Miracles of Confusion

[Image: a grainy photograph of a couple of volcanoes someplace. (Maybe another
planet.) Or are they? See the note at the foot of this post for more information.]

From whiskey river:

Dharma

The way the dog trots out the front door
every morning
without a hat or an umbrella,
without any money
or the keys to her doghouse
never fails to fill the saucer of my heart
with milky admiration.

Who provides a finer example
of a life without encumbrance —
Thoreau in his curtainless hut
with a single plate, a single spoon?
Gandhi with his staff and his holy diapers?

Off she goes into the material world
with nothing but her brown coat
and her modest blue collar,
following only her wet nose,
the twin portals of her steady breathing,
followed only by the plume of her tail.

If only she did not shove the cat aside
every morning
and eat all his food
what a model of self-containment she
would be,
what a paragon of earthly detachment.
If only she were not so eager
for a rub behind the ears,
so acrobatic in her welcomes,
if only I were not her god.

(Billy Collins [source])

…and:

Tour

Near a shrine in Japan he’d swept the path
and then placed camellia blossoms there.

Or — we had no way of knowing — he’d swept the path
between fallen camellias.

(Carol Snow [source])

Not from whiskey river:

People have reality-dampers.

It is a popular fact that nine-tenths of the brain is not used and, like most popular facts, it is wrong. Not even the most stupid Creator would go to the trouble of making the human head carry around several pounds of unnecessary gray goo if its only real purpose was, for example, to serve as a delicacy for certain remote tribesmen in unexplored valleys. It is used. And one of its functions is to make the miraculous seem ordinary and turn the unusual into the usual.

Because if this was not the case, then human beings, faced with the daily wondrousness of everything, would go around wearing big stupid grins, similar to those worn by certain remote tribesmen who occasionally get raided by the authorities and have the contents of their plastic greenhouses very seriously inspected. They’d say “Wow!” a lot. And no one would do much work.

Gods don’t like people not doing much work. People who aren’t busy all the time might start to think.

Part of the brain exists to stop this happening. It is very efficient. It can make people experience boredom in the middle of marvels.

(Terry Pratchett [source])

…and:

The usual techniques for proving things are often inadequate because they are merely concerned with truth. For more practical objectives, there are other powerful — but generally unacknowledged — methods. Here is an (undoubtedly incomplete) list of them:

Proof of Blatant Assertion:
Use words and phrases like “clearly…,””obviously…,””it is easily shown that…,” and “as any fool can plainly see…”

Proof by Seduction:
“If you will just agree to believe this, you might get a better final grade.”

Proof by Intimidation:
“You better believe this if you want to pass the course.”

Proof by Interruption:
Keep interrupting until your opponent gives up.

Proof by Misconception:
An example of this is the Freshman’s Conception of the Limit Process: “2 equals 3 for large values of 2.” Once introduced, any conclusion is reachable.

Proof by Obfuscation:
A long list of lemmas is helpful in this case — the more, the better.

Proof by Confusion:
This is a more refined form of proof by obfuscation. The long list of lemmas should be arranged into circular patterns of reasoning — and perhaps more baroque structures such as figure-eights and fleurs-de-lis.

Proof by Exhaustion:
This is a modification of an inductive proof. Instead of going to the general case after proving the first one, prove the second case, then the third, then the fourth, and so on — until a sufficiently large n is achieved whereby the nth case is being propounded to a soundly sleeping audience.

(Armen H. Zemanian, reportedly published in The Physics Teacher, May 1994 [canonical source not available online])

…and:

Why They Turned Back/Why They Went On

Because a black bird flew across the road;
Because the attendant at the pump turned surly;
Because the uncertain weather
Made Mother nervous,
And, back home, the telephone kept ringing
In an empty house;
Because a white bird flew across the road.

How far had they come?
How far did they go?

Seeing, along river after river,
Between shores of brush and willow,
Only the bend ahead and the bend behind
Under a sky featureless and hard
As a shallow bowl; through tautologies
Of a landscape unendingly repeated
Mile after mile; down Main Street
After Main Street, replications
Of the same petty civic scenery;
Hearing the ghosts of trains
Crossing between cornfields,
Clattering over the points, moaning
Above creosote and cinders,
As if the imagination
Could produce nothing more
Than the same landscape, cornfields,
Rivers, and Main Streets
Pulling them, like a magnet, not toward
But away from, not into the future,
But away from the past;

Until a white bird flew across the road
With its mysterious message, that said to some,
“Turn back,” and to the rest, “Go on.”

(Constance Urdang [source])

___________________________________

About the image: Unremarkable, isn’t it? It’s a little hard to picture just where on Earth these volcanoes (or whatever they are) might be, but otherwise it’s very straightforward. If not on Earth, obviously they’re volcano-like features somewhere.

Unless, well, unless they’re not. Consider:

From the page at the Stanford University site where I found these images:

The images… are the same except for being flipped (not rotated) up and down using a simple image processing program.

If you rotate this book by 180 degrees, you will see that the mound in [the first figure] changes into a crater, and conversely the crater in [the second image] changes into a mound. When we interpret these shapes, we assume that the illuminant is elevated. This assumption about the position of the illuminant guides our inference about the shape of objects in the image. The distinction between mound and crater in these images is mediated mainly by the shading differences. Hence, rotating the images changes the shading relationship and we reinterpret the shape. Ramachandran (1988; see also Knill and Kersten, 1991) has demonstrated this phenomenon in a number of different ways. He argues further that the brain simplifies the interpretation of images by assuming the illumination consists of a single light source.

I found another demonstration of the principle here, using the famous photograph of Buzz Aldrin’s footprint on the surface of the moon. The blogger there adds, though:

No matter which version of the photo you are observing, if you contort yourself and try to look at it upside down, it won’t switch — your brain simply won’t permit it.

My brain won’t permit it, all right: it flat-out refuses to let me “contort myself” this way in the first place. :)