Meaning: This quote by Edwin Armstrong, an American electrical engineer and inventor, reflects his skepticism towards relying solely on mathematical findings in the pursuit of knowledge and truth. Armstrong's remark suggests that while mathematics can provide valuable insights and understanding, it should not be the sole basis for drawing conclusions or making important decisions. Instead, he emphasizes the importance of critically examining what people think they know and being cautious of the potential misinformation or misconceptions that can lead to trouble.

In his statement, Armstrong highlights the idea that ignorance is not the primary cause of problems in the world. Instead, it is the confidence in knowledge that is flawed or incorrect that can lead to detrimental outcomes. This perspective challenges the common belief that ignorance is the root of societal issues and instead directs attention to the dangers of false or misguided knowledge.

One interpretation of Armstrong's quote is that he is cautioning against the blind trust in mathematical models and calculations without considering the broader context, potential limitations, and real-world implications. While mathematics has proven to be a powerful tool for understanding natural phenomena, technological advancements, and complex systems, it is not infallible and can sometimes fall short in capturing the full complexity of reality.

Armstrong's skepticism towards the exclusive reliance on mathematics may stem from his own experiences as an inventor and engineer. Throughout his career, he made significant contributions to the development of radio and electronic communication technologies, including the invention of FM (frequency modulation) radio. His innovative work likely required a balance of mathematical principles and practical experimentation, leading him to appreciate the importance of a multidisciplinary approach to problem-solving and innovation.

The quote also reflects a broader philosophical and epistemological perspective on the nature of knowledge and truth. It resonates with the idea that human understanding is not solely derived from empirical observations or mathematical abstractions but is also shaped by social, cultural, and historical factors. Armstrong's emphasis on the "things people know that ain't so" points to the prevalence of misconceptions, biases, and false beliefs that can influence individuals and societies.

In the context of technological and scientific advancements, Armstrong's quote serves as a reminder of the need for critical thinking, skepticism, and interdisciplinary collaboration. While mathematics and quantitative analysis are indispensable tools in many fields, they should be complemented by qualitative insights, ethical considerations, and a deep understanding of human behavior and society.

In conclusion, Edwin Armstrong's quote provides a thought-provoking perspective on the limitations of relying solely on mathematics for understanding the world. It challenges the notion that ignorance is the primary source of trouble and instead draws attention to the potential pitfalls of misplaced confidence in flawed knowledge. By acknowledging the complexities of human understanding and the potential for misinformation, Armstrong's quote encourages a more nuanced and critical approach to knowledge acquisition and decision-making.