Science: quotes, facts and reflections - Page 7

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Werner Heisenberg's uncertainty principle, published in 1927, says that some pairs of quantities cannot both be known exactly at the same time. The best-known pair is a particle's position and its momentum, which is its mass multiplied by its velocity.

Heisenberg was 25 and working with Niels Bohr in Copenhagen when he wrote the paper. He first explained the limit with an imagined microscope: to see an electron you must hit it with light, and the light knocks it off course. Bohr showed that this explanation was flawed. The deeper reason is that a particle also behaves like a wave. A wave squeezed into a small space has to be made of many different wavelengths, and in quantum physics wavelength sets momentum, so a sharp position means a spread of possible momenta. Later in 1927 the American physicist Earle Kennard wrote down the exact limit, set by Planck's constant, a tiny number. That is why the effect rules the world of atoms but is invisible for a football. Heisenberg received the 1932 Nobel Prize in Physics.

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Albert Einstein's equation E=mc², published in 1905, says that mass and energy are equivalent: E is energy, m is mass and c is the speed of light. Because c² is so huge, one gram of mass corresponds to about 90 trillion joules, the energy of some 21,000 tonnes of TNT.

Einstein was 26 and working at the patent office in Bern when the idea appeared, in a short paper of November 1905 titled “Does the Inertia of a Body Depend Upon Its Energy Content?”. It was one of four papers from what is called his miracle year. The equation does not mean matter is easily turned into energy. In a nuclear power station, splitting uranium atoms converts only about 0.1% of their mass; chemical reactions change mass too, but by amounts far too small to weigh. The Sun, fusing hydrogen into helium, turns about four million tonnes of mass into light and heat every second. After the atomic bombs of 1945, E=mc² became linked in the public mind with nuclear weapons and turned into the most famous equation in the world.

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Absolute zero, −273.15°C, is the lowest temperature possible: the point at which a substance has given up all the heat energy it can lose. Scientists have come within 38 trillionths of a degree of it, but the laws of physics say it can never be reached exactly.

In 1848 William Thomson, later Lord Kelvin, worked out that temperature has a natural floor at about −273°C, and the kelvin scale used by scientists starts there: 0 kelvin is absolute zero. Early in the 20th century the chemist Walther Nernst showed why it cannot be reached. This became the third law of thermodynamics: no process can remove the last of a system's heat in a finite number of steps. Even at absolute zero, particles would not be perfectly still, because quantum physics leaves them a minimum jiggle called zero-point energy. Close to absolute zero, matter behaves strangely: some metals carry electricity with no resistance at all, and liquid helium flows without friction. Deep space, warmed by the afterglow of the Big Bang, sits at about 2.7 kelvin. The record of 38 trillionths of a degree was set at the University of Bremen.

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Stretched end to end, the DNA inside a single human cell would be about two metres long, yet it fits into a nucleus about six thousandths of a millimetre across. That is like packing more than 20 kilometres of fine thread into a tennis ball.

This is possible because the DNA is wound up with great care. The double helix wraps around tiny spools of proteins called histones, each spool taking about 150 “letters” of DNA, and the spools sit along the strand like beads on a string. The beads coil and fold again into a fibre called chromatin, and before a cell divides, chromatin is packed tighter still into the 46 chromosomes visible under a microscope. The German biochemist Albrecht Kossel discovered histones in 1884; the beads were first seen with an electron microscope in 1974. The packing is not only storage: when the cell loosens a stretch, it can read the genes there, and when it keeps a stretch tight, those genes stay switched off. Each nucleus holds its own two-metre copy, about three billion letters inherited from each parent.

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Honey keeps for a remarkably long time. It is only about 18% water, with so much sugar that it draws water out of microbes instead of feeding them, and it is acidic enough to stop many of them growing. Kept sealed, it does not go off.

