This quote emphasizes the power of thoughts and ideas and the potential they hold for growth and development. When Thoreau refers to a thought as a "nest egg," he is suggesting that like an egg which has the potential to grow into a bird, a thought or idea, when nurtured and developed, can grow into something much larger and more significant. The act of welcoming and recording these thoughts is akin to providing a safe and nurturing environment for these ‘eggs’ to hatch and grow.

The second part of the quote, "by the side of which more will be laid," suggests the cumulative nature of thoughts and ideas. One thought or idea often leads to another, creating a chain of thoughts that can lead to a wealth of knowledge or a profound understanding of a particular subject. In other words, the more we think and record our thoughts, the more thoughts we generate, creating a cycle of intellectual growth and development.

In today’s world, this quote could be applied to many areas of life, including personal development, education, and business. For instance, in personal development, the act of journaling or keeping a diary can be seen as a way of welcoming and recording thoughts, allowing one to reflect on these thoughts and generate new insights and ideas. This process can lead to personal growth and a deeper understanding of oneself.

In the realm of business and innovation, this quote underscores the importance of brainstorming and ideation. By welcoming and recording all ideas, no matter how outlandish or improbable they may seem, businesses can foster an environment of creativity and innovation where new and potentially groundbreaking ideas can emerge.

In education, this quote can be seen as an endorsement of critical thinking and active learning. By encouraging students to actively engage with the material, to question, think and record their thoughts, educators can help students develop a deeper understanding of the subject matter and foster a love of learning.

In conclusion, Thoreau’s quote is a powerful reminder of the potential of thoughts and ideas and the importance of providing a nurturing environment for these ‘nest eggs’ to grow and develop. Whether in personal development, business, or education, the act of welcoming and recording thoughts can lead to significant growth and progress.