language, math, photography

Perpendicular: Upright or Uptight?

Calling 90 degrees a “right” angle is a little misleading.  Yes, spatial coordinates should usually be based on perpendicular lines.  But 90 degrees is often just one among many, and perpendicular may not be right for the job.

Perpendicular ~ Pic and a Word Challenge #269

The ceiling should be perpendicular to the wall
(and the wall to the floor).


Even the klutz who built my house got that right.



The right angle for slicing a pizza depends on
how many slices are needed.


© sabelnik | 123RF Stock Photo



haiku, photography

Seeking Solitude

«You may use my image in your post, or any image you have created.»  So say the rules of Patrick Jennings’ series of challenges.  For challenge #257, I did both at once.  (Details are at the end of this post.)  The image illustrates my haiku about solitude, which is sometimes an aspiration rather than a condition.

Solitude ~ Pic and a Word Challenge #257


Not Alone
|Lonely in the crowd
|and weary of empty talk,
|I seek solitude.

Image Notes and Credits

I was intrigued by the landscape’s azure sky in

© Patrick Jennings

While the sky is fine just as it is, it is also a good place for an overlay with text or another image.

I had already used a downloaded image of a wearisome crowd to illustrate the first 2 lines of my haiku Not Alone:
cartoon people in the crowd

© Igor Zakowski | 123RF Stock Photo
(Image has been cropped.)

I decided to illustrate the whole haiku by overlaying the landscape’s sky with the crowd image, opaque at the top and then gradually fading out of sight toward the bottom.  By the time I noticed that my photo editor does not support opacity gradients in overlays, I had my heart set on the project.  Hmmm.  Overall opacity of 60% in the overlay looks good, apart from the sharp horizontal line at the bottom of the overlay.  Hmmm.  My editor does have enough functionality to make that boundary a little blurry and wobbly, with one eye of Ms Purple Hair left staring at the viewer.

haiku, humor, photography

Lines Plan Their Day

«Let’s twist and ripple across the computer screen
in an exuberant pseudorandom dance
that won’t repeat for centuries.»


«Maybe tomorrow.  Still sore from yesterday.
I pulled red line duty and
people stepped on me as they crossed.»


«Hmmm.  Let’s just mark a few straight edges
of flat surfaces in the real world
until U feel better.»
«I’m up for that if we keep the angles simple.»


Images #1 and #2 in my response to

Lines | The Daily Post

were selected and cropped from bursts of photos while running the Mystify screen saver.  Image #3 is a photo of an architectural detail, edited to compensate for my inability to compose precisely w/o a viewfinder.  (Glad I eventually replaced the old camera by one with both a screen and a viewfinder.)  Here is a haiku about the kind of silliness exemplified by the dialog in my response:

What the World Needs
|More silliness from
|those who know they are silly;
|less from the others.

flowers, haiku, photography

Elegy in 3-5-3



© Matsuo Basho (Tr. Jane Reichhold)
|falling to the ground
|a flower closer to the root
|bidding farewell


Carpe Diem Weekend-meditation #14 Revise That Haiku


© Chèvrefeuille
|tears flow
|falling to the ground
|autumn leaves


Elegy for Tando
|Flowers fall,
|but seeds will ripen.
|Some will sprout.


haiku, humor, math, philosophy, photography, science

They Are Beyond Space & Time

Taught myself a crash course in digital photo manipulation for a post on how Plato recovered from a hangover and bounced back from an encounter with intellectual ancestors of Karl Popper.  Hope I did not flunk.

Numbers ~ Pic and a Word Challenge #106

Plato woke up with a nasty hangover after a symposium that had gone badly for him.  Some new sophists who called themselves “natural philosophers” had come to Athens, and the kind of philosophizing they advocated was anything but natural to Plato.

The new sophists spoke about “observations” and “conjectures” and “predictions” rather than abstract reasoning about perfect ideal forms.  Plato could tolerate his student Aristotle’s interest in easy casual observations and simple inferences from them, but the new sophists were different.  They wanted to measure minute details of how the shadows on the walls of Plato’s metaphorical cave flickered.  They would consider anything imaginable as a candidate for “explaining” their observations, even things so fanciful that Homer would never have dared to sing of Odysseus encountering them on his way back to Ithaca.

Instead of trying to establish a conjecture by reasoning to it from first principles, the new sophists wanted to reason from it to a prediction about what they would observe.  Conjectures that led to many diverse predictions matching what was actually observed were to be accepted as true, but only until somebody came up with “better” conjectures that yielded more accurate predictions by more elegant reasoning.  As one of the brasher “natural philosophers” said,

All knowledge is provisional,
never more than the best we have at the moment.

Flummoxed by such craziness, Plato had been hitting the wine harder than usual.  He had passed out just as another “natural philosopher” began replying to the brash one:

Well, that is a little over the top.  For example, …

All that was last night, when stars had carpeted an inky black sky.  Now the sky was light blue, the sun was shining, and Plato’s head was aching.  He winced when he remembered a new sophist’s remark that each star might be something much like the sun but almost inconceivably farther away.  That example of a loony conjecture had prompted a nightmare with Athens (and its circling sun) lost in a humongous whirling vortex of innumerable stars (rather than stationary near the center of the universe, as Athens so obviously was).

The cash bar at the symposium had been pricey, and Plato wondered if he still had enough money to buy some willow bark to ease his headache.  He put his coins on the nearest flat surface and counted them.  Five should be plenty.  Then he noticed that three coins had the side with the face of a leader facing upwards, while two coins had the side with the leader’s mansion facing upwards.  Suddenly, Plato felt much better.  He even felt ready for another encounter with that brash sophist.


Plato’s Challenge
|Three plus two was five
|before any mind could know.
|Where do numbers live?