Thursday, May 10, 2018

Topology for artists - workshop sketch 1

One of my little dreams is to make and give a workshop about topology for artists.
It might be called: What you didn't know about spaces. Topology for artists.
These are preliminary notes. Previous ones are here: YouTube Topology

I've learned that there are two starting points for topology. The first starts in geometry and shapes and is artistic. The second starts from point set topology and is philosophical (even including Husserl, see below). These paths are connected, but I don't know how (yet).

Note: I used a spatial metaphor in the above paragraph unintentionally. Unconsciously I map topology itself onto some abstract space. Connectedness and path-connectedness are topological terms themselves. You can even map the whole of mathematics onto a space.

Looking for inspiration I found the following semi-popular books about topology. This is the geometric approach. I will maybe order both of them, but the second one is quite expensive:
From the first book: the projective plane built from a Mobius strip. This shape can only exist in the fourth dimension:
From the second book: a hexagonal Mobius strip with one twist. This on exists comfortably in three dimensional space:
Then there is interesting free material on the internet by Matilde Marcolli. This is also more geometric:
With a nice illustration of the four possibilities for folding and gluing a two dimensional surface, yielding three and four dimensional objects:
Then I found this inspiring article, where topology is extended into mereology. This is more (analytically) philosophical. I knew about the term mereology from this book, but I didn't know it used topological building blocks. This is exactly where I would like to go:
A basic introduction of topological ideas (and there is also a very interesting section on Husserl that I don't quote here):
... topology takes as its starting point the intuitive notion of boundary. ... Imagine a solid and homogeneous ... sphere. We can distinguish ... two parts of the sphere which do not overlap (they have no parts in common): on the one hand is its boundary, its exterior surface; on the other hand is its interior, the difference between the sphere and this exterior surface (that which would result if, per impossibile, the latter could be subtracted from the former).
And (this is mereology):
The property of being a (single, connected) body is a topological spatial property, as also are certain properties relating to the possession of holes (more specifically: properties relating to the possession of tunnels and internal cavities). The property of being a collection of bodies and that of being an undetached part of a body, too, are topological spatial properties. It is a topological spatial property of a pack of playing cards that it consists of this or that number of separate cards, and it is a topological spatial property of my arm that it is connected to my body.
And a more formal look at the concepts:
We may define a closed object as an object which is identical with its closure. An open object, similarly, is an object which is identical with its interior. The complement of a closed object is thus open, that of an open object closed. 
To be continued.

Saturday, April 28, 2018

A strange country

The past is a foreign country; they do things differently there.
 L.P. Hartley, The Go-Between

I was again reminded of the truth of this wisdom (or platitude, or both) when I prepared to clean out this book I got from the second-hand market. This is 1966, but it looks different, ancient and also strangely modern. It looks like a parallel timeline that never really happened. But it did happen. And now it's gone more completely than the Middle Ages.
At the municipal graveyard

This is from Toon, Foto's van Robby Pauwels, 1966, by Toon Hermans, Robby Pauwels, Andries Blitz, (De erven de wed. J. van Nelle N.V., Rotterdam). A book about a well known and talented Dutch entertainer (he called himself a clown). He died not too long ago. But how different it all looks!
Innsbruck, just before we would start decorating the Christmas tree

It might have been in the depths of the Cold War, with the hippies, student revolts and the invasion of Czechoslovakia a few years into the future. Charles de Gaulle and Harold Wilson were in power. How calm and peaceful this time looks, compared with today.
Wall flowers

Saturday, April 7, 2018

The flaming sun and De Chirico - 2

I'm always intrigued by the presence of the surreal "sun in splendor" in ordinary surroundings, creating a strident contrast. Especially in the boring suburbs of Rotterdam. I have written about this symbol before and will give more examples below.

It also reminds me of the late work of Georgio de Chirico. This Neometaphysics (1968-76) period is usually ignored by art critics but I find it very fascinating. It resonates with my interest in sky mysteries. See for example the Sun on the Easel from 1973.
The official explanation says the following, and this could be an explanation for the ubiquity of the symbols:
... while thinking of Italy, its cities and ruins ... the suns and stars had returned to earth like peace-loving immigrants. Without doubt, they must have turned themselves off in the sky, because I saw them light-up once again at the entrances and gates of many of these houses ...
But another very interesting explanation says the following. I encourage you to read all of it:
In this canvas, Sun on the Easel, the theme of insight and out-sight is clearly apparent as he places a glowing sun (representing exterior sight) and a bright moon (interior thought) inside his studio with their darkened counterparts outside.
And I agree with this assessment of the quality of the late work of De Chirico:
The final Metaphysical paintings are powerful poems on the sun. Painters have painted sunsets, none have painted the idea of the sun, the power of the sun, the enigma of the sun. This is an amazing series of paintings.
The suns that we see on the outskirts of Rotterdam and in shopping malls are just as surreal as the De Chirico paintings.
The sun symbol is old (Medieval) and irresistible. It infiltrates our bland modern surroundings.
And the black sun in the De Chirico paintings could be the black sun of the night:
For the Mexicans there were two suns, the young Day Sun and the ancient Dark Sun. Some scholars regard the mythological Black Sun as the ancient female origin of all, it is both tomb and womb.
Another interpretation holds that the sun god Huitzilopochtli crossed the underworld during the night bestowing light to the forgotten souls, however, he demanded human blood as payment to his tasks.