Bees work hard for this. Nectar is 70 to 80% water; bees evaporate most of it in the hive, then cap each cell of finished honey with wax. They also add an enzyme, glucose oxidase, which produces gluconic acid and small amounts of hydrogen peroxide, a mild disinfectant. Honey's average pH is about 3.9. Its weak point is moisture: honey draws water from damp air, and if it takes up too much, the yeasts in it start to ferment it, which is how mead is made. Honey is not sterile, though. It can carry dormant spores of the bacterium that causes botulism, harmless to adults but risky for babies, so it should not be given to children under one. The oldest known honey remains, found in clay jars in an ancient tomb in Georgia during the building of an oil pipeline, are between 4,700 and 5,500 years old.

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The observable universe very likely holds more stars than there are grains of sand on Earth. One estimate puts all the sand on Earth's beaches and deserts at about 7.5 quintillion grains, a 75 followed by 17 zeros; estimates of the number of stars are more than a thousand times higher.

Neither number can be counted. The sand figure, from researchers at the University of Hawaii, multiplies the grains in a teaspoon by a rough volume for the world's beaches and deserts. The star count multiplies the number of galaxies by the number of stars in a typical galaxy. Our own galaxy, the Milky Way, has between 100 and 400 billion stars. Deep images of the sky once suggested some two trillion galaxies; newer measurements point to a few hundred billion, which still gives somewhere between 10²² and 10²⁴ stars. On a clear, dark night the naked eye can see only a few thousand of them. Carl Sagan used the image of all the grains of sand on all the beaches of Earth in his 1980 television series Cosmos, and made the comparison famous.

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Many human genes have a counterpart in the banana, descended from the same ancestral gene; biologists call such genes homologous. Both come from a single-celled ancestor that lived over a billion years ago, and many still do basic jobs such as copying DNA and dividing cells.

The anatomist Richard Owen first used the word homology in biology in 1843, for body parts that match across species, such as the bones in a human arm and in a bat's wing. Darwin's theory of evolution later explained why they match: they come from a common ancestor. Once genomes could be read, the same idea was applied to genes. The banana genome was sequenced in 2012, and comparisons show that many human genes have a recognisable counterpart in it, mostly genes for work every complex cell must do, such as building proteins, producing energy and repairing DNA. Popular figures such as “we share 60% of our DNA with bananas” are misleading, though: matching genes are often quite different in detail, and any percentage depends on what is being counted.

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The universe is about 13.8 billion years old, yet the observable universe, the part whose light has had time to reach us, is about 93 billion light-years across. The difference comes from the expansion of space while that light was travelling.

A light-year is the distance light travels in a year, about 9.5 trillion kilometres. The oldest light we can detect, the cosmic microwave background, set off about 380,000 years after the Big Bang. During its 13.8-billion-year journey, space kept stretching, so the matter that sent it is now about 46 billion light-years away in every direction, which gives a diameter of about 93 billion. This does not break the rule that nothing travels faster than light: galaxies are not racing through space; the space between them is growing. The expansion was discovered in the 1920s by Georges Lemaître and Edwin Hubble. How big the whole universe is remains unknown; it may even be infinite.

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Strong gravity makes time pass more slowly, an effect called gravitational time dilation. Near a black hole it becomes extreme: a clock close to the edge would tick far more slowly than one far away, and to a distant watcher, a clock falling in would seem almost to stop.

Albert Einstein first predicted the effect in 1907, and it is part of his general theory of relativity of 1915. It happens on Earth too, only on a tiny scale. In 1971 physicists flew atomic clocks around the world on airliners and measured the small differences from clocks on the ground that relativity predicted, and laboratory clocks can now detect the effect over a height difference of less than a metre. GPS satellites depend on it: mostly because gravity is weaker at their height, their clocks gain about 38 millionths of a second a day, and without correction the positions they give would drift by around 11 kilometres a day. A black hole's edge, the event horizon, is the boundary beyond which nothing, not even light, can get out; seen from far away, the slowing of time becomes total there.

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In the Fibonacci sequence, 1, 1, 2, 3, 5, 8, 13, 21…, each number is the sum of the two before it. It really does appear in plants: the spirals on a sunflower head or a pine cone usually come in two neighbouring Fibonacci numbers. But many popular examples, such as the nautilus shell, do not fit.

