Posted in Books, Educational Reform, Teaching & Learning, Tips for Students, Tips for Teachers

The Role of Neural Associations in Learning

Excerpted from Triggers, by Stanley Mann:

“Multisensory imagination is the world’s finest teaching machine, and we all possess it.  We simply need to learn how to use it.”

I just came across this great quote in a book I’m reading. The book is about using triggers, or neural associations, to direct one’s attention in constructive ways. The quote comes from a chapter on using triggers to enhance learning ability. It resonates with me on a number of levels.

First of all, the idea of multisensory imagination is a little-known but extremely powerful learning enhancement tool, and is the sort of thing that we should be teaching kids about in school instead of pumping them full of facts and figures. To truly learn anything you have to make it real in your mind, fully engaging with it in your imagination with as many sensory channels as possible; both sight and sound at the very least, and ideally touch, smell, and taste if possible. Conversely, teaching can’t work unless it engages the imagination and the emotions through multiple sensory channels. Educators and curriculum designers need to be mindful of this principle in order to be effective.

Secondly, triggers in general, and learning triggers in particular, rely on the principle of association. Our brains are constantly making associations among various environments, stimuli, and emotional states based on our experience. Neurons that fire together wire together, so when two experiences are repeatedly juxtaposed, they tend to become linked. This means that to optimize your learning process, you need to create a positive physical and mental learning environment for yourself, so that you are comfortable and feeling good while you are learning. Conversely, if the learning environment is physically or mentally uncomfortable, such as by feeling coercive and emotionally unsafe, then the negative feelings it evokes will come to be associated with the process of learning itself, causing them to be re-experienced whenever future learning endeavors are undertaken. This is another principle of human psychology that educators and legislators need to take heed of.

Posted in Books, Inspiration, Math

Schneider On A Better World Through Mathematics

Excerpted from A Beginner’s Guide to Constructing the Universe, by Michael S. Schneider:

In this time of rapid change and transition of the roles of traditions and institutions, we have the opportunity to restructure education and teach children differently, to expose them to harmony in all its forms, in nature, music, art, and mathematical beauty.  Perhaps children steeped in harmony will become a generations of adults who will strive to achieve harmony in the world.  And perhaps they will transform our relationships with our environmental matrix to treat the soil, water, air, plants, and creatures differently, cooperatively, in ways born of understanding of the whole, respect for its parts, compassion, and common purpose.  Comprehending nature’s speech will let us listen to what she is telling us in her own native language, which is also our own.  If we can see and understand nature as a harmony in which there is room for diversity and in which we participate, we’ll want to transform ourselves and our relationships to align with that harmony.

We often act as if inner human nature was unconnected with outer nature, and we judge the outer world by one standard, ourselves by another.  Familiarity with the principles of geometry can help reconcile this artificial division.  The geometry outside us shows us the principles within ourselves.  It’s time we, as a global whole, relinquish old models of looking and learning and begin to cooperate.  Literacy in nature’s script dispels the stereotype of nature as disorganized, unintelligible, and hostile.  This book is about reshaping our vision and constructing a new perspective aligned with life-facts.  Learning nature’s language and reading its message helps abolish the attitude of separateness and encourages us to appreciate diversity.  It will lead to nothing less than our own transformation as we find all nature’s principles within ourselves.

To learn to view the world in terms of its patterns requires a shift within us.  But once this shift occurs and we see the familiar world in terms of its shapes and principles, a light turns on and the world brightens, comes into sharper relief.  Everything speaks its purpose through its patterns.  Even without knowing it we use the same designs found in nature.  Look at a microscopic diatom and see a cathedral rose window.  Ultimately, the same energy that motivates and guides the natural world does the same for us.  All universal designs are found in human body proportions, which we have seen can be repackaged to produce the proportions of a crystal, plant, animal, solar system, and galaxy.  It is as if the universe is one single organism, motivated by a single power, developing in many ways to gradually become aware of itself through the awareness of the creatures and forces it produces.

Posted in Books, Physics

Feynman On Memorization

Excerpted from Feynman’s Tips on Physics, by Richard P. Feynman:

It will not do to memorize the formulas, and to say to yourself, “I know all the formulas; all I gotta do is figure out how to put ’em in the problem!”