But it might also be related to alchemy:

Sol niger (black sun or the crows head) can refer to the first stage of the alchemical magnum opus, the nigredo (blackening). In a text ascribed to Marsilio Ficino three suns are described: black, white, and red, corresponding to the three most used alchemical color stages. 

And the motif of the moon embracing the sun can also be seen in the De Chirico paintings. This website says the following, but they forget to mention the moon!
Interestingly, one gem of the Di Donna effort is de Chirico’s “The Two Suns,” a wonderful late painting from 1969 in which art triumphs over life: A vivid sun blazes from the artist’s easel while a black one sets over the city beyond.
Most likely we will never know the correct interpretation of the De Chirico symbolism. Many ideas above are plausible, but they don't explain the cables linking the black and the golden sky bodies. Is it just an electric cable? Are these artificial sceneries in a theatre, that will be hauled upwards by some mechanism? We can only wonder and remember when we see a mysterious sun in the forgettable outskirts.

Tuesday, March 27, 2018

The best topology on YouTube

One of my little dreams is to make and give a workshop about topology for artists. It might be called:

What you didn't know about spaces.
Topology for artists.

I don't know if I'll ever do it, but in the meantime I've had much fun with watching topology lectures on YouTube. There are many excellent ones.

I'm using the free book Topology without tears by Sidney Morris to learn the subject. It's very structured, rigorous and tough. It has many exercise problems. It is very challenging for me but strangely addictive. There are also several videos for the book. These are also rigorous and challenging, but worth watching very much:

Richard Southwell has a great series of introductory lectures on topology. He also makes nice models using 3D-printing:

A short introductory series written by Victor Victorov and edited and presented by James Dilts. Topology of the Real Line:

An anonymous author gives a great series of introductory lectures on topology, starting with point-set topology:

And another anonymous author gives a great series of introductory lectures on topology, also starting with point set topology:

Just one example of applied topology. But a very good one:

John Elliot includes a lot of topology in his series on functional analysis. He starts from measure spaces and open balls:

A beginner's course in Algebraic Topology, given by N J Wildberger. Mathematics with roots in the work of Riemann, Klein and Poincare in the latter half of the 19th century.

A very inspirational series of lectures by Dr Tadashi Tokieda. Very different from the others:

Frederic Schuller gives several university level courses on mathematics and topology. The first lectures can be followed by anyone with bachelor-level math knowledge. They're extremely well structured. The first series starts from the fundaments of mathematics:

The wealth - nature boundary

Elements of the Dutch landscape - 14 - updated after finding more examples

During our walks we often pass through the village - nature boundary. Often the most expensive-looking houses are placed on this borderline.

There is nothing surprising about this. The most expensive houses should be located on the most expensive plots. And the most expensive plots should be those that border open views over land or water.

I have not had the time to read about this phenomenon in my "Urban economics" book, but I expect it will be explained there.

Hitland - Capelle aan den IJssel
A FENCE (Carl Sandburg - Chicago Poems)
Now the stone house on the lake front is finished
and the workmen are beginning the fence.
The palings are made of iron bars with steel points
that can stab the life out of any man who falls on them.
As a fence, it is a masterpiece,
and will shut off the rabble and all vagabonds and hungry men
and all wandering children looking for a place to play.
Passing through the bars and over the steel points will go nothing
except Death and the Rain and To-morrow.

Let us note however that Brussels for instance has a different sociospatial structure (see Goffette-Nagot et al. (2000)). Brueckner et al. (1999) cite three types of amenities: natural (parks or rivers for instance), historical (e.g. monuments) and modern ones (theaters, swimming pools, etc.).

Where in cities do ”rich” and ”poor” people live? The urban economics model revisited Remi Lemoy, Charles Raux, Pablo Jensen
It might be an artefact of a protected nature boundary. It you're looking out into a protected nature reserve there is a guarantee that your view will remain intact. This should enhance your property value.


Sunday, March 25, 2018

Truncated windmills

Elements of the Dutch landscape - 6 - updated after seeing several of these in Schiedam

In the book The innocence of Father Brown G.K.Chesterton has included a story called The wrong shape. Just before the group stumbles upon a murder scene - disguised as a suicide - Father Brown meditates upon good and bad shapes of objects and buildings:
Father Brown had stopped for a moment, and picked up out of the long grass, where it had almost been wholly hidden, a queer, crooked Oriental knife, inlaid exquisitely in coloured stones and metals. ...
"It's very beautiful," said the priest in a low, dreaming voice; "the colours are very beautiful. But it's the wrong shape.
"What for?" asked Flambeau, staring.
"For anything. It's the wrong shape in the abstract. Don't you ever feel that about Eastern art? The colours are intoxicatingly lovely; but the shapes are mean and bad-- deliberately mean and bad. ...
"Why, look at it," cried Father Brown, holding out the crooked knife at arm's length, as if it were some glittering snake. "Don't you see it is the wrong shape? Don't you see that it has no hearty and plain purpose? It does not point like a spear. It does not sweep like a scythe. It does not look like a weapon. It looks like an instrument of torture." 
"Well, as you don't seem to like it," said the jolly Harris, "it had better be taken back to its owner. Haven't we come to the end of this confounded conservatory yet? This house is the wrong shape, if you like."
"You don't understand," said Father Brown, shaking his head. "The shape of this house is quaint--it is even laughable. But there is nothing wrong about it."
Walking through the Dutch landscape you frequently come upon buildings with the wrong shape. These are the truncated windmills. At some time the windmill lost its function and it got too costly to maintain the superstructure. So it was demolished and removed. What remains is a castrated, claustrophobic bunker that does not reach for sky and wind anymore. Not really a corpse but more a zombie.
Father Brown seemed to be studying the paper more than the corpse; he held it close to his eyes; and seemed trying to read it in the twilight. ...  
Darkness full of thunder followed, and after the thunder Father Brown's voice said out of the dark: "Doctor, this paper is the wrong shape." 
"What do you mean?" asked Doctor Harris, with a frowning stare.
"It isn't square," answered Brown. "It has a sort of edge snipped off at the corner. What does it mean?"

Sunday, March 18, 2018

Urban mushroom diary - 17 - winter 2017

Urban mushroom diary - 17 - Rotterdam, winter 2017
I'm always looking for city mushrooms in nature and culture.
Interesting to see how fungi invade our world.

On 11 November 2017 I saw these mushroom composites by Carsten Höller. At first sight they looked like random postmodern juxtapositions without further meaning. Wikipedia says:
Mushrooms became a regular feature of Höller's work from 1994. He has since realized several works with the fly-agaric mushroom, including the Mushroom Suitcase series and the Upside Down Mushroom Room. His fly-agaric replicas are large-scale and often spin or hang upside down from the ceiling.
I fully endorse this statement by the artist:
I find mushrooms incredible … their sole function is to lift their spores out of the ground to be carried away by the wind. So why do they have this immense variety of shapes, colors, and constituents, some of them psychoactive? As far as we know, they don’t communicate with other mushrooms above the ground, and they don’t use these toxins to protect themselves. There’s something else going on that we don’t understand.
On 5 December 2017 is saw a mushroom exhibit in Boijmans Museum in Rotterdam. One of the artists was growing mycelium and mushrooms as a basis for ecological materials. As always the fungal shapes were fascinating. (I forgot to note the name of the artist.) I might try it myself sometimes.
More mushroom shapes were found in the exhibit of Tal R. I liked it very much. I have bought the catalogue but I'm still in the dark about the meaning of this artwork. I expect that his obsessions have nothing to do with my obsessions. Larger than life mushrooms are spooky. Just imagine ...
And on 22 December 2017 in Den Bosch I saw this wonderful extravagant and expensive mushroom fashion. I threw away the picture with the designers name and no I cannot find it anywhere.
And in Den Bosch and later on 1 January 2018 I saw these standard banal mushrooms. I like these too. If I made art I would use these as my inspiration.

Then on 1 January 2018 in the Chaamse bossen I saw these remains of mushrooms from the last season. There are many strange dilapidates shapes that you see nowhere else. I have written about these indescribable Lovecraftian shapes before. They remind me of melting snow. The last one could be Tremella mesenterica.
But even in winter some mushrooms remain legible but (for me) indeterminate. For example I could maybe recognize the Xeromphalina Campanella but the book says that it does not grow in our region. It might also be Xeromphalina kauffmanii. Then there is the very fragile Russula that still survived into the winter. It might be Russula Torulosa.

Urban mushroom diary:
1: Start of the obsession, books, lawns, 2:Dreams, lawns, books and newspapers, 3:Gouda shop windows, 4:Rotterdam lawn, 5:Hoek van Holland wood, 6:Autumn newspapers, 7:Switzerland to Rotterdam, 8: Warffemius mushroom paintings, 9: Münster, documenta14 and Rotterdam, 10: Spore prints, 11: Dead man's fingers, 12: The lower Rhine, 13: Oostvoorne, 14: Rotterdam, 15: Rotterdam, the easy species, 16: ..., 17: Urban winter.