Inversion
Carl Jacobi was a renowned 19th-century German mathematician who made profound contributions to the field of differential equations. One aspect that set Jacobi apart was his unique problem-solving approach. Jacobi believed that when one inverts known facts in a particular discipline, additional knowledge can be revealed that was previously unknown. He always encouraged his graduate students to invert the known confines of the field and examine what they found there.
Jacobi’s approach, known as “inversion,” involves thinking in a contrarian way and challenging assumptions. By asking questions that invert a problem, such as “What would happen if we did the opposite?” or “How can we make the problem worse?”, one can identify the things that are preventing them from achieving their goals and find new solutions and insights that they may have missed otherwise. Inversion is now considered an analytic strategy fundamental to scientific and mathematical thinking, and it can be applied to many other areas of life, such as business, personal relationships, and self-improvement.
Inversion is not just about thinking differently but also about challenging one’s assumptions. By questioning preconceived ideas and beliefs, one can identify the things that are preventing them from achieving their goals. Inversion can thus help people to break free from the constraints of conventional thinking and achieve success in many areas of life.
Teleology
Aristotle’s conceptualization of the universe was based on the idea of teleology, that is, everything had a purpose or a final end point – which is rest. Thus, a ball’s final resting place is the ground and when it is thrown up, it moves towards that final resting place on the floor. Thanks to Newton’s first law of motion, Aristotle’s idea no longer relevant in a scientific context. However, I think it still has a metaphorical extension that is still applicable in a psychological and spiritual sense. This metaphor suggests that the human soul has a natural tendency to strive towards a higher purpose or state of being, which can be seen as the final resting place of the human spirit.
However, negative emotions and actions can act as weights that draw the soul towards a state of unrest, which can be seen as the depths of hell. This metaphorical extension of Aristotle’s universe has implications for how we live our lives. It suggests that we should strive towards a higher purpose or state of being, and avoid negative emotions and actions that can weigh us down. By doing so, we can achieve a state of spiritual rest and fulfillment. The metaphor of the soul as a traveler on a journey towards a final resting place can help us understand the importance of living a purposeful and virtuous life.
Lindy Effect
In a paper titled, “Implications of the Copernican principle for our future prospects”, astrophysicist J. Richard Gott III describes how in 1969, he visited the Stonehenge (which was estimated to be over 3000 years old) and the Berlin Wall (8 years at the time). Gott then wondered which of the two structures will outlast the other. As you probably know, the Berlin Wall was destroyed in 1991, while Stonehenge continues to exist to this day. Gott then mathematically proposed an argument that the longer a thing exists, the more likely it will continue to exist. This has been popularly called the Lindy Effect. This principle also applies to other areas of life, such as literature and medicine. Older books, which have stood the test of time, often contain more wisdom and practical knowledge than newer books, which may be trendy but lack staying power. The same is true of medicine, where herbal remedies that have been used for centuries are often more effective than newer drugs, which may have side effects or other problems. Using the Lindy Effect as a guide, we can focus on systems and structures that have been vetted by time, rather than always chasing the latest fad or trend. This can help us to make better decisions and achieve more lasting success.
Length of Days
Proverbs 3:1-2 says, ‘My son, forget not my law; but let thine heart keep my commandments: For length of days, and long life, and peace, shall they add to thee.’ The text encourages us to keep God’s commandments, and promises that doing so will result in “length of days” and “long life.” While these two concepts may seem similar, there is a subtle difference between them.
“Long life” refers to growing to a full, old age before expiring. This is a concept that most people are familiar with. However, “length of days” refers to the ability to make the most of each day. This means being able to accomplish more in a day than others can in a month or a year.
This idea may not be intuitive to everyone, but it is a powerful concept that can transform one’s productivity. Time is a property that is bound to the physical realm, but God is spirit and transcends the physical. This implies that when you partner with God, you unlock the potential for greater productivity and efficiency. By tapping into God’s wisdom, guidance, and strength, we can achieve more than we ever could on our own.
