First Blog

The Eight Stages of Understanding . Problem-solving is a broad category of intellectual activities. It requires knowledge of multiple sorts as outlined below. It is part of the pyramid of understanding, but a seriously important part. However, most of us can have successful careers having only problem-solving skills. Higher-order understanding is more significant in the world of theories and ideas, the meaning of solutions, and how they fit into the intellectual scheme. The list below is reminiscent of Bloom’s Taxonomy, but refined for our purposes. One of our tools for problem-solving, used by all, is at the very base. One can’t know everything, and we’re never protected from it. Thus ignorance, and how we deal with it, is in everyone’s world. ·         Ignorance:  lacking knowledge or awareness. ·         Awareness: awareness that there is something unknown or not understood. ·         Knowledge: acquisition of factual information and concepts related to the subject. ·         Compre

  How is math used in everyday life? This is a big question requiring a big answer.   It is amazing at just how many uses are significant.   Math is everywhere, all the time, and constant as we move on.   Yet, few of us actually need to do any calculations beyond the basics. Knowing is has invaded almost everything is important to know.  A. Medicine. CAT scans and MRI scans require deep math at their basis. Modeling of DNA and sequencing of genes use much math. The origin was with SONAR, where the computer was the human brain, i.e. operator. It is well past that now. The mathematics is called tomography. It takes the scans and uses them to reconstruct the complex images within the brain or body. B. Transportation. Routing of vehicles (trucks and aircraft, etc) to maximize efficiency of costs use deep math. Involves one of the most difficult math problems called “The Traveling Salesman Problem.” It is still open, i.e. unsolved. C. Electronics. Use the math of all of electromagneti

FLOPS.   What is a FLOPS? It is the number of multiplications a computer can compute in one second,  far less than additions, though not quite.   It is the number of floating point operations a computer can compute in a single second.   A floating point number has a bunch of digits (e.g. 12) times a power of ten.   For example, most computers would have native trouble with the number 12345678901234546789012345, but they do well with approximations such as 1234567890 x 10^16. This means you lose some precision, i.e. accuracy, but you get the magnitude.     Let’s not devolve into software that can handle very high precision numbers, or the precise representation of floating point numbers inside the computer. It is enough here to know that we are working with numbers having a fixed number of digits together with a power of ten.   Let’s just talk about the FLOPS, floating point operations per second, of the native hardware. You know computers are fast, and expensive computers