There's always another new module to add to your mental software!
A little extra
Help for understanding science a little bit better
Using it, too
And understanding and using math, also.

Science is simple
Science is subtle

Science is magic that you discover by looking
in places you never before thought to look.

Try taking these five little steps
They can get you up and looking out over the world from a little better viewpoint:

first step
next step
third step
next step
fifth step
seek the truth
the whole truth
recognize relevance
reject irrelevance
see higher dimensions
know when to multiply when to divide
purge contradictions
take it all in
unclutter your thoughts
sidestep simplemindedness
learn to use ratios
don't be silly

We prefer to find only the evidence that proves
that our wishes have come true.

Real science searches for all that's relevant, especially all that could prove us wrong.

"There's a sucker born every..."
when can it happen?
ranking athletes

proportioning out the costs

How to rebalance?

converting units
Sometimes you know! 

Green and orange are different.

Yes I can!!
No you can't!

How can our senses fool us?

How can others fool us?

How can we fool ourselves?

Sometimes the sun can burn.  Sometimes it can't.  What is relevant to making sunlight "actinic" and what isn't? The basketball coach wants the tallest.  The football coach wants the heaviest.  Everybody ranks them by putting them in a line (one dimension).  Everybody can do better.
We must be sure we understand when to add, when to multiply, when to subtract, when to divide, and how to convert from inches to meters, feet to furlongs, euros to dollars, etc, etc...
Math starts here...
Personal opinion can be simply wrong...and for reasons we don't suspect.  Science keeps discovering ways we can be wrong in ways we never thought possible.



A short quiz:

If you've already taken the step, the question will probably seem too easy to be worth asking.  If you haven't taken the step the question might seem rather baffling.  Science concepts are like that.  That's what makes science "magic you find in places you never before thought to look."

How do we get fooled?
We stop looking once we've found what we like.
Cigarette advertising of the 1940's effectively carried the message: "Cigarette smoking is good for your health.  A very high percentage of people believed that message: they wanted to improve their health, and the advertisements filtered out the bad evidence and stressed that which sounded good.  A very high percentage of smokers died of diseases caused by thier smoking.

We can fool ourselves, too:  We get a great idea and then look about us and accentuate the positive, eliminate the negative, and don't mess around with Mr. Inbetween.

So which, if any, of these ideas might be self-deceptions which attract us because we want to believe them (and haven't yet understood the science which makes them very, very improbable):  Loch Ness Monster, Bigfoot, magical pyramids, telekinesis, therapeutic touch, channeling, exterestrials on Earth, astrology, recovered memories, dowsing, biorhythms, black holes in space, reincarnation, possession by spirits, ESP, tritanopia, perpetual motion?

See some of that advertising--and learn some great rules for advertisers.

What about pseudoscience?

What about misunderstandings?



Heat causes sunburn.  That's correct, but for subtle reasons that lie deep inside the magic of science..  Heat is more mystery than we might imagine.

High temperature does not cause sunburn.  You can lie in the sun on the beach for hours, without any tan or sun block at all, when the temperature is over 90 and not get burned or tanned.  And the next day you can be exposed to the sun for ten minutes, with the temperature in the low 40's, and end up with a sunburn from that exposure.

You can't see or feel what causes sunburn on human skin.  (Many insects can, however.)

Sort through all the possibilities and influneces and discover what is relevant to sunburn and what is not.  And why is "Heat causes sunburn" correct?

What other creatures have what perceptions that humans lack?

What's the difference between heat and temperature?

More heat than light?  Examine some common misconceptions.


biggest    best    larger   worse   Dumb Dumber Dumbth etc, etc
 Do you sense something wrong with ranking people or things with words like these -- these comparatives and superlatives?  Perhaps morally wrong or ethically wrong?

Well, there's something logically wrong there, too.  How should we rank athletes by size?  Paints by color?  People by intelligence? 

Arrange paint chips so that similarity and proximity correlate.

Look at a strange mistake made by the producers of a TV program about colorblindness.

Order the athletes by...

How high is that wall?
The tallest of the people in the sunlight is about six feet tall.  They are about 60% of the distance from the camera to the base of the vertical wall.  Estimate the height of the wall from the given information. 
The wall leads to some canyon country math.
Assuming that the costs are proportioned out equally among the people paying, which of the following would cost you the most, which the least: Your state of three million people funds a new freeway costing six billion dollars; your city of a hundred thousand funds a new soccer stadium costing four million; your country of 250 million funds a new Coast Guard rescue vessle costing 600 million?

Much of physics is done with simple proportions.  One of the simplest is Newton's Second Law of Motion: F = ma

Primitive math

Primitive man
Click on him to see...

Wason's Cards

Click on the house and the cards to see further.
To the colorblind person who painted this house, the notion that  grass green and orange are different is "merely a matter of personal opinion," and, to him, his opinion that they are not different is just as good as the next guy's who says they are different.

If he's going to really understand all those opinions, he will have to study just what color really is and how our eyes and brain work to give us our color vision.  It's much harder for him to understand why his opinion is simply wrong, and seemingly silly to the seeing, than it is for a person with full, normal human color vision.  Full human color vision simply sees.

Now, solve this problem: 

In a set of cards each card has a number on one side and a letter on the other.  Four cards are lying on a table.  They show an "I", an "N", a "6", and a "3".  Someone suggests the hypothesis: If a card has a vowel on one side then it has an odd  number on the other side.  The problem is to determine which cards must be turned over to test the hypothesis.  No card is to be turned over unless necessary to test the hypothesis.

A lot of understanding of how science happens, and why its concepts are often so difficult, is buried in the details of a tale of two very bright people and how they saw (and didn't see) this problem:  LOOK AND SEE!

And solve this one:
A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes.  He can do this job easily by making six cuts through the cube, keeping the pieces together in the cube shape.  Can he reduce the number of necessary cuts by rearranging the pieces after each cut?  Either show how or prove that it's impossible.

Clicking on the green blocks will lead you to three puzzles and three secrets of science.  Remember, "Learning is not your goal, seeing is."

Briefly put:
Consider everything that's important.
It's very easy to overlook essentials.
Dismiss the irrelevant.
Irrelevant things are always creeping into our thoughts.
Be able to use ratios where you should.
When to add; when to multiply; when to subtract; when to divide?
Side step contradictions and recognize the undeniable.
Many contradictions are subtle; many undeniable things are unpleasant.
Don't deceive yourself; don't let others deceive you.
It's very easy to overlook essentials which you would rather not hear about.
When you can see from this vantage point,
look for examples of wrong turns you may have made in the past.
Look for places you can help others climb up the steps.


spatial visualization
Mach & Heidinger

Some graduates of courses in education will recognize where these five steps came from.  The source is very familiar, but this presentation has made it all less abstract and more in terms of everyday experience.  Here's a clue: The commonality (the underlying abstraction) to all five steps is the development of mental skills for recognizing multiple, interacting variables and influences and correctly identifying their relationships.  The source is identified in one of the links from this page.  What's the source?