(after we have glanced at the topic, we will now extract the keywords establishing their meanings and relating them with whatever we can with the terms, anecdotes, or some historical event)
(What comes to our mind when we think of the word ‘mathematics’ – numbers, data, facts, equations, numerals, integers, laws of geometry, statistics, graphs, trigonometry, calculus, algebra, etc. Mathematics as a subject evokes fear and a sense of restlessness. It looks boring and difficult.
Music – an art form, patterns of sound, harmony of melody, symmetry of composition, balance. Music is innate. It’s cultural. It can be developed. It stimulates. It is linked to emotions. It’s spiritual. It inspires. It uplifts.)
The phrase “Mathematics is the music of reason” very beautifully encapsulates the amicable relationship shared between mathematics and human intellect. While mathematics tries to add rhythm and resonance to make an orderly understanding, music appeals to our hearts and souls. Mathematics resonates with our intellect while music captivates our soul.
Mathematics and music both serve as the universal languages. Mathematics is the language of the intellectuals while music is the language of the aesthetics. As Shakespeare has said, “Music is the food of love”
It means that those who are in love, understand the rhythm and patterns of music very deeply.
It means that music serves as the life–breath of love as it caters to our emotions. On the superficial level, there seems no connection between these two. But when we delve deeper into their essence, their harmonious relationship becomes apparent. Both are such types of disciplines that have transcended boundaries and cultures etc. They establish a connection with the fabric of the universe by resonating with the themes and patterns inherent therein.
(Transitioning from the intro to the body should be smooth and lucid. It should contain our course of action.)
This discourse establishes a relationship between mathematics and reason by exploring the depth of their meanings. Both fields are ever-present and ever-evolving underpinning advancements in the fields.
(talking about the historical context of the topic can be a good start for the body)
Historical Context –
Ancient Civilizations and Mathematics
The most revered ancient civilization of the Indian subcontinent i.e. the Indus Valley Civilization had its very foundation rooted in mathematics. Its grid pattern of streets, use of weights and measures, use of seals for trade and commerce, the great bath, etc. are all examples of mathematics.
Later on, with the coming of the new age, the significance of maths kept on increasing. Aryabhatta, the great mathematician came during the Gupta period. He contributed to the fields of astronomy and mathematics. He also did phenomenal work in the field of quadratic equations which are taught even today. The world is indebted to the Indian mathematician Brahma Dutta who invented zero.
In the world also, the Egyptian Pyramids speak volumes of their mathematical brilliance. Their inclination on a certain angle, aligning them to cosmic events showcases a deep understanding of geometry and the everlasting legacy of mathematics.
Mathematics and the Nature
Mathematics serves as the language of the universe. The natural laws are guided by mathematics. Ranging from the orbits of the planets to the growth of populations to the calculation of astronomical distances are all governed by the magic of mathematics. Also, scientists and engineers always rely on maths for their inventions and thus contribute towards the betterment of society.
Mathematics in Art and Architecture
Temples, monuments and various other architectural buildings offer evidence of intricate geometric patterns of mathematics. While living in our homes we might not be able to give attention to the mathematical precision out in its construction.
Mathematical precision is also very much required in sculptures, paintings, and whatnot!
Mathematics in our Daily Lives
Mathematics is not an instrument of scholars and intellectuals only rather it is a discipline that intertwines with our routine life. From daily groceries to monthly budgets all require mathematics. The disciplines like cooking and sports might seem unrelated to mathematics but they also require it. We need balanced amounts of different ingredients to come out with perfect dishes and mathematical statistics is also required in sports for determining the wins and losses of a particular team.
What is bargaining? This is an art used by the buyer that is backed by mathematical reasoning in our daily lives. Whether it is the vendor or the buyer both need it.
(Here, we come to the point that what is reasoning?)
Reason – logic, rationality. The mindset that looks for cause–effect relationships. The truth that explains. What can be proved? Which has scientific evidence. Thinking and questioning mind. Debates, curiosity, etc.)
Role of Reasoning in Daily Decision-Making
We might underestimate the crucial role played by mathematics in our daily lives. Our daily decisions are backed by mathematical reasoning consciously or unconsciously. Mathematics comes to our rescue not only in finding the quickest route to our work but also in determining the best saving (or investment) plans. It enables an individual to think critically and analyze problems. Thus, mathematical reasoning involves the recognition of problem patterns and deriving solutions to them.
Now that we have explored the relationship between the three i.e. mathematics, art, and our daily lives; we will try to find out the rhythm or a deeper connection that tries to bind mathematics with music.
(Relationship between Mathematics and Music)
Music (Rhythm and Time): Maths ( calculations) behind beats
Mathematics is not boring. Its beauty lies in the fact that it gives rationality and scientific study a coherence and a pattern that is similar to rhythm, and symmetry in music. Every musical beat has some rhythm or pattern that is backed by some mathematical logic or patterns.
Scales and Frequencies: Mathematics Behind Music
The harmonious and soothing sound that we here is a result of a specific ratio of frequencies. If this ratio gets disturbed sound patterns are also disturbed. Therefore, each note in music is woven into a pattern with a series of repeated rhythms that is based on mathematical calculations.
Mathematics and Classical Compositions
The composition of classical ragas is a prime example of the harmonious relationship of patterns based on mathematics. Mathematics serves as a binding agent across cultures
Mathematics as the language of the Universe
Mathematical language is the universal language. Mathematical truths are the universal truths. They transcend boundaries, cultures, and epochs without any change. They remain constant whether it is the Pythagoras Theorem or some Algebra all are shared globally. There have been great Indian mathematicians in ancient as well as Modern times like Aryabhatta, Brahma Dutta and M. Vishweshvaraiya etc. who contributed largely to the field of mathematics.
(We will come here with the benefits of mathematics)
Cognitive Benefits gained from mathematical reasoning
More than solving equations, mathematics shapes our minds. It enhances our creativity and problem-solving skills. These skills help us in decision making thus easing our lives.
Challenges and Criticism
The Debate on Mathematical Education Methods
Our traditional education system emphasizes rote learning and memorization which has the potential of stifling our creativity. It often poses a challenge to mathematics as mathematics relies on practical applications.
Sometimes, over–reliance on mathematics has serious repercussions. Flawed mathematical models that are not driven by real-world uncertainties result in economic downturns and thus have practical implications.
(Pre – conclusion remarks)
But still, we know that without mathematics, all scientific study will become disconnected and will remain in silos of unrelated observations that cannot converge. Without equations, data-driven analysis, quantification, and numerical rigor it will be impossible for any reasoning or logical interpretation to drive universal laws or theories that capture the essence of scientific investigation.
Thus, by discerning from its ancient roots to contemporary relevance, mathematics shows a harmonious pattern that is in sync with musical compositions. Mathematics has symmetry much like music.
Conclusion
The adage, “mathematics is the music of reason” holds as there is mathematics involved in logical reasoning. Reasoning thus has specific patterns as in music. There is an amicable blend of logic and patterns in mathematics that resonates with music. There is a symphony in mathematical reasoning which has the potential to enrich not only our cognition but also elevating the societies.
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