Penrose Connections

Two years ago I was granted a sabbatical to study the history of mathematics in northern Europe from the Renaissance to the present, and I kept a blog at this link about that trip.  Two months ago opportunity came up to revisit one of the locations I had spent time in on sabbatical, the amazing city of Edinburgh.

Even though I was there "just for fun" this time, I couldn't help but look into some of the things related to math that I had missed initially.  One mathematician I'm quite interested in is Roger Penrose whose "impossible shapes" made it into the movie Inception.

Penrose's mathematical work takes inspiration from many places, including the world of art.  He collaborated with artist M. C. Escher, and he had an uncle who was an artist and a collector of surrealist art.  This uncle was Roland Penrose, and his collection is housed at "Modern Two" in Edinburgh.  The rest of this blog consists of photographs I took in the Roland Penrose Gallery of "Modern Two."  They may give a sense of one influence in the life of mathematician Roger Penrose.

Maternity by Miro

Never Again by Tanguy

Magritte

The Black Flag by Magritte

Untitled by Roland Penrose

The Joy of Living by Ernst

Hat in Hand, Hat on Head by Ernst

By Roland Penrose

Confluence

I love it when one of my students gets inspired by the math and uses it creatively in another discipline.  The sculpture pictured here is by my Math 101 student Brisa who created it in such a way to evoke the Sierpinski Gasket fractal.

Have a Better Day

Last night when my niece, Sierra, found out I'd had a bad day, she drew me this "have a better day tomorrow" picture, and I did have a WAY better day today than yesterday!  Thanks Sierra!  :-)

Remembering

Jacob introduced me to a "new" artist (new to me anyway), and I want to remember who she is - hence this post of one of her pieces.  The artist is Maria Remedios Varo, and I love her work!

Escher

I'll be giving a talk this spring titled "Infinite Possibility: The Importance of Mathematical Play." One of my three topics will be M. C. Escher's work with tessellations. I was sharing about this with a friend today and was surprised to learn that Escher is not universally known. His work has been a part of my life so long I thought everyone was familiar with it, so I decided to post a few of my favorites of his work - each having some mathematical aspect to it.

Artprize - Shimmering Stones

I wish I could be in Grand Rapids right now to take in Artprize (September 22-October 10). In 192 venues in downtown GR the work of 1713 artists is displayed. The pubic votes on their favorites, and the winner is announced October 7. The photograph above, by Bill Vriesema, is part of one of the displays that caught my eye online. You can view others by clicking Artprize. All sorts of art - big and small - painting and sculpture - you name it - is part of this - and you can vote for your favorites online!

Exploring

I love this woodcut - can't find a title or artist name, though - anybody know?

Today I tried to post more pictures to my last post, but I find my summer draws me to ponder and explore. Books I'm exploring right now are:

Is God a Mathematician? by Mario Livio
The Math Book by Clifford Pickover
The Ragamuffin Gospel by Brennan Manning
The Myst Reader by Rand Miller
That Hideous Strength by C. S. Lewis

Artful Whimsy

My boys and I have always had a fondness for the art of Salvador Dali and Rene Magritte. Many years ago Jacob, our resident artist, made a number of drawings inspired by the work of these artists. One of them is included at the top of this post. Today he decided to update the process using his computer knowledge. Below is what he created this afternoon inspired by his work of years ago.You should be able to enlarge the images by clicking on them.

Here is a related Magritte, La Chateau des Pyrenees:

Timeless(time)ness

"When time from time shall set me free."

- e.e. cummings

I'm Telling You It's Not Straight!

I found this while exploring mathpuzzle.com. It was created by Seb Przd. More of his work can be found at this flickr site. His work is quite Escheresque, and I like what I term the "small world" images as well. (They are actually called stereographic projections, and well worth checking out!)

Far Better Artist!

I teach math, and I can't draw a circle to save my life.
This elephant can draw a self portrait!
I stand amazed!

