First Blog

Problem Solving – Paradoxes   1.      Introduction . Paradoxes have long been a true source of problems for professionals and the laity alike. They are often set as puzzlers. They demonstrate traps of logic, science, and life itself. Some are even linguistic, having to do with meaning. They can occur almost anywhere aside from books on them. They can be embedded within wicked problems, a home for vague language and conflicting values, uncertainty, and multiple solutions. Even logical fallacies can counted as paradoxes until they are identified. Oftentimes, paradoxes signal a major revision to the meanings of terms and even to the logical foundations of how we think.  Let’s begin with a definition. Definition: A paradox is a seemingly absurd or self-contradictory statement or proposition that when investigated or explained may prove to be well founded or true. In many cases, it helps refine logic and understanding. They push the bou...

You want to learn?  You want to achieve?  You want to know?  Go to school, say the educators. Sometimes schools feed information and learning; sometimes schools teach how to learn. The how is what you need, and these are most important ways to learn.         First, we learn from reading books or being taught in the classroom. We learn by solving given problems. Practice and repetition, this is the role and scope of all school teaching. Occasionally, inspiration occurs.           Second we learn from examples and experience. Seeing many examples, some working and some not, and knowing why helps. These build our knowledge and intuition of reality.  Knowledge is a pathway to solving problems, while intuition provides a pathway to innovation.  More simply, we learn by doing.  Attending the school of hard knocks is an expression of this.         Third, we learn from mistakes*....