First Blog

  What made Einstein so great? The best answer is nobody knows. However, there are conditions under which he learned. First, he had a home tutor who was mathematically and physics trained. This person probably insisted the young Albert think deeply about what he was learning and how to explain it thoroughly. This put Albert into a mode of internalizing everything he learned, and learning how to explain it. This is simply not taught in schools these days, but if you look at notables such as Richard Feynman, his father taught him to think similarly. Even Isaac Newton once said, “I think about a problem constantly until I can see clean through it.” The lesson learned here is that one key to understanding is to contain the entirety of your subject all within the mind. You’ll note, all his life he was concerned with the very foundations of physics by way of understanding and explanation. Next, we come to the man himself. He was obviously highly intelligent, and having learned to think

It's that gifting time of the year. So, I thought to take a closer look at the gifts I have already. Not just the kids, car, house, and health, but the real gifts, as in those I was born with. They are many, so many it is troubling why I have them. Among them is the gift of problem-solving. Another is the gift of curiosity. This article  is about them all, with a closer look at faith.  December 20, 2022 Gifts to Humankind by G Donald Allen Upon us now is the season of giving. Just as important is to inventory those gifts we have been given. And they are many. At Thanksgiving, we count our blessings. Today we travel well beyond counting to those wondrous gifts given to us at birth. These gifts co-mingle, coalesce, contravene, and entangle to make us what we have become. Not material, nor theoretical, and without position or location, they are undeniable. They are within the domains of psychology, chemistry, and sociology, forming our very human foundations. Evolution or design

Given are two answers. A. Here’s the standard answer to your question. Study hard, learn much, do problems, and then you will understand. Then study harder.  B. Here’s an alternative answer. Do what wisdom does when understanding is delayed. Example. Infinity. It is safe to say no one really understands infinity. BUT, what most of us* do is learn the rules of infinity and work within them. Over and over again. Eventually, you are accustomed to all the rules, and this becomes your understanding. Your alternative is to learn the rules of the subject you have trouble with. Learn to work with them. Review and do dozens upon dozens of problems. By and by, you will be accustomed to them; you will have facility with them, and this will convert to your understanding. I know this sounds a bit cynical, but it does work. Please note, this alternative is not a shortcut. Both take much time and work. This is how most people understand God, who like infinity, is beyond comprehension. ---------------

What is it like to finally understand a new concept which at first seemed like a foreign language to you? Two answers are evident. A. When understanding for the first time, it seems like reaching the peak of a mountain. A triumph. B. After a bit of time, you think of why you did not understand it in the first place. “It is so easy,” you might think. This is the apparent paradox of understanding. It goes from impossible to easy in just one step.

  Suppose a new concept, edict, or law comes your way. In simplified terms, you have four options,  rejection, acceptance, understanding,  and  belief . The “pusher” to anyone of these is your degree of doubt. Total doubt leads to rejection, while absolutely no doubt (or certainty) leads to belief. I’m not convinced the latter is absurd as claimed by Voltaire, as total belief a necessary state for the creation of or proof of new ideas. Others prefer to understand or at least try to understand the condition at hand. This illustrates partial doubt but a measure of conviction necessary for understanding. Finally, a state of resident doubt but required compliance leads us to acceptance. For example, in your work you may accept some rules of the employers but neither believe nor understand them. In politics, you will see much belief and rejection but little understanding. Many simply accept what is promoted.

  The Pollinator . Another way to view the teacher is that of a pollinator . She picks up knowledge, the pollen of intelligence, and transmits it to students where it germinates into full understanding. The teacher is the carrier, but it is the student who absorbs and digests it, creating understanding for an improved life. Neither is the center of this symbiosis; each needs the other. It’s become a natural mating essential for humans and many other species where learning advanced skills for life are crucial.

Learning is the task of schools and us all.  Yet, learning has its own components: memory, understanding, application. The first step, memory, precludes all others.  A person with no memory of the “something” can never learn much about anything. From memory, a student has a chance of understanding through various mechanisms, not the least important of which is analogy through previously understood concepts.  Thus, understanding and learning are bootstrapping processes. But now comes the most important stage of learning, and that is applications or better known as problem-solving.  We  conclude… The greatest learning engine is problem-solving.  Give a lecture and only a fraction learn. Call for a group involvement and more learn.  Ask them to solve a problem, and all learn. Not solving a problem is a key learning experience.  It exposes gaps in understanding. It points to needs.  It is an essential component of growth. How many times has the teacher heard this, “I understa

Learning is the goal of schools.  Yet, learning has its own components: memory, understanding, application.  The first step, memory, precludes all others.   A person with no memory of the “something” can never learn much about it. From memory, a student has a chance of understanding through various mechanisms, not the least important of which is analogy through previously understood concepts.   Thus, understanding is a bootstrapping process. But now comes the most important stage of learning, and that is problem-solving.   We   conclude… The greatest learning engine is problem-solving.  Give a lecture and only a fraction remember. Call for a group discussion and more remember.  Ask them to solve a problem, and all remember - and learn.

From computer gaming, to video streaming, to safe-spacing, to virtual friending, to at-home working, to neo -spiritual believing, it seems younger Americans are shifting from the old-world of living to a new -world of fantastical being, realizing, understanding . When you believe in the consequences of an unproven theory, you live in faith or fantasy. (Welcome alt-universe believers. Not to mention anti-oxidants-cure-all fans.)    To extend your range of influence beyond your domain of authority is both tactically and strategically risky. (Welcome Pope Francis and Hollywood types.)

It may be widely believe that knowledge progresses gradually, in small steps, in gentle increments, or in slight gradations.  It may be not so, even for us as individuals.  New knowledge or understanding often begins with insights.  When you gain an insight, and it is true, it becomes applicable and remains so from then on.     This changes one’s problem solving game. This insight provides a new tool or rule, but importantly   it creates a discontinuity in your problem solving methods.    So, we might ask whether insights can come gradually?   In some cases, probably yes, though examples are difficult to furnish.  The emergence of infinity, often credited to Cantor, took centuries of dancing around the edges by philosophers.  The germ theory of disease so often attributed to Pasteur was anticipated almost with the invention of the microscope.   On the other hand plate tectonics seemed to arise by a simple insight by a single person, Alfred Wegener, in 1912 and took a mere half

Vision for the blind By trade, I am a mathematician.  I can do lots of tricks in math, but only in math.  But there are so many things I just don't know.   Why don't I know?  What prevents me from knowing?  Why can't I answer so many questions?  This has to do with mental capacity, of course.   (See, http://used-ideas.blogspot.com/2012/05/how-to-teach-ant-how-to-read.html )   Still I keep trying.   This is despite the serious models presented to us by scientists and theologians to help me along. Let me explain understanding through the metaphor of sight. We use this metaphor all the time.  "I see it," is the most familiar expression.  Yet the deeper questions are how clearly you may see it, or how deep is your vision.   Vision-type statements involving understanding include. ·          I see what you mean. ·          It is still fuzzy, but I am getting on to it. ·          I saw through it at once. ·          They recognized the facts of the situat