Now, you may succeed with this for a while, and the more you work on memorizing the formulas, the longer you’ll go on with this method – but it doesn’t work in the end.

You might say, “I’m not gonna believe him, because I’ve always been successful: that’s the way I’ve always done it; I’m always gonna do it that way.”

You are not always going to do it that way: you’re going to flunk – not this year, not next year, but eventually, when you get your job, or something – you’re going to lose along the line somewhere, because physics is an enormously extended thing: there are millions of formulas! It’s impossible to remember all the formulas – it’s impossible!

And the great thing that you’re ignoring, the powerful machine that you’re not using, is this: suppose Figure 1 – 19 is a map of all the physics formulas, all the relations in physics. (It should have more than two dimensions, but let’s suppose it’s like that.)


Now, suppose that something happened to your mind, that somehow all the material in some region was erased, and there was a little spot of missing goo in there. The relations of nature are so nice that it is possible, by logic, to “triangulate” from what is known to what’s in the hole. (See Fig. 1-20.)

And you can re-create the things that you’ve forgotten perpetually – if you don’t forget too much, and if you know enough. In other words, there comes a time – which you haven’t quite got to, yet – where you’ll know so many things that as you forget them, you can reconstruct them from the pieces that you can still remember. It is therefore of first-rate importance that you know how to “triangulate” – that is, to know how to figure something out from what you already know. It is absolutely necessary. You might say, “Ah, I don’t care; I’m a goodmemorizer! In fact, I took a course in memory!”

That still doesn’t work! Because the real utility of physicists – both to discover new laws of nature, and to develop new things in industry, and so on – is not to talk about what’s already known, but to do something new – and so they triangulate out from the known things: they make a “triangulation” that no one has ever made before. (See Fig. 1-21.)

In order to learn how to do that, you’ve got to forget the memorizing of formulas, and to try to learn to understand the interrelationships of nature. That’s very much more difficult at the beginning, but it’s the only successful way.

Posted in Books, Inspiration, Math

Schneider On Harmony

Excerpted from A Beginner’s Guide to Constructing the Universe, by Michael S. Schneider:

Symbolic and sacred mathematics encode subtle experiences whose purpose is different from that of secular mathematics. They can invigorate, refine, and elevate us. Our role as geometers is to discover the inherent proportion, balance, and harmony that exist in any situation. The study and experience of numeric and geometric proportion infuses in us an appreciation of proportion everywhere. The study of balance teaches us to recognize and seek a sense of balance in our lives. The study of harmony develops our sense of harmony in all relationships. Actually to see and work with unity and wholeness in geometry and natural forms, rather than just read about them, can help abolish our false notion of separateness from nature and from each other. It is this notion that ultimately fuels competition for the “goods of the earth” and contributes to environmental crises.

Posted in Books, Inspiration, Math

Schneider On Universal Principles

Excerpted from A Beginner’s Guide to Constructing the Universe, by Michael S. Schneider:

Studying, contemplating, and living in agreement with universal principles is a social responsibility and can be a spiritual path. it is becoming clear that when we cooperate with nature’s ways we succeed; when we resist, we struggle. Implications for our environmental crises are obvious. Rather than an antagonist, nature can be our teacher to learn from and cooperate with to mutual benefit. To understand nature better, we first need to recognize the roles of its basic patterns.

Posted in Books, Inspiration, Math

Schneider On Nature’s Patterns

Excerpted from A Beginner’s Guide to Constructing the Universe, by Michael S. Schneider:

Nature’s patterns and those of our inner life are familiar to everyone and always available to us. The  power which we seek is the power with which we seek. When we feel separate from the archetypes of nature, number, and shape we make them mystical, but this only keeps our selves in a mist. There is no need for secrecy and “occultism” any longer. These are everyone’s life-facts. We can apply them to better appreciate the world, and we’ll need them once we realize the urgency of cooperating with the way the world works.

Posted in Books, Inspiration, Math

Schneider On Sacred Mathematics

Excerpted from A Beginner’s Guide to Constructing the Universe, by Michael S. Schneider:

When the lessons of symbolic or philosophical mathematics seen in nature, which were designed into religious architecture or art, are applied functionally (not just intellectually) to facilitate the growth and transformation of consciousness, then mathematics may rightly be called “sacred.”