Directed by Roy Andersson
An extremely poignant short film from Swedish director Roy Andersson, well known for the individuality and singular style of his work. Here, he explores purpose, pain and ordinariness, leaving an indelible mark on the mind. A most excellent style of film, the revival of which is quite necessary.
Franz Kafka 1925
Though never completed, it is undisputedly one of Kafka's most enigmatic tales. it tells the story of a man arrested and prosecuted by a remote, inaccessible authority, with the nature of his crime revealed neither to him nor the reader. Absurd as always, with highly relevant philosophical dimensions.
Russian-born painter Wassily Kandinsky is credited as a leader in avant-garde art as one of the founders of pure abstraction in painting in the early 20th century. He saw the music in colour, he explored it with an obsession with Monet and proves that lines can speak.
Kynodontas | Dogtooth 2009
Directed by Yorgos Lanthimos
The stunning white light in this film makes it's dark heart almost undetectable. To get you in the spirit, it's worth first taking a look at Radford's adaptation of George Orwell's 1984 if you haven't already, just to see how Greek director Yorgos Lanthimos so startlingly again paints control, concentrating all this into the odd microcosm of a family home . Using excellent cinematography, Thimios Bakatakis captures the sometimes warped ordinariness we unquestioningly accept as life and the implications of abandoning the world of manipulation. We're left altogether with deep, dark, stylized perfection, memorably portraying the creepy bliss of forcefully prolonged childhood. To say less, these are subtitles worth reading.
Die Zerreißen |The Tear
He crosses his legs and uncrosses them again quickly because it is uncomfortable and he thinks we're looking he should know by now that no one looks at anyone on this train as we have too much work and focus on the things that have always mattered to a man such as birthday cards and hot dinner cooked in the real kitchen of a real house sitting on an edge or to an angle resting all upon one side in an almost debonair way as if he was in control of everything a train does and where it leads us isn't certain yet and its not as if we'll all go together but it pays a man to think of life in parts rather than in pennies or in frames as this is not the movie he plays unending under his hat an entire production pouring behind his eyes but as always time our train tears to a halt because we've run out and cannot finish what we started
Copyright Kristof Bernhardt (2014)
It was so cold that morning. The biting chill didn’t stop him, half asleep, from peeking past his many scarves and up into the sky, to leer at the sun who hung among doting clouds at such a convenient distance from the earth. It was quick, when those hollow voices that echoed in every direction, faded in with a noisy clamour of shoes on the weary pavement. But it was the sea of people whose shoes clicked and snapped violently against the concrete that finally woke him. Not far down the street, big busses were pulling in like red elephants with those un-ignorable screechy groans, grinding briefly to halt before heaving sonorously as they gussied up again to assume a place in the traffic. If you’d bothered to turn and maybe look just passed the curtain of people, then you might have seen him huddled against a scraggy poster board. Really, he’d been hoping that a masked thing would have snuffed him out already somewhere during the night , maybe leaving no more than a blot of ink, spat against the sidewalk - just vanish him like that - but no. It was too easy for him, reaching into his inner pocket and pulling out the black hat, laying it on the ground and starting another day. ‘I’ll ask as usual’ was his first thought- ‘Any spare change please?’ .But lately he’d been feeling the pennies they gave were taking far too much from him, and that if he should beg for anything it’d be another chance. But even he knew those passing strangers couldn’t spare him that. He put the hat away. This man then straightened his aching back to wipe his face with the back of a hand, and clasping the bearded jaw for a second, denied that he’d changed at all. ‘What a waste-’ he sighed to himself under breath. But it was no use getting into all that again – it was already agreed and for sure, it would be taken care of today. So he stood up to feel every joint unlatch and muscle sigh finally as he crept out of that street–ascent of man all over again.
