history, photography, STEM

Beyond Measuring the Earth

Geometry began with practical measurements over moderate distances.  Boundaries of Egyptian farmers’ fields had to be restored after the Nile’s annual floods.  A taut rope between two posts marked where an edge of the base of a pyramid would be laid.  And so on.  This prosaic technology inspired ancient Greeks to create something weird and wonderful.

People like Pythagoras and Euclid reimagined the pyramid builders’ rope as perfectly straight (not sagging a little), so thin that it had no thickness at all, and extending forever beyond the posts.  Crazy.  They called it a “line” and found that they could reason about such things, proving new statements by deductions from what they already knew.

Those ancient geometers discovered much that was true and good and beautiful in the imagined world of points and lines, and a few of them took the first tentative steps toward using their discoveries to help answer questions about the experienced world of posts and ropes and much else.  Eratosthenes kept the promise made by “geo”+”metry” when he measured the circumference of planet Earth, even tho it was impractical to try to wrap a tape measure around it.

Modern STEM is rooted in ancient geometry (among other things), and a long hard slog has progressed from measuring the Earth to understanding it.  Our understanding is not perfect and never will be, but maybe it is good enough to help us save the Earth.  From us.  I hope we can rise to that challenge, and that I have risen to this one:

Geometry ~ Pic and a Word Challenge #269


Image Sources

  • The colorful frame around the image is upsized from my much smaller diagram for Bhaskara’s elegant proof of Pythagoras’ Theorem.  The resulting fuzziness of the points and line segments is a reminder that we cannot experience the ideal perfection of geometric shapes.  But we can refer to the shapes when we tell each other stories about what we experience!  (Tho often hard to read w/o wrangling equations, scientific theories are among the best stories we can tell.)  The colors of the line segments tie the image to the theorem’s bottom line w/o using letters that would clutter the diagram:
      a² +  b²  c²
  • The Blue Marble image overlaid on the diagram was downloaded from NASA Visible Earth: The Blue Marble.   Making NASA’s image cost a lot more than making mine.  That’s OK.  It was money well spent.
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humor, photography, STEM

Tamed But Not Stifled

It is fun to imagine being able to fly.  I am an adult who might enjoy imagining flight but would not jump off a balcony and try to fly.  It is definitely not fun when a child (or a nominal adult with an assault rifle) acts on wild imaginings.  How can wild imagination be tamed but not stifled?
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As Patrick Jennings remarks in

« Imagination ~ Pic and a Word Challenge #129 »,

a world seen without imagination would be sadly plain and gray.  Imagination can be fun.

It is fun when Patrick sees a reflection (of a dark building with a bright light) and imagines a dragon breathing fire.


Breathing Fire © Patrick Jennings

It is fun when I see a decorative gourd and imagine a phallus going soft after sex.


Phallic Gourd © Mellow Curmudgeon

It is fun to imagine being able to fly.

Both Patrick and I are adults who might enjoy imagining flight but would not jump off a balcony and try to fly.  It is definitely not fun when a child (or a nominal adult with an assault rifle) acts on wild imaginings.  How can wild imagination be tamed but not stifled?

While there seems to be no single simple answer, the methods of STEM do rather well.  We soak imagination with other things, many of which have rhyming names: calculation; experimentation; observation; replication; validation; verification.  Yes, it is hard work.  We often get ourselves soaked, with perspiration.

Sometimes we get consternation, when we find that what we fondly imagine cannot happen.

Sometimes we get wings.


Image downloaded from Imgur has been lightly cropped.

engineering, humor, STEM

Creativity Averted Catastrophe

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before-afterDesigned and built long before there were supercomputers, the great Gothic cathedrals often developed cracks and bulges.hernia-support-belt_200x206

When more buttressing did not look like it would be enough to avert a catastrophic collapse at Amiens, the engineers there devised a way to get the net effect of putting a really big and really strong hernia support belt around the cathedral walls.  Cathedrals don’t wear clothes; how do U hide such a belt?  How do U cinch it?  How do U accomplish all that with medieval technology?

The answers are sketched in the Wikipedia article on the Amiens Cathedral and visualized in a 2010 NOVA episode on PBS: Building the Great Cathedrals.  (To read more detail, look for “iron” in the transcript.)  U can blame me for bringing up hernias.

Dunno whether the engineers at Amiens were called ingénieurs at the time; at least one of them should have been called créatif.  The cathedral is an enduring monument to the faith of many and the creativity of some, including a few engineers.