Extending the range of calipers

[mklotz]

Over the years I've tutored lots of folks in various mathematical subjects. It always puzzled me that people who seemed otherwise of normal ability could be so dumbfounded by a subject that has been in the core of education for thousands of years. The way it's taught has been much criticized, and rightly so. The failure to explain why you need to know this and how it will help you in your career is often singled out. But we're never told why we need to learn history or literature and folks seem to be able to "learn" those subjects.

Those thoughts encouraged me to write an attempt to explain my idea of what was happening. It's presented below. I welcome your comments.

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Perhaps there's a key to why so many people can't deal with mathematics. Most things in life offer a chance for interpretation. Trends in history, the author's message, the meaning of an artwork - each is open to varying views by different people. In fact, often when taught, these varying interpretations are exploited in the instruction methodology. Who hasn't encountered a question in a humanities exam where one is invited to discuss the 'meaning' of a passage or outline the 'most important' features of a book?

Math, on the other hand, is absolute. It offers no latitude for interpretation. If asked for the prime factors of a number, you must come up with the same answer as everyone else or you're wrong. No "well that's another way to look at it, Johnny" in math.

Faced with an absolutist system, people feel they're losing their freedom. They can't relate to a world with absolutist laws that are completely beyond their interpretation and manipulation. Their reaction is to mentally "run away" from a system they view as confining although most will manufacture some rationalization for their retreat.

The hard sciences, chemistry and physics, are similar. What's taught at the high school and lower college level is pretty much immutable. Sure, at the higher level, there may be future alterations to the laws of these disciplines, but at the lower level things are pretty much cast in concrete. There's even a principle in physics that says that any future laws or changes to laws have to reduce to known laws when used at the scale at which the known laws work. Relativity must, and does, become Newtonian physics at speeds well below that of light.

So, again, at the lower education levels, the physics/chemistry student is faced with a system he can't possibly manipulate if he wants to produce realistic and acceptable answers. As with math, the first impulse is to run away.

And run they do. Even when faced with a simple tidbit of math from which something could be learned, e.g. a simple linear equation that wraps up a collection of hard to remember tidbits, most mathophobes will refuse to read it, much less attempt to understand it.
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[Mook]

This is unusual way to extend the range of a caliper.

[mklotz]

This is unusual way to extend the range of a caliper...

A variation of an old dodge used to measure where obstructions or the lack of a sufficiently long ruler prevent direct measurement. An example would be measuring the distance between two parallel walls spaced somewhere between 12 and 18 inches apart when all you have is a 12" and 6" ruler.

Useless for accurate measurement of a diameter unless you have some other way of ensuring the calipers measure along a diameter.