The sequence is named after Leonardo of Pisa, known as Fibonacci, who used it in his 1202 book Liber Abaci to solve a puzzle about breeding rabbits. Indian scholars had described it centuries earlier, while counting the rhythms possible in Sanskrit poetry. In plants the pattern comes from the way they grow: each new seed or leaf forms at about 137.5 degrees from the last, the so-called golden angle, which packs them without gaps, and the spirals that result come in Fibonacci numbers. Not every species follows it, however. The nautilus shell is a spiral, but not the golden spiral it is often said to be, and many claims about the proportions of human faces and bodies are stretched to fit.

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In 1931 the Austrian logician Kurt Gödel proved that no single set of rules can settle every question about numbers. Any system of axioms, the basic assumptions from which proofs are built, that is free of contradictions and strong enough for ordinary arithmetic leaves some statements it can neither prove nor disprove.

At the time, the German mathematician David Hilbert hoped to put all of mathematics on a complete and consistent footing, so that every true statement could in principle be proved. Gödel, then in his mid-twenties and working in Vienna, showed that this cannot be done. His method was to turn statements about proofs into statements about numbers, and then build one that in effect says “this statement cannot be proved”. His second theorem added that such a system cannot prove its own consistency. The theorems apply to systems whose rules can be checked mechanically, like a computer program, and to one set of rules at a time: adding a new axiom settles some questions but always leaves new ones open. They do not mean mathematics is unreliable. Gödel later worked at the Institute for Advanced Study in Princeton, where he became a close friend of Albert Einstein.

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Water expands when it freezes, making ice less dense than liquid water and allowing it to float.

In liquid water, molecules tumble past one another and pack fairly closely. As water freezes, weak attractions between molecules called hydrogen bonds lock them into a hexagonal lattice with a lot of open space, so ice takes up about 9% more room than the same water. That is why frozen pipes burst and why only about a tenth of an iceberg shows above the surface. Liquid water is densest at about 4 °C, so in winter water at that temperature sinks to the bottom of a lake while colder water, and then ice, gathers at the top. The ice acts as a lid that insulates the water beneath, which is why fish and other life can survive the winter in lakes that freeze over. Most substances behave the other way and shrink as they solidify.

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Sound needs a medium such as air, water or solid matter to travel, so empty space is silent to human ears.

Sound is a wave of pressure: a vibrating object pushes on the particles next to it, which push on their neighbours. It travels at about 343 metres per second in air and more than four times faster in water. In 1660 the English scientist Robert Boyle showed that as air was pumped out of a glass jar, the sound of what was inside faded away. Space is not perfectly empty, but between the stars there is on average only about one atom in each cubic centimetre, far too little to carry sound we could hear. That is why astronauts on spacewalks talk by radio. Yet very thin gas can carry immense waves: in 2003 astronomers found pressure ripples in the gas around a black hole in the Perseus galaxy cluster, a note about 57 octaves below middle C.

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Old window panes are sometimes thicker at the bottom, but not because glass slowly flows like a liquid. Glass is a solid whose atoms lack a regular crystal pattern, and at room temperature it does not flow in any measurable way.

In solids such as salt or ice, atoms sit in a repeating crystal pattern. Glass is an amorphous solid: its atoms are frozen in a disordered arrangement, much like a liquid's, which is how the myth took hold. Measurements say otherwise. A 2017 study of medieval glass from Westminster Abbey calculated that it could flow at most about one nanometre, a millionth of a millimetre, in a billion years. The uneven panes come from how glass used to be made. In the crown method, a glassblower spun a hot blob into a wide disc that was never the same thickness all over, and glaziers often set the heavier edge at the bottom. Some old panes are in fact thicker at the top. Flat, even float glass became common only in the 1960s.

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Your genome, the full set of DNA instructions in your cells, is extremely similar to anyone else's. A common shorthand is that two people match at about 99.9% of comparable DNA positions.

The human genome is about 3.2 billion DNA letters long, so even 0.1% amounts to millions of differences. In 2015 the 1000 Genomes Project, which read the DNA of people from 26 populations, found that a typical person differs from the standard reference genome at 4 to 5 million sites. Most are single-letter changes, but longer stretches that are missing, repeated or reversed affect more letters in total, which is why some scientists put the overall match closer to 99.4%. As a species, humans are genetically quite uniform: roughly 85% of variation is found between individuals within the same population rather than between populations. These small differences still matter, shaping traits such as eye colour, how the body handles medicines and the risk of some diseases.

