incommensurable quantity

简明释义

不可通约量

英英释义

例句

1.In mathematics, the concept of an incommensurable quantity refers to two lengths that cannot be expressed as a ratio of whole numbers.

在数学中，不可度量的量的概念指的是两个长度无法用整数的比率来表示。

2.The artist felt that the value of her work was an incommensurable quantity that could not be measured in money.

这位艺术家觉得她作品的价值是一个不可度量的量，无法用金钱来衡量。

3.The diagonal of a square is an incommensurable quantity compared to its side length.

正方形的对角线与其边长是一个不可度量的量。

4.In physics, certain constants may represent incommensurable quantities when comparing different units.

在物理学中，某些常数在比较不同单位时可能代表不可度量的量。

5.Philosophers often discuss the incommensurable quantity of subjective experiences versus objective measurements.

哲学家们常常讨论主观体验与客观测量之间的不可度量的量。

作文

In the realm of mathematics and philosophy, the concept of an incommensurable quantity is often discussed in relation to the nature of numbers and measurements. An incommensurable quantity refers to two quantities that cannot be measured by a common unit, meaning there is no way to express their ratio as a simple fraction. This notion can be traced back to ancient Greek mathematicians, particularly the Pythagoreans, who discovered that the diagonal of a square could not be expressed as a ratio of two whole numbers. This revelation posed significant philosophical implications, challenging the very foundations of mathematical understanding at the time.The idea of incommensurable quantities extends beyond mathematics into various aspects of life, including art, ethics, and even personal relationships. For instance, when we consider the value of a piece of art, it becomes clear that its worth cannot be quantified solely in monetary terms. The emotional connection, historical significance, and individual interpretation all contribute to its value, making it an incommensurable quantity in the context of human experience. Similarly, when discussing moral values, we often encounter situations where different ethical principles cannot be easily compared or measured against one another. For example, how does one weigh the importance of freedom against the need for security? Such dilemmas illustrate that certain aspects of life are inherently incommensurable, defying straightforward quantification.Moreover, the recognition of incommensurable quantities encourages us to embrace complexity and ambiguity in our thinking. In a world increasingly driven by data and metrics, it is vital to acknowledge that not everything can be reduced to numbers. By appreciating the incommensurable, we cultivate a more nuanced understanding of our surroundings and ourselves. This perspective allows for a richer engagement with the world, prompting deeper reflections on what truly matters.In conclusion, the concept of incommensurable quantities serves as a powerful reminder that some aspects of existence resist simple categorization or measurement. Whether in mathematics, art, or moral philosophy, recognizing the limitations of quantification can lead to a more profound appreciation of the complexities of life. As we navigate our experiences, let us remain open to the incommensurable, allowing it to enrich our understanding and foster a greater sense of empathy toward others. Ultimately, acknowledging the incommensurable quantity within our lives can guide us toward a more holistic view of the world, one that celebrates both the measurable and the immeasurable.

在数学和哲学领域，不可度量的数量这一概念常常与数字和测量的本质相关联。不可度量的数量指的是两个数量无法通过共同单位进行测量，即没有办法将它们的比率表示为一个简单的分数。这个概念可以追溯到古希腊数学家，特别是毕达哥拉斯，他们发现正方形的对角线无法用两个整数的比率来表示。这一发现对哲学产生了重大影响，挑战了当时数学理解的基础。不可度量的数量的概念超越了数学，延伸到生活的各个方面，包括艺术、伦理，甚至人际关系。例如，当我们考虑一件艺术品的价值时，很明显，它的价值不能仅仅用金钱来量化。情感联系、历史意义和个人解读都对其价值有所贡献，使其在人的体验中成为一种不可度量的数量。同样，在讨论道德价值时，我们常常会遇到不同伦理原则之间无法轻易比较或衡量的情况。例如，自由的重要性如何与安全的需求相权衡？这样的困境表明，生活中的某些方面本质上是不可度量的，无法简单地量化。此外，认识到不可度量的数量鼓励我们在思维中接受复杂性和模糊性。在一个日益依赖数据和指标的世界中，承认并非所有事物都能简化为数字是至关重要的。通过欣赏不可度量的，我们培养出对周围环境和自我的更细致理解。这种视角使我们能够更丰富地参与世界，促使我们对真正重要的事物进行更深刻的反思。总之，不可度量的数量这一概念作为一个强有力的提醒，表明某些存在的方面抵制简单的分类或测量。无论是在数学、艺术还是道德哲学中，认识到量化的局限性可以导致对生活复杂性的更深刻欣赏。在我们经历的过程中，让我们对不可度量的保持开放态度，使其丰富我们的理解，并促进对他人的更大同情心。最终，承认生活中的不可度量的数量可以引导我们朝向更全面的世界观，庆祝可测量与不可测量的共存。