Understanding science concepts
frequently requires that we see implication relationships and easily distinguish
implication from other Boolean relationships–such as the inverse of the
implication, mutual exclusion, and equivalence, for example. These
insights are needed if we are to sort through multiple variables, influences
and hypotheses and find which are relevant and which are not. They're
important to statistical reasoning, too, and modern science knows—in fact
the world is fundamentally statistical. Science sees statistics.
The energy concept is widely
misunderstood because such insights are too often obscure. The word
"energy," was coined by Aristotle from roots meaning "at work." The
human notion of work–and all that goes with it: fatigue and rest, hunger
and food, engines and fuel, etc–didn't get worked out scientifically until
the mid 19th century. Now we know that the scientific use and
the colloquial (including Aristotle's) uses are vastly different.
The scientific "energy" is simple, abstract, and conserved. The
colloquial "energy" is complex, concrete, and not conserved. It's
profoundly statistical, too. ("Once
used you can't
use it again," said the Oregon governor's energy advisor. But he
had invoked the laws of thermodynamics to prove his point, so he was clearly
confusing the two meanings.)
Good, clear insight into
the mysteries of multiple influences is rare enough that many physics textbook
authors improperly define energy with, "Energy is the capacity to
do work." [What's that?]
That's impossible on at least two grounds:
Definition requires (logical)
equivalence. That is, if you have energy you must have capacity
to do work, and if you have capacity to do work you must have energy.
However, the actual relationship here is (logical) implication. If
you have capacity to do work you must have energy. True! (Alternatively
worded, "Capacity to do work implies energy.") But energy
can be unavailable for doing work. (Energy does not imply
capacity to do work.) And so the actual relationship is implication,
not equivalence. The statement cannot, because of elementary logic,
be a defintion.
Furthermore, "Energy is the
capacity to do work" improperly inverts an implication. "Is"
"implies" or "is a kind of," because usage has established that meaning.
But the correct statement would then be "Capacity to do work is energy.
You would never say "A vegetable is a potato," but you know "A potato is
a vegetable" is perfectly correct.
And you certainly wouldn't
with "A vegetable is a potato." Those errant textbook authors are
making the same error. But the error is in a slightly more abstract
setting; it's "at the edge of human comprehension." Furthermore,
they have even defended their faulty definition in the teaching literature
when other physicists have explained the error. Those who see the
error are often embarrased by those who don't, embarrased for the profession.
The issue has "buzz-saw certainty"
embeded in its logic.
When you see it, you wonder
how anyone could not.
When you don't see it, you
wonder what all the fuss is about; there's simply nothing "out there" to
(Our exemplar is Martin Gardner's
Experiment is one thing
Logic is another
And both must be
woven into a fabric of scientific thinking. Warp without woof
is unraveled thought.
Establishing the nature of
energy was a matter for experiment. The ultimate goal of those experiments
was to become able to use observation to anticipate some real-world outcomes
of things we do in the real world. This is scientific experiment
and requires that we understand how to recognize and deal with multiple
influences...and so keep straight those Boolean relationships.
It also requires that we understand
how to deal simultaneously with many influences which are further complicated
by uncertainty and randomness. We must understand statistical reasoning.
However, buzz-saw certainty
deals with another issue: logical consistency. When we don't see
the logical relationships we can appear ridiculous to those who do see.
Buzz-saw certainty alone doesn't deal with observation, so it can't prove
or disprove a hypothesis, such as Laetrile as a cancer cure or the reality
of extraterrestrial visits to Earth. But the logical consistency
is necessary, if not sufficient, for analyzing the observational
data...and to avoid looking absurd.