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Algebra takes its name from al-jabr, a word in the title of a textbook written in Baghdad around 820 by the Persian mathematician Muhammad ibn Musa al-Khwarizmi. His own name, turned into Latin as Algoritmi, gave us the word algorithm.

Al-Khwarizmi worked in Baghdad under the caliph al-Ma'mun, at the centre of learning known as the House of Wisdom. His book, The Concise Book of Calculation by Restoration and Balancing, showed step by step how to solve equations. Al-jabr, “restoration”, meant moving a subtracted quantity to the other side of an equation; al-muqabala, “balancing”, meant cancelling equal terms on both sides. Robert of Chester translated the book into Latin in 1145, and it remained a main mathematics textbook in European universities until the 16th century. Another of his works explained the Hindu-Arabic numerals we use today. Its 12th-century Latin translation opened with the words “Dixit Algorizmi”, “so said al-Khwarizmi”, and from his Latinised name, algorism, later algorithm, came to mean a step-by-step method of calculation. His name itself means “the man from Khwarazm”, a region in today's Uzbekistan and Turkmenistan.

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Bananas are slightly radioactive. They are rich in potassium, and a tiny share of all natural potassium is the radioactive form potassium-40. In an average banana about 15 atoms decay every second, far too few to harm anyone.

Only about 0.012% of natural potassium is potassium-40, and it decays very slowly: it takes 1.25 billion years for half of any amount to break down. Because potassium is everywhere, more than 4,000 potassium-40 atoms also decay inside an adult's body every second. The 'banana equivalent dose', about 0.1 microsieverts (a unit for the effect of radiation on the body), has been used since at least 1995 to explain very small doses to the public; a chest CT scan gives about 70,000 of them. It is only a teaching aid, not a real cumulative dose: the kidneys keep the body's potassium level steady, so eating bananas does not build up radioactivity. Even so, a lorry-load of bananas can set off the radiation alarms used at US ports to detect smuggled nuclear material.

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Ordinary matter, everything made of atoms from stars to people, is only about 5% of the universe. About 27% is dark matter, detected only through its gravity, and about 68% is dark energy, which drives the universe's accelerating expansion.

The first clue came in 1933, when the Swiss astronomer Fritz Zwicky found that galaxies in the Coma Cluster moved far too fast to be held together by the matter he could see; he called the missing mass dunkle Materie, 'dark matter'. In the 1970s Vera Rubin and Kent Ford showed that stars at the edges of spiral galaxies orbit about as fast as those nearer the centre, again pointing to unseen mass. Dark energy came later: in 1998 two teams studying distant exploding stars found that the universe's expansion is speeding up, work that won the 2011 Nobel Prize in Physics. The shares come from the Planck satellite's maps of the cosmic microwave background, the faint afterglow of the Big Bang. What either dark component actually is remains unknown.

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The human body gives off a very faint visible light, a by-product of chemical reactions in its cells. In a 2009 Japanese study, ultra-sensitive cameras filmed it in total darkness; it is about 1,000 times too weak for the naked eye to see.

The study, led by Masaki Kobayashi and published in PLoS ONE, filmed five healthy young men in a completely dark room with a camera cooled to minus 120 °C. Their faces glowed most, especially around the cheeks and mouth, and the light followed a daily rhythm: weak in the morning and strongest around 4 pm. The researchers link it to metabolism. As cells turn food into energy they produce free radicals, highly reactive molecules that react with fats and proteins; some of the products release a tiny amount of energy as light. Scientists call this ultraweak photon emission, or biophotons. It was first reported by the Russian biologist Alexander Gurwitsch in the 1920s, and it has nothing to do with the 'auras' of popular mysticism.

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The Sun is white. Its light mixes all the colours of the rainbow, and seen from space, or high in a clear sky, it shines white. It looks yellow, orange or red only when it is low, because its light then crosses more air, which scatters away part of the blue.

