose the law of motion in explaining the
movement of objects (Newton 59). These three rules can be applied on all
objects in spite of their shapes, sizes, time and also the space they are
located in (Newton 66-68). Therefore, the law standardizes the movement of
celestial objects and terrestrial objects, in which they are separated into two
systems in Aristotelian physics (Cohen 55). Apart from that, natural selection is a principle to
illustrate the beauty.

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In On the Origin of Species, some European claimed that every
species was created independently. By the observation and investigation into the
characteristics organisms in South America, Darwin pondered that all species
are not separately created. After doing experiments, he made a conclusion that
every species is formed by natural selection (Darwin 84). It is mean by “through
Divergence of Character and Extinction, on the descendant from a common parent,
Explains the grouping of all organic beings” (Darwin 73). Regardless of the
species or living places, all organism including human are under the principle
of natural selection to evolve.

 

Both are the examples show the way people
understand the world by simplicity. In Newton’s establishment of Law of Motion,
it uses three simple rules to explain all the phenomena of the world to make it
more understandable in knowing the nature. While Darwin investigates in all
kind of species and finally concludes one principle of the nature’s operating
method, the natural selection, which can be applied on all organism. A variety
of things happened in the world can simply be analyzed into few rules to comprehend.

The characteristic simplicity of intellectual beauty can be found in the
findings of either Newton or Darwin experiments.

 

Intellectual beauty can be seen in the way of
pursuing and establishing the understanding of nature. In Element, in approving the existence of geometry, Euclid first give
twenty-three definitions to it (Euclid 275-276). He introduces that his
geometry is an axiomatic system which is the summary of all theorems from small
number of axioms (Euclid, 276-277). Then he uses five axioms or postulates as a
self-evident truth to prove it (Dunham 262). Looking on to Newton’s approach in
formulating law of motion, showing in The
Principia, defines his ideas by giving five definitions (Newton 63-65).

After that, the axiom or called the law of motion is confirmed by three
different laws. From the examples, we can see that the approach of proving the
existence of geometry by Euclid is as same as the way used by Newton. They both
provide definition of the structure to their theory. Furthermore, what they
announced axiom to elaborate their theory and its potential limitations. These
two methods show harmony of intellectual beauty. The similarities are hidden in
these completely distinctive ideas. One is about dynamics, such as standardizing
the movement of the objects while one is about mathematical rules. They are
describing two independent systems but the process of proving the truth are
similar to each other. It means that the two rules are discordant at first we
see, but then if we pay more attention on it, we may notice that there is a
resemblance even the matters are not the same. The above is part of the beauty
of harmony in understanding our world in mathematics and science in nature.

 

Having a sense in beauty is a help in understanding
our nature. In DNA: The Secret of Life,
the discovery of deoxyribonucleic acid (DNA) structure can be an example to
illustrate the idea. At the beginning, Watson tries so many experiment and makes
assumptions that DNA would be a chain or a three-chain model (Watson 130). However,
he still cannot figure out the structure of DNA. Occasionally, by looking at
the X-ray photos of A and B form of DNA, the differences in the amount of water
in DNA molecule gives an inspiration to Watson (Watson 130). He then discovered
DNA as a helix. After trying very hard, he proposed that things are not so
complicated in the nature and would be similar and simpler. “As a biologist, I
preferred the idea of a genetic molecule made of two, rather than three
components” said by Watson (Watson 131). So, he used the idea of genetics which
contains a pair of chromosome as the assumption to hypothesize that DNA could
be a double helix module. And finally, he concluded that DNA is a twisted
ladder of the double helix (Watson 140). We can see that, from this example, if
we are sensible to beauty in which the discrepancies behind may have something
in common, and pay effort to pursue what we believe, nature thus can be interpreted
in various ways easily. Sense of harmony provides us with some ideas in solving
the sophisticated problem in science. It is applicable in understanding our
nature.

 

When conducting experiments or doing research
studies, some of the scientists may go to the extreme, in the infinitely great
and in the infinitely small (Poincaré 163). Analyzing DNA structure and examine
the movement in the universe are examples of macroscopic and microscope aspects
in understanding the world respectively. Different theories and phenomena can
have similar or even the same principle behind which makes it very simple to
understand the world. Because of have resemblance in structure, Albert Einstein
tries to propose the unified field theory to summarize the fundamental elements
reaction in the nature (Sauer, 2007). What Einstein believe is that the world
can be used by one principle to explain all the similarities among the nature as
well as to unifying his general theory of relativity with electromagnetism
(Sauer, 2007). Ultimately, the world is a very simple and harmonious which the
intellectual beauty is obtained by uncovering the nature.

 

In conclusion, people use different ways in
understanding our nature. Physical, ecological and mathematical perspectives
are shown as the examples to illustrate how beauty can be found in the process
and the result in pursuing the understanding of our nature. Beauty in nature is
a motivation of the scientists to do the research and experiments. It is
believed that beauty is embodied as a part of understanding in nature. Indeed,
searching for the intellectual beauty can lead to not only obtainment the
knowledge that not yet be discovered, but also the comprehension of the nature.

Therefore, we can have a better understanding on the place we are living.