|This page was originally posted for discussion within Oregonians for Rationality of that organization's booth at da Vinci Days celebration in Corvallis, Oregon, July 15-16, 2000. It is now being linked from our Web site because of its general interest.|
|This object can easily be made by cutting a card and then folding it. If you don't image three dimensional relationships fairly well, it can look impossible. We plan to have pieces of stiff paper and scissors so people can try to do it.|
|These six blocks can be packed into the box with space left over and with nothing sticking out of the box. It's surprisingly tricky.|
|These blocks can be packed into a larger cubical box with no spaces unoccupied and nothing sticking out. This looks very easy. It is not! Both this puzzle and the previous can be reasoned; it's not just a matter of trial and error.|
The simple mathematical principle which easily leads to a solution to the two box-packing puzzles was seen as obvious by very few of the visitors, but some discovered it with a little guidance. The smaller puzzle was easily solved by many; the larger may not have been solved by anyone without help. (One person worked on it for many hours.) This is a remarkable puzzle which demonstrates the value of reasoning. We might provide a brief description of how to make it. [DONE! Click on the picture of it above.] (It came from an article in Scientific American.)
We distributed a few printed descriptions of the Steinhaus version of the Soma cube puzzle:
Note the photo of the dalmation below. It's where these patterns had their beginning.
June 22, 2000
|The two "Human Vision" posters on the left illustrate the importance
of edges to our vision. Up close, the portrait at the top is just
a bunch of tally marks.
(Lower poster) The eye is almost unrecognizable up close: it's a half-tone of huge dots. The gargoyle (on the left) is composed entirely of little icons: close up, the gargoyle is completely unrecognizable. The dalmatian is the famous photo that illustrates what happens when edges are taken away.
The three posters on the right:
"See like a giant!" illustrates how climbers can find routes using large-base stereoscopic pairs of photos. Arches National Park's Old Maid's Bloomers (sometimes called "Delicate Arch") illustrates the distinction between eye-crossing and eye-spreading for unaided stereoscopic viewing.
The crystal model photos illustrate how we make something look very big by taking a stereoscopic pair with a very small inter-camera distance.
|This is a large sheet of tiles made into a piece of wallpaper. The tiles are random-dot stereograms, six of which are show on the right. When we approach a repeating pattern such as this, we frequently fuse adjacent tiles—or further. This is "the wallpaper effect."||When different tiles are fused, we see a stereoscopic pattern within the tiles. Most people who perceive the patterns are surprised and reach out to touch the hovering objects and the holes. When their hand enters their field of view, correct fusion occurs and the 3-D objects suddenly vanish. This usually startles.|
|We are gathering the pieces to do Martin Gardner's checkerboard and dominoes puzzle. See it.|
These two puzzles are great exemplars for the concept of logical imperative and a model for the idea that some simple things simply cannot be denied. When they are denied, the one doing the denying simply is not "seeing" some subtle subtext of the question.
are three very special items. Ask yourself, "What
insights could have great influence on causing better problem solving if
only more people could see the world through them?" Here are three
we think would have as great an influence for a better functioning society
as any. They are very simple. They are very subtle. They
are very valuable.
Posters illustrating valuable ideas:
(food for the imagination)
If it’s the basketball coach, he means who’s the tallest.
If it’s the football coach, me means who’s the heaviest.
If it’s the rescuer needing help to lift the beam up, he means who’s the strongest.
If it’s the Mafia boss wanting a bodyguard, he means who’s the most skilled fighter.
Then, who’s the smartest?Who cares?
If it’s the spelling bee judge, she mean who has the biggest memory and best recall.
If it’s the corporate executive wanting a secretary, she means who’s the best organized.
If it’s the army general wanting someone to fight the battle, he means who’s the most skilled with computers.
If it’s the head of state needing to solve a political problem, he means who can deal with the most parameters.
If it’s the chief engineer, she means . . . ???
|Whoever, or whatever,
setting people up along a line doesn’t compare them usefully.
They must be considered in a space of many dimensions.
Comparatives and superlatives almost always mean something different
The only way to line those ellipse people up by size and make it look right, is to put them into two dimensions.
This is because ellipses have both height and width (major axis and minor axis).
That’s two parameters.
So a line doesn’t work. It takes
a space—two dimensions.
from what you imagined.
The truth is always, "It depends, it depends..."
(The following html "poster" has a layout quite different from the actual poster we've printed. The printed poster has no background colors and many more graphics.)
FOOD FOR THE IMAGINATION
You, too, can prove* anything your heart desires. It’s easy. Just…
That's the Prove Anything Ploy(PAP)
of raptors are flying above.
One of them comments:
"Hey guys! There’s a gull who ignores
his disconfirmations. Let’s take him!"
"Good grief!" she thought to herself. "Another supermarket supersucker!"
"I'll reinvest it," said the man to the checkout clerk. "Give me two more tickets.
The first tool of the consummate liar?
Statistics is the modern human tool for predicting the future. It’s the best we’ve got for facing the realities of chaotic events, multiple influences, and uncertainties of life.
Statistics is the first tool of the consummate swift out to prey upon the ultimate gull. We can avoiding becoming a gull by taking the second glances that the swift has discovered. Be a swift, not a gull!
Statistics is the first tool of the consummate scientist facing the uncertainties of the world. Math is a marvelous tool box of deep-looking second glances.
So look again
...and again ...and again ...and
again ...and again ...and
again… ...and again ..........
(As above, the following html poster differs from the printed poster:)
FOOD FOR THE
What causes sunburn?
When can it happen?
Why does sunbathing sometimes never produce a suntan?What does a bee know that you don’t?
How can you “see” how actinic the sunlight is?
[From each of the following captions
However, if you are protanopic
(a colorblindness), you see this range.
A bee sees what we can’t see but need to see for avoiding sunburn. It took our ancestors many millennia to figure out how to “see” beyond our human perception.
Arizona newspapers print daily data that you need to discover one of the sun’s secrets. But you have to add something almost nobody thinks to add: the angle of the sun (here given from the zenith). Then you have to sort through the mess of parameters and pick the relevant from the irrelevant.
(solar noon = 12:09)
Sun angles from the zenith, for Tucson, AZ, where the instrument used is located.
(solar noon = 12:29)
Table printed in many Arizona newspapers.
|When the sun gets much below
about 45º from the horizon, almost all of the actinic ultraviolet
is gone. You can use the length of your shadow on a horizontal surface
to get a quick and easy measure of the sunlight’s actinicity. If
your shadow is longer than you are tall, there’s very little ultraviolet.
The same atmospheric effect
that makes the sky blue scatters the uv into outer space: not very effectively
when the sun is high; but when the sun is low...there goes the uv.
(It’s called Rayleigh scattering)
Identifying and sorting through multiple influences is one of the big differences between science and non-science, between "rationality" and nonsense. The insights needed are what Jean Piaget identified as the most sophisticated and advanced mental developments that occur during normal human development (formal operations). When they are seen, they are obvious; when not seen, they seem inconceivable.