Sunlight contains every visible wavelength in fairly balanced amounts, which our eyes read as white; its output actually peaks in the green part of the spectrum. Air molecules scatter short, blue wavelengths far more than red ones, an effect named after the physicist Lord Rayleigh. That scattered blue light is what makes the sky blue. Astronomers do class the Sun as a G-type star, loosely called a 'yellow dwarf', but the label reflects its surface temperature of about 5,500 °C, not the colour we see. Cultures picture it differently too: the Sun on Japan's flag is red.

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A teaspoon of healthy soil can hold between 100 million and 3 billion bacteria, along with fungi, other microbes and tiny animals. Together they break down dead plants and return the nutrients that new plants need.

Soil life includes bacteria, fungi, archaea (single-celled microbes that form a branch of life separate from bacteria), protists (single-celled organisms such as amoebae) and animals such as nematode worms, mites and earthworms. Many fungi join plant roots in partnerships called mycorrhizae, trading water and minerals for the plant's sugars. Soil microbes touch daily life too. The smell of damp earth after rain comes partly from geosmin, a compound made by Streptomyces and other bacteria, and in 1943 streptomycin, the first antibiotic that worked against tuberculosis, was isolated from a Streptomyces bacterium living in soil. A 2023 study in the journal PNAS estimated that about 59% of all species on Earth live in soil, which makes it the richest single habitat known.

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Water's triple point is the one combination of temperature and pressure at which ice, liquid water and water vapour can all exist together in balance: 0.01 °C at a pressure of about 612 pascals, roughly 0.6% of normal air pressure at sea level.

Most substances have their own triple point, and it shows that freezing and boiling depend on pressure as well as temperature. Below the pressure of water's triple point, ice cannot melt; it turns straight into vapour, which is how freeze-drying removes water from foods and medicines. Because the triple point is so exact and easy to recreate in a sealed glass cell of pure water, scientists used it to define temperature itself. From 1954 the kelvin, the scientific unit of temperature, was fixed so that water's triple point was exactly 273.16 kelvin, which put 0 °C at 273.15 kelvin. In 2019 the kelvin was redefined using a constant of nature, the Boltzmann constant, which links temperature to the energy of moving particles. The triple point is now a measured value, though still almost exactly 0.01 °C, and laboratories still use triple-point cells to check thermometers.

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Satellites show that lightning flashes about 44 times a second across the whole planet: nearly 4 million flashes a day and about 1.4 billion a year. It happens about ten times more often over land than over the oceans.

The figure comes from NASA's Optical Transient Detector, a camera on a small satellite launched in 1995 that watched for the brief flashes of storms, day and night. In 2003 scientists used its data to estimate 44 flashes a second, well below the figure of 100 that had been quoted since 1925, when it was worked out from weather stations' records of days with thunder. Most flashes stay inside a cloud or jump between clouds; fewer reach the ground. The place with the most lightning on Earth is Lake Maracaibo in Venezuela, where storms light up the sky on 140 to 160 nights a year. A lightning channel heats the air around it to about 30,000 °C, roughly five times hotter than the surface of the Sun, and the air expands so violently that we hear the shock as thunder.

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The human genome, the complete set of DNA instructions for building a person, is about 3.1 billion base pairs long. Each pair is a rung on the twisted DNA ladder, made of two chemical 'letters' from a four-letter alphabet: A, C, G and T.

Printed in ordinary type, those 3.1 billion letters would fill thousands of books. Most cells carry two copies, one inherited from each parent; red blood cells, which lose their nucleus, are the main exception. Stretched out, the DNA in a single cell would be about 2 metres long, yet it is wound tightly around proteins so that it fits inside a nucleus a few thousandths of a millimetre across. Only about 1 to 2% of the genome spells out recipes for proteins, in roughly 20,000 genes; much of the rest helps control when and where genes are switched on, and the role of some stretches is still debated. The Human Genome Project published an essentially complete sequence in 2003, and the last gaps were filled in 2022, when the Telomere-to-Telomere consortium read one human genome from end to end.

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