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.

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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:

Topology Without Tears by Sidney A. Morris

Topology Without Tears - Video 1 - Pure Mathematics

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

Richard Southwell - Topology for beginners

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

General topology introduction

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

XylyXylyX - What is a manifold?

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

The Math Sorcerer - Topology

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

The inscribed square problem

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

John Eliott - Functional analysis

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.

Algebraic Topology by N J Wildberger

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

Tadashi Tokieda - Course on Topology & Geometry

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:

Frederic Schuller - Lectures on the Geometric Anatomy of Theoretical Physics

Frederic Schuller - International Winter School on Gravity and Light 2015

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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.

Dordrecht

Hekendorp

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.

Dordrecht

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.

Zoetermeer

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

Hazerswoude

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.

Hazerswoude

Alblasserdam

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:

Schiedam

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.

Zoetermeer

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?"

Zoetermeer

Schiedam

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.

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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.

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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.

Urban moons - 2

This is also: Particles of deep topography nr. 32.

I am fascinated by the moon observed from city streets. This is an imperfect observation. There is light pollution and rooftops get in the way. Streetlights and billboards mingle with the sky objects. But I like this imperfection. I'm happy with the reflections of sunlight from office windows and with multiple moons as seen through glass. Almost as strange as lost Carcosa.

The conjunction of a streetlamp, the moon and Jupiter.

Rotterdam evening on 19 December 2013, 21:28.

Along the shore the cloud waves break, The twin suns sink behind the lake, The shadows lengthen In Carcosa. 

Strange is the night where black stars rise, And strange moons circle through the skies, But stranger still is Lost Carcosa. 

Songs that the Hyades shall sing, Where flap the tatters of the King, Must die unheard in Dim Carcosa. 

Song of my soul, my voice is dead, Die thou, unsung, as tears unshed, Shall dry and die in Lost Carcosa.

The Song of Lost Carcosa

Often the moon can be seen in conjunction with other bodies, most often Venus and Jupiter. Saturn is also prominent but Mars is often too dim to be visible. Often you can see the path of the ecliptic through the sky. Multiple heavenly bodies are beautiful even if they're artificial and imaginary. Like the poem by Cees Buddingh.

Moon, Venus and Jupiter in morning sky of Rotterdam.

9 December 2015, 7:30 - Mars is also there, but invisible in the photograph

The lamp above my table
mirrors itself twice
in the panes of my bay window. 

Like motionless, cream-coloured celestial bodies
they hang above my Banka Street
invisible to those who walk beneath them. 

Visible / invisible - by Cees Buddingh, a Dutch poet from Dordrecht  

My moon fascination may have started early. I remember walking with my father through the city streets of Prague, the full moon high above the houses. Even though I was close to a trusted figure, the whole scene filled me with fear and awe. I still have it sometimes, but (alas) not as intensely anymore. The sensation is comparable to looking at a De Chirico painting.

A ring around the moon in the center of Rotterdam.
Moon above a frozen Rotterdam park lake.

31 October 19:00 - 1 January 2009, 17:40

Above them, the moon is round and bright; but its brightness is of a dull sort, like the flat whiteness that appears in the spaces of complex designs embellishing the page of a book. 

They are staring into the blackness where the other one has disappeared. Around them, crisscrossing shafts of tall grasses; above them, the moon is round and bright.

Noctuary (Thomas Ligotti)

While studying in Delft I spent the evening with a friend and we had a philosophical discussion about consciousness and perception. It was night and it was dark outside. At one point he said:

Now if you looked out of this window and saw a huge luminous face in front of it - you wouldn't know what to make of it - because it's outside of your normal experience.

I was scared and fascinated by this image and I drove home extra quickly on my bicycle. The full moon didn't help to calm me. And even now I get slight shivers when I think about it - especially when I have to cross unknown dark hallways at night.

The moon above trees on the outskirts of the city.

Rotterdam evening on 16 September 2009, 19:46.

... the thinnest blade of moon which seemed to belong to this town as it belonged to no other place on earth ... 

... I could see the moon shining between the close rooftops, and I thought that it subtly shifted phases before my eyes, bloating a bit into fullness. The doctor caught me staring. 

"It's not going haywire up there, if that's what is bothering you."  

"But it seemed to be changing." 