Some days it just warms up. All of a sudden, after a horrible morning, things just start being nice. It was like this today, so the bees were humming by cosily and even the odd butterfly could be seen bobbing weightlessly past, flapping orange wings. The people who rushed were locked away in offices by now so only the daring, the satisfied, and joggers were left. As he passed through the square, some people glanced over, in fact some really starred as he shuffled by, bundled up like a Mongolian baby. From a perspective, he seemed to glide, like an apparition along a string of café’s and baristas dotted together, lively with chatter and laughing and continental breakfasts. There were all kinds of people in hats and sunglasses seated in patio chairs, lounging underneath parasols, nattering carelessly as he walked by, tuning in and out of every conversation.
‘He should at least show some interest in the kids-’, ‘she’ll think she was right, she always thinks she’s right’ ‘No, I ended up buying the blue dress actually-’. ‘You should visit more often – we miss you’ .He always listened. Having no one to talk to, the least he could do was listen, but as if he should care – none of it caught him; this was a man whose lust for life had drowned long ago in the same waters that were keeping theirs so cheerfully afloat.
It’d been a while since he’d wandered so aimlessly like this, and somehow he eventually found himself at the city’s edge, crossing those wire fences that you aren’t supposed to. But then it was easy. Finally sinking whole into that feeling and tumbling down to find himself surrounded by long shoots of mad, grassy stuff that went on uninterrupted for as far as he could see. Save what he was hoping – ahead, cutting straight through the wild, and surely enough was a single track far in the middle. It was on this, trains sped past like lightening and set the grass alive from the fierce wind that followed. Nestled in this expanse, he sat up to glimpse those last moments of the sun’s warm company, now sinking beneath blue and pink-orange marbled sky. Closing those eyes, he could remember it all - the story of himself, and he thought now that if what they said was true and home is where the heart is; he must really be homeless after all. From the corner of his eyes he caught some movement, and for what the grassy shoots would allow, he could make out some distant noise and some peaking lights - yellow, red, blue. Made him smile. Like he did on the cliff edge long ago, remembering how city life seemed so attractive to those who never lived it. He sighed. The crickets were singing to him now, everywhere was that radiant indigo you get as daylight departs and he couldn’t. ‘I’ll try’ he said as he got up to his feet, straining more to see those little people in the distance, waving off the careless tracks. He was already heading back across the wild when a train flew past behind him, thundering by with a sonorous howl. His train. No. Indeed, he was sick of this story and sick of everything - but now, the irrepressible signs of life had said ‘yes’ and were hinting that he might still live too.
Copyright Brin Lautrec (2001)
Mathematics and Reality: Is Mathematics a symbolic Universe Invented by the Human Mind?
by Paul Hartal.
Mathematics is a model of exact reasoning, the most precise branch of human knowledge. Using logic as its main instrument, mathematics probes the numerical and spatial relations of axiomatic systems by means of strict rules and careful analysis. It is a ubiquitous and indispensable subject because every human endeavor involves some form of arithmetic. In the sciences mathematics plays a salient role as their basic tool. The master mathematician and physicist Carl Friedrich Gauss (1777-1855) said that “Mathematics is the Queen of the Sciences and Arithmetic the Queen of Mathematics” (1). But to what extent does this noble and virtuous subject reflect reality? And to what degree can we trust mathematical accuracy? Is it not overrated?
Drawing on the mathematical genius of such giants as Euler, Lobachevski, Riemann, Russell and Einstein; I shall explore in this article an array of inherent contradictions in the logical foundations of the Queen of Sciences and discuss some major mathematical earthquakes that shook its theoretical bedrock. I also delve into certain aspects of The Theory of Relativity and Quantum Mechanics, the notion of time, as well as the mathematical revolutions of non-Euclidean geometry, transfinite sets and Gödel’s Theorem.
Chapter 1: An infallible delegate of truth?
