i
So I put a portrait of Tschirnhaus on my wall. I’m not sure how accurate it is. He has a high forehead and a good, direct stare, but the engraver was mostly interested in his wig. I wonder if I will call him Ehrenfried, or Walther, or if he is to be Tschirnhaus. We stare at each other.
The young German mathematician was also twenty-four when he reached Paris and his first position as tutor for Colbert’s son. To be a mathematician, a philosopher, an enquirer into the properties of the world, you need someone to support you. You cannot be brilliant without a sponsor. Tschirnhaus was adept at making friends, good at learning how to create an impression, the result, I am convinced, of being the seventh child in a family.
He was the youngest son, born on the family estate in Kieslingswalde, Germany. It wasn’t a grand house, more old rectory than schloss, comfortably set amongst the rolling Silesian hills and birch woods. And it was a modest household, the family unusual amongst their neighbours in their fierce attentiveness to education – something due perhaps to the mixture of a Saxon father and a Scottish mother. Unlike other boys who could have spent their hours fencing and hunting he was given private lessons in mathematics. At seventeen he left home for the University of Leiden to study medicine, mathematics and philosophy. It was at Leiden that Tschirnhaus met Spinoza.
Spinoza was the exception to every rule. Spinoza had given away his patrimony to his sister, was independent of patronage, expelled from the Jewish community of his birth, excoriated by the Christian, he was living as a private scholar, making his living from grinding lenses. Imagine meeting him as a young man. His writings strip away your remaining pieties.
Spinoza gave Tschirnhaus his first letters of introduction. They were to the secretary of the Royal Society in London and to Isaac Newton. He was on his way. For four years he travelled in Holland, Italy, France, England and Switzerland, a series of extraordinary encounters with philosophers and ideas. And it also feels slightly enchanted, one letter of introduction leading to another, one door opening to a year in Paris with Colbert, another to a visit to one scientist in The Hague and then to another in Milan until you see a beautiful diagram, a map of thinking about the world.
Tschirnhaus, 1708
If x means y, go to z.
Tschirnhaus began work on his first mathematical equation, A method for removing all intermediate terms from a given equation. He published it in the Acta Eruditorum, the journal of empirical learning across Europe. These are four pages of brilliance in which he takes on algebraic equations and sets down ‘some things concerning this business, enough at least for those who have some grounding in the analytic art, since the others could scarcely be content with so brief an exposition’.
Idiotically, I buy the Latin exposition of The Tschirnhaus Equation from a bookseller in Amsterdam, and in one moment prove how caught up I am in the world of ownership when his exposition is about thinking, simplifying, lucidity, cutting away the extraneous. It is about brevity.
I pay far too much. Who else wants these four pages?
ii
Tschirnhaus’s journey towards his discovery of porcelain is a series of reflections and mirrorings.
Optics are at the heart of debate because light is a problem. How does it move? How fast does it move? Where does the heat come from? Lenses and mirrors are provocative artefacts, bending and intensifying light, exploding distances, bringing planets and dust into focus. Porcelain is white and hard but lets light through. How can this be?
Caute, be cautious, says the ring on Spinoza’s left hand in his room in the village outside Leiden. He grinds his lenses, day after day, deepening then eliding the curves, working out his problems as the fine white silica dust settles on the bench. He has written, amongst everything else, on the rainbow.
Light causes fearsome argument. No one can agree.
Isaac Newton’s Opticks, or, a Treatise of the Reflexions, Refractions, Inflexions and Colours of Light examines the question of how light is not modified, but separated:
I procured me a Triangular glass-Prisme, to try therewith the celebrated Phaenomena of Colours … I have often with Admiration beheld, that all the Colours of the Prisme being made to converge, and thereby be again mixed, reproduced light, intirely and perfectly white … Hence therefore it comes to pass, that Whiteness is the usual colour of Light; for, Light is a confused aggregate of Rays indued with all sorts of Colours, as they are promiscuously darted from the various parts of luminous bodies.
Newton writes to Leibniz: ‘I was so persecuted with discussions arising from the publication of my theory of light that I blamed my own imprudence for parting with so substantial a blessing as my quiet to run after a shadow.’
To be a young philosopher is to be part of this turmoil and it seems that everyone on his journey across Europe grinds lenses, dreams of telescopes, writes about prisms and rainbows, sends instruments across the world to delight the Chinese emperor, makes mirrors or employs them to create great heat.
In Lyon Tschirnhaus meets François Villette, the inventor who has demonstrated a great burning mirror in the Petite Galerie at Versailles in front of the Sun King, illuminating the whole room using only the mirror and a single candle. In Milan, Tschirnhaus recounts to Leibniz, he has spent time with the scientist and mathematician Manfredo Settala who uses burning mirrors to melt materials, and has talked to him of its potentialities for ruby glass and porcelain.
For a lay audience, the burning mirrors are spectacle with the power of the sun brought into close and exhilarating contact, the surfaces of the mirrors ‘so accurately formed and so well polished that a piece of lead or tin placed in the focus began immediately to melt, stone and slate became instantly red hot, pumice stone melted, and copper and silver melt in five or six minutes … wet wood kindled in an instant, water in small vessels boiled’.
There is terror too in this sublimity. You see the way that materials change in front of you, impossible to experience if the substances are shrouded in fire inside a furnace.
So Tschirnhaus, young and engaged, works away at the issues that vex his contemporaries, writing on catacaustic curves, ‘the envelope of light rays emitted from a point source after reflection from a given curve’. And, of course, he starts to make his own lenses. He is starting to focus.
iii
And I have to focus too.
I’m writing this in the very early morning. I can’t sleep at the moment, so I’m sitting at the kitchen table at five with a blackbird noisily announcing itself in the garden. It is August and there are chestnut trees in the road outside the house in full pomp, so that the light that comes in is dappled. The glass in the windows could be a little cleaner. There is a water jug on the table, and I’m watching the light play on the wall opposite me, and there are shudders like ripples in a stream, and a rainbow and great Gerhard Richter-like smudges across the top that move across an installation I made last year for Sue, seven stacked dishes inside a white lacquered cabinet. The top dish is gilded on the inside so that there is a reflected halo above it.
I don’t know what is going on with light at all.
I want to draw lines across the kitchen, sweeping parabolas across furniture and floors, mark the changes minute by minute by minute.
I do know that light is demonstrably an area for the ‘investigation of difficult things by the Method of analysis’, as Newton memorably put the challenge of scientific experimentation. This is simultaneously an arena of poetic and metaphorical possibility. Spinoza, after all, has compared human nature ‘with a regular or flat mirror that reflects all the rays in the universe without distorting them’. Newton has wondered whether colours and the musical octave might be analogous. Do colours have harmonies?
If so what is the sound of white?
My only certainty, buoyed by sleeplessness, is that light is part of this journey towards porcelain. Keats wrote in the margin of his copy of Milton’s Paradise Lost of ‘A sort of Delphic Abstraction a beautiful thing made more beautiful by being reflected and put in a Mist.’ By which he means, I think, I hope, that he too sees the beauty and is thoroughly confused.
I am caught up in my weather system, the turbulence of optics and mirrors and philosophers.