Some common mistakes of pseudoscience:
is the behavior all advertisers love to see: unskeptical acceptance of the lures they dangle. The opposite is the reasoning Consumer Reports assumes that its readers use. Seeking disconfirmations is essential to good thinking; easy acceptance of confirmations as "proof" is a short route to pseudoscience–and to the gullibility hoped for by those advertisers. We recognize the advantage of being able
to make things come true by wishing them true. . Nothing in the world
indicates that we can use thoughts to affect reality, but New Age wishful
thinkers often suggest that quantum mechanics suggests that we might.

QUANTUM MECHANICS 
takes many forms. Stop looking once we've found a hint that the alluring hypothesis might be true, and we will not discover the many, many disconfirmations the rest of the universe will thrust upon us. Pseudoscience usually overlooks at least one or two modern science concepts that contradict the alluring hypothesis. Pseudoscience often overlooks logical errors. Pseudoscience often contradicts principles of math and statistics. Pseudoscience tends to ignore the many factors that interact and focus only on the most easily seen factor. 
OVERSIMPLIFICATION
several examples OVERSIMPLIFICATION
Science:
simple but subtle
Knowledge
for use

is the sense that comparing by size implies
lining up on a line. Intelligence being defined as "IQ" ("gfactor")
is one of the most common examples. A good way to observe the fallacy
of gfactor intelligence is to work the more subtle puzzles in small groups
of people (Wason Card Selection, Monty Hall Choice, Colored Squares &
Triangles). (Because this activity reveals so very
many different intellectual skills, everyone can expect to encounter
some that cause difficulty. Education rarely addresses a lot of these,
and they will be unfamiliar. Don't let it bruise egos.)

Ellipses 
fails to adequately understand the [huge] limitation of our evolved perceptions and reasoning powers. Our impressions of color, color vision, and colorblindnesses might begin to shed light on anthropocentrism. A protanopic color blind person cannot begin to see what a color normal person actually sees as color, while a color normal can gain some sense of what a protanopic colorblind person sees. The four (plus) color vision of birds cannot be sensed by a human being, except as abstractions derived from mathematics (Hilbertspace analysis). Both bird and human color are extremely limited projections,"shadows," from a space of infinite dimensions (that's the "color" of a spectroscope), and it's practically infinitesimally limited by being vision of the narrowest of ranges of existing wavelengths of radiation. The conceptual discoveries since Galileo and Newton have called on the best skills a human mind can muster. Newton's "theory of fluxions" (calculus), the thermodynamicist's use of partial derivatives, Boltzman's use of statistics, Maxwell's use of vector derivatives, Einstein's depiction of the gravitational constant as a tensor, the quantum mechaniker's depiction of measurable variables as mathematical operators, or as vectors in a Hilbert space, and now particles as "strings" vibrating in some highdimensional space. The more we discover the more we realize that grasping reality takes more skills than we can muster. We master only shadows. That we cannot imagine how life could appear
on earth (or evolve) without a guiding intelligence, imagined as being
in some sense humanlike, is a observation about human imagination, not
about the richness of our universe.

So much of science serves to remove us from our shell of egocentrism. Like a baby chick we must peck our way out to see the world outside. The shell, a very tough, durable shell, is the extremely limited range of reality our perceptions reveal to us and the even more restricted insight we have of the patterns, and patterns of patterns, that we have labeled "abstractions." Until we realize that these abstractions are the substance of math and science–and are the most powerful tools a human being can wield to comprehend the world–and until we see them as embeded reality, we are, in the realms of math, hopelessly lost without a map. Examine Feynman's
"...reality is not a figment
of our consciousness ... but exists outside us and beyond us and our task
is to find as much about reality as we possibly can "

more often than not, include those mathematical abstractions mentioned above: derivatives, vectors, tensors, statistics, etc. Even the simplest of math, such as ratio and proportion, is sometimes unseen. Many science concepts are concepts built on such mathematical abstractions: they are patterns found among those abstractions. The oversimplification of seeing all rankings as linear rankings, is the failure to sense multidimensional orderingsuch as vectors and tensors make. "Childlike" (or "Naive") describes this
"Abstraction blindness" because the insights are those described by Jean
Piaget as the last mental developments to develop in our advance toward
maturity: the "formal operations."

Today,
linguists, especially those with a deep understanding of mathematics, give
metaphor a very large role in our thinking. See the "levels"
of abstraction as described by Keith Devlin  and become familiar with
the Lakoff
Principle. (Also,
be sure to read Lakoff's little book, Don't Think of an Elephant, Chelsea
Green, 2004. It has profound insights.)

are usually the result of missed concepts. Most of the puzzles used at Da Vinci Days illustrate "imperatives" (We need several good framesetting terms for this concept – it's one of the most important concepts for understanding pseudoscience.) The 5X5X5 cube assembly puzzle is a particularly good illustration. Before we see the principle, we have no idea why the puzzle isn't fitting together. When we do see it we understand that those three pieces must follow a specific rule: It's an imperative, because of a simple principle of arithmetic. Not expecting to get rich from the lottery is an imperative because of the nature of statistics – and the assurance that the lottery is not rigged in our favor. The fact that energy cannot be defined
with "Energy is the capacity to do work" is an imperative because of the
elementary logic of implications: definition requres equivalence, and "capacity
to do work implies energy" is the most the statement can say. That's
because energy is not sufficient for doing work by being often unavailabale
for doing work. Many people find this logic to be a bit slippery.

Many of the puzzles taken
to Da Vinci Days illustrate this important concept. A principle not
followed is often a principle not understood ("Eureka!"). The geometric
principle of Garnder's "Buzz Saw problem" cannot
be denied. The arithmetic principle of the 5X5X5
cube
assembly cannot be avoided. The parity principle of the
chessboard
and dominos puzzle is the solution.
The deeper abstractions, such as the distinction between equivalence and implication, have equivalent imperative quality and are very commonly missed. Mistakes then are made, often serious ones. (The many errors noted HERE need to be reorganized to make them more generally understandable.) "Once you've seen it you can never again not see it." Vandana
Shiva

starts with difficulty conceptualizing
and using ratio and proportion. It's a widely recognized problem.

Ratio & Proportion 
is probably the most common error of elementary logic. We can hear a confusion of all with some, or of necessity with sufficiency, with almost every political argument offered. "That bill would not cure the problem; drop the idea!" Now, that argument says the bill is not necessary on the basis that it is not sufficient, one kind of improperly inverted implication. It would be naive to dismiss this error as "an overstatement." It's a logical error. March 30, 2006 
Logic relationships 