Mathematics undoubtedly represents a crowning accomplishment of the human intellect but does it correspond to the material world? The popular conception envisions mathematics as the infallible delegate of undisputable truths. The orator E. Everett (famous for delivering a long speech in 1863 at Gettysburg that eclipsed the brief address of Lincoln), expressed this credo by claiming that “In the pure mathematics we contemplate absolute truths, which existed in the Divine Mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven” (2).
In contrast to this, the philosopher Bertrand Russell in 1901 uttered that “Mathematics may be defined as the subject matter in which we never know what we are talking about, nor whether what we are saying is true” (3). I think that Russell’s definition shines not merely in lettered wit but also in erudite wisdom. Unlike Everett, who probably was not aware of non-Euclidean geometries and lived prior to the age of the sweeping mathematical mutinies ushered in by Cantor and Gödel, Russell was one of the leading mathematicians of the 20th century and understood very well that common sense logic can be misleading.
Figure 2: ‘Oh La la’, Acrylic on canvas, 60 cm x 45 cm, 2009.
Similarly to mathematics, painting is also a semiotic system, a particular universe of symbols. Both mathematics and art are concerned with abstract ideas. Like pure mathematics, abstract art does not imitate reality but renders it. And paralleling pure mathematics, abstract art also involves the study of forms devoid of subject matter. Pure mathematics and abstract art both express aesthetic dimensions of the human experience. They are both meaningless in themselves and acquire meaning only through interpretation.
Albert Einstein (1879-1955), probably the greatest scientist since the time of Sir Isaac Newton (1642-1726), held up the judgment that mathematics failed the test of reliable correspondence with the material universe. He saw mathematics as a rather autonomous discipline, which seemed to be enveloped in an elective membrane that filtered relations with nature. It offered no guaranties regarding the relevance of mathematical formulae to the physical world. In his 1921 lecture on Geometry and Experience delivered before the Prussian academy of Sciences in Berlin, Einstein summed up the epistemological status of the Queen of Sciences this way: “As far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality” (4).
Figure 1: ‘The Mathematician’, Acrylic on canvas, 60 cm x 45 cm, 2003 (Collection of Hanseo University Art Museum, Seoul).
Constructed from geometrical elements and algebraic formulae, the symbolic hero of this painting displays in its centre a colorful circle that comprises two pentagons and a five-pointed star, the Pentagram of Pythagoras. The square root of 2, on the right, involves the Pythagoras’ Theorem and a mathematical revolution 2,500 years ago: The discovery of the irrational numbers. Pythagoras taught that the universe was governed by whole numbers. Historians say that one day his disciple, Hippasos of Metapontum, had calculated the length of the diagonal of a square whose side was one unit and he found that it could not be expressed as a whole number or a ratio. The length was somewhere between 1 and 2, the square root of 2 (1, 4141). The discovery horrified the Pythagorean Society because it threatened their core beliefs and hurt their pride. They tried to suppress the discovery and according to legend they even murdered Hippasos. In any case this ancient mathematical scandal resulted in the bifurcation of geometry and arithmetic.
Russell realized that perceived mathematical truths are not necessarily absolute and thus he knew what he was talking about. In this respect his quite astounding statement deflates the arrogance flying aloft on the balloon of common sense. Nevertheless, trusting intuition and logic, contemporary neo-Platonists hold that ideal truths exist in the transcendental mind of universal consciousness; and I tend to believe this myself.
Russell’s definition also reflects the essential trait of mathematics as an abstract branch of knowledge. Furthermore, it delivers a thundering revision of the traditional view of the Queen of Sciences as the study of number, quantity and measurement.
Mind you, the attributes of number, quantity and measurement alone can never create great mathematics, because they are only the basic tools, or raw materials of the trade. These raw materials are in a sense like the basic tools of the artist. However, even the highest quality of a brush, canvas and colors on the painter’s palette by themselves cannot produce art. So in order to make an ingenious work in mathematics, or a magnificent masterpiece in painting, the act of creation must occur, in which both the mathematician and the artist apply their basic tools to the subject through cognitive processes that tap their talents, skills and intellect.