Thanks for sending this on Amy!

A Little Art for Today

Rene Magritte is my favorite artist. His most recognizable paintings are those of men in bowler hats or, what is probably his MOST famous, Ceci n’est pas une pipe (which is a pipe that is not a pipe, or is it a pipe, or . . .). My favorite painting of his is La flèche de Zénon (Zeno’s Arrow). Here are a couple of others:

Spring by Caleb

Shul

I have always loved old stone walls such as the one in the photograph below. I love the hollows left by the stones that are missing. There is a beauty there, and the beauty is in the history and the meaning, the fact that something WAS there and made an impression. It is an emptiness that is not empty; the emptiness itself signifying something. The hollows always leave me wondering, “What was the color of the rock that was there? What was its texture? Whose hand placed it there? When did that hand place it there? When did it fall out and why? What was this wall built to keep out or to keep in?” With all of this in mind, I took the following photo, which I entitled “Shul.”

"Shul" is a Tibetan word defined as “an impression – a mark that remains after that which made it has passed by – a footprint, for example." From what I understand, it can also be used to describe such things as the hollow in the ground where a house once stood, the spaces worn in a rock where a river runs in flood, the indentation in the grass where a deer slept the night. Shul is an impression of something that used to be there, but this hollow signifies meaning rather than emptiness.

Art in the Middle

It is a running joke with my students that I cannot draw a circle. Unfortunately it is often necessary for a math teacher to draw circles. The very best of my attempts end up looking like eggs - and really pathetic eggs at that! I just laugh right along with them and say, "There's a reason I teach math and not art!"

The artwork above is by my middle child, age 12 - merely some doodles he was doing in the car one day. It is clear that he gets his "art genes" from his father and not his mother!

All Things

I have many favorite trees. Rocks, trees and water have always been very restorative to my spirit. In contemplating them, I find myself ministered to in very specific ways.

I've watched the progress of this little tree over the course of many years, and I had always felt sorry for it, for what it had to overcome to grow, for the fact that it had been bent by the presence of the huge boulder in its way, for the barren place on which it is growing, for all its obstacles.

It finally dawned on me that as this tree grows, it is going to push that boulder over! It is this little tree that is going to triumph! This reminds me of Philippians 4:13

I can do all things through Christ, who strengthens me.

Semi-related comment: this boulder reminds me of La flèche de Zénon by René Magritte.

A

The title of this post is “A,” as in “Q&A,” so if you haven’t read “Q” yet, check it out.



This image isn’t a meteor or disguised space-craft or a catapulted rock. In fact, this boulder is not moving at all. This painting by René Magritte (1898-1967) is entitled La flèche de Zénon (Zeno’s Arrow).

Why “Zeno’s Arrow?” This is a boulder not an arrow.

Well, Zeno (490BC-425BC) is known for his paradoxes dealing with motion, two at least “proving” that motion is impossible.

1) DICHOTOMY PARADOX: In order to move a given distance an object must reach the halfway point, but before it travels from the starting point to the halfway point it must get halfway there, and before it reaches that point . . . (you see where this is going – nowhere!). If space can be infinitely divided, then an infinite number of time intervals must pass before an object moves any given distance, therefore it cannot move.

2) ARROW PARADOX: When an arrow is in a place just its own size, it’s at rest. At every moment of its flight, the arrow is in a place just its own size. Therefore at every moment of its flight, the arrow is at rest (i.e. not moving).

Although it seems gravity should pull the boulder into the ocean, according to these paradoxes the boulder is at rest and will remain so.

These paradoxes may sound silly (since you know that things actually do move), but try disproving them logically! If they don't work, why not?

Q

What is this?

- a boulder catapulted towards the ocean?
- a meteorite?
- the asteroid that killed the dinosaurs?
- an alien spacecraft in disguise?
- another planet with different graviation?
- a VERY heavy raincloud?
- something else?


Answer