Grimscribe (Thomas Ligotti)

Accepted theory is that the moon was created in a collision between the proto-earth and another planetoid. The molten material formed the earth-moon system. The light (molten) material escaped to form the moon, the heavy elements settled to form the earth.

The conjunction of a streetlamp, the moon and Jupiter.

Rotterdam evening on 9 September 2009, 21:03.

The wind picked up and a torn kite struggled to free itself from the clutches of an elm across the street. Above the trees the October sky remained lucid, as if a glossy veneer had been applied across the night. The moon brightened to a teary gleam, while voices below waned.

Noctuary (Thomas Ligotti)

Sources

alexandra-lethbridge-hunting-for-the-invisible

alexandra-lethbridge

alexandra lethbridge

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About this series - Over the years I've collected many place descriptions. It's a waste to keep them on my harddisk. So I'll publish them from time to time. I will add some pictures when suitable.
Enhanced and amplified topographies can be found in a broad range of literature. The best ones link to metaphysics or mysticism and (pre-) load the landscape with unexpected layers, sheets, slabs and strata of meaning. We can appropriate all this work to enrich our everyday surroundings.
Previous posts are 1:The paranoid method, 2:Rooftops and sacrifices, 3:Oil and electricity, 4:Sewing machines, 5:Rooftops and apparitions, 6:Woods, 7:Mushrooms, 8:Formlessness (2d), 9:Formlessness (3d), 10:Autumn, 11:Monsters and mad scientists, 12:Empty spaces, 13:Stars and planets, 14:Addiction against emptiness, 15:Suggestive vagueness, 16: Ominous places and books, 17: Military technology, 18: Ominous telephones, 19: Observation, 20: History distortion, 21: Spy stories, 22: Dead places, 23: Mannequins, 24: Secret walks, 25: Stories, 26: Other dimensional portraits, 27: Mysterious fragments, 28a: Dino Buzzati, 28b: Mushrooms, 29, 30, 31, 32: Carcosa moons.

Guidebook from 1979

I'm making space for new books and I have to discard some of my old books. But I want to share their beauty and weirdness with you. For 4 euro I bought this guidebook from 1979. There was this one page that absolutely blew me away:

The type, the spacing and the modernism ... everything was perfect. This was the most beautiful page from the book. Another page was similarly beautiful, including the contrast between nature and cityscape:

And then there was this introductory text. I have removed the specifics of the place, because this is the archetypical psychogeographic text. It might fit any place. It could be Damascus, Sarajevo, Berlin, Rotterdam, Dresden or Nanjing. It sounds like a chapter from Italo Calvino's Invisible Cities:

Of the many towns and cities that lie scattered across the vast expanse of the _____ there are some that, like a mirror, have reflected the fate of the country and the whole nation and have revealed the character of the _____ people. Among them the heroic city of _____ is something of a legend. From all over the world people come to _____ to see the city, for which one of the greatest battles of the _____ war was fought, the battle of _____. Here, on the banks of the _____ began the death-throes of _____.

But victory was bought at a high price: thousands of young lives destroyed, thousands of hopes shattered, thousands of books unread and unwritten, thousands of tasks undone. Instead of a town stood mile after mile of charred ruins, a grotesque tableau of gutted windows, burned out squares and blackened facades, a desert of rubble and bombed-out buildings.

More than thirty years have gone by. _____ is now a beautiful new town. Wide tree lined boulevards cross its spacious squares; tall poplars and fragrant limes stir in the breeze; the sun flashes from the windows of the modern houses, shimmers in the puddles left by the heavy rain and catches the port-holes of passing ships.

We invite you to this city, full of sun and light, this new town on the _____. _____, like any other _____ town, is a hive of noise and activity, from the laughter of children at school to the rumble of machinery on the building sites. Its eyes are firmly fixed on the future, but its memory remains in the past, memory of those heroic sacrifices that were made in the name of the present.

As anyone who has ever been to _____ will tell you, there is no aspect of the daily life of that city which does not reflect the great tribute which the citizens of today owe to the defenders of yesterday. Our guide, then, will take you into two worlds - the world of the present and the world of the past, for the past determines the present as the present determines the future.

Now ... would you have guessed?

Volgograd, A short Guide, N.T. Morozova, N.D. Monakhova, Moscow, Progress Publishers, 1979, Translated from the Russian by Barry Costello

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