What We Cannot Know. Marcus du Sautoy

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СКАЧАТЬ Mendeleev arranged them in increasing relative weight, but he realized that to get the patterns he could see emerging he needed to be flexible.

      He’d written the known elements down on cards and was continually placing them on his desk in a game of chemical patience, trying to get them to yield their secrets. But nothing worked. It was driving him crazy. Eventually he collapsed in exhaustion and the secret emerged in a dream that, when he woke, gave him the pattern for laying out the cards. One of the important points that led to his successful arrangement was the realization that he needed to leave some gaps – that some of the cards from the pack were missing.

      The key to his arrangement was something called the atomic number, which depended on the number of protons inside the nucleus rather than the combination of protons and neutrons that gave rise to the overall weight. But since no one had any clue yet about these smaller ingredients, Mendeleev was guessing somewhat at the underlying reason for his arrangement.

      It was a bit like recognizing that a conventional pack of cards can be laid out in suits, but also that across those suits there are cards that are of equal value. A periodicity of eight seemed to underlie the elements, so that elements eight along seemed to share very similar properties. Eight on from lithium was sodium, followed after another eight by potassium. All soft shiny highly reactive metals. Similar patterns matched up gases with related properties.

      This rule of eight had been picked up before Mendeleev’s breakthrough and was called the law of octaves. It was compared to the musical octave: if I play the eight notes of a major scale on my cello, the top and bottom notes sound very similar and are given the same letter names. When this law of atomic octaves was proposed by its originator John Newlands, it was laughed out of the Royal Society. ‘Next you’ll be trying to tell us that the elements can be understood by putting them in alphabetical order,’ joked one Fellow. Mendeleev’s arrangement confirmed to a certain extent the veracity of this law of octaves. It was this idea of repeating or periodic patterns that led to Mendeleev’s arrangement being called the periodic table.

      Mendeleev’s genius was to realize that if sometimes the elements didn’t quite match up, it perhaps indicated a missing element. The gaps in his table were probably his most insightful contribution. The fact that there was a hole in the 31st place of his table, for example, led Mendeleev to predict in 1871 the existence and properties of a new substance that would later be called gallium. Four years later French chemist Lecoq de Boisbaudran isolated the first samples of this new atom, predicted thanks to the mathematical patterns discovered by Mendeleev.

       RECIPE FOR MAKING A DICE

      Here then was a list of the atoms that were meant to make up all of matter. For example, my dice is made from putting together carbon atoms, oxygen atoms and hydrogen atoms into a structure called cellulose acetate. My own body is predominantly made up of combinations of these atoms but with a different structure. The cellulose acetate is a homogeneous structure free from bubbles, which makes it more likely to be fair. The more antique dice were made from a nitrate-based cellulose concocted by John Wesley Hyatt in 1868. His cocktail of nitric acid, sulphuric acid, cotton fibres and camphor produced an impressive substance with great tensile strength that resisted the effects of water, oils and even diluted acids.

      Hyatt’s brother named it celluloid and it became a highly cost-effective substitute for objects that had previously been carved out of ivory or horn. Billiard balls and removable collars, piano keys and even my dice were made from this synthetic plastic. The dice that were made from cellulose nitrate were the industry standard in the early twentieth century, but after several decades of use they would almost instantaneously crystallize and decompose, crumbling in on themselves and releasing nitric acid gas.

      The real collectors’ dice are those Vegas dice made from cellulose nitrate in the late Forties that avoided this crystallization. My dice won’t suffer the same fate. Here is a picture of how the atoms are put together inside my dice.

      The identification of these elements was not a proof of a discrete model of matter. There was no reason that this picture of the ingredients of my dice couldn’t be a formula for the way a continuous structure combines. Although the chemists were tending towards an atomistic view of the universe, this was far from the case in the physics community. Those, like the German physicist Ludwig Boltzmann, who proposed atomic models of matter were laughed out of the lab.

      Boltzmann believed that this atomic theory was a powerful way to interpret the concept of heat based on the idea that a gas was made up of tiny molecules bashing around like a huge game of micro-billiards. Heat was just the combined kinetic energy of these tiny moving balls. Using this model, combined with ideas of probability and statistics, he was successfully able to explain the large-scale behaviour of a gas. But most physicists were still committed to a continuous view of matter and were very dismissive of Boltzmann’s ideas.

      Boltzmann was so ridiculed that he was forced to retreat from his belief that this billiard-ball theory of matter represented a true picture of reality, and instead was obliged to refer to it as a heuristic model if he wanted to get his ideas in print. As Ernst Mach, his great nemesis in the debate about the reality of atoms, declared mockingly: ‘Have you ever seen an atom?’

      Boltzmann was plagued by fits of depression, and there is evidence that he was in fact bipolar. The rejection of his ideas by the scientific community is believed to have contributed to the depression that struck in 1906 and that led to him hanging himself during a holiday with his family near Trieste while his daughter and wife were out swimming.

      It was a tragic end, not least because the most convincing evidence that he was right was just emerging. And it was one of the big names of physics who produced ideas that supported the atomistic view and were very hard to ignore. The work that Einstein and others did on Brownian motion would prove extremely difficult to explain for those who, like Mach, believed in a continuous view of the world.

       POLLEN PING-PONG

      Although conventional microscopes don’t allow one to see individual atoms, they did allow scientists in the nineteenth century to see the effect that these atoms were having on their surroundings. It’s called Brownian motion after Robert Brown, who in 1827 noticed the random behaviour of small particles of pollen floating on the surface of water. Since pollen was organic, Brown’s first thought was that it might be exhibiting signs of life as it jumped around the surface. A similar random behaviour of coal dust floating on alcohol had also been observed by Dutch scientist Jan Ingenhousz in 1785. When Brown saw the pollen’s behaviour replicated by inorganic matter, he was rather stumped as to what was causing the jittery motion.

      It’s striking that the idea that it might be invisible atoms bashing into the larger visible material had been suggested by the Roman poet Lucretius in his didactic poem On the Nature of Things:

      Observe what happens when sunbeams are admitted into a building and shed light on its shadowy places. You will see a multitude of tiny particles mingling in a multitude of ways … their dancing is an actual indication of underlying movements of matter that are hidden from our sight … It originates with the atoms which move of themselves. Then those small compound bodies that are least removed from the impetus of the atoms are set in motion by the impact of their invisible blows and in turn cannon against slightly larger bodies. So the movement mounts up from the atoms and gradually emerges to the level of our senses, so that those bodies are in motion that we see in sunbeams, moved by blows that remain invisible.

      This was written in 60 BC, but it would take Einstein’s mathematical analysis of the СКАЧАТЬ