Waves with its crest and trough is not merely theoretical ideas found in textbooks and mathematics. These oscillations resemble the triumphs and challenges, moments of joy and misery of our lives that leads us to development and resilience.
Mathematically, waves are functions that rise to crests or the highest points and falls to troughs or the lowest points. These oscillations are controlled by laws of nature and happens in precision. Similarly, everyone experiences high points in life, personal achievement, personal growth, family and relationships, financial and material success, moments of joy and fulfillment. But these could be preceded or succeeded by challenges that tests our strength. These cycles are unavoidable and intrinsic in human experience.
Consider the wave’s crest. It stands for the times when life feels boundless and thrilling. These are the moments when our efforts pay off. Standing at the crest is like reaching the top of the mountain, it offers breathtaking view and a sense of achievement that justifies every struggle. However, just as waves are not permanent, these high points may not last forever.
Conversely, the trough can feel overwhelming. These are the times when life seems burdensome and progress is elusive. Personal struggles, career and financial challenges, relationship breakdowns, personal failures, regrets, and loss drag us down like the ebb of waves. However, we do acquire strength and resilience in these troughs. Like troughs that is an integral part of a wave’s cycle, our challenges are crucial to our development. They teach us humility and inspire as to rise anew.
The sine and cosine functions, which are sophisticated mathematical formulas that precisely map oscillations, controls waves. Their form is just as beautiful as their predictability. While life is far less predictable, it is possible to feel better knowing its oscillatory nature. The highs serve as a reminder that the lows are temporary, while the lows give significance to the highs. Our journey is a narrative defined by the interplay between crests and troughs.
Thus, let us emulate the waves that keeps going despite its ups and downs. The continuous oscillation of waves shall remind us that life’s highs and lows are transitions rather than end points. Every swing is a chance for development, a chapter in our story. Perspective is the key in navigating life’s waves. We attain equilibrium when we celebrate our crests without complacency and face our troughs with hope. Life finds its balance throughout time, just as every wave returns to equilibrium.
Ultimately, crests and troughs serve as reminder of our humanity. They teach us to enjoy the highs and endure the lows. In doing so, we navigate the waves of existence and harmonize with them creating a melody that is exclusively our own.
Rozsi P. Tobias serves as an assistant professor at Benguet State University – Bokod Campus. She holds a masters degree in mathematics.
The Teachers' Guide International Magazine, January 31, 2025 (ISSN